Five modules give the load a shallow footing can carry before the ground fails under it, by the methods of Terzaghi, Meyerhof, Hansen and Vesic and for an earthquake. This page helps you choose the module that matches your footing and links to the manual of each.
The Bearing Capacity family has five modules. They answer one question: how much load can a shallow footing carry before the ground fails under it? They differ in the method and in the corrections they apply. Pick the one that matches your footing and your load.
Your question
Module
The classical bearing capacity equation, for a strip, square or circular footing, in general or local shear
Each manual follows the same plan: what the module calculates, what you need before you start, a quick start, the screen, every input, the factors and the choices, the results, the report, a worked example you can reproduce, a table of how each input changes the answer, the messages the module gives, and answers to common questions.
What the five modules share
The workspace. The drawing, the tabs, Analyze and the input lock, units and the report follow the same layout as the other GeoTerva modules. See the workspace guide.
The mechanism to scale. Each module draws the failure mechanism under your footing to scale.
The factors. Each module works out the bearing capacity factors and the corrections of its own method and prints them.
The result. The ultimate and the allowable bearing capacity, gross and net.
The check. You enter the applied pressure and the module checks it against the allowable value, with the verdict PASS or FAIL.
Groundwater. The water table can lie at any depth; the unit weights are adjusted for it.
Decide whether you need the classical equation, the general equation with its corrections, the slope and tilt corrections, or the seismic case.
Describe the footing and the soil
Enter the footing shape and size, its depth, the strength and the unit weights of the soil and the water table.
Enter the load and the safety factor
Give the applied pressure, the load inclination where the module takes one, and the factor of safety.
Analyze and read the verdict
Press Analyze. Read the ultimate and allowable bearing capacity, the factors and the verdict, then save a report with the cover filled in.
Frequently asked questions
How do I calculate the bearing capacity of a shallow footing with GeoTerva?
Open the module for the method you use, for example Meyerhof. Enter the footing, the soil, the water table and the factor of safety, give the applied pressure, press Analyze, and read the ultimate and the allowable bearing capacity and the PASS or FAIL verdict.
Which method should I use?
Terzaghi gives the classical equation. Meyerhof takes any shape and depth and an inclined load. Hansen and Vesic add the corrections for sloping ground and a tilted base. Run two methods on the same footing and compare the results.
Which module gives the bearing capacity in an earthquake?
Seismic bearing capacity, by Richards, Elms and Budhu, for a strip footing, with the horizontal seismic coefficient acting on the soil.
Does the module show the factors it used?
Yes. Each module prints the bearing capacity factors and the corrections of its method with their numbers.
Can I include the water table?
Yes. The water table can lie at any depth and the unit weights are adjusted for it.
Do the modules give the gross and the net bearing capacity?
Yes. Each module gives the ultimate and the allowable bearing capacity, both gross and net.
Calculate the bearing capacity of a shallow footing by Terzaghi’s equation: the ultimate and the allowable pressure, gross and net, with the failure mechanism drawn to scale and a PASS or FAIL check against your applied pressure. This manual walks through the screen, every input, the failure mode and the water table, the results and the report, with a worked example you can reproduce.
Terzaghi gives the bearing capacity of a shallow footing by Terzaghi’s equation (1943): the pressure the ground can take at the base of the footing before it fails in shear, as an ultimate value and as an allowable value at the factor of safety you choose, each gross and net. It draws the failure mechanism to scale under the footing and writes out the working. The soil is one layer below the footing, with its cohesion, friction angle and unit weight; you choose the footing shape, general or local shear, and the water table.
The ultimate bearing capacity is the sum of three terms, for the cohesion, the surcharge of the soil above the base and the self-weight of the soil in the failure zone:
qu = sccNc + qNq + sγ · ½ γBNγ
Nc, Nq and Nγ are the bearing capacity factors, which depend on the friction angle φ alone. q is the overburden at the base level, γ the unit weight in the failure zone (reduced below the water table) and B the width of the footing. The shape factors are sc = 1 and sγ = 1 for a strip, sc = 1.3 and sγ = 0.8 for a square and sc = 1.3 and sγ = 0.6 for a circular footing. The allowable pressures are:
A strip, square or circular footing: the width B (the diameter of a circle) and the founding depth Df, which must not exceed B.
General shear or local shear failure of the soil; local shear takes c′ = ⅔ c and φ′ = arctan(⅔ tan φ), as described below.
One soil below the footing: c, φ and the unit weight γ.
A water table at any depth, with the saturated unit weight; or none.
An optional applied vertical pressureqapplied at the base, which the module checks against the allowable pressures: PASS or FAIL.
The factor of safetyFS.
The module takes a vertical load. It gives the pressure at the base; the settlement of the footing is a separate question that the stress and settlement modules answer.
Which module for which footing
Shape factors for a rectangle, depth factors and an inclined load: Meyerhof.
A footing near a slope, a tilted base and an inclined load: Hansen and Vesic.
Have these ready from your design and your ground investigation:
What
Notes
The footing: shape, B, Df From: Your design
Width (the shorter side; the diameter of a circle) and the depth of the base below the ground surface. Df must not exceed B.
c, φ and γ of the soil From: Boring logs and tests
One set of values for the soil below the footing, to a depth of about one width under the base. φ from 0° to 50°.
The water table From: Groundwater readings
Its depth Dw from the ground surface and the saturated unit weight γsat; or none.
The factor of safety From: Your design basis
At least 1. The example uses 3.
The applied pressure (optional) From: Your structural analysis
The vertical gross pressure at the base, V/A, with service (unfactored) loads: the column load plus the weight of the footing and of the soil above it, over the base area.
Quick start in seven steps
Open the module and choose the units
Open Terzaghi from the Bearing Capacity family. Pick SI · kN, SI · tf or US in the header; you can change it at any time.
Describe the footing
In Footing choose Strip, Square or Circular and type the width B and the founding depth Df.
Enter the soil
In Soil type c, φ and γ and choose General shear or Local shear.
Enter the groundwater
In Groundwater choose Present and type γsat and the depth Dw, or choose None.
Enter the load and the factor of safety
In Loads type the applied vertical gross pressure qapplied if you want the footing checked; in Analysis Settings set FS.
Press Analyze
Press Analyze at the foot of the Model tab. The bar reads Analysed, the inputs lock and the drawing shows the Capacity view.
Read the answer
The Results tab gives the four pressures, the load the footing can carry, the check and the contribution of each term. The Calculations tab writes out the steps; the Report tab saves a PDF or a Word file.
The screen: section, capacity and factors
The layout is the one every GeoTerva module shares, described in the workspace guide. For this module the drawing has three views, chosen with the buttons above it:
Section is the footing in the ground, drawn to scale: the column, the base, the founding depth, the water table and the failure mechanism of the method for your friction angle, with the zones labelled. Zone I is the elastic wedge under the base, zone II the radial shear zone bounded by a log spiral and zone III the passive wedge. The Section view carries the load Q, the labels B and Df, the water table and a legend naming the zones (the base angle of the elastic wedge equals φ); after Analyze the surcharge q and the ultimate bearing capacity qu are added at the base level.
Capacity shows the three terms of qu as one stacked bar with their shares, then the gross pressures (qu and qall,g) and the net pressures (qu,net and qall,n) as bars, and the three factors. It reads “Press Analyze” until the model is analysed. When you entered an applied pressure it adds a bar for it with FSactual and PASS or FAIL.
Factors plots Nc, Nq and Nγ against the friction angle on a logarithmic scale from 0° to 50°, with a dashed line at your φ and the values read off. For local shear it marks the reduced angle φ′.
Section before Analyze: the footing, the water table and the mechanism, to scale.
Section after Analyze: qu is added at the base.
Capacity after Analyze.
Factors: the three curves and your design values.
The Show chips
Above the Section view a Show bar has two chips, Failure mechanism and Dimensions, both on by default. The (?) beside Show says that the drawing is display only. With Failure mechanism off the zone labels, the wedge and spiral lines and the legend line disappear and a note says that the mechanism is hidden; with Dimensions off the labels and lines of B and Df disappear. Both chips are on again after a reload. The Capacity and Factors views have no chips.
The Show bar of the Section view.
Entering the model, section by section
The Model tab has six sections: Model data, Footing, Soil, Groundwater, Loads and Analysis Settings. Click a title to open a section: of the five after Model data only one is open at a time, so opening one closes the previous one (Model data opens and closes on its own); Next and Back at the foot walk you through them, and Analyze waits below the last one. Where a unit is shown twice or three times, such as m · ft, the units are those of SI · kN, SI · tf and US in turn, and equal ones are merged. Defaults are shown in SI; after a unit switch the boxes show the converted values, unrounded (the 1.5 m footing reads 4.92126 ft).
Model data
The first section holds the model name, Save to file…, Open file…, Quick Save… with its list, Load, Delete and Reset to defaults. It works as described in the workspace guide.
Model data.
Footing
The Footing shape buttons are Strip, Square and Circular; the example is square. A strip is a footing long compared with its width, so the module works per metre of length; the square and circular footings are sized by B. The note under the fields reminds you that B is the shorter side and Df the depth of the base below the ground surface.
Footing: shape, width and depth.
Footing fields
Field
Default
What to enter
Footing width / diameter B m · ft
1.5
The shorter side of the footing, or the diameter of a circle. At least 0.05 m.
Founding depth Df m · ft
1
The depth of the base below the ground surface. Zero or more, and not more than B.
Soil
One soil below the footing. Failure mode has General shear, the default, and Local shear, which the label describes as reducing c and φ. The note says that the soil is one layer below the footing, characterised by c, φ and γ.
Soil: strength, unit weight and failure mode.
Soil fields
Field
Default
What to enter
Cohesion c kPa · kg/cm² · psf
15.2
Zero or more.
Friction angle φ °
20
From 0° to 50°.
Unit weight (above GWT) γ kN/m³ · t/m³ · pcf
17.8
At least 0.1. Used for the surcharge q and, with no water table, for the self-weight term.
Groundwater
Water table has Present and None. With None the two boxes disappear and the unit weight γ is used everywhere. Three read-only cards under the boxes follow your inputs: the surcharge q at the base, the water case and the ratio Df / B.
The water case card reads above the base when Dw < Df, within B below the base when the water table lies between the base and one width below it, deeper than B below that, and none without a water table.
Groundwater, with the three cards.
Groundwater fields (shown with the water table present)
Field
Default
What to enter
Saturated unit weight γsat kN/m³ · t/m³ · pcf
19
At least 0.1, and above the unit weight of water (9.81 kN/m³).
Water table depth Dw m · ft
2
Measured from the ground surface. Zero or more.
Loads
One optional box, Applied vertical gross pressure at the baseqapplied, empty by default. Enter V/A from your structural analysis with service loads: the vertical load of the column together with the weight of the footing and of the soil above it, over the base area. A (?) beside the heading opens a window with a drawing of what the pressure contains and of the gross and the net check. Leave the box empty to get the bearing capacity without a check.
Loads.
The (?) window of Loads.
Analysis Settings
The Factor of safetyFS divides the ultimate pressures to give the allowable ones. Default 3; at least 1.
Analysis Settings.
Choosing the footing, the failure mode and the water
Four decisions shape the answer. The first three are choices on the screen; the fourth, the water table, comes from your inputs.
Choice
What it does
Footing shape Strip, Square, Circular
Sets the shape factors sc and sγ and the plan area for the load Qall. For the example: 442.1 kPa strip, 514.6 kPa square, 506.4 kPa circular.
Failure mode General shear, Local shear
General shear uses c and φ as entered. Local shear replaces them by c′ = ⅔ c and φ′ = arctan(⅔ tan φ) and uses the same equation. The example falls to 235.8 kPa.
Water table Present, None
Changes q and the unit weight in the self-weight term, by the case below.
General or local shear
General shear is the failure with a clear surface from the footing to the ground surface, in dense sand and stiff clay. Local shear stands for the failure of loose sand and soft clay, where the strength is not fully mobilised; the module then works with the reduced values and the Calculations tab states them. For the example φ′ = 13.64° and c′ = 10.13 kPa.
The water table
The module reads the depth Dw from the ground surface and uses one of three cases:
Above the base (Dw < Df): the surcharge is q = γDw + γ′ (Df − Dw) and the self-weight term uses the submerged unit weight γ′ = γsat − 9.81.
Within one width below the base (Dw ≥ Df and D = Dw − Df ≤ B): q = γDf, and the self-weight term uses γav = [Dγ + γ′ (B − D)] / B.
Deeper than B below the base: the water table lies below the failure zone and has no effect; q = γDf and the term uses γ.
Without a water table the last case applies. With the example, a water table at 2 m is 1 m below the base: γav = 14.93 kN/m³ and q = 17.80 kPa.
Analyze and read the results
Press Analyze. The bar counts through four steps (bearing-capacity factors, corrections, groundwater, ultimate and allowable pressure), the inputs lock, and the bar and a message tell you the outcome: Analysed — bearing capacity calculated; applied pressure not provided, or with qapplied, Analysed — PASS: qapplied ≤ qall,g, FSactual = 3.43 or Analysed — FAIL: qapplied > qall,g, FSactual = 2.06. The answer is on the Results tab; the drawing changes to the Capacity view. The module stays on the Model tab, so press Results to see it.
The bar after Analyze.
The Results tab has these blocks:
Bearing capacity: four cards, the gross ultimate bearing capacity qu, the net ultimate qu,net = qu − q, the gross allowable qall,g = qu / FS and the net allowable qall,n = (qu − q) / FS; under them the gross allowable vertical load Qall (kN, or per metre for a strip), the overburden q and FS.
Design check: NOT CHECKED without qapplied; with it, PASS or FAIL for the gross and for the net check.
Factors and values, step by step: the main number of each step of the working.
Contribution of each term: the three terms with their values and their share of qu.
The Results tab of the example, without an applied pressure.
The check against the applied pressure
Enter qapplied in Loads and the module compares it with the allowable pressures. Gross is compared with gross and net with net, never one with the other: the gross check is qapplied ≤ qall,g; the net check is qapplied − q ≤ qall,n. Each comes with its actual factor of safety: gross FSactual = qu / qapplied, net FSactual,net} = qu,net / qapplied,net. The results say that the gross check governs: when it passes, the net check passes too. With the example, an applied pressure of 150 kPa gives PASS (gross 3.43, net 3.76) and 250 kPa gives FAIL (gross 2.06, net 2.14).
Design check, 150 kPa: PASS.
Design check, 250 kPa: FAIL.
The Warnings button of the bar opens the list of warnings and notes. For the inputs of this module the list reads “No warnings — the method's assumptions hold for these inputs.”
The Calculations tab, the Report and the Theory tab
The Calculations tab writes the analysis as an answer sheet, one card per step; each card opens and closes. It starts with Given and what is sought, then:
Check the shallow-footing assumption: Df / B, and that Df ≤ B.
Read the bearing-capacity factors: Nc, Nq and Nγ for φ, with the rows of the table around it. Local shear adds a step, Reduce the strength for local shear, before the factors.
Locate the groundwater table: the case, q and the unit weight of the self-weight term.
Write the bearing-capacity equation for the shape: the equation, your numbers substituted, qu and the contribution of each term.
Apply the factor of safety: the net ultimate and the gross and net allowable pressures.
Compute the gross allowable loadQall.
Check the applied foundation pressure: the check, or a note that no pressure was entered.
It ends with a boxed Answer. All numbers follow the unit system of the header.
Calculations: groundwater and the equation, with your numbers.
The Report
The Report tab has a cover form (project, location, client, report number, date, prepared by, title or qualification, checked by and optional notes), kept in the browser and printed on the cover. Save as PDF and Download Word (.docx) produce the report. It has six parts (a seventh, Warnings and notes, is added if an analysis carries a caution; this single-soil module raises none): 1. Introduction and scope, 2. Input data, 3. Calculation (a numbered step for each step above), 4. Results, 5. Summary and 6. References, with the drawings.
The Report tab: cover form and the first page.
The Theory tab
The Theory tab explains the method in 14 sections: Scope and assumptions; General and local shear failure; The failure mechanism; The passive force on the wedge; The surcharge term — Nq; The cohesion term — Nc; The self-weight term — Nγ; The bearing-capacity equation; Square and circular footings; Local shear failure; The water table; Allowable pressure and the check; Worked examples; References.
Worked example
The module’s own example, which you can reproduce with Reset to defaults and Analyze: a square footing B = 1.5 m at Df = 1 m, c = 15.2 kPa, φ = 20°, γ = 17.8 kN/m³, γsat = 19 kN/m³, water table Dw = 2 m, FS = 3, general shear.
An independent calculation of these numbers agrees with the module. In US the same footing gives qu = 10.75 ksf, qall,g = 3.583 ksf and qall,n = 3.459 ksf; in SI · tf, 52.47 t/m², 17.49 t/m² and 16.89 t/m². The same answer in three unit systems.
How each input changes the answer
Each row changes one thing in the example (all other inputs as in the example: B = 1.5 m, Df = 1 m, square, c = 15.2 kPa, φ = 20°, γ = 17.8 kN/m³, γsat = 19 kN/m³, Dw = 2 m, FS = 3). Pressures in kPa.
Change
qu
qall,g
qall,n
The example
514.6
171.5
165.6
Strip footing no shape factors
442.1
147.4
141.4
Circular footing
506.4
168.8
162.9
Local shear c′ and φ′ at two thirds
235.8
78.61
72.68
B = 2.5 m the water table is 1 m below the base, within B: γav = 12.63 kN/m³
528.0
176.0
170.1
B = 1 m the water table is one width below the base, so the term uses γ
507.9
169.3
163.4
Df = 0.5 m q = 8.9 kPa
454.6
151.5
148.6
Df = 1.5 m q = 26.7 kPa; Df = B
574.5
191.5
182.6
Df = 0 q = 0, so net equals gross
388.4
129.5
129.5
c = 0
165.0
55.01
49.08
c = 30 kPa
854.9
285.0
279.0
φ = 0° Nc = 5.70, Nq = 1, Nγ = 0
130.4
43.48
37.54
φ = 25°
797.7
265.9
260.0
φ = 30°
1,305
435.1
429.2
γ = 20 kN/m³ γsat stays 19
534.2
178.1
171.4
Dw = 0.5 m water above the base
470.0
156.7
152.2
Dw = 1 m water at the base
502.1
167.4
161.4
Dw = 4 m, or no water table the same answer for both
520.9
173.6
167.7
FS = 2 qu does not depend on FS
514.6
257.3
248.4
FS = 4
514.6
128.6
124.2
Friction angle moves the answer steeply: qu rises from 514.6 kPa at 20° to 1,305 kPa at 30°, about 2.5 times, because all three factors grow with φ.
Cohesion matters most at small φ: with c = 0 the example still carries 165.0 kPa, from the surcharge and self-weight terms.
Water lowers the capacity: a water table at the surface (Dw = 0) gives 438.0 kPa against 520.9 kPa with none.
Width has a modest effect here: only the self-weight term depends on B.
Messages and what they mean
A condition of the method is not met. The bar turns amber, names the problem and disables Analyze; hovering over it shows a shorter version. Change the inputs marked in red and the bar returns to normal.
The bar when the founding depth exceeds the width.
Message
What to do
Cannot be analysed — Df = 2.00 m exceeds B = 1.50 m Terzaghi’s equation assumes a shallow footing, Df ≤ B.
Reduce Df, widen the footing, or use Meyerhof or Hansen. The module gives no result for a footing deeper than its width.
Cannot be analysed — γsat ≤ γw — the submerged unit weight would not be positive A negative effective weight is not physical.
Check γsat; it must exceed 9.81 kN/m³. A value of 9.5 or of 9.81 gives this message.
Cannot be analysed — qu = … does not exceed the overburden q = … at the base level The soil would fail under less than the pressure that already acts at the base, so there is no bearing capacity to report.
Give the soil some cohesion or friction, for example when c and φ are both zero.
Cannot analyse — 1 input error for example: Friction angle (φ) must be at most 50°.
A dialog lists every value that is missing or out of range, such as Cohesion (c) is missing, Factor of safety (FS) must be at least 1, or Footing width / diameter (B) must be at least 0.05 m. Nothing is calculated until you correct them.
The dialog for a missing value.
No bearing capacity. If qu does not exceed the overburden q (for example c = 0 and φ = 0), the bar turns amber with “Cannot be analysed — qu = … does not exceed the overburden q = … at the base level” and Analyze stays disabled; give the soil some cohesion or friction. No warnings. For this module’s single soil the Warnings list of a valid run reads “No warnings”.
Good practice
Check the footing is shallow. The equation applies when Df ≤ B; for a deeper footing use a method with depth factors.
Use service loads for qapplied and include the weight of the footing and of the soil above it; the module compares the pressure with the allowable value at the factor of safety you set.
Choose the failure mode on the soil. General shear for dense sand and stiff clay, local shear for loose sand and soft clay; the example drops from 514.6 to 235.8 kPa between the two.
Give the water table its real depth. It reduces qu when it reaches the failure zone.
One soil below the footing. The values you enter are taken for the whole failure zone; choose the values of the weaker soil within about one width under the base.
Vary one input at a time from the example to see its effect, as in the table above.
Gross with gross, net with net. Compare qapplied with the gross values and qapplied − q with the net ones.
Frequently asked questions
What does the Terzaghi module give?
The ultimate bearing capacity of a strip, square or circular footing, gross and net, the allowable pressures at your factor of safety, the load the footing can carry, the contribution of each term, the failure mechanism drawn to scale and, when you enter an applied pressure, PASS or FAIL. The example gives 514.6 kPa ultimate and 171.5 kPa gross allowable.
What is the difference between gross and net?
The gross pressures are the total pressure at the base. The net pressures are what the footing adds to the overburden q already acting at the base level: qu,net = qu − q. The gross allowable is qu / FS; the net allowable is (qu − q) / FS.
Do I have to enter the applied pressure?
No. Leave it empty and the module calculates the bearing capacity; the Design check then reads NOT CHECKED. Enter qapplied (V/A with service loads) to get PASS or FAIL for the gross and the net check.
Why does the module stop when Df is larger than B?
Terzaghi’s equation is for a shallow footing, Df ≤ B, so that the soil above the base acts as a surcharge. The bar says so and Analyze stays disabled. Reduce Df, widen the footing or use Meyerhof or Hansen.
What does Local shear do?
It replaces c by ⅔ c and φ by arctan(⅔ tan φ) and runs the same equation, for loose sand and soft clay. The example falls from 514.6 to 235.8 kPa.
How is the water table treated?
By its depth from the ground surface. Above the base it reduces the surcharge and uses the submerged unit weight in the self-weight term; within one width below the base the term uses a weighted average; deeper than that it has no effect. The Groundwater section shows the case.
Can I enter several soil layers?
No. The module takes one soil below the footing, with c, φ and γ. For a layered profile, enter the values of the weaker layer within about one width under the base.
What values does the module accept?
The width at least 0.05 m, the founding depth zero or more and not above the width, the cohesion zero or more, the friction angle from 0° to 50°, the unit weights at least 0.1 (the saturated one above 9.81 kN/m³), the water depth zero or more and the factor of safety at least 1. A missing or out-of-range value stops the analysis with a message that names it.
Can I drag or zoom the drawing?
No. The drawings have no drag handles and no zoom; change the values in the Model tab and the drawing follows. After Analyze the inputs are locked until you press Edit inputs.
Which units does it use?
SI · kN, SI · tf or US, switchable in the header at any time, even after Analyze. Pressures are in kPa, t/m² or ksf. The example gives 514.6 kPa, 52.47 t/m² or 10.75 ksf.
What does the report contain?
A cover with your project details and the answer, then six parts: introduction and scope, input data, the calculation step by step, results, summary and references, with the drawings. A seventh part, Warnings and notes, is added when an analysis carries a caution; this single-soil module raises none for its inputs. It is saved as a PDF or a Word file.
Does the module remember my inputs?
Yes. Every change is kept in the browser, and the page opens again on the model you last worked on, analysed if it was. Reset to defaults brings back the example; Save to file and Quick Save keep copies.
Calculate the ultimate and the allowable bearing capacity of a shallow footing by Meyerhof’s general equation, with De Beer shape factors, Hansen depth factors and Meyerhof inclination factors, for a vertical or an inclined load and any water table. This manual walks through the screen, every input, the results and the report, with a worked example you can reproduce.
Meyerhof gives the ultimate and the allowable bearing capacity of a shallow footing by Meyerhof’s general equation, for a strip, square, rectangular or circular footing at any depth, under a vertical or an inclined load. The module draws the failure mechanism to scale under the footing, works out the bearing capacity factors and the three corrections of the method, and gives the gross and the net ultimate capacity and the gross and the net allowable pressure. If you enter the applied pressure at the base, it checks it and answers PASS or FAIL.
qu = cFcsFcdFciNc + qFqsFqdFqiNq + ½ γBFγsFγdFγiNγ
The factors come from closed forms, none from a table:
Nq = exp(π tan φ) tan²(45° + φ/2) and Nc = (Nq − 1) cot φ (Reissner, Prandtl; Meyerhof 1963), and Nγ = 2(Nq + 1) tan φ (Vesic 1973).
Shape factors of De Beer (1970), from the ratio B/L: Fcs = 1 + (B/L)(Nq/Nc), Fqs = 1 + (B/L) tan φ, Fγs = 1 − 0.4 B/L.
Depth factors of Hansen (1970): Fqd = 1 + 2 tan φ (1 − sin φ)² k and Fcd = Fqd − (1 − Fqd)/(Nc tan φ), with k = Df/B (or arctan(Df/B) in radians when Df/B is above 1); Fγd = 1. At φ = 0 the cohesion factor is 1 + 0.4 k.
Inclination factors of Meyerhof (1963): Fci = Fqi = (1 − β/90°)² and Fγi = (1 − β/φ)², which is 0 once β reaches φ.
Here q is the overburden at the base level and γ the unit weight in the self-weight term; both follow the groundwater you describe. The equation returns the vertical component of the ultimate load; the module also gives the allowable resultant load at the angle β.
Which module for which job
The same family has Terzaghi (general and local shear, vertical load), Hansen and Vesic (also a tilted base and sloping ground) and the seismic strip footing of Richards, Elms and Budhu. The family page compares them.
Use Meyerhof when the footing has any shape and depth and the load is vertical or inclined on level ground, and you want every factor printed with its numbers.
The stress the footing adds to the ground below, for settlement, is the job of Stresses in a soil mass.
Before you start: what you need
Have these ready from your design and your ground investigation:
What
Notes
The footing From: your design
The shape, the width B (the shorter side; the diameter of a circle), for a rectangle the length L, and the founding depth Df.
The soil under the footing From: your ground investigation
The effective cohesion c, the friction angle φ and the unit weight γ above the water table. The module takes one soil for the whole footing.
The groundwater From: the borings
Whether a water table is present, its depth Dw from the ground surface and the saturated unit weight γsat.
The load From: your structural analysis
The inclination β of the load from the vertical. Optional: the vertical gross pressure at the base qapplied, which is V/A with service loads, including the weight of the footing and of the soil above it.
The factor of safety From: your design basis
The module opens with 3.
Quick start in seven steps
Open the module and choose the units
Open Meyerhof from the Bearing Capacity family. Pick SI · kN, SI · tf or US in the header; you can change it at any time, also after Analyze.
Describe the footing
In Footing pick Strip, Square, Rectangular or Circular and type B (and L for a rectangle) and the depth Df.
Enter the soil and the water
In Soil type c, φ and γ. In Groundwater choose Present or None; if present, type γsat and the depth Dw.
Enter the load
In Loads type the inclination β (0 for a vertical load) and, if you have it, the applied pressure qapplied.
Set the factor of safety
In Analysis Settings type FS (at least 1).
Press Analyze
Press Analyze at the foot of the Model tab. The bar reads Analysed, the inputs lock, and the drawing switches to the Capacity view.
Read the answer
The Results tab gives qu, qu,net, qall,g and qall,n, the allowable load, and PASS or FAIL when you entered qapplied. The Calculations tab writes out every factor and the Report tab saves a PDF or a Word file.
The screen: section, capacity and factors
The layout is the one every GeoTerva module shares, described in the workspace guide. The drawing on the left has three views, chosen with the buttons above it, and the panel on the right has the tabs Model, Results, Calculations, Report and Theory.
Section is a cross section through the footing, drawn to scale: the footing with the load arrow at the angle β, the ground surface, the base level, the water table, the overburden q at the base, and Meyerhof’s failure mechanism for the φ you entered: I the elastic wedge under the footing at the base angle 45° + φ/2, II the radial shear zone bounded by a log spiral, and III the passive wedge at 45° − φ/2. Under the footing it shows qu once analysed. The drawing follows your inputs as you type.
Capacity is the view the module switches to when you press Analyze. It shows the three terms of qu (cohesion, surcharge, self-weight) as one bar, the gross pressures qu and qall,g, the net pressures qu,net and qall,n above the overburden, and all twelve factors with their values.
Factors plots Nc, Nq and Nγ against φ from 0° to 50° on a logarithmic scale, with a dashed line at your φ and the three values on it.
Section before Analyze: the geometry and the mechanism for the inputs.
Section after Analyze: the box under the footing gives qu.
Capacity: the terms, the pressures and the factors.
Factors: the three curves and your φ.
The Show chips
Above the Section a bar holds two chips, Failure mechanism and Dimensions, both on by default. The first draws the three zones and the second the dimension lines of B and Df; the water table, the load arrow and the labels stay when they are off. The small ? beside Show says that the drawing is display only. The Capacity and Factors views have no chips.
The Show bar.
Section with Failure mechanism off.
Section with Dimensions off.
Dragging and zoom
Nothing in the drawings can be dragged and the views have no zoom: the drawings follow the numbers you type. After Analyze the inputs are locked until you press Edit inputs, which also clears the results. The unit system can still be changed.
Entering the model, section by section
The Model tab has six sections: Model data, Footing, Soil, Groundwater, Loads and Analysis Settings. Model data opens and closes on its own; opening any of the other five sections closes the one that was open. On a fresh start Model data and Footing are open. Next and Back at the foot walk you through them, and Analyze waits at the bottom. In the tables, a unit shown more than once, such as kPa · kg/cm² · psf, gives the units of SI · kN, SI · tf and US in turn. Defaults are shown in SI. A value that is outside its range is refused when you press Analyze, see Messages.
Model data
The first section holds the model name, Save to file…, Open file…, Quick Save… with its list and Load and Delete, and Reset to defaults. It works as described in the workspace guide. Reset returns the example at once and the page keeps it as the model of the browser.
Model data.
Footing
Choose the footing shape with the four buttons. B is the width, the shorter side (the diameter of a circle), and Df the depth of the base below the ground surface. Rectangular adds the length L, which must not be shorter than B. A strip is treated as plane strain (B/L = 0, every shape factor 1) and its loads are per metre of length; a square and a circle both use B/L = 1, so a circle of diameter B gives the same pressures as a square of side B (520.0 kPa in the example).
Footing: a square footing.
Footing fields
Field
Unit
Default
Footing shape Strip, Square, Rectangular or Circular.
choice
Square
Footing width (short side) B At least 0.05 m.
m · m · ft
1.2
Footing length (long side) L Only for a rectangle; at least 0.05 m and not shorter than B.
m · m · ft
1.2
Founding depth Df At least 0 (a footing on the surface).
m · m · ft
1
Footing with Rectangular: the length box appears.
Soil
One soil under the footing, described by three numbers. The note says that the soil below the footing is characterised by c, φ and γ. Use effective-stress parameters for a drained analysis.
Soil.
Soil fields
Field
Unit
Default
Cohesion c At least 0.
kPa · kg/cm² · psf
0
Friction angle φ From 0 to 50°. At 0 the module uses Nc = 5.14, Nq = 1 and Nγ = 0 (a clay under undrained loading).
°
32
Unit weight (above GWT) γ At least 0.1. Used for the soil above the water table, or everywhere when there is no water table.
kN/m³ · t/m³ · pcf
16
Groundwater
Choose Present or None. With None the two water boxes are hidden and the unit weight γ is used everywhere. With Present enter the saturated unit weight and the depth of the water table from the ground surface. Three read-outs under the boxes follow your inputs: the surcharge q at the base, the water case (above the base, within B below the base, or deeper than B) and the ratio Df/B.
Groundwater with its three read-outs.
Groundwater fields
Field
Unit
Default
Water table Present or None.
choice
Present
Saturated unit weight γsat At least 0.1 and above the unit weight of water (9.81 kN/m³). Shown when the water table is present.
kN/m³ · t/m³ · pcf
19.5
Water table depth Dw At least 0, from the ground surface. Shown when the water table is present.
m · m · ft
0.5
Loads
The inclination β of the load from the vertical, and the optional applied pressure. qapplied is the vertical gross pressure at the base: the vertical load of the column plus the weight of the footing and of the soil above it, divided by the base area (V/A, with service loads). With an inclined load enter the pressure of the vertical component, V/A, not the resultant Q/A. Leave it empty and the module gives the capacity; the Design check reads NOT CHECKED until you enter the pressure. The ? beside Applied load opens an explanation with a drawing.
Loads.
Load fields
Field
Unit
Default
Load inclination from vertical β From 0 to 89°. 0 is a vertical load.
°
10
Applied vertical gross pressure at the base (optional) qapplied At least 0 when given.
kPa · t/m² · ksf
empty
The ? of the Loads section: what the applied pressure is.
Analysis Settings
One number, the factor of safety applied to the ultimate capacity.
Analysis Settings.
Analysis field
Field
Unit
Default
Factor of safety FS At least 1.
—
3
Choosing the shape, the water and the load
There is no method to choose: the equation is Meyerhof’s. What you decide is the footing, the water and the load.
Choice
What it does
Strip
Plane strain: B/L = 0, so Fcs = Fqs = Fγs = 1. In the example it gives qu = 372.4 kPa against 520.0 kPa for the square. The allowable load is per metre of length.
Square / Circular
B/L = 1: Fcs = 1.65, Fqs = 1.62, Fγs = 0.6000 in the example. The area for the allowable load is B² or πB²/4.
Rectangular
B/L between 0 and 1. With L = 2.4 m the example gives 446.2 kPa, between the strip and the square.
Water table: None or deeper than B
No water effect: q = γDf and γ in the self-weight term.
Water table: within B below the base
The self-weight term takes a weighted unit weight between γ and the submerged weight.
Water table above the base
The overburden is split into a moist and a submerged part and the self-weight term uses the submerged weight γ′ = γsat − 9.81.
Load inclination β
Reduces every term; the self-weight term is zero once β ≥ φ. The equation gives the vertical component; the resultant is that divided by cos β.
Which should I pick?
The shape that matches the plan: a wall footing is a strip; a column footing is square or rectangular; a tank or a silo base is circular. For a rectangle enter the shorter side as B.
The water table that governs the design, which may be the highest level during the life of the structure. The module reads the depth from the ground surface.
β = 0 for a vertical load. For an inclined load give the angle of the resultant, and enter qapplied as V/A of the vertical component.
Analyze and read the results
Press Analyze. The bar changes to Analysed — bearing capacity calculated; applied pressure not provided (or Analysed — PASS / FAIL when you entered qapplied) and says “The inputs are locked. Edit inputs clears the results; the unit system can still be changed.” The page stays on the Model tab: open the Results tab for the answer. Before you press Analyze the bar reads “Not analysed”; the drawing follows the inputs.
The Results tab of the example.
Card
The example
Gross ultimate bearing capacity qu
520.0 kPa
Net ultimate bearing capacity qu,net = qu − q
507.1 kPa
Gross allowable qall,g = qu / FS
173.3 kPa
Net allowable qall,n = (qu − q) / FS
169.0 kPa
Gross allowable vertical load Qall
249.6 kN
Allowable resultant load at β = 10°, Qall(incl)
253.4 kN
Overburden at the base q
12.85 kPa
Below the cards, the Design check box compares the applied pressure with the allowable one, and Factors and values, step by step lists every factor with its value and the answer of each step. A last table, Contribution of each term, gives the cohesion, surcharge and self-weight terms in kPa and as a share of qu; in the example the surcharge term is 470.17 kPa (90.4 %), the self-weight term 49.82 kPa (9.6 %) and the cohesion term zero. With qapplied entered, the Capacity view adds lines “qapplied … FSactual … — PASS/FAIL” under the gross and the net pressures. Gross and net are never mixed: the gross applied pressure is compared with the gross allowable one and the net applied pressure with the net allowable one.
The design check
The check compares qapplied with qall,g and its net part qapplied − q with qall,n, and gives the actual factor of safety FSactual = qu / qapplied. Without qapplied the box reads NOT CHECKED and the bar says “applied pressure not provided”: the capacity is given and the check waits for the pressure.
With qapplied = 150 kPa the example reads PASS (173.3 kPa allowable, FSactual = 3.47); with 200 kPa it reads FAIL (FSactual = 2.60 against FS = 3.00, both the gross and the net line FAIL).
The design check with 200 kPa: FAIL.
The bar with PASS.
The bar with FAIL.
Using the numbers
qu is the pressure at which the ground fails. The allowable pressures divide it by FS; which of the two (gross or net) your design follows is for you to state.
The allowable vertical load is qall,g times the base area (B × L, πB²/4 for a circle) and, for a strip, per unit length (kN/m, tf/m or kip/ft). With an inclined load the second line is Qall / cos β.
The pressures are in kPa, t/m² or ksf by the unit system. The example gives 53.02 t/m² and 10.86 ksf for qu.
After you change the unit system the drawings stay in SI (the view says so) and the boxes show the converted values unrounded. Changing it after Analyze re-states the cards without a new run. Edit inputs unlocks the inputs and clears the results.
Warnings and notes
The bar carries a Warnings (0) button after Analyze. It opens a window that reads “No warnings — the method’s assumptions hold for these inputs.” A condition that stops the analysis is shown before the analysis, see Messages. The one caution is a load inclination larger than φ.
The Calculations tab, the report and the Theory tab
The Calculations tab opens with Given and what is sought and then writes out the working in nine numbered steps with your numbers:
Compute the bearing-capacity factors — Nq, Nc and Nγ with their formulas.
Apply shape factors — B/L and Fcs, Fqs, Fγs.
Apply depth factors — Df/B, the form used (linear, or with arctan above 1) and Fcd, Fqd, Fγd. When Df/B lies between 0.6 and 1.6 the step notes that the two forms meet at 1 with a step, so qu changes by a few per cent as Df/B crosses 1.
Apply inclination factors — Fci, Fqi, Fγi.
Locate the groundwater table — the case, q and the unit weight of the self-weight term.
Write the general bearing-capacity equation — the equation with your numbers, the three terms and qu, then the share of each term.
Apply the factor of safety — qu,net, qall,g and qall,n.
Compute the gross allowable load — Qall, and Qall(incl) when β is above 0.
Check the applied foundation pressure — the PASS or FAIL lines, or the note that no pressure was entered.
A last box, Answer, gives the result in a sentence.
The Calculations tab: step 1 results and the start of step 2.
The report
In the Report tab fill in the cover (project, location, client, report number, date, prepared by, title or qualification, checked by, and optional notes). The details are kept in this browser and saved with the model file. Save as PDF and Download Word (.docx) produce the summary report; the preview below the buttons is the report itself, and it is built after you press Analyze.
The report has six parts: 1 Introduction and scope, 2 Input data (a table and the section drawing), 3 Calculation (the steps above), 4 Results (with the drawing of the terms and the pressures), 5 Summary and 6 References. When the analysis carries a caution, a part Warnings and notes comes before the Summary and the report has seven parts. It states the units used.
The Report tab: the cover details, the two buttons and the first page.
The Theory tab
The Theory tab has fifteen sections: The general equation, Meyerhof’s slip-line field, Stresses on the equivalent free surface, The radial zone and the wedge, The angle θ and the surface footing, The self-weight term, The bearing-capacity factors, Shape factors, Depth factors, Inclination factors, The complete equation, The water table, Allowable pressure and the check, Worked example and References. Each opens when you click its title.
Worked example: the module’s own example
The module opens on this example, so you can follow the numbers on your own screen.
The water table (0.5 m) is above the base (1 m). γ′ = 19.5 − 9.81 = 9.69 kN/m³, q = 0.5 × 16 + 0.5 × 9.69 = 12.85 kPa, and the self-weight term uses γ′ = 9.69 kN/m³.
qu,net = 520.0 − 12.85 = 507.1 kPa; qall,g = 520.0 / 3 = 173.3 kPa; qall,n = 507.1 / 3 = 169.0 kPa; Qall = 173.3 × 1.2 × 1.2 = 249.6 kN; and Qall(incl) = 249.6 / cos 10° = 253.4 kN. These are the cards of the Results tab.
Other unit systems
The default example in SI · tf gives qu = 53.02 t/m² and in US 10.86 ksf: the same pressure in other units. Two checks by hand, calculated outside the module:
US. A square footing B = 4 ft at Df = 3 ft, c = 0, φ = 30°, γ = 110 pcf, no water table, vertical load. Nq = 18.40, Nc = 30.14, Nγ = 22.40; q = 3 × 110 = 330 psf; Fqs = 1.577, Fγs = 0.6, Fqd = 1.217. qu = 0.330 × 1.577 × 1.217 × 18.40 + ½ × 0.110 × 4 × 0.6 × 22.40 = 11.65 + 2.96 = 14.6 ksf. The module gives 14.61 ksf, qall,g = 4.870 ksf and Qall = 77.92 kip.
SI · tf. A strip B = 1.5 m at Df = 1 m, c = 0.1 kg/cm², φ = 28°, γ = 1.8 t/m³, no water table, vertical load: Nq = 14.72, Nc = 25.80, Nγ = 16.72, no shape factors, q = 1.8 t/m². The module gives qu = 85.68 t/m², qall,g = 28.56 t/m² and Qall = 42.84 tf/m; the same case in SI · kN is 840.2 kPa.
SI · kN. The default example above, 519.99 kPa, was reproduced independently from the formulas to the second decimal; so were the strip, the rectangle and every row of the table below.
How each input changes the answer
Each row changes one thing in the example (a 1.2 m square footing, Df = 1 m, c = 0, φ = 32°, γ = 16 kN/m³, γsat = 19.5 kN/m³, the water table at 0.5 m, β = 10°, FS = 3) and runs the module again; the clay rows change the soil and the water as stated. The numbers are the ones the module gives, so you can reproduce any row. Pressures are in kPa; qall,g is qu divided by FS.
The example with one change at a time
Change
qu
qall,g
The example: square 1.2 m, Df = 1 m, c = 0, φ = 32°, γ = 16, γsat = 19.5, Dw = 0.5 m, β = 10°, FS = 3 The reference
520.0
173.3
Strip No shape correction: the lowest of the shapes
372.4
124.1
Rectangle, L = 1.8 m Between the strip and the square
470.8
156.9
Rectangle, L = 2.4 m Halfway between the strip and the square (B/L = 0.5)
446.2
148.7
Circular, B = 1.2 m The same as the square
520.0
173.3
Df = 0 (on the surface) No surcharge: q = 0
63.34
21.11
Df = 0.5 m Water table at the base level
315.3
105.1
Df = 1.2 m Df/B = 1
611.2
203.7
Df = 2 m The deep form of the depth factors (Df/B above 1)
911.2
303.7
Df = 3 m Capacity rises strongly with depth
1,324
441.3
B = 0.6 m Within 1 % of the example: the surcharge term falls with B through the depth factors and the self-weight term rises
515.9
172.0
B = 2 m Within 1 % of B = 1.2 m
518.0
172.7
φ = 25° Much lower: qu is very sensitive to φ
213.4
71.15
φ = 38° More than doubles qu
1,203
400.9
φ = 45° Very high; check that φ is a design value
3,703
1,234
c = 5 kPa The cohesion term appears
807.5
269.2
c = 20 kPa The cohesion term is large
1,670
556.7
γ = 18 kN/m³ Raises the surcharge above the water table
556.6
185.5
γsat = 21 kN/m³ Raises the submerged weight
555.2
185.1
Water table: None No submerged weight: higher
667.9
222.6
Dw = 0 (at the surface) Everything submerged: lower
404.5
134.8
Dw = 1 m (at the base) Surcharge dry, self-weight submerged
635.5
211.8
Dw = 1.6 m (0.6 m below the base) Within one width below the base: a weighted unit weight
651.7
217.2
Dw = 3 m Deeper than B below the base: the same as no water
667.9
222.6
β = 0 (vertical load) The highest: no inclination factor
700.5
233.5
β = 20° Strong reduction
374.8
124.9
β = 32° (= φ) Fγi = 0: the self-weight term drops out
247.1
82.38
β = 40° (above φ) A caution appears; Fγi is still 0
The pattern follows the equation. The friction angle, the load inclination and the founding depth change qu strongly; depth raises it through q and the depth factors; the shape factors lower it from the square to the strip; and the water table lowers it by cutting the unit weights. For B between 0.6 and 2 m the result changes by under 1 %, because the growing self-weight term is nearly offset by the falling depth factors; wider footings gain again (B = 5 m gives 610.9 kPa). The factor of safety does not change qu; it divides it: FS = 2 gives qall,g = 260.0 kPa and FS = 2.5 gives 208.0 kPa.
Messages: when the module stops, and what it notes
The module checks the inputs as you type and again when you press Analyze. There are three kinds of message.
A condition of the method is not met (before Analyze)
While you type, the bar turns brown and reads Cannot be analysed — with the condition; Analyze is disabled and the boxes keep their colour. Nothing is calculated.
The bar when L is shorter than B.
When
Message and what to do
A rectangle with L shorter than B
“L = 0.8000 m is shorter than B = 1.20 m.” De Beer’s shape factors are defined with B as the shorter side and L ≥ B the longer one. Swap the two values, or enter the longer side as L.
γsat is not above the unit weight of water, with the water table present
“γsat ≤ γw — the submerged unit weight would not be positive.” A negative effective weight is not physical. Check γsat.
qu does not exceed the overburden q
For example φ = 0 and c = 0 in the example: “qu = 10.15 kPa does not exceed the overburden q = 12.85 kPa at the base level.” The soil would fail under less than the pressure that already acts at the base. Check the loads and the inputs. The same stop appears for β = 89° in the example.
An input is empty or outside its range (when you press Analyze)
A window titled Cannot analyse — 1 input error (or 2 input errors …) lists each message; the limits are shown in the units of the unit system chosen.
The window when the width is empty.
When
Message
A required box is empty
“Footing width (short side) (B) is missing.”
A value is below its limit
“Footing width (short side) (B) must be at least 0.05 m.” (in US, “… at least 0.16405 ft.”), “Founding depth (Df) must be at least 0 m.”, “Cohesion (c) must be at least 0 kPa.”, “Factor of safety (FS) must be at least 1.”, “Applied vertical gross pressure at the base (optional) (qapplied) must be at least 0 kPa.”
A value is above its limit
“Friction angle (φ) must be at most 50°.”, “Load inclination from vertical (β) must be at most 89°.”
Several are wrong
The window lists them together, for example “3 input errors”.
A caution after Analyze
When β is larger than φ the analysis runs and a Warnings (1) window opens: “β = 40.00° exceeds φ = 32.00°. Fγi assumes β ≤ φ; beyond that it is taken as 0, so the self-weight term drops out. Check the load inclination, or read this as a rough bound.” The Results tab then carries the badge CHECK THE WARNINGS and the bar a warning count. With usual values the Warnings window reads “No warnings — the method’s assumptions hold for these inputs.”
The caution for β above φ.
Good practice and common mistakes
Enter qapplied as V/A of the vertical component. It includes the weight of the footing and of the soil above it. Entering the resultant Q/A with an inclined load makes the check too severe.
Mind gross and net. The module gives both; state which convention your design follows. The gross check is the stricter of the two.
Use the water table that governs. The module reads Dw from the ground surface, not from the base.
Put the shorter side in B. A rectangle with L shorter than B is refused.
Use design values of φ and c.qu rises steeply with φ: 25° gives 213.4 kPa and 38° gives 1,203 kPa in the example.
One soil only. The module takes one soil under the footing; if the ground changes within about one width below the base, run it with the weaker soil for a conservative value.
Read the unit boxes. After you switch the system, type values in the units shown beside the boxes.
Keep a record. The report is the record of an analysis; use Quick Save… or Save to file… to keep the model.
Frequently asked questions
Which equation does the module use?
Meyerhof’s general bearing capacity equation: qu = cFcsFcdFciNc + qFqsFqdFqiNq + ½ γBFγsFγdFγiNγ, with De Beer’s shape factors, Hansen’s depth factors and Meyerhof’s inclination factors. For the example it gives 520.0 kPa.
Which footing shapes can I analyse?
Strip, square, rectangular and circular, at any ratio Df/B. A circle is treated like a square of side B (the diameter), and a strip has no shape correction.
Does it handle an inclined load?
Yes, through β from 0 to 89° and the inclination factors. The equation returns the vertical component of the ultimate load; the module also gives the allowable resultant load Qall / cos β. When β is larger than φ the self-weight term is taken as zero and a caution is shown.
What is the difference between the gross and the net values?
The gross values are total pressures at the base. The net values take away the overburden q that already acts at the base level. qall,g = qu / FS and qall,n = (qu − q) / FS. A gross applied pressure is compared with the gross value and a net one with the net value.
What do I enter as the applied pressure?
The vertical gross pressure at the base, V/A: the vertical load of the column plus the weight of the footing and of the soil above it, over the base area, with service loads. With an inclined load use the vertical component. It is optional; without it the module gives the capacity and the Design check reads NOT CHECKED.
How is the water table handled?
Choose Present or None. With a water table, give its depth from the ground surface and the saturated unit weight. Above the base it splits the overburden and makes the self-weight term submerged; up to one width below the base it gives the self-weight term a weighted unit weight; deeper than that it has no effect.
Why does the width change the capacity so little?
In this example, for widths up to about 2 m, two effects offset each other: a wider footing has a larger self-weight term, but its ratio Df/B is smaller, so the depth factors and the surcharge term are lower. In the example B = 0.6, 1.2 and 2 m give 515.9, 520.0 and 518.0 kPa.
What values does the module accept?
B and L at least 0.05 m, Df and Dw at least 0, c at least 0, φ from 0 to 50°, β from 0 to 89°, the unit weights at least 0.1, FS at least 1, and every box filled except the applied pressure. Anything else stops the analysis with a message that names the value.
Which units does it use?
SI · kN, SI · tf or US, switchable in the header at any time, even after Analyze. The pressure is in kPa, t/m² or ksf, the load in kN, tf or kip (per metre or per foot for a strip) and lengths in m or ft. The default example gives 520.0 kPa, 53.02 t/m² or 10.86 ksf.
What does the report contain?
A cover with your project details and the answer, then six parts (seven when the analysis carries a caution, with Warnings and notes before the summary): introduction and scope, input data with the section drawing, the calculation step by step, results with the drawing of the terms and pressures, summary and references. It is saved as a PDF or a Word file.
Does the module remember my inputs?
Yes. Every change is kept in the browser, and the page opens again on the model you last worked on, including its analysed state. Reset to defaults brings back the example; Save to file and Quick Save keep copies.
Can I drag things on the drawing?
No. The drawings follow the numbers; the Show chips only switch the mechanism and the dimensions on and off in the Section view.
Calculate the ultimate and allowable bearing capacity of a strip, square, rectangular or circular footing by Hansen’s equation, with its inclination, base-tilt and ground-slope factors, and check an applied pressure against it. This manual walks through the screen, every input, the results, the calculations and the report, with worked examples you can reproduce.
Hansen gives the ultimate and the allowable bearing capacity of a shallow footing by Hansen’s (1970) equation. It is the module of the family to use when the footing is near sloping ground, when its base is tilted from the horizontal, or when the load is inclined: besides the usual shape and depth corrections it applies Hansen’s inclination, base-tilt and ground-slope factors, and Hansen’s own bearing capacity factor Nγ.
qu = cNcscdcicbcgc + qNqsqdqiqbqgq + ½ γBNγsγdγiγbγgγ
The three terms are the cohesion term, the surcharge term (the weight of the soil above the base, q) and the self-weight term. Nc, Nq and Nγ depend on the friction angle φ alone; s are the shape factors, d the depth factors, i the inclination factors, b the base-tilt factors and g the ground-slope factors. For a level base on level ground under a vertical load the last three sets are all 1. At φ = 0 the cohesion term takes Hansen’s additive form, which the Calculations tab writes out.
What you can describe
A strip, square, rectangular or circular footing: width B (the diameter of a circle), length L of a rectangle, and the founding depth Df.
One soil below the footing: cohesion c, friction angle φ and unit weight γ, with an optional water table (saturated unit weight and depth Dw).
A base tiltη and a ground slopeω (both in degrees).
The load as one load case: the horizontal pressure h = H/A and, optionally, the vertical gross pressure qapplied = V/A at the base.
The factor of safety FS.
The module gives the gross and the net ultimate bearing capacityqu and qu,net, the gross and the net allowable pressuresqall,g and qall,n, the gross allowable load Qall, all the factors with their values, the working step by step, a drawing of the failure mechanism to scale and a report as a PDF or a Word file. When you also enter qapplied it checks the footing and shows PASS or FAIL.
Which module of the family for which case
A vertical or inclined load on level ground, with shape, depth and inclination factors: Meyerhof.
The classical equation, with general and local shear: Terzaghi.
The same corrections as in this module, with Vesic’s factors: Vesic.
Have these ready from your design and your soil data:
What
Notes
The footing From: your design
Shape, width B (the shorter side), length L for a rectangle, and the depth Df of the base below the ground surface.
The soil From: your investigation
Cohesion c, friction angle φ (0 to 50°) and unit weight γ of the soil below the footing. Use effective-stress parameters for a drained case and undrained cohesion with φ = 0 for a clay under short-term loading.
The water table From: the borehole logs
Its depth Dw below the ground surface and the saturated unit weight γsat, when water is within reach of the footing.
Base tilt and ground slope From: your layout
η, the tilt of the base from the horizontal, and ω, the slope of the ground next to the footing, both in degrees (0 to 45°). Leave both at 0 for a level base on level ground.
The load of the case From: your structural analysis
The horizontal pressure h = H/A and the vertical gross pressure qapplied = V/A at the base, with service (unfactored) loads: the column load plus the weight of the footing and of the soil on it, over the base area. Needed for the check, and needed whenever h is above zero.
The factor of safety From: your design rules
FS, at least 1.
Quick start in seven steps
Open the module and choose the units
Open Hansen from the Bearing Capacity family. Pick SI · kN, SI · tf or US in the header; you can change it at any time.
Describe the footing
In Footing choose Strip, Square, Rectangular or Circular and type B (and L for a rectangle) and Df.
Enter the soil and the water
In Soil type c, φ and γ. In Groundwater choose Present or None; with water, type γsat and Dw.
Enter the tilt, the slope and the load
In Base tilt and ground slope type η and ω. In Loads type h and, for the check, qapplied. In Analysis Settings type FS.
Press Analyze
Press Analyze at the foot of the Model tab. The bar reads Analysed with the verdict when qapplied is entered, and the inputs lock.
Read the answer
The Results tab gives the gross and net ultimate bearing capacity, the gross and net allowable pressures and the check. The Capacity and Factors views draw them.
Take the working and the report
The Calculations tab writes out the steps with your numbers. The Report tab saves a PDF or a Word file.
The screen: section, capacity and factors
The layout is the one every GeoTerva module shares, described in the workspace guide: the drawing on the left, the tabs on the right. The drawing has three views, chosen with the buttons above it:
Section is a cross section through the footing in the ground, drawn to scale: the footing, the depth Df, the width B, the surcharge q at the base level and, after Analyze, qu under the base. It shows the general shear mechanism of the method for your φ: the elastic wedge under the base (I), the radial shear zone (II) and the passive wedge (III). It follows the inputs as you type.
Capacity is the answer drawn: a bar split into the cohesion, surcharge and self-weight terms; the gross pressures qu and qall,g; the net pressures qu,net and qall,n; and the factors of the equation. Before Analyze it says “Press Analyze”.
Factors plots Nc, Nq and Nγ against φ (logarithmic scale), with the values at your φ marked.
Section: the footing and the failure mechanism drawn to scale for φ = 25°.
Capacity after Analyze.
Factors: Nc, Nq and Nγ against φ.
The Show chips
Above the Section, a bar holds two chips, both checked by default. Failure mechanism draws the three zones of the mechanism, and Dimensions draws the dimension lines of B and Df. The Capacity and Factors views have no chips.
Section with Dimensions off.
Dragging and zoom
The drawings are set by the numbers: nothing on them can be dragged and they have no zoom buttons. Change the inputs on the Model tab and the Section follows.
The angles and the load on the drawing
The Section draws the angles you enter. With η above 0 a dashed ray marks the base tilt (“base tilt η = …°”); with ω above 0 the ground slope is drawn and labelled “ground slope ω = …°”; and when h and qapplied are entered the load arrow reads “Q inclined …° from vertical”, the angle being arctan(h/qapplied), even before Analyze. When the sloping ground drops below the base level inside the mechanism the drawing says “Caution: the sloping ground drops below the base level inside the mechanism; the part of the mechanism above the ground is not drawn.” The factors that follow from the angles are listed on the Capacity view, on the Results tab and in the Calculations. The (?) window of the Base tilt and ground slope section draws the two angles, see below.
The whole window after Analyze.
Entering the model, section by section
The Model tab has seven sections: Model data, Footing, Soil, Groundwater, Base tilt and ground slope, Loads and Analysis Settings. Each opens when you click its title, and opening one closes the one that was open; Next and Back walk you through them, and Analyze waits below the last one. In the tables, a unit shown three times gives the units of SI · kN, SI · tf and US in turn. Defaults are shown in SI; in the other systems the boxes show the converted values, for example 6.56168 ft for B = 2 m, 208.854 psf for c = 10 kPa or 114.586 pcf for γ = 18 kN/m³.
Model data
The first section holds the model name, Save to file…, Open file…, Quick Save… with its list and Load and Delete, and Reset to defaults. It works as described in the workspace guide. The list reads “— no quick saves yet —” until you save a version.
Model data.
Footing
Choose the shape with the four buttons; the Square is selected at the start. The footing takes its dimensions from B and Df, and L appears for a rectangle. The shape sets the ratio B/L of the shape factors: 0 for a strip, 1 for a square and for a circle (whose B is the diameter) and B/L for a rectangle.
Footing.
Footing fields
Field
Unit
Default
Footing width (short side) B The width, the shorter side; the diameter of a circle. At least 0.05 m.
m · ft
2
Footing length (long side) L At least 0.05 m, and not shorter than B. Shown when the shape is Rectangular.
m · ft
2
Founding depth Df The depth of the base below the ground surface. Zero or more.
m · ft
1
Soil
One soil below the footing, described by c, φ and γ. For layered ground enter the values of the layer that governs under the footing, the weaker one for a conservative result.
Soil.
Soil fields
Field
Unit
Default
Cohesion c Zero or more.
kPa · kg/cm² · psf
10
Friction angle φ From 0 to 50°. At 0 the cohesion term takes the additive form of the undrained case.
°
25
Unit weight (above GWT) γ The unit weight of the soil above the water table. At least 0.1 kN/m³.
kN/m³ · t/m³ · pcf
18
Groundwater
Choose Present or None. With a water table the saturated unit weight and the depth Dw are asked for. Three small read-outs follow your inputs: the surcharge q at the base, the water case, and Df/B. The cases are the ones the Calculations tab names: the water table above the base, at or within one width below it (the self-weight term then uses a weighted unit weight), or deeper than one width below it (no effect).
Groundwater.
Groundwater fields
Field
Unit
Default
Water table: Present or None None means no water table within the depth of influence.
—
None
Saturated unit weight γsat The unit weight below the water table. Shown when the water table is Present.
kN/m³ · t/m³ · pcf
19
Water table depth Dw Measured from the ground surface. Zero or more. Shown when the water table is Present.
m · ft
3
Base tilt and ground slope
The two angles that distinguish Hansen’s equation. η tilts the base of the footing from the horizontal; ω is the slope of the ground next to the footing, falling away from it. Both reduce the capacity; with both at 0 every b and g factor is 1. The (?) beside the heading opens a window with a drawing of the two angles and the formulas.
Base tilt and ground slope.
Tilt and slope fields
Field
Unit
Default
Base tilt from horizontal η From 0 to 45°.
°
0
Ground slope near the footing ω From 0 to 45°; for φ above 0 it may not exceed φ.
°
0
The (?) window: the two angles drawn.
Loads
The load is one load case: the horizontal pressure h = H/A and the vertical gross pressure qapplied = V/A at the base, with service loads. The inclination factors use both, so qapplied is needed whenever h is above 0. Without qapplied the module gives the bearing capacity and the check reads NOT CHECKED. The (?) opens a window with a drawing of the load case, the gross and the net check.
Loads.
Load fields
Field
Unit
Default
Horizontal pressure at the base, H/A h Zero or more.
kPa · t/m² · ksf
0
Vertical gross pressure at the base, V/A qapplied Optional; needed with h above 0 and for the check. Zero or more.
kPa · t/m² · ksf
empty
Analysis Settings
The factor of safety divides the ultimate capacity into the allowable pressures.
Analysis Settings.
Analysis field
Field
Unit
Default
Factor of safety FS At least 1.
—
3
Choosing the shape, the water and the load case
The module has one method, Hansen’s; what you choose is the description of the footing and of the case.
Choice
What it does
Shape
Sets B/L in the shape factors sc = 1 + (B/L)(Nq/Nc), sq = 1 + (B/L) sin φ, sγ = 1 − 0.4(B/L). A strip carries no shape correction. For the example, a strip gives qu = 592.0 kPa, a 2 × 4 m rectangle 678.5 kPa and a square 765.1 kPa; a circle of the same B gives the same as the square.
Water table
Changes the surcharge q and the self-weight term. A table above the base gives q = 13.6 kPa (against 18.0) at Dw = 0.5 m; one at the base roughly halves the self-weight term; one deeper than one width below the base changes nothing.
Horizontal load h
Reduces every term through the inclination factors. It needs qapplied, and it must stay below qapplied + c cot φ (below c when φ = 0).
Tilt η and slope ω
Reduce the capacity through the b and g factors. ω may not exceed φ.
Which should I pick?
Hansen’s equation when the footing is at the top of a slope or an embankment, when the base is sloped, or when the horizontal load is significant. For a level base and level ground under a vertical load the inclination, tilt and slope factors are 1 and the equation reduces to the shape and depth factors with Hansen’s own Nγ.
The load case from your analysis: give h and qapplied from the same load combination, with service loads. A slope or a tilt does not need a horizontal load; a horizontal load needs qapplied.
φ = 0 for a clay under short-term loading, with the undrained cohesion as c; Nγ is then 0 and the self-weight term vanishes.
Analyze and read the results
Press Analyze. The bar changes to Analysed — bearing capacity calculated; applied pressure not provided, or, when you entered qapplied, to Analysed — PASS: … or Analysed — FAIL: … with the actual factor of safety. It says “The inputs are locked. Edit inputs clears the results; the unit system can still be changed.” The page may stay on the Model tab: open the Results tab for the answer. Two buttons sit in the bar: Warnings (n), and Edit inputs, which unlocks the inputs and clears the results.
The Results tab of the example.
Card
The example
Gross ultimate bearing capacity qu
765.1 kPa
Net ultimate bearing capacity qu,net = qu − q
747.1 kPa
Gross allowable qall,g = qu / FS
255.0 kPa
Net allowable qall,n = (qu − q) / FS
249.0 kPa
Gross allowable vertical load Qall
1,020 kN
Below the cards the Design check says NOT CHECKED until you enter qapplied. Then a table lists the factors step by step (NcNqNγ, the shape, depth, inclination, base-tilt and ground-slope factors, the groundwater table, qu, the allowable pressures and Qall), and a table gives the contribution of each term with its share of qu. For a strip Qall is per metre of length (kN/m, tf/m or kip/ft).
The check
With qapplied entered the module compares gross with gross and net with net: the gross check qapplied ≤ qall,g and the actual factor of safety FSactual = qu / qapplied, and the net check qapplied − q ≤ qall,n. The gross line and the net line each carry a PASS or FAIL badge; the gross check governs: when it passes, the net check passes too. For the example, qapplied = 200 kPa passes with FSactual = 3.83 and 300 kPa fails with 2.55 (the gross allowable pressure is 255.0 kPa).
A case that fails the gross check: 100.00 kPa against 94.13 kPa.
Using the numbers
qu is the failure pressure, not a working value. Compare the applied pressure with the allowable pressure of the same kind: a gross applied pressure with qall,g, a net one with qall,n. The two are two conventions of applying the factor of safety.
Pressures are in kPa, t/m² or ksf by the unit system; the same example gives 78.01 t/m² (SI · tf) and 15.98 ksf (US). The drawings stay in SI whatever the unit system.
Changing the unit system after Analyze re-states the Results without a new run.
Warnings and notes
The bar carries a Warnings (n) button. For usual values the window reads “No warnings — the method’s assumptions hold for these inputs.” A caution, such as the sliding one below, opens the window by itself when you analyse and adds “— 1 warning” to the bar. A condition that stops the analysis is shown as a message, see Messages.
The Calculations tab, the report and the Theory tab
The Calculations tab opens with Given and what is sought and then writes out the working in numbered steps, each with the formulas and your numbers:
Compute the bearing-capacity factors — Nc, Nq and Hansen’s Nγ = 1.5(Nq − 1) tan φ.
Apply shape factors — sc, sq, sγ with B/L (the φ = 0 form s′c = 0.2B/L for an undrained soil).
Apply depth factors — dc = 1 + 0.4k, dq = 1 + 2 tan φ (1 − sin φ)² k and dγ = 1, with k = Df/B, or arctan(Df/B) when Df/B is above 1. Around Df/B = 1 the step writes out that the two forms meet with a step of a few per cent.
Apply inclination factors — from h/(qapplied + c cot φ); all 1 when h = 0 (and i′c = 0 in the φ = 0 form).
Apply base-tilt factors — bc = 1 − η/147°, bq = e−2η tan φ, bγ = e−2.7η tan φ.
Locate the groundwater table — q and the unit weight of the self-weight term.
Write Hansen’s equation — the three terms and qu, with the contribution of each term.
Apply the factor of safety, Compute the gross allowable load, and, with qapplied, Check the applied foundation pressure, ending with the Answer.
The Calculations tab: the first steps with the example’s numbers.
The report
In the Report tab fill in the cover (project, location, client, report number, date, prepared by, title or qualification, checked by, and optional notes). The details are kept in this browser and saved with the model file. Save as PDF and Download Word (.docx) become available once the model is analysed; the preview below the buttons is the report itself.
The report has six parts: 1 Introduction and scope, 2 Input data (a table of the inputs with the section drawing), 3 Calculation (the steps of the Calculations tab), 4 Results (with the Capacity drawing), 5 Summary and 6 References; when the analysis carries a caution it has seven, with 5 Warnings and notes, 6 Summary and 7 References. It states the units used.
The Report tab: the cover details and the two buttons.
The Theory tab
The Theory tab explains Hansen’s equation in sections: why Hansen’s Nγ differs from the others (with a table against φ), the shape and depth factors, the inclination factors, the base-tilt and ground-slope factors, putting the equation together, the undrained case (φ = 0), how the module’s numbers were checked, and the reference.
Worked example: the module’s own example
The module opens on this example, so you can follow the numbers on your own screen.
Inputs of the example
Section
Input
Value
Footing
Shape, B, Df
Square, B = 2 m, Df = 1 m
Soil
c, φ, γ
10 kPa, 25°, 18 kN/m³
Groundwater
Water table
None
Base tilt and ground slope
η, ω
0°, 0°
Loads
h, qapplied
0, empty
Analysis Settings
FS
3
Step 1: the factors of the equation
Nq = eπ tan 25° tan²(45° + 25°/2) = 10.66, Nc = (Nq − 1)/tan 25° = 20.72 and Nγ = 1.5(Nq − 1) tan 25° = 6.758. For a square, B/L = 1: sc = 1 + Nq/Nc = 1.515, sq = 1 + sin 25° = 1.423, sγ = 1 − 0.4 = 0.600. With k = Df/B = 0.5: dc = 1 + 0.4 × 0.5 = 1.200, dq = 1 + 2 tan 25° (1 − sin 25°)² × 0.5 = 1.155, dγ = 1. The inclination, tilt and slope factors are 1.
qu = 376.6 + 315.5 + 73.0 = 765.1 kPa. The surcharge q = 18 × 1 = 18.0 kPa, so qu,net = 747.1 kPa. With FS = 3, qall,g = 765.1 / 3 = 255.0 kPa and qall,n = 747.1 / 3 = 249.0 kPa, and Qall = 255.0 × 2 × 2 = 1,020 kN. These are the cards of the Results tab.
An inclined case with a tilt and a slope
Change the example to η = 5°, ω = 5°, h = 50 kPa, qapplied = 100 kPa and FS = 1.8. With x = h/(qapplied + c cot φ) = 50 / (100 + 21.44) = 0.4117: iq = (1 − 0.5 × 0.4117)⁵ = 0.3159, ic = iq − (1 − iq)/(Nq − 1) = 0.2451 and, on the tilted base, iγ = (1 − (0.7 − 5/450) × 0.4117)⁵ = 0.1887. The base-tilt factors are bc = 1 − 5/147 = 0.9660, bq = e−2 × 0.08727 × tan 25° = 0.9218 and bγ = 0.8959; the ground-slope factors are gc = 0.9660 and gq = gγ = (1 − 0.5 tan 5°)⁵ = 0.7996. The terms are 86.1 + 73.4 + 9.9, so qu = 169.4 kPa and qall,g = 94.13 kPa. The module gives the same, and qapplied = 100 kPa is above 94.13 kPa: FAIL, FSactual = 1.69. The net check, 82.00 kPa against qall,n = 84.13 kPa, passes; the gross check governs.
Other unit systems
The same example reads 78.01 t/m² in SI · tf and 15.98 ksf in US: the same pressure in other units. Two checks entered in the units of the system, with the cohesion in the unit the box shows:
US. A square footing of 6 ft at 3 ft depth, c = 300 psf, φ = 30° and γ = 120 pcf. Nc = 30.14, Nq = 18.40, Nγ = 15.07, sc = 1.610, sq = 1.5, sγ = 0.6, dc = 1.2, dq = 1.144; q = 0.36 ksf. The terms are 0.3 × 30.14 × 1.610 × 1.2 = 17.47, 0.36 × 18.40 × 1.5 × 1.144 = 11.37 and ½ × 0.12 × 6 × 15.07 × 0.6 = 3.26 ksf, so qu = 32.10 ksf. The module gives 32.10 ksf, qall,g = 10.70 ksf and Qall = 385.2 kip.
SI · tf. A rectangle 1.5 × 3 m at 1 m depth, c = 0.1 kg/cm² (1 t/m²), φ = 30° and γ = 1.8 t/m³. B/L = 0.5: sc = 1.305, sq = 1.25, sγ = 0.8, dc = 1.267, dq = 1.192. The terms are 49.84 + 49.37 + 16.27 t/m², so qu = 115.5 t/m². The module gives 115.5 t/m², qall,g = 38.49 t/m² and Qall = 173.2 tf.
How each input changes the answer
Each row changes one thing in the example (a 2 m square footing at 1 m depth, c = 10 kPa, φ = 25°, γ = 18 kN/m³, no water, level, vertical load, FS = 3) and runs the module again. The numbers are the ones the module gives, so you can reproduce any row; pressures are in kPa.
The example with one change at a time
Change
qu
qall,g
The example: square 2 m, Df = 1 m, c = 10, φ = 25°, γ = 18, FS = 3 The reference
765.1
255.0
Shape: strip No shape correction: the cohesion and surcharge terms drop, the self-weight term rises
592.0
197.3
Shape: rectangle, L = 4 m Between the strip and the square
678.5
226.2
Df = 0 No surcharge term, and dc = 1
386.8
128.9
Df = 2 m The surcharge term grows with the depth
1228.2
409.4
Df = 3 m Df/B above 1: the depth factors take the arctan form
1579.5
526.5
B = 3 m A wider footing: almost the same qu, because the depth factors fall as B grows
766.5
255.5
c = 0 The cohesion term vanishes
388.5
129.5
c = 20 kPa The cohesion term doubles
1141.6
380.5
φ = 0 (c = 10) Undrained form: Nc = 5.14, Nγ = 0
90.0
30.0
φ = 30° Nc = 30.14, Nq = 18.40, Nγ = 15.07
1313.8
437.9
φ = 35° The capacity more than triples
2382.6
794.2
γ = 20 kN/m³ Larger q and self-weight
808.2
269.4
Water table at Dw = 0.5 m, γsat = 19 Above the base: q and the self-weight term fall
652.1
217.4
Water table at the base, Dw = 1 m Only the self-weight term falls
729.3
243.1
Base tilt η = 10° bc, bq and bγ below 1
677.6
225.9
Ground slope ω = 10° gc and gq = gγ below 1
595.8
198.6
Ground slope ω = 20° A steeper slope, a lower capacity
467.6
155.9
η = 10° and ω = 10° Both reductions together
533.0
177.7
h = 20 kPa with qapplied = 100 kPa The inclination factors reduce all three terms
476.3
158.8
FS = 2 qu is the same; qall,g rises
765.1
382.5
The pattern follows the equation. The friction angle moves the answer most among the rows (35° gives about three times the value at 25°); the depth, through q and the depth factors, comes next, and the cohesion term is proportional to c. A tilt of 10° takes 11 per cent off, a slope of 10° 22 per cent, and both together 30 per cent. The factor of safety does not change qu. A footing that is wider at a fixed depth is not always stronger, because k = Df/B falls: compare neighbouring widths before settling on one.
Messages: when the module stops, and what it cautions
The module checks the numbers before it calculates. When one cannot be used it stops, and nothing is calculated; the limits are shown in the units of the unit system chosen.
Input limits
If an input is outside its limits or empty, pressing Analyze opens a window titled Cannot analyse — 1 input error (or 2 input errors …) that lists each message.
The window Analyze opens when the width is 0.
When
Message
The width is below 0.05 m
“Footing width (short side) (B) must be at least 0.05 m.”
A value is empty
“Footing width (short side) (B) is missing.”
The friction angle is above 50°
“Friction angle (φ) must be at most 50°.”
The tilt is above 45° (the slope likewise)
“Base tilt from horizontal (η) must be at most 45°.”
The factor of safety is below 1
“Factor of safety (FS) must be at least 1.”
Conditions the equation cannot take
These stop the analysis with a bar that reads Cannot be analysed — … and a line saying what to do; the Analyze button is dimmed until you change the inputs.
The slope above the friction angle.
When
Message and what to do
A rectangle has L shorter than B
“Cannot be analysed — L = 1.00 m is shorter than B = 2.00 m”. Hansen’s shape factors take B as the shorter side: swap the two values.
ω is above φ (φ above 0)
“Cannot be analysed — ω = 26.00° exceeds φ = 25.00°”. The ground-slope factors assume ω ≤ φ; check the two angles, or check the stability of the slope instead.
h is above 0 and qapplied is empty
“Cannot be analysed — enter qapplied for this load case”. Enter qapplied or set h to 0.
h reaches qapplied + c cot φ
“Cannot be analysed — h = 130.00 kPa reaches v + c·cot φ = 121.45 kPa” (for qapplied = 100 kPa and the example soil). The inclination factors vanish there; reduce h, check qapplied, and check the footing against sliding.
φ = 0 and h reaches c
“Cannot be analysed — h = 15.00 kPa reaches the undrained base resistance c = 10.00 kPa” (for c = 10 kPa). Beyond h = c the base slides before it can fail in bearing: reduce h or check c, and check the footing against sliding. With c = 0 any h above 0 stops at φ = 0; at φ = 0 this stop replaces the sliding caution.
At φ = 0 the horizontal load, the tilt and the slope together outweigh the rest
“Cannot be analysed — 1 + s′c + d′c − i′c − b′c − g′c = -0.0332 ≤ 0” (a strip at the surface with c = 40 kPa, h = 39 kPa, qapplied = 100 kPa and η = ω = 45°). Reduce h, the tilt or the slope.
Water with γsat not above the unit weight of water
“Cannot be analysed — γsat ≤ γw — the submerged unit weight would not be positive”. Check γsat.
The sliding caution
When h is above the sliding resistance qapplied tan φ + c the analysis still runs, and a caution opens by itself. With h = 60 kPa and qapplied = 100 kPa the window reads “h = 60.00 kPa exceeds the sliding resistance v·tan φ + c = 56.63 kPa.” and the bar reads “Analysed — FAIL … — 1 warning”. The bound takes the base friction as φ and the adhesion as c; check sliding with the friction and adhesion of the real base.
The sliding caution.
Good practice and common mistakes
Give h and qapplied from the same load combination, with service (unfactored) loads: the inclination factors use their ratio, and the check uses the same qapplied.
Put the footing weight and the soil on it into qapplied. It is the gross pressure at the base: the column load plus the weight of the footing and of the soil above it, over the base area.
Compare like with like. Gross applied pressure against qall,g, net against qall,n; the gross check is the stricter.
Check sliding and the stability of the slope separately. The factors only reduce the capacity; the module cautions when h passes qapplied tan φ + c, and a footing on or near a slope needs a check of the slope as a whole.
Use φ = 0 with the undrained cohesion for a clay under short-term loading; use drained parameters for the long term.
Keep to one method’s numbers. Hansen’s Nγ is smaller than Vesic’s at the same φ (6.76 against 10.88 at 25°); do not mix factors of different methods.
Watch Df/B near 1. The depth factors change form there, and the Calculations tab says so.
Check the units after switching the system: type values in the units shown beside the boxes (cohesion in psf in the US system and in kg/cm² in SI · tf).
Keep a record. The report is the record of an analysis; use Quick Save… or Save to file… to keep the model.
Frequently asked questions
What is Hansen’s equation for?
It gives the bearing capacity of a shallow footing and, besides the usual shape and depth corrections, corrects for an inclined load, a tilted base and ground that slopes away from the footing. The module writes every factor out and gives the gross and the net capacity.
How is it different from the Meyerhof module?
Hansen uses its own Nγ, which is smaller than Vesic’s at the same φ (6.76 against 10.88 at 25°), and its own inclination factors, which use the horizontal and the vertical pressure of one load case rather than an angle. Hansen’s module also takes a base tilt and a ground slope, which the Meyerhof module does not.
Why does it ask for the vertical pressure when I enter a horizontal load?
The inclination factors depend on h/(qapplied + c cot φ), the horizontal pressure against the vertical one of the same load case. Without qapplied the module stops with “enter qapplied for this load case”.
What is the difference between gross and net?
The gross pressures are the total pressure at the base. The net ones are what the footing adds to the overburden q that already acts at that level: qu,net = qu − q. The gross allowable pressure divides the whole capacity by FS, the net one only the part above q. Compare a gross applied pressure with the gross value and a net one with the net value.
What do the tilt and the slope do?
Both reduce the capacity. For the example, a tilt of 10° takes the qu from 765.1 to 677.6 kPa, a slope of 10° to 595.8 kPa, and both together to 533.0 kPa. They are limited to 45°, and the slope may not exceed φ.
Why does the module stop when the slope is steeper than φ?
The ground-slope factors assume ω ≤ φ, and a steeper slope is not stable on its own. The module says so and suggests checking the stability of the slope instead.
What happens at φ = 0?
The cohesion term takes Hansen’s additive form, Nc = 5.14, Nγ = 0 and the self-weight term is zero. For the example soil with φ = 0 the module gives qu = 90.0 kPa; a strip with c = 40 kPa gives 264.7 kPa.
How does the water table enter?
Through the surcharge q and the self-weight term. A table above the base lowers both, one at the base lowers the self-weight term, and one more than a width below the base has no effect.
Does a circular footing have its own factors?
It takes the shape factors of a square of the same B, where B is the diameter, so the example gives the same qu for the two. The plan area used for Qall is πB²/4.
Which units does it use?
SI · kN, SI · tf or US, switchable in the header at any time. Pressures are in kPa, t/m² or ksf, loads in kN, tf or kip (per metre or foot of length for a strip) and lengths in m or ft. Cohesion is in kPa, kg/cm² or psf. The drawings stay in SI.
What does the report contain?
A cover with your project details and the answer, then the parts introduction and scope, input data with the section drawing, the calculation step by step and results with the Capacity drawing, then, when the analysis carries a caution, a Warnings and notes part, and finally the Summary and References. It is saved as a PDF or a Word file once the model is analysed.
Does the module remember my inputs?
Yes. Every change is kept in the browser, and the page opens again on the model you last worked on, analysed and locked if you left it so. Reset to defaults brings back the example; Save to file and Quick Save keep copies.
Calculate the ultimate and allowable bearing capacity of a strip, square, rectangular or circular footing by Vesic’s equation: an inclination exponent that follows the footing’s own B/L and the direction of the load, and Vesic’s base-tilt and ground-slope factors. This manual walks through the screen, every input, the results and the report, with worked examples you can reproduce.
Vesic gives the ultimate and the allowable bearing capacity of a shallow footing on one soil, by Vesic’s equation (1973, 1975). It draws the failure mechanism to scale under the footing, works out the bearing capacity factors and the corrections for the shape and the depth of the footing, the inclination of the load, the tilt of the base and the slope of the ground, and gives the gross and the net ultimate capacity and the gross and the net allowable pressure. You enter the pressure that the footing applies and the module checks it: PASS or FAIL.
qu = cNcFcsFcdicbcgc + qNqFqsFqdiqbqgq + ½ γBNγFγsFγdiγbγgγ
The three terms are the cohesion term, the surcharge term (the soil above the base, q) and the self-weight term. What sets this module apart is the inclination factors: their exponent m is worked out from the B/L ratio of the footing and from the direction in which the horizontal load acts, and the base tilt and the ground slope have their own factors.
What you can describe
A strip, square, rectangular or circular footing: the width B (the shorter side, or the diameter of a circle), for a rectangle the length L, and the founding depth Df.
One soil below the footing with the cohesion c, the friction angle φ and the unit weight γ, and, if there is groundwater, the saturated unit weight γsat and the depth Dw of the water table.
A tilted base (the angle η) and sloping ground next to the footing (the angle ω).
One load case: the horizontal pressure h = H/A and the vertical gross pressure qapplied = V/A at the base, and the direction of the horizontal load, parallel to B or to L.
The factor of safety FS.
Which bearing capacity module for which job
A vertical load on level ground, with general or local shear: Terzaghi.
Shape, depth and an inclined load, with Meyerhof’s inclination factors: Meyerhof.
Hansen’s own factors (including his Nγ and shape factors) for the inclination, a footing near a slope or a tilted base: Hansen.
This module when the exponent of the inclination factors should follow the footing’s own B/L and the direction of the load, with Vesic’s base-tilt and ground-slope factors.
The module gives the bearing pressure. The settlement of the footing, its sliding along the base, the eccentricity of the load and the overall stability of a slope are checked with the matching modules and your own design checks; the Stresses in a soil mass family gives the stresses below a footing for settlement work.
Before you start: what you need
Have these ready from your design:
What
Notes
The footing From: your foundation design
The shape, the width B (and the length L of a rectangle) and the founding depth Df.
The soil From: your soil investigation
c, φ and γ of the soil below the footing, in the terms of the analysis you follow (effective stress parameters for drained conditions, φ = 0 and the undrained c for a short-term clay).
The groundwater From: the borehole logs
The depth Dw of the water table below the ground surface and the saturated unit weight γsat; or none.
The tilt and the slope From: the drawings
η and ω in degrees; both 0 for a level base on level ground.
The load From: your structural analysis
The horizontal pressure h = H/A and the vertical gross pressure qapplied = V/A of one load case, with service (unfactored) loads. qapplied includes the weight of the footing and of the soil above it.
The factor of safety From: your design basis
At least 1; 3 is the default.
Quick start in eight steps
Open the module and choose the units
Open Vesic from the Bearing Capacity family. Pick SI · kN, SI · tf or US in the header; you can change it at any time.
Describe the footing
In Footing choose Strip, Square, Rectangular or Circular and type B (and L for a rectangle) and Df.
Enter the soil and the groundwater
In Soil type c, φ and γ. In Groundwater choose Present and type γsat and Dw, or None.
Enter the tilt, the slope and the load
In Base tilt and ground slope type η and ω (0 if level). In Loads choose the direction of the horizontal load, then type h and qapplied.
Set the factor of safety
In Analysis Settings type FS.
Press Analyze
Press Analyze at the foot of the Model tab. The drawing changes to the Capacity view and the bar reads PASS or FAIL.
Read the answer
The Results tab gives qu, qu,net, qall,g and qall,n, the design check and every factor.
Take the working and the report
The Calculations tab writes out the steps with your numbers; the Report tab saves a PDF or a Word file.
The screen: section, capacity and factors
The layout is the one every GeoTerva module shares, described in the workspace guide. The drawing has three views, chosen with the buttons above it:
Section is the cross section through the footing, drawn to scale: the footing, the ground surface, the water table, Df and B, and the failure mechanism of the method for your φ: an elastic wedge under the base (I), a radial shear zone (II) and a passive wedge (III). It follows the inputs as you type. After Analyze it also shows qu under the base and the surcharge q.
Capacity is empty until you press Analyze (it says “Press Analyze”). Afterwards it shows the three terms of qu as one bar with their shares, the gross pressures (qu, qall,g and qapplied) and the net pressures (qu,net, qall,n and the net applied pressure) as bars with the verdict, and all the factors of the equation.
Factors draws Nc, Nq and Nγ against φ on a logarithmic scale, with the values at your φ. It follows φ and does not wait for Analyze.
Section view of the default example, before Analyze.
Section view after Analyze: the inclined load, the tilted base and the sloping ground.
Capacity view after Analyze.
Factors view.
What the Section shows of the load, the tilt and the slope
The load. A horizontal pressure with qapplied entered draws the load Q inclined from the vertical by the angle whose tangent is h/qapplied (8.5° for h = 12 and qapplied = 80 kPa). With Parallel to L and h above 0 the arrow stays vertical and is labelled “h acts along L (out of this section)”.
The tilt. A base tilt η above 0 draws the base ray dashed and labels it “base tilt η = …°”.
The slope. A ground slope ω above 0 draws the ground falling away from the footing and labels it “ground slope ω = …°”. When the slope drops below the base level inside the mechanism, a caution line under the drawing says that the part of the mechanism above the ground is not drawn.
The drawing follows the inputs before Analyze.
Direction Parallel to L: the horizontal load acts out of the plane of the section.
The Show chips
Above the Section a bar holds two chips, Failure mechanism and Dimensions, both on by default. Switching them off hides the zones and their legend, or the dimension lines of B, Df and the water table depth; the footing, the soil, the load and the value of qu stay. With the mechanism hidden the drawing says “The failure mechanism is hidden (Show: Failure mechanism).” The ? beside Show shows a tip saying that the drawing is to scale for your φ and is for display only. The Capacity and Factors views have no chips.
The Show bar.
Both chips off.
What you can drag
Nothing. The drawings are pictures of the model: the values are changed by typing them in the Model tab, and the drawing follows. There are no zoom buttons, and the mouse wheel does not zoom.
Dimensions off.
Entering the model, section by section
The Model tab has seven sections: Model data, Footing, Soil, Groundwater, Base tilt and ground slope, Loads and Analysis Settings. A section opens when you click its title; Next and Back walk you through them, and Analyze waits at the foot of the tab. In the tables a unit shown three times, such as kPa · t/m² · ksf, gives the units of SI · kN, SI · tf and US in turn. Defaults are shown in SI; in the other systems the boxes show the converted values. A box that is empty or outside its limit stops the analysis with a message, see Messages.
Model data
The first section holds the model name, Save to file…, Open file…, Quick Save… with its list and Load and Delete, and Reset to defaults. It works as described in the workspace guide. The note says that every change is kept in this browser, so the page opens again with the model you last worked on.
Model data.
Footing
Choose the shape with four buttons. B is the width: the shorter side, or the diameter of a circle. L appears only when the shape is Rectangular, and must be at least B. A strip has no length: the module takes B/L = 0 for it, so it receives no shape correction, and its allowable load is given per metre of strip (kN/m, tf/m or kip/ft). A square and a circle take L = B, so B/L = 1.
Footing.
Field
Unit
Default
Footing shape Strip, Square, Rectangular or Circular.
—
Square
Footing width (short side) B At least 0.05 m.
m · ft
1.2
Footing length (long side) L Shown for a rectangle only. At least 0.05 m, and not shorter than B.
m · ft
1.2
Founding depth Df The depth of the base below the ground surface. 0 or more.
m · ft
1
Soil
One soil, below the footing, to the depth of the failure mechanism. The module takes the three values you type; it does not average layers.
Soil.
Field
Unit
Default
Cohesion c 0 or more.
kPa · kg/cm² · psf
0
Friction angle φ From 0 to 50°.
°
32
Unit weight (above GWT) γ At least 0.1 kN/m³. The moist unit weight of the soil above the water table.
kN/m³ · t/m³ · pcf
16
Groundwater
Choose Present or None. With None the two boxes disappear and the moist γ is used for the surcharge and for the self-weight term. With Present, Dw is measured from the ground surface. Three read-outs follow the inputs: the surcharge q at the base, the water case (“above the base”, “within B below the base”, “deeper than B” or “none”) and Df / B. A water table below the base but within one width B of it gives the self-weight term a weighted unit weight; deeper than B below the base it has no effect.
Groundwater.
Field
Unit
Default
Saturated unit weight γsat At least 0.1; it must exceed the unit weight of water (9.81 kN/m³).
kN/m³ · t/m³ · pcf
19.5
Water table depth Dw 0 or more, from the ground surface.
m · ft
0.5
Base tilt and ground slope
Two angles in degrees, both 0 for a level base on level ground; then every base-tilt and ground-slope factor equals 1. The ? beside the heading opens a window with a drawing of the two angles and the factors. η tilts the base of the footing from the horizontal; ω is the slope of the ground surface next to the footing, falling away from it. Both reduce the bearing capacity.
Base tilt and ground slope.
Field
Unit
Default
Base tilt from horizontal η From 0 to 45°.
°
0
Ground slope near the footing ω From 0 to 45°; with φ above 0 it may not exceed φ.
°
0
The ? window of the section: the two angles and their factors.
Loads
The load is one load case: the pressures h = H/A and qapplied = V/A of the same combination of service loads. The inclination factors use both, and the check of the footing uses qapplied. qapplied is the vertical gross pressure at the base: the vertical column load together with the weight of the footing and of the soil above it, divided by the base area. It is optional: without it the module gives the bearing capacity and does not check the footing; with h above 0 it is needed. Horizontal load direction has two buttons, Parallel to B and Parallel to L, and sets the exponent m. The ? beside Applied load opens a window with the drawing of the load case.
Loads.
Field
Unit
Default
Horizontal load direction Parallel to B or Parallel to L.
—
Parallel to B
Horizontal pressure at the base, H/A h 0 or more.
kPa · t/m² · ksf
0
Vertical gross pressure at the base, V/A qapplied Optional; 0 or more. Needed when h is above 0.
kPa · t/m² · ksf
empty
The ? window of the Loads section.
Analysis Settings
One number: the factor of safety. The allowable pressures are the capacities divided by it.
Analysis Settings.
Field
Unit
Default
Factor of safety FS At least 1.
—
3
The inclination exponent, the tilt and the slope
Everything in the equation except the inclination, the tilt and the slope is the same as in the Meyerhof module: the factors Nc and Nq of Prandtl and Reissner, Nγ = 2 (Nq + 1) tan φ of Vesic, the shape factors of De Beer and the depth factors of Hansen. The Hansen module uses its own Nγ and shape factors, so the same footing gives a different answer there even with no inclination.
The exponent m: footing shape and direction of the load
The inclination factors raise the ratio x = h / (qapplied + c cot φ) to a power, and that power depends on the footing:
m = (2 + B/L) / (1 + B/L) for a horizontal load parallel to B, m = (2 + L/B) / (1 + L/B) for a load parallel to L
iq = (1 − x)m, iγ = (1 − x)m + 1, ic = iq − (1 − iq) / (Nq − 1) (not below 0)
The exponent m for some B/L, by load direction
B/L
Load ∥ B
Load ∥ L
0 (strip)
2.000
1.000
0.2
1.833
1.167
0.4
1.714
1.286
0.6
1.625
1.375
0.8
1.556
1.444
1 (square, circle)
1.500
1.500
A strip is taken as B/L = 0: m = 2 for a load across the strip (B) and 1 for a load along it (L). A square and a circle have B/L = 1, so m = 1.5 whichever direction you choose, and the two direction buttons give the same qu. For a rectangle the direction matters: the same 1.2 m × 3 m footing with h = 20 and qapplied = 150 kPa gives qu = 458.2 kPa with the load parallel to B (m = 1.714) and 487.2 kPa parallel to L (m = 1.286). With h = 0 the inclination factors are 1 and the direction has no effect.
For φ = 0 the module uses ic = 1 − mh / (cNc) and iq = iγ = 1.
Base tilt and ground slope
bq = bγ = (1 − η tan φ)², bc = bq − (1 − bq) / (Nq − 1) (η in radians)
At φ = 0 the cohesion factors are bc = 1 − 2η/(π + 2) and gc = 1 − 2ω/(π + 2), the angles in radians, and the other two factors are 1 for the tilt, and (1 − tan ω)² for the slope. These are Vesic’s own forms; they differ from Hansen’s (for the ground slope, (1 − 0.5 tan ω)⁵), so the same footing gives a different answer in the two modules.
How the choices are made
Direction of the load follows the way the structure pushes the footing. Choose the one that matches the horizontal load of the load case; for a square or circular footing it does not matter.
h and qapplied come from one load combination. The module does not take the resultant Q/A: enter the pressure of its vertical component as qapplied.
η and ω are 0 for a level base on level ground. The factors only reduce the capacity; a footing on or near a slope also needs the stability of the slope as a whole to be checked.
Analyze and read the results
Press Analyze. The bar counts through four steps (bearing capacity factors, corrections, groundwater, ultimate and allowable pressure), the inputs lock, and the drawing changes to the Capacity view. The page stays on the Model tab: open the Results tab for the answer. A message at the bottom of the window (“Analysed — PASS: see the Results tab and the Calculations.”) tells you the outcome for a moment.
With qapplied entered, the bar reads Analysed — PASS: qapplied ≤ qall,g, FSactual = 3.35 (green) or FAIL: qapplied > qall,g, FSactual = … (red).
Without qapplied it reads Analysed — bearing capacity calculated; applied pressure not provided, and nothing passes: the Design check shows NOT CHECKED.
Edit inputs unlocks the inputs and clears the results; the unit system can be changed while the model is locked.
The bar after Analyze: PASS.
A line under the cards gives the gross allowable vertical load Qall (for a strip it is per unit length, in kN/m, tf/m or kip/ft), the overburden q at the base and FS.
The Results tab (the inclined example).
Card
Meaning
Example
Gross qu
Failure pressure
700.5 kPa
Net qu,net
qu − q
687.6 kPa
Gross qall,g
qu / FS
233.5 kPa
Net qall,n
(qu − q) / FS
229.2 kPa
The Design check compares qapplied with qall,g and shows the actual factor of safety qu / qapplied; the same is done for the net pressures (qapplied − q against qall,n). A gross pressure is compared with the gross values and a net one with the net values; the gross check governs. Below it Factors and values, step by step lists the factors of every step, and Contribution of each term gives the three terms of qu with their shares (in the default example 0.0 %, 85.0 % and 15.0 %).
Using the numbers
qapplied is the pressure from service loads; the footing is checked against the allowable pressure, not against qu.
The gross allowable load Qall is qall,g times the base area (B × L, πB²/4 for a circle, B per metre for a strip).
Changing the unit system after Analyze re-states the numbers without a new run.
Warnings and notes
The bar carries a Warnings (0) button; with a caution it reads Warnings (1) and the window opens by itself when the analysis finishes. With nothing wrong it says “No warnings — the method’s assumptions hold for these inputs.” The conditions that stop the analysis and the cautions are listed under Messages.
The Calculations tab, the report and the Theory tab
The Calculations tab opens with Given and what is sought and then writes out the working in eleven numbered steps; each opens and closes with its heading:
Compute the bearing-capacity factors:Nc, Nq, Nγ.
Apply shape factors:Fcs, Fqs, Fγs from B/L (all 1 for a strip).
Apply depth factors:Fcd, Fqd, Fγd with k = Df/B, or its arctangent in radians when Df/B exceeds 1.
Apply inclination factors: the exponent m, the ratio x and ic, iq, iγ; with h = 0 the step says that all three equal 1.
Apply base-tilt factors:bc, bq, bγ.
Apply ground-slope factors:gc, gq, gγ.
Locate the groundwater table: the case, q and the unit weight of the self-weight term.
Write Vesic’s equation: the three terms and qu, with a table of their shares.
Apply the factor of safety:qu,net, qall,g, qall,n.
Compute the gross allowable load:Qall.
Check the applied foundation pressure: the gross and net checks and the actual factors of safety (only with qapplied).
The Calculations tab of the inclined example, with the steps of the shape and the depth factors closed.
The report
In the Report tab fill in the cover (project, location, client, report number, date, prepared by, title or qualification, checked by, and optional notes). Save as PDF and Download Word (.docx) produce the summary report; the preview below the buttons is the report itself. The details are kept in this browser and saved with the model file.
The report has six parts: 1 Introduction and scope, 2 Input data (a table of the inputs and the section drawing), 3 Calculation (the eleven steps), 4 Results (with the Capacity drawing), 5 Summary and 6 References; when the analysis carries a caution it has seven, with 5 Warnings and notes, 6 Summary and 7 References. It states the units used.
The Report tab: the cover details, the two buttons and the top of the preview.
The Theory tab
The Theory tab explains the method in six sections: what Vesic contributed, the exponent that depends on the shape of the footing and the direction of the load (with a table of m against B/L), the base-tilt and ground-slope factors, what is unchanged from the other modules, how the numbers were checked, and the reference.
Worked example: the module’s own example, then an inclined load
The module opens on this example, so you can follow the numbers on your own screen.
Inputs of the example
Section
Input
Value
Footing
Shape, B, Df
Square, 1.2 m, 1 m
Soil
c, φ, γ
0 kPa, 32°, 16 kN/m³
Groundwater
Present, γsat, Dw
19.5 kN/m³, 0.5 m
Base tilt and ground slope
η, ω
0°, 0°
Loads
h, qapplied
0 kPa, empty
Analysis Settings
FS
3
Step 1: the factors
With φ = 32°: Nq = eπ tan 32° tan²(45° + 16°) = 23.18, Nc = (Nq − 1) / tan 32° = 35.49, Nγ = 2 (Nq + 1) tan 32° = 30.21. For a square B/L = 1: Fcs = 1 + Nq/Nc = 1.653, Fqs = 1 + tan 32° = 1.625 and Fγs = 1 − 0.4 = 0.6. With k = Df/B = 0.8333: Fqd = 1 + 2 tan 32° (1 − sin 32°)² k = 1.230, Fcd = Fqd − (1 − Fqd) / (Nc tan 32°) = 1.241 and Fγd = 1. The inclination, tilt and slope factors are all 1.
Step 2: the groundwater
The water table (0.5 m) is above the base (1 m): q = 16 × 0.5 + (19.5 − 9.81) × 0.5 = 12.845 kPa, and the self-weight term takes the submerged unit weight γ′ = 19.5 − 9.81 = 9.69 kN/m³.
The module gives 700.5 kPa, with the shares 0.0 %, 85.0 % and 15.0 %. The net ultimate capacity is 700.46 − 12.845 = 687.6 kPa, and with FS = 3 the allowable pressures are 233.5 kPa (gross) and 229.2 kPa (net). The allowable load Qall = 233.49 × 1.2 × 1.2 = 336.2 kN.
The check
Enter qapplied = 200 kPa: the module reads PASS, FSactual = 700.46 / 200 = 3.50, and for the net pressures 187.16 kPa ≤ 229.20 kPa with 3.67. Enter 900 kPa: FAIL, FSactual = 0.7783.
An inclined load on a tilted base near a slope
Change the example to a rectangle L = 3 m, h = 12 kPa, qapplied = 80 kPa, η = 5°, ω = 10°, the direction parallel to B; the other inputs stay. Then B/L = 0.4 and m = (2 + 0.4) / (1 + 0.4) = 1.714; x = 12 / 80 = 0.15, iq = 0.851.714 = 0.7568, iγ = 0.852.714 = 0.6433, ic = 0.7568 − 0.2432 / 22.18 = 0.7459. The tilt gives bq = bγ = (1 − 0.08727 × tan 32°)² = 0.8939 and bc = 0.8891; the slope gives gq = gγ = (1 − tan 10°)² = 0.6784 and gc = 0.6639. With the shape factors of B/L = 0.4 (Fqs = 1.250, Fγs = 0.84) the terms are 210.11 and 57.57 kPa:
qu = 210.11 + 57.57 = 267.68 kPa
The module gives qu = 267.7 kPa, qall,g = 89.23 kPa, qall,n = 84.94 kPa, and the check reads PASS with FSactual = 267.68 / 80 = 3.35 (net 3.79); the allowable load is 89.23 × 1.2 × 3 = 321.2 kN. These are the figures on the pictures of this page. For comparison, a rectangle 1.2 m × 3 m with h = 20 and qapplied = 150 kPa on a level base and level ground gives 458.2 kPa (see the tables below).
Other unit systems
US.B = 4 ft, L = 10 ft, Df = 3 ft, c = 100 psf, φ = 30°, γ = 110 pcf, γsat = 125 pcf, Dw = 5 ft, h = 0.4 ksf, qapplied = 3 ksf, FS = 3. A computation of Vesic’s equation with these values gives qu = 13.07 ksf; the module gives qu = 13.07 ksf, qall,g = 4.358 ksf, qall,n = 4.248 ksf and Qall = 174.3 kip.
SI · tf.B = 1.5 m, L = 3 m, Df = 1.2 m, c = 0.5 kg/cm², φ = 30°, γ = 1.7 t/m³, γsat = 1.95 t/m³, Dw = 2 m, h = 2 t/m², qapplied = 15 t/m², FS = 3. The same computation gives 275.0 t/m²; the module gives qu = 275.0 t/m², qall,g = 91.68 t/m² and Qall = 412.6 tf.
The default example in SI · tf gives qu = 71.43 t/m² and in US 14.63 ksf: the same 700.5 kPa in other units.
How each input changes the answer
Every row changes one thing in the example (a square footing, B = 1.2 m, Df = 1 m, c = 0, φ = 32°, γ = 16 and γsat = 19.5 kN/m³, water table at 0.5 m, FS = 3, no horizontal load) and runs the module again. The numbers are the ones the module gives, so you can reproduce any row. Pressures are in kPa.
The example with one change at a time
Change
qu
qall,g
The example The reference
700.5
233.5
Strip footing B/L = 0: no shape correction
541.9
180.6
Rectangle, L = 3 m B/L = 0.4
605.3
201.8
Circular footing Same qu as the square; the load Qall differs by the area
700.5
233.5
φ = 28°
420.2
140.1
φ = 36°
1,206
402.0
c = 10 kPa The cohesion term appears
1,428
476.1
Df = 0 Footing on the surface: no surcharge
134.0
44.67
Df = 2 m
1,196
398.5
B = 2 m Wider: the self-weight term grows
726.2
242.1
γ = 18 kN/m³
746.8
248.9
Groundwater None
915.3
305.1
Water table at 3 m More than B below the base: same as None
915.3
305.1
Water table at the surface (Dw = 0)
554.3
184.8
Factor of safety 2 qu stays; qall,g = qu / 2
700.5
350.2
The ground-water rows follow the water case: a table 0.5 m below the ground lowers qu from 915.3 to 700.5 kPa, and one at the surface to 554.3 kPa; a table deeper than B below the base acts as none.
A rectangle 1.2 m × 3 m with h = 20 and qapplied = 150 kPa, one change at a time
Change
qu
qall,g
The load, parallel to B m = 1.714
458.2
152.7
Parallel to L m = 1.286
487.2
162.4
h = 40
332.6
110.9
h = 0 Vertical load only
605.3
201.8
η = 5°
409.6
136.5
ω = 10°
310.9
103.6
η = 5° and ω = 10°
277.9
92.64
The same load on other shapes (h = 20, qapplied = 150 kPa, the square of the example)
Shape
qu
qall,g
Square m = 1.5 in either direction
553.8
184.6
Circular m = 1.5
553.8
184.6
Strip, load across (B) m = 2
389.4
129.8
Strip, load along (L) m = 1
449.3
149.8
The example on its own, with only a tilt or a slope
Change
qu
qall,g
η = 10°
556.0
185.3
η = 20°
428.2
142.7
ω = 10°
475.2
158.4
ω = 25° Close to the limit ω ≤ φ
199.5
66.50
The pattern follows the equation. qu grows with φ and Df and falls when the water table rises into the failure zone. A horizontal load takes capacity away faster as h approaches qapplied + c cot φ, and by more for a strip loaded across it than for a square, because m is larger. A ground slope costs more than the same angle of base tilt: for φ = 32°, 10° of slope takes qu from 700.5 to 475.2 kPa and 10° of tilt to 556.0 kPa. For a clay with φ = 0 and c = 50 kPa (no water) the module gives qu = 425.3 kPa, and 299.1 kPa for a 1.2 × 3 m rectangle with η = 5°, ω = 10° and h = 20, qapplied = 100 kPa.
Messages: when the module stops, and what it notes
The module checks the numbers before it calculates. A condition it cannot calculate with is a stop; nothing is analysed, the bar reads Cannot be analysed and gives the reason and what to change, and Analyze stays unavailable until the inputs are changed.
The bar names the condition before you press Analyze.
When
Message
L is shorter than B (rectangle)
“L = 0.8000 m is shorter than B = 1.20 m.” Swap the values, or enter the longer side as L.
h above 0 and qapplied empty
“enter qapplied for this load case.” Enter the gross vertical pressure, or set h = 0.
h reaches qapplied + c cot φ
“h = 160.00 kPa reaches v + c·cot φ = 100.00 kPa.” The inclination factors vanish there, and the base has slid long before it. Reduce h or check qapplied, and check the footing against sliding.
φ = 0 and h reaches c
“h = 60.00 kPa reaches the undrained base resistance c = 50.00 kPa.” (With c = 0 any h above 0 does.) Beyond h = c the base slides before it can fail in bearing.
φ is above 0 and ω is steeper than φ
“ω = 40.00° exceeds φ = 32.00°.” The ground-slope factors assume ω ≤ φ; check the stability of the slope instead.
γsat not above the unit weight of water
“γsat ≤ γw — the submerged unit weight would not be positive.” Check γsat.
A value outside its limit or an empty box gives a window titled Cannot analyse — 1 input error (or more) when you press Analyze, listing each message in the units of the unit system:
When
Message
η or ω above 45°
“Base tilt from horizontal (η) must be at most 45°.” (the same for the ground slope)
φ above 50°
“Friction angle (φ) must be at most 50°.”
FS below 1
“Factor of safety (FS) must be at least 1.”
A box empty
“Footing width (short side) (B) is missing.” (the same for any required box; qapplied may stay empty)
The caution
When φ is above 0 and h exceeds the sliding resistance qapplied tan φ + c but is still below qapplied + c cot φ, the module calculates and adds a caution: “h = 150.00 kPa exceeds the sliding resistance v·tan φ + c = 124.97 kPa. A footing that slides never reaches its bearing capacity; …” Check sliding with the friction and the adhesion of the real base. The Warnings window opens by itself after Analyze and the button reads Warnings (1). The check against qapplied is made as usual.
The caution about sliding.
Notes in the working
Df/B near 1. The depth factors use k = Df/B up to 1 and its arctangent above; the working notes that qu changes by a few per cent as Df/B crosses 1 (705.2 kPa at B = 1 m and Df = 1 m, 674.7 kPa at B = 0.9 m).
ic below 0. The cohesion factor is held at 0.
Good practice and common mistakes
Enter the pressure of the vertical component.qapplied is V/A with the weight of the footing and of the soil above it, from service loads. Do not enter the resultant.
Keep h and qapplied in one load case. Combining the h of one combination with the qapplied of another gives inclination factors that belong to no load.
Choose the direction for the rectangle. The exponent differs by about 0.4 between the two directions of a footing with B/L = 0.4; for a square it makes no difference.
Gross against gross, net against net. The check does this for you; keep to one convention in your report.
Check sliding and the slope. A base that slides never reaches its bearing capacity, and a footing near a slope needs the stability of the slope as a whole to be checked as well; the module gives the bearing pressure.
Keep ω within φ and use the soil parameters of the analysis. Effective stress parameters for a drained case; φ = 0 with the undrained c for a short-term clay.
Watch the water table. It lowers qu when it is above the base or within B below it; the read-outs in Groundwater show which case you are in.
Compare methods. The same footing in Hansen and Meyerhof shows how much the method itself contributes.
Keep a record. The report is the record of an analysis; Quick Save… or Save to file… keep the model.
Frequently asked questions
What does the module calculate?
The ultimate bearing capacity qu of a shallow footing on one soil by Vesic’s equation, the net capacity qu − q, and the gross and net allowable pressures at your factor of safety. With the applied pressure qapplied entered it gives PASS or FAIL. For the default example qu = 700.5 kPa and qall,g = 233.5 kPa.
What is the exponent m?
The power in the inclination factors: m = (2 + B/L) / (1 + B/L) for a horizontal load parallel to B and (2 + L/B) / (1 + L/B) for a load parallel to L. It is 2 or 1 for a strip, 1.5 for a square or a circle, and 1.714 or 1.286 for a footing with B/L = 0.4.
Which direction do I choose for the horizontal load?
The direction in which the horizontal load H acts relative to the footing: parallel to the width B or to the length L. It matters for a rectangle and a strip; for a square and a circle both give the same answer. With h = 0 it has no effect.
What do I enter as qapplied, and is it required?
The vertical gross pressure at the base, V/A, from service loads, including the weight of the footing and of the soil above it. It is optional: without it the module gives the capacity and nothing passes. With a horizontal pressure h above 0 it is required, because the inclination factors use h and qapplied together.
What do the base tilt and the ground slope do?
They reduce the capacity through the factors b and g: bq = bγ = (1 − η tan φ)² and gq = gγ = (1 − tan ω)². For the example, a slope of 10° gives qu = 475.2 kPa and a tilt of 10° gives 556.0 kPa, against 700.5 kPa on level ground.
Why does the module stop when ω is larger than φ?
The ground-slope factors assume ω ≤ φ; a steeper slope is not stable on its own. Check the stability of the slope instead. The tilt and the slope are accepted up to 45°.
What is the difference between gross and net?
The gross pressures include the overburden q at the base level; the net ones are what the footing adds to it. qu,net = qu − q and qall,n = (qu − q) / FS. A gross applied pressure is compared with the gross allowable pressure and a net one with the net; the gross check governs.
How does groundwater enter?
With the water table above the base the surcharge uses the submerged weight below it and the self-weight term takes the submerged unit weight. Below the base but within B the self-weight term takes a weighted unit weight; deeper than B it has no effect. For the example the water table at 0.5 m gives qu = 700.5 kPa against 915.3 kPa without water.
Can I drag the footing or zoom the drawing?
No. The drawings are pictures of the model; you change the model by typing in the Model tab, and the drawing follows. The Show chips switch the failure mechanism and the dimensions on and off.
Which units does it use?
SI · kN, SI · tf or US, switchable in the header at any time. Pressures are in kPa, t/m² or ksf, cohesion in kPa, kg/cm² or psf, unit weights in kN/m³, t/m³ or pcf, lengths in m or ft. The default example gives 700.5 kPa, 71.43 t/m² or 14.63 ksf.
Does the module remember my inputs?
Yes. The values you type are kept in the browser and the page opens again on the model you last worked on. A model that was analysed reopens analysed. Reset to defaults brings back the example; Save to file and Quick Save keep copies.
What does the report contain?
A cover with your project details and the answer, then six parts (seven when the analysis carries a caution, which adds warnings and notes): introduction and scope, input data with the section drawing, the calculation step by step, results, summary and references. It is saved as a PDF or a Word file.
Work out the bearing capacity of a strip footing during an earthquake, by the Coulomb wedges of Richards, Elms and Budhu: the horizontal seismic coefficient, the static and seismic factors side by side, the capacity as bars, the wedges drawn to scale, and the allowable pressures with a PASS or FAIL check. This manual walks through the screen, every input, the results and the report, with a worked example you can reproduce.
Seismic bearing capacity gives the ultimate and the allowable bearing pressure of a strip (continuous) footing on a c–φ soil while an earthquake acts on it, by the theory of Richards, Elms and Budhu (1993). The failure mechanism is two Coulomb wedges: an active wedge under the footing and a passive wedge beside it, with the wall friction δ = φ/2 on the vertical face between them. The earthquake enters as a pseudo-static body force, the horizontal seismic coefficient kh (and, if you wish, the vertical one kv), which tilts the resultant of weight and inertia by the angle θ and makes the wedges shallower.
The factors come in closed form, once for the static case and once for the earthquake. The ultimate bearing capacity is the same sum of three terms in both:
qu = cNc + qNq + ½ γBNγ (static)
quE = cNcE + qNqE + ½ γBNγE (earthquake)
with the surcharge q = γDf of the soil above the base, and θ = tan⁻¹[kh / (1 − kv)]. The allowable pressures and the check of your applied pressure are built on the seismic capacity quE; the static value qu of the same wedges is reported beside it, so you see what the earthquake takes away.
What you can describe
A strip footing of width B founded at the depth Df, on one soil below the footing described by c, φ and γ.
The earthquake by kh (0 to 0.8) and kv (0 to 0.5).
A factor of safetyFS for the allowable pressures, and an optional applied vertical gross pressureqapplied that the module checks (PASS or FAIL).
The module draws the two wedges to scale under the footing, shows the capacity as bars, plots the three factors against φ, writes out every step, and prepares a PDF or Word report.
What belongs to other modules
Static design of footings.Terzaghi for general and local shear, with a water table; Meyerhof for strip, square, rectangular and circular footings with shape, depth and inclination factors; Hansen and Vesic for sloping ground, a tilted base and an inclined load. The static value this module prints is the capacity of its own two-wedge mechanism, not the classical Prandtl-type value those four give.
Undrained clay with φ = 0. The wedges need a friction angle; the module stops for φ = 0 and points to Terzaghi or Meyerhof.
An independent horizontal force, a moment or an eccentricity of the footing. The inertia of the soil is already carried by kh, so no separate horizontal load is entered here; for those effects use a method with inclination factors (Meyerhof, Hansen, Vesic).
The earth pressure on a wall in an earthquake: Mononobe–Okabe.
Before you start: what you need
Have these ready from your design:
What
Notes
The footing width B and the founding depth Df
Your design. A continuous footing: B is its width. Df is the depth of the base below the ground surface, zero or more.
The cohesion c, friction angle φ and unit weight γ
Tests or correlations. The soil below the base. φ must be above zero for the analysis to run, and the module accepts up to 50°.
The seismic coefficients kh and kv
Your seismic design. The module takes the values you enter. kh is the horizontal coefficient, kv the vertical one; with kv = 0 only the horizontal inertia acts.
A factor of safety FS
Your design. At least 1. The allowable pressures are the capacity divided by it.
The applied pressure qapplied (optional)
Your structural analysis. The vertical gross pressure at the base, V/A: the column load together with the weight of the footing and of the soil above it, divided by the base area, from service loads.
Quick start in eight steps
Open the module and choose the units
Open Seismic bearing capacity from the Bearing Capacity family. Pick SI · kN, SI · tf or US in the header; you can change it at any time, even after Analyze.
Describe the footing
In Footing enter the width B and the founding depth Df. The shape is fixed to Strip (continuous).
Describe the soil
In Soil enter c, φ and γ of the soil below the footing.
Enter the applied pressure (optional)
In Loads enter qapplied to have the footing checked; leave it blank to get the capacity only.
Set the factor of safety
In Analysis Settings enter FS.
Enter the earthquake
In Earthquake enter the horizontal seismic coefficient kh and the vertical one kv.
Press Analyze
Press Analyze at the foot of the Model tab. The bar reads Analysed, the inputs lock, and a window lists the warnings, if any. The module stays on the Model tab; the result is on the Results tab.
Read the answer, the working and the report
The Results tab gives quE (gross and net), the allowable pressures, the static capacity and the design check; the Section, Capacity and Factors buttons change the drawing. Calculations shows every step, Report saves a PDF or Word file, Theory derives the method.
The screen: section, capacity and factors
The layout is the one every GeoTerva module shares, described in the workspace guide. The drawing on the left has three views, chosen with the buttons above it, and the five tabs Model, Results, Calculations, Report and Theory are on the right.
Section: the footing and the two wedges
Section is a cross-section through the footing, drawn to scale for the friction angle you enter: the footing and the column with the load Q, the ground surface, the depth Df and the width B as dimensions, as dimensions. It is drawn as soon as the numbers are valid, before Analyze. After Analyze it adds the capacity qu (the seismic one when kh > 0) in a box at the base, the upward arrows, and the surcharge q = γDf written at the base level.
The failure mechanism is the pair of wedges of the theory:
Wedge I (ABC) is the active wedge under the footing; its slip plane AC rises at the angle αA from the horizontal. Its depth under the base is B tan αA.
Wedge III (BCD) is the passive wedge beside the footing; its plane CD is at the angle αP. The two wedges meet on the vertical face BC, where the wall friction δ = φ/2 acts.
With kh > 0 the earthquake wedges are drawn solid and the static wedges stay dashed, so you see how the mechanism shrinks. The note under the drawing gives the angles and, on the second line, θ = tan⁻¹[kh/(1 − kv)].
For the default example the angles are αA = 53.97° and αP = 23.85° (static), αAE = 36.21° and αPE = 6.26° (earthquake). The active wedge is then B tan αAE = 1.10 m deep instead of 2.06 m.
Section after Analyze: earthquake wedges solid, static wedges dashed.
Section before Analyze: the geometry and the wedges are drawn; the capacity box, the arrows and the surcharge label are not yet.
With kh = 0 there is no earthquake: the wedges are the static ones, and nothing is dashed.
With kh = 0.4 (θ = 21.8° against φ = 25°) the active wedge is shallow and the passive plane has no real solution, so the passive wedge is drawn collapsed.
The Show chips
Above the section a Show bar has two chips, both on by default. Failure mechanism shows or hides the wedges (with them hidden, a note says so); Dimensions shows or hides the dimension lines. Pointing at the (?) beside Show gives a short tooltip. The chips belong to the Section view only.
The Show bar of the Section view.
Failure mechanism switched off: the wedges disappear, the dimensions stay.
Capacity: the three terms and the pressures
Capacity shows quE as one bar made of its three terms, the cohesion term cNcE, the surcharge term qNqE and the self-weight term ½ γBNγE, each with its value in the legend and, where the segment is wide enough, its share in the bar. Below it the gross pressures (quE and qall,g) and the net pressures (qu,net and qall,n) are bars on a common scale. When you enter qapplied, a bar for it appears in each group with the actual factor of safety and PASS or FAIL, and a dashed line marks the allowable value. At the foot the six factors are listed: Nc, Nq, Nγ (static) and NcE, NqE, NγE (earthquake).
Capacity view with qapplied = 150 kPa: the applied bars are red and say FAIL.
Factors: the three factors against the friction angle
Factors plots Nc, Nq and Nγ against φ from 0° to 50° on a logarithmic scale and marks your φ with a dashed line and the three values. With kh = 0 the curves are the static factors; with kh > 0 they are the seismicNcE, NqE and NγE at your θ, and the curves start at φ = θ, where the wedges close. The note says which of the two you are looking at. For the default example the marks read NcE = 7.53, NqE = 4.51 and NγE = 2.57.
Factors view: the seismic curves at θ = 14.0°, starting where φ = θ.
Nothing to drag, zoom or pan
The drawing has no drag handles and no zoom: change the values in the Model tab and the drawing follows. After Analyze the inputs are locked until you press Edit inputs, which clears the results; the unit system can still be changed. The drawings stay in SI (m · kPa) when you choose another unit system, and a note under them says so.
Model data: keep, save and reset
The Model data section at the top of the Model tab says that every change is kept in this browser. It holds a Model name, Save to file… and Open file… for a file you keep with the project or send on, Quick Save… with a list to Load or Delete a saved state, and Reset to defaults. When you reload the page the module reopens with your values, the unit system and, if you had analysed, the results.
Entering the model, section by section
The Model tab has, after Model data, five sections. Each opens when you click its title; Next and Back at the foot walk you through them. The tables list every field with its symbol, the unit in each unit system and its default. Where a unit is shown more than once, such as m · ft, the units are those of SI · kN, SI · tf and US in turn. A value outside the range, or a blank box, stops the analysis with a message that names it (see Messages).
Footing
The shape selector holds one option, Strip (continuous), under the label “plan of the foundation”. A note under the fields says that B is the width and Df the depth of the base below the ground surface.
The Footing section.
Footing fields
Field
Default
What to enter
Footing width (continuous footing) B · m · ft
1.5
Width of the strip. At least 0.05 m.
Founding depth Df · m · ft
1
Depth of the base below the ground surface. Zero or more; zero gives q = 0 and the surcharge term vanishes.
Soil
One soil below the footing, as the note says: “One soil below the footing, characterised by c, φ and γ.” No water table is asked for: the module takes none in the failure zone, and the soil above the base acts as the surcharge q = γDf only.
The Soil section.
Soil fields
Field
Default
What to enter
Cohesion c · kPa · kg/cm² · psf
30
Zero or more. In SI · tf the box is in kg/cm², and 30 kPa reads 0.305915.
Friction angle φ · °
25
From 0° to 50°, and above zero for the analysis to run.
Unit weight γ · kN/m³ · t/m³ · pcf
17
At least 0.1 kN/m³.
Loads
One optional field under the heading Applied load, “one load case at the base — service loads”. Leave it blank and the module reports the capacity and says the footing is not checked; enter a value and the module compares it with the allowable pressures. The (?) beside the heading opens a window with a sketch of qapplied = (V + Wf + Ws) / A and of the gross and net checks.
The (?) window of the applied load.
Loads field
Field
Default
What to enter
Applied vertical gross pressure at the base (optional) (optional) qapplied · kPa · t/m² · ksf
blank
The vertical gross pressure at the base, V/A, from service loads. Zero or more.
Analysis Settings
Analysis Settings field
Field
Default
What to enter
Factor of safety FS · —
3
At least 1. It divides the capacity for the allowable pressures.
Earthquake
The two coefficients of the pseudo-static earthquake. Together they give θ = tan⁻¹[kh / (1 − kv)], the tilt of the resultant of the weight and the inertia; the module shows θ in the working and under the drawing.
The Earthquake section.
Earthquake fields
Field
Default
What to enter
Horizontal seismic coefficient kh · —
0.25
From 0 to 0.8. Zero gives the static case: the seismic factors equal the static ones.
Vertical seismic coefficient kv · —
0
From 0 to 0.5. A larger kv makes θ larger at the same kh.
Units
SI · kN uses m, kPa and kN/m³. SI · tf uses m, t/m² for pressures, t/m³ for unit weight, kg/cm² for the cohesion box, and tf/m for the load. US uses ft, psf for the cohesion, pcf for the unit weight, ksf for pressures and kip/ft for the load. Values you typed are converted when you switch, and the boxes may then show unrounded numbers such as 4.92126 ft for a 1.5 m width.
Static and seismic factors: what changes
There is no method to choose in this module: the theory is fixed and so are its assumptions. What you control is how strong the earthquake is, and the module shows both sides of it.
Factors:Nc, Nq, Nγ (static) and NcE, NqE, NγE (earthquake).
Coefficients of the wedges:KA, KP (Coulomb) and KAE, KPE (Mononobe–Okabe, at θ).
Wedge angles:αA, αP and αAE, αPE, with α = φ − θ in place of φ.
Capacity:qu is reported beside the answer; quE is the value the allowable pressures and the check are built on.
The factors follow from the wedges: Nq = KP / KA, Nγ = tan αA (KP / KA − 1) and Nc = (Nq − 1) cot φ, and the seismic factors have the same forms with the earthquake quantities. The earthquake takes from the three terms very different amounts. For the default example the factors fall from Nc = 18.59, Nq = 9.67, Nγ = 11.92 to NcE = 7.53, NqE = 4.51, NγE = 2.57, that is to 0.405, 0.466 and 0.216 of the static values: the self-weight term loses most.
Analyze and read the results
Press Analyze. If an input is missing or out of range, a window titled Cannot analyse lists what to correct. If the mechanism cannot be worked out (for example kh too large) the bar above the Analyze button turns amber and says why, and the button is greyed. Otherwise the bar reads Analysed, the inputs lock, and a window shows the warnings (if there are any). The module stays on the Model tab; open Results. Edit inputs in the bar clears the results and unlocks the inputs; Warnings reopens the window.
After Analyze the bar offers Warnings and Edit inputs.
On the Results tab and in the drawings the seismic capacity is labelled qu and the static one qu,static; the working calls the seismic one quE.
The Results tab, from the top:
A banner with the number of warnings and the first one.
Bearing capacity, with four large cards in two columns: GrossquE and qall,g = quE / FS, and Netqu,net = quE − q and qall,n = (quE − q) / FS. Below them the static capacity qu,static, the gross allowable load per metre of footing Qall = qall,g × B, the overburden q and FS. A note says that a gross applied pressure is compared with the gross values and a net one with the net values, never one with the other.
Design check.NOT CHECKED when qapplied is blank; otherwise PASS or FAIL with a row for the gross check, the actual factor of safety FSactual = quE / qapplied, the net check and its factor of safety. The gross check governs: when it passes, the net check passes too.
Factors and values, step by step, a table with the wedge angles and factors of each step: static, seismic, the surcharge, the two capacities, the allowable pressures and Qall.
Contribution of each term (seismic): the cohesion, surcharge and self-weight terms, each in pressure and as a percentage of quE.
Warnings, repeated at the foot.
Results for the default example.
The Design check with qapplied = 150 kPa.
Gross and net
The gross pressures are the total pressure at the base; the net pressures are what the footing adds to the overburden q that already acted there. They are two conventions for applying the factor of safety, not conversions of one another: the gross convention divides the whole capacity by FS, the net convention only the part above q, so qall,n + q is larger than qall,g and the gross convention is the stricter. For the default example qall,g = 111.76 kPa and qall,n = 106.09 kPa. State which convention your design follows.
Calculations, Report and Theory
The Calculations tab writes the working in steps, each with its formula, your numbers and the result:
Given and what is sought: your inputs, the footing assumptions and what is found.
Static factors from Coulomb’s wedges: δ = φ/2, KA, KP, the wedge angles αA, αP with the depth B tan αA, and Nq, Nγ, Nc.
Seismic factors: θ, KAE, KPE, α = φ − θ, αAE, αPE, the depth B tan αAE, the factors NqE, NγE, NcE and their ratios to the static ones. With kh = 0 the step says that the seismic factors equal the static ones.
Surcharge at the base level: q = γDf.
Static ultimate bearing capacity: qu term by term.
Seismic ultimate bearing capacity: quE term by term, with the contribution table. From here on qu in the working stands for quE.
Apply the factor of safety: qu,net, qall,g, qall,n.
Compute the gross allowable load: Qall.
Check the applied foundation pressure: the PASS or FAIL rows, or the statement that no pressure is entered.
Then come the warnings and the Answer sentence. The equations are typeset, and the same text is the calculation part of the report.
The Calculations tab: the first steps with typeset formulas.
Report
The Report tab has a Report cover form (Project, Location, Client, Report no., Date, Prepared by, Title / qualification, Checked by and optional Notes), which is kept in the browser and saved with the model file, and two buttons: Save as PDF (the report opens in a print window; choose Save as PDF there) and Download Word (.docx). Both are available once the model is analysed; below them a preview shows the report. It has seven parts: introduction and scope, input data (with the section drawing), the calculation, results (with the capacity drawing), warnings and notes, a summary and references.
The Report tab: the warnings banner and the Report cover form.
Theory
The Theory tab derives the method in ten sections: Scope and assumptions; The static failure surface; The surcharge term; The self-weight term; The static bearing capacity; Earthquake loading; How much the earthquake takes away; Allowable pressure and the check; Worked example (computed live from the module’s opening model); and References. Open all and Close all expand or fold the sections. Its figures are drawn to scale from the equations.
Worked example
The opening model: a strip footing B = 1.5 m at Df = 1 m on soil with c = 30 kPa, φ = 25°, γ = 17 kN/m³, in an earthquake with kh = 0.25 and kv = 0, with FS = 3. Each number below is on the screen when you run the module.
Step
Result
Static wedges, δ = φ/2 = 12.50°
KA = 0.3674, KP = 3.552; αA = 53.97°, αP = 23.85°
Static factors
Nq = KP/KA = 9.67, Nγ = 11.92, Nc = 18.59
Earthquake angle
θ = tan⁻¹ 0.25 = 14.04°; α = φ − θ = 10.96°
Seismic wedges
KAE = 0.6006, KPE = 2.709; αAE = 36.21°, αPE = 6.26°; the active wedge is 1.10 m deep (2.06 m static)
The earthquake leaves 38 % of the static capacity. With no applied pressure the design check reads NOT CHECKED. Enter qapplied = 100 kPa and it reads PASS: FSactual = 335.28 / 100 = 3.35, against 3.00; the net pressure 83.00 kPa is below qall,n = 106.09 kPa, with FSactual,net = 3.83. With qapplied = 150 kPa it reads FAIL: FSactual = 2.24, and the net factor 2.39. With kh = 0 and qapplied = 200 kPa the same footing passes, with FSactual = 4.37.
The same example in other units
Switch to US and the example reads B = 4.92126 ft, Df = 3.28084 ft, c = 626.563 psf and γ = 108.22 pcf; the module gives quE = 7.002 ksf, qu,static = 18.26 ksf, qall,g = 2.334 ksf, qall,n = 2.216 ksf and Qall = 11.49 kip/ft. Switch to SI · tf and it gives quE = 34.19 t/m², qu,static = 89.14 t/m² and Qall = 17.09 tf/m. Each equals the SI · kN answer, converted: 335.28 kPa / 47.88 = 7.002 ksf and 335.28 kPa / 9.807 = 34.19 t/m².
How each input changes the answer
Each row is a run of the module that changes one input from the default example (B = 1.5 m, Df = 1 m, c = 30 kPa, φ = 25°, γ = 17 kN/m³, kh = 0.25, kv = 0, FS = 3). Pressures are in kPa; “Share” is quE as a fraction of the static qu of the same soil.
The earthquake coefficient
kh (θ)
NcE · NqE · NγE
quE
Share
0 (0°, static)
18.59 · 9.67 · 11.92
874.1
100 %
0.1 (5.71°)
13.54 · 7.31 · 7.01
620.0
71 %
0.2 (11.31°)
9.36 · 5.36 · 3.74
419.6
48 %
0.25 (14.04°), default
7.53 · 4.51 · 2.57
335.3
38 %
0.3 (16.70°)
5.84 · 3.72 · 1.65
259.5
30 %
0.4 (21.80°)
2.74 · 2.28 · 0.4230
126.2
14 %
0.45 (24.23°)
1.07 · 1.50 · 0.0735
58.68
7 %
The static capacity is qu = 874.1 kPa in every row. The capacity falls steadily and then steeply as θ approaches φ = 25°: at kh = 0.4 it is 14 % of the static value and at 0.45 it is 7 %. At kh = 0.4 and 0.45 the module warns that the mechanism is near its limit. At kh = 0.5 it stops, because θ = 26.57° is not below φ.
The other inputs
Change
quE
qall,g
Default
335.3
111.8
kv = 0.2
241.7
80.58
c = 0
109.4
36.48
c = 60 kPa
561.1
187.0
φ = 20°
191.9
63.98
φ = 30°
559.9
186.6
B = 3 m
368.0
122.7
Df = 0
258.6
86.20
Df = 2 m
411.9
137.3
γ = 19 kN/m³
348.2
116.1
FS = 2
335.3
167.6
kv. Raising kv from 0 to 0.2 at kh = 0.25 raises θ from 14.04° to 17.35°, takes the factors to 5.44 · 3.54 · 1.45 and lowers quE from 335.3 to 241.7 kPa.
Cohesion. The cohesion term is linear in c: c = 0 gives 109.4 kPa (static 316.4), c = 60 kPa gives 561.1 kPa. The factors do not change.
Friction angle.φ changes the factors and the room before the wedges close. At φ = 20° the same kh = 0.25 gives θ/φ = 0.70, the factors 4.52 · 2.65 · 0.8925 and quE = 191.9 kPa; at 30° it gives the factors 11.70 · 7.76 · 6.03 and 559.9 kPa.
Width. Only the self-weight term depends on B: doubling it from 1.5 to 3 m raises quE from 335.3 to 368.0 kPa, while the allowable load Qall rises from 167.64 to 368.0 kN/m.
Depth.Df acts through q = γDf. At Df = 0, q = 0, the surcharge term vanishes and the net and gross values are equal (258.6 kPa); at 2 m quE is 411.9 kPa.
Unit weight.γ acts through the surcharge and self-weight terms: 19 kN/m³ gives 348.2 kPa.
Factor of safety.FS does not change quE; at FS = 2 the allowable pressure is 167.6 kPa instead of 111.8 kPa.
Messages: stops, cautions and notes
Messages are shown in three places: a window titled Cannot analyse when a field is wrong, an amber bar above the Analyze button when the mechanism cannot be worked out, and the Warnings window with the banner on the results tabs.
Kind
When
What the module says
Stop
φ = 0
The amber bar reads “Cannot be analysed — φ = 0.00°: the theory needs a friction angle”, and below it: “The method builds the capacity from Coulomb wedges in a frictional soil. Enter φ > 0, or use Terzaghi or Meyerhof for undrained clay.”
Stop
θ is not below φ
The amber bar reads “Cannot be analysed — kh is too large for this mechanism — θ = 26.57° ≥ φ = 25.00°”, and below it: “At θ = φ the two wedges close on one another and the seismic factors no longer apply: kh/(1 − kv) = 0.5000 against tan φ = 0.4663. Reduce kh below (1 − kv) tan φ = 0.4663, or check φ.”
Stop
A value is out of range
The window title counts the errors (“Cannot analyse — 1 input error”, “— 2 input errors”) and each message is on its own line, in the order B, Df, c, φ, γ, kh, kv, qapplied, FS. Field errors come before the mechanism stops. For example φ = 55° with kh = 0.9 lists “Friction angle (φ) must be at most 50°.” and “Horizontal seismic coefficient (kh) must be at most 0.8.” The messages: “Friction angle (φ) must be at most 50°.”, “Horizontal seismic coefficient (kh) must be at most 0.8.”, “Vertical seismic coefficient (kv) must be at most 0.5.”, “Footing width (continuous footing) (B) must be at least 0.05 m.”, “Unit weight (γ) must be at least 0.1 kN/m³.”, “Factor of safety (FS) must be at least 1.”, “Cohesion (c) must be at least 0 kPa.”, “Founding depth (Df) must be at least 0 m.”, “Applied vertical gross pressure at the base (optional) (qapplied) must be at least 0 kPa.”
Stop
A required box is blank
“Footing width (continuous footing) (B) is missing.” and likewise for the other required fields, for example “Horizontal seismic coefficient (kh) is missing.” qapplied may stay blank.
Warning
θ is above 0.85 φ, or the passive angle has no real solution
“The mechanism is close to its limit — θ = 21.80° against φ = 25.00°.” The wedges are closing: α = φ − θ = 3.20°, NqE → 1, NγE → 0, NcE → 0, so the net capacity approaches zero. If αPE has no real solution it is shown as “—” and the passive wedge is drawn collapsed; the N factors stay finite. The module advises reading this as the limit of the method, not a design capacity, and checking whether sliding or seismic displacement governs.
Warning
c is above zero
“Assumption: the cohesion term uses NcE = (NqE − 1) cot φ.” It gives the share of the cohesion term in quE and the sensitivity case quE(c = 0). With c = 0 the warning does not appear.
Status
After Analyze
“Analysed — bearing capacity calculated; applied pressure not provided.” With a pressure entered it reads, for example, “Analysed — PASS: qapplied ≤ qall,g, FSactual = 3.35” or “Analysed — FAIL: qapplied > qall,g, FSactual = 2.24”, followed by the number of warnings.
With kh = 0.4 the warnings window lists two entries, the caution about the limit first and then the cohesion assumption, with quE(c = 0) = 44.09 kPa.
The Warnings window for kh = 0.4.
The amber bar for kh = 0.5.
Good practice and common mistakes
Run the static case too. Set kh = 0 and the module gives the static capacity of the same wedges; the ratio quE / qu is the share the earthquake leaves.
Take the check from quE. The allowable pressures and the PASS or FAIL are built on the seismic capacity. The static value is for comparison.
Mind the limit. Near θ = φ the capacity is small and falls fast; the module marks it with a caution. Treat the number as the limit of the method, and check sliding and seismic displacement.
Enter the gross pressure.qapplied is V/A including the footing and the soil above it, from service loads. Do not enter a net pressure; a gross pressure is compared with the gross values and a net one with the net values.
Keep the soil one soil. The module reads one set of c, φ and γ for the zone below the base; no water table is taken in the failure zone.
Use the right module for the rest. A clay with φ = 0, a square or circular footing, or an inclined load need the static modules of this family: Terzaghi, Meyerhof, Hansen or Vesic.
Mind the unit of the cohesion box. In SI · tf it is kg/cm², not t/m².
Save what you need. The model is kept in your browser, but Save to file keeps it with the project.
Frequently asked questions
What does the Seismic bearing capacity module calculate?
The static and the seismic ultimate bearing capacity of a strip footing on c–φ soil by the Coulomb-wedge theory of Richards, Elms and Budhu (1993), the gross and net allowable pressures from the seismic capacity, the allowable load per metre, and a PASS or FAIL check of an applied pressure. For the default example (B = 1.5 m, Df = 1 m, c = 30 kPa, φ = 25°, γ = 17 kN/m³, kh = 0.25) the seismic capacity is 335.3 kPa and the static 874.1 kPa.
What is the difference between Nc, Nq, Nγ and NcE, NqE, NγE?
The first three are the factors of the two Coulomb wedges with no earthquake; the second three are the same factors with the earthquake angle θ, worked out from the Mononobe–Okabe coefficients. For the default example they are 18.59, 9.67, 11.92 against 7.53, 4.51, 2.57. The seismic capacity quE uses the second set and is what the allowable pressures are built on.
How do I choose kh and kv?
They come from your seismic design; the module takes the values you enter, kh from 0 to 0.8 and kv from 0 to 0.5. With kv = 0 only the horizontal inertia acts, and θ = tan⁻¹ kh. Since the module draws the wedges and writes θ for every run, you can change kh and see at once what it does.
How much does an earthquake reduce the bearing capacity in the module?
For the default soil the capacity is 71 % of the static value at kh = 0.1, 48 % at 0.2, 38 % at 0.25, 30 % at 0.3 and 14 % at 0.4. The reduction grows faster as θ approaches φ, and the self-weight term falls the most.
Why does the module stop when kh is large?
The seismic factors need θ below φ. At θ = φ the two wedges close on one another, so for φ = 25° and kv = 0 the module stops at kh = 0.4663 and tells you the limit (1 − kv) tan φ. Just below it, above θ = 0.85 φ, it gives a caution that the capacity is near the limit of the method.
Is the footing checked against the static or the seismic capacity?
Against the seismic capacity quE. The gross check compares qapplied with qall,g = quE / FS, the net check compares qapplied − q with qall,n; the static capacity is shown beside the answer for comparison. With kh = 0 the two are equal.
Can I use it for a square or circular footing, or for clay with φ = 0?
No. The module is for a continuous (strip) footing on a soil with φ > 0, and its shape selector holds one option. For φ = 0 it stops and points to Terzaghi or Meyerhof; for other footing shapes and static design use the other modules of the family.
Why is the static capacity different from the other bearing capacity modules?
The static value here is the capacity of the same two-wedge mechanism that gives the seismic one, not the classical Prandtl-type value of Terzaghi, Meyerhof, Hansen or Vesic. It is the value the seismic capacity is reduced from. For a static design, use those modules.
Does the module include the water table or a horizontal load?
No water table is taken in the failure zone, and the soil above the base acts as the surcharge q = γDf only. The pseudo-static horizontal inertia is carried by kh, so no separate horizontal load is entered; an independent horizontal force, a moment or an eccentricity is outside this calculation, and a method with inclination factors (Meyerhof, Hansen, Vesic) is the place for the inclined load.
What is the warning about the cohesion term?
The cohesion term uses NcE = (NqE − 1) cot φ, the static relation carried over to the earthquake case. When c is above zero the module says so and gives the share of the term in quE (67.4 % for the default example) and the capacity with c = 0 (109.45 kPa). With c = 0 there is no warning.
Can I drag the wedges or zoom the drawing?
No. The drawing has no drag handles and no zoom; the Show chips switch the wedges and the dimensions on and off. Change the values in the Model tab and the drawing follows. After Analyze the inputs are locked until you press Edit inputs.
Does the module remember my inputs, and which units does it use?
Yes: every change is kept in the browser, and the page reopens on your last model, its unit system and its results. Reset to defaults brings the example back in the unit system you have chosen; Save to file and Quick Save keep copies. The units are SI · kN, SI · tf or US, switchable at any time. The default example gives 335.3 kPa, 34.19 t/m² or 7.002 ksf.
Three modules design a cantilever or anchored sheet-pile wall: the pressure diagram, the depth of embedment, the maximum moment, the anchors and the steel section. This page helps you choose the module that matches the ground and links to the manual of each.
The Sheet-Pile Walls family has three modules. All of them build the pressure diagram on the wall, find the depth of embedment, give the maximum moment and check the steel section. They differ in the ground they take and in the extra cases and checks they add. Pick the one that matches your profile.
Your ground and wall
Module
A wall driven into sand, free-standing or held by anchors, with the water on both faces
A profile of sand and clay layers in any order, with one to four rows of inclined anchors, their free and bond lengths, and the short-term and long-term cases of the clay
Each manual follows the same plan: what the module calculates, what you need before you start, a quick start, the screen, every input section by section, the choices that decide the margin, the results, the report, a worked example you can reproduce, a table of how each input changes the answer, the messages the module gives, and answers to common questions.
What the three modules share
The workspace. The drawing, the tabs, Analyze and the input lock, units and the report follow the same layout as the other GeoTerva modules. See the workspace guide.
Eleven input sections. The Model tab runs from the model data, the soil layers and the groundwater, through the wall and its embedment, the base heave check, the ground anchors, the surcharges and the earthquake, to the design factors, the sheet pile and the design code.
Two ways to the embedment. The depth found by equilibrium is increased by a factor, or a factor of safety is applied to the passive pressure; you can also give the depth and have it verified.
The steel section. The sheet pile is checked to EN 1993-1-1 or AISC 360-22.
Two views. The section, with the pressure diagrams, and a 3D view.
Handles on the drawing. Before Analyze you can drag the toe, a layer boundary and the water levels; each manual lists what moves.
What each module takes, side by side
In sand
In clay
Anchored, layered
Soil
Sand in up to four layers
Undrained clay in up to four layers
Up to six layers, each sand or clay
Wall
Cantilever, or up to four anchor rows
Cantilever, or up to four anchor rows
Cantilever, or one to four rows of inclined anchors
Special to it
Sloping surface
Tension crack, water-filled or dry
Short- and long-term cases, anchor free and bond lengths
Also takes
Water on both faces, uniform, strip and point loads, earthquake
Water on both faces, six surcharges, earthquake, bottom heave
Water on each face, uniform, strip and point loads, earthquake, bottom heave, displacement
The three modules take water at its own level on each face of the wall.
A typical sheet-pile design in order
Choose the module
Pick the one that matches the ground and open its manual for the fields.
Describe the ground and the wall
Enter the layers, the water, the retained height and, if the wall is anchored, the anchor rows.
Choose the margin
Decide the route to the embedment and give the loads on the ground and the earthquake if they apply.
Choose the steel and the code
Pick the grade and the section and the design code, then press Analyze.
Read and report
Read the embedment, the anchor forces, the maximum moment and the utilisation, then save a report with the cover filled in.
Frequently asked questions
How do I design a sheet-pile wall with GeoTerva?
Open the module for the ground, Sheet pile in sand, Sheet pile in clay or Anchored sheet pile on layered soil. Enter the layers, the water and the wall, choose the route to the embedment and the steel, press Analyze, and read the embedment, the maximum moment, the anchor forces and the section check.
Which module do I use for a wall in sand and clay together?
Anchored sheet pile on layered soil. It takes any profile of sand and clay layers, each layer as drained sand or as clay in the short and the long term, and it works as a cantilever or with anchors.
Which standard does the section check follow?
The sheet pile is checked to EN 1993-1-1 or to AISC 360-22; you choose the design code in the last section of the Model tab.
Can I give the depth of embedment myself?
Yes. The embedment can be calculated by the program or given; a given depth is verified.
How many anchor rows can a wall have?
Each of the three modules takes a cantilever wall or a wall held by up to four anchor rows. The anchored module on layered soil takes the rows as inclined ground anchors and gives their free and bond lengths.
Does the water table matter?
Yes. The modules take the water at its own level on each face of the wall, and the water in the tension crack of the clay.
Design a cantilever or anchored sheet-pile wall driven into sand: the net pressure diagram, the depth of embedment by a depth factor or a factor of safety on the passive coefficient, the anchor forces, the maximum moment and the check of the steel section. This manual walks through the screen, every input, the choices, the results and the report, with a worked example you can reproduce.
Sheet pile in sand designs a cantilever or anchored sheet-pile wall driven into sand. It builds the net pressure diagram on the wall, finds the depth of embedment from the equilibrium of the diagram, gives the maximum bending moment and the section modulus it asks for, verifies the sheet pile you give to EN 1993-1-1 or AISC 360-22, and estimates the movement of the wall. With rows of ground anchors the wall is held at their levels and the module gives the anchor force of each row.
The soil is sand, entered in up to four layers from the top of the wall down the whole profile: the layers above the dredge line press on the wall as Rankine active pressure, and the layers below it act on both faces, active on the retained side and passive on the excavation side:
The net pressure below the dredge line starts at the active pressure there and falls to zero at the point E, a distance L3 below the dredge line. A cantilever wall is then balanced by an equation of the fourth degree in the depth of the toe below E (the toe-pressure reversal is idealised as the conventional limit-equilibrium method does), and the maximum moment lies where the shear is zero.
What you can describe
A wall of height L above the dredge line, as a cantilever or with one to four rows of ground anchors.
Up to four layers of sand, each with its own unit weights and friction angle.
Water on the retained side, at the same level on the excavation side or at a different level (the net hydrostatic pressure is added; no seepage).
A level or sloping retained surface, and up to six surcharges: uniform, strip and point loads.
A pseudo-static earthquake check with Mononobe–Okabe pressures.
The embedment calculated by the module, by a depth factor or by a factor of safety on Kp, or given by you and verified.
The sheet pile by its grade, its section modulus and its second moment of area.
The pressure of a strip or point load on a wall: Surcharge loads.
Before you start: what you need
Have these ready from your design and your ground investigation:
What
Notes
The wall height L Your design
From the top of the wall to the dredge line (the excavation level). At least 0.5 m.
The sand layers Boring logs and tests
For each layer from the top down: thickness (not the last), moist and saturated unit weight, friction angle φ′ from 15° to 45°, and the horizontal subgrade reaction kh for the displacement.
The water levels Groundwater readings
The depth Dw of the water table behind the wall and, if it differs, the level in the excavation; or no water.
Surcharges, slope, anchors Your design loading
Uniform, strip and point loads; the slope angle β; for each anchor row its depth, spacing, inclination, lock-off load and lengths.
The design route Your design basis
A depth factor f (1.2 to 1.3 is usual) or a factor of safety FSp on Kp.
The sheet pile
The maker’s table
The steel grade, the section modulus per metre of wall and its second moment of area; the code and its factors.
Quick start in eight steps
Open the module and choose the units
Open Sheet pile in sand from the Sheet-Pile Walls family. Pick SI · kN, SI · tf or US in the header; you can change it at any time, even after Analyze.
Enter the sand
In Soil layers fill the New layer form and press + Add layer, or change the first layer, Sand-1, by pressing its row. The last layer runs on below the toe.
Set the water, the wall and the embedment
In Groundwater choose the levels. In Wall and embedment type L and leave the depth Calculated by the program (or give it).
Add what acts on the wall
Choose Sloping in Terrain, add rows of anchors in Ground anchor, loads in Surcharge and switch on the Earthquake check, as your design needs. A wall without anchors is a cantilever.
Choose the safety route and the sheet pile
In Design factors choose the depth factor or the factor of safety on Kp. In Sheet pile and Design code give the grade, the section modulus and the code.
Press Analyze
Press Analyze at the foot of the Model tab. The bar reads Analysed — the sheet-pile wall calculated and the inputs lock. If something needs your attention a window with the warnings opens by itself.
Read the answer
The Results tab gives the diagrams, the embedment, the moment, the section modulus asked for, the verdict on the sheet pile given and the displacement; with anchors, the anchor force of each row.
Take the working and the report
The Calculations tab writes out every step with your numbers. The Report tab saves a PDF or a Word file.
The screen: section, 3D and the handles
The layout is the one every GeoTerva module shares, described in the workspace guide: the drawing on the left, the tabs Model, Results, Calculations, Report and Theory on the right. The drawing has two views, chosen with the buttons above it:
Section is the wall with the retained layers, the water levels, the dredge line, the anchors and the loads. It follows your inputs. Before Analyze it shows the wall, the layers, the water levels, the loads and the dredge line, with a dashed toe marked “embedment: found by the analysis”; after it, the net pressure diagram, Dtheory, Ddesign, the total length and Mmax, which is green where the sheet pile given carries it and red where it does not.
3D is a length of the wall in perspective, with the corrugated sheet piling driven to the design depth, the layers, the excavation and the water table; the retained soil is on the left here, and on the right in the Section view.
Section before Analyze: the geometry and the water.
Section after Analyze: the diagram, the depths and the moment.
3D after Analyze: the retained soil is on the left here, and on the right in the Section view.
Show chips and zoom
This module has no Show chips: the drawing always shows everything. Each view has −, a percentage and + at the lower right and a button that fits the whole drawing in the pane.
Handles on the drawing
Before Analyze you can pull these on the Section, and the field in the Model tab follows:
The water table and, when the level in the excavation is different, the water level in the excavation: up or down in steps of 5 cm; the water table cannot go above the top of the wall (depth 0), and the excavation level not above 0.1 m depth.
A layer boundary: the thickness above it and the thickness below it change together, and the layer below keeps at least 10 cm.
The toe of the sheet pile: pulling it switches the embedment to Given — verify it and sets the depth D (at least 0.1 m).
A strip load by its body or by either edge, and a point load: along the ground, in steps of 5 cm.
Press a layer, an anchor or a load on the drawing without pulling and it opens in its form. After Analyze there are no handles and the inputs are locked; Edit inputs unlocks them and clears the results. The unit system can still be changed.
A strip load and a point load on the Section, before Analyze; both can be dragged.
Entering the model, section by section
The Model tab has eleven sections: Model data, Soil layers, Groundwater, Wall and embedment, Terrain, Ground anchor, Surcharge, Earthquake, Design factors, Sheet pile and Design code. Each opens when you click its title; Next and Back at the foot walk you through them, and Analyze waits in the bar below. Where a unit is shown twice or three times, such as m · ft, the units are those of SI · kN, SI · tf and US in turn, and equal ones are merged. Defaults are shown in SI.
Model data
The first section holds the model name, Save to file…, Open file…, Quick Save… with its list and Load and Delete, and Reset to defaults, as described in the workspace guide. After Analyze the model is locked, and so are Reset, Open and Load until you press Edit inputs.
Model data.
Soil layers
A form over a table. The New layer form takes the name, thickness, unit weights, friction angle and subgrade reaction of one layer; + Add layer puts it at the bottom of the table, and a counter shows how many of the four layers there are. The table lists every layer with a swatch of its colour on the drawing. Press a row (or the layer on the drawing) to change it in the form, which then reads Editing · Layer 2 and offers Done and Delete layer; changes apply as they are entered. × takes a layer out. The first item, Sand-1, is already in the table with the defaults; the form for a new layer opens with a thickness of 2 m.
Soil layers: the form over the table.
Layer fields
Field
Default
What to enter
Name
automatic
Shown in the table and on the drawing: Sand-1, Sand-2 … (optional)
Thickness H m · ft
5 (first layer); 2 (form)
From the top of the wall down. At least 0.1 m. The last layer has no thickness: it runs on below the toe, and its row shows a dash.
Moist unit weight γ kN/m³ · t/m³ · pcf
15.9
At least 1. Used above the water table.
Saturated unit weight γsat kN/m³ · t/m³ · pcf
19.33
At least 1, and above the unit weight of water, 9.81 kN/m³, for a layer that reaches below the water table.
Friction angle φ′ °
32
From 15° to 45°. It gives Ka and Kp of the layer.
Dry unit weight γd kN/m³ · t/m³ · pcf
15
At least 1 and not above γsat. Shown only when the earthquake check is on with free pore water.
At least 0.1 MN/m³. It gives the stiffness of the soil springs of the displacement estimate; the embedment and the moment do not use it.
Three layers, the second one pressed: it is edited in the form.
The thicknesses are measured from the top of the wall and add up down the profile; the dredge line is where L puts it, so a layer may begin above it and run on below it, and a layer wholly below it acts on both faces. The profile in the picture (2 m, 3 m, then the last layer) has its dredge line at the end of the second layer.
Groundwater
Water table has None and Present; the unit weight of water, 9.81 kN/m³, is shown. With Present, Level in the excavation has Same as retained side, the default, and Different level, which asks for the depth Dw,exc. With None the saturated unit weights are not used.
Groundwater fields
Field
Default
What to enter
Water table depth (retained side) Dw m · ft
2
Measured down from the top of the wall. Zero or more.
Water level in the excavation Dw,exc m · ft
6
Also measured down from the top of the wall; a depth less than L puts free water in the excavation, a depth more than L a lowered level. Shown when the level is different.
At the same level the hydrostatic pressures on the two faces cancel and only effective pressures load the wall; the drawing then shows the water standing in the excavation to the same level. With a different level each face carries the hydrostatic pressure of its own water level, and the net pressure is added. If you choose Different level and type the retained-side level, the result is the same as for the same level and a note says so.
Wall and embedment
The height L and the choice Depth of embedment: Calculated by the program (the design depth comes out of the analysis) or Given — verify it, which shows the depth D and verifies it.
Wall and embedment.
Wall fields
Field
Default
What to enter
Height of the wall above the dredge line L m · ft
5
At least 0.5 m. The soil below it is the lower part of the profile.
Depth of embedment below the dredge line D m · ft
5
At least 0.1 m. Shown when the embedment is Given.
Terrain
Retained ground surface: Level or Sloping, rising away from the wall without end. Sloping asks for the angle β (default 15°, from 0° to 45°).
A sloping retained surface on the Section.
Ground anchor
The wall is a cantilever until you add an anchor. Once you add the first row, a Tendon choice (Strand or Bar, each with a ? that opens a help window) appears above the form. Fill the New anchor form and press + Add anchor: up to four rows, listed in a table below; press a row or the anchor on the drawing to change it. Rows are taken in order of depth.
Ground anchor: the form for a row.
Anchor fields (the form, and each row of the table)
Field
Default
What to enter
Depth of the anchor za m · ft
1.5 (rows 2 to 4: 3, 3.8, 4.5)
Below the top of the wall, above the dredge line: 0 ≤ za < L. Rows stand at least 0.25 m apart.
Horizontal spacing s m · ft
2.5
At least 0.5 m. Each anchor carries the reaction of its row over this width.
Inclination below the horizontal α °
15
From 0° to 60°.
Prestress (lock-off) force per anchor P0 kN · tf · kip
250
Zero or more. It starts the anchor spring of the displacement estimate.
Free length Lf m · ft
7
At least 0.5 m.
Bond (root) length Lb m · ft
6
At least 0.5 m. It places the bond zone.
Cross-section area of the tendon At cm² · in²
5.6
Gives the stiffness of the anchor with its free length.
Surcharge
New load: choose Uniform, Strip or Point, fill its values and press + Add load: up to six loads, listed in a table with their kind, magnitude and position. Loads stand on the ground behind the wall. Press a row or the load on the drawing to change it.
Surcharge: three loads in the table.
Surcharge fields
Field
Default
What to enter
Uniform surcharge on the retained surface q kPa · t/m² · ksf
10
Zero or more.
Strip load qs kPa · t/m² · ksf
20
The pressure the strip carries.
Near edge from the wall / far edge from the wall x1, x2 m · ft
1 / 3
0 ≤ x1 < x2. A strip placed at 0 m is taken at 0.30 m by the module.
Point load Q kN · tf · kip
50
Zero or more; it must be above zero to analyse.
Distance from the wall x m · ft
2
Zero or more.
Combination factor in the earthquake ψ2
1
From 0 to 1; it scales the load in the earthquake check. Shown when the earthquake check is on.
Earthquake
Seismic situation: Not checked or Pseudo-static check (Mononobe–Okabe). With the check on, Pore water during the earthquake has Moves with the soil and Free (very permeable), each with a ?; free water asks for the dry unit weight γd of each layer. The coefficients are yours, from your seismic code.
The Section after Analyze with the earthquake check on.
Earthquake fields
Field
Default
What to enter
Horizontal seismic coefficient kh
0.15
From 0 to 0.6.
Vertical seismic coefficient kv
0.075
From 0 to 0.4. Both senses, up and down, are checked.
Design factors
Embedment route: Increase D theory by a factor (the depth factor f) or Factor of safety on Kₚ (the factor FSp). See the next section.
Design factors: the factor of safety route.
Design factors
Field
Default
What to enter
Depth increase factor f
1.3
From 1 to 1.6. Shown with the route that increases Dtheory.
Factor of safety on KpFSp
1.5
From 1 to 3. Shown with the route that reduces Kp.
Sheet pile
Steel grade: S235, S275, S355 or Typed. Section modulus given: Elastic Wel or Plastic Wpl, each with a ?. The yield strength follows the grade until you type a value of your own.
Sheet pile.
Sheet pile fields
Field
Default
What to enter
Yield strength fy kPa · t/m² · ksf
275000 kPa, from the grade
Filled from the grade (S235, S275, S355); type your own over it, or choose Typed.
Section modulus of the sheet pile W cm³/m · in³/ft
1400
Per metre of wall, from the maker’s table; the elastic or the plastic column as chosen. May be left empty.
Second moment of area of the sheet pile I cm⁴/m · in⁴/ft
21000
Per metre of wall; used for the displacement estimate.
Design code
Verify the steelwork to: EN 1993-1-1 (Eurocode 3) or AISC 360-22; with AISC, Design methodLRFD or ASD. Each choice has a ? that opens a help window with its equation.
Design code.
Design code fields (the factors of the code chosen are shown)
Field
Default
What to enter
Load factor on the earth pressure (AISC, LRFD) γH
1.6
From 1 to 2.
Partial factor on the earth-pressure moment (EN 1993-1-1) γF
1.35
From 1 to 1.6.
Partial factor on a cross-section resistance (EN 1993-1-1) γM0
1
From 1 to 1.3.
Choosing the embedment, the wall type and the code
Four decisions shape the answer.
The embedment route
Route
Effect
Increase D theory by a factor
The diagram is built with the full Kp; Dtheory is the depth that balances it exactly, and Ddesign = f × Dtheory. The moment is that of the balanced diagram, so f changes the depth only. f = 1.3: Dtheory = 5.403 m, Ddesign = 7.023 m, Mmax = 209.6 kN·m/m. f = 1.2 gives 6.483 m and f = 1.5 gives 8.104 m, with the same moment.
Factor of safety on Kₚ
Kp is divided by FSp before the diagram is built, which lengthens the depth and raises the moment. The depth found is the design depth, with no further increase; do not add a depth factor on top. FS = 1.5: Dreq = Ddesign = 7.102 m, Mmax = 263.5. FS = 2: 8.837 m and 325.9.
For this wall a factor of 1.5 on Kp asks for a deeper toe and a larger moment than a depth factor of 1.3. In the first route the first card reads Theoretical embedment depth; in the second it reads Required embedment depth.
Calculated or given depth
With Given — verify it you type D and the module verifies it. Below Dtheory the wall is not in equilibrium even with the full Kp and the analysis stops (see Messages). Above it, the module compares the given depth with the required design depth of your route and shows the factor of safety on Kp that the given depth mobilises. With D = 8 m the example gives PASS on the depth (required 7.023 m, FSp,mob = 1.762); the moment is the larger of the design diagram and of the diagram at the given depth, here 294.9 kN·m/m, so the sheet pile, utilisation 1.034 FAIL, now fails. A given depth that falls short is drawn in red with the required toe and the shortfall.
A given depth that is short of the required one.
Cantilever or anchored
The wall is a cantilever until you add an anchor. With one row the module uses the free earth support method: the toe is free, the depth comes from the moments about the anchor and the anchor force from horizontal equilibrium. With two to four rows the wall is made determinate by hinges at the anchors below the uppermost, and the part below the lowest anchor is designed by free earth support about it; this idealisation is applied to the limit-equilibrium diagram of the module. Anchors shorten the embedment and cut the moment: for the example with one anchor at 1.5 m the module gives Dtheory = 1.928 m, Ddesign = 2.506 m, Mmax = 40.17 kN·m/m; with a second at 3 m, 1.662 m, 2.161 m and 19.06 kN·m/m.
Two rows of anchors: the embedment is a third of the cantilever one.
The code
EN 1993-1-1: the design moment is MEd = γFMmax (default γF = 1.35), the resistance Mc,Rd = Wfy / γM0, and the section modulus asked for is Wreq = MEdγM0 / fy. AISC 360-22, LRFD: Mu = γHMmax against φbMn with φb = 0.90; ASD: the working moment against Mn / Ωb with Ωb = 1.67. Mn is fyWpl for a plastic modulus (taken as compact) or fyWel at first yield. For the example the module gives Wreq = 1,029 cm³/m by EN 1993-1-1, 1,355 by LRFD and 1,273 by ASD, with utilisations 0.7349 PASS, 0.9677 PASS, near capacity and 0.9091 PASS.
Analyze and read the results
Press Analyze. The bar changes to Analysed — the sheet-pile wall calculated and says “The model is locked … Edit inputs clears the results; the unit system can still be changed.” The Model tab stays on screen: open Results to read the answer. The Section view now shows the net pressure diagram, the depths and Mmax. A button on the bar reads Notes (n) or Warnings (n), and when there are warnings a window opens by itself.
The Results tab begins with the diagrams.
Card
The example
Theoretical embedment depth Dtheory
5.403 m
Design embedment depth Ddesign
7.023 m
Maximum bending moment Mmax
209.6 kN·m/m
Section modulus the sheet pile needs (EN 1993-1-1) Wreq
1,029 cm³/m
Utilisation of the sheet pile given by its modulus ηsp
0.7349 PASS
Top displacement of the wall (subgrade reaction, indicative) ytop
155.8 mm
The cards change with the case. With the factor of safety route the first card is the Required embedment depth; with a given depth the second card reads Design embedment depth — given with PASS or FAIL, and two more cards give the Required design embedment depth and the Factor of safety the given depth mobilises on Kp; with the earthquake check on a card Embedment required in the seismic situation shows DE with its verdict. If the section modulus is left empty, only Wreq is given and no section is verified.
The verdict words
The utilisation ηsp is the design moment over the resistance of the sheet pile given. It reads PASS at 1 or less and FAIL above 1; very close to 1 (0.9677 in the AISC example) it reads PASS, near capacity. The same word appears in the report.
The tables
Values, step by step: the coefficients, the pressures, L3, P and its arm, the root L4, the toe pressures, the depths, Mmax, the design moment, Wreq, the verification and the displacements, one row per step.
Pieces of the pressure diagram above E: each triangle and rectangle with its area and its arm above E.
The layers down to the toe and the coefficients of their springs: kh, φ′, K0, Ka, Kp of each layer.
Displacement, bending moment and the pressures on the two faces along the wall: the values behind the displacement diagram.
With anchors the tables add the pressures at the breaks of the diagram, the moment about the anchor for trial depths, and an anchor table with, per row, za, s, α, the force per metre F, the reaction on the tendon axis TLEM = Fs / cos α, its vertical part, P0, the place of the bond zone and a PASS or FAIL on it. For the example with one anchor, F = 35.86 kN/m and TLEM = 92.8 kN.
The Results tab with a given depth that falls short: the warning bar and the diagrams.
Using the numbers
The forces and moments are per metre of wall: kN/m and kN·m/m (tf/m and tf·m/m in SI · tf; kip/ft and kip·ft/ft in US); the section modulus is per metre of wall too.
Mmax is the characteristic moment of the theoretical diagram; the factor of the code is applied once, in the design moment.
The displacement is an order-of-magnitude estimate on elastic springs.
Changing the unit system after Analyze re-states the cards, the Section and Results drawings, the tables and the working in the new units; the 3D view keeps its labels in m and kN.
The Calculations tab, the report and the Theory tab
The Calculations tab starts with Given and what is sought and writes the working in numbered steps with your numbers, ending with the answer. For the cantilever wall of the example the steps are:
Earth-pressure coefficients — Ka and Kp of each layer.
Active pressure above the dredge line — at every boundary of the profile.
Net pressure below the dredge line — L3, the zero point E.
Resultant of the active diagram and its arm about E — P and z̄, with the table of pieces.
Toe intercept and the coefficients of the embedment equation — σ′5 and the four coefficients.
Solve the embedment equation — the root L4, with the residual and a graph.
Pressures at the toe and the toe block — σ′3, σ′4, L5 and the closing check.
Theoretical and design depth of embedment — the depths and the total length (with the safety route, Required and design depth).
Maximum bending moment — z′ and Mmax, with the shear and moment diagrams.
Take the design moment — MEd (for AISC LRFD, Take the required moment).
Sheet pile — the section modulus asked for — Wreq.
Sheet pile — the section given verified — Mc,Rd and ηsp.
Wall displacement — subgrade reaction method — the estimate on springs.
With anchors the steps from the embedment on change: the depth by free earth support, the moment, and a step Ground anchors — their forces and the place of their bond zones. With the earthquake check on, steps are added for the seismic coefficients, the hydrodynamic pressure of free water, the embedment and moment in the seismic situation and the sheet pile in it. Then come Notes and assumptions and the Answer.
Given and what is sought.
Step 12: the section given verified.
The report
In the Report tab fill in the cover (project, location, client, report number, date, prepared by, title or qualification, checked by, and optional notes), kept in this browser and saved with the model file. Save as PDF and Download Word (.docx) produce the summary report.
The report has seven parts: 1 Introduction and scope, 2 Input data, 3 Calculation (3.1 to 3.13 for a cantilever wall), 4 Results, 5 Assumptions and notes, 6 Summary and 7 References, with the section drawing and the diagrams.
The Report tab: the cover details, the two buttons and the first page.
The Theory tab
The Theory tab has nineteen sections: Sheet-pile walls and this module; How a cantilever wall moves; Active pressure above the dredge line; The net pressure below the dredge line; Equilibrium: the embedment equation; The depth of embedment; The maximum bending moment; No water table; Water at different levels on the two faces; Verifying the sheet pile to EN 1993-1-1; Verifying the sheet pile to AISC 360-22; The sloping retained surface; The anchored wall; The seismic situation; The displacement of the wall; A worked example, by the module; The opening wall, verified to EN 1993-1-1; What the module assumes; and References.
Worked example: the module’s own example
The module opens on this example, so you can follow the numbers on your own screen.
Inputs of the example
Input
Value
Soil layers: Sand-1
γ = 15.9, γsat = 19.33 kN/m³; φ′ = 32°
Groundwater: Water table
Present, Dw = 2 m, same level on both faces
Wall and embedment: Wall
L = 5 m, depth calculated
Design factors: Route
Depth factor f = 1.3
Sheet pile, Design code: Steel
S275 (fy = 275,000 kPa), Wel = 1,400 cm³/m; EN 1993-1-1, γF = 1.35, γM0 = 1.00
Step 1: the coefficients
Ka = tan²(45° − 32°/2) = 0.3073 and Kp = tan²(45° + 32°/2) = 3.2546.
Step 2: the active pressure above the dredge line
At the water table, σ′v = 15.9 × 2 = 31.80 kPa and σ′1 = 0.3073 × 31.80 = 9.77 kPa. At the dredge line, with γ′ = 19.33 − 9.81 = 9.52 kN/m³, σ′v = 31.80 + 9.52 × 3 = 60.36 kPa and σ′2 = 0.3073 × 60.36 = 18.55 kPa.
Step 3: the zero point
Below the dredge line the net pressure falls with the slope γ′(Kp − Ka) = 9.52 × 2.9473 = 28.06 kPa per m, so L3 = 18.55 / 28.06 = 0.6610 m.
Step 4: the resultant
Four pieces: ½ × 9.77 × 2.00 = 9.771 kN/m at an arm of 4.328 m above E; 9.77 × 3.00 = 29.31 at 2.161 m; ½ × 8.78 × 3.00 = 13.16 at 1.661 m; ½ × 18.55 × 0.6610 = 6.129 at 0.4407 m. So P = 58.38 kN/m and z̄ = 130.19 / 58.38 = 2.2303 m.
Step 5 and 6: the embedment equation
σ′5 = 60.36 × 3.2546 + 28.06 × 0.6610 = 214.99 kPa. The coefficients are A1 = 7.66, A2 = 16.64, A3 = 151.33 and A4 = 230.63, and
σ′3 = 4.742 × 28.06 = 133.05 kPa, σ′4 = 214.99 + 28.06 × 4.742 = 348.04 kPa and L5 = 1.07 m, which lies between 0 and L4, so the diagram closes. Dtheory = 0.6610 + 4.742 = 5.40 m, Ddesign = 1.30 × 5.40 = 7.02 m and the total length is 5.00 + 7.02 = 12.02 m. The shear is zero at z′ = √(2 × 58.38 / 28.06) = 2.0398 m below E, where
MEd = 1.35 × 209.58 = 282.93 kN·m/m; Wreq = 282.93 × 1.00 / 275,000 = 1,028.83 cm³/m; Mc,Rd = 1,400×10⁻⁶ × 275,000 / 1.00 = 385.00 kN·m/m, so ηsp = 282.93 / 385.00 = 0.7349, PASS. The displacement of the top is 155.8 mm toward the excavation.
These are the cards of the Results tab.
Other unit systems
The default example in US gives Dtheory = 17.73 ft, Ddesign = 23.04 ft, Mmax = 47.11 kip·ft/ft, Wreq = 19.14 in³/ft and ηsp = 0.7349 PASS: the same wall (5.403 m is 17.73 ft; 209.6 kN·m/m is 47.11 kip·ft/ft). Two checks with values typed in the other systems and recomputed by hand:
US. One layer of 110 pcf sand at 30°, no water, L = 15 ft, depth factor 1.3: Ka = 1/3, and the hand calculation gives Dtheory = 15.06 ft, Ddesign = 19.58 ft and Mmax = 46.41 kip·ft/ft. The module gives 15.06 ft, 19.58 ft and 46.41 kip·ft/ft.
SI · tf. One layer of 1.7 t/m³ sand at 30°, no water, L = 4 m, f = 1.4: by hand Dtheory = 4.017 m, Ddesign = 5.624 m and Mmax = 13.60 tf·m/m. The module gives 4.017 m, 5.624 m and 13.60 tf·m/m.
How each input changes the answer
Each row changes one thing in the example (cantilever, one layer of 15.9 / 19.33 kN/m³ sand at 32°, L = 5 m, water table 2 m on both faces, f = 1.3, S275 with Wel = 1,400 cm³/m, EN 1993-1-1 with γF = 1.35) and runs the module again. The numbers are the ones the module gives. Each result is Dtheory / Ddesign in m on the first line, then Mmax in kN·m/m and the utilisation ηsp of the sheet pile given, with the verdict word.
The wall, the soil and the water
Change
Result
The default example The reference
5.403 / 7.023 m 209.6 · 0.7349 PASS
L = 4 m A lower wall: everything falls
4.438 / 5.769 m 114.9 · 0.4029 PASS
L = 6 m The moment rises by more than half and the sheet pile no longer carries it
6.352 / 8.258 m 342.9 · 1.202 FAIL
φ′ = 28° A smaller friction angle: more active and less passive pressure
6.696 / 8.705 m 293.8 · 1.030 FAIL
φ′ = 36° The opposite
4.401 / 5.721 m 153.0 · 0.5366 PASS
γ = 18, γsat = 20 kN/m³ A heavier sand raises the pressures
5.518 / 7.174 m 238.1 · 0.8349 PASS
Water table: None The depth falls by about a metre; the moment is about the same
4.528 / 5.887 m 212.1 · 0.7437 PASS
Dw = 4 m A lower water table gives more effective weight above it: larger pressures
5.866 / 7.626 m 256.6 · 0.8996 PASS
Dw = 1 m A higher one gives smaller pressures
5.037 / 6.548 m 173.1 · 0.6070 PASS
Different level, Dw,exc = 4 m Free water 1 m deep in the excavation, 2 m lower than behind the wall: the net water pressure is added
7.879 / 10.24 m 510.0 · 1.788 FAIL
The embedment route and the sheet pile
Change
Result
f = 1.2 Only the design depth changes
5.403 / 6.483 m 209.6 · 0.7349 PASS
f = 1.5 Only the design depth changes
5.403 / 8.104 m 209.6 · 0.7349 PASS
Factor of safety FSp = 1.5 on Kp The first card is the required depth; moment and depth both rise
7.102 / 7.102 m 263.5 · 0.9241 PASS
FSp = 2.0 A larger moment: the sheet pile fails
8.837 / 8.837 m 325.9 · 1.143 FAIL
W = 1,000 cm³/m The demand is the same; the section is too light
5.403 / 7.023 m 209.6 · 1.029 FAIL
γF = 1.0 A smaller design moment: lower utilisation
5.403 / 7.023 m 209.6 · 0.5444 PASS
AISC 360-22, LRFD γH = 1.6 on the moment against φbMn
5.403 / 7.023 m 209.6 · 0.9677 PASS
AISC 360-22, ASD The working moment against Mn / 1.67
5.403 / 7.023 m 209.6 · 0.9091 PASS
Loads and ground
Change
Result
Uniform surcharge 10 kPa Adds Ka q above the dredge line and Kp q to the passive pressure at the toe
6.149 / 7.993 m 305.5 · 1.071 FAIL
Uniform surcharge 20 kPa About twice the increase
6.819 / 8.864 m 410.9 · 1.441 FAIL
Strip load 20 kPa, 1 m to 3 m The pressure comes from the elastic solution, doubled for a rigid wall
6.315 / 8.209 m 344.2 · 1.207 FAIL
Point load 50 kN at 2 m A smaller effect than the strip
5.741 / 7.464 m 256.0 · 0.8975 PASS
Sloping surface, β = 15° The horizontal part of the sloping Rankine pressure
5.642 / 7.335 m 232.1 · 0.8137 PASS
β = 25° Closer to φ′: much larger pressures
6.346 / 8.249 m 305.5 · 1.071 FAIL
A second layer below the dredge line: 18 / 20 kN/m³, φ′ = 38° A stronger sand at the toe shortens the wall
4.251 / 5.526 m 172.3 · 0.6041 PASS
Anchors, and a given depth
Change
Result
One anchor row at 1.5 m (s = 2.5 m, 15°) The wall is held at the anchor: a third of the cantilever depth and a fifth of the moment
1.928 / 2.506 m 40.17 · 0.1408 PASS
One anchor row at 3 m A lower anchor: a shallower toe and about half the moment
1.414 / 1.838 m 21.66 · 0.07594 PASS
Two rows, at 1.5 m and 3 m Hinge idealisation: the moment halves again
1.662 / 2.161 m 19.06 · 0.06685 PASS
Embedment given, D = 8 m The depth passes; the moment is that of the given depth and the sheet pile fails
5.403 / 8.000 m 294.9 · 1.034 FAIL
Embedment given, D = 5.5 m Between Dtheory and the required depth: the depth fails
5.403 / 5.500 m 212.5 · 0.7450 PASS
The pattern follows the formulas. The depth and the moment follow Ka, Kp, the effective weights and the loads; the depth factor leaves the moment alone but a factor of safety on Kp raises both; an anchor holds the top of the wall and the embedment becomes a question of the toe alone. With the earthquake check on, the card DE compares the depth the seismic pressures need with the design depth: for the example with kh = 0.15 it reads 9.987 m FAIL against 7.02 m, and with kh = 0.05 and kv = 0 the check passes.
Messages: when the module stops, and what it notes
The module checks the numbers before it calculates. When one cannot be used it stops and nothing is calculated.
A value outside its limits opens Cannot analyse — 1 input error (or 2, 3 …) listing each message, and the box is marked in red.
A condition of the solution that is not met opens Cannot analyse — a condition of the solution is not met, which ends “Nothing was calculated. Change the inputs marked in red, then press Analyze again.”
The limits are shown in the unit system chosen.
The window when the wall height is zero.
When
Message
Stop: A value outside its limits
“Height of the wall above the dredge line (L) must be at least 0.5 m.” · “Friction angle (φ′1) must be at least 15°.” or “… at most 45°.” · “Moist unit weight (γ1) must be at least 1 kN/m³.” · “Depth increase factor (f) must be at least 1.” · “Factor of safety on Kp (FSp) must be at least 1.” or “… at most 3.” · “Water table depth (retained side) (Dw) must be at least 0 m.” · “Depth of embedment below the dredge line (D) must be at least 0.1 m.” · “Inclination below the horizontal (α) must be at most 60°.” · “Horizontal seismic coefficient (kh) must be at most 0.6.” · “Combination factor in the earthquake (ψ2) must be at most 1.”
Stop: The level in the excavation is Different but empty
“Water level in the excavation (Dw,exc) is missing.”
Stop: Saturated unit weight at or below that of water, with a water table
“Sand: saturated unit weight must exceed γw. Below the water table the overburden uses γ′ = γsat − γw. Enter the saturated unit weight.”
Stop: An anchor at or below the dredge line
“The anchor must stand above the dredge line. za is its depth below the top of the wall: 0 ≤ za < L.”
Stop: Two anchor rows less than 0.25 m apart
“Anchor row 2: two rows of anchors stand at nearly the same depth. The rows need at least 0.25 m between them to be separate supports.”
Stop: The slope as steep as the friction angle
“Sand: the slope angle β = 40° must be smaller than φ′ = 32°.” followed by the reason: a sand does not stand on a slope steeper than its friction angle.
Stop: A strip or point load with a sloping surface
“Strip and point loads cannot be combined with a sloping retained surface.” Use uniform loads, or a level surface.
Stop: A strip with its far edge not beyond its near edge, or a point load of zero
“Load 1 (strip load): the strip must have its far edge beyond its near edge.” · “Load 1 (point load): the point load must be greater than zero.”
Stop: Free pore water with a dry unit weight above the saturated one
“Sand: the dry unit weight γd must be greater than zero and not above γsat.”
Stop: A given depth below Dtheory
“NO EQUILIBRIUM AT THE GIVEN EMBEDMENT — even full passive resistance is insufficient.” It names the depth the diagram needs and the design route’s depth. Drive the sheet pile deeper or choose Calculated by the program.
Stop: A head the sand cannot balance
“No depth of embedment balances the diagram with the levels entered.” Happens, for instance, with the example and the excavation level at the top of the wall (Dw,exc = 0).
The window for a given depth of 5 m.
When more than one value is wrong the window lists them together. The layer or row number is part of the symbol: φ′1 belongs to layer 1.
Warnings
A warning marks a result that the module calculates but that fails a check. The button on the bar reads Warnings (n), and the window opens by itself after Analyze:
The sheet pile does not carry the moment: “The sheet pile given does not carry the design moment: MEd / Mc,Rd = 1.07 …”, with the resistance, the demand and the section modulus the wall asks for. Take a heavier sheet pile or a higher grade. In the earthquake the same message is about the seismic moment.
Large displacement: “ytop = 259.3 mm, 5.2 % of the retained height L …” raised at 5 % of L. The estimate is a small-displacement idealisation; read it as an order of magnitude.
The embedment is too short for the earthquake: “The design embedment is too short for the seismic situation: DE = 9.99 m > Ddesign = 7.02 m …”
A given depth that falls short: “The given depth of embedment D = 5.50 m is shorter than the depth the design requires, 7.02 m. At the given depth the passive resistance mobilises a factor of safety of only 1.03 on Kp …”, with a note that the displacement is then indicative only.
Notes
A note states an assumption of the calculation; the button reads Notes (n) when nothing fails. The default example carries three: the sheet pile is checked on the modulus given as the modulus of the whole wall (a U-pile wall may have it reduced where the interlocks can slip, a Z-pile wall carries the full value); the moment is factored by γF before the code check; and the displacement is estimated on springs and indicative. Other notes appear with the case:
The factor of safety route: the factor was applied to Kp before the diagram was built, and no depth factor is to be added on top.
Water at different levels: the hydrostatic pressures on the two faces are independent; seepage is not part of the model. Equal levels under Different level give a note that the result is that of the same level.
Loads and slope: the uniform surcharge adds Ka q above the dredge line and Kp q at the toe on the retained side; strip and point loads come from the elastic solution for a rigid wall and the equilibrium is solved numerically; a slope uses the horizontal part of the sloping active pressure.
Anchors: the anchor table gives the reaction TLEM of the design diagram, and the vertical component (9.61 kN/m for the one-anchor example) is listed for your axial and toe-bearing design; TLEM is a reaction, not a lock-off or a test load.
Plastic modulus: used with the section taken as class 1 or 2.
No section modulus: the modulus needed is found and no section is verified.
AISC with an EN grade: used by its yield strength.
Good practice and common mistakes
Know which face is which. The retained soil is on the right of the drawing, the excavation on the left; the dredge line is the excavation level.
Water at the same level on both faces is a design statement: the drawing shows free water standing in the excavation. If the excavation is dewatered, choose Different level and enter the level there.
Enter the saturated unit weight above 9.81 kN/m³ for any layer that reaches below the water table.
Choose the route once. With the factor of safety on Kp do not add a depth factor on top; the depth found is the design depth.
Read Mmax as characteristic. The code factor is applied in the design moment; the section modulus is per metre of wall.
Give the section modulus of the whole wall, from the maker’s table, and take the interlocks and the shear of the wall from the maker’s data.
With anchors, use the reaction TLEM, the vertical component and the bond zone from the anchor table for the design of the tendons and the toe.
Use the earthquake check to compare: the depth DE and the seismic moment are shown next to the static design.
Do not rely on the handles after Analyze: they are gone and the inputs are locked until Edit inputs.
Keep the model: the page opens on the default every time; use Save to file… or Quick Save…, and the report as the record.
Frequently asked questions
How is the embedment of a cantilever sheet pile in sand found?
The active pressure above the dredge line and the net pressure below it (active less passive) are balanced by the equilibrium of forces and moments about the toe, with the toe pressures reversed over a block L5. That gives an equation of the fourth degree in the depth L4 of the toe below the zero point E, which the module solves. Dtheory = L3 + L4; for the example it is 5.403 m.
What is the difference between the depth factor and the factor of safety on Kp?
The depth factor multiplies the balanced depth: the example goes from 5.403 m to 7.023 m at 1.3 and the moment is unchanged. The factor of safety divides Kp before the diagram is built, so the depth and the moment both rise: 7.102 m and 263.5 kN·m/m at 1.5.
Where is the maximum moment, and is it factored?
At the depth z′ below E where the shear is zero; it is the characteristic moment of the balanced diagram, 209.6 kN·m/m for the example. The code factor (γF = 1.35 for EN 1993-1-1, γH = 1.6 for AISC LRFD, none for ASD) is applied once, to get the design moment.
How do I enter a wall with a lowered water level in the excavation?
In Groundwater choose Present, then Different level, and enter the depth Dw,exc below the top of the wall. A depth greater than L is below the dredge line. The net hydrostatic pressure is added, with no seepage.
How many anchors can I add, and how are they treated?
Up to four rows. One row is designed by free earth support: the toe is free and the anchor force comes from horizontal equilibrium. Two or more rows use a hinge idealisation on the limit-equilibrium diagram. Each row has a depth, a spacing, an inclination, a lock-off load and lengths; the anchor table gives the reaction per anchor.
How do I verify an embedment I already have?
Choose Given — verify it and type D. Below Dtheory the analysis stops; above it the module shows whether the depth reaches the required design depth and the factor of safety on Kp it mobilises, and it draws the shortfall in red.
Which sheet-pile checks does the module make?
The sheet pile is verified in bending on the section modulus per metre of wall to EN 1993-1-1 (resistance Wfy / γM0) or AISC 360-22 (LRFD or ASD). Leave the modulus empty and the module gives the modulus you need.
Can I drag things on the drawing?
Before Analyze: the water levels, the layer boundaries, the toe (which makes the embedment given), and strip and point loads. After Analyze there are no handles; press Edit inputs.
Does the module remember my inputs?
No: it opens on the default example every time; only the unit system you chose is remembered, and the default values are shown in it (5 m reads 16.4042 ft in US). Save to file keeps the model with the project and Quick Save keeps versions in the browser.
What does the earthquake check do?
It replaces the Rankine coefficients by Mononobe–Okabe ones with the coefficients kh and kv you give (both senses of kv), with restrained or free pore water, and compares the embedment the seismic pressures need, DE, with the design embedment, and the sheet pile with the seismic moment.
Which units does it use?
SI · kN, SI · tf or US, switchable in the header at any time. The default example gives Ddesign = 7.023 m, 7.023 m or 23.04 ft; Mmax is 209.6 kN·m/m, 21.37 tf·m/m or 47.11 kip·ft/ft.
What if the sheet pile fails?
The utilisation reads FAIL and a warning says what the wall asks for. Choose a heavier section or a higher grade, or reduce the moment with anchors, a lower wall or a stronger sand.
Design a cantilever or anchored sheet-pile wall in undrained clay: the tension crack above the dredge line, the net pressure of 4cu below it, the check that the wall can be balanced, the embedment, the maximum moment and the steel section to EN 1993-1-1 or AISC 360-22. This manual walks through the screen, every input, the results and every message, with a worked example you can reproduce.
Sheet pile in clay designs a cantilever or anchored sheet-pile wall whose soil is undrained clay, from the top of the wall down below the toe. It draws the net pressure diagram, finds by limit equilibrium the depth of embedment the wall needs, gives the maximum bending moment, and checks the steel sheet pile you give it to EN 1993-1-1 or AISC 360-22. With rows of ground anchors the same wall is an anchored wall, and the module then also gives the anchor reactions and the position of their bond zones.
The clay is analysed in total stress with its undrained shear strength cu and φ = 0, so Ka = Kp = 1. With σv the vertical stress, γ the unit weight and q a surcharge, the active and passive pressures of a layer are:
σa = σv − 2cu, σp = σv + 2cu, σv = q + ΣγiHi
Above the dredge line only the retained clay acts on the wall, and its active pressure is taken as zero where σv − 2cu would be negative: that is the tension crack, which the module fills with water to its top unless you choose a dry crack. Below the dredge line the clay acts on both faces of the wall, and the net pressure on the wall is the difference of the two faces:
where r is the retained side and e the excavation side. Below the dredge line this is a constant: the overburden difference less 4cu. Before the embedment is looked for, the module checks that this net pressure turns toward the retained soil, which is the condition for any depth to balance the wall; see Messages.
What you can describe
Clay layers: up to four, from the top of the wall down, each with its unit weights, its cu and a horizontal subgrade reaction kh. The last layer runs on below the toe.
A retained height L above the dredge line, with the embedment calculated by the module or given for you to verify.
Water: a water table on the retained side and the same level or a different level in the excavation.
Ground anchors: none (a cantilever wall) or one to four rows, each with its depth, spacing, inclination, lengths and tendon area.
Surcharges: up to six loads, each uniform, a strip or a point load.
The earthquake: a pseudo-static check of the wall as designed.
The bottom heave of the base of the excavation.
The safety route of the embedment, the tension-crack and active-pressure options, the steel grade and section modulus, and the design code.
It draws the section, a 3D view, the net pressure, the shear force and the bending moment, writes out the working step by step, and prepares a PDF or Word report.
Which module for which wall
The soil is clay from top to bottom: this module. Sand is not entered here; a wall in sand uses Sheet pile in sand, and sand and clay together use Anchored sheet pile on layered soil, with drained or undrained layers, up to four anchor rows and the short- and long-term scenarios.
Have these ready from your design and your ground investigation:
What
Where from, and notes
The retained height L
Your design. Top of the wall to the dredge line, at least 0.5 m. The Theory tab gives up to about 6 m as the usual range of a cantilever wall.
The clay layers
Boring logs, vane or triaxial tests. Per layer, top down: thickness (not the last), moist and saturated unit weight, cu (at least 1 kPa), kh.
The water levels
Groundwater readings. Depth below the top of the wall behind the wall and, if different, in the excavation; or none.
Anchors, loads
Your design. Per anchor row: depth, spacing, inclination, free and bond length, tendon area; the surcharges behind the wall.
The sheet pile
The maker’s table. Yield strength (from the grade), section modulus per metre of wall, second moment of area for the displacement.
Quick start in eight steps
Open the module and choose the units
Open Sheet pile in clay from the Sheet-Pile Walls family. Pick SI · kN, SI · tf or US in the header; you can change it at any time.
Enter the clay layers
In Soil layers fill the New layer form and press + Add layer, once per layer, from the top down. The last layer has no thickness: it runs on below the toe.
Set the water and the wall
In Groundwater choose None or Present; in Wall and embedment type L and choose Calculated by the program.
Add anchors and loads if there are any
In Ground anchor press + Add anchor for each row (none keeps the wall a cantilever); in Surcharge press + Add load for each load.
Choose the safety, the steel and the code
In Design factors set the embedment route and the crack options; in Sheet pile the steel grade and the section modulus; in Design code EN 1993-1-1 or AISC 360-22.
Press Analyze
Press Analyze in the bar at the foot of the Model tab. The bar reads Analysed and the model locks. The module stays on the Model tab: open Results.
Read the answer
The Results tab gives the pressure, shear and moment diagrams, the values step by step and, last, the cards: Dtheory, Ddesign, Mmax, Wreq, the utilisation of the pile, the heave factor and the top displacement.
Take the working and the report
The Calculations tab writes out the steps with your numbers; the Report tab saves a PDF or a Word file.
The screen: section and 3D
The layout is the one every GeoTerva module shares, described in the workspace guide. The drawing has two views, chosen with the buttons above it:
Section is the wall with the retained and the lower clay layers, the dredge line, the water levels and the dimensions. It follows your inputs. Before Analyze it draws the active pressure above the dredge line and a sketch of the embedment (“embedment: found by the analysis”); after it, the net pressure diagram with P and its resultant, the stresses σ2, σ3 and σ4, the point E, Dtheory, Ddesign and Mmax, which is green where the sheet pile given carries it and red where it does not. With anchors the section also shows each row with its depth and inclination.
3D is an oblique view of a length of the wall, the corrugated sheet piling driven to the design depth, the retained layers and the excavation, with L and D marked and, after Analyze, a line with Mmax, Wreq and the utilisation.
Section before Analyze.
Section after Analyze: the net pressure and the embedment depths.
3D after Analyze.
Section with one anchor row.
Dragging, and what is locked
Nothing is dragged after Analyze. Before Analyze a few handles on the Section drawing move inputs, in steps of 5 cm; the Model tab follows:
The boundary between two layers moves up and down and changes the thickness of the layer above it (the layer below it keeps at least 10 cm).
With Given — verify it the toe line moves up and down and changes D. Pulling it in the calculated mode switches the embedment to Given.
With a water table, the water level on the retained side moves, and the level in the excavation too when you chose a different level.
A strip load (by its body, or by its near or far edge) and a point load move along the ground. Anchors are not dragged.
The wall height L has no handle; type it in Wall and embedment. Pressing a layer, a load or an anchor on the drawing opens it in its form (the form then reads Editing · Layer 2, for example, with Done and Delete layer, and says that changes apply as they are entered).
There are no Show chips on the drawing. Each view has −, a percentage and + at the lower right and a button that fits the whole drawing in the pane.
Entering the model, section by section
The Model tab has eleven sections: Model data, Soil layers, Groundwater, Wall and embedment, Base heave, Ground anchor, Surcharge, Earthquake, Design factors, Sheet pile and Design code. Each opens when you click its title; Next and Back at the foot walk you through them, and Analyze waits in the bar below. In the tables a unit shown two or three times, such as m · ft, gives the units of SI · kN, SI · tf and US in turn, and equal ones are merged. Defaults are shown in SI. After a switch of the unit system the boxes show the converted values, unrounded.
Model data
The first section holds the model name, Save to file…, Open file…, Quick Save… with its list and Load and Delete, and Reset to defaults. It works as described in the workspace guide. Its note says that the page opens every time on the default model, not analysed.
Model data.
Soil layers
The section is a form over a table. The New layer form takes the name and the values of one layer; + Add layer puts it at the bottom of the table, and a counter beside the button shows how many of the four layers there are. The Soil layers table lists every layer with a swatch of its colour on the drawing. Press a row, or the layer on the drawing, to change it in the form; press × to take it out. Every layer is undrained clay, from the top of the wall down the whole profile, across the dredge line and below the toe. The layers below the dredge line act on both faces. The profile opens with the two layers of the example in the table; the New layer form opens with the values of a further layer, which differ.
Soil layers: the form over the table.
Layer fields (the form, and each row of the table)
Field
Default
What to enter
Name —
automatic
Optional; empty gives Clay-1, Clay-2 …
Thickness H m · ft
5 (Clay-1); 2 (form)
At least 0.1 m. The last layer has none: its row shows a dash (“it runs on below the toe”).
Moist unit weight γ kN/m³ · t/m³ · pcf
18, 19 (rows); 15.9 (form)
At least 1. Used above the water table, or everywhere without one.
Saturated unit weight γsat kN/m³ · t/m³ · pcf
19, 19.5 (rows); 19.33 (form)
At least 1, and above 9.81 kN/m³ where there is a water table: below it γsat − γw is used.
Undrained shear strength cu kPa · kg/cm² · psf
30, 70 (rows); 30 (form)
At least 1 kPa. The layer is taken with φ = 0, so Ka = Kp = 1.
At least 0.1 MN/m³. The spring stiffness of the displacement only.
Groundwater
Water table has the buttons None and Present; the unit weight of water, γw = 9.81 kN/m³, is shown. With Present, Level in the excavation appears with Same as retained side and Different level, and a box for the water table depth Dw below the top of the wall on the retained side (2 m by default) and, for a different level, Dw,exc in the excavation (6 m by default; both at least 0 m). With the same level the pore pressures of the two faces cancel from the net pressure; with different levels their difference is added as a net hydrostatic pressure, without seepage. With None the unit weight is the moist one everywhere and the only water is that of the tension crack.
Groundwater, with the table None.
Wall and embedment
Depth of embedment has Calculated by the program, where the design depth comes out of the analysis, and Given — verify it, where you type the depth D of the toe below the dredge line (default 5 m, at least 0.1 m) and the module verifies it. L, the height of the wall above the dredge line, is 5 m by default and at least 0.5 m.
Wall and embedment.
Base heave
Bottom heave check has Check (the default) and Not checked. With Check you give the width of the excavation B (10 m, at least 0.5 m), optionally its length in plan Lexc and the depth T of a hard stratum below the dredge line, and the required factor of safety FSreq (1.5; from 1 to 3). The module compares the shear resistance of the clay under the base with the weight of the soil beside the cut; see Analyze and read the results.
Base heave.
Ground anchor
The wall is a cantilever until an anchor is added. The New anchor form takes one row; + Add anchor puts it in the table below, up to four rows, with a counter. Each row has its depth za below the top of the wall (above the dredge line, at least 0.25 m from the next row), its horizontal spacing s along the wall, its inclination α below the horizontal (0° to 60°), the prestress P0, the free length Lf, the bond length Lb (at least 0.5 m) and the tendon area At. Defaults of the form: 1.5 m, 2.5 m, 15°, 250 kN, 7 m, 6 m and 5.6 cm². Tendon: Strand (default) or Bar sets the minimum free length checked, 4.5 m or 3 m; it appears once a row exists. With anchors the wall is solved by the free earth support method: see Cantilever or anchored.
Ground anchor.
Surcharge
Up to six loads on the ground behind the wall. In the New load form choose the Kind of load: Uniform (a surcharge q on the whole retained surface, 10 kPa), Strip (a strip load qs, 20 kPa, between a near edge x1 = 1 m and a far edge x2 = 3 m from the wall) or Point (a load Q of 50 kN at x = 2 m); then + Add load. With the earthquake on, each load also has a combination factor ψ2 (1, from 0 to 1). A uniform load adds to the vertical stress at every depth; strip and point loads add lateral pressure on the wall. The lateral pressure of a strip or point load is worked out in the Surcharge loads manuals.
Surcharge.
Earthquake
Seismic situation has Not checked and Pseudo-static check. The check is of the wall as designed: the undrained wedge of the clay with its critical plane at 45°, both senses of the vertical coefficient, and your kh (0.15, from 0 to 0.6) and kv (0.075, from 0 to 0.4) from your seismic code.
Earthquake.
Design factors
Three choices and a number; they are explained in How the module treats the clay. Embedment route: Increase D theory by a factor (the factor f, 1.5 by default, from 1 to 1.6) or Factor of safety on the passive pressure (the factor FSp, 1.5, from 1 to 3). Active pressure of the clay below the dredge line: Classical — not cut at zero or No-tension cutoff. Tension crack above the dredge line: Water-filled to its top or Dry — water only below the water table.
Design factors.
Sheet pile
The Steel grade is S235, S275 (default) or S355, or Typed; the yield strength fy follows the grade (275 000 kPa for S275, chip “from the grade”) until you type a value of your own, and must be at least 100 000 kPa. Section modulus given says which catalogue column the value of W is: Elastic Wel (default) or Plastic Wpl. W (1 400 cm³/m) and I (21 000 cm⁴/m) are optional. Without W the module gives the modulus the wall needs and verifies no section; without I it gives no displacement.
Sheet pile.
Design code
Verify the steelwork to: EN 1993-1-1 (Eurocode 3) with the partial factor γF on the earth-pressure moment (1.35, from 1 to 1.6) and γM0 on the resistance (1, from 1 to 1.3), or AISC 360-22, where LRFD takes the load factor γH on the earth pressure (1.6, from 1 to 2) and ASD none.
Design code.
How the module treats the clay: the crack, the net pressure and the anchors
The tension crack above the dredge line
In a retained clay the active pressure σv − 2cu is negative near the top, down to the depth zc where it is zero. The module takes the clay as unable to pull on the wall: no soil pressure acts down to zc, and the crack is a gap. In the example zc = 2 × 30 / 18 = 3.33 m. Water-filled to its top, the default, loads the wall over the crack with the water pressure γw (z − zt), zt being the top of the crack: 9.81 × 3.33 = 32.70 kPa at zc, which is 54.50 kN/m of the 79.50 kN/m resultant. Dry — water only below the water table leaves that water out. The drainage of the site must then keep the crack dry, and the module says so as a warning. The difference is large because the crack water is the larger part of the load: with a dry crack the example gives Dtheory = 0.6780 m and Mmax = 15.53 kN·m/m instead of 2.288 m and 181.9 kN·m/m.
The net pressure of 4cu below the dredge line
Below the dredge line the clay of the retained side pushes with σv − 2cu and the clay of the excavation side resists with σv + 2cu, so the net pressure is the difference of the overburdens of the two faces less 4cu. In the example, just below the dredge line: 90 − 140 − 0 − 140 = −190 kPa, which is σ3; the minus sign means toward the retained soil, so the clay below the dredge line holds the wall. At the toe the pressure on the other face is σ4 = 4cu + (the difference of the overburdens) = 370 kPa. Because the undrained cohesion acts on both faces, the unit weight of the clay below the dredge line does not change the answer in a profile of one layer there: Clay-2 at 21 instead of 19 kN/m³ gives the same Dtheory = 2.288 m.
Classical — not cut at zero, the default, keeps the active pressure σv − 2cu of the clay below the dredge line even where it is negative, as the classical cohesive free-earth formulation does; this is what gives the constant σ3. No-tension cutoff does not take the active pressure of the clay below zero on either face below the dredge line. The result depends on the choice. In the example the cutoff gives Dtheory = 2.691 m, Ddesign = 4.036 m and Mmax = 187.3 kN·m/m, against 2.288 m, 3.433 m and 181.9 kN·m/m. The Calculations tab states the figures of the other choice “for comparison”.
Can the wall be balanced? The check before the embedment
Before it looks for the depth, the module checks that a depth exists. The net pressure just below the dredge line, 4cu less the difference of the overburdens, must turn toward the retained soil. If it does not, no embedment can balance the diagram and the module stops with “No depth of embedment balances the diagram” and the advice to raise cu or lower the retained height. In the example, Clay-2 with cu = 10 kPa leaves 90 − 40 = +50 kPa below the dredge line, toward the excavation, and stops; with cu = 30 kPa the net pressure is −30 kPa and the embedment is long, Dtheory = 7.303 m.
The depth of embedment and its safety
The theoretical depth is the one at which the diagram is in equilibrium with no margin. The margin goes in by one of two routes. With Increase D theory by a factor the design depth is f × Dtheory: 1.5 × 2.2884 = 3.433 m, a pile of 5 + 3.433 = 8.433 m. With Factor of safety on the passive pressure the whole passive pressure (σv + 2cu) is divided by FSp before the depth is found; the card then reads Required embedment depth (passive pressure / FSp). With FSp = 1.5 the example gives 2.775 m and with 2 it gives 3.174 m. The maximum moment is that of the theoretical diagram; stretching the toe by f does not change it.
With Given — verify it the module checks your depth against the required one. At D = 3.5 m (the required depth is 3.433 m) the card Design embedment depth — given reads PASS, with the required depth and the factor of safety the given depth mobilises on the passive pressure, 2.470. At 3 m it reads FAIL (1.772) with a warning, and with a depth shorter than Dtheory the module stops (see Messages).
Cantilever or anchored
With no anchor the wall is a cantilever: it is fixed only by the clay below the dredge line, and the diagram is closed with the toe reversal σ4 over the block L5. With one or more anchor rows the wall is held near its top. For one row the module uses the free earth support method: the embedment comes from the moments about the anchor and the anchor force from horizontal equilibrium; the diagram is cut off at the free toe with no reversal. With two to four rows the structure is idealised with hinges at the anchors below the uppermost and simple spans between them, with the embedment by free earth support about the lowest anchor. With anchors the first card reads Theoretical embedment depth — the equilibrium depth of the adopted limit-equilibrium model, not a minimum constructible penetration. The anchor reaction per metre of wall is F; the force in each anchor is TLEM = Fs / cos α, and its vertical part is TLEM sin α.
One anchor row at 1.5 m (15°, 2.5 m apart) on the example gives Dtheory = 0.1659 m, Ddesign = 0.2489 m (a pile of 5.25 m), Mmax = 28.05 kN·m/m, F = 47.97 kN/m and TLEM = 124.2 kN. A hand check: F = P − σ3D = 79.50 − 190 × 0.1659 = 47.97 kN/m, and 47.97 × 2.5 / cos 15° = 124.2 kN. The module notes that the equilibrium depth of a strong clay can be very short “not a minimum constructible penetration”; choose the penetration from driveability, heave, overall stability and practice. The Theory tab gives up to about 6 m as the usual range of a cantilever wall.
Analyze and read the results
Press Analyze. The bar changes to Analysed — the sheet-pile wall calculated. The module stays on the Model tab (the bar, with Warnings or Notes, Edit inputs and Analyze, belongs to that tab): open the Results tab. The Section view now shows the net pressure.
The tab has three drawings, then the tables, and the cards last, under Sheet-pile wall:
Net lateral pressure diagram on the cantilever wall: the active diagram above the dredge line in pieces (1, 2 …), P and its height z̄ above E, the net line through E, σ3 and σ4 and the block L5. The pressure axis is compressed so that the toe ordinates fit beside the active block.
Shear force and bending moment along the wall: Mmax where the shear is zero, green where the sheet pile given carries it.
Displacement and bending moment — subgrade reaction method: the displacement of the wall on springs, indicative.
The pressure, shear and moment diagrams of the example.
Values, step by step lists the step values; five more tables give the working in numbers: the effective overburden, pore pressures and net pressure at the depths where a line of the diagram changes; the pieces of the pressure diagram above E; the trial depths of embedment with the residual about the toe (it changes sign at the root); the layers down to the toe with their springs, which also lists φ′, cu, K0, Ka and Kp of each layer; and the displacement, moment and pressures along the wall. With anchors the trial-depth table gives the moment about the anchor, and a table of the anchors is added.
Values, step by step, for the example.
Card
What it is
The example
Theoretical embedment depth Dtheory
The depth at which the diagram is in equilibrium, no margin.
2.288 m
Design embedment depth Ddesign
After the safety route; the total pile length is shown beneath the cards.
3.433 m (8.433 m long)
Maximum bending moment Mmax
At the zero of the shear, below E.
181.9 kN·m/m
Section modulus the sheet pile needs Wreq
The number a sheet-pile table is looked up with (EN 1993-1-1 or AISC 360-22 as chosen).
893.0 cm³/m
Utilisation of the sheet pile ηsp
Design moment over the resistance of the section given; PASS up to 1, FAIL above. Only when W is given.
0.6379 PASS
Factor of safety against bottom heave FSheave
Only when the heave check is on; PASS at or above FSreq.
4.234 PASS
Top displacement of the wall ytop
Subgrade reaction, indicative; only when I is given.
9.362 mm
The cards of the example.
The sheet pile
The moment is factored once. With EN 1993-1-1, MEd = γFMmax = 1.35 × 181.91 = 245.58 kN·m/m, Wreq = MEdγM0 / fy, and the section given is held to Mc,Rd = Wfy / γM0 (with the elastic modulus, first yield). With AISC 360-22 the example needs 1,176 cm³/m by LRFD (Mn with φb = 0.90 and the moment factored by γH = 1.6) and 1,105 cm³/m by ASD (Ωb = 1.67), with the utilisation 0.8400 and 0.7891. The depth of embedment keeps the margin of its own route and is not factored again. S355 instead of S275 lowers Wreq to 691.8 cm³/m, S235 raises it to 1,045 cm³/m. The grade fills fy; type fy with Typed for any other steel.
Bottom heave
The base can fail by bulging up. The module compares the resistance of the clay under the base, 5.14cu(1 + 0.2B″/Lexc) with the cohesion of Clay-2 below the dredge line, plus the side shear csideH/B′ along the retained height, with the weight of the retained soil σv(H) plus the surcharge: uniform loads in full, a strip load by its part within B′ spread over B′, a point load within B′ spread over a square B′ × B′, and a load beyond B′ left out. Water standing on the base is deducted from σv(H). B′ is B/√2, or the depth T of a hard stratum when that is smaller, B″ = √2 B′, and without Lexc the excavation is taken as long. The embedment of the sheet pile is not credited. For the example: (5.14 × 70 + 30 × 5 / 7.07) / 90 = 4.23. Other runs: a 15 m wide excavation with Clay-2 at 40 kPa gives 2.442; a hard stratum 1 m below the dredge line, 5.664; a length of 20 m, 4.633; a 20 kPa surcharge, 3.464. The module notes that the formula is the source’s, extended to layers: the clay under the base carries the bearing term, the cohesion averaged over the retained height the side shear.
Anchored wall
With one anchor row the embedment step becomes free earth support.
With anchors the embedment step reads Depth of embedment by the free earth support method, and a table The anchors, their reactions and their bond zones gives for each row za, s, α, F, TLEM, TLEM sin α, P0, the position xb of the start of the bond zone behind the wall, the distance xreq it must have behind the active wedge and a Check (PASS in the example: 6.761 m against 3.188 m). The top displacement can be negative: y is positive toward the excavation. A note gives the vertical component of the anchor forces: in the example “12.85 kN/m per metre of wall in all”; the sheet pile is verified in bending only.
The earthquake
With the pseudo-static check on, a card Embedment required in the seismic situation DE is added with its own verdict. With kh = 0.15 and kv = 0.075 the example gives DE = 2.503 m, PASS against Ddesign = 3.433 m, and Mmax,E = 184.99 kN·m/m; the two senses of kv are tabulated. The static results above are unchanged. With kh = 0.45 and kv = 0.2 the required depth is 3.58 m, above the design depth, and the module warns (see Messages).
Using the numbers
The forces are per metre of wall (kN/m, tf/m or kip/ft), the moments in kN·m/m, tf·m/m or kip·ft/ft, and W and I per metre of wall. The anchor force TLEM is per anchor.
Depths are measured below the dredge line; the total length of the sheet piles is L + Ddesign.
Values are rounded where they are drawn. After a unit switch the drawings keep their labels in m, kN and kPa; the cards, the tables and the report are re-stated.
The default example in SI · tf gives Mmax = 18.55 tf·m/m (181.91 kN·m/m is 18.55 tf·m/m) and in USDtheory = 7.508 ft, Mmax = 40.89 kip·ft/ft (181.91 kN·m/m is 40.89 kip·ft/ft), Wreq = 16.61 in³/ft and ytop = 0.3686 in. The heave working carries its intermediate values forward at the precision printed in the chosen units (for example 1.46 ksf), so US reads 4.229 and SI · tf 4.233 against 4.234 in SI · kN.
The Calculations tab, the report and the Theory tab
The Calculations tab opens with Given and what is sought and then writes out twelve numbered steps with your numbers, ending with the notes and the answer. With anchors the embedment step is the free earth support one.
The first block of the Calculations tab.
Earth-pressure coefficients — the undrained pressures, Ka = Kp = 1, and 2cu of each layer.
Active pressure above the dredge line — σv at the boundaries, the tension crack depth and its water, σ′2 at the dredge line and, for comparison, the depth and moment with a dry crack.
Net pressure below the dredge line and the zero point E — p written out, the table of overburdens, pore pressures and net pressure at each depth where it changes; E at the dredge line when the net pressure is already negative there. For comparison, the figures with the no-tension cutoff.
Resultant of the diagram above E and its arm — the pieces, P and z̄.
Depth of the toe from horizontal and moment equilibrium — σ3, σ4, L5 and the trial depths with their residual (with anchors: Depth of embedment by the free earth support method).
Theoretical and design depth of embedment, and the total pile length.
Maximum bending moment — the depth of zero shear and the moment, with the diagram.
Take the design moment.
The section modulus EN 1993-1-1 (or AISC 360-22) asks for.
The section given verified.
Bottom heave of the base.
Wall displacement — subgrade reaction method, with the moment of that model, which is indicative.
The tab ends with Notes and assumptions and the Answer. A drawing of the net pressure and one of the shear and moment sit inside the steps; the working of step 9 for the example, Wreq = 245.58 × 1.00 / 275 000 = 893.01 cm³/m, is:
One step of the Calculations tab.
The report
In the Report tab fill in the cover (project, location, client, report number, date, prepared by, title or qualification, checked by, and optional notes). The details are kept in this browser and saved with the model file. Save as PDF and Download Word (.docx) produce the summary report; the preview below the buttons is the report itself.
The report has seven parts: 1 Introduction and scope, 2 Input data, 3 Calculation (3.1 to 3.12, one for each step), 4 Results, 5 Assumptions and notes, 6 Summary and 7 References. The cover gives the answer and states the units.
The Report tab: the cover details, the two buttons and the first page.
The Theory tab
The Theory tab has seventeen sections: Sheet-pile walls and this module; How a cantilever wall moves; Active pressure of the retained clay; The net pressure in the clay; Equilibrium and the depth of embedment in clay; The depth of embedment; Water at different levels on the two faces; Verifying the sheet pile to EN 1993-1-1; Verifying the sheet pile to AISC 360-22; The anchored wall; The seismic situation; The displacement of the wall; The base of the excavation: bottom heave; A worked example, by hand and by the module; The opening wall, verified to EN 1993-1-1; What the module assumes; and References. Each opens when you click its title.
Worked example: the module’s own example
The module opens on this example, so you can follow the numbers on your own screen.
Inputs of the example
Section
Input
Value
Soil layers
Clay-1
5 m; γ = 18 kN/m³ (saturated 19); cu = 30 kPa; kh = 15 MN/m³
S275 (fy = 275 000 kPa), W = 1 400 cm³/m; EN 1993-1-1, γF = 1.35, γM0 = 1
Step 1: the pressure above the dredge line
σv = 18 × 5 = 90 kPa at the dredge line and σa = 90 − 2 × 30 = 30.00 kPa. The crack reaches zc = 60 / 18 = 3.333 m, where its water pressure is 9.81 × 3.333 = 32.70 kPa. The diagram has two pieces: the crack water, ½ × 32.70 × 3.333 = 54.50 kN/m with its centroid 5 − 2.222 = 2.778 m above the dredge line, and the clay, ½ × 30.00 × 1.667 = 25.00 kN/m at 5 − 4.444 = 0.5556 m.
The net pressure just below the dredge line is already negative, so the zero point E is at the dredge line (L3 = 0).
Step 2: the net pressure and the toe
σ3 = 140 + 140 − 90 = 190.00 kPa toward the retained soil; at the toe σ4 = 140 + 90 + 140 = 370.00 kPa. For a trial depth D horizontal equilibrium gives L5 = 2 (190 D − P) / (190 + 370), and moment equilibrium about the toe is a residual that changes sign at the right depth:
P (D + z̄) − 190 D² / 2 + L5² (190 + 370) / 6 = 0
At D = 2.288 m: L5 = 2 × (190 × 2.288 − 79.50) / 560 = 1.269 m and 79.50 × 4.367 − 95 × 5.235 + 1.610 × 560 / 6 = 347.2 − 497.3 + 150.3 = 0. So Dtheory = 2.288 m, Ddesign = 1.5 × 2.288 = 3.433 m, and the pile is 5 + 3.433 = 8.433 m long. These are the first cards of the Results tab; the module’s trial table shows the residual 78.15, 41.80, 0 and −47.25 kN·m/m at 1.831, 2.060, 2.288 and 2.517 m.
Step 3: the moment and the sheet pile
The shear is zero z′ = P / σ3 = 79.50 / 190 = 0.4184 m below E, where Mmax = 79.50 × (0.4184 + 2.079) − 190 × 0.4184² / 2 = 181.91 kN·m/m. Then MEd = 1.35 × 181.91 = 245.58 kN·m/m, Wreq = 245.58 / 275 000 = 893.0 cm³/m, Mc,Rd = 1 400 × 10⁻⁶ × 275 000 = 385.00 kN·m/m and ηsp = 245.58 / 385.00 = 0.6379: PASS.
Every figure above is one the module gives (2.288 m, 3.433 m, 181.9 kN·m/m, 893.0 cm³/m, 0.6379, 4.234).
The same wall with the other options
Dry crack: P = 25.00 kN/m at 0.5556 m, Dtheory = 0.6780 m, Mmax = 15.53 kN·m/m (by hand: 0.678 m and 15.53 kN·m/m), a warning, and 0.05447 for the utilisation.
One anchor row: F = 79.50 − 190 × 0.1659 = 47.97 kN/m; 0.1659 m, 28.05 kN·m/m (see Cantilever or anchored).
Surcharge 20 kPa, uniform: σa at the dredge line becomes 50.00 kPa, zc = 2.222 m, σ3 = 170 kPa, Dtheory = 2.413 m, Mmax = 175.3 kN·m/m, and the heave factor falls to 3.464 (hand: 381.0 / 110 = 3.46).
Clay-1 20 kPa: Dtheory = 2.315 m (hand: 2.3145 m; the module rounds to 2.315), Mmax = 172.6 kN·m/m.
Other unit systems
In SI · tf the example gives Mmax = 18.55 tf·m/m (181.91 / 9.807) and in USDtheory = 7.508 ft (2.288 m × 3.2808), Mmax = 40.89 kip·ft/ft (181.91 × 0.2248) and Wreq = 16.61 in³/ft (893.0 cm³/m / 53.76): the same wall in other units. The utilisation 0.6379 is the same in all three. The heave factor differs in the last digit (US 4.229, SI · tf 4.233, SI · kN 4.234) because its working carries intermediate values forward at the precision printed in the chosen units.
How each input changes the answer
Each row changes one thing in the example (two clay layers, Clay-1 5 m thick, γ = 18 and 19 kN/m³, γsat = 19 and 19.5, cu = 30 and 70 kPa, L = 5 m, no water and no load, f = 1.5, water-filled crack, classical formulation, S275, W = 1 400 cm³/m, EN 1993-1-1) and runs the module again. The numbers are the ones the module gives. Mmax is in kN·m/m. In the passive-route rows there is no theoretical depth (a dash) and the design depth is the required depth Dreq.
The soil and the wall
Soil and wall
Change
Dtheory Ddesign m
Mmax ηsp
The example (reference)
2.288 3.433
181.9 0.6379
cu of Clay-1 = 20 kPa (a shallower crack)
2.315 3.472
172.6 0.6053
cu of Clay-1 = 50 kPa (the crack reaches the dredge line)
2.811 4.216
243.9 0.8554
cu of Clay-2 = 50 kPa
3.083 4.624
194.0 0.6803
cu of Clay-2 = 100 kPa
1.787 2.680
175.5 0.6153
cu of Clay-2 = 120 kPa
1.597 2.395
173.4 0.6080
L = 4 m
2.639 3.959
132.5 0.4648
L = 6 m
2.790 4.185
267.2 0.9371
γ of Clay-1 = 20 kN/m³
2.332 3.498
178.8 0.6269
γ of Clay-2 = 21 kN/m³
2.288 3.433
181.9 0.6379
Clay-1 3 m thick, Clay-2 retained below it
2.822 4.232
244.4 0.8569
cu of Clay-2 = 30 kPa
7.303 10.95
270.6 0.9489
The weaker or the stronger Clay-2 moves Dtheory the most among the rows tabulated, because σ3 = 4cu − (the overburden) is the pressure that holds the wall: 50 kPa gives 3.083 m and 100 kPa 1.787 m, while Mmax changes little (194.0 and 175.5 kN·m/m), as the retained pressure is the same. The strength and weight of the retained clay change the load: Clay-1 at 50 kPa gives a large moment, Mmax = 243.9 kN·m/m, because its crack reaches the dredge line and the crack water (9.81 × 5 = 49.05 kPa) becomes the load. The unit weight of Clay-2 drops out of the answer when Clay-2 alone lies below the dredge line, as in the row with 21 kN/m³.
Water, the crack and the loads
Water, crack and loads
Change
Dtheory Ddesign m
Mmax ηsp
Uniform surcharge 20 kPa
2.413 3.619
175.3 0.6148
Strip load 20 kPa from 1 m to 3 m
2.775 4.163
260.4 0.9131
Point load 50 kN at 2 m
2.469 3.704
210.2 0.7372
Water table 2 m, same level on both faces (γsat 19 and 19.5)
2.134 3.202
170.7 0.5984
Water 2 m behind the wall, 5 m in the excavation
2.764 4.146
238.8 0.8373
Dry crack
0.6780 1.017
15.53 0.05447
No-tension cutoff
2.691 4.036
187.3 0.6568
No-tension cutoff, dry crack
0.8395 1.259
16.10 0.05647
The margin, the anchor and the steel
Safety, anchor and steel
Change
Dtheory Ddesign m
Mmax ηsp
f = 1.3
2.288 2.975
181.9 0.6379
f = 1.0
2.288 2.288
181.9 0.6379
Passive route, FSp = 1.5
— 2.775
187.5 0.6575
Passive route, FSp = 2
— 3.174
192.1 0.6736
One anchor row at 1.5 m
0.1659 0.2489
28.05 0.09837
Given D = 3 m
2.288 3.000
190.1 0.6666
Given D = 5 m
2.288 5.000
209.7 0.7353
W = 800 cm³/m
2.288 3.433
181.9 1.116
AISC 360-22, LRFD
2.288 3.433
181.9 0.8400
AISC 360-22, ASD
2.288 3.433
181.9 0.7891
S355 instead of S275 does not change the pressure or the depth: Wreq falls to 691.8 cm³/m and ηsp to 0.4941. The given-depth rows show how the verdict follows the depth: 3 m is short of the 3.433 m the design needs (FAIL and a warning), 5 m passes. The W = 800 cm³/m row fails (η above 1) with a warning, and a dry crack or an anchor reduces the demand on the pile enormously.
Messages: when the module stops, and what it says
The module checks the numbers it needs before it calculates. When one cannot be used it stops and nothing is calculated; otherwise it calculates and lists warnings and notes.
A value outside its range stops the analysis with a window titled Cannot analyse — 1 input error (or 2 input errors …) that lists each message; the box of the value is marked in red in the Model tab. The limits are shown in the units of the unit system chosen.
A condition of the solution that is not met stops it in a window titled Cannot analyse — a condition of the solution is not met, which ends “Nothing was calculated. Change the inputs marked in red, then press Analyze again.”
Warnings (△) and notes (○) are listed on the Warnings (n) or Notes (n) button of the bar; the button reads Warnings when there is at least one warning. The window is titled Warnings (1) or Notes and assumptions (7).
The window Analyze opens when the wall height is 0.2 m.
The window for Clay-2 with cu = 10 kPa.
Stops: a value out of range
When
The message
What to do
L below 0.5 m, or empty
“Height of the wall above the dredge line (L) must be at least 0.5 m.” / “… is missing.”
Enter the height.
A thickness below 0.1 m
“Thickness (H1) must be at least 0.1 m.”
Enter a thickness.
cu below 1 kPa, or empty
“Undrained shear strength (cu,1) must be at least 1 kPa.” / “… is missing.”
Enter cu of the layer.
A unit weight below 1
“Moist unit weight (γ1) must be at least 1 kN/m³.”
Enter the unit weight.
A negative water depth
“Water table depth (retained side) (Dw) must be at least 0 m.”
Enter zero or more.
f outside 1 to 1.6
“Depth increase factor (f) must be at least 1.” / “… at most 1.6.”
Enter f in range.
FSp below 1
“Factor of safety on the passive pressure (FSp) must be at least 1.”
Enter 1 or more.
fy below 100 000 kPa
“Yield strength (fy) must be at least 100000 kPa.”
Choose a grade or type fy.
W below 1 cm³/m
“Section modulus of the sheet pile (W) must be at least 1 cm³/m.”
Enter W or leave it empty.
D given below 0.1 m
“Depth of embedment below the dredge line (D) must be at least 0.1 m.”
Enter the depth.
B below 0.5 m
“Width of the excavation (B) must be at least 0.5 m.”
Enter the width.
α above 60°, Lb below 0.5 m
“Inclination below the horizontal (α) must be at most 60°.” / “Bond (root) length (Lb) must be at least 0.5 m.”
Enter a value in range.
kh above 0.6
“Horizontal seismic coefficient (kh) must be at most 0.6.”
Enter kh from your code.
A different level chosen, none typed
“Water level in the excavation (Dw,exc) is missing.”
Enter it or choose Same as retained side.
When more than one value is wrong the window lists them together: L = 0.2 m and cu = 0 of Clay-1 give “2 input errors”. In the table the layer or row number is part of the symbol: H1, cu,1 and γ1 belong to layer 1.
Stops: a condition of the solution
When
The message
What to do
γsat at or below 9.81 with a water table
“Clay-1: saturated unit weight must exceed γw. Below the water table the overburden uses γ′ = γsat − γw. Enter the saturated unit weight.”
Enter γsat above 9.81 kN/m³.
An anchor at or below the dredge line
“The anchor must stand above the dredge line. za is its depth below the top of the wall: 0 ≤ za < L. …”
Enter za < L.
Two rows less than 0.25 m apart
“Anchor row 2: two rows of anchors stand at nearly the same depth. The rows need at least 0.25 m between them to be separate supports. …”
Separate the rows.
A strip with the far edge not beyond the near edge
“Load 1 (strip load): the strip must have its far edge beyond its near edge. x1 is the distance of the near edge from the wall and x2 that of the far edge: 0 ≤ x1 < x2. …”
Enter x1 < x2.
No depth balances the wall
“No depth of embedment balances the diagram. The net pressure below the dredge line never falls to zero, or the passive resistance never catches up with the active thrust. In the clay the net pressure 4cu less the difference of the overburdens of the two faces must turn toward the retained soil (the source’s σ6 = 4cu − (γL1 + γ′L2) > 0): raise cu, lower the retained height.” With a different water level “or the unbalanced head”, and with the passive route “reduce FSp”.
Raise cu below the dredge line or lower L. Clay-2 at 10 kPa, or an anchor at 3 m in the example, gives it.
A given depth too short
“NO EQUILIBRIUM AT THE GIVEN EMBEDMENT — even full passive resistance is insufficient. At the given depth D = 2.00 m the wall is not in equilibrium even with the full passive coefficient: the diagram with Kp needs Dtheory = 2.29 m. No factor of safety can be given for it. Drive the sheet pile deeper than 2.29 m — the design route asks 3.43 m — or choose “Calculated by the program” …”
Give a depth above Dtheory, or let the module calculate it.
Warnings
A warning does not stop the analysis; the results are calculated and the bar reads Warnings (n).
When
The warning
What to do
The pile given does not carry the moment
“The sheet pile given does not carry the design moment: MEd / Mc,Rd = 1.12. Mc,Rd = 220.00 kN·m/m per metre of wall, against 245.58 kN·m/m. The wall asks for 893.01 cm³/m. Take a heavier sheet pile or a higher grade.” (with W = 800 cm³/m; the card reads FAIL)
A heavier pile or a higher grade.
The given depth is short of the design depth
“The given depth of embedment D = 3.00 m is shorter than the depth the design requires, 3.43 m. At the given depth the passive resistance mobilises a factor of safety of only 1.77 on the passive pressure. Drive the sheet pile deeper, or choose “Calculated by the program” …” The displacement is then marked indicative only.
Deepen the wall.
A dry crack
“The tension crack is taken dry: the drainage of the site must keep it dry. No water acts in the crack. Keep the dry crack only where the drainage of the site keeps it dry; otherwise take it water-filled, the default.”
Water-filled unless the site is drained.
The seismic depth is longer
“The design embedment is too short for the seismic situation: DE = 3.58 m > Ddesign = 3.43 m. … Drive the sheet pile to at least DE below the dredge line, or review kh and kv.” (with kh = 0.45, kv = 0.2)
Deepen the wall or review kh and kv.
The water table is below the dredge line
“The water table (Dw = 6.00 m) lies below the dredge line (L = 5.00 m), inside or below the embedment. … The embedment is taken as submerged on both faces over its whole depth … as if the table stood at the dredge line: conservative … If the table is certainly below the toe, set the water table to None.”
None, if the table is below the toe.
The bond zone is too close to the wall
“The bond zone of anchor row 1 is too close to the wall (free length under 4.5 m). … Lengthen the free length or steepen the anchor so that its bond zone starts at least 4.22 m behind the wall, with a free length of at least 4.5 m.” (with Lf = 3 m, Lb = 2 m; the check reads FAIL)
A longer free length.
The toe block does not fit
“The toe block L5 = 0.000 m does not lie between 0 and L4 … The net-pressure diagram cannot be closed. … the depth printed here is not a valid design.” With a second warning that the subgrade reaction model finds no equilibrium. It appears for a water table at the top of the wall, Dw = 0.
Check the water level and the soil.
Notes
The Notes (7) of the example, and their conditions:
The tension crack is taken filled with water to its top; choose the dry crack only where the drainage of the site keeps it dry.
When the equilibrium depth is very short: “Dtheory is the equilibrium depth of the adopted limit-equilibrium model, not a minimum constructible penetration …” (a strong clay, an anchored wall, a dry crack).
The sheet pile is checked on the modulus given, as the modulus of the whole wall; a wall of U-piles may have its modulus reduced where the interlocks can slip, a wall of Z-piles carries the full value.
The overall stability of the wall and the ground, a deep slip surface below the toe, is verified separately with a slope-stability analysis of the excavation.
The classical formulation, the factored moment, the extension of the heave formula to layers and the subgrade reaction displacement (a model parameter kh; indicative, no displacement limit is checked) are stated as assumptions; with an anchor the note on the vertical component of the anchor forces; with the earthquake the pseudo-static assumptions; with different water levels the independent hydrostatic pore pressures.
Without W: “No section modulus was given for the sheet pile: the modulus it needs is found, and no section is verified.” Without I: “No second moment of area was given for the sheet pile: the displacement of the wall is not computed.”
Good practice and common mistakes
Enter every layer as the clay it is, with cu. The module takes the profile as undrained from top to bottom; for a sand backfill use Sheet pile in sand, and for sand and clay together Anchored sheet pile on layered soil.
Decide the crack before the number. A water-filled crack is the larger load on the wall in the example (54.50 of 79.50 kN/m); run the dry crack only if the site is drained, and compare.
Compare the classical and cutoff options for a strong clay below the dredge line; the result depends on the choice.
The theoretical depth is not a length to build. Choose the penetration from driveability, heave, overall stability, the long term and practice; the module says so itself for very short depths.
Check the base. Keep the heave check on for a cut in clay and give the excavation width; a hard stratum below the cut raises the factor.
Check the long term separately. The module works in total stress; the drained condition of the same clay is a separate design case.
Give the section modulus to have the pile verified, and the second moment of area to have the displacement; type fy for a steel that is not one of the three grades.
Read the displacement as indicative. It rests on kh, a model parameter, and on characteristic pressures.
Do not forget the overall stability. A slip surface below the toe is not part of the design of the wall.
Save before you leave. The page opens on the default model; use Save to file… or Quick Save….
Frequently asked questions
How does the module find the depth of embedment in clay?
It builds the net pressure diagram — the active pressure of the retained clay above the dredge line, and below it the difference of the two faces, the overburden difference less 4cu — closes it with the toe reversal, and solves horizontal and moment equilibrium for the depth at which the wall balances. The design depth is the theoretical depth times f, or the depth found with the passive pressure divided by FSp. For the example: 2.288 m theoretical and 3.433 m design.
What is the tension crack and why does it carry water?
Where σv − 2cu is negative the retained clay cannot pull on the wall, so no soil pressure is taken there and a crack opens. By default the crack is water-filled to its top and its water pressure loads the wall; choose the dry crack only where the site is drained. In the example the crack is 3.33 m deep and its water is 54.50 of the 79.50 kN/m.
Why does the module say that no depth of embedment balances the diagram?
The net pressure just below the dredge line, 4cu less the difference of the overburdens of the two faces, must turn toward the retained soil. If the clay below the dredge line is too weak for the retained height it does not, and no embedment can balance the wall: raise cu or lower L. Clay-2 at 10 kPa under the example’s 5 m of retained clay stops the analysis.
What do the classical and the no-tension cutoff options change?
Below the dredge line the classical formulation keeps the active pressure σv − 2cu of the retained clay even where it is negative; the cutoff does not take the active pressure of the clay below zero on either face below the dredge line. In the example the cutoff gives 2.691 m of Dtheory against 2.288 m. The Calculations tab gives the figures of the other option for comparison.
How do I make it an anchored wall?
In Ground anchor fill the New anchor form and press Add anchor; with one row the wall is solved by the free earth support method, with two to four rows by the hinge idealisation. The module gives F per metre of wall, TLEM per anchor and the position of the bond zone. One row at 1.5 m on the example gives Dtheory = 0.1659 m and TLEM = 124.2 kN.
Can I give the depth of embedment and have it checked?
Yes: in Wall and embedment choose Given — verify it and type D. The card then reads PASS or FAIL with the required depth and the factor of safety the given depth mobilises. A depth shorter than the theoretical one stops the analysis; with the example, 3 m is a FAIL with a warning and 3.5 m a PASS.
Which codes does it check the steel to?
EN 1993-1-1 with the factors γF and γM0, or AISC 360-22 by LRFD (load factor γH, φb = 0.90) or ASD (Ωb = 1.67). The card gives the modulus the wall needs and, if you give W, the utilisation with PASS or FAIL.
What does the bottom heave check use?
The bearing resistance of the clay under the base, 5.14cu(1 + 0.2B″/Lexc), plus the side shear of the retained height, against the weight of the retained soil and the surcharge (uniform loads in full, a strip load by its part within B′ spread over B′, a point load within B′ spread over a square B′ × B′); B′ is B/√2 or the depth of a hard stratum if smaller. The example gives 4.23, above the required 1.5.
Does the module remember my inputs?
No. The page opens every time on the default model, not analysed; only the unit system is kept. Use Save to file or Quick Save to keep a model, and Open file or Load to bring it back.
Can I drag things on the drawing?
Before Analyze: the boundary between layers, the toe line (with the embedment given), the water levels, and a strip load (by its body or either edge) or a point load along the ground; anchors are not dragged. After Analyze the model is locked until you press Edit inputs.
Which units does it use, and what are the units of the answer?
SI · kN, SI · tf or US, switchable in the header at any time, even after Analyze. The depths are in m or ft, the moment in kN·m/m, tf·m/m or kip·ft/ft and the section modulus in cm³/m or in³/ft. The default example gives Mmax = 181.9 kN·m/m, 18.55 tf·m/m or 40.89 kip·ft/ft.
What does the report contain?
A cover with your project details and the answer, then seven parts: introduction and scope, input data, the calculation step by step, results, assumptions and notes, summary and references, with the drawings. It is saved as a PDF or a Word file once the model is analysed.
Design a sheet-pile wall in a profile of sand and clay layers, as a cantilever or held by up to four rows of inclined ground anchors: the pressures on both faces, the embedment, the anchor forces, the maximum moment, the anchors, the steel section, the bottom heave, the displacement and the earthquake. This manual walks through the screen, every input, the choices that decide the margin, the results and the report, with a worked example you can reproduce.
Anchored sheet pile on layered soil designs a sheet-pile wall in a profile of sand and clay layers, down the whole wall. The wall may be a cantilever or be held by up to four rows of inclined ground anchors. The module builds the pressure on both faces of the wall layer by layer, finds the embedment below the dredge line by limit equilibrium, gives the anchor forces, the maximum bending moment and the depth where it acts, and then checks the anchors (free length and bond), the steel section, the bottom heave of a clay base, the displacement of the wall and, if you switch it on, the earthquake.
Every layer is sand or clay, and a clay is analysed in the short term (undrained, in total stress with cu) and in the long term (drained, in effective stress with c′ and φ′). When the profile has a clay, both scenarios are run and the larger value of each result designs the wall. The pressures are Rankine pressures on a vertical wall with no wall friction:
Ka = tan²(45° − φ′/2), Kp = tan²(45° + φ′/2), pa = max(0, Kaσ′v − 2c′√Ka) + u
Water stands at its own level on each face of the wall; uniform, strip and point surcharges can be listed on the retained surface; the net pressure is the retained pressure less the passive resistance of the excavation side, and the statics are solved on it: free earth support about one row of anchors, the hinge method for several rows, and the conventional toe-block method for a cantilever.
What you can describe
A profile of up to six layers from the top of the wall down, each Sand — drained, c′ and φ′ or Clay — cu short term, c′ and φ′ long term; the layers run across the dredge line and below the toe.
Water on the retained side and, if you wish, at a different level in the excavation.
A cantilever, or one to four rows of anchors, each with its own depth, spacing, inclination, lock-off force, free and bond lengths.
Uniform, strip and point surcharges (up to six loads in a list).
An embedment calculated by the module or given by you and verified.
The margin on the embedment: a factor on the depth, or a factor of safety on the passive pressure.
The steel section by its modulus and grade, verified to EN 1993-1-1 or AISC 360-22.
A bottom-heave check and a pseudo-static earthquake check.
Which module for which wall
A wall in a single layer of sand, cantilever or anchored: Sheet pile in sand.
A wall in undrained clay above and below the dredge line: Sheet pile in clay.
A profile of several layers of sand and clay, or a wall held by more than one row of anchors, or the short- and long-term scenarios of a clay side by side: this module.
Combine the results with your own checks of the overall stability of the excavation and, for anchored walls, of the deep-seated stability of the anchored block; the module reminds you of both in every anchored run (see Messages).
Before you start: what you need
Have these ready from your design and your ground investigation:
What and source
Notes
The soil profile Boring logs and tests
For each layer from the top of the wall down: thickness, moist and saturated unit weight, φ′ and c′, and for a clay cu. The last layer runs on below the toe.
Wall height L Your design
From the top of the wall to the dredge line. At least 0.5 m.
The water Groundwater readings
The depth Dw of the water table on the retained side, and the level in the excavation if it differs.
The anchors Your design
Depth za, horizontal spacing s, inclination α, lock-off force, free length, bond length, tendon area, grout body diameter and the ultimate bond stress from your tests or tables.
The loads Your design loading
Uniform, strip and point loads behind the wall, with their position.
The sheet pile The maker’s table
Steel grade, section modulus per metre of wall and, for the displacement, the second moment of area.
Quick start in eight steps
Open the module and choose the units
Open Anchored sheet pile on layered soil from the Sheet-Pile Walls family. Pick SI · kN, SI · tf or US in the header; you can change it at any time.
Describe the soil
In Soil layers fill the New layer form (sand or clay, thickness, unit weights, strength) and press + Add layer. The layers go from the top down; the last one has no thickness and runs below the toe.
Enter the water, the wall and the anchors
In Groundwater give the water table, in Wall and embedment the height L, and in Ground anchor add the rows with + Add anchor, or remove them for a cantilever.
Add the loads and the earthquake
In Surcharge add uniform, strip or point loads; in Earthquake switch the pseudo-static check on if you need it.
Choose the margin and the section
In Design factors set the factor on the depth (or on the passive pressure) and the scenario of the clay; in Sheet pile and Design code give the steel and the code.
Press Analyze
Press Analyze at the foot of the Model tab. A window lists the warnings, the bar reads Analysed, the inputs lock and the drawing shows the pressure and the design embedment. A mistake in the inputs opens Cannot analyse with the fields to correct.
Read the results
The Results tab gives the diagrams, the values step by step, the cards and the verdicts. A Warnings button lists what needs your attention.
Take the working and the report
The Calculations tab writes out every step with your numbers; the Report tab saves a PDF or a Word file.
The screen: views, zoom and dragging
The layout is the one every GeoTerva module shares, described in the workspace guide: the drawing on the left, the tabs Model, Results, Calculations, Report and Theory on the right. The drawing has two views, chosen above it:
Section is the wall with the soil layers, their unit weight and strength, the water tables, the anchors with their depth and inclination, the surcharge loads and the dimensions. It follows your inputs. After Analyze it adds the active pressure on the retained face, the resultant P with the zero-pressure point E, the theoretical and the design embedment Dtheory and Ddesign, and, for a cantilever, the reversed pressures at the toe.
3D is an oblique view of a length of the wall with the retained soil on one side and the excavation on the other, the anchors in their rows and the water table. After Analyze it adds the design embedment and a line with Mmax, Wreq and the utilisation η.
The module on its default model, before Analyze.
Section before Analyze.
Section after Analyze.
3D after Analyze.
Zoom
Each view has −, a percentage and + at the lower right, and a button that fits the whole drawing in the pane. The mouse wheel zooms as well. The module has no Show chips: the drawings are fixed.
Dragging and picking on the drawing
Before Analyze, parts of the section drawing can be dragged and every row of a list can be picked:
The water tableDw: drag its handle up or down; it moves in steps of 0.05 m and cannot go above the top of the wall (0 m). With Different level, the level in the excavation Dw,exc has a handle of its own.
A layer boundary: drag it in steps of 0.05 m. Between two layers that both have a thickness, the layer above grows and the one below shrinks by the same amount; the boundary above the last layer changes only the layer above. A layer keeps at least 0.1 m.
The toe of the wall: drag the toe handle; the embedment switches to Given — verify it and the depth follows the pointer (at least 0.1 m).
Strip and point loads: drag a strip load by its body, its near edge or its far edge, and a point load by its mark, in steps of 0.05 m.
Picking: press a layer, an anchor or a surcharge load on the drawing and its section opens with that row in the form (Editing · …); this is the same as pressing the row in the table.
The handles update the box of the same field, so you can see the value you drop. After Analyze the handles are gone and the inputs are locked: the bar says “The model is locked — its inputs, and Reset, Open and Load. Edit inputs clears the results; the unit system can still be changed.” Edit inputs unlocks the model, clears the results and takes the drawing back to the inputs.
A cantilever after Analyze: the pressures at the toe are drawn.
Loads and unequal water levels, after Analyze.
Entering the model, section by section
The Model tab has eleven sections: Model data, Soil layers, Groundwater, Wall and embedment, Base heave, Ground anchor, Surcharge, Earthquake, Design factors, Sheet pile and Design code. Each opens when you click its title; Next and Back at the foot walk you through them, and Analyze waits below the last one. The tables list every field with its symbol, the unit in each unit system and its default. Where a unit is shown twice or three times, such as m · ft, the units are those of SI · kN, SI · tf and US in turn, and equal ones are merged. Defaults are shown in SI; in US the boxes show the converted values, for example 24.606 ft for the 7.5 m wall, and a unit switch may show them unrounded.
Model data
The first section holds the model name, Save to file…, Open file…, Quick Save… with its list and Load and Delete, and Reset to defaults. It works as described in the workspace guide. Reset returns the default model; after Analyze, Open, Load and Reset are locked until you press Edit inputs.
Model data.
Soil layers
The section is a form over a table. The New layer form takes the name, the soil (Sand — drained, c′ and φ′ or Clay — cu short term, c′ and φ′ long term) and the values of one layer. + Add layer puts it at the bottom of the table, and a counter beside the button shows how many of the six layers there are. A clay adds the field cu to the form. The Soil layers table lists every layer with a swatch of its colour on the drawing. Press a row to change that layer in the form: the form then reads Editing · Layer 2 Clay-2, offers Done and Delete layer, and the note says that changes apply as they are entered. × takes a layer out.
A sand is always analysed drained, with c′ and φ′, in every scenario. A clay is analysed undrained in the short term and drained in the long term, so it needs all of cu, c′ and φ′. The same form values start the first layer and the New layer form (sand, 3 m, 18, 20, 30°, 0, 20 MN/m³; a clay form starts with cu = 40 kPa).
Soil layers: the form over the table.
Layer fields (the form, and each row of the table)
Field
Default
What to enter
Name
automatic
Shown on the drawing and in the tables. Blank gives Sand-1, Clay-2 … by the soil and the position. (optional)
Soil
Sand
Sand (drained) or Clay (short term and long term), as on the two buttons.
Thickness Hi m · ft
3
From the top of the wall down. At least 0.1 m. The last layer has no thickness: its row shows a dash and it runs on below the toe.
Moist unit weight γ kN/m³ · t/m³ · pcf
18
At least 1. Used above the water table of each face.
Saturated unit weight γsat kN/m³ · t/m³ · pcf
20
At least 1. Used below the water table of each face.
Effective friction angle φ′ °
30
From 0° to 50°, and above 0° for a layer that is analysed drained. A sand uses it always; a clay in the long term.
Effective cohesion c′ kPa · kg/cm² · psf
0
Zero or more. Zero for a clean sand.
Undrained shear strength cu kPa · kg/cm² · psf
40
At least 1. The short-term strength of the clay, with φ = 0. Also used by the heave check and by the clay in the earthquake. Shown when the soil of the layer is Clay.
Dry unit weight γd kN/m³ · t/m³ · pcf
17 · 17 · 18
At least 1. Only the dry mass of a sand carries inertia when the pore water is free in the earthquake. Layers 1 to 3 of the default model have 17, 17 and 18. Shown when the earthquake check is on, the pore water is Free and the soil is Sand.
Used only for the displacement: the stiffness of the soil on both faces of the wall. A model parameter rather than a soil constant. (optional) Leave it empty and the displacement is not computed. Layers 1 to 3 of the default model have 20, 15 and 40.
A row pressed: the layer is edited in the form.
Groundwater
Water table has None and Present (the default); the unit weight of water γw = 9.81 kN/m³ is shown. With water present, Level in the excavation has Same as retained side (the hydrostatic pressures on the two faces balance) and Different level, which adds a second box. The module takes each face hydrostatic with its own level and no seepage; see Messages for the validity banner this puts on the results.
Groundwater with a different level in the excavation.
Groundwater fields
Field
Default
What to enter
Water table depth (retained side) Dw m · ft
8.5
Measured down from the top of the wall, behind the wall. A depth below the toe has no effect on the wall. Shown when the water table is Present.
Water level in the excavation Dw,exc m · ft
8
Also measured down from the top of the wall. A depth smaller than L means water standing in the excavation above the dredge line. Shown when the level in the excavation is Different.
Wall and embedment
Depth of embedment has Calculated by the program (default) and Given — verify it. Calculated: the embedment comes out of the analysis. Given: you enter the depth of the toe below the dredge line; the module still solves the depth the design needs, compares the two with the utilisation URD = Dreq / Dgiven and finds the factor of safety the given depth mobilises on the passive pressure.
Wall and embedment with the depth given.
Wall fields
Field
Default
What to enter
Height of the wall above the dredge line L m · ft
7.5
From the top of the wall to the dredge line. At least 0.5 m. The layers run on below it, and the part of the profile below the dredge line acts on both faces.
Depth of embedment below the dredge line D m · ft
6
At least 0.1 m. Shown when the embedment is Given.
Base heave
A cut in clay can fail by the base bulging up. Bottom heave check has Check (default) and Not checked. The check takes the clay under the dredge line; it does not apply to a base of sand, and the module says so (see Messages). The width B is needed, and the other three fields are optional or have defaults.
Base heave.
Base heave fields
Field
Default
What to enter
Width of the excavation B m · ft
10
The size of the failure surface follows from it.
Length of the excavation in plan Lexc m · ft
empty
Optional. Empty means a long excavation, with the shape term taken as 1.
Depth of a hard stratum below the dredge line T m · ft
empty
Optional. A hard stratum at 0 m means heave cannot develop.
Required factor of safety against heave FSreq
1.5
From 1 to 3. The result is PASS at or above it.
Ground anchor
The wall is a cantilever until an anchor is added. The section holds the choices that apply to every row, a New anchor form and a table. Tendon is Strand (default) or Bar and sets the minimum free length. Critical surface for the free length is Automatic (one sand over the retained height) or Given — plane at an angle. + Add anchor puts the form into the table, up to four rows; press a row (or the anchor on the drawing) to edit it, Done returns the form for a new row, × takes a row away. The rows are taken in order of depth.
The two rows of the default model are at za = 1.5 m, α = 15° and za = 4.5 m, α = 20°; the form starts at za = 6 m, α = 20° (and a third and fourth row would default to 6 m and 7 m).
Ground anchor: the form over the table.
Anchor fields (the form, and each row of the table)
Field
Default
What to enter
Required factor of safety of the bond FSreq
2
From 1 to 4. A default, not a code requirement.
Angle of the given surface from the horizontal θs °
60
From 20° to 85°. Shown when the critical surface is Given.
Depth of the anchor za m · ft
1.5 · 4.5 · 6 · 7
Strictly between the top of the wall and the dredge line.
Horizontal spacing s m · ft
2.5
At least 0.5 m. Each anchor carries the reaction of its row over this spacing.
Inclination below the horizontal α °
15 · 20
From 0° to 60°; beyond 45° the module cautions.
Prestress (lock-off) force per anchor P0 kN · tf · kip
250
Zero or more.
Free length Lf m · ft
9
At least 0.5 m. The unbonded length; it also sets the stiffness of the anchor in the displacement model.
Bond (root) length Lb m · ft
8
At least 0.5 m.
Cross-section area of the tendon At cm² · in²
5.6
Four 0.6 in strands are about 5.6 cm².
Diameter of the grout body Db m · ft
0.2
From 0.05 m to 1 m. The bonded diameter, not the tendon.
Ultimate bond stress τult kPa · t/m² · ksf
150
From your tests or tables; at least 1.
Tendon capacity Tcap kN · tf · kip
empty
Optional. Empty reports the force only.
Surcharge
Loads on the ground behind the wall. In the New load form choose the kind of load, enter its values and press + Add load; up to six loads go into the table, which shows each kind, magnitude and position. The first load of the default model is a uniform surcharge of 10 kPa over the whole surface. Uniform loads add together; strip and point loads add their lateral pressure by the elastic solutions for a rigid wall.
Surcharge: three loads in the list.
Surcharge fields
Field
Default
What to enter
Uniform surcharge on the retained surface q kPa · t/m² · ksf
10
Over the whole surface; adds to the vertical stress at every depth. Shown when the kind is Uniform.
Strip load qs kPa · t/m² · ksf
20
The pressure of the strip. Shown when the kind is Strip.
Near edge and far edge from the wall x1, x2 m · ft
1 and 3
The far edge is beyond the near edge. Shown when the kind is Strip.
Point load Q kN · tf · kip
50
A concentrated load. Shown when the kind is Point.
Distance from the wall x m · ft
2
A load closer than 0.30 m is taken at 0.30 m. Shown when the kind is Point.
Earthquake
Seismic situation has Not checked (default) and Pseudo-static check. With the check on, Pore water during the earthquake asks whether the water Moves with the soil or is Free (very permeable), and the two coefficients appear. The module takes the wall as designed, layer by layer: Mononobe–Okabe in a sand and in a drained clay, a 45° wedge in an undrained clay, and both senses of kv.
Earthquake with the check on.
Earthquake fields
Field
Default
What to enter
Horizontal seismic coefficient kh
0.15
Up to 0.6; take it from your seismic code. Shown when the check is on.
Vertical seismic coefficient kv
0.075
From 0 to 0.4; take it from your seismic code. Shown when the check is on.
Design factors
Three choices decide where the margin of safety goes and which analyses are run; they are explained in the next section.
Design factors.
Design factors
Field
Default
What to enter
Depth increase factor f
1.3
From 1 to 1.6. Dreq = f × Dtheory. Shown when the route is Increase D theory by a factor.
Factor of safety on the passive pressure FSp
1.5
From 1 to 3. The passive pressure is divided by it before the embedment is solved. Shown when the route is Factor of safety on the passive pressure.
Sheet pile and design code
Steel grade is a list of S235, S275 (default), S355 and Typed; the yield strength fy follows the grade (the field shows “from the grade”) and is typed freely with Typed. The section is given by its modulus per metre of wall, and Section modulus given says whether that is the Elastic Wel (default) or the Plastic Wpl column of the maker’s table. I is the second moment of area, used only for the displacement.
Sheet pile.
Sheet pile fields
Field
Default
What to enter
Yield strength fy kPa · t/m² · ksf
275000 (S275)
From the grade, or typed.
Section modulus of the sheet pile W cm³/m · in³/ft
1400
(optional) Empty gives Wreq only, with no section verified.
Second moment of area of the sheet pile I cm⁴/m · in⁴/ft
21000
(optional) Empty and the displacement is not computed.
Design code has EN 1993-1-1 (Eurocode 3) (default) and AISC 360-22. With EN 1993-1-1 the earth-pressure moment is multiplied once by γF (default 1.35, from 1 to 1.6) and the resistance is Mc,Rd = Wfy / γM0 (γM0 default 1, from 1 to 1.3). With AISC 360-22 you also choose LRFD (the moment factored by γH, default 1.6, from 1 to 2, against the design strength) or ASD. The embedment keeps the margin of its own route and is not factored again.
Choosing the method and the margin
Four decisions shape the answer beyond the soil and the loads.
Choice and options
What it does
Embedment route Increase D theory by a factor, Factor of safety on the passive pressure
The margin goes onto the depth after the analysis, or into the passive pressure before it. With the example, the factor 1.3 gives Dreq = 3.124 m from Dtheory = 2.403 m; a factor of safety of 1.5 on the passive pressure gives 3.273 m.
Scenario of the clay layers Short and long term — both run, Short term only, Long term only
Both run by default, and the larger of each result designs the wall. With the example, the short term alone gives 2.014 m and the long term 3.124 m.
Tension crack Water-filled, Dry
Where the active pressure of a clay (or a c′ soil) would be negative, the soil is taken to crack: with water in the crack, its pressure γw(z − zt) acts on the wall.
Critical surface (anchored) Automatic (one sand over the retained height), Given — plane at an angle
The surface that the free length must clear. Automatic: a plane from the foot of the wall at the dredge line rising at 45° + φ′/2, available when a single sand layer makes up the retained height; otherwise enter the angle you have established.
Depth factor or factor of safety on the passive pressure
With the depth factor route the diagram is solved with the full passive resistance and the depth found, Dtheory, is multiplied by f; the moment and the anchor forces are those of the diagram with the full passive pressure. With the factor of safety route the passive soil pressure (in a clay the whole of it, σv + 2cu) is divided by FSp before the depth is solved, so the moment and the anchor forces change too: in the example Mmax goes from 121.4 to 153.3 kN·m/m and T2 from 352.0 to 386.6 kN. The Calculations tab prints the other route’s depth as well. A factor of 1 (2.403 m in the example) removes the margin and the module notes it.
Short term and long term
When the profile has a clay, the module runs two analyses on the same profile: in the short term the clay is undrained (active σv − 2cu but never less than the pore water, passive σv + 2cu); in the long term every layer is drained. The anchor forces, the embedment and the moment are each the larger of the two. In the example the long term governs both the embedment (3.124 m against 2.014 m) and the moment (121.4 against 59.49 kN·m/m); that is why the tension crack choice makes no difference there, since the long-term profile has no negative active pressure (the dry crack run gives the same 3.124 m). A profile of sand alone has one analysis. The Calculations tab prints the scenarios side by side and says which one governs.
The anchored wall in the statics
One row: free earth support. The anchor is a simple support, the toe is free, and the moment about the anchor gives the embedment.
Several rows: the hinge method. A hinge at every anchor below the uppermost, simple spans between the anchors, and free earth support below the lowest one.
No anchor: the conventional cantilever method with the toe block, where the pressure reverses below a point near the toe.
The force of a row per metre of wall is F; the force in each anchor is T = Fs / cos α along the tendon, and Tv = T sin α is its vertical part, reported for the vertical equilibrium of the wall.
The smallest admissible embedment is the design. When there are several admissible roots, the module says so and takes the smallest.
Press Analyze and read the results
Press Analyze. The module checks the inputs first and shows Cannot analyse with each fault if there are any; otherwise it calculates, the bar reads Analysed — the sheet-pile wall calculated (with the number of warnings), the inputs lock, and a Warnings window opens if there is anything to report. The module stays on the Model tab; the answer is in the Results tab, and the drawing shows the pressure and the embedment. Before Analyze the Results tab reads “Press Analyze on the Model tab to calculate the sheet-pile wall.”
What the Results tab holds
A bar of warnings with a Warnings (n) button.
Three diagrams: the components of the lateral pressure on the two faces and the net pressure; the shear force and bending moment with the anchor forces as jumps of the shear and Mmax where the shear is zero; and the displacement and bending moment of the wall by the subgrade reaction method.
Values, step by step: the headline value of every calculation step.
Tables: the layers and their coefficients, the three stress fields, the components of the pressure at the events of the model, the roots of the moment equation, the resultants, the scenarios side by side and the anchors with their forces, free lengths and bond.
The cards and the list of results, with a verdict where there is one.
The diagrams of the default model.
Values, step by step.
The two scenarios side by side.
The cards.
The cards and the list
Result
Symbol
Meaning
Embedment the design needs
Ddesign
The depth of the toe below the dredge line: Dreq (the route’s margin included). With a given depth it reads Embedment of the wall as given, with a verdict.
Maximum bending moment
Mmax
Per metre of wall; with a given depth it is the larger of the design diagram and the given-depth equilibrium case and reads “designed for”.
Utilisation of the sheet pile given
ηsp
MEd / Mc,Rd (or Mu / φMn in AISC 360-22); PASS up to 1, and PASS · NEAR close to it.
Factor of safety against bottom heave
FSheave
Against the required value of the Base heave section.
Theoretical embedment
Dtheory
The depth with the full passive resistance.
Depth of the maximum moment
zM
Below the top of the wall, where the shear is zero.
Anchor force along the tendon, per anchor
T1, T2 …
One per row, from the larger scenario; with a given depth, “designed for” the larger of the two cases.
Free length required
Lf,req
Where the automatic or given critical surface is available. A free length shorter than this is a stop, so a result that is shown is always PASS.
Preliminary bond factor of safety
FSbond
Tult / max(T, P0) with Tult = π DbLbτult; PASS at or above the required value.
Free length against the minimum
Lf
The free length you gave against the minimum for the tendon (4.5 m strand, 3 m bar).
Lock-off load against the bond capacity
ηlock
P0 / Tult, a check that the inputs of an anchor agree with each other; PASS up to 1.
Section modulus the sheet pile needs
Wreq
The number to look a sheet-pile table up with.
Top displacement of the wall
ytop
By the subgrade reaction method; indicative.
The verdict words are those of the module: PASS, FAIL, PASS · NEAR, and PRELIMINARY (when the water stands at different levels, see Messages). The earthquake adds its own results (below).
Given depth
With Given — verify it, the module also gives Dreq, the utilisation URD = Dreq / Dgiven and the factor of safety FSp,mob the given depth mobilises on the passive pressure, and it works a second case with the wall in equilibrium at the given depth; the moment and the anchor forces are the larger of the two cases. In the example, a depth of 2.5 m gives URD = 1.250 (FAIL) and FSp,mob = 1.056; a depth of 4 m gives URD = 0.7810 (PASS) and FSp,mob = 1.907, but the maximum moment is then 180.0 kN·m/m against 121.4 with the depth calculated, because a longer wall in equilibrium with a partly mobilised passive resistance bends more, and T2 is 413.3 kN.
The earthquake
With the pseudo-static check on, the Results tab adds a fourth diagram, Seismic situation — net pressure and bending moment (with Mmax,E = 277.21 kN·m/m for the example), and the embedment required in the seismic situationDE, the maximum bending momentMmax,E and the utilisation of the sheet pileηE in the seismic situation, the seismic anchor forceTE of each row and the preliminary bond factor of safetyFSbond,E, which is held to the required factor divided by 1.33. With the default coefficients (0.15 and 0.075, pore water moving with the soil) the example gives DE = 4.348 m (FAIL, since it is more than the design embedment 3.124 m), Mmax,E = 277.2 kN·m/m, ηE = 0.7200 (PASS), TE,1 = 213.3 kN, TE,2 = 623.3 kN and FSbond,E of row 2 = 1.210 (FAIL). With the pore water free it gives DE = 4.089 m, Mmax,E = 266.5 kN·m/m and ηE = 0.6922 (PASS).
The Calculations tab, the report and the Theory tab
The Calculations tab writes the working with your numbers, one step at a time, each with its equations. For the default model there are fourteen steps: Layer framework and Rankine coefficients, Vertical stresses on the two faces, Lateral pressures by layer framework, Tension cut-off and the crack (when a tension zone arises), Embedment — hinge method, free earth support below the lowest anchor, Anchor reactions, Shear force and bending moment, Short-term and long-term scenarios, Ground anchors — free length and preliminary bond, Take the design moment, Sheet pile — the section modulus … asks for, Sheet pile — the section given verified, Bottom heave of the base and Wall displacement — subgrade reaction method. A cantilever has the conventional-method step in place of the hinge steps; a given depth, the earthquake and the displacement add their own. The scenario that governs the embedment is the one printed in full.
The Calculations tab: the first steps.
The Report tab has a Report cover (project, location, client, report number, date, prepared by, title, checked by and optional notes, kept in the browser and with the model file) and a preview of the summary report with Save as PDF and Download Word (.docx). The report has seven parts: Introduction and scope, Input data, Calculation, Results, Assumptions and notes, Summary and References, with a panel What passes and what does not that lists every check with the number it turned on and its verdict. The rows for the stability of the anchored block and of the whole excavation carry the word NOT CHECKED: they are reminders that those checks are made separately.
The Report tab: the cover and the buttons.
The Theory tab is a reading page with a contents list, Open all and Close all, and 21 sections, from Sheet-pile walls on layered soil (what the wall does and what the module designs): the wall and how it is held; the stresses on the two faces; the earth pressure in a drained layer and in an undrained clay; short and long term; surcharges; the net pressure diagram; where the margin of safety goes; the cantilever and its toe block; one row of anchors; several rows; shear force and bending moment; the anchors; the seismic situation; verifying the sheet pile; bottom heave; the displacement; the opening model worked through; what the module assumes; and the references.
Worked example: the default model
The default model is a 7.5 m wall in a profile of Sand-1 (3 m, γ = 18 kN/m³, φ′ = 30°), Clay-2 (6 m, γ = 19, γsat = 19.5 kN/m³, φ′ = 24°, c′ = 5 kPa, cu = 45 kPa) and Sand-3 (γ = 19, γsat = 21, φ′ = 36°); water at 8.5 m on both faces; a 10 kPa surcharge; anchors at 1.5 m (15°) and 4.5 m (20°), spacing 2.5 m, P0 = 250 kN, Lf = 9 m, Lb = 8 m, Db = 0.2 m, τult = 150 kPa; both scenarios, the depth factor 1.3; a sheet pile of 1400 cm³/m in S275, EN 1993-1-1.
The module also warns that the free length was not checked against a critical surface (the retained profile is layered, so no automatic surface applies), and gives notes for the tension cut-off, the scenarios and the moment factor.
Checking it by hand
The net pressure is the active pressure of the retained side, pa = Kaσ′v − 2c′√Ka plus the water, less the passive pressure of the excavation side, pp = Kpσ′v + 2c′√Kp plus the water, with Ka = 0.3333, 0.4217, 0.2596 and Kp = 3.000, 2.371, 3.852 in the three layers (the Calculations tab prints them). An independent integration of this net pressure with the hinge method gives the same results:
Quantity
Hand check
Module
Dtheory (the moment about anchor 2 vanishes)
2.403 m
2.403 m
F1 and F2
41.69 and 132.31 kN/m
41.69 and 132.32 kN/m
T1 = 41.69 × 2.5 / cos 15°
107.9 kN
107.9 kN
T2 = 132.31 × 2.5 / cos 20°
352.0 kN
352.0 kN
Mmax
121.4 kN·m/m at 6.82 m (a finer sum)
121.4 kN·m/m at 6.825 m
Tult = π × 0.2 × 8 × 150; FSbond
754.0 kN; 754.0/250 = 3.016 and 754.0/352.0 = 2.142
3.016 and 2.142
Wreq = 163.92 / 275 000
596.1 cm³/m
596.1 cm³/m
Mc,Rd = 1400 cm³/m × 275 MPa; ηsp
385.0 kN·m/m; 163.92/385.0 = 0.4258
385.00; 0.4258
FSheave = (5.14 × 45 + 27 × 7.5/7.07) / (149.5)
259.9 / 149.5 = 1.74
1.739
The free length required of an automatic surface can be checked the same way. With one sand layer over the retained height (Sand-1 made 9 m thick, φ′ = 30°), the plane rises at 45° + 15° = 60° from the foot of the wall: sc = (7.5 − 1.5) / (cos 15° tan 60° + sin 15°) = 3.106 m, and Lf,req = 3.106 + max(1.5 m, 7.5/5 m) = 4.606 m; the module gives 4.606 m for row 1 and 3.023 m for row 2 (hand: 3.023 m).
The same model in US units and in SI · tf
Switch the unit system in the header: the model is the same. In US the module gives Ddesign = 10.25 ft (Dtheory = 7.884 ft), Mmax = 27.30 kip·ft/ft at zM = 22.39 ft, T1 = 24.26 kip, T2 = 79.14 kip and Wreq = 11.09 in³/ft; the ratios (ηsp 0.4258, FSheave 1.739) are unchanged. In SI · tf it gives Ddesign = 3.124 m, Mmax = 12.38 tf·m/m, T1 = 11.00 tf and T2 = 35.90 tf. These agree with the kN results: 107.9 kN = 24.26 kip = 11.00 tf, and 121.43 kN·m/m = 27.30 kip·ft/ft = 12.38 tf·m/m.
How each input changes the answer
Every row is a run of the module that changes one input of the default model (the soil, water, anchors, loads and the 1.3 depth factor of the example above) and leaves the rest. D is the embedment the design needs (m), M the maximum moment (kN·m/m) and T₁ / T₂ the anchor forces (kN) of rows 1 and 2.
Change
D
M
T₁ / T₂
Default model
3.124
121.4
107.9 / 352.0
Wall height 9 m Row 2 bond fails (FS 1.496); the sheet pile of the example is over-used
4.373
291.5
107.9 / 504.0
Wall height 6 m
2.435
31.24
107.9 / 219.4
Surcharge 30 kPa Bottom heave drops to 1.534
3.433
152.2
167.8 / 438.4
No surcharge
2.965
106.9
77.92 / 309.7
Water table at 3 m (both faces)
3.169
86.44
106.0 / 274.6
No water
2.825
117.3
107.9 / 347.3
Water in the excavation at 7 m, retained side 8.5 m Results carry PRELIMINARY in place of PASS
3.510
127.6
107.9 / 359.0
Clay cu 25 kPa (from 45) Bottom heave 0.9660 (FAIL); row 2 bond fails
3.946
237.6
107.9 / 548.0
Clay cu 90 kPa Only the heave changes, to 3.477
3.124
121.4
107.9 / 352.0
Clay c′ 0 (from 5 kPa)
3.523
162.6
114.2 / 437.7
Clay φ′ 18° (from 24°)
3.633
180.7
114.7 / 474.6
Last sand φ′ 32° (from 36°)
3.574
127.4
107.9 / 358.8
Last sand φ′ 40°
2.834
117.7
107.9 / 347.8
First sand γ 20 (from 18)
3.218
130.4
116.8 / 379.0
Depth factor 1.0 (from 1.3) No margin on the depth
2.403
121.4
107.9 / 352.0
Depth factor 1.6 The upper limit; only the depth changes
3.845
121.4
107.9 / 352.0
Factor of safety 1.5 on the passive pressure
3.273
153.3
107.9 / 386.6
Short term only
2.014
59.49
88.78 / 151.5
Anchor 1 inclination 30° (from 15°) Only T1 changes: 41.69 × 2.5 / cos 30°
3.124
121.4
120.3 / 352.0
Spacing 4 m (both rows) Row 2 bond fails
3.124
121.4
172.6 / 563.2
Anchor 2 at 6 m (from 4.5 m)
2.641
65.71
161.8 / 371.5
Anchor 2 removed (one row) Sheet pile of the example fails
3.765
295.9
331.7 / —
A third row at 6 m Rows at 1.5, 4.5 and 6 m: T₃ = 260.7
2.641
47.39
107.9 / 166.2
No anchors (cantilever) The sheet pile of the example fails (η 4.243) and the displacement is large
10.44
1,210
— / —
Reading the table:
A taller wall or a heavier load raises the embedment, the moment and the anchor forces together, and the bond of the lower row is the first check to fail.
The strength of the clay moves the short term and the heave check strongly, but the design stays with the long term while it governs; a weaker cu reaches the design when the short term takes over (3.946 m).
Water at 3 m instead of 8.5 m raises Ddesign only slightly (3.169 m) while it lowers Mmax (86.44) and T2 (274.6); with no water the embedment is 2.825 m. Try the water table of your site rather than guessing its effect.
The factor of the depth route changes only the depth; the factor of safety on the passive pressure changes the whole diagram.
The lowest row sets the embedment: a lowest row at 6 m gives Dreq = 2.641 m with two rows and 2.641 m with three; the third row at 6 m also lowers Mmax from 121.4 to 47.39 kN·m/m.
Messages
Messages come in four levels. Stops (a red ■ in the Cannot analyse window) mean that nothing was calculated; fix the field named. Cautions (△) are calculated results that need your attention. Notes (○) and information (●) state an assumption or a fact about the run. They appear in the Warnings window, in the bar and list of the Results tab, and in the report. Quotations below are the module’s text, with the numbers of the run that triggered them.
Input errors
Cannot analyse — 1 input error: “Thickness (H1) must be at least 0.1 m.” The same form for “Effective friction angle (φ′1) must be at most 50°.”, “Height of the wall above the dredge line (L) must be at least 0.5 m.”, “Inclination below the horizontal (α) must be at most 60°.”, “Depth increase factor (f) must be at least 1.”, “Horizontal seismic coefficient (kh) must be at most 0.6.”, “Diameter of the grout body (Db) must be at most 1 m.”, “Required factor of safety of the bond (FSreq) must be at most 4.”, “Depth of embedment below the dredge line (D) must be at least 0.1 m.” The fields are marked in red.
“Width of the excavation (B) is missing.”, “Water table depth (retained side) (Dw) is missing.”, “Water level in the excavation (Dw,exc) is missing.” and “Undrained shear strength (cu,2) is missing.” for a clay layer without cu.
Stops from the analysis
A stop: nothing was calculated.
“Anchor 2 at za = 8.00 m is not strictly between the top of the wall and the dredge line (L = 7.50 m).” Place every anchor between 0 and L.
“Anchors 1 and 2 are less than 0.25 m apart (za = 1.50 m and 1.60 m).” Merge the two rows or move one.
“Sand-1 has no effective friction angle φ′, which the drained analysis needs.” (and the same for the long term). A drained layer needs φ′ above 0.
“No embedment up to Dmax = 30.00 m balances the wall.” The passive resistance never catches up with the retained pressure; raise the passive resistance, lower the water in the excavation, or add an anchor. The pressure diagram is drawn so that the cause can be seen.
“The embedment roots found (short term) leave the anchor in compression.” The anchor is too low, or not needed: raise it or remove it (a single anchor at 7.4 m triggers it in the example).
“Anchor 1 has a free length of 3.00 m, shorter than the 4.61 m that puts its bond zone behind the critical surface.” With a given plane at 60°. Lengthen the free length to at least Lf,req, or flatten the anchor. The same stop arises with the automatic surface when one sand makes up the retained height.
Cautions
Free length of the anchors not checked against a critical surface — shown in the default model: the retained profile is layered or clay, so no automatic plane applies. Enter the plane you have established (Given — plane at an angle) or verify the position of the bond zones separately.
Deep-seated stability of the block between the wall and the anchors — shown in every anchored run; it is verified separately.
“Anchor 2: the preliminary bond capacity Tult = 754.0 kN gives FSbond = 1.50 < 2.00 against max(T, P0) = 504.0 kN, the anchor force.” Lengthen the bond length, enlarge the grout body, or reduce the spacing. When the lock-off load is the larger, the message says “the lock-off load”.
“Anchor 2: the lock-off force P0 = 250.0 kN exceeds the entered preliminary ultimate bond capacity Tult = π Db Lb τult = 188.5 kN.” The inputs of the anchor do not agree.
“Anchor 2: T = 352.0 kN exceeds the tendon capacity 300.0 kN.”
“Anchor 1 is inclined at α = 50.00 °, outside the usual range 0–45°.”
“Anchor 1 has a free length of 3.00 m, less than the 4.50 m … asks for a strand tendon.” A short free length also makes the displacement “based on invalid anchor geometry” (a note).
“The sheet pile given does not carry the design moment: MEd / Mc,Rd = 1.49.” Take a heavier sheet pile or a higher grade.
“The embedment given, D = 2.50 m, is less than the embedment the design needs, Dreq = 3.12 m (URD = 1.250).”
“Factor of safety against bottom heave FS = 0.9660 is below the required 1.50.”
“A dry tension crack was chosen: drainage condition must justify a dry tension crack.”
“Strip load 2 starts at the wall (x1 = 0.00 m)” — the elastic solution is singular at the wall; keep the near edge clear if the layout allows.
“Large displacement: ytop = 1,849.3 mm, 24.7 % of the retained height.” The beam on springs is a small-displacement idealisation.
Anchor goes slack in the displacement model — a tendon takes tension only.
Earthquake: “A saturated sand lies within the wall in the seismic situation: screen it for liquefaction.”; “The design embedment is too short for the seismic situation: DE = 4.35 m > Ddesign = 3.12 m.”; the seismic bond, tendon and section cautions; and “SEISMIC METHOD DOMAIN EXCEEDED” when θ ≥ φ′ (kh = 0.3, kv = 0.15 in the example), where the Mononobe–Okabe coefficient has no real solution.
“DESIGN VALIDITY: PRELIMINARY — SEEPAGE EFFECT NOT INCLUDED.” With Different level water the pressures are hydrostatic on each face with no seepage: every PASS is shown as PRELIMINARY, and a second caution names the piping and base-heave check of the unequal heads as yours to make.
Notes and information
“The overall stability of the wall and the ground has not been evaluated.” — shown in every run, a cantilever too: verify it separately, with a slope-stability analysis of the excavation.
“The active soil pressure is clipped at zero over 3.00 m–4.37 m; the crack is taken water-filled.” with the result of the other crack assumption (“With the crack dry the design gives Dreq = 3.12 m …”).
“Short- and long-term scenarios both run: Dreq 2.01 m / 3.12 m, Mmax 59.49 kN·m/m / 121.43 kN·m/m (short / long); the larger of each designs the wall.”
“No passive-pressure reduction applied and no depth factor: Dreq = Dtheory …” (factor 1).
“The base of the excavation was not checked against bottom heave”, “A hard stratum at the base — bottom heave cannot develop” and “Bottom heave — not applicable: the soil immediately beneath the base of the excavation, Sand-3 (sand, from 9.00 m), is not an undrained clay.”
“No section modulus was given for the sheet pile: the modulus it needs is found, and no section is verified.” and “No second moment of area was given for the sheet pile: the displacement of the wall is not computed.”
“The sheet pile is taken as of class 1 or 2 — the section class is not verified.” with the plastic modulus; the modulus is taken for the whole wall.
“Point load 2 at x = 0.10 m is taken at 0.30 m from the wall.” and the information that a point load is taken at its most loaded section for the whole wall.
Given depth: “The depth of embedment has been given and verified …”; and, when the lowest anchor takes no tension in the given-depth case, a note that it adds nothing to the design actions.
Good practice
Check the profile before the numbers. The drawing follows your inputs: the layer colours, the dredge line, the water table and the anchors should look like your section before you press Analyze.
Keep both scenarios for a clay. The long term governed the example, but a weaker cu (25 kPa instead of 45) makes the short term govern; the module cannot know which in advance, so leave Short and long term — both run.
Keep the water-filled crack unless the site drains the crack; the module cautions on a dry crack and prints the water-filled result.
Give a bond stress with a source.τult drives the bond check; the module treats it as the engineer’s number and the factor of 2 as a default.
Use a surface you have established for the free length when the retained profile is layered; the automatic plane is for one sand over the whole retained height.
Read the given-depth case as two cases. The moment and anchor forces are the larger of the design diagram and the equilibrium at your depth.
Treat PRELIMINARY as preliminary. With different water levels the result carries no PASS; do the seepage and piping checks.
Use the displacement as an indication. It depends directly on kh and on the second moment of area you give; the limit-equilibrium design does not depend on it.
Save the model to a file before you close the page; the module opens on the default model every time.
Put your own checks beside the result: the overall stability of the excavation, the deep-seated stability of the anchored block, the anchor tests, and the section classification of the sheet pile.
Frequently asked questions
What is the difference between this module and Sheet pile in sand or in clay?
Those two take a single kind of soil. This module takes a profile of up to six layers, each sand or clay, up to four rows of anchors, the scenarios of a clay side by side, and water at its own level on each face. See Sheet pile in sand and Sheet pile in clay.
Do I have to enter both short-term and long-term strength for a clay?
Yes. Every clay layer needs cu, c′ and φ′ whichever scenario you run; Short term only and Long term only in Design factors just run one analysis on them. A missing value stops the analysis with a message naming the layer, for example “Effective friction angle (φ′2) is missing.”
Why does the embedment come out larger than the one from the theory?
Because of the margin. Dreq is Dtheory multiplied by the depth factor (1.3 by default), or the depth found with the passive pressure divided by a factor of safety. Both depths are printed in the Calculations tab.
Which scenario governs, short term or long term?
The Calculations tab prints both side by side and marks the one that governs the embedment and the one that governs the moment. In the example the long term governs both; the module takes the larger of each quantity anyway, row by row for the anchors.
How many rows of anchors can I use, and how does the module treat them?
None to four. One row is free earth support; two to four rows use the hinge method, with a hinge at every anchor below the uppermost. Anchors must lie strictly between the top of the wall and the dredge line and at least 0.25 m apart.
Why does the module say the free length was not checked against a critical surface?
The automatic plane (45° + φ′/2 from the foot of the wall at the dredge line) applies when one sand layer makes up the whole retained height. For a layered or clay retained profile, choose Given — plane at an angle and enter the angle you have established; the module then tests every anchor against it.
What does PRELIMINARY mean in place of PASS?
It appears when the water stands at different levels on the two faces. The module takes each face hydrostatic with no seepage, so it issues no PASS; the pressures are valid within that model, and the seepage and piping checks are yours.
Can I give the depth of embedment myself?
Yes: choose Given — verify it in Wall and embedment. The module still solves the depth the design needs, gives URD and the factor of safety the given depth mobilises on the passive pressure, and designs the moment and the anchors for the larger of the design case and the given-depth case.
Why is the moment larger when I give a longer embedment?
A longer wall in equilibrium with a partly mobilised passive resistance can bend more than the design diagram. The module works that case and keeps the larger moment and anchor forces. In the example a given depth of 4 m raises Mmax from 121.4 to 180.0 kN·m/m.
Does the module keep my model when I reload the page?
No. It opens on the default model every time. Use Save to file… and Open file…, or Quick Save…, to keep a model; the report cover details are kept in the browser and with the model file.
Can I change the units after Analyze?
Yes. The module says that the unit system can still be changed while the model is locked; the inputs lock until you press Edit inputs, which also clears the results.
Which codes does the sheet pile check use?
EN 1993-1-1 (with γF on the moment and γM0 on the resistance) or AISC 360-22 (LRFD with γH, or ASD). The check uses the section modulus per metre you give, as the modulus of the whole wall, with the elastic or the plastic column of the maker’s table.
Seven modules give the extra lateral pressure a wall takes from loads on the ground behind it. This page helps you choose the module that matches your load and links to the manual of each.
The Surcharge Loads family has seven modules. All of them answer the same question: how much extra lateral pressure does a wall take from a load on the ground behind it? Pick the one whose load looks like yours.
The load behind your wall
Module
One to three concentrated loads, such as a wheel, a column or a crane outrigger
Each manual follows the same plan: what the module calculates, what you need before you start, a quick start, the screen and its views, every input, the results, the report, a worked example you can reproduce, a table of how each input changes the answer, the messages the module gives, and answers to common questions.
What the seven modules share
The workspace. The drawing, the tabs, Analyze and the input lock, units and the report follow the same layout as the other GeoTerva modules. See the workspace guide.
Three views. Every module draws the load and the pressure diagram in elevation, in plan and in 3D.
Loads moved on the drawing. In the modules that place a load at a distance from the wall, you can drag the load on the drawing to move it; the diagram and the numbers follow. The Uniform load covers the whole surface, so there is nothing to drag.
The answer. The lateral pressure with depth, the resultant and the height at which it acts, for design of the wall.
Open the module that matches the load and enter the wall height and the load, with the distances measured as the module asks.
Analyze and read the diagram
Press Analyze. Read the pressure with depth, the resultant and its height, and look at the plan and 3D views to see that the load sits where you meant it.
Move the load
Where the load has a position, drag it on the drawing to see how the position changes the pressure and the resultant, then type the values you settle on.
Combine and report
Add the resultant of each load to the earth pressure on the wall, save a report from each run, and fill in the cover so that the project and the checker are named on it.
Frequently asked questions
How do I calculate the lateral pressure on a wall from a surcharge with GeoTerva?
Open the module that matches the load, enter the wall height and the load, press Analyze, and read the pressure with depth, the resultant and the height at which it acts.
Which module do I use for a uniform surcharge over the whole surface?
Use Uniform load. It gives a constant pressure K·q with its resultant at mid-height.
Which module do I use for a strip footing or a road lane beside the wall?
Use Strip load: a uniform load on a strip between two distances from the wall.
Can I analyse several loads of different kinds together?
Each module takes one kind of load. Run the modules one after the other and add the resultants.
Can I move a load on the drawing?
Yes, for the loads that have a position. Drag the load on the drawing; the diagram and the numbers follow. The Uniform load covers the whole surface, so it has nothing to drag.
Which views does a surcharge module draw?
Elevation, plan and 3D, with the load and the pressure diagram in each.
Work out the extra lateral pressure that a concentrated load on the ground puts on a wall behind which it stands: the pressure diagram, its resultant PH and the height L of the resultant, for one to three loads. This manual walks through the screen, every input, the two methods, the results and the report, with a worked example you can reproduce.
Point load gives the extra horizontal pressure that a concentrated load on the ground behind a vertical wall puts on the wall. For a wall of height H, a load Qp on the ground surface and its horizontal distance x from the wall, it returns the pressure diagram down the wall, on the load’s own section, and two numbers that describe it:
PH = ∫ σH dz over the wall height, L = ∫ σH (H − z) dz / PH
PH is the resultant of the pressure, a force per metre of wall, and L is the height of the resultant above the base of the wall: the area and the centroid of the pressure diagram. The module also gives the peak pressure σH,max and the depth where it occurs. Each result is drawn on the wall in elevation, in plan and in 3D.
What you can describe
A wall of height H, and one to three point loads, each with its own distance x and its own load Qp. All the loads stand on one line perpendicular to the wall, and their pressures add.
Two methods: the elastic solution for a rigid wall (the default; twice the Boussinesq stress, Mindlin 1936) and the Terzaghi–NAVFAC chart (Terzaghi 1954).
Three unit systems, switched in the header: SI · kN, SI · tf and US.
No soil parameter is entered: the pressure follows from the geometry and the load.
What belongs to other modules
The module gives the pressure that the load adds. The earth pressure, the water pressure and the other actions of a complete wall analysis are separate; the result here is the surcharge component that is combined with them.
A load that stands on the wall itself or almost against it is better taken as an area load or as a load on the wall; the module says so when a load is that close (see Messages).
Before you start: what you need
Have these ready from your layout drawings and your loading:
What
Where it comes from
Notes
Wall height H
Your design
The height of the wall over which the pressure is added up. It must be greater than zero.
Point load Qp
Your loading
A concentrated load acting on the ground surface: a wheel, a crane outrigger, a column on a pad, a stack. One value of force for each load.
Distance x
Your layout
The horizontal distance from the face of the wall to the load, measured perpendicular to the wall. Zero or more.
How many loads
Your layout
Up to three, all on one line perpendicular to the wall. For loads side by side along the wall, work each position in turn: the module gives the pressure on the section through the loads.
The method
Your design basis
The elastic solution for a rigid wall (default) or the Terzaghi–NAVFAC chart. Choosing the method compares them.
Quick start in seven steps
Open the module and choose the units
Open Point load from the Surcharge Loads family. Pick SI · kN, SI · tf or US in the header; you can change it at any time.
Enter the wall height
In Geometry, enter the wall height H.
Choose the method
In Method, pick Elastic · rigid wall (the default) or Terzaghi–NAVFAC chart. The (?) beside each opens a window with a sketch and the equation.
Describe the load
In Point loads, enter the distance x from the wall and the load Qp. Press + Add point load for a second and a third load, up to three. Or drag the load in the drawing.
Check the drawing
The drawing follows the inputs: the wall, the load or loads and their distances in Elevation, Plan and 3D View.
Press Analyze
Press Analyze. The bar turns green, the inputs lock, and the pressure diagram and the resultant appear on the drawings.
Read the answer
The Results tab gives the resultant force, its depth, the peak pressure and where it occurs; Calculations shows every step; Report saves a PDF or a Word file.
The screen: three views and dragging the load
The layout is the one every GeoTerva module shares, described in the workspace guide. The drawing on the left has three views, chosen with the buttons above it; the Model, Results, Calculations, Report and Theory tabs are on the right.
Elevation is a section through the wall and the load: the wall on the left, the ground to the right, the load as an arrow on the ground surface with its distance x, and the wall height H. After Analyze it adds the pressure diagram on the face of the wall, and the resultant PH as an arrow at its height L above the base.
Plan looks down on the wall and the load. After Analyze it draws how the peak pressure falls away along the wall on either side of the load.
3D View shows the wall, the ground and the load in one picture, with the pressure on the wall face, the resultant arrow and a box with PH and L.
Before Analyze the drawings show the geometry alone, and the chips Pressure distribution and Resultant are greyed out, with the note “The pressure and the resultant appear after Analyze”. The chip Dimensions is always available: it switches the dimension lines, their labels and the extension lines on and off.
The Elevation view before Analyze: the geometry alone.
Elevation after Analyze: the pressure diagram, the resultant PH and its height L.
Plan after Analyze: the peak pressure along the wall.
3D View after Analyze.
Show chips
After Analyze, Pressure distribution and Resultant switch the pressure diagram and the resultant arrow on and off in the drawings (the resultant is shown in Elevation and in 3D View). With several loads the chips become three groups: the pressure distribution and the resultant force, each with All loads and one chip for every load, and Drawing with Dimensions. The chip of a load carries its colour, the same colour as the load in the drawing and in the Model tab.
Dragging the load
Before Analyze, drag the load in any of the three views to change its distance x: press on the dot at the foot of the arrow and move it along the ground. The box in the Point loads section follows while you drag. The distance snaps to 0.05 of the length unit shown (0.05 m or 0.05 ft) and cannot go below 0 or past the far edge of the drawing in that view. The drawing keeps its scale while you drag and refits when you let go. With several loads each load has its own handle, and the one nearest the pointer is picked up. Dragging changes x only; Qp and H are typed.
The hint “Drag Qp in the drawing to change the load distance” shows below the drawing while the inputs are open. After Analyze the inputs are locked and the load cannot be dragged: press Edit inputs first.
Entering the model, section by section
The Model tab has three sections: Geometry, Method and Point loads. Each opens when you click its title, and Next and Back at the foot walk you through them. Where a unit is shown twice or three times, such as m · ft, the units are those of SI · kN, SI · tf and US in turn, and equal ones are merged. The defaults are shown in SI; in another unit system the boxes show the converted values.
Geometry
The wall height is the only geometry besides the position of the loads.
Geometry: the wall height.
Geometry field
Field
Symbol
Unit
Default
What to enter
Wall height
H
m · ft
15.00
The height of the wall over which the pressure is added up. It must be greater than zero.
Method
Two buttons choose the method; the note under them says what the chosen method does. The (?) beside a method opens a window with a sketch, the equation and a line With the current inputs that gives PH and L by both methods for your values, so you can compare without changing the choice.
Method: two buttons, each with a (?) window.
Choice
Options
Default
Calculation method
Elastic · rigid wallTerzaghi–NAVFAC chart
Elastic · rigid wall
Point loads
Every load has a card with a colour dot, a cross to remove it, and two boxes. With one load the symbols are x and Qp; with several they are x1, Qp,1, x2, Qp,2 and so on, and the cards are called Load 1, Load 2 and Load 3.
Point loads: one load.
Fields of each load
Field
Symbol
Unit
Default
What to enter
Horizontal load distance
x
m · ft
5.00
Horizontal distance from the wall to the load, zero or more. In the elastic method a load nearer than 0.30 m (0.9843 ft in US) is calculated at 0.30 m.
Surface point load
Qp
kN · tf · kip
38.00
The load on the ground surface, zero or more.
Adding and removing loads
+ Add point load adds a load. It starts a fifth of the wall height beyond the last one (rounded to 0.5 m, and at least 1 m), with the same load: with the example wall it starts at x = 8 m, then 11 m. The cursor moves to its distance box.
The cross on a card removes that load. It is disabled while only one load is left.
At three loads the button reads Up to 3 point loads and is disabled.
All loads stand on one line perpendicular to the wall; their pressures add. Each load has its own colour in the cards, the drawings and the chips.
After Analyze the add and remove buttons are disabled with the rest of the inputs.
Point loads: three loads, 3 m, 6 m and 9 m.
Units
The unit system is chosen in the header and applies to the boxes, the drawings, the results and the report. You can change it before or after Analyze.
Quantity
SI · kN
SI · tf
US
Length (H, x, L, depths)
m
m
ft
Load Qp
kN
tf
kip
Resultant PH
kN/m
tf/m
kip/ft
Pressure σH
kPa
t/m²
ksf
Choosing the method
Both methods describe a wall that does not yield, and both give a pressure diagram whose area is PH and whose centroid is at L. They differ in how the distance of the load counts.
The two methods
Elastic · rigid wall (default)
Terzaghi–NAVFAC chart
Basis
The stress of a point load in an elastic half-space (Boussinesq), doubled for a smooth, unyielding wall by the method of images (Mindlin 1936), with Poisson’s ratio 0.5.
The chart of Terzaghi (1954) as carried by NAVFAC DM-7.02, in two closed forms by the distance ratio m = x/H.
Pressure on the load’s section
σH = (3Qp/π) · x²z / R⁵, with R² = x² + z²; the peak is at z = x/2.
With n = z/H: Case 1 (m ≤ 0.4) σH = 0.28 (Qp/H²) n²/(0.16 + n²)³; Case 2 (m > 0.4) σH = 1.77 (Qp/H²) m²n²/(m² + n²)³.
Effect of the distance
Counts at every x ≥ xmin = 0.30 m. A load nearer than that is calculated at 0.30 m, and a caution says so.
Counts only beyond 0.4H. A load within 0.4H is taken as if it stood at 0.4H: the same diagram however close it is.
Along the wall (Plan, 3D)
The full rigid-wall field, with R² = x² + y² + z²; the peak lies deeper away from the load.
The pressure of the section is reduced by cos²(1.1θ), with θ the plan angle from the load’s perpendicular.
The two methods against the distance of the load
The table gives PH and L for the module’s example (H = 15 m, Qp = 38 kN) with the load at several distances, each run on the module. The chart keeps one diagram while the load is within 0.4H = 6 m, and then follows the distance; the elastic solution follows the distance everywhere, and grows steeply as the load nears the wall.
Resultant PH (kN/m) and its height L above the base (m), H = 15 m, Qp = 38 kN
x (m)
Elastic PH
Elastic L
Chart PH
Chart L
Chart case
1
12.09
14.01
1.99
8.81
Case 1
2.5
4.82
12.59
1.99
8.81
Case 1
5
2.34
10.59
1.99
8.81
Case 1
6
1.91
9.94
1.99
8.81
Case 1
6.1
1.88
9.88
1.98
8.74
Case 2
8
1.35
8.87
1.38
7.61
Case 2
10
1.00
8.05
0.9755
6.74
Case 2
15
0.5213
6.80
0.4402
5.45
Case 2
With the load at 0.30 m, the nearest the elastic solution takes it, PH is 40.32 kN/m at L = 14.70 m; see Messages for the caution that goes with a load that close.
Which should I pick?
Use the elastic solution (the default) when the distance of the load matters to you, as in a check of a crane, a stockpile or a truck at different positions: moving the load changes the answer at every distance down to 0.30 m.
Use the chart when your design basis names the Terzaghi–NAVFAC point-load chart. Its diagram is the one many sheet-pile and trench manuals use; within 0.4H it does not react to the distance.
Run both. The window opened by the (?) beside a method gives PH and L by both for the current inputs. For the example they are 2.34 kN/m (elastic) and 1.99 kN/m (chart), and the elastic resultant acts higher: 10.59 m against 8.81 m above the base.
The (?) window of a method: sketch, equation and the current inputs worked by both methods.
Analyze and read the results
Press Analyze. The bar at the foot of the Model tab, which read “Not analysed”, now reads “Analysed — the lateral pressure calculated”; the inputs are locked, and the pressure diagram and the resultant appear on the drawings. Edit inputs unlocks the inputs and clears the results; the bar says the unit system can still be changed while the model is analysed.
The Results tab shows cards. With one load:
Distance ratiom = x/H, the ratio the pressure was calculated at. For an elastic load held at 0.30 m a line under the value says “x/H = … as entered · calculated at xmin”.
Calculation method (Elastic, with “(rigid wall)” beside it) for the elastic solution, or Calculation case (Case 1 for m ≤ 0.4, Case 2 for m > 0.4) for the chart.
Resultant forcePH, in force per metre of wall, at the section of the load.
Resultant depth, below the ground surface. The height L above the base is H minus this depth, and the Calculations tab gives both.
Peak pressureσH,max and the Depth of peak pressure.
The Results tab of the example.
Several loads
With two or three loads the cards give the Resultant force, all loads, the resultant depth, the peak pressure and its depth for the summed diagram, and then a card for each load, in its colour: its own PH, with its m, its L and, for the chart, its case. The loads add: the total PH is the sum of the loads’ resultants, and the total L is where their moments about the base balance. The peak of the summed diagram can lie between the peaks of the single loads.
Three loads at 3, 6 and 9 m.
Elevation with three loads: the summed diagram, one dashed diagram and one resultant per load, and the total resultant.
Plan with three loads on one line perpendicular to the wall.
What the numbers are
PH is the force of the surcharge pressure per unit length of wall at the section of the load (along the wall at the load’s own position, y = 0). The Plan and 3D views show how the pressure falls off on either side.
L is measured up from the base; the card gives the same level as a depth below the ground.
The resultant is the area of the pressure diagram over the full height of the wall, so it depends on H even when the peak pressure does not (see how each input changes the answer).
The Calculations tab, the report and the theory
The Calculations tab writes out the working, step by step, with the numbers of your model. After Analyze it has five steps:
Distance ratio (Distance ratios with several loads) — m = x/H for each load (for the chart, with its case; for an elastic load held at 0.30 m, the ratio it was calculated at).
Pressure distribution — the equation of the method, the pressure at the depth of the peak, and the peak σH,max. With several loads, the pressure of each load at that depth and their sum.
Resultant — PH = (Qp/H) × I0, with I0 the dimensionless area of the diagram, and the value of PH; with several loads, one line per load and the sum.
Location — L = H × I1/I0, with I1 the dimensionless moment about the base, and L above the base and below the surface; with several loads, the balance of moments.
Plan distribution — the equation for the pressure along the wall (the elastic field with y, or the chart’s cos²(1.1θ)). y and θ are not inputs: the Plan and 3D views sweep them.
Cautions and notes about the run are printed in the Calculations tab where they arise.
The Calculations tab: the first two steps of the example.
The report
The Report tab turns the same working into a summary report. Fill in the cover (Project, Location, Client, Report no., Date, Prepared by (name), Title / qualification, Checked by and optional Notes). The details are kept in this browser. After Analyze, press Save as PDF or Download Word (.docx).
The report has a cover page with the key results, then: 1 Introduction and scope, 2 Input data (the inputs table and the three drawings), 3 Calculation (one part per step), 4 Results, 5 Summary and 6 References. When the run has cautions or notes, an Assumptions and notes section is added after Results, and the Summary and References move down by one. The report is in the unit system shown, and states it with the conversion constants.
The Report tab: the cover form and the buttons.
The Theory tab explains the method: what the module computes, the two methods, the elastic method, the chart method, the resultant and its location, the pressure in plan and several loads, a worked example and the references.
Worked example: the module’s own example
The module opens on this example, so you can follow the numbers on your own screen.
Inputs of the example
Section
Input
Value
Geometry
Wall height
H = 15 m
Method
Calculation method
Elastic · rigid wall
Point loads
Distance, load
x = 5 m, Qp = 38 kN
Step 1: the distance ratio
m = x/H = 5.00/15.00 = 0.3333.
Step 2: the pressure and its peak
On the load’s section the pressure is σH = (3Qp/π) x²z/R⁵ with R² = x² + z². It peaks at z = x/2 = 2.50 m. There R² = 25 + 6.25 = 31.25 m², R⁵ = 5,459.2 m⁵, so
The area of the diagram over the wall height is PH = (Qp/H) I0, with, for the elastic solution, I0 = [1/m − m²/((1 + m²)√(1 + m²))]/π. For m = 1/3 the bracket is 3 − 0.111111/1.171214 = 2.905131, so I0 = 0.92473 and
PH = 38/15 × 0.92473 = 2.34 kN/m
Step 4: its height
The moment about the base gives I1 = I0 − 1/(π(1 + m²)√(1 + m²)) = 0.92473 − 0.27178 = 0.65295, so
L = H × I1/I0 = 15 × 0.65295 / 0.92473 = 10.59 m above the base
That is 4.41 m below the ground surface, the “Resultant depth” of the Results tab.
The same load by the chart
With the chart, m = 0.3333 ≤ 0.4, so Case 1 governs and the load is taken as if it stood at 0.4H = 6 m: PH = 1.99 kN/m at L = 8.81 m, and the peak pressure is 0.2737 kPa at 4.24 m, z = √0.08 H. Moving the load anywhere inside 6 m leaves these numbers unchanged.
Three loads
Add two more loads, with x = 3, 6 and 9 m and Qp = 40, 60 and 30 kN, and run the elastic method again. The three loads give PH = 4.21, 3.02 and 0.9165 kN/m, at L = 12.15, 9.94 and 8.43 m. For the first, m = 0.2, I0 = 1.5795 and PH = 40/15 × 1.5795 = 4.21 kN/m. The pressures add, so the total is PH = 4.21 + 3.02 + 0.9165 = 8.15 kN/m, and its height is where the moments about the base balance:
L = (4.21 × 12.15 + 3.02 × 9.94 + 0.9165 × 8.43) / 8.15 = 10.91 m above the base (4.09 m below the ground)
The peak pressure of the summed diagram is 1.63 kPa at 1.72 m. By the chart the same three loads give PH = 6.16 kN/m at L = 8.56 m.
How each input changes the answer
Each row below changes one thing in the example and runs the module again. The numbers are the results the module gives, in the SI · kN system, so you can reproduce any row.
The example with one change at a time
Change
PH (kN/m)
L (m)
σH,max (kPa)
at depth (m)
What happens
The default example
2.34
10.59
0.4154
2.50
The reference: H = 15 m, x = 5 m, Qp = 38 kN
Load at 2.5 m
4.82
12.59
1.66
1.25
Closer: the pressure is larger and acts higher
Load at 10 m
1.00
8.05
0.1039
5.00
Farther: smaller and lower
Load at 0.1 m
40.32
14.70
115.40
0.1500
Held at 0.30 m; a caution says so
Load 76 kN
4.69
10.59
0.8309
2.50
Twice the load: everything doubles
Wall 10 m
2.20
6.07
0.4154
2.50
PH falls because the diagram is cut shorter; the peak does not change
Wall 20 m
2.38
15.37
0.4154
2.50
PH rises a little; the peak does not change
Chart
1.99
8.81
0.2737
4.24
Case 1; the same for any x up to 6 m
Chart, load at 8 m
1.38
7.61
0.1557
5.66
Case 2: the distance counts again
Chart, wall 10 m
2.27
5.25
0.3986
3.54
0.4H = 4 m; the load at 5 m is now Case 2
What the rows show
The load scales everything.PH and the pressure are proportional to Qp; L does not depend on it.
The distance moves the diagram. In the elastic solution the peak sits at z = x/2 and equals 0.2733 Qp/x² (0.4154 kPa at 5 m, 1.66 kPa at 2.5 m); PH falls as the load moves away (12.09, 4.82, 2.34 and 1.00 kN/m at 1, 2.5, 5 and 10 m).
The wall height changes the resultant, not the peak. In the elastic solution the peak depends on x and Qp only; the height decides how much of the diagram is on the wall, so PH and L change.
The chart ignores the distance inside 0.4H, and follows it beyond: PH is 1.99 kN/m with the load at 6 m, 1.98 kN/m at 6.1 m and 1.38 kN/m at 8 m.
Messages: stops, cautions and notes
The module tells you in plain words when something prevents the calculation and when a result needs care.
A stop means nothing is calculated. The bar reads “Cannot be analysed” followed by the reason; a red message appears in the Model tab above the bar; the drawings say “Not calculated”; and pressing Analyze opens a window with the message and “Nothing was calculated. Change the inputs marked in red, then press Analyze again.”
A stop: the wall height was set to zero.
Kind
When
Message and what to do
Stop
The wall height is zero, negative or empty
“The wall height H must be greater than zero.” A zero or negative wall height makes m = x/H and n = z/H undefined; a negative distance or load, or an empty box, has no meaning here. “Correct the highlighted value in the Model tab.”
Stop
A distance is negative or empty
“The horizontal distance x must be zero or more.” (with several loads: “The horizontal distance x₂ of load 2 must be zero or more”.) Correct the value the message names.
Stop
A load is negative or empty
“The point load Qₚ must be zero or more.” (with several loads: “The point load of load 2 must be zero or more”.) Several faults are listed together, separated by semicolons.
Caution (amber, in the Model tab)
Elastic method: a load nearer the wall than xmin = 0.30 m
“The load is nearer the wall than xmin = 0.30 m and calculated at 0.30 m. The elastic pressure grows without limit as a point load reaches the wall, and a real load that close is spread over a footprint.” Take a load this close separately, as an area load or as a load on the wall itself. With several loads it names them: “Load 1 is nearer…” or “Loads 1 and 2 are nearer…”.
Note (in the Calculations tab and the report)
Chart method: a load within 0.30 m of the wall
“The load is within 0.30 m of the wall. The chart holds any load within 0.4H at 0.4H, so it returns the same pressure however close the load stands.” Take a load this close separately, as above.
A caution shows in the Model tab under the load cards as soon as the inputs call for it, and again in the Calculations tab and the report; a note shows in the Calculations tab and the report. In the example, a load at 0.1 m by the elastic method:
The Results tab then shows the ratio the load was calculated at (0.0200) and “x/H = 0.006667 as entered · calculated at xmin”, the method card reads “(at xmin)”, and the report gets its Assumptions and notes section.
A caution: the load is held at 0.30 m.
Good practice and common mistakes
Measure x from the face of the wall, along the ground, perpendicular to it, to the point where the load acts.
Treat a spread load as a spread load. A point load is the right idealisation for a footing or a wheel that is small against its distance from the wall. For a load that is wide, or very close, use the Area loads, Strip load or Line load module.
Say which method your design basis uses. The elastic solution reacts to the distance at every distance; the chart does not inside 0.4H. Run both and keep the one your basis asks for.
Read PH as a force per metre at the load’s section. Along the wall the pressure falls away (see Plan); the figure is not a total over the wall.
Use L for the point of application. It is the height of the centroid of the whole diagram, above the base.
Add the load to the other actions. The module gives the surcharge component only; combine it with the earth and water pressures of your wall analysis.
Check the units after you switch the system: type values in the units shown beside the boxes.
Read the cautions and notes. They list what the module assumed for this run, and they are printed in the report.
Frequently asked questions
How do I calculate the lateral pressure on a wall from a point load?
Enter the wall height H, the load Qp and its horizontal distance x from the wall in GeoTerva’s Point load module and press Analyze. The module gives the pressure diagram on the load’s section, its resultant PH in force per metre of wall, the height L of the resultant above the base, and the peak pressure and its depth, by the elastic solution for a rigid wall or by the Terzaghi–NAVFAC chart.
Should I use the elastic method or the chart?
The elastic solution (the default) follows the distance of the load at every distance down to 0.30 m. The chart takes a load within 0.4H as if it stood at 0.4H, so it does not react to the distance there. Use the one your design basis names; the (?) window beside each method gives PH and L by both for your inputs. For the module’s example they are 2.34 kN/m and 1.99 kN/m.
Why does the pressure not change when I move the load closer, with the chart?
The chart holds any load within 0.4H of the wall at 0.4H, so inside that range it returns the same diagram. With H = 15 m the example gives 1.99 kN/m and L = 8.81 m for any x up to 6 m. Switch to the elastic solution if you want the distance to count.
What does the caution about 0.30 m mean?
In the elastic solution the pressure grows without limit as a point load reaches the wall, so a load nearer than xmin = 0.30 m is calculated at 0.30 m, and the module says so. A real load that close is spread over a footprint: take it as an area load or as a load on the wall.
What is PH and where does it act?
PH is the resultant of the surcharge pressure on the wall, the area of the pressure diagram over the wall height, in force per metre of wall (kN/m, tf/m or kip/ft), at the section through the load. It acts at the height L above the base, the centroid of the diagram; the Results tab also gives that level as a depth below the ground.
How many loads can I enter, and where must they be?
Up to three. They all stand on one line perpendicular to the wall, each with its own distance x and load Qp, and their pressures add: the total PH is the sum, and L is where the moments about the base balance. Press + Add point load to add one; the cross on a card removes it.
Can I move the load by dragging it?
Yes, before Analyze: drag the dot at the foot of the load arrow in Elevation, Plan or 3D View. The distance changes in steps of 0.05 of the length unit shown, from 0 to the far edge of the drawing in that view, and the box follows. After Analyze the inputs are locked until you press Edit inputs.
How does the module relate to the earth pressure on the wall?
It gives the surcharge component, the pressure added by the load, which you combine with the earth pressure, the water pressure and the other actions of your wall analysis.
Which module do I use for a line, strip, triangular or uniform load?
Which units does the module use, and what does the report contain?
SI · kN, SI · tf or US, switched in the header. The report carries the cover, the introduction, the input data with the three drawings, the working, the results, a summary and the references, in the unit system shown, as a PDF or a Word file.
Calculate the extra lateral pressure that a uniform load on a long strip behind a wall puts on it: the pressure at every depth, its resultant and the depth of the resultant. This manual walks through the screen, the drawing in elevation, plan and 3D, every input, the two methods, the results and the report, with a worked example you can reproduce.
Strip load gives the extra lateral pressure on a wall from a uniform load on a long strip of the ground behind it. You give the height of the wall, the distance of the near and the far edge of the strip from the wall and the load per unit area; the module gives the pressure at every depth, its resultantPH per unit length of wall, the depth zR at which the resultant acts, and the peak pressure with its depth.
The strip is long and parallel to the wall, so the problem is two-dimensional and every result is per unit length of wall. At a depth z the two rays from the point of the wall to the edges of the strip make the angles that give the pressure:
β is the angle the strip subtends at the wall point, α is the angle of its bisector from the vertical and ψ depends on the method you choose: 2 for a rigid wall, 1 for the half-space (a wall that gives way). The resultant is the area of the pressure diagram over the height of the wall, and zR is the depth below the ground at which the first moment of the diagram balances.
What you can describe
A wall of any heightH, with the ground surface level with its top.
A strip from x1 to x2 measured from the wall, with a uniform loadq. The strip may start at the wall face (x1 = 0).
Two methods: Elastic · rigid wall (the default) and Elastic · half-space.
SI · kN, SI · tf or US units, switchable at any time.
What you get
The pressure diagram on the wall, drawn in elevation, in plan and in 3D, with the resultant and its level.
The resultant forcePH per unit length of wall and its depthzR, the peak pressureσH,max and the depth of the peak.
The working step by step, with a table of the pressure at 31 depths, and a summary report as PDF or Word.
This module gives the pressure that the strip adds. No soil properties are asked: the elastic strip-load solution depends on the geometry and the load only.
The load is a surface load on a long strip. The result is the horizontal pressure and its resultant on the wall: the surcharge component, to be combined with the earth, water and other actions of your wall analysis.
Before you start: what you need
Four numbers and one decision are enough:
What
Where it comes from
Notes
Wall height H
Your design
The height over which the pressure is added up, measured from the ground surface down. It must be greater than zero.
Near edge x1
The layout of the load
The distance from the wall to the edge of the strip nearer to it. Zero or more; zero puts the edge at the wall face.
Far edge x2
The layout of the load
The distance from the wall to the farther edge. It must lie beyond x1; the width of the strip is b = x2 − x1.
Strip load q
Your design basis
The load per unit area on the strip, zero or more.
The method
How the wall behaves
Elastic · rigid wall is for a wall that does not yield; Elastic · half-space for a wall that deflects enough to relieve the soil.
Quick start in eight steps
Open the module and choose the units
Open Strip load from the Surcharge Loads family. Pick SI · kN, SI · tf or US in the header; you can change it at any time. Open Strip load.
Enter the wall height
In Geometry, type the wall height H.
Place the strip
In Geometry, type the near edge x1 and the far edge x2, or drag the edges or the body of the strip on the drawing.
Enter the load
In Strip load, type the load q on the strip.
Choose the method
In Method, pick Elastic · rigid wall or Elastic · half-space. The (?) beside each opens a drawing of the pressure and the formula.
Press Analyze
Press Analyze. The bar turns green and reads Analysed, the inputs lock, and the pressure diagram and the resultant appear on the drawing.
Read the answer
The Results tab gives the strip width, the method, the resultant PH and its depth zR, the peak pressure and its depth. Switch the drawing between Elevation, Plan and 3D View.
Check the working and take the report
The Calculations tab shows every step; the Report tab saves a PDF or a Word file.
The screen: three views, the Show chips and dragging
The layout is the one every GeoTerva module shares, described in the workspace guide. For this module the drawing on the left has three views, chosen with the buttons above it:
Elevation shows the wall in section, the strip on the ground with the value of q over its arrows, the pressure diagram on the wall, and the resultant PH with its level zR. The diagram carries the construction of α and β at the depth of the peak pressure, with the values written at the foot of the drawing.
Plan shows the strip beside the wall seen from above, with the peak pressure along the wall. The module says there: “Long strip parallel to the wall” (plane strain: the load is the same at every section, results per unit length of wall).
3D View shows the strip on the ground and the pressure on the wall as a curtain, with PH at zR.
The Elevation view before Analyze: the geometry alone, with the distances of the edges from the wall. The pressure and the resultant are off until you analyse.
The Elevation view after Analyze: the pressure diagram, the resultant and its level.
The Plan view: the strip from above, the same load at every section of the wall.
The 3D View: the strip and the pressure curtain on the wall.
The Show chips
Above the drawing three chips switch parts of it on and off:
Pressure distribution: the pressure diagram on the wall, with the angles in the elevation. It is available once the model is analysed; before that the module says “The pressure and the resultant appear after Analyze”.
Resultant: the resultant arrow and its level. The chip’s hint says it acts in the Elevation and 3D views. It too is available after Analyze.
Dimensions: the distances, the width and the height. It works at any time, before and after Analyze.
Dragging the strip
Under the drawing the module says: “Drag the strip's edges to change x₁ or x₂, or its body to move the whole strip”. It works in all three views, and the boxes of the Model tab follow as you drag, so the two always agree.
An edge changes x1 or x2. The edges never pass each other, and the near edge stops at the wall (x1 = 0).
The body moves the whole strip and keeps its width; it stays on the ground surface and within the extent of the drawing.
Positions snap to 0.05 of the unit shown (0.05 m, or 0.05 ft in US units). Type the number to set a value more finely.
After Analyze the strip cannot be dragged: the inputs are locked, and the hint under the drawing is hidden. Edit inputs unlocks the model.
Entering the model, section by section
The Model tab has three sections, Geometry, Strip load and Method. Each opens when you click its title; Next and Back at the foot walk you through them, and the Analyze bar stays at the bottom. The drawing follows every value you type. The tables list each field with its symbol, its unit in the three unit systems (m · ft means m in the two SI systems and ft in US; equal units are merged) and its default, shown in SI · kN.
Geometry
The wall and the place of the strip. The three distances are measured horizontally from the wall, along the ground surface.
Geometry: the wall height and the two edges of the strip.
Geometry fields
Field
Symbol
Unit
Default
What to enter
Wall height
H
m · ft
25.00
Height of the wall, from the ground surface to its base. It must be greater than zero.
Near edge distance
x1
m · ft
4.00
Distance from the wall to the near edge of the strip. Zero or more; it must be less than x2. Zero puts the strip against the wall face.
Far edge distance
x2
m · ft
12.00
Distance from the wall to the far edge of the strip. It must be greater than x1; the width of the strip is b = x2 − x1.
Strip load
The load on the strip. It is uniform across the strip and the same along it.
Strip load: one value.
Strip load field
Field
Symbol
Unit
Default
What to enter
Uniform strip surcharge
q
kPa · t/m² · ksf
20.00
Load per unit area on the strip, zero or more. The pressure on the wall is proportional to it.
Method
Two buttons choose how the wall is taken to behave; the note under them says it in a line, and the (?) beside each opens a window with a drawing of the pressure and the formula, with the result of the current inputs by both methods. Choosing the method says more.
Method: the two buttons and the note under them.
Choice
Options
Default
Calculation method
Elastic · rigid wallElastic · half-space
Elastic · rigid wall
Units
The unit selector in the header works at any time, before and after Analyze. The boxes are re-written in the new units, and the drawing, the results, the calculations and the report follow. The same example in the three systems:
The default inputs in each unit system
Field
SI · kN
SI · tf
US
Wall height
25.00 m
25.00 m
82.02 ft
Near edge distance
4.00 m
4.00 m
13.12 ft
Far edge distance
12.00 m
12.00 m
39.37 ft
Uniform strip surcharge
20.00 kPa
2.04 t/m²
0.4177 ksf
The results of the default example in each unit system
Result
SI · kN
SI · tf
US
Resultant force PH
91.95 kN/m
9.38 tf/m
6.30 kip/ft
Resultant depth zR
8.29 m
8.29 m
27.19 ft
Peak pressure σH,max
8.46 kPa
0.8629 t/m²
0.1767 ksf
Depth of peak pressure
3.81 m
3.81 m
12.49 ft
They are the same answer in other units. In the tf system the force is per metre of wall in tf (1 tf = 9.80665 kN), and the pressure is in t/m².
Choosing the method
Both methods use the same stress of a strip load on an elastic half-space; they differ in what the wall does to it. They share the angles β and α, so the diagram has the same shape; only its size differs.
The two methods
Method
Pressure
ψ
The wall
What it means
Elastic · rigid wall (default)
σH = (2q/π) [β − sin β cos 2α]
2
Smooth and unyielding
The wall stops the soil at its face from moving horizontally. A mirror-image strip on the other side of the face reproduces that exactly, which is why the stress is doubled (the method of images).
Elastic · half-space
σH = (q/π) [β − sin β cos 2α]
1
Deflects enough to relieve the soil
The same stress as if the wall were absent, on a vertical plane at the position of the wall.
The half-space pressure is half the rigid-wall pressure at every depth, so its resultant is half as large and acts at the same depth. For the default example the module gives 45.97 kN/m against 91.95 kN/m, both at 8.29 m below the ground.
The (?) window of the half-space method: the dashed curve is the rigid wall, twice the pressure.
Which should I pick?
Rigid wall is the module’s default. Use it for a wall that does not yield.
Half-space is for a wall that deflects enough to relieve the soil. It gives the lower of the two pressures.
Compare. Run both on the same layout and note the two results. The (?) window of either method also prints the result of the current inputs by both forms.
Analyze and read the results
Press Analyze. The bar changes to “Analysed — the lateral pressure calculated” and says: “The inputs are locked. Edit inputs clears the results; the unit system can still be changed.” The Results and Calculations tabs say, until then: “Press Analyze on the Model tab to calculate the lateral pressure.”
The Results tab shows six cards:
Strip width: b = x2 − x1.
Calculation method: Elastic, with “(rigid wall)” or “(half-space)”.
Resultant force: PH, per unit length of wall (kN/m, tf/m or kip/ft).
Resultant depth: zR, below the ground surface.
Peak pressure: the largest ordinate of the pressure diagram, σH,max.
Depth of peak pressure: where that ordinate is.
For the default example: PH = 91.95 kN/m at zR = 8.29 m, and σH,max = 8.46 kPa at 3.81 m.
The Results tab of the example.
How to read the pressure diagram
It starts at zero at the ground surface when the strip is clear of the wall (x1 > 0), rises to a peak and falls away with depth. In the example the table of the Calculations tab goes from 0.00 kPa at the surface to 8.42 kPa at 4.17 m, and falls to 0.6971 kPa at the base.
The resultant is the area of that diagram; zR is its centroid, measured down from the ground. The Calculations tab also gives the height above the base (16.71 m in the example).
The pressure scales with q and the diagram does not depend on the height of the wall: a taller wall adds the lower part of the same diagram, so PH grows and the peak stays where it is.
The Calculations tab and the report
The Calculations tab writes out the working in four numbered steps and a table of the pressure profile:
Strip geometry: b = x2 − x1, and the method with its ψ.
Angles at a depth: β and α, in degrees and in radians, worked at the depth of the peak pressure.
Horizontal pressure: the pressure equation with your numbers, giving σH,max.
Pressure profile, every H/30: a table of z, β, α and σH at 31 depths from the surface to the base.
Resultant and its depth: PH = ψ (q/π) H (θ2 − θ1) with θi = tan−1(xi/H), and zR = ∫ zσH dz / PH, below the ground and above the base.
The Calculations tab: the first three parts.
The module says there that both integrals are evaluated numerically to full precision, and that the area also has the exact closed form that is shown as the working. In the example θ1 = tan⁻¹(4.00 / 25.00) = 0.158655 rad and θ2 = tan⁻¹(12.00 / 25.00) = 0.447520 rad, so the closed form gives PH = 91.95 kN/m, as the cards say.
The report
The Report tab turns the same working into a summary report. Fill in the cover (project, location, client, report number, date, prepared by, title or qualification, checked by, notes) and press Save as PDF or Download Word (.docx); the report is made from the analysed model, so press Analyze first. The preview below shows the cover, with the resultant, its depth and the peak pressure, and the whole report. It has six parts: 1 Introduction and scope, 2 Input data (with the three figures: elevation, plan and 3D), 3 Calculation, 4 Results, 5 Summary and 6 References. When the run has a note, the report adds Assumptions and notes after Results and the parts after it move down by one. The units line states the conversion constants. The report prints a little more than the cards: 8.29 m below the ground is 8.287 m in its results table, and the peak pressure is 8.462 kPa.
The Report tab: the cover details, the two buttons and the start of the preview.
The Theory tab explains the method in five numbered parts: Strip load on a wall, Pressure at a depth, Resultant and line of action, Worked example and References.
Worked example: the module’s own example
The module opens on this example each time the page is opened, so you can follow the numbers on your own screen.
Inputs of the example
Section
Input
Value
Geometry
Wall height
H = 25.00 m
Geometry
Near and far edge
x1 = 4.00 m, x2 = 12.00 m
Strip load
Load
q = 20.00 kPa
Method
Method
Elastic · rigid wall (ψ = 2)
Step 1: the strip
The strip is b = 12.00 − 4.00 = 8.00 m wide, from 4.00 m to 12.00 m from the wall.
Step 2: the angles at the depth of the peak
The peak pressure is at z = 3.81 m (the module works at the unrounded depth, 3.8084 m, and shows it as 3.81 m). There β = tan⁻¹(12.00 / 3.81) − tan⁻¹(4.00 / 3.81) = 25.987° = 0.45355 rad and α = tan⁻¹(4.00 / 3.81) + β / 2 = 59.399° = 1.03670 rad. The drawing shows the two rays from that point of the wall to the edges of the strip, with the angles.
The module prints σH = 2 × 20.00 / π × [0.45355 − sin(0.45355) × cos(2.07341)] = 8.46 kPa at z = 3.81 m. As a check at another depth, take z = 5.00 m, one row of the pressure table: β = 28.720°, α = 53.020°, so σH = 2 × 20 / π × [0.50126 − sin 28.720° × cos 106.040°] = 8.07 kPa, which is the value in the table (5.00 | 28.720 | 53.020 | 8.07).
This is the area of the diagram. Its centroid is at zR = 8.29 m below the ground; the Calculations tab says “zR = 8.29 m below the ground (16.71 m above the base)”. The module evaluates zR numerically from the diagram (it also has an exact closed form), and the report prints it as 8.287 m.
How each input changes the answer
Each row below changes one thing (or the two edges together) in the example and runs the module again. The numbers are the results the module gives, so you can reproduce any row. The method is the rigid wall unless the row says otherwise.
The example with one change at a time
Change
PH (kN/m)
zR (m)
σH,max (kPa)
at z (m)
What happens
The default example
91.95
8.29
8.46
3.81
The reference
Half-space method
45.97
8.29
4.23
3.81
Exactly half of the rigid-wall values at every depth; zR is the same
Wall height 15 m
79.09
6.54
8.46
3.81
Less of the diagram: PH and zR both fall (the lower, heavier part is cut off); the peak and its depth do not change
Wall height 40 m
97.68
9.62
8.46
3.81
More of the diagram: PH grows a little, zR deepens; the peak does not change
Strip at the wall face (x1 = 0)
142.45
6.32
20.00
0.00
The peak is at the ground surface and equals q; the strip is 12 m wide
Strip nearer: x1 = 2, x2 = 10
95.71
6.72
11.53
2.33
The same width, nearer: a higher and shallower peak, a larger PH
Strip further: x1 = 8, x2 = 16
82.64
10.63
5.57
6.40
The same width, further away: a lower, deeper peak and a smaller PH
Strip further still: x1 = 20, x2 = 28
53.22
14.06
2.76
13.60
Further again: the load acts on the wall much deeper
Wider strip: x2 = 20
164.28
10.01
11.53
4.66
The far edge moves out to 20 m: width 16 m, a larger PH
Narrower strip: x2 = 6
24.47
6.12
3.32
2.81
A strip 2 m wide: the force falls to about a quarter
Strip load q = 40 kPa
183.90
8.29
16.92
3.81
Twice the load: twice the pressure and the force; the depths are the same
Strip load q = 10 kPa
45.97
8.29
4.23
3.81
Half the load: half the pressure and the force
Strip load q = 0
0.00
8.29
0.00
0.00
No pressure; the module still reports zR from the geometry
Strip at the wall face, half-space
71.23
6.32
10.00
0.00
Strip at the wall face by the half-space method: the peak at the surface is q/2
Three things stand out. The distance matters as much as the load: moving the same 8 m strip from 4–12 m to 20–28 m takes PH from 91.95 to 53.22 kN/m and zR from 8.29 m to 14.06 m. The width counts: the strip to 20 m gives 164.28 kN/m. The load is a straight proportion: 10, 20 and 40 kPa give 45.97, 91.95 and 183.90 kN/m.
Messages: stops and notes
The module says in plain words when something prevents the calculation, and it points to the box to correct. A mistake shows as soon as you type it: a red message appears in the Model tab above the Analyze bar and the bar turns brown and reads “Cannot be analysed”, with the first problem. If you press Analyze anyway a window with the title Cannot be analysed lists the problems; nothing is calculated.
A stop on the Model tab: the red message above the Analyze bar and the brown bar.
The window that Analyze opens: the message, then “Nothing was calculated”.
Kind
When
Message and what to do
Stop
The wall height is zero, negative or empty
“The wall height H must be greater than zero.” Enter a height above zero.
Stop
The near edge is negative or empty
“The near-edge distance x₁ must be zero or more.” Zero puts the strip against the wall.
Stop
The far edge is empty
“Enter the far-edge distance x₂.” Fill in x2.
Stop
The far edge is not beyond the near edge (equal or less)
“The far edge x₂ must lie beyond the near edge x₁.” The strip must have a width.
Stop
The load is negative or empty
“The strip surcharge q must be zero or more.” Enter q of zero or more.
Stop
More than one of these at once
The messages are joined: “The wall height H must be greater than zero; The strip surcharge q must be zero or more.” and the window says “Correct the highlighted values in the Model tab.”
Note
The strip starts at the wall face (x1 = 0)
“The strip starts at the wall face. At the ground surface the angles take their limits from below (β = 90°, α = 45°), so the pressure there is ψq/2 rather than zero.” The note is shown in the Calculations tab, and the report adds it in Assumptions and notes. The result is valid.
Every stop is followed by: “The strip must have a positive width (x₂ > x₁ ≥ 0) on a wall of positive height, and a load of zero or more. Correct the highlighted value in the Model tab.” With two or more faults at once the module says “values” (plural). The note about the wall face is the only note this module gives.
Good practice and common mistakes
Measure x1 and x2 from the wall. They are horizontal distances along the ground surface, from the wall to the two edges of the strip, as the drawing dimensions show.
Check that the load is a long strip. The module takes the strip as long and parallel to the wall, with the same load at every section. For a load of limited length along the wall use the rectangular areas, and for a single load the point load.
Choose the method for the wall. The rigid-wall form is twice the half-space form, so the choice changes every pressure and the resultant by a factor of two. Run both when you are unsure how the wall behaves.
Combine the result with the rest of your wall analysis. The module gives the surcharge component, from the strip alone and with no soil properties; combine it with the earth, water and other actions of your wall analysis.
Watch the wall height. A taller wall adds the lower part of the same diagram. The force grows more slowly as H increases (79.09 kN/m at 15 m, 91.95 kN/m at 25 m, 97.68 kN/m at 40 m), and the peak does not change.
Fine-tune by typing. Dragging snaps to 0.05; type the distances you mean.
Check the units after you switch the system: type values in the units shown beside the boxes.
Note what you need. The module does not keep the values you type when the page is closed or reloaded; note the layout and the results of each run, or save the report as PDF or Word.
Frequently asked questions
How do I calculate the lateral pressure on a wall from a strip load?
Enter the wall height H, the distances x1 and x2 of the near and far edge of the strip from the wall and the load q, choose the method, and press Analyze. The module gives the resultant PH per unit length of wall, the depth zR at which it acts and the peak pressure, from σH = ψ (q/π) [β − sin β cos 2α]. For the module’s example it gives 91.95 kN/m at 8.29 m.
What is the difference between Elastic · rigid wall and Elastic · half-space?
The rigid-wall method doubles the elastic strip-load stress (ψ = 2) for a wall that does not yield; the half-space method uses the stress as if the wall were absent (ψ = 1), for a wall that deflects enough to relieve the soil. At every depth the half-space pressure is half the rigid-wall pressure, so its resultant is half as large and acts at the same depth: 45.97 kN/m against 91.95 kN/m for the example.
What do x1 and x2 measure?
The horizontal distance from the wall to the near edge (x1) and to the far edge (x2) of the strip, along the ground surface. x2 must be greater than x1, and x1 may be zero. The width of the strip is b = x2 − x1.
Why is the pressure zero at the ground surface?
When the strip is clear of the wall (x1 > 0) the angle it subtends at a point of the wall at the surface is zero, so there is no pressure there. It rises to a peak below the surface, 8.46 kPa at 3.81 m in the example, and falls with depth.
What happens when the strip touches the wall?
With x1 = 0 the angles take their limits at the surface and the pressure there is ψq/2 rather than zero: 20.00 kPa for the rigid wall with q = 20 kPa, and 10.00 kPa by the half-space method. The module gives a note about it, and the result is valid.
Does the result depend on the soil?
No soil properties are asked for. The elastic strip-load solution depends on the geometry and the load only. The module gives the surcharge component; combine it with the earth, water and other actions of your wall analysis.
Does a taller wall change the pressure?
The pressure at a given depth does not depend on the height of the wall, so the peak and its depth stay the same. A taller wall adds the lower part of the diagram, so the resultant grows and acts deeper: 79.09 kN/m at 15 m, 91.95 kN/m at 25 m and 97.68 kN/m at 40 m.
What is the unit of the resultant force?
Force per unit length of wall: kN/m in SI · kN, tf/m in SI · tf and kip/ft in US. The strip is long, so every result is per unit length of the wall.
Can I move the strip with the mouse?
Yes, before Analyze. Drag an edge to change x1 or x2, or the body to move the strip with its width kept. It works in the Elevation, Plan and 3D views and the boxes follow. After Analyze the model is locked; Edit inputs unlocks it.
Why can I not edit the inputs after Analyze?
After a run the inputs are locked, so that the drawing, the results, the calculations and the report all describe the same model. Press Edit inputs to unlock them; the results are cleared. The unit system can still be changed. The workspace guide describes the lock.
Does the module remember my inputs?
No. It opens on its example (a 25 m wall, a 20 kPa strip from 4 m to 12 m, the rigid wall) each time the page is opened. The unit system is remembered.
How do I compare the two methods?
Run the first and note the results, press Edit inputs, choose the other method and run again. The (?) window of each method also prints the resultant of the current inputs by both forms.
Calculate the extra lateral pressure that a long line load parallel to a wall adds to the wall: the pressure at every depth, its peak, the resultant and the depth of the resultant. This manual walks through the screen, every input, the two methods, the results and the report, with a worked example you can reproduce.
Line load gives the extra lateral pressure that a long line load on the ground, running parallel to a wall, pushes on the wall. It gives the pressure σH at every depth, the resultantPH per unit length of wall, and the depth zR below the ground at which the resultant acts. With m = x/H and n = z/H, the pressure of the default method is
σH = (4P / πH) · m² n / (m² + n²)², PH = P · I0, zR = H · I1 / I0
P is the line load, a force per unit length of the line; x is its distance from the wall; H is the wall height. I0 and I1 are the area and the first moment of the pressure diagram over the height of the wall, written in closed form, so the resultant and its depth are exact. The wall is taken as smooth and unyielding, and the line load is long, so the problem is two-dimensional and every result is per unit length of wall.
What you can describe
A wall of height H (greater than zero), standing at the edge of the ground surface that carries the load.
A line load P of zero or more, parallel to the wall, at a distance x of zero or more from it.
One of two methods: Elastic · rigid wall (the default) and the Terzaghi–NAVFAC chart.
The module draws the load and the pressure diagram in elevation, in plan and in 3D, gives the six numbers of the Results tab, writes out the working, and prepares a PDF or Word report. You can drag the line on the drawing to change its distance from the wall.
What belongs to other modules
This is the surcharge component only: the extra pressure from this one line. It is added to the earth pressure, the water pressure and the other surcharges in the wall calculation, where you combine them.
The height over which the pressure is worked out, from the ground surface to the base of the wall. It must be greater than zero.
The line load P
Your design loading
A force per unit length of the line, in kN/m (tf/m or kip/ft in the other systems). Zero or more. A narrow strip of width b carrying a pressure q acts as a line load P = qb when b is small against its distance from the wall.
The distance x
Your layout
Measured on the ground, from the face of the wall to the line. Zero or more. A line nearer than 0.30 m is calculated at 0.30 m by the elastic method; see Messages.
The method
Your design basis
Elastic · rigid wall, or the Terzaghi–NAVFAC chart. The two give the same result once x is beyond 0.4H.
The module needs no soil properties: the pressure follows from the geometry and the load alone.
Quick start in seven steps
Open the module and choose the units
Open Line load from the Surcharge Loads family. Pick SI · kN, SI · tf or US in the header; you can change it at any time. Open Line load.
Enter the geometry
In Geometry, type the wall height H and the distance x from the wall to the line.
Enter the line load
In Line load, type the load P per unit length of the line.
Choose the method
In Method, pick Elastic · rigid wall or Terzaghi–NAVFAC chart. The (?) beside each opens a window with a sketch of what it assumes.
Press Analyze
Press Analyze at the foot of the Model tab. The bar reads Analysed, the inputs lock, and the pressure and the resultant appear on the drawing.
Read the answer
The Results tab gives six numbers: the distance ratio, the method (or case), the resultant PH, its depth zR, the peak pressure and its depth. Elevation, Plan and 3D View change the view.
Take the working and the report
The Calculations tab shows the three steps with your numbers and the pressure at every H/30. The Report tab saves a PDF or a Word file.
The screen: three views and a line you can drag
The layout is the one every GeoTerva module shares, described in the workspace guide. For this module the drawing has three views, chosen with the buttons above it:
Elevation is a section through the wall and the ground: the wall, the soil, the line load as an arrow with its value, the distance x and the wall height H. After Analyze it adds the pressure diagram on the wall, with ordinates at every tenth of the height, a dashed line at the peak with its depth, the resultant PH acting on the wall with its depth zR, and a note with the peak pressure.
Plan looks down on the ground. The line is drawn parallel to the wall, with rings along it and a filled dot in the middle, and its distance from the wall. After Analyze a band along the wall shows that the same pressure acts at every section, and a note at the foot of the drawing says the load is long, the problem is plane strain and the results are per unit length of wall.
3D View shows the wall, the ground behind it and the line with a row of arrows. After Analyze the pressure is drawn as a curtain on the wall face, with the resultant PH as an arrow at its depth and the dimensions H, x and zR.
Elevation before Analyze: the geometry alone, with the Show bar and the note about dragging.
Elevation after Analyze: the pressure on the wall, its peak and the resultant with its depth.
Plan after Analyze: the line parallel to the wall and the band of pressure along it.
3D View after Analyze.
The Show chips
Above the drawing a Show bar has three chips. Pressure distribution and Resultant are available after Analyze; until then they are greyed and the bar says “The pressure and the resultant appear after Analyze”. Dimensions can be switched at any time: it shows or hides the dimension lines with their values. Pressure distribution switches the pressure diagram, its peak and the note with the peak; Resultant switches the resultant arrow, its label and its depth, in the elevation and the 3D view (a plan has no place for a resultant).
Dragging the line
Before you analyse you can move the line instead of typing: press the load arrow (or, in the plan, the line; in the 3D view, the line or one of its arrows) and drag it sideways. The distance box follows the drawing and the drawing follows the box. The distance moves in steps of 0.05 (m or ft, as shown), cannot go below zero, and stops at the edge of the drawing. The note under the drawing says “Drag the line load P in the drawing to change its distance from the wall”. After Analyze the inputs are locked, the drag is off and that note is hidden; Edit inputs gives it back.
Entering the model, section by section
The Model tab has three sections. Each opens when you click its title; Next and Back at the foot walk you through them, and Analyze waits below the last one. The tables list every field with its symbol, the unit in each unit system and its default. Where a unit is shown twice or three times, such as m · ft, the units are those of SI · kN, SI · tf and US in turn, and equal ones are merged. Defaults are shown in SI; in SI · tf the line-load box shows 10.20 tf/m, and in US the boxes show 82.02 ft, 16.40 ft and 6.85 kip/ft for the same wall and load.
Geometry
Two numbers: the height of the wall and the distance of the line from it.
Geometry: the wall height and the distance of the line.
Geometry fields
Field
Symbol
Unit
Default
What to enter
Wall height
H
m · ft
25
The height of the wall over which the pressure is worked out, from the ground surface to the base. It must be greater than zero; a blank or zero box stops the analysis.
Line-load distance from wall
x
m · ft
5
The distance on the ground from the wall to the line, zero or more. With the elastic method a distance below 0.30 m (0.9843 ft) is calculated at 0.30 m and the module says so. With the chart method a distance within 0.4H gives the same result.
Line load
One number: the load per unit length of the line.
Line load: the force per unit length.
Line load field
Field
Symbol
Unit
Default
What to enter
Surface line load
P
kN/m · tf/m · kip/ft
100
The force per unit length of the line, zero or more. The pressure and the resultant are proportional to it; zero gives zero pressure.
Method
Two buttons choose the solution; each has a (?) that opens a help window. A line under the buttons says what the method assumes, and it follows the unit system.
Method: two solutions, each with a (?) window.
Choice
Options
Default
Calculation method
Elastic · rigid wallTerzaghi–NAVFAC chart
Elastic · rigid wall
Choosing the method
Both methods use the same equation once the line is beyond 0.4 wall heights from the wall (m > 0.4). They differ for a line that is closer.
Method
Pressure σH
Closer than m = 0.4
Resultant and depth
Elastic · rigid wall (the default)
(4P / πH) · m² n / (m² + n²)² at every distance
The distance counts at every x of 0.30 m or more. The pressure peaks at n = m/√3, that is z = x/√3, and grows without limit as the line reaches the wall; a line nearer than 0.30 m is calculated at 0.30 m.
PH = P · (2/π) / (1 + m²), zR = H · I1 / I0, with I1 = (2/π) [m tan⁻¹(1/m) − m² / (1 + m²)]
Terzaghi–NAVFAC chart
Case 2 (m > 0.4): the same equation. Case 1 (m ≤ 0.4): σH = (P / H) · 0.203 n / (0.16 + n²)²
The line is taken as if it stood at m = 0.4, so its distance has no effect while x ≤ 0.4H. The peak is at n = 0.4/√3.
Case 1: PH = 0.5469 P (from I0 = 0.1015 (1/0.16 − 1/1.16)), zR = H · I1 / I0 with I1 = 0.203 [tan⁻¹(2.5)/0.8 − 1/2.32]
How far apart the two methods are
The table gives the module’s own results for the example wall (H = 25 m, P = 100 kN/m) as the line moves away from the wall.
Elastic and chart results against the distance of the line (kN/m, m)
Distance x
Elastic PH
Elastic zR
Chart PH
Chart zR
0.1 m (0.004H); elastic at 0.30 m
63.65
0.4641
54.69
9.81
1 m (0.04H)
63.56
1.49
54.69
9.81
2 m (0.08H)
63.26
2.84
54.69
9.81
5 m (0.2H), the example
61.21
6.14
54.69
9.81
7.5 m (0.3H)
58.41
8.21
54.69
9.81
10 m (0.4H); chart still Case 1
54.88
9.81
54.69
9.81
12.5 m (0.5H); the methods agree from here
50.93
11.05
50.93
11.05
15 m (0.6H)
46.81
12.02
46.81
12.02
25 m (H)
31.83
14.27
31.83
14.27
50 m (2H); peak at the base
12.73
15.91
12.73
15.91
Inside 0.4H the chart result does not move: PH stays at 54.69 kN/m and zR at 9.81 m, while the elastic resultant rises towards 2P/π = 63.7 kN/m and its depth shrinks towards the wall top. The peak pressure differs much more than the resultant: at 1 m the elastic peak is 41.35 kPa and the chart peak 4.12 kPa.
The (?) windows
The (?) beside each method opens a window with a sketch of the wall, the line, the pressure diagram and its peak, the equations, and a line headed With the current inputs that gives PH and zR for your H, x and P by both methods side by side (61.21 kN/m at 6.14 m by the elastic solution and 54.69 kN/m at 9.81 m by the chart, for the example). Reading a window changes nothing in the model.
The (?) window of the elastic method: the sketch, and the line with the current inputs.
The sketch of the chart method’s (?) window: a line inside 0.4H is taken at 0.4H.
Which should I pick?
Start with the default, Elastic · rigid wall. The distance counts at every x, so you see what moving the line does, and it needs nothing but H, x and P.
Use the Terzaghi–NAVFAC chart when your design basis is that chart. Its result is the same as the elastic one beyond 0.4H and is held at the m = 0.4 values inside it.
Compare when the line is close. Inside 0.4H the two methods give different pressures and depths; run both (Edit inputs between runs) and keep the one your design basis calls for.
Beyond 0.4H the choice does not matter: the two give the same numbers.
Analyze and read the results
Press Analyze. The bar changes to Analysed — the lateral pressure calculated and says “The inputs are locked. Edit inputs clears the results; the unit system can still be changed.” The Results tab shows six cards, and the drawing now carries the pressure and the resultant.
The Results tab of the example.
Card
What it is
The example
Distance ratio m
The distance of the line in wall heights, x / H. If the line is nearer than 0.30 m, the card shows the ratio as calculated and a line under it gives the ratio as entered.
0.2000
Calculation method, or Calculation case
For the elastic method: Elastic (rigid wall), or Elastic (at x min) when the line was moved out to 0.30 m. For the chart: Case 1 (m ≤ 0.4) or Case 2 (m > 0.4).
Elastic (rigid wall)
Resultant force PH
The area of the pressure diagram over the height of the wall, per unit length of wall.
61.21 kN/m
Resultant depth zR
The depth below the ground at which PH acts. The calculation also gives its height above the base, H − zR.
6.14 m
Peak wall pressure σH,max
The largest pressure on the wall.
8.27 kPa
Depth of peak pressure
The depth at which that pressure acts.
2.89 m
Using the numbers
The pressure diagram is not a rectangle or a triangle but a curve that starts at zero at the ground, peaks and dies away with depth. In the wall calculation add it, point by point or as the resultant PH at zR, to the earth-pressure and water-pressure diagrams.
PH is a force per unit length of wall. P is a force per unit length of the line, and for a line parallel to the wall these are the same length.
The peak of the elastic diagram is at z = x/√3 below the ground, unless that is deeper than the wall, in which case the peak is at the base: with x = 50 m the module gives a peak depth of 25.00 m, the wall height.
The module supplies a lateral action to combine with the other pressures in your wall calculation.
Changing the unit system after Analyze re-states the cards, the drawing and the report without a new run. Edit inputs unlocks the model and clears the results.
With the Terzaghi–NAVFAC chart the second card reads Calculation case and gives Case 1 (m ≤ 0.4) or Case 2 (m > 0.4), and the elevation marks 0.4H on the ground line.
The Results tab of the example by the chart method.
The elevation for the chart method: the peak is deeper and lower than the elastic one, and 0.4H is marked on the ground.
The Calculations tab and the report
The Calculations tab writes out the working in three numbered steps, each with its equation, the equation with your numbers, a short note and the result:
Distance ratio — m = x / H with your numbers. For the elastic method a note says that one equation holds for every distance; for the chart it says which case governs, and when the elastic line was moved out to 0.30 m it shows both ratios. The result: m.
Pressure at a depth — n = z / H at the depth of the peak, the equation for σH and the peak pressure with its depth, followed by a table of z, n and σH at every H/30 (31 rows, from the ground to the base).
Resultant and its depth — PH = ∫ σH dz = P · I0 and zR = H · I1 / I0, the closed forms of I0 and I1, their values, and the results with the height of the resultant above the base.
The Calculations tab: the steps with the example’s numbers.
Before Analyze the tab says “Press Analyze on the Model tab to calculate the lateral pressure.” A caution of the run is printed at the end of the working.
The report
In the Report tab fill in the cover (project, location, client, report number, date, prepared by, title, checked by, and optional notes). The cover details are kept in this browser. After Analyze, Save as PDF and Download Word (.docx) are available; before it they are greyed out. The preview below the buttons is the report itself.
The report has six parts: 1 Introduction and scope, 2 Input data, 3 Calculation (one part for each of the three steps), 4 Results, 5 Summary and 6 References. When the run has a caution, as when the line was moved out to 0.30 m, an Assumptions and notes part follows the results and the last two parts move down by one. The report carries the elevation, the plan and the 3D drawing, and states the units with the conversion constants.
The Report tab: the cover details, the two download buttons and the start of the preview.
The Theory tab has five sections: Line load on a wall, The two methods, Resultant and line of action (with a table of both methods against the distance of the line), Worked example, and References.
Worked example: the module’s own example
The module opens on this example, so you can follow the numbers on your own screen.
Inputs of the example
Section
Input
Value
Geometry
Wall height, distance of the line
H = 25 m, x = 5 m
Line load
Load
P = 100 kN/m
Method
Method
Elastic · rigid wall
Step 1: the distance ratio
m = x / H = 5.00 / 25.00 = 0.2000. The line is beyond 0.30 m, so it is calculated where it stands.
Step 2: the peak of the pressure
The peak is at n = m/√3 = 0.2000/1.7321 = 0.1155, that is z = 0.1155 × 25 = 2.89 m. There the pressure is
zR = H · I1 / I0 = 25.00 × 0.15038 / 0.61213 = 6.14 m below the ground, or 18.86 m above the base
These are the six numbers of the Results tab and the three steps of the Calculations tab.
The same wall by the chart
Choose Terzaghi–NAVFAC chart (after Edit inputs) and analyse again. m = 0.2 is not above 0.4, so Case 1 governs: the line is taken as if it stood at m = 0.4. I0 = 0.1015 (1/0.16 − 1/1.16) = 0.54688, so PH = 54.69 kN/m; I1 = 0.203 [tan⁻¹(2.5)/0.8 − 1/2.32] = 0.21454, so zR = 25 × 0.21454 / 0.54688 = 9.81 m. The peak is at z = 0.4 × 25/√3 = 5.77 m, where σH = 4.12 kPa.
A smaller wall, a nearer line
For H = 6 m, x = 2 m and P = 40 kN/m, m = 0.3333. By the elastic method I0 = (2/π) / (1 + 1/9) = 0.57296, so PH = 40 × 0.57296 = 22.92 kN/m, and I1 = 0.63662 × (⅓ tan⁻¹(3) − 0.1) = 0.20139 gives zR = 6 × 0.20139 / 0.57296 = 2.11 m; the peak is 8.27 kPa at 1.15 m. By the chart (m ≤ 0.4, Case 1) the module gives PH = 21.88 kN/m at 2.35 m, with a peak of 6.87 kPa at 1.39 m.
How each input changes the answer
Each row below changes one thing in the example (H = 25 m, x = 5 m, P = 100 kN/m, elastic) and runs the module again. The numbers are the ones the module gives, in the units of SI · kN, so you can reproduce any row. The four columns are the resultant PH in kN/m, its depth zR in m, the peak pressure σH,max in kPa and its depth in m.
The example with one change at a time
Change
PH (kN/m)
zR (m)
σH,max (kPa)
Peak depth (m)
The default example: H = 25 m, x = 5 m, P = 100 kN/m, elastic
61.21
6.14
8.27
2.89
H = 15 m
57.30
5.27
8.27
2.89
H = 20 m
59.92
5.79
8.27
2.89
H = 30 m
61.94
6.39
8.27
2.89
H = 40 m
62.68
6.72
8.27
2.89
x = 1 m
63.56
1.49
41.35
0.5774
x = 2 m
63.26
2.84
20.67
1.15
x = 7.5 m
58.41
8.21
5.51
4.33
x = 15 m
46.81
12.02
2.76
8.66
x = 25 m
31.83
14.27
1.65
14.43
x = 0.1 m (m = 0.0120, calculated at 0.30 m)
63.65
0.4641
137.83
0.1732
P = 50 kN/m
30.61
6.14
4.13
2.89
P = 200 kN/m
122.43
6.14
16.54
2.89
P = 0
0.00
6.14
0.00
2.89
Chart method
54.69
9.81
4.12
5.77
Chart, H = 15 m
54.69
5.88
6.87
3.46
Chart, H = 40 m
54.69
15.69
2.58
9.24
Chart, P = 200 kN/m
109.38
9.81
8.24
5.77
Wall height. A lower wall cuts off more of the tail of the diagram, so PH falls; a higher wall adds a little and PH approaches 2P/π = 63.7 kN/m. The peak does not change.
Distance. A nearer line gives a sharp, shallow peak (five times higher at 1 m than at 5 m) and a shallow resultant; a farther line gives a lower, deeper, broader diagram. At 0.1 m the line is calculated at 0.30 m, with a caution.
Load. The pressure and the resultant are proportional to P; the depths do not change. With P = 0 the pressure and the resultant are zero, and the depths are those of the geometry.
Chart. Case 1 holds the distance out of the result: a lower peak, a deeper resultant, PH = 0.5469 P whatever H is, and the depths follow H.
The pattern follows the formulas: PH and the pressure are proportional to P; the elastic peak, σH = 9P / (4√3 π x) at z = x/√3, depends on the distance and not on the wall height (while the peak lies above the base of the wall; 41.35, 20.67 and 8.27 kPa at 1, 2 and 5 m); and PH falls as the line moves away, from about 2P/π at the wall.
Messages: stops and cautions
The module tells you in plain words when something prevents the calculation and when a result needs care. There are two kinds.
A stop: nothing is calculated
The module checks the three numbers it needs. When one cannot be used it stops:
A message appears in the Model tab above the Analyze bar, and the bar turns brown and reads Cannot be analysed, followed by the message.
If you press Analyze, a window titled Cannot be analysed gives the message and says “Nothing was calculated. Change the inputs marked in red, then press Analyze again.”
The Results tab says “Not calculated — see the Model tab.”, the Calculations tab shows the message, and the drawings say “Not calculated — correct the highlighted input in the Model tab”.
A stop: a wall height of zero. The window, the message in the Model tab and the brown bar.
Kind
When
Message and what to do
Stop
The wall height is zero, negative or empty
“The wall height H must be greater than zero.” Enter a height above zero.
Stop
The line-load distance is negative or empty
“The line-load distance x must be zero or more.” Enter zero or a positive distance.
Stop
The line load is negative or empty
“The line load P must be zero or more.” Enter zero or a positive load.
Every stop continues with the same sentences: “A zero or negative wall height makes m and n undefined; a negative distance or load, or an empty box, has no meaning here. Correct the highlighted value in the Model tab.” When more than one value is wrong the messages are joined in one stop, for example “The wall height H must be greater than zero; The line-load distance x must be zero or more; The line load P must be zero or more.” The message names the value that has to change.
A caution: the line is nearer than the least distance
With the Elastic · rigid wall method the pressure peak grows without limit as the line reaches the wall. A line nearer than 0.30 m (0.9843 ft in US) is therefore calculated at 0.30 m, and the module says so. A distance of exactly 0.30 m is calculated as entered. The chart method has no such limit, because it holds the line at 0.4H from the wall inside that distance.
A caution in the Model tab: the line is nearer than 0.30 m and is calculated at 0.30 m.
Kind
When
Message and what to do
Caution
Elastic method and x below 0.30 m
“The line load is nearer the wall than xmin = 0.30 m and is calculated at 0.30 m. The elastic pressure grows without limit as the line reaches the wall, and a real load that close has a width. Take a load this close separately — as a strip load, or as a load on the wall itself.”
The caution stays in the Model tab and is printed at the end of the Calculations tab; the report adds an Assumptions and notes part. On the Results tab the first card shows the ratio as calculated, with a line “x/H = … as entered · calculated at x min” under it, and the second card reads Elastic (at x min). For the example wall with the line at 0.1 m the module gives PH = 63.65 kN/m at 0.4641 m and a peak of 137.83 kPa at 0.1732 m, the same as at 0.30 m.
Good practice and common mistakes
Use this module for a load that is narrow. A line is a load whose width is small against its distance from the wall. For a load with a width, the Strip load module takes the width into account.
Enter P per unit length of the line, in kN/m, not as a total force. For a narrow strip of width b carrying q, use P = qb.
Measure x on the ground from the face of the wall to the line, the distance drawn in the elevation.
Read PH per unit length of wall. Multiply by a length of wall only when you need a total force on that length.
Add the result to the other pressures.σH is the surcharge component of this one line; the wall calculation combines it with the earth pressure, the water pressure and the other loads.
Run both methods when the line is within 0.4H of the wall and keep the one your design basis calls for. Beyond 0.4H they agree.
Watch the peak close to the wall. The elastic peak grows as 1/x: the module gives 41.35 kPa at 1 m and 137.83 kPa at 0.30 m for the example load. A line that close has a width: see the caution above.
Note your values. The module opens on its example every time and does not keep what you typed; the report is the record of an analysis.
Check the units after switching the system: type values in the units shown beside the boxes.
Frequently asked questions
How is the lateral pressure from a line load calculated?
For a long line load P parallel to a wall of height H, at a distance x from it, with m = x/H and n = z/H, the elastic solution for a rigid wall gives σH = (4P / πH) m² n / (m² + n²)² at every depth. The resultant PH = P · (2/π) / (1 + m²) is the area of the diagram over the height of the wall. For the module’s example it is 61.21 kN/m, acting 6.14 m below the ground.
Why is the elastic stress doubled?
A smooth, unyielding wall stops the soil at its face from moving horizontally. That doubles the horizontal stress of the elastic half-space, and a mirror-image line load on the far side of the wall face reproduces it exactly (the method of images). The module’s help window for the method draws the mirror-image line.
Where is the peak pressure, and how large is it?
For the elastic method the peak is at z = x/√3 below the ground and equals 9P / (4√3 π x), which does not depend on the wall height. The module gives 8.27 kPa at 2.89 m for the example. If x/√3 is deeper than the wall, the peak is at the base of the wall. For the chart method inside 0.4H the peak is at 0.4H/√3.
What is the difference between the elastic method and the Terzaghi–NAVFAC chart?
They use the same equation when the line is beyond 0.4 wall heights from the wall. Inside that distance the chart takes the line as if it stood at m = 0.4, so its distance has no effect and the resultant stays at 0.5469 P; the elastic method lets the distance count, so a nearer line gives a higher, shallower peak. For the example the two give 61.21 and 54.69 kN/m.
What is the least distance, 0.30 m?
With the elastic method the pressure peak grows without limit as the line reaches the wall, while the resultant stays finite. A line nearer than 0.30 m is calculated at 0.30 m and the module cautions you; a real load that close has a width, and the caution suggests a strip load or a load on the wall itself. The chart method has no such limit.
Are the results per metre?
Yes. The line load is long, so the problem is two-dimensional (plane strain): P is a force per unit length of the line, and PH is a force per unit length of wall. The same pressure acts at every section along the wall.
Does the result include the earth pressure and the water pressure?
No. The result is the surcharge component of this one line load. You add it to the earth-pressure and water-pressure diagrams, and to the other surcharges, in the wall calculation.
What values does the module accept?
The wall height must be greater than zero, the distance of the line zero or more and the line load zero or more. Anything else, or an empty box, stops the analysis with a message that names the value.
Can I drag the line on the drawing?
Yes, before you analyse. Drag the load arrow in the elevation, the line in the plan or the line in the 3D view; the distance box follows, in steps of 0.05 (m or ft). After Analyze the inputs are locked and the drag is off until you press Edit inputs.
Which units does it use, and what are the units of the answer?
SI · kN, SI · tf or US, switchable in the header at any time, even after Analyze. The pressure is in kPa, t/m² or ksf, the resultant per unit length in kN/m, tf/m or kip/ft, and the depths in m or ft.
Does the module remember my inputs?
No. It opens on its example (25 m wall, 100 kN/m at 5 m, elastic) each time the page is opened. The report cover details you type are kept in the browser, and the unit system is remembered.
What does the report contain?
A cover with your project details and a summary, then six parts: introduction and scope, input data, the calculation step by step, results, summary and references, with the elevation, plan and 3D drawings. A caution of the run adds an Assumptions and notes part. It is saved as a PDF or a Word file after Analyze.
Calculate the extra horizontal pressure that a long triangular surface load puts on a vertical wall, with the resultant force and its depth. This manual walks through the screen, the dragging of the load, every input, the two methods, the results and the report, with a worked example you can reproduce.
Triangular load gives the extra horizontal pressure that a long surface load of triangular shape puts on a vertical wall, with the resultant forcePH of that pressure and the depthzR at which the resultant acts. The load lies on the ground behind the wall and runs parallel to it: its intensity is zero at the distance x from the wall, rises in a straight line to the peak q over a width c, and falls in a straight line back to zero over a width b.
The pressure at a depth z below the ground is the sum of the elastic line-load stresses (Flamant) of all the slices of the load, integrated exactly. The module then integrates the pressure over the height of the wall:
w(s) is the intensity of the load at the distance s from the wall. ψ is 2 for a rigid wall that does not yield and 1 for the half-space, as if the wall were absent: you choose between them in the Method section. All results are per unit length of wall.
What you can describe
A wall heightH and one triangular load by three distances, x, c and b, and its peak q.
Two methods: Elastic · rigid wall (the default) and Elastic · half-space.
Any of the three unit systems, SI · kN, SI · tf and US.
The elastic solution contains no soil property, so the module asks for none: no unit weight, no friction angle, no stiffness.
What belongs to other modules
This module treats one triangular load. For other shapes of load behind a wall use the other modules of the family: the Point load, the Line load, the Strip load (a uniform load on a strip), the Ramp load, the Uniform load and the Area loads.
The result is the pressure of the surcharge alone. It is one component to be combined with the other lateral actions of your retaining-system analysis, which this module does not calculate.
The load is long and parallel to the wall, so the pressure is the same along the whole wall and the answer is a force per metre of wall, kN/m in the default unit system.
Before you start: what you need
Have these ready from your site plan and your design:
What
Where it comes from
Notes
The wall height H
Your design
The height of the wall over which the pressure is added up. PH counts the pressure from the ground surface down to H and no deeper.
The position of the load: x, c, b
Site plan, loading drawing
x is the distance from the wall to the foot of the rising branch, c the width of the rising branch up to the peak, b the width of the falling branch. The drawings measure x from the face of the wall that the soil bears on.
The peak intensity q
Loading data
The intensity at the peak of the triangle, in kPa (t/m² or ksf in the other unit systems). The intensity is zero at the two feet of the triangle.
How the wall behaves
Your design
A wall that does not yield takes the rigid-wall method; a wall that deflects enough for the soil at its face to move takes the half-space method.
Quick start in eight steps
Open the module and choose the units
Open Triangular load from the Surcharge Loads family. Pick SI · kN, SI · tf or US in the header; you can change it at any time, even after Analyze.
Enter the wall and the position of the load
In Geometry, enter the wall height H, the distance x to the load start, the rising width c and the falling width b. The drawing follows every value as you type.
Enter the peak intensity
In Triangular load, enter the peak surcharge intensity q.
Choose the method
In Method, pick Elastic · rigid wall (twice the elastic stress, the default) or Elastic · half-space (the elastic stress as it is).
Adjust the load on the drawing if you like
Before you analyse, drag the load to move it, its peak to change c or its far end to change b. The boxes in the Model tab follow.
Press Analyze
Press Analyze. The inputs lock, the pressure diagram and the resultant appear on the drawings, and the Results, Calculations and Report tabs fill in.
Read the results
The Results tab gives the resultant force PH, its depth zR, the peak wall pressure and its depth. The Show chips above the drawing switch the pressure diagram, the resultant and the dimensions on and off.
Check the working and make the report
The Calculations tab writes out every step with its numbers. The Report tab turns them into a summary report you can save as a PDF or a Word file.
The screen: three views and the drag handles
The layout is the one every GeoTerva module shares, described in the workspace guide. The drawing on the left has three views, chosen with the buttons above it:
Elevation is a section through the wall and the ground: the wall, the triangle of the load with its peak value q, the dimensions x, c, b, x + c and x + c + b, and the wall height H.
Plan looks down on the ground: the wall on the left and the load as a band parallel to it, shaded by the intensity from 0 to q and back to 0.
3D View shows the wall, the load and the pressure in three dimensions.
Before Analyze the drawing is the geometry alone: the load, q over its peak and the distances. The three round markers are the handles.
After Analyze the Elevation view adds the pressure diagram with the radii R1, R2, R3 and the angles α, β at the depth of the peak pressure, and the resultant.
The Plan view: the band of the load shaded by its intensity. The note below says the pressure is the same along the whole wall.
The 3D view: the load on the ground and the pressure on the wall as a curtain, with PH and zR.
Show chips
Three chips above the drawing choose what it shows. Pressure distribution draws the pressure diagram on the wall, with the radii and angles of the Elevation view. Resultant draws the resultant force and its depth in the Elevation and 3D views. Dimensions draws the distances, widths and heights. Until you analyse, the first two are not available: the note beside the chips says “The pressure and the resultant appear after Analyze”. Dimensions works at any time.
Dragging the load
Before you analyse, the load can be moved on the drawing in any of the three views. The line under the drawing says: “Drag the load to move it, its peak to change c, or its far end to change b”.
Handle
What it changes
The body of the load, or the marker at its start (the one nearest the wall)
x, the distance to the load start. The whole load moves; c and b stay. x cannot go below zero.
The peak (Elevation: the round marker at the top of the triangle; Plan: the solid line; 3D: the round marker on the peak line of the strip)
c, the rising width. x and b stay. The width keeps a minimum of 0.05.
The far end (Elevation: the round marker at the right foot; Plan: the dashed line; 3D: the round marker on the far edge of the strip, the one farthest from the wall)
b, the falling width. x and c stay.
The values snap in steps of 0.05 in the unit shown, the widths keep a minimum of 0.05, and the load stops at the right edge of the drawing. The boxes of the Model tab show the new values as you drag. After Analyze the handles are plain dots and the inputs are locked; Edit inputs unlocks them again and clears the results.
Entering the model, section by section
The Model tab has three sections: Geometry, Triangular load and Method. Each opens when you click its title; Next and Back at the foot walk you through them. The tables list every field with its symbol, the unit and its default. Where a unit is shown twice or three times, such as m · ft, the units are those of SI · kN, SI · tf and US in turn, and equal ones are merged. Defaults are shown in SI; in another unit system the boxes show the converted values.
Geometry
The wall and the position of the load along the ground behind it. The four distances are also what the drag handles change.
Geometry: the wall height and the three distances of the load.
Geometry fields
Field, unit and default
What to enter
Wall height Hm · ft · default 25.00
The height of the wall; the pressure is added up from the ground surface to this depth. It must be greater than zero.
Distance to load start xm · ft · default 3.00
The distance from the wall to the foot of the rising branch. Zero is allowed: the load then starts at the wall.
Rising branch width cm · ft · default 4.00
The width over which the intensity rises from 0 to q. It must be greater than zero. The peak lies at x + c from the wall.
Falling branch width bm · ft · default 10.00
The width over which the intensity falls from q back to 0. It must be greater than zero. The load ends at x + c + b.
Triangular load
One number: the intensity at the peak of the triangle. It may be zero or more; with zero the pressure is zero.
The intensity at the peak, at the distance x + c from the wall. The intensity is zero at the start and at the far end of the load. The pressure on the wall is in direct proportion to q.
Method
Two buttons choose how the wall is treated. A (?) beside each one opens a window with a drawing, the formula and, for your current inputs, the resultant of both methods.
Under the buttons the module says what the selected method does: “Twice the elastic stress (ψ = 2), for a wall that does not yield.” for the rigid wall, and “The elastic stress in a half-space (ψ = 1), as if the wall were absent — for a wall that deflects.” for the half-space.
Method: two options, each with a (?) window.
Choice
Options
Default
Calculation method
Elastic · rigid wallElastic · half-space
Elastic · rigid wall
The (?) window of the rigid-wall method: the sketch with the mirror-image load, the formula, and the resultant of both methods for the inputs as they stand.
The Analyze bar
Under the three sections a bar shows the state of the model. It reads Not analysed with the line “Enter the wall, the triangular load and the method, then press Analyze. The drawings follow the inputs.” until you press Analyze. After a run it reads “Analysed — the lateral pressure calculated” and says that the inputs are locked, that Edit inputs clears the results and that the unit system can still be changed.
The Model tab with the example and the Analyze bar at the foot.
Choosing the method
Both methods use the same elastic stress of the triangular load. They differ in one factor, ψ, that says how the wall treats it:
Method
ψ
What it assumes
Result
Elastic · rigid wall (default)
2
A wall that does not yield. It keeps the soil at its face from moving horizontally, which a mirror-image load on the other side of the face reproduces, so the elastic stress is doubled.
The larger pressure and force.
Elastic · half-space
1
A wall that deflects enough for the soil at its face to move, so that nothing holds it back: the stress is taken as it is in the half-space, as if the wall were absent.
Half the rigid-wall pressure at every depth. The resultant acts at the same depth.
Which should I pick?
Match the method to the wall. A wall that is held and does not yield takes the rigid-wall method. A wall that deflects enough for the soil at its face to move takes the half-space method.
If you are not sure, run both. The (?) windows show both resultants for your inputs, and one run each gives the full results. On the example the rigid wall gives 78.41 kN/m and the half-space 39.21 kN/m, both at 8.82 m below the ground.
Nothing else changes. The depth zR, the depth of the peak and the shape of the diagram are the same for both; only the size of the pressure differs.
Analyze and read the results
Press Analyze. The inputs lock, the pressure and the resultant appear on the drawings, and the Results tab shows seven cards. Before you analyse, the tab says “Press Analyze on the Model tab to calculate the lateral pressure.”
The Results tab of the example.
Card
What it is
Example
Peak location
The distance from the wall to the peak of the load, x + c
7.00 m
Total load width
The width of the whole triangle, c + b
14.00 m
Resultant force
The resultant PH of the pressure over the wall height, per metre of wall
78.41 kN/m
Resultant depth
The depth zR of the resultant below the ground
8.82 m
Peak wall pressure
The largest horizontal pressure on the wall, σH,max
6.63 kPa
Depth of peak pressure
The depth below the ground at which that peak acts
4.14 m
Calculation method
The method used, with the wall type
Elastic (rigid wall)
On the Elevation view the pressure diagram shows the pressure on the wall at every depth, with the rays R1, R2, R3 and the angles α, β drawn at the depth of the peak pressure, and a note with that depth and the two angles. The resultant is an arrow at its depth, with its value and a dimension zR from the ground. In the 3D view the same pressure stands on the wall as a curtain of curves.
The chips work independently: here the pressure diagram is off and the resultant and the dimensions stay on.
Here the dimensions are off: the drawing is left with the load, the pressure and the resultant.
Units after Analyze
The unit system can be changed after a run: the inputs and the results follow. On the example the US system gives the resultant as 5.37 kip/ft at 28.92 ft below the ground, with a peak pressure of 0.1386 ksf at 13.59 ft. In SI · tf the resultant is 8.00 tf/m and the peak pressure 0.6765 t/m².
The Calculations tab and the report
The Calculations tab writes out the working in four numbered steps:
Load geometry — the three positions x, x + c and x + c + b, with the peak at 7.00 m and the end at 17.00 m on the example, and the method with its factor ψ.
Radii and angles at a depth — R1, R2, R3, α and β at the depth of the peak pressure.
Horizontal pressure — the equation with the functions A(s) and B(s), the pressure at the depth of the peak, and a table of the pressure profile at every H/30 of the wall height, with R1, R2, R3, α, β and σH in each row.
Resultant and its depth — PH and zR, both below the ground and above the base of the wall.
The Calculations tab: each step has its equations, then the numbers for your inputs.
The Report tab turns the same working into a summary report. Fill in the cover (project, location, client, report number, date, prepared by, title or qualification, checked by, and optional notes) and press Save as PDF or Download Word (.docx). The cover details are kept in your browser. The report has six parts: 1 Introduction and scope, 2 Input data (with the three drawings), 3 Calculation (one part for each step above), 4 Results, 5 Summary and 6 References. It is written in the unit system shown, and its units line gives the conversion constants.
The Report tab: the cover form, then the summary report with its two buttons.
The report gives the results with a little more precision than the cards: on the example PH = 78.41 kN/m, zR = 8.816 m and σH,max = 6.635 kPa.
The Theory tab explains the method in six numbered sections: Triangular load on a wall, Radii and angles, Horizontal pressure, Resultant and line of action, Worked example and References. The worked example there is fixed: it does not follow your inputs.
Worked example: the module’s own example
The module opens on this example, so you can follow the numbers on your own screen.
Inputs of the example
Section
Input
Value
Geometry
Wall height, distance to load start
H = 25 m, x = 3 m
Geometry
Rising and falling widths
c = 4 m, b = 10 m
Triangular load
Peak surcharge intensity
q = 20 kPa
Method
Calculation method
Elastic · rigid wall, ψ = 2
Step 1: the load
The peak lies at x + c = 3 + 4 = 7.00 m from the wall and the load ends at 7 + 10 = 17.00 m, so its total width is c + b = 14.00 m. The load on the ground is the area of the triangle, ½ × 20 × 14 = 140 kN per metre of wall.
Step 2: the pressure at the depth of the peak
The peak pressure acts at z = 4.14 m. There the three rays have the lengths R1 = √(3² + 4.14²) = 5.11 m, R2 = √(7² + 4.14²) = 8.13 m and R3 = √(17² + 4.14²) = 17.50 m, and the angles are α = 23.471° and β = 16.917°. The module’s equation gives σH = 6.63 kPa for the rigid wall; the half-space gives half of it, 3.32 kPa.
The pressure profile at a few depths (rigid wall), from the Calculations tab
z (m)
α (°)
β (°)
σH (kPa)
0.00
0.000
0.000
0.00
2.50
20.152
11.288
5.81
5.00
23.499
19.148
6.49
10.00
18.293
24.542
3.95
15.00
13.707
23.559
2.14
25.00
8.799
18.573
0.72
The pressure is zero at the ground surface, reaches its peak of 6.63 kPa at 4.14 m and falls to 0.72 kPa at the foot of the 25 m wall.
Step 3: the resultant
Integrating the pressure over the wall height gives the resultant PH = 78.41 kN/m. The depth where its moment balances is zR = 8.82 m below the ground, which is 16.18 m above the base of the wall.
A check by hand
A wall that went down without limit would take, from a load of 140 kN/m, the force ψ × 140 / π = 2 × 140 / π = 89.13 kN/m, whatever the distance x. A 25 m wall takes 78.41 kN/m of it, about 88 %, which is what you expect when most of the pressure acts within the upper part of the wall. Running the module with a wall height of 1000 m gives 89.12 kN/m, and with the half-space method 44.56 kN/m, which is half of it. An independent numerical integration of the line-load stresses of the triangle also reproduces 6.635 kPa at 4.14 m, 78.41 kN/m and 8.816 m.
How each input changes the answer
Each row below changes one thing in the example (two for the rows that set both widths) and runs the module again. The numbers are the results the module gives, in the units of SI · kN, so you can reproduce any row. The four columns are the resultant PH in kN/m, its depth zR in m, the peak pressure σH,max in kPa and its depth in m.
The example with one change at a time
Change
PH (kN/m)
zR (m)
σH,max (kPa)
Peak depth (m)
The default exampleThe reference
78.41
8.82
6.63
4.14
Half-space methodHalf the pressure at every depth; the same depths
39.21
8.82
3.32
4.14
Peak 40 kPaEverything is in proportion to q: double the pressure and force, the same depths
156.83
8.82
13.27
4.14
Peak 10 kPaHalf the pressure and force
39.21
8.82
3.32
4.14
Load starts at the wall (x = 0)The load is as close as it can be: more force, nearer the surface
83.46
6.53
10.12
1.93
Load starts 6 m from the wallFurther away: less force, deeper
72.25
10.51
4.91
6.14
Load starts 10 m from the wallFurther still
63.33
12.13
3.65
8.64
Rising branch 8 mA wider load, so more load: more force, deeper
93.61
10.15
6.50
5.35
Rising branch 2 mA narrower load: less force
69.40
7.98
6.74
3.49
Falling branch 5 mA shorter tail: less load and less force
52.58
7.91
5.15
3.69
Falling branch 20 mA longer tail: more load and more force, deeper
122.12
10.04
8.59
4.80
Symmetric 7 and 7The same load (140 kN/m) with its centre moved from 9 m to 10 m from the wall: a little less force, deeper
76.44
9.45
5.87
4.78
Narrow load 1 and 1 at 3 mA load of 20 kN/m only: a small force
12.41
5.14
2.07
2.26
Wall 3 m highThe depth of the peak (4.14 m) is below the base, so the largest pressure is the one at the base
11.43
1.92
6.27
3.00
Wall 5 m highOnly the pressure down to 5 m is added up
24.53
3.03
6.63
4.14
Wall 10 m highA shorter wall: less force, shallower resultant
50.89
5.24
6.63
4.14
Wall 15 m highLess force than the 25 m wall
65.64
6.81
6.63
4.14
Wall 40 m highMore force: the lower part adds a little
84.49
10.41
6.63
4.14
Wall 1000 m highThe limit of a very tall wall, 2 × 140 / π = 89.13 kN/m
89.12
13.96
6.63
4.14
Three things stand out. The pressure is in direct proportion to q, and the method only scales it. Distance matters: moving the load from the wall to 10 m away takes the force from 83.46 to 63.33 kN/m and pushes its depth from 6.53 m to 12.13 m. And the wall height sets how much of the diagram is counted: the peak pressure of 6.63 kPa stays the same as long as the wall reaches the depth of the peak, 4.14 m.
Messages: when the module will not calculate
The module checks the five inputs. When a value is not usable it does not guess: it stops and tells you which one. A box left empty counts as a value that cannot be used.
A stop: the wall height is 0. Nothing is calculated.
When
Message
The wall height H is zero, negative or empty
“The wall height H must be greater than zero”
The distance x is negative or empty
“The distance x must be zero or more”
The rising width c is zero, negative or empty
“The rising width c must be greater than zero”
The falling width b is zero, negative or empty
“The falling width b must be greater than zero”
The peak intensity q is negative or empty
“The peak surcharge q must be zero or more”
Each message continues: “The triangle needs positive widths on a wall of positive height, and a load of zero or more. Correct the highlighted value in the Model tab.” When several inputs are wrong the messages are listed together in one line, separated by semicolons. The message appears in four places:
above the Analyze bar in the Model tab;
in the bar itself, which reads “Cannot be analysed — ” followed by the message;
in a window titled Cannot be analysed, opened by pressing Analyze, which ends “Nothing was calculated. Change the inputs marked in red, then press Analyze again.”;
on the drawings, which read “Not calculated”, and in the Results tab, which reads “Not calculated — see the Model tab.”
Correct the value and press Analyze again. A zero peak intensity q is accepted: the module runs and gives a force of 0.00 kN/m. A load that starts at the wall (x = 0) is accepted too.
Good practice and common mistakes
Choose the method for the wall, not for the answer. The rigid-wall and half-space results differ by exactly a factor of 2; decide which describes your wall before you read either.
Measure x from the wall. It is the distance to the foot of the rising branch, not to the peak. The peak is at x + c, and the Results tab shows it as the peak location.
Remember the shape. The load rises over c, the side nearer the wall, and falls over b, the side further away. Check the drawing against your plan before you analyse.
Give the full wall height.PH is the pressure added up down to H. A wall height that stops short of the depth of the peak cuts the diagram, as the 3 m and 5 m rows of the table show.
Take the result per metre. The load is long and parallel to the wall, so PH is in kN/m. It does not include the ends of a load of finite length.
Combine it with the other actions. This is the pressure of the surcharge alone; add it to the earth and water pressures and the other loads of your analysis as your standard requires.
Check the units after you switch the system: type values in the units shown beside the boxes. The module converts the boxes for you when you switch.
Frequently asked questions
How do I calculate the lateral pressure on a wall from a triangular surcharge?
Describe the wall height H, the distance x from the wall to the start of the load, the rising width c, the falling width b and the peak intensity q, choose the rigid-wall or half-space method and press Analyze. GeoTerva’s Triangular load module adds up the elastic line-load stresses of the load exactly and gives the pressure on the wall, the resultant force PH per metre of wall and its depth zR, with every step of the working.
What is the difference between the rigid-wall and the half-space method?
They use the same elastic stress. The rigid-wall method doubles it (ψ = 2) for a wall that does not yield; the half-space method takes it as it is (ψ = 1), as if the wall were absent, for a wall that deflects. The half-space pressure is half the rigid-wall pressure at every depth, and the resultant acts at the same depth. On the module’s example the resultants are 78.41 kN/m and 39.21 kN/m.
Does the module need soil properties?
No. The elastic solution it uses contains no unit weight, friction angle or stiffness, so the only inputs are the wall height, the three distances of the load, the peak intensity and the method.
What do “Peak location” and “Total load width” mean?
The peak location is the distance from the wall to the peak of the triangle, x + c, 7.00 m on the example. The total load width is c + b, the width of the whole triangle, 14.00 m on the example.
Where is the pressure largest?
At a depth that depends on the geometry. On the example the peak is 6.63 kPa at 4.14 m below the ground; with the load starting at the wall it is 10.12 kPa at 1.93 m, and with the load starting 10 m away it is 3.65 kPa at 8.64 m. The pressure at the ground surface is zero.
Does the wall height change the pressure?
Not the pressure at a given depth, but how much of it is added up. PH is the area of the diagram from the ground surface down to H: on the example it is 50.89 kN/m for a 10 m wall, 78.41 kN/m for 25 m and 84.49 kN/m for 40 m. For a very tall wall the force approaches ψ times the load on the ground divided by π: 89.13 kN/m here, the value the 1000 m row of the table nearly reaches.
Can the load start at the wall?
Yes: x may be zero. The example with x = 0 gives PH = 83.46 kN/m at zR = 6.53 m. A negative distance is refused.
Can I move the load with the mouse?
Yes, before you analyse. Drag the load to move it, its peak to change the rising width or its far end to change the falling width, in the Elevation, Plan or 3D view; the boxes follow. After Analyze the inputs and the handles are locked until you press Edit inputs.
Are the results per metre of wall?
Yes. The load is long and parallel to the wall, so the pressure is the same along the whole wall and PH is a force per unit length: kN/m, tf/m or kip/ft.
What does the report contain?
A cover with your project details, an introduction and scope, the input data with the three drawings, the calculation step by step with the pressure profile, the results table with PH, zR and σH,max, a summary and the references. Save it as a PDF or download it as a Word file.
What does the message “Cannot be analysed” mean?
One of the five inputs cannot be used: the wall height or a width is zero or negative, the distance or the peak intensity is negative, or a box is empty. The message names the input; correct it and press Analyze again.
Can I put several loads on the same wall?
This module takes one triangular load. For a point, line, strip, ramp, uniform or rectangular loads use the other manuals of the Surcharge loads family.
Calculate the extra lateral pressure that a uniform surcharge over the whole retained surface adds to a wall: the coefficient, the pressure, its resultant and the depth of the resultant. This manual walks through the screen, every input, the choice of coefficient, the results and the report, with a worked example you can reproduce.
Uniform load gives the extra lateral pressure that a load spread over the whole ground surface behind a wall pushes on the wall. The load raises the vertical stress by q at every depth, and the wall feels the fraction K of it, so the added pressure is the same from the top of the wall to its base:
σH = K · q, P = σH · H, zR = H / 2
σH is the lateral pressure the surcharge adds, P is its resultant per unit length of wall, and zR is the depth below the ground at which P acts. K is the lateral earth-pressure coefficient: you choose it by how the wall behaves, as the at-rest coefficient, the active coefficient, or a value you enter.
What you can describe
A wall of height H (greater than zero) with a uniform surcharge q of zero or more over the whole retained surface.
The coefficient in one of three ways: At rest · rigid wall (K0 = 1 − sin φ′, Jaky), Active · yielding wall (Ka = tan²(45° − φ′/2), Rankine) or Enter K, a value from 0 to 3 that you supply.
The module gives the coefficient, the pressure, the resultant and its depth, draws the load and the pressure diagram in elevation, in plan and in 3D, writes out the working, and prepares a PDF or Word report.
What belongs to other modules
This is the surcharge component only. It is added to the earth-pressure and water-pressure diagrams of the wall calculation, where you combine the three.
A load that stops short of the wall or has a limited width is not uniform in this sense. Those cases have their own modules: Point load (a concentrated load behind the wall), Strip load (a uniform load on a strip parallel to the wall), Line load (a line load parallel to the wall), Triangular load (a load that rises linearly across a strip), Area loads (rectangular loaded areas in plan) and Ramp load (a load rising from zero to a plateau).
Before you start: what you need
Have these ready from your design:
What
Where it comes from
Notes
The wall height H
Your design
The height over which the pressure acts, from the ground surface to the base of the wall. It must be greater than zero.
The surcharge q
Your design loading
A load per unit area on the ground behind the wall, spread over the whole retained surface. Zero or more.
How the wall behaves
Your design
A wall that is propped, anchored or otherwise cannot move keeps the soil at rest. A wall that yields enough lets the soil reach its active state. This decides the coefficient.
The friction angle φ′ of the retained soil
Tests or correlations
An effective friction angle, from 0° to below 90°. Needed for the at-rest and active options.
Or the coefficient K itself
Another source
For a case the two formulas do not cover: an overconsolidated K0, a Coulomb Ka for a rough or inclined wall, or a value measured or back-analysed on site. From 0 to 3.
Quick start in seven steps
Open the module and choose the units
Open Uniform load from the Surcharge Loads family. Pick SI · kN, SI · tf or US in the header; you can change it at any time.
Enter the wall height
In Geometry, type the wall height H.
Enter the surcharge
In Uniform load, type the surcharge q. It acts over the whole retained surface.
Choose the coefficient
In Lateral pressure coefficient, pick At rest · rigid wall, Active · yielding wall or Enter K. The first two ask for the friction angle φ′; the third asks for K. The (?) beside each option opens a window with a sketch of what it assumes.
Press Analyze
Press Analyze at the foot of the Model tab. The bar reads Analysed, the inputs lock, and the pressure and the resultant appear on the drawing.
Read the answer
The Results tab gives K, the lateral pressure σH, the resultant force P and the resultant depth zR. The Elevation, Plan and 3D View buttons change the view.
Take the working and the report
The Calculations tab shows the three steps with your numbers. The Report tab saves a PDF or a Word file.
The screen: three views of the wall
The layout is the one every GeoTerva module shares, described in the workspace guide. For this module the drawing has three views, chosen with the buttons above it:
Elevation is a section through the wall and the retained ground: the wall, the soil, the load as a row of arrows with its value, and the wall height H. After Analyze it adds the pressure diagram on the wall (a rectangle, with its value σH and the coefficient), the resultant P acting on the wall at mid-height, and the depth zR.
Plan looks down on the retained ground. The load covers all of it; after Analyze the strip of pressure along the wall is drawn, with a note that the pressure is the same at every section and depth and that results are per unit length of wall.
3D View shows the wall, the loaded ground behind it and, after Analyze, the pressure as a curtain on the wall face, the resultant P and the dimensions H and zR.
Elevation before Analyze: the geometry alone. The note under the drawing says the load covers the whole retained surface.
Elevation after Analyze: the pressure on the wall, the resultant and its depth.
Plan after Analyze: the pressure along the wall.
3D View after Analyze.
The Show chips
Above the drawing a Show bar has three chips. Pressure distribution and Resultant are available after Analyze, and until then the bar says “The pressure and the resultant appear after Analyze”. Dimensions can be switched at any time: it shows or hides the dimension lines with their values: H, and zR when the resultant is shown, in the elevation and the 3D view. The Resultant chip acts on the elevation and the 3D view; a plan has no place for a resultant.
The Show bar before Analyze.
The Show bar after Analyze.
Entering the model, section by section
The Model tab has three sections. Each opens when you click its title; Next and Back at the foot walk you through them, and Analyze waits below the last one. The tables list every field with its symbol, the unit in each unit system and its default. Where a unit is shown twice or three times, such as m · ft, the units are those of SI · kN, SI · tf and US in turn, and equal ones are merged. Defaults are shown in SI; in SI · tf the surcharge box shows 1.02 t/m², and in US the boxes show 19.69 ft and 0.2089 ksf for the same wall and load.
Geometry
One number: the height of the wall.
Geometry: the wall height.
Geometry field
Field
Symbol
Unit
Default
What to enter
Wall height
H
m · ft
6.00
The height of the wall over which the surcharge pressure acts, from the ground surface to the base. It must be greater than zero; a blank or zero box stops the analysis.
Uniform load
One number: the surcharge. The load acts over the whole retained surface, from the wall to the far edge of the drawing, so no distance from the wall is asked for.
Uniform load: the surcharge.
Uniform load field
Field
Symbol
Unit
Default
What to enter
Uniform surcharge
q
kPa · t/m² · ksf
10.00
The load on the ground behind the wall, as a pressure, spread over the whole retained surface. Zero or more; zero gives zero pressure.
Lateral pressure coefficient
Three buttons choose how K is found; each has a (?) that opens a help window. The box under them follows the choice: the friction angle φ′ for the first two options, the coefficient K for Enter K. A line under the boxes states the formula of the option chosen or, for Enter K, where such a coefficient can come from.
The coefficient: three options, then the friction angle (or K).
Fields of the coefficient section
Field
Symbol
Unit
Default
What to enter
Soil friction angle
φ′
°
30
Effective friction angle of the retained soil, from 0° to below 90°. It gives K0 or Ka, depending on the option. Shown when At rest · rigid wall or Active · yielding wall is chosen.
Lateral pressure coefficient
K
—
0.5
The coefficient you supply, from 0 to 3. The friction angle is not used. Shown when Enter K is chosen.
Choosing the lateral pressure coefficient
The pressure is the load times a coefficient, so the choice of K is the one decision in this module. The three options:
Option
Coefficient
Use it when
What the module says
At rest · rigid wall (the default)
K0 = 1 − sin φ′, Jaky, normally consolidated soil
The wall is propped, anchored or otherwise cannot move.
The wall does not yield, so the soil keeps its at-rest state.
Active · yielding wall
Ka = tan²(45° − φ′/2), Rankine, vertical wall and level ground
The wall yields enough for the soil to reach its active state.
The pressure is smaller than at rest. The active state needs the wall to move; a propped or anchored wall does not reach it.
Enter K
K from 0 to 3, as you enter it
The two formulas do not cover the case: an overconsolidated K0, a Coulomb Ka for a rough or inclined wall, or a value measured or back-analysed on site.
The friction angle is not used.
How the two formulas compare
For the same friction angle the at-rest coefficient is the larger. The table gives K as the module returns it for each friction angle. Under the example surcharge of 10 kPa the pressure σH in kPa is ten times K.
The coefficient against the friction angle (as the module gives it)
φ′
At rest K0
Active Ka
20°
0.6580
0.4903
25°
0.5774
0.4059
30°
0.5000
0.3333
35°
0.4264
0.2710
40°
0.3572
0.2174
At φ′ = 0° both options return K = 1.0000, so the surcharge acts on the wall at full value.
The (?) windows
The (?) beside each option opens a window with a sketch of the wall, the load and the pressure rectangle for that option, the formula, and a line headed With the current inputs that gives K, σH and P and the depth of P for your H, q and φ′. Reading a window changes nothing in the model.
The (?) window of the active option.
Which should I pick?
Start from how the wall is held. A wall that is propped, anchored or cast against something rigid does not move: leave the default, At rest · rigid wall.
Choose Active only when the wall really yields enough for the soil to reach its active state. If you cannot tell, run both and compare: the at-rest value is the larger for the same friction angle.
Use Enter K for a value from elsewhere: an overconsolidated K0, a Coulomb Ka for a rough or inclined wall, a measured value. The module accepts 0 to 3.
Analyze and read the results
Press Analyze. The bar changes to Analysed — the lateral pressure calculated and says “The inputs are locked. Edit inputs clears the results; the unit system can still be changed.” The Results tab shows four cards, and the drawing now carries the pressure and the resultant.
The Results tab of the example.
Card
Symbol
What it is
The example
Pressure coefficient
K
The coefficient used, with its kind in brackets: (K0, at rest), (Ka, active) or (entered).
0.5000
Lateral pressure
σH
The pressure the surcharge adds to the wall, the same at every depth.
5.00 kPa
Resultant force
P
The resultant per unit length of wall, in kN/m (tf/m or kip/ft in the other systems).
30.00 kN/m
Resultant depth
zR
The depth below the ground at which P acts, always H/2; it is also the height of P above the base.
3.00 m
Using the numbers
The pressure diagram is a rectangle: σH over the full height H. In the wall calculation add it to the earth-pressure and water-pressure diagrams.
P is a force per unit length of wall, and acts at zR = H/2 below the ground.
Changing the unit system after Analyze re-states the cards, the drawing and the report without a new run. Edit inputs unlocks the model and clears the results.
The Calculations tab and the report
The Calculations tab writes out the working in three numbered steps. Each step shows its equation (or, for an entered K, the value), the equation with your numbers, and the result; the first two steps add a short note:
Lateral earth-pressure coefficient — K0 = 1 − sin φ′, or Ka = tan²(45° − φ′/2), or the value entered, with the number it gives.
Lateral pressure — σH = K · q, with the note that a load over the whole retained surface raises the vertical stress by q at every depth, so the added pressure is the same from the top of the wall to its base.
Resultant and its depth — P = σH · H and zR = H / 2, with the results.
The Calculations tab: three steps with the example’s numbers.
Before Analyze the tab says “Press Analyze on the Model tab to calculate the lateral pressure.”
The report
In the Report tab fill in the cover (project, location, client, report number, date, prepared by, title, checked by, and optional notes). The details are kept in this browser. After Analyze, Save as PDF and Download Word (.docx) are available; before it they are greyed out. The preview below the buttons is the report itself.
The report has six parts: 1 Introduction and scope, 2 Input data, 3 Calculation (one part for each of the three steps), 4 Results, 5 Summary and 6 References. It carries the elevation, the plan and the 3D drawing, and states the units with the conversion constants.
The Report tab: the cover details, the two download buttons.
The Theory tab has five sections: Uniform load on a wall, Lateral pressure, Resultant and line of action, a worked example, and References.
Worked example: the module’s own example
The module opens on this example, so you can follow the numbers on your own screen.
Inputs of the example
Section
Input
Value
Geometry
Wall height
H = 6 m
Uniform load
Surcharge
q = 10 kPa
Lateral pressure coefficient
Option, friction angle
At rest · rigid wall; φ′ = 30°
Step 1: the coefficient
K0 = 1 − sin 30° = 1 − 0.5 = 0.5000.
Step 2: the lateral pressure
σH = K · q = 0.5000 × 10.00 = 5.00 kPa, at every depth from the top of the wall to its base.
Step 3: the resultant and its depth
P = σH · H = 5.00 × 6.00 = 30.00 kN/m, zR = H / 2 = 6.00 / 2 = 3.00 m
These are the four numbers on the Results tab, and the three steps of the Calculations tab.
The same wall, active
Choose Active · yielding wall and press Analyze again (after Edit inputs). Ka = tan²(45° − 30°/2) = tan²(30°) = 0.3333, so σH = 3.33 kPa and P = 20.00 kN/m at 3.00 m: two thirds of the at-rest force.
The same kind of wall in US units
Switch to US and enter H = 20 ft and q = 0.25 ksf with the at-rest coefficient at 30°. The module gives K = 0.5000, σH = 0.1250 ksf, P = 2.50 kip/ft at zR = 10.00 ft, which is 0.5 × 0.25 = 0.125 ksf, 0.125 × 20 = 2.50 kip/ft and 20/2 = 10 ft by hand.
How each input changes the answer
Each row changes one thing in the example (H = 6 m, q = 10 kPa, φ′ = 30°, at rest) and runs the module again. The numbers are the ones the module gives, so you can reproduce any row.
The example with one change at a time
Change
K
σH (kPa)
P (kN/m)
zR (m)
What happens
The default example: at rest, φ′ = 30°
0.5000
5.00
30.00
3.00
The reference
Active wall
0.3333
3.33
20.00
3.00
Ka = tan²(30°) replaces K0; the pressure and the force are two thirds
K entered = 0.3
0.3000
3.00
18.00
3.00
The friction angle is not used; σH = 0.3 × 10
K entered = 3
3.0000
30.00
180.00
3.00
The largest value the module accepts
φ′ = 25° (at rest)
0.5774
5.77
34.64
3.00
A smaller friction angle gives a larger K0
φ′ = 35° (at rest)
0.4264
4.26
25.59
3.00
A larger friction angle gives a smaller K0
φ′ = 40° (at rest)
0.3572
3.57
21.43
3.00
Smaller again
Active, φ′ = 35°
0.2710
2.71
16.26
3.00
The active coefficient is again the smaller of the two
φ′ = 0° (at rest)
1.0000
10.00
60.00
3.00
K = 1: the full surcharge acts on the wall
H = 4 m
0.5000
5.00
20.00
2.00
σH does not change; P and zR follow H
H = 8 m
0.5000
5.00
40.00
4.00
The same, upward
q = 20 kPa
0.5000
10.00
60.00
3.00
σH and P double
q = 0
0.5000
0.00
0.00
3.00
No pressure; the resultant is zero
The pattern follows the formulas: P = KqH is proportional to each of the three, and zR depends on the wall height alone.
Messages: when the module stops
The module checks the numbers it needs: the wall height, the surcharge, and the friction angle (or the entered K). When one of them cannot be used it stops, and nothing is calculated.
A red message appears in the Model tab above the Analyze bar, and the bar turns brown and reads Cannot be analysed, followed by the message.
If you press Analyze, a window titled Cannot be analysed gives the message and says “Nothing was calculated. Change the inputs marked in red, then press Analyze again.”
The Results tab says “Not calculated — see the Model tab.”, and the drawings say “Not calculated — correct the highlighted input in the Model tab”.
A stop in the Model tab: a wall height of zero.
The window that Analyze opens.
Kind
When
Message and what to do
Stop
The wall height is zero, negative or empty
“The wall height H must be greater than zero.” Enter a height above zero.
Stop
The surcharge is negative or empty
“The surcharge q must be zero or more.” Enter zero or a positive load.
Stop
At rest or Active is chosen and φ′ is outside 0° to below 90°, or empty
“Enter a friction angle φ′ from 0° to below 90°.” Enter an angle in that range, or choose Enter K.
Stop
Enter K is chosen and K is outside 0 to 3, or empty
“Enter a coefficient K between 0 and 3.” Enter a value in that range.
Every message continues with the same two sentences: “The pressure needs a positive wall height, a load of zero or more and a valid coefficient. Correct the highlighted value in the Model tab.”
When more than one value is wrong, the messages are joined in one stop, for example “The wall height H must be greater than zero; The surcharge q must be zero or more.” With Enter K chosen the friction angle is not used, so its box is not checked.
Good practice and common mistakes
Choose K by how the wall is held, not by habit. The default, at rest, is for a wall that does not move. Choose active only when the wall yields enough to reach that state; if you are not sure, run both and compare.
Use this module only for a load over the whole retained surface. A load of limited width or length, or one that starts away from the wall, belongs to the Strip load, Area loads or Ramp load module, or to the point, line or triangular ones.
Enter q as a pressure, load per unit area, not as a force per metre of wall. In US units q is in ksf: 10 kPa is 0.2089 ksf.
Read P per unit length. It is in kN/m, so multiply by the length of wall only when you need a total force on a length of wall.
Add the result to the other pressures.σH is the surcharge component only; the wall calculation combines it with the earth pressure of the soil and the water pressure.
Use Enter K for a value from another source, from 0 to 3, such as an overconsolidated K0 or a Coulomb Ka. The friction angle is then not used.
Note your values. The module opens on its example every time and does not keep what you typed; the report is the record of an analysis.
Check the units after switching the system: type values in the units shown beside the boxes.
Frequently asked questions
How is the lateral pressure from a uniform surcharge calculated?
A load q over the whole retained surface raises the vertical stress by q at every depth, and the wall feels the fraction K of it: σH = K · q. The resultant is P = σH · H per unit length of wall, acting at zR = H/2 below the ground. For the module’s example, K0 = 0.5000, σH = 5.00 kPa and P = 30.00 kN/m at 3.00 m.
Why is the pressure the same at every depth?
Because the load covers the whole retained surface, it raises the vertical stress by the same q at every depth, and the coefficient K is a constant. The diagram is a rectangle from the top of the wall to its base, so the resultant is at mid-height.
Should I use the at-rest or the active coefficient?
Use at rest, K0 = 1 − sin φ′, for a wall that cannot move: propped, anchored or otherwise held. Use active, Ka = tan²(45° − φ′/2), only for a wall that yields enough for the soil to reach its active state. For φ′ = 30° the two coefficients are 0.5000 and 0.3333.
What if the load does not cover the whole surface?
Then it is not a uniform load in the sense of this module. A load on a strip parallel to the wall, a line load, a point load, a triangular load, a ramp load or rectangular loaded areas each have their own Surcharge Loads module, which gives the pressure at each depth and its resultant.
Does the result include the earth pressure of the soil and the water pressure?
No. The result is the surcharge component only. You add it to the earth-pressure and water-pressure diagrams in the wall calculation.
What values does the module accept?
The wall height must be greater than zero, the surcharge zero or more, the friction angle from 0° to below 90° (for the at-rest and active options) and an entered coefficient from 0 to 3. Anything else stops the analysis with a message that names the value.
Can I drag the load on the drawing?
No: a uniform load covers the whole retained surface, so it has no position. Change q, H or K in the Model tab; the drawing follows. After Analyze the inputs are locked until you press Edit inputs.
Which units does it use, and what are the units of the answer?
SI · kN, SI · tf or US, switchable in the header at any time, even after Analyze. The pressure is in kPa, t/m² or ksf, and the resultant per unit length in kN/m, tf/m or kip/ft; the depth is in m or ft.
Why does the resultant act at mid-height?
The pressure is constant over the height of the wall, so its resultant, σHH, acts at the middle of the rectangle: zR = H/2 below the ground, which is also H/2 above the base.
What does the report contain?
A cover with your project details and a summary, then six parts: introduction and scope, input data, the calculation step by step, results, summary and references, with the elevation, plan and 3D drawings. It is saved as a PDF or a Word file after Analyze.
Does the module remember my inputs?
No. It opens on its example (6 m wall, 10 kPa, 30°, at rest) each time the page is opened. The report cover details you type are kept in the browser, and the unit system is remembered.
Calculate the extra lateral pressure a wall takes from rectangular loaded areas on the ground behind it: the pressure at a section along the wall, its resultant and depth, and the bending moment about the base. This manual walks through the screen, every input, how to move the loads, the two methods, the results and the report, with a worked example you can reproduce.
Area loads gives the extra lateral pressure on a wall from one or more rectangular loaded areas on the ground behind it. Each rectangle carries a uniform surcharge q. The module works out the pressure the loads put on the wall at a vertical section of your choice, from the top of the wall to its base, and from that diagram the resultantVx(H), its depth zR and the bending momentMy(H) about the base. All of them are per unit length of wall at that section.
The pressure comes from the elastic stress under a point load (Boussinesq), added up over every rectangle:
ψ is the wall factor of the method you choose: 2 for a rigid wall (the default), 1 for the half-space. The integral along the wall is exact and the integral across it is adaptive, so the rectangle is not replaced by a set of point loads.
What you can describe
A wall of height H and the Poisson’s ratio μ of the soil, from 0 to 0.5.
Up to 20 rectangular loads. Each has its pressure q, the position of its centre (X0 from the wall face, Y0 along the wall) and its sides (Lx across the wall, Ly along it).
The section Ys along the wall at which the pressure is evaluated.
The method: Elastic · rigid wall or Elastic · half-space.
The number of rows nz of the table of the wall integration, from 1 to 200.
The module draws the loads and the pressure diagram in elevation, in plan and in 3D, shows the pressure and the resultant of the sum and of each load alone, writes out the working, and prepares a PDF or Word report. You can drag a load on the drawing to move or resize it.
What belongs to other modules
This is the surcharge component only: it is added to the earth-pressure and water-pressure diagrams of the wall calculation.
A load of another shape has its own module: Point load (a concentrated load), Strip load (a uniform load on a strip parallel to the wall), Line load (a line load parallel to the wall), Triangular load (a load that rises linearly across a strip), Uniform load (a uniform surcharge over the whole surface) and Ramp load (a load rising from zero to a plateau).
Use Area loads when the loaded areas have a finite length along the wall and the pressure at a particular section matters: footings, slabs, stockpiles, a loaded platform.
Before you start: what you need
Have these ready from your design, and a plan of the loads with the wall face as the reference line:
What
Where it comes from
Notes
The wall height H
Your design
The height over which the pressure is integrated, from the ground surface to the base of the wall. It must be greater than zero.
Poisson’s ratio μ of the soil
Tests or typical values
From 0 to 0.5. The module opens on 0.5; a lower value brings a small tension near the surface and a caution (see Messages).
For each load: the pressure q
Your loading
A load per unit area, zero or more.
For each load: the distance X0 of its centre from the wall face and the side Lx across the wall
Your plan
The rectangle must lie behind the wall face: X0 is at least Lx/2. The near edge is at X0 − Lx/2.
For each load: the position Y0 of its centre along the wall and the side Ly along it
Your plan
Y0 is measured from an origin you choose on the wall, and the section Ys is measured from the same origin. Ly must be greater than zero.
The section Ys
Your design
The vertical line along the wall at which you want the pressure, for example the most loaded one. Any number.
How the wall behaves
Your design
A wall that does not move takes the rigid-wall method; a wall that deflects enough to relieve the soil takes the half-space method.
Quick start in eight steps
Open the module and choose the units
Open Area loads from the Surcharge Loads family. Pick SI · kN, SI · tf or US in the header; you can change it at any time. Open Area loads.
Enter the wall and the section
In Analysis, type the wall height H, Poisson’s ratio μ and the section coordinate Ys.
Describe the loads
In Rectangular area loads, fill in q, X0, Y0, Lx and Ly of Load 1 and Load 2, or drag them on the drawing. Press ＋ Add area load for another rectangle and the cross on a card to remove one.
Choose the method
In Method, pick Elastic · rigid wall (the default) or Elastic · half-space. The (?) beside each opens a window with a sketch of what it assumes.
Set the rows of the table
In Numerical integration, leave nz at 20, or change the number of rows of the depth table. From 2 rows upwards the answers do not depend on it.
Press Analyze
Press Analyze at the foot of the Model tab. The bar reads Analysed, the inputs lock, and the pressure diagram and the resultants appear on the drawing.
Read the answer
The Results tab gives the peak pressure, the base shear Vx(H), the base moment My(H) and the resultant depth, and the share of each load. The Elevation, Plan and 3D View buttons change the view.
Take the working and the report
The Calculations tab shows the five steps with your numbers. The Report tab saves a PDF or a Word file.
The screen: three views and the loads you can drag
The layout is the one every GeoTerva module shares, described in the workspace guide. In this module the Model tab is one page of four sections, and the drawing has three views, chosen with the buttons above it. Before Analyze a view shows the geometry alone: the wall, the ground, the loads with their values and the dimensions. After Analyze the pressure and the resultants are added.
Elevation is a section through the wall at Ys: the wall, the ground and each load as a bar with arrows and its value. The dimension lines give the distance from the wall to the near edge of each load and its width Lx. After Analyze it adds the pressure diagram on the wall, the peak σx,max with its depth, the resultant of each load alone (Vx and its height L above the base) and the resultant of all the loads with Vx(H), My(H) and its height above the base.
Plan looks down on the ground. The wall is on the left with the origin and the axes: X is measured from the wall face, Y along the wall from the origin. Each load is a coloured rectangle with its value; the dashed green line is the section Ys. The dimensions give the near edge, Lx, the lower edge and Ly. The plan is the same before and after Analyze.
3D View shows the wall, the loaded ground and, after Analyze, the pressure on the section, the resultants and the dimensions. A box at the top lists the resultant of each load, and a box at the foot the resultant of all of them.
Elevation before Analyze: the geometry alone, with the Show chips greyed except Dimensions.
Elevation after Analyze: the pressure on the wall, the resultant of each load and of the sum.
Plan: the loads behind the wall and the section line.
3D View after Analyze.
Choosing and moving a load
Click a load’s card in the Model tab, or the load on the drawing, to select it: its card is outlined, and its handles appear on the drawing. The note under the drawing reads “Drag a load to move it and its edges to resize it — in Elevation across the wall only, in Plan also along it and the section line Yₛ”. Dragging changes the boxes in the Model tab, so the two always agree.
View
What you drag
What changes
Elevation
The body of a load
X0: the load moves across the wall, towards or away from it. Y0 does not change.
Elevation
The near or far end of a load bar
X0 and Lx: the near or the far edge moves.
Plan
The body of a load
X0 and Y0: the load moves in both directions.
Plan
A side of a load (the small squares of the selected load)
The near or far edge (X0, Lx), or the lower or upper edge (Y0, Ly).
Plan
The section line, by its circle beside the wall or by the dashed line itself
Ys.
3D View
Nothing
The 3D view shows the model; change it in the other views or in the Model tab.
A dragged edge or position snaps to 0.05 m (0.05 ft in US units). A side cannot be made narrower than 0.05 m, and a load cannot be dragged across the wall face: its near edge stops at the wall. Dragging is available before Analyze; after it the inputs are locked, the note under the drawing is hidden, and Edit inputs unlocks them.
Plan with three loads. The new load, in green, is selected and overlaps the orange one.
The Show chips
Above the drawing a Show bar controls what is drawn. With one load it has three chips, Pressure distribution, Resultant and Dimensions. With two or more loads it has three groups: Pressure distribution, Resultant force and Dimensions, each with an All loads chip for the sum and one chip for each load (q1, q2, … in the colour of the load). The pressure and the resultant chips are available after Analyze; until then the bar says “The pressure and the resultant appear after Analyze”. The Dimensions chips can be switched at any time.
The pressure chip of a load draws the diagram of that load alone as a dashed curve in its colour, and its resultant chip draws the arrow of that load alone. They are useful to see which load governs. The Resultant chips act on the elevation and the 3D view; the plan has no place for a resultant.
Only the chips of q1 on: the diagram and the resultant of Load 1 alone.
Entering the model, section by section
The Model tab has four sections, always on the page: Analysis, Rectangular area loads, Method and Numerical integration. All four sections stay on the page; Next and Back at the foot of the highlighted section move the highlight to the next or the previous one and scroll to it, and Analyze waits below the last. The tables list every field with its symbol, the unit in each unit system and its default. Where a unit is shown twice or three times, such as m · ft, the units are those of SI · kN, SI · tf and US in turn, and equal ones are merged. Defaults are shown in SI. In SI · tf the load box shows 5.10 t/m²; in US the boxes show 29.53 ft for the wall, 6.56 ft for Ys, 1.04 ksf, 3.28 ft, 6.56 ft, 3.94 ft and 11.81 ft for Load 1.
Analysis
The wall and the section.
Analysis: wall height, Poisson’s ratio and the section.
Fields of the Analysis section
Field
Symbol
Unit
Default
What to enter
Wall height
H
m · ft
9
The height of the wall over which the pressure is integrated, from the ground surface to the base. It must be greater than zero.
Poisson ratio
μ
—
0.5
Poisson’s ratio of the soil, from 0 to 0.5. At 0.5 the term (1 − 2μ) of the stress formula vanishes; below 0.5 a small tension appears near the surface.
Wall-section coordinate
Ys
m · ft
2
The section along the wall at which the pressure is evaluated, measured along the wall from the same origin as Y0. Any number.
Rectangular area loads
One card for each load, numbered and coloured: the colour is the one the load has in the drawings and in the Show chips. A card has the five fields below (the defaults are those of Load 1; Load 2 differs in X0), and two values the module works out for you and cannot be edited: the areaA = LxLy and the loadP = qA in kN (tf or kip).
Rectangular area loads: a card for each load.
Fields of each load
Field
Symbol
Unit
Default
What to enter
q
q
kPa · t/m² · ksf
50
The surcharge on the rectangle, as a pressure. Zero or more.
X₀
X0
m · ft
1 (Load 1), 3.4 (Load 2)
Distance of the centre of the rectangle from the wall face. At least Lx/2, so that the rectangle lies behind the wall face.
Y₀
Y0
m · ft
2
Position of the centre along the wall, from the same origin as Ys.
Lₓ
Lx
m · ft
1.2
Side across the wall (perpendicular to the wall face). Greater than zero.
Lᵧ
Ly
m · ft
3.6
Side along the wall. Greater than zero.
Adding, removing and selecting loads
＋ Add area load adds a rectangle. It starts as a copy of the selected load, with the same q, Y0, Lx and Ly, placed just beyond its far edge: X0 is moved on by Lx plus 0.5 m (0.5 ft in US units). The new load becomes the selected one. If the place is already taken by another load, the two overlap, and the pressures of overlapping loads add (the what-if table shows the effect); type or drag the new load to where you want it.
The cross (✕) on a card removes that load. It is there when there are two or more loads: one load always remains.
Up to 20 loads. At 20 the button reads “Up to 20 area loads” and is disabled.
A load is selected by clicking its card, by typing in one of its boxes, or by clicking it on the drawing. The selected load is outlined on its card and has handles on the drawing.
A box with a value the module cannot use (a negative q, a side of zero, a load that crosses the wall face) stops the analysis and the message names the load (see Messages).
Method
Two buttons, each with a (?). The line under them states the factor of the option chosen. They are described in Choosing the method.
Method: rigid wall or half-space.
Numerical integration
One number, the rows of the depth table of the working. Every rectangle is integrated exactly along the wall and adaptively across it, so no number of area elements is asked for.
Numerical integration: the rows of the depth table.
Field of the Numerical integration section
Field
Symbol
Unit
Default
What to enter
Vertical increments
nz
—
20
The number of rows of the depth table, H/nz apart: a whole number from 1 to 200. From 2 rows upwards it does not change any result (see How each input changes the answer); keep it at 2 or more.
The whole Model tab, with the Analyze bar at its foot.
Choosing the method, μ and the section
The two methods
Option
Wall factor
What it assumes
Use it when
Elastic · rigid wall (the default)
ψ = 2
A smooth wall that does not move. Mirroring every load across the wall face cancels the wall-normal displacement and the shear on that plane, so the pressure on the wall is exactly twice the half-space stress, for any Poisson’s ratio.
The wall is a smooth wall that does not move.
Elastic · half-space
ψ = 1
The elastic stress in a half-space, as if the wall were absent.
The wall deflects enough to relieve the soil.
The second gives half the first everywhere: on the module’s example σx,max is 26.91 kPa for a rigid wall and 13.45 kPa for the half-space, and Vx(H) is 50.23 and 25.12 kN/m. The depth of the peak and the resultant depth are the same. The (?) beside each option opens a window with a sketch of the wall, the load and the pressure for that option, the formula, and a line headed With the current inputs that gives Vx(H) and σx,max for both methods at your inputs.
Reading a window changes nothing in the model.
The (?) window of the rigid-wall method.
Poisson’s ratio μ
μ enters the stress formula through the term (1 − 2μ). At the default of 0.5 the term is zero. With μ below 0.5 the pressure is smaller (on the example), and the elastic solution gives a small tension near the surface; the module then shows a caution and keeps the sign in the results (see Messages). On the example, μ = 0.3 gives Vx(H) = 32.72 kN/m, against 50.23 kN/m at 0.5.
The section Ys
The module gives the pressure at one vertical section of the wall, at Y = Ys. The loads need not cross it: a load that does not reach the section still contributes, less the farther it is, and the Results tab marks it “off the section”. To find the most loaded part of the wall, run the module at several sections: on the example, the section through the centre of the loads gives Vx(H) = 50.23 kN/m, and a section 0.2 m beyond the end of the loads gives 26.36 kN/m.
The rows nz
nz sets how many rows the table of the wall integration has. The shear force and the moment are integrated between the rows, not summed from them. From 2 rows upwards, nz does not change any result:nz = 5 and nz = 100 give the same answers as 20. With 1 row the shear, the moment and the resultant depth are the same, but the peak pressure is read from the two table rows only, so keep nz at 2 or more (the default is 20).
Analyze and read the results
Press Analyze. The bar changes to Analysed — the lateral pressure calculated and says “The inputs are locked. Edit inputs clears the results; the unit system can still be changed.” The Results tab shows eight cards and a list of the loads, and the drawing now carries the pressure and the resultants.
The Results tab of the example.
Card
Symbol
What it is
The example
Peak lateral pressure
σx,max
The largest ordinate of the pressure diagram on the wall at the section.
26.91 kPa
Depth of peak pressure
z
The depth below the ground at which the peak occurs.
0.4460 m
Base shear
Vx(H)
The resultant of the pressure on the wall, per unit length of wall: the shear force at the base.
50.23 kN/m
Base moment
My(H)
The moment of the pressure about the base, per unit length of wall.
363.53 kN·m/m
Total loaded area
The sum of the areas LxLy of all the loads.
8.64 m²
Total vertical load
The sum of qLxLy: the load on the ground, not the load on the wall.
432.00 kN
Calculation method
Elastic, with the wall in brackets: (rigid wall) or (half-space).
Elastic (rigid wall)
Resultant depth
zR
The depth below the ground at which Vx(H) acts. Its height above the base is H − zR.
1.76 m
The Loads list
Below the cards each load has a line with its colour, its area A and its load P. With two or more loads the line also gives the shear force Vx of that load alone and the height L of its resultant above the base, the same numbers as the arrows on the drawing: on the example Load 1 gives 33.14 kN/m at 7.86 m and Load 2 gives 17.09 kN/m at 6.03 m, and the two add up to 50.23 kN/m. A load whose length along the wall does not include the section is marked “off the section”.
Using the numbers
Vx(H) and My(H) are per unit length of wall at the section. Add the pressure diagram, or Vx(H) acting at the height H − zR above the base, to the earth-pressure and water-pressure diagrams of the wall calculation.
The resultant of the sum is drawn on the elevation with its height above the base (L = 7.24 m on the example, which is H − zR = 9 − 1.76 to the rounding of the figures).
Changing the unit system after Analyze re-states the cards, the drawing and the report without a new run. Edit inputs unlocks the model and clears the results.
The Calculations tab and the report
The Calculations tab writes out the working in five numbered steps, each with its equations, a short note and the numbers:
Wall, section and method — the method with its factor ψ, H, μ and Ys, and a table of the loads: q, X0, Y0, Lx, Ly, A and P.
Rectangles relative to the section — x1 = X0 − Lx/2, x2 = X0 + Lx/2, y1 = Y0 − Ly/2 − Ys and y2 = Y0 + Ly/2 − Ys for each load, with their values.
Point-load stress (Boussinesq) — the horizontal stress σx perpendicular to the wall under a point load.
Integration over each rectangle — the integral along the wall and across it; at the depth of the peak the stress of each load and their sum σx,max; then the table of the wall integration, every H/nz: z, σx, Vx and My.
Shear force and bending moment — Vx(H), My(H) and the resultant depth zR.
The Calculations tab: the method, the loads, then the steps.
Before Analyze the tab says “Press Analyze on the Model tab to calculate the lateral pressure.” Cautions and notes of the run appear at the end of the working.
The report
In the Report tab fill in the cover: Project, Location, Client, Report no., Date, Prepared by (name), Title / qualification, Checked by and optional Notes. The details are kept in this browser. After Analyze, Save as PDF and Download Word (.docx) are available; before it they are greyed out, and the tab says “Press Analyze on the Model tab to calculate the lateral pressure.”
The report has six parts: 1 Introduction and scope, 2 Input data, 3 Calculation (3.1 to 3.5, one for each step), 4 Results, 5 Summary and 6 References. It carries the elevation, the plan and the 3D drawing, and states the units with the conversion constants. When the run has a caution or a note, an Assumptions and notes part is added after Results, and the parts after it move down by one.
The Report tab: the cover details, the two buttons and the start of the preview.
The Theory tab has six sections: Area loads on a wall, Stress from a point load, Integrating a rectangle, Shear force and bending moment, a worked example and References.
Worked example: the module’s own example
The module opens on this example, so you can follow the numbers on your own screen.
Inputs of the example
Section
Input
Value
Analysis
Wall height, Poisson’s ratio, section
H = 9 m, μ = 0.5, Ys = 2 m
Rectangular area loads
Load 1
q = 50 kPa, X0 = 1 m, Y0 = 2 m, Lx = 1.2 m, Ly = 3.6 m
Rectangular area loads
Load 2
The same, with X0 = 3.4 m
Method
Method
Elastic · rigid wall (ψ = 2)
Numerical integration
Rows
nz = 20
Step 1: the loads and their position
Each rectangle has the area A = 1.2 × 3.6 = 4.32 m² and the load P = 50 × 4.32 = 216.00 kN; together 8.64 m² and 432.00 kN. Relative to the wall and the section: x1 = 1 − 0.6 = 0.4 m and x2 = 1 + 0.6 = 1.6 m for Load 1, 2.8 to 4.0 m for Load 2; for both, y1 = 2 − 1.8 − 2 = −1.8 m and y2 = 2 + 1.8 − 2 = 1.8 m, so the section runs through the middle of both.
Step 2: the pressure on the wall
The stress under a point load is integrated over each rectangle and doubled for the rigid wall. The sum has its peak at the depth z = 0.4460 m: Load 1 gives 24.98 kPa there, Load 2 gives 1.93 kPa, and σx,max = 24.98 + 1.93 = 26.91 kPa. The pressure then falls quickly with depth. The table of the wall integration, as the Calculations tab gives it:
Rows of the table of the wall integration (the example, 20 rows of 0.45 m)
z (m)
σx (kPa)
Vx (kN/m)
My (kN·m/m)
0.00
0.00
0.00
0.00
0.4500
26.91
8.45
1.45
0.9000
20.89
19.44
7.84
1.80
10.31
32.80
32.06
3.60
3.46
43.85
102.82
5.40
1.35
47.85
185.91
9.00
0.2848
50.23
363.53
Step 3: the resultant and the moment
The shear force grows with depth and reaches Vx(H) = 50.23 kN/m at the base: 33.14 from Load 1 and 17.09 from Load 2. The moment about the base is My(H) = 363.53 kN·m/m, and the resultant acts at zR = 1.76 m below the ground, that is 7.24 m above the base, which the elevation shows as L. As a check, Vx(H) (H − zR) = 50.23 × (9 − 1.76) = 363.7 kN·m/m, equal to My(H) to the rounding of zR.
The same wall on the half-space
Choose Elastic · half-space (after Edit inputs) and analyze again: σx,max = 13.45 kPa, Vx(H) = 25.12 kN/m and My(H) = 181.77 kN·m/m, exactly half of the rigid-wall values, at the same depths 0.4460 m and 1.76 m.
How each input changes the answer
Each row changes one thing in the example and runs the module again. The numbers are the ones the module gives, so you can reproduce any row.
The example with one change at a time
Change
σx,max (kPa)
Vx(H) (kN/m)
My(H) (kN·m/m)
zR (m)
The default example
26.91
50.23
363.53
1.76
Half-space method
13.45
25.12
181.77
1.76
q = 100 kPa on both loads
53.81
100.46
727.07
1.76
H = 6 m
26.91
48.55
214.84
1.58
H = 12 m
26.91
50.76
515.15
1.85
μ = 0.3
20.19
32.72
244.28
1.53
Ys = 0 m
10.26
26.36
178.85
2.21
Ys = 4 m
10.26
26.36
178.85
2.21
Ys = 8 m
0.4061
2.44
11.53
4.27
Load 2 removed
25.03
33.14
260.49
1.14
Load 2 at X0 = 6.4 m
25.35
41.45
299.42
1.78
Load 1 at X0 = 0.6 m
50.00
52.86
399.02
1.45
A third load at X0 = 4.6 m
27.77
62.82
431.30
2.13
A third load added and left where it starts
30.58
70.95
497.90
1.98
Ly = 10 m on both loads
28.49
66.51
455.90
2.15
nz = 5
26.91
50.23
363.53
1.76
nz = 100
26.91
50.23
363.53
1.76
What each row shows. The depth of the peak is given where it differs from the example’s 0.4460 m.
Half-space method. Every value is half of the rigid-wall value; the depths are the same.
q = 100 kPa on both loads. Doubling q doubles the pressure, the shear and the moment; the depths do not change.
H = 6 m. The peak is unchanged; the pressure below 6 m is lost, so the moment drops most.
H = 12 m. A little more shear and moment: the pressure is small at depth.
μ = 0.3. Lower pressure, and a tension near the surface: a caution is raised (the peak is at 0.4733 m).
Ys = 0 m. The section is 0.2 m beyond the lower end of the loads (the peak is at 0.5759 m).
Ys = 4 m. The same, 0.2 m beyond the upper end: the loads are symmetric about Y = 2 m (the peak is at 0.5759 m).
Ys = 8 m. Far from the loads: small pressure, and the peak is deep (the peak is at 3.09 m).
Load 2 removed. Load 1 alone: the 33.14 kN/m of its line in the Loads list (the peak is at 0.4189 m).
Load 2 at X0 = 6.4 m. A farther load contributes less (the peak is at 0.4236 m).
Load 1 at X0 = 0.6 m. Its near edge is at the wall face: the peak is at the surface and the Calculations tab notes it (the peak is at 0.00 m).
A third load at X0 = 4.6 m. Same size, behind the other two (4.0 to 5.2 m): a smaller addition (the peak is at 0.4599 m).
A third load added and left where it starts. It starts at X0 = 2.7 m and overlaps Load 2, so it adds much more (the peak is at 0.5019 m).
Ly = 10 m on both loads. More load along the wall: more pressure at the section (the peak is at 0.4706 m).
nz = 5. No change.
nz = 100. No change.
The pattern: the pressure is linear in q and adds up load by load, it falls quickly with distance from the wall and from the section, and the method only scales it by a factor of two.
Messages: stops, cautions and notes
The module checks the numbers it needs. When one cannot be used it stops, and nothing is calculated; when a result needs care it raises a caution; and it adds a note where it assumed something.
Stops
A red message appears in the Model tab above the Analyze bar, and the bar turns brown and reads Cannot be analysed, followed by the message.
If you press Analyze, a window titled Cannot be analysed gives the message and says “Nothing was calculated. Change the inputs marked in red, then press Analyze again.”
The Results tab says “Not calculated — see the Model tab.”, and the drawings say “Not calculated — correct the highlighted input in the Model tab”.
A stop: Load 1 has X0 = 0.4 m with Lx = 1.2 m, so it would cross the wall face.
Kind
When
Message and what to do
Stop
The wall height is zero, negative or empty
“The wall height H must be greater than zero.” Enter a height above zero.
Stop
μ is outside 0 to 0.5, or empty
“Poisson's ratio μ must lie between 0 and 0.5.” Enter a value in that range.
Stop
Ys is empty
“The section coordinate Yₛ must be a number.” Enter the section.
Stop
nz is not a whole number from 1 to 200
“The vertical increments nz must be a whole number from 1 to 200.” Enter a whole number in that range.
Stop
A load whose near edge is in front of the wall face (X0 < Lx/2)
“Load 1 crosses the wall face: X₀ must be at least Lₓ/2.” (the number is that of the load) Increase X0 or reduce Lx.
Stop
A load with a negative or empty q, or a side that is zero, negative or empty
“Load 2: q must be zero or more and Lₓ, Lᵧ greater than zero.” (the number is that of the load) Correct the load named.
Every stop continues with the same two sentences: “Every rectangle must lie behind the wall face (X ≥ 0) with positive plan dimensions, on a wall of positive height. Correct the highlighted value in the Model tab.” When more than one value is wrong, the messages are joined in one stop, separated by semicolons, for example “Load 1 crosses the wall face: X₀ must be at least Lₓ/2; Load 2: q must be zero or more and Lₓ, Lᵧ greater than zero.”
Caution and note
Kind
When
Message and what to do
Caution
Some ordinates of the pressure are negative, which happens when μ is below 0.5
“Some ordinates are negative (tension). With μ below 0.5 the elastic solution gives a small tension near the surface, and soil cannot pull on a wall. The sign is kept in the results; ignore the negative part if it is not wanted.” It appears in the Model tab, at the end of the Calculations tab and in the report, in a part called Assumptions and notes.
Note
A load starts at the wall face (X0 = Lx/2)
“A load starts at the wall face. The stress under a load edge on the wall is singular at the surface; the integrals stay finite and are evaluated adaptively.” It appears in the Calculations tab and in the report.
With μ = 0.3 the first row of the table of the wall integration is σx = −8.36 kPa at the ground surface for the example. With μ = 0 the example gives Vx(H) = 6.45 kN/m and a resultant depth of −1.14 m: the tension near the surface then outweighs the pressure there, and the diagram is the better guide than the single number.
Good practice and common mistakes
Measure X0 to the centre.X0 is the distance from the wall face to the centre of the rectangle, not to its near edge. The near edge is X0 − Lx/2, and the dimension lines of the drawing show it.
Use one origin along the wall.Y0 of every load and Ys are measured from the same origin. A section that does not lie within the length of a load is not wrong, but it gives a smaller pressure.
Look for the governing section. The module gives the pressure at one section. Run it at the section through the middle of the heaviest load and at the others that matter, and design for the largest.
Choose the method from the wall. Rigid wall for a smooth wall that does not move, half-space for a wall that deflects enough to relieve the soil; the rigid-wall values are twice the half-space ones.
Watch overlapping loads. A load added to the list starts beside the selected one and can overlap another. Overlapping rectangles add their pressures, so move or retype it.
Keep μ at 0.5 unless you have a reason. Lower values reduce the pressure and bring a tension near the surface; the module keeps the sign.
Use the Show chips to see which load governs. The dashed curve and the arrow of each load alone are on the drawing.
Enter q as a pressure, load per unit area, not as a force. The module shows the load P = qA beside each card as a check.
Read the results per unit length.Vx(H) is in kN/m of wall at the section, and My(H) in kN·m/m.
Add the result to the other pressures. The result is the surcharge component only; the wall calculation combines it with the earth pressure and the water pressure.
Note your values. The module opens on its example every time and does not keep what you typed; the report is the record of an analysis.
Check the units after switching the system: type values in the units shown beside the boxes.
Frequently asked questions
How do I calculate the lateral pressure on a wall from a rectangular surface load?
The horizontal stress under a point load (Boussinesq) is integrated over the rectangle and the stresses of all the rectangles add; for a wall that does not move the result is doubled. In GeoTerva’s Area loads module you enter the wall height, the section along the wall and, for each load, the pressure, the position of its centre and its two sides, press Analyze, and read the pressure diagram, the resultant Vx(H), its depth and the moment My(H). For the module’s example, Vx(H) = 50.23 kN/m and σx,max = 26.91 kPa.
What is the difference between the rigid-wall and the half-space method?
The rigid-wall method (ψ = 2) is for a smooth wall that does not move: a mirror-image load across the wall face cancels the wall-normal displacement, so the pressure on the wall is twice the half-space stress. The half-space method (ψ = 1) takes the elastic stress as if the wall were absent, for a wall that deflects enough to relieve the soil. The second gives exactly half the first everywhere.
What is the section Ys?
The vertical line along the wall at which the pressure is worked out. The module gives the pressure diagram, the resultant and the moment per unit length of wall at that section. Loads that do not reach the section still contribute, less the farther away they are. Run the module at the sections that matter and design for the largest.
How are X0, Y0, Lx and Ly measured?
X0 is the distance from the wall face to the centre of the rectangle and Lx its side across the wall, so the near edge is at X0 − Lx/2 and must not be in front of the wall. Y0 is the position of the centre along the wall and Ly the side along it. Y0 and the section Ys are measured from the same origin, which you place where you like.
How many loads can I enter, and how do I move one?
Up to 20. Press ＋ Add area load for another, and the cross on a card to remove one. To move a load, type new values or drag it on the drawing: in Plan the body moves it in both directions, a side resizes it, and the section line has its own handle; in Elevation a load moves across the wall only. The 3D view is not draggable.
Do overlapping loads add?
Yes. The pressures of the rectangles add, so two rectangles on the same ground are counted twice. A load added with Add area load starts as a copy of the selected one, just beyond its far edge, and can overlap another load: move it or retype it.
Why does a lower Poisson’s ratio give a caution?
The stress formula has a term (1 − 2μ) that is zero at μ = 0.5. Below 0.5 the elastic solution gives a small tension near the surface, and soil cannot pull on a wall. The module keeps the sign in the results and says so; ignore the negative part if it is not wanted.
What values does the module accept?
The wall height greater than zero, μ from 0 to 0.5, a number for Ys, nz a whole number from 1 to 200, and for each load q of zero or more, positive sides Lx and Ly, and X0 of at least Lx/2. Anything else stops the analysis with a message, which names the load.
Does the number of rows nz change the answer?
Not from 2 rows upwards. It sets the rows of the table of the wall integration, and the shear force and the moment are integrated between the rows, so the answers do not depend on it. With 1 row the shear, the moment and the resultant depth are the same, but the peak pressure is read from the two table rows only, so keep nz at 2 or more (the default is 20).
Does the result include the earth pressure of the soil and the water pressure?
No. The result is the surcharge component only. You add it to the earth-pressure and water-pressure diagrams in the wall calculation.
Which units does it use, and what are the units of the answer?
SI · kN, SI · tf or US, switchable in the header at any time, even after Analyze. Pressures are in kPa, t/m² or ksf, the resultant per unit length in kN/m, tf/m or kip/ft, the moment per unit length in kN·m/m, tf·m/m or kip·ft/ft, and lengths in m or ft.
Does the module remember my inputs?
No. It opens on its example (a 9 m wall and two loads of 50 kPa) each time the page is opened. The unit system and the report cover details you type are kept in the browser. The report is the record of an analysis.
Calculate the extra lateral pressure on a wall from a long surface load that rises like a ramp from zero to a plateau: the pressure diagram, its resultant and the depth it acts at. This manual walks through the screen, the inputs, the two methods, the results and the report, with a worked example you can reproduce.
Ramp load gives the extra horizontal pressure on a wall from a long surface load that runs parallel to it and rises like a ramp: the load is zero at a distance x from the wall, rises in a straight line to its full intensity q at x + c, and stays at q beyond. It draws the pressure on the wall and gives its resultantPH (a force per unit length of wall), the depthzR at which the resultant acts below the ground, and the peak pressureσH,max.
The pressure at a depth z comes from adding up the elastic stresses of the line loads that make up the ramp and the plateau, which has a closed form:
σH = ψ · q / (π c) × [ cβ − xα + 2z ln(R2 / R1) ]
R1 and R2 are the distances from the point on the wall to the start and to the end of the ramp, α and β are the two angles they make, and ψ is 2 for a wall that does not yield or 1 for a wall that deflects (see Choosing the method). The resultant PH is the area of the pressure diagram over the wall height H, and zR is the depth of its centroid.
What you can describe
A wall of height H, with the ground level with its top.
A ramp load that starts a distance x from the wall (it can start at the wall, x = 0), rises over a width c and continues at the plateau intensityq.
Two methods: Elastic · rigid wall and Elastic · half-space.
The load is long and parallel to the wall, so every result is per unit length of wall.
The result is the pressure that the load adds. The pressure of the soil itself, the water and any other action on the wall are combined with it in your own analysis of the wall.
The module asks for no soil properties: the elastic solution does not use them.
Before you start: what you need
Have these four numbers and one decision ready:
What
Where it comes from
Notes
Wall height H
Your design
The pressure is worked out from the ground surface down to this depth. It must be greater than zero.
Distance x from the wall to the start of the ramp
The layout of the load
Zero or more. x = 0 puts the foot of the ramp at the wall.
Ramp width c
The layout of the load
Greater than zero. The load reaches its full value q at x + c from the wall.
Plateau intensity q
Your loading
Zero or more. The intensity beyond the ramp; the ramp rises to it from zero.
Wall behaviour
Your design
Rigid wall (a wall that does not yield) or half-space (a wall that deflects). It sets ψ = 2 or 1.
Quick start in seven steps
Open the module and choose the units
Open Ramp load from the Surcharge Loads family. Pick SI · kN, SI · tf or US in the header; you can change it at any time. Open Ramp load.
Describe the wall and the ramp
In Geometry, enter the wall height H, the distance x from the wall to the start of the ramp and the ramp width c. The drawing follows each number, and you can drag the load instead of typing x and c.
Enter the plateau intensity
In Ramp load, enter q, the intensity the ramp rises to and keeps beyond x + c.
Choose the method
In Method, pick Elastic · rigid wall (the default, for a wall that does not yield) or Elastic · half-space (for a wall that deflects). The (?) beside each opens a window with a sketch and the formula.
Press Analyze
Press Analyze at the foot of the Model tab. The bar turns green and reads Analysed, the inputs lock, and the drawings show the pressure on the wall and its resultant.
Read the answer
The Results tab gives the resultant force PH, its depth zR and the peak pressure with its depth. The Calculations tab writes out the working.
Take the report
In the Report tab fill in the cover and press Save as PDF or Download Word (.docx).
The screen: views, chips and dragging
The layout is the one every GeoTerva module shares, described in the workspace guide: the drawing on the left, the five tabs on the right. This module’s Model tab is shorter than most: it has three sections (Geometry, Ramp load and Method) and no Model data section. Your values are not kept when you close the page, so keep a note of them or save the report; the unit system you choose and the cover details of the Report tab are remembered by the browser.
123456789
The workspace of Ramp load after Analyze, on the example.
Family menu. Opens the list of the seven Surcharge Loads modules.
Units. SI · kN, SI · tf or US; it can be changed at any time, also after Analyze.
Account menu.
Views. Elevation, Plan and 3D View.
Show chips. Pressure distribution, Resultant and Dimensions.
The knee of the ramp. The hollow dots on the load are its drag handles.
The pressure on the wall, with its resultant.
The five tabs. Model, Results, Calculations, Report and Theory.
The results. Six cards.
The three views
Elevation is the section through the wall: the wall, the ground, the ramp and plateau drawn as a load with arrows, the distance chain wall → x → x + c, and the wall height H. After Analyze it adds the pressure diagram on the wall with ordinate lines, the rays R1 and R2 and the angles α and β at the depth of the peak pressure (with a line that reads their values), and the resultant as an arrow with PH and the depth zR.
Plan looks down on the ground: the wall as a bar on the left, the ramp as a band whose shading follows the intensity from 0 to q, and the same edge distances. After Analyze a blue strip along the wall is the pressure on it.
3D View shows the wall, the ramp rising to its plateau and, after Analyze, the pressure curtain on the face of the wall with the resultant as an arrow at its depth.
Before Analyze a drawing is the geometry alone, so you can check the layout against your plans: the load, its value over the arrows, the distances and the wall height. The pressure and the resultant appear after Analyze.
Elevation before Analyze: the geometry alone.
After Analyze the view carries the pressure diagram, the construction lines that explain it, and the resultant.
Elevation after Analyze.
Plan after Analyze.
3D View after Analyze.
The Show chips
The chips above the drawing choose what is drawn. Pressure distribution and Resultant are available after Analyze and are on when it finishes (the resultant is drawn in the Elevation and 3D views). Dimensions switches every dimension line and its label, and can be used before Analyze too.
Only the pressure distribution on: the resultant and the dimensions are switched off.
Dragging the load
Under the drawing the module says: “Drag the load to move it, or its knee at x + c to change the ramp width c”. Both handles are hollow dots on the load, in all three views.
The start (the dot at the foot of the ramp, or anywhere on the load) moves the whole load: x changes, c and q stay.
The knee (the dot where the ramp reaches q) changes the ramp width c; the start stays where it is.
The boxes in the Model tab follow the pointer. Values go in steps of 0.05 in the unit shown; x cannot go below zero and c cannot go below 0.05.
The handles move within the ground that is drawn. In 3D View the pointer is followed along the slanted line that leads away from the wall.
After Analyze the inputs are locked, the hint disappears and the handles no longer move the load. Edit inputs unlocks them.
Entering the model, section by section
The Model tab has three sections. The one you are working on is highlighted and carries Back and/or Next (Next on the first section, Back on the last); the other two stay in view. Boxes accept any number; a value that breaks a rule is reported at once by a message (see Messages). The unit shown beside each box follows the unit system in the header; the defaults below are shown in the three systems.
Geometry
The wall and where the load stands in relation to it. All three are lengths.
Geometry: H, x and c.
Fields of Geometry
Field
Symbol
Unit
Default
What to enter
Wall height
H
m · ft
25 m (82.02 ft)
Greater than zero. The depth over which the pressure diagram and its resultant are worked out; the ground is level with the top of the wall.
Distance to ramp start
x
m · ft
2 m (6.56 ft)
Zero or more. The horizontal distance from the wall to the foot of the ramp, where the load is zero.
Ramp width
c
m · ft
5 m (16.40 ft)
Greater than zero. The horizontal width over which the load rises from zero to q. The load is at q from x + c outwards.
Ramp load
The intensity of the plateau.
Ramp load: the plateau intensity.
Field of Ramp load
Field
Symbol
Unit
Default
What to enter
Plateau surcharge intensity
q
kPa · t/m² · ksf
20 kPa (2.04 t/m², 0.4177 ksf)
Zero or more. The intensity the ramp rises to at x + c and keeps beyond.
Method
Two buttons choose the solution. Under them the module repeats what the chosen one means: “Twice the elastic stress (ψ = 2), for a wall that does not yield.” for the rigid wall, and “The elastic stress in a half-space (ψ = 1), as if the wall were absent — for a wall that deflects.” for the half-space. A (?) beside each button opens its help window.
Method: the rigid wall or the half-space.
Choice in Method
Choice
Options
Default
Calculation method
Elastic · rigid wallElastic · half-space
Elastic · rigid wall
Units
The header selector switches between SI · kN (m, kPa, kN/m), SI · tf (m, t/m², tf/m) and US (ft, ksf, kip/ft). The boxes, the drawings, the cards and the report all follow it. The example in the three systems gives PH = 443.49 kN/m, 45.22 tf/m and 30.39 kip/ft; the model itself does not change.
Choosing the method
Both methods use the same ramp load and the same expression; they differ in the factor ψ that scales it, and so in what they say about the wall.
The two methods
Method
ψ
What it assumes
Result on the example
Elastic · rigid wall (default)
2
A smooth, unyielding wall: it stops the soil at its face from moving horizontally. The module reproduces this with a mirror-image load on the far side of the face (the method of images), so the pressure on the wall is the half-space stress doubled.
PH = 443.49 kN/m
Elastic · half-space
1
A wall that deflects enough for the soil to follow, so the pressure on it is the elastic stress in a half-space as if the wall were absent.
PH = 221.74 kN/m
The half-space diagram is half the rigid-wall diagram at every depth and the resultant acts at the same depth. On the example zR is 13.68 m in both, and the peak pressure is 19.94 kPa for the rigid wall and 9.97 kPa for the half-space.
The (?) beside a method opens its help window: a sketch of the ramp beside the wall with the pressure diagram on the face (for the rigid wall also the image load), the formula with R1, R2, α and β, and a line headed With the current inputs that gives PH, zR and the peak pressure for both methods on your numbers.
The (?) window of the rigid wall, on the example.
The help window of the half-space method has the same layout: the same ramp, with the label “wall absent”, the pressure diagram on the plane of the wall at half the width, and the same line With the current inputs.
The (?) window of the half-space method, on the example.
Which should I pick?
Rigid wall is the module’s default and the one for a smooth, unyielding wall: a wall that does not yield.
Half-space is for a wall that deflects enough for the soil to follow.
Compare the two. They differ by a factor of two on the pressure and its resultant; the depth of the resultant is the same. Run one, then press Edit inputs, switch the method and run again.
Analyze and read the results
Press Analyze. The bar at the foot of the Model tab turns green and reads Analysed — the lateral pressure calculated; the inputs and the method buttons lock, and the unit system can still be changed. Edit inputs clears the results and unlocks the model.
The Model tab after Analyze: the green bar and Edit inputs.
The Results tab shows six cards:
Ramp end: x + c, where the load reaches q.
Calculation method: Elastic, with the wall behaviour in brackets.
Resultant force: PH, the area of the pressure diagram, per unit length of wall.
Resultant depth: zR, below the ground.
Peak wall pressure: the largest ordinate of the diagram, σH,max.
Peak-pressure depth: where that ordinate is.
The Results tab on the example.
Reading the numbers
PH is a force per unit length of wall (kN/m, tf/m or kip/ft).
zR is measured down from the ground. The Calculations tab also gives the height above the base: on the example zR = 13.68 m below the ground, 11.32 m above the base.
The resultant lies below mid-height of the wall (12.50 m on the example) because the pressure grows with depth.
In every run of this page that has a load the largest pressure is at the base of the wall, so the peak-pressure depth equals H; the card tells you where it is for your own geometry.
The Pressure profile
The table “Pressure profile, every H/30” in the Calculations tab lists the ordinates at 31 depths, from the ground to the base in 30 equal steps of H, with the rays and angles behind each.
The Calculations tab and the report
The Calculations tab writes out the working in four steps:
Load geometry — the ramp end x + c and what the chosen method means (ψ = 2 or 1).
Radii and angles at a depth — R1, R2, α and β with their numbers, at the depth of the peak pressure (z = 25.00 m on the example).
Horizontal pressure — the equation with your numbers put in and the answer σH,max, followed by the table Pressure profile, every H/30: z, R1, R2, α (°), β (°) and σH at 31 depths from the ground to the base.
Resultant and its depth — PH and zR, with zR also given above the base.
The Calculations tab: the first two steps of the example.
The Report tab
The Report tab fills in a cover page and builds a summary report from the same working. The cover has Project, Location, Client, Report no., Date, Prepared by (name), Title / qualification, Checked by and an optional Notes box that is printed only when it is filled in. Press Save as PDF or Download Word (.docx).
The report has six parts: 1 Introduction and scope, 2 Input data (with the elevation, plan and 3D drawings as figures), 3 Calculation (the four steps and the pressure profile), 4 Results, 5 Summary and 6 References. It states the resultant to four significant figures, for example PH = 443.5 kN/m, and its Summary closes with a sentence that puts PH, zR and the peak pressure in words.
The Report tab: the cover form.
The Theory tab explains the method in six numbered sections: Ramp load on a wall, Radii and angles, Horizontal pressure, Resultant and line of action, Worked example and References. Each section opens and closes, and Open all and Close all do it for the lot. Its worked example is fixed on the numbers of the module’s example and does not follow your inputs.
Worked example: the module’s own example
The module opens on this example, so you can follow every number on your own screen.
Inputs of the example
Section
Input
Value
Geometry
Wall height
H = 25 m
Geometry
Distance to ramp start
x = 2 m
Geometry
Ramp width
c = 5 m
Ramp load
Plateau surcharge intensity
q = 20 kPa
Method
Calculation method
Elastic · rigid wall, ψ = 2
Step 1: the geometry
The ramp ends at x + c = 2.00 + 5.00 = 7.00 m, as the Ramp end card says. The load is zero at 2 m from the wall, rises in a straight line to 20 kPa at 7 m and stays at 20 kPa beyond.
Step 2: the pressure at 5 m depth, by hand
At z = 5.00 m the two rays have lengths R1 = √(2² + 5²) = 5.385 m and R2 = √(7² + 5²) = 8.602 m. The angles are α = tan⁻¹(7/5) − tan⁻¹(2/5) = 54.462° − 21.801° = 32.661° = 0.57004 rad and β = 90° − 54.462° = 35.538° = 0.62025 rad. Then
The table “Pressure profile, every H/30” in the Calculations tab has this depth in its row for 5.00 m: R1 5.39, R2 8.60, α 32.661°, β 35.538° and σH 16.92 kPa. With the half-space method ψ = 1 and the ordinate is half of it, 8.46 kPa.
Step 3: the pressure at the base
The Calculations tab works the equation at the depth of the peak pressure, z = 25.00 m: R1 = 25.08 m, R2 = 25.96 m, α = 11.068° = 0.19318 rad, β = 74.358° = 1.29779 rad, and
The module integrates the diagram over the 25 m: PH = 443.49 kN/m, acting at zR = 13.68 m below the ground (11.32 m above the base). A quick check on the size of the number: the average ordinate is 443.49 / 25 = 17.74 kPa, between the 16.92 kPa found at 5 m and the 19.94 kPa at the base, as it should be for a diagram that grows with depth. With the half-space method PH = 221.74 kN/m, exactly half, at the same depth.
How each input changes the answer
Each row changes one thing in the example and runs the module again, in SI · kN with the rigid-wall method unless a row says otherwise. The numbers are the module’s own.
The example with one change at a time
Change and why
PH (kN/m)
zR (m)
σH,max (kPa)
The exampleThe reference
443.49
13.68
19.94
Half-space method (ψ = 1)Every ordinate halves; the depth does not move
221.74
13.68
9.97
q = 40 kPaThe pressure is proportional to q: PH doubles
886.98
13.68
39.88
q = 10 kPaPH halves
221.74
13.68
9.97
x = 0The load starts at the wall: more force, acting higher
468.38
13.19
19.98
x = 5 mThe load is further out: less force, acting lower
407.49
14.28
19.78
x = 10 mStill less, and lower
352.75
15.00
19.17
c = 0.5 mThe load comes in almost at once at x: more force
471.43
13.16
19.99
c = 2 mA steeper ramp than the example
462.00
13.35
19.98
c = 10 mThe load reaches q further out: less force, acting lower
414.10
14.11
19.76
c = 20 mLess again
362.68
14.67
19.02
H = 10 mThe same load on a shorter wall: less area under the diagram
146.97
5.90
19.27
H = 15 mLess area under the diagram
244.78
8.54
19.74
H = 40 mA taller wall takes more of the diagram; zR moves down
743.02
21.27
19.98
q and the method scale everything. Doubling q doubles PH and the peak; the half-space method halves them. Neither moves zR.
x and c change the shape. Pushing the load away from the wall, or spreading the ramp over a wider band, lowers PH and lowers the point where it acts.
H sets how much of the diagram is counted. The peak pressure is at the base in these runs, so it rises with H (19.27, 19.74, 19.94 and 19.98 kPa for 10, 15, 25 and 40 m).
Messages
A model that follows the four rules of the table runs without a warning. When a number breaks a rule the module stops: nothing is calculated and it says why, in three places at once.
A red box under the Method section, live as you type, with the message and what to do.
The bar turns brown and reads Cannot be analysed, followed by the message.
Pressing Analyze opens a window titled Cannot be analysed that repeats the message and adds: “Nothing was calculated. Change the inputs marked in red, then press Analyze again.” The drawing reads “Not calculated — correct the highlighted input in the Model tab”, the Results tab reads “Not calculated — see the Model tab.” and the Calculations tab repeats the message.
A stop: the ramp width c was set to zero. Nothing is drawn or calculated until it is corrected.
When (all are stops)
Message
The wall height H is zero, negative or empty
“The wall height H must be greater than zero.”
The distance x is negative or empty
“The distance to the ramp start x must be zero or more.”
The ramp width c is zero, negative or empty
“The ramp width c must be greater than zero.”
The plateau intensity q is negative or empty
“The plateau surcharge q must be zero or more.”
Several values are wrong
The messages are listed together, separated by semicolons.
Each message continues with the same explanation: “The ramp needs a positive width on a wall of positive height, starting at or beyond the wall, and a load of zero or more. Correct the highlighted value in the Model tab.”
Before the first run the Results and Calculations tabs read “Press Analyze on the Model tab to calculate the lateral pressure.” Edit inputs returns to that state.
Good practice and common mistakes
Measure x from the wall to the foot of the ramp, where the load is zero, and c across the ramp. The distance chain in the drawing shows what the module understood: check it against your plan.
Choose the method for the wall you have. The rigid wall is the default and gives twice the half-space pressure; do not leave it unchecked.
Read PH per unit length of wall. The load is long and parallel to the wall, so the force is per metre (or foot) of wall.
Add the result to the other actions on the wall. The module gives the pressure of the load alone. If the ground carries several loads, run each in its own module with the same method and add the pressures at the same depth in your own analysis.
Check the units after you switch the system: type values in the units shown beside the boxes.
Look at the drawing before you analyse. A load that lands in the wrong place is easiest to see in the geometry-only drawing, and you can drag it into place.
Keep a record. The model is not kept between visits: save the report, which prints the inputs, the working and the results.
Frequently asked questions
How do I calculate the lateral pressure on a wall from a ramp surcharge?
The pressure at a depth is the sum of the elastic stresses of the line loads that make up the ramp and its plateau. In GeoTerva’s Ramp load module you enter the wall height H, the distance x to the foot of the ramp, the ramp width c, the plateau intensity q and the method, press Analyze, and read the resultant PH, its depth zR and the peak pressure. On the module’s example PH = 443.49 kN/m at zR = 13.68 m.
What is a ramp load?
A long load parallel to the wall that is zero at a distance x from it, rises in a straight line to q at x + c and stays at q beyond. The Triangular load module has a load that rises to a peak and falls again, and the Strip load module a uniform load on a strip.
Should I use the rigid-wall or the half-space method?
The rigid-wall method (the default) is for a wall that does not yield: the pressure is twice the half-space stress. The half-space method is for a wall that deflects enough for the soil to follow and gives half of it. On the example they give 443.49 and 221.74 kN/m.
What do x and c measure?
x is the horizontal distance from the wall to the foot of the ramp, where the load is zero; c is the horizontal width over which the load rises to q. The load is at q from x + c outwards, a distance the Ramp end card gives.
Why is the result a force per metre?
The load is long and parallel to the wall, so the pressure is the same along it and the module gives the resultant per unit length of wall: kN/m, tf/m or kip/ft.
Why does the resultant act below mid-height of the wall?
Because the pressure grows with depth. On the example the resultant acts 13.68 m below the ground on a 25 m wall; the mid-height is 12.50 m.
Does the module need soil properties?
No. The pressure comes from the elastic solution for the load and the wall, which does not use unit weights or strength. The soil’s own earth pressure is a separate action, combined with this one in your analysis of the wall.
Can I move the load on the drawing?
Yes, until you press Analyze. Drag the load to move it (x changes) or the knee at x + c to change the ramp width c, in the Elevation, Plan or 3D View. The boxes follow in steps of 0.05 in the unit shown.
What happens with q = 0?
The module runs and gives PH = 0.00 kN/m and a peak pressure of 0.00 kPa. It still reports a resultant depth, here 13.68 m, the depth at which the resultant would act on this geometry.
How can I check a result by hand?
Put x, c, q and a depth z into the equation; the Calculations tab lists R1, R2, α, β and σH at 31 depths to compare with. At 5 m on the example, 2 × 20 / (π × 5) × [5 × 0.62025 − 2 × 0.57004 + 10 ln(8.602 / 5.385)] = 16.92 kPa.
Which units does the module use, and does it keep my model?
SI · kN, SI · tf or US, switchable in the header at any time, also after Analyze; the browser remembers the choice and the cover details of the Report tab. The values are not kept when you close the page: save the report, which prints the inputs and the results.
TerzaghiThe classical bearing capacity equation, for general and local shear.
MeyerhofThe general equation with shape, depth and inclination factors.
HansenOne equation for sloping ground, a tilted base and an inclined load.
VesicVesic’s factors, with the inclination exponent taken from the footing’s own B/L.
Seismic bearing capacityA strip footing during an earthquake, by Coulomb wedges.
