Four modules give how far a foundation settles, now and over time: the consolidation of clay layers, the immediate settlement of clay and of sand, and the total over a profile of both. This page helps you choose the module that matches your ground and links to the manual of each.
The Settlement family has four modules. They answer one question: how far does a foundation settle? The stress increase below the foundation is summed layer by layer down to the influence depth, and the stresses and the settlement are drawn as colour bands over the section. The modules differ in the kind of settlement they work out. Pick the one that matches your ground and the question you need answered.
Your question
Module
The primary consolidation of clay layers and how fast it happens, with the excavation, the swelling and the recompression of each layer
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 answer, 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 four 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 foundation. A rectangular or strip foundation, with its size, its depth and the pressure it applies.
Layer by layer. The stress increase is worked out in every layer, down to the influence depth, and the settlement of each layer is added.
Colour bands. The stresses and the settlement are drawn as colour bands over the section.
The report. Every module saves a report with the cover filled in.
The two elastic modules apply Steinbrenner’s influence factors layer by layer and give the settlement at the centre, at the corner and for a rigid foundation.
A typical settlement calculation in order
Choose the module
Pick the one that matches the ground and the settlement you need, and open its manual for the fields.
Describe the foundation
Enter its shape and size, its depth and the pressure it applies.
Describe the layers
Enter the thickness and the soil parameters of every layer, and the water table.
Analyze and read the answer
Press Analyze. Read the settlement of every layer and the total, look at the colour bands, then save a report with the cover filled in.
Frequently asked questions
How do I calculate the settlement of a foundation with GeoTerva?
Open the module for your ground: Consolidation settlement for clay layers, Elastic settlement, cohesive or granular for the immediate settlement, or Settlement 2D for the total over both kinds of layer. Enter the foundation and the layers, press Analyze, and read the settlement of every layer and the total.
Which module gives the total settlement of clay and sand together?
Settlement 2D. It adds the immediate settlement of every layer, clay undrained and sand drained, to the consolidation of the clay layers.
Which modules draw the settlement against time?
Consolidation settlement and Settlement 2D draw the settlement against time by Terzaghi’s theory.
What is the difference between the cohesive and the granular elastic modules?
The cohesive module takes clay and silt that settle undrained, with the undrained modulus. The granular module takes sand and gravel that settle drained, with the drained modulus and Poisson’s ratio. Granular soil has no consolidation to add.
What do centre, corner and rigid settlement mean?
The elastic modules give the settlement at the centre and at the corner of a flexible foundation, and the settlement of a rigid foundation.
Where does the influence depth stop?
The stress increase is summed layer by layer down to the influence depth, which the modules take by the stress ratio or from a rigid base.
Calculate the primary consolidation settlement of clay layers under a raft or a strip, including the heave of the excavation, the recompression and the virgin compression, the calculation depth and the settlement against time. This manual walks through the screen, every input, the options, the results and the report, with a worked example you can reproduce.
Consolidation settlement gives the primary consolidation settlement of clay layers under a rectangular (raft) or strip foundation, and how fast it develops. It follows every slice of clay along its stress path: the initial stress, the unloading and swelling when you excavate to the foundation level, the reloading back to the initial stress, the recompression up to the preconsolidation pressure σ′p and the virgin compression beyond it. The settlement is summed slice by slice down to a calculation depth, and Terzaghi’s theory gives the settlement against time.
Sc = Sb + Sr + Sv, Snet = Sc + heave
Sb is the reloading along the swelling line (Cs) back to σ′v0, Sr is the recompression (Cr) from σ′v0 up to σ′p, and Sv is the virgin compression (Cc) beyond σ′p. Settlement is positive and heave negative unless you change the sign in the header.
What you can describe
A profile of clay layers from the ground surface down, each with its unit weights, its compressibility (e0, Cc, Cr, Cs or mv), its Cv, its OCR or laboratory σ′p, and one or two-way drainage.
A water table, hydrostatic below it and unchanged by the excavation.
An excavation to the foundation level, with its own plan if it differs from the foundation, and the choice of where the settlement is measured from.
A rectangular or strip foundation with its gross pressure at the foundation level.
The calculation depth: the influence depth, where the stress increase has fallen to a share p of q, or the bottom of the profile.
The module gives the heave, the settlement of every layer and of the foundation, the stress path of every slice, the settlement–time curve with t50 and t90, and colour bands of stress, strain and settlement over the whole section. It writes out the working and prepares a PDF or Word report.
The stress increase is the Boussinesq stress under the centre of the foundation. The stress under other points, loads of other shapes and their charts are in the Stresses in a soil mass modules.
The module gives the settlement, not the bearing capacity: for that, see the Bearing capacity modules.
Before you start: what you need
Have these ready from your investigation and design:
The soil profile (boreholes): layer depths from the ground surface, without gaps; the unit weight γ above the water table and γsat below it.
e0, Cc, Cr, and Cs if you have it (oedometer tests): for the e – log σ′ method. Cs is the swelling index; left empty, Cs = Cr is used.
Or mv (oedometer tests): for the mv method, a single linear coefficient.
OCR, or σ′p of each layer (oedometer tests, stress history): the preconsolidation pressure, as OCR or as a laboratory value (one definition for the whole model).
Cv of each layer, and the drainage (oedometer tests, the stratigraphy): only for the settlement–time curve. Double drainage uses H/2 as the drainage path, single uses H.
The water table depth zw (boreholes, piezometers): below the ground surface; it is not changed by the excavation.
The excavation depth Dexc (your design): the foundation level. Zero, or “No”, puts the foundation at the ground surface.
The foundation B, L, qgross (your design): width, length (not for a strip) and the gross pressure at the foundation level.
Quick start in seven steps
Open the module and choose the units
Open Consolidation settlement from the Settlement family. Pick SI · kN, SI · tf or US in the header; you can change it at any time, even after Analyze. The sign selector beside it chooses settlement + or settlement −.
Describe the soil
In Soil profile give the depth to the bottom of each layer, its name and its unit weights. Press Next and, in Compressibility, fill one row per layer. Enter the water table in Groundwater.
Describe the excavation
In Excavation choose Yes or No, give Dexc, and pick the plan and where the settlement is measured from.
Describe the foundation
In Foundation pick Rectangle / raft or Strip and enter B, L and qgross. The three read-outs under the boxes give the foundation level, qremoved and qnet.
Choose the analysis
In Analysis Settings choose the compressibility method, the definition of σ′p, the calculation depth, the slice thickness Δz and whether you want the settlement–time curve.
Press Analyze
Press Analyze at the foot of the Model tab. The bar reads Analysed, the inputs lock, and the drawing switches to the Contours view.
Read the results and take the report
The Results tab gives the heave, the settlement and the table by layer and by slice; Calculations writes out any slice; Report saves a PDF or a Word file.
The screen: five views of the section
The layout is the one every GeoTerva module shares, described in the workspace guide. The drawing on the left has five views, chosen with the buttons above it; the Model, Results, Calculations, Report and Theory tabs are on the right. Every view has a bar of chips above it; the chips only change what is drawn, never the calculation.
Section is the soil profile with the water table, the excavation, the foundation, its load and the calculation slices on the vertical through the centre. It follows the inputs live, before Analyze. After Analyze it adds the heave, the settlement and the net value to the title. Chips: Slices, Dimensions, Layer labels.
Contours paints a field over the whole section as 36 equal colour bands with a legend. The Field chips are σv, u, σ′v0, σ′p, Δσexc, Δσload, σ′exc, σ′final (the default), εv and S; the other chips are Foundation and Layer labels.
Stresses plots the vertical stresses on the centre line against depth, with the stress changes beside them. Seven chips switch the curves: σv, u, σ′v0, σ′p, σ′exc, σ′final and the net change.
Settlement paints the settlement of a point at each depth with a trough drawn over the foundation, and a bar for every slice (heave, Cs back, Cr, Cc). Field chips: Strain εv, Settlement S (the default), Heave, Net; other chips: Trough, Labels, Slice bars.
Time plots the settlement against time for the whole profile and for each layer. Chips: Total and one per layer, and a Log or Linear time axis.
Section before Analyze: the geometry, the slices and the calculation depth.
Contours after Analyze: σ′final, the default field.
Stresses: the stress path of the centre line.
Settlement: the field, the trough and the slice bars.
Time: the total and the layers, with t50 and t90.
Before and after Analyze
The page opens on the Contours view, which has nothing to paint yet: it shows the layers and the words “Press Analyze”. The Section view follows your inputs while you edit. After Analyze the drawing switches to Contours; after Edit inputs it returns to Section. When the page opens again on a model you saved, it starts on Section, or on Contours if that model was analysed.
The chips of the Contours view.
Entering the model, section by section
The Model tab has a Model data card and six sections. The sections work as a walk-through: one is open at a time, and Back and Next at the foot of each move to the neighbour; clicking a title opens that section and closes the other. Analyze waits below the last one. The tables give the unit in SI · kN first; SI · tf and US show the same values converted, for example 100 kPa is 10.2 t/m² and 2.09 ksf. Defaults are the example project.
Model data
This card keeps your work. Model name labels it. Save to file… writes a .json file and Open file… reads one back. Quick Save… asks for a name and keeps this version in the browser; choose it in the list and press Load to come back to it, Delete removes it. Reset to defaults returns to the example. A line under the buttons reports what happened. Every change is also kept automatically: the page opens again on the model you last worked on, analysed or not.
Model data: save, open, quick save, reset.
Soil profile
One row per layer from the ground surface down. From is read-only: it is the bottom of the layer above (0 for the first). Type the bottom of each layer in To; the next layer starts there. A value at or above the top of the layer is ignored. + Add layer appends a layer 2 m thick below the last one, and × deletes a layer (the last remaining layer cannot be deleted). Nothing in the profile can be edited after Analyze until you press Edit inputs.
Clay-5 (the number follows the layers present), γ 18.5, γsat 19.0, e0 0.9, Cc 0.3, Cr 0.05, Cs empty, mv 0.0003 1/kPa, Cv 1 m²/yr, OCR 1.2, σ′p 100 kPa, double drainage
Compressibility
One row per layer. A layer, or the part of a layer, above the foundation level is removed by the excavation: its row says “Above the foundation level — removed by the excavation; only its unit weight is used.” A layer below the calculation depth says “Below the calculation depth zlim … — not compressed.” The label of the last layer shows “→” and the calculation depth when it continues down to it. Boxes the chosen method does not use are shaded: e0, Cc, Cr and Cs with the mv method, mv with the e – log σ′ method, Cv when the settlement–time curve is off.
Drainage is Double (path H/2) or Single (path H). The fill layer carries the same kind of values (it has OCR 2.0 and e0 0.80), used only if the excavation is switched off and the fill lies below the foundation level.
Compressibility: one row per layer.
Box
Default, Clay-1 · 2 · 3
e0 (—)
1.05 · 0.85 · 0.65
Cc (—)
0.25 · 0.30 · 0.18
Cr (—)
0.05 · 0.06 · 0.03
Cs (—)
empty (= Cr) · 0.04 · 0.02
mv (1/kPa)
0.00040 · 0.00025 · 0.00012
Cv (m²/yr · ft²/yr)
2.00 · 1.00 · 3.00
OCR (—)
1.6 · 1.3 · 2.2
σ′p (kPa), laboratory
80 · 90 · 150 · 350 (four layers)
Drainage
Double · Double · Double
Groundwater
One number: the depth zw of the water table below the ground surface, default 1.50 m. Pore pressure is hydrostatic below it (γw = 9.81 kN/m³) and the excavation does not change the water table. A water table deeper than the whole profile simply means no layer is submerged.
Groundwater: the water table depth.
Excavation
No puts the foundation at the ground surface; Yes (the default) excavates to Dexc, which is then the foundation level. The plan buttons are Same as foundation, Own plan and Wide (I = 1); the displacement buttons are Kept — from the original ground and Reset to zero before loading; the table uses their short names.
Excavation: depth, plan and reference of the settlement.
Choice
What it does
Dexc (m · ft), default 3.00
Excavation depth, zero or more. The stress removed is qremoved, the initial effective stress at that depth.
Same as foundation (default)
The unloading acts through the Boussinesq influence of the foundation’s own B × L.
Own plan
Two more boxes, Bexc and Lexc (the length is not asked for a strip), give a different excavation plan. They start at the foundation size.
Wide
The unloading acts with I = 1 at every depth, as for an excavation much wider than deep.
Kept (default)
The settlement is the net deformation after loading, measured from the original ground. A load that only restores the removed overburden causes no settlement.
Reset to zero
The settlement is measured from the heaved excavation base and includes the recompression of the heave.
Foundation
Rectangle / raft (default) or Strip. The length box disappears for a strip. Three read-outs follow the inputs: the foundation level, qremoved and qnet = qgross − qremoved. The stress increase below the foundation is computed from qgross (the excavation unloading is a separate phase), so qnet is a reading, not an input.
Foundation: shape, size and pressure.
Field
Default
Width B (m · ft)
20.00; at least 0.1
Length L (m · ft)
30.00; at least 0.1; not for a strip
Gross pressure qgross (kPa · t/m² · ksf)
100; zero or more
Analysis Settings
The section holds the choices that decide the method; they are described under “Choosing the method and the options” below. Its boxes: p (5 to 50 %, default 10, a value outside the range is brought back to the nearest limit), and Δz (default 0.50 m, between 0.05 and 2 m in the box). Three read-outs give the calculation depth zlim, the depth below the foundation level, and where the soil profile ends; a note says whether the last layer continues, the soil below zlim is left out, or the two coincide. The (?) beside the depth rule opens a window that explains the influence depth.
Analysis Settings.
Choosing the method and the options
Six choices shape the answer. Each row of the next table is the example with only that choice changed; the numbers are those of the module, in mm, as heave / Sc.
The example with one choice changed
Choice
Heave / Sc mm
Settlement mm
The example
-104.4 / 311.3
206.9
mv method
-186.4 / 468.6
282.2
Laboratory σ′p
-104.4 / 304.8
200.3
Profile bottom
-102.1 / 303.9
201.8
Reset to zero
-104.4 / 311.3
311.3
Wide plan
-131.8 / 297.8
166.0
Strip, B = 20 m
-112.6 / 340.3
227.7
The rows in order: the example (e – log σ′, OCR, influence depth 10 %, kept from the original ground); the mv method (the mv of each layer, linear); laboratory σ′p of 80, 90, 150 and 350 kPa; a calculation depth that stops at 30.00 m; reset to zero (settlement measured from the excavation base); the wide plan (unloading with I = 1); and a strip of the same width with endless length.
e – log σ′ or mv
e – log σ′ (Cc / Cr / Cs / e0) follows the stress path: S = C · ΔH/(1 + e0) · log10(σ′ end / σ′ start) on each branch. Use it when you have oedometer curves.
mv is linear and has one coefficient for unloading and reloading: δH = mv · Δσ′ · ΔH. It has no σ′p and no virgin branch. With the same soil it gives 468.6 mm of loading settlement here against 311.3 mm, because one coefficient is carried over the whole range; use it with a mv measured over the stress range of the foundation.
OCR or laboratory σ′p
With OCR, σ′p = OCR · σ′v0 at every slice, so it grows with depth. With the laboratory value, each layer has one σ′p, never taken below σ′v0. Either way σ′p is the historical maximum and the excavation does not reduce it. An OCR below 1, or a laboratory σ′p below σ′v0, is replaced by σ′v0 and reported as a warning (see Messages).
The calculation depth
The stress increase never reaches zero, so the sum needs a lower end. With Influence depth (Δσ = p · q) it ends where the stress increase under the centre has fallen to p of q; for the example, p = 10 % gives zlim = 3.00 + 50.94 = 53.94 m. The profile of the example ends at 30 m, so the last layer is taken to continue down to zlim with the same properties, and the Section view, the Results table and the report say so. If the profile is deeper than zlim, the soil below it is not compressed. With Bottom of the profile the sum stops at the last layer, an incompressible stratum is assumed below it, and the stress increase left there is shown as a share of q.
The (?) window of the depth rule.
The excavation and the reference of the settlement
An excavation unloads the clay, which swells (the heave). When the foundation loads it the clay first retraces its swelling line back to σ′v0; only a load above that gives a net settlement from the original ground. With Kept the settlement of the foundation is Snet = Sc + heave, 206.9 mm here, and it is reported as 0 if the net value is negative, with a note that the ground ends above its original level. With Reset, the heave is regarded as already finished before the building and the settlement is Sc, 311.3 mm, the number that answers “the excavation stayed open and heaved before the building: how much does the building settle?”. The heave itself is reported separately in both cases.
Choosing the excavation plan
Same as foundation is the usual choice. Wide unloads with I = 1 at every depth (a larger heave, -131.8 mm); Own plan lets the unloading act through another B × L, for example a basement larger than the raft (40 × 60 m gives -119.4 mm of heave, 10 × 15 m gives -84.2 mm).
Analyze and read the results
Press Analyze. After a short progress line the bar reads Analysed — 3 layers, 102 slices down to 53.94 m, the inputs are locked (“Edit inputs clears the results; the unit system can still be changed.”), a message appears for a moment (“Analysed — the colour bands show the selected field; see also Stresses, Settlement, Time and the Results tab.”) and the drawing switches to Contours. The Model tab stays on the screen; open Results for the numbers. If the run has cautions, a Warnings window opens by itself (see Messages).
The Results tab of the example.
Card
What it is
Example
Excavation heave (swelling)
The swelling of the clay when the excavation unloads it, negative.
-104.4 mm
Settlement of the foundation
From the original ground (Kept), from the excavation base (Reset), or from the ground surface (no excavation).
+206.9 mm
Loading phase Sc
The compression from the excavation base, with Sb, Sr and Sv written out under it (after a reset the third card shows the net value from the original ground).
+311.3 mm; reloading +104.4, Cr +71.6, Cc +135.3
A line under the cards gives qgross, qremoved, qnet, the foundation level, the method, the source of σ′p and the calculation depth with its rule.
The table by layer
One row per layer that is compressed, with its thickness H (from the foundation level or the top of the layer down to its bottom or zlim), the heave, Sb, Sr, Sv, Sc, the net value, and, with the time curve on, Hdr, t50 and t90. A remark under the name says when part of a layer is removed by the excavation, when the last layer continues to zlim (assumed), or when a layer is compressed only down to zlim. The Total row gives the sums and the t50 and t90 of the summed curve. The table fits the width of the panel. The note below it states the sign convention and what each column is.
The example, by layer (mm)
Layer
Heave / Sc mm
Net mm
Clay-1 H = 4.00 m, 1.00 m removed
-62.3 / +138.6
+76.3
Clay-2 H = 9.00 m
-33.0 / +144.9
+111.9
Clay-3 H = 37.94 m
-9.1 / +27.8
+18.7
Total
-104.4 / +311.3
+206.9
The table by slice
Below it, Slice by slice lists the σ′v0, σ′p, σ′exc, σ′final, the Regime of every slice (Cr → Cc, Cr only, Cc only, Cs (heave recovered), Cs (net unloading); mv with that method), the heave, Sc and the net value. All columns adds ΔH, σv0, u0, Δσexc, Δσload, Sb, Sr and Sv. A click on a row opens the working of that slice in the Calculations tab.
Slice by slice.
Using the numbers
The settlement of the foundation is the centre value on the vertical through the centre of the foundation; the module does not give the value at the edge or the differential settlement.
Read t50 and t90 of the Total row as the times when the summed curve reaches 50 % and 90 % of the loading settlement Sc. The heave is taken as complete before the loading.
Changing the units or the sign after Analyze re-states the results without a new run. With Sign: settlement − every displacement changes sign (the card reads −206.9 mm); strains and stresses keep compression positive.
The Calculations tab, the report and the Theory tab
The Calculations tab writes out the working for one slice, chosen in the Slice list at the top (the list gives z, the layer and the net value of each slice; a click on a row of the slice table also opens it). The regime of the slice is shown beside the list. The steps open and close with a click:
Initial stresses — σv0 = Σ γ·h, u0 and σ′v0 with your numbers.
Preconsolidation pressure — σ′p = OCR · σ′v0, or the laboratory value.
Excavation — unloading and swelling — qremoved, Δσexc, σ′exc and the heave of the slice (Excavation alone, with no heave, when there is none).
Foundation loading — Boussinesq — the influence factor at z′ below the foundation level, Δσload and σ′final.
Compression of the slice — the regime, then Sb, Sr, Sv and their sum; with the mv method, Sc = mv·Δσ′·ΔH.
Layer and total — the calculation depth, the layer’s sums, the totals and the settlement of the foundation.
Time — only with the time curve on and a Cv: Hdr, t50 and t90 of the layer and of the whole profile.
The working is always written in the classical sign (settlement +, heave −); with the other sign selected a note above it says so.
The Calculations tab, first slice.
The report
In the Report tab fill in the cover: project, location, client, report number, date, prepared by, title / qualification, checked by and optional notes. The cover is kept in this browser and saved with the model file. After Analyze, Save as PDF (the print window, where you choose “Save as PDF”) and Download Word (.docx) are available; before it they are greyed out and the tab says to press Analyze. The preview below the buttons is the report itself.
The report has eight parts: 1 Introduction and scope, 2 Soil profile and parameters, 3 Excavation, foundation and calculation depth, 4 Stress path and assumptions, 5 Consolidation settlement, 6 Slice by slice, 7 Time-dependent consolidation, 8 Summary. It carries the section, stress, settlement and time drawings and states the units. When the run carries warnings, the Report tab shows the same warning bar as the Results tab.
The report cover.
The Theory tab
The Theory tab has fifteen sections, each of which opens and closes: Scope, Stress path, Slices and initial stresses, Preconsolidation pressure, Excavation — unloading and swelling, Stress increase — Boussinesq, Depth of the settlement calculation, Compression regimes, Where the settlement is measured from, the mv method, Time-dependent consolidation, Colour-band fields, Sign convention and assumptions, Outside the scope, and References.
Worked example: the module’s own example
The module opens on this example, so you can follow every number on your own screen. A 20 × 30 m raft carries qgross = 100 kPa at the bottom of a 3 m excavation in four clay layers (0–2, 2–7, 7–16 and 16–30 m), with the water table at 1.5 m, the OCR method and the influence depth p = 10 %.
Stresses at the first slice
The first slice is 0.50 m thick, centred at z = 3.25 m in Clay-1. σv0 = 18.0 × 1.50 + 19.0 × 0.50 + 18.0 × 1.25 = 59.00 kPa and u0 = 9.81 × (3.25 − 1.50) = 17.17 kPa, so σ′v0 = 41.83 kPa; σ′p = 1.60 × 41.83 = 66.93 kPa. The removed overburden is qremoved = σ′v0(3.00 m) = 18.0 × 1.5 + 19.0 × 0.5 + 18.0 × 1.0 − 9.81 × 1.5 = 39.78 kPa, so at z′ = 0.25 m (I = 1.0000) σ′exc = 41.83 − 39.78 = 2.05 kPa and σ′final = 2.05 + 100 × 1.0000 = 102.05 kPa.
Compression of the first slice
heave = −0.050 × 0.50/(1 + 1.05) × log10(41.83/2.05) = −15.98 mm (Cs = Cr = 0.05, not given)
Sb = +15.98 mm, Sr = 0.050 × 0.50/2.05 × log10(66.93/41.83) = +2.49 mm, Sv = 0.250 × 0.50/2.05 × log10(102.05/66.93) = +11.17 mm
Sc = 15.98 + 2.49 + 11.17 = 29.64 mm and the net value is 29.64 − 15.98 = 13.66 mm: the numbers of the Calculations tab for this slice. The same calculation, repeated for the 102 slices down to zlim = 3.00 + 50.94 = 53.94 m, gives the totals below.
The example, totals (mm)
Quantity
Value
Excavation heave
-104.4
Sb · Sr · Sv
+104.4 · +71.6 · +135.3
Sc (loading, from the excavation base)
+311.3
Settlement of the foundation (from the original ground)
+206.9
Time
Clay-1 drains both ways, so Hdr = 4.00/2 = 2.00 m and t50 = 0.197 × 2.00²/2.00 = 0.39 yr, t90 = 0.848 × 2.00²/2.00 = 1.7 yr. Clay-3 is the thick layer (H = 37.94 m below the foundation level, Hdr = 18.97 m, Cv = 3.00 m²/yr) and takes t90 = 102 yr by itself. The summed curve reaches 50 % of Sc at 1.2 yr and 90 % at 17 yr, the values of the Total row.
Independent check
The same model was calculated again outside the module: the Boussinesq influence by numerical integration over the loaded rectangle, the slices, the stress path and Terzaghi’s series written from the formulas above. It gives the heave −104.4 mm, Sc 311.3 mm, the net settlement 206.9 mm, t50 = 1.19 yr and t90 = 16.8 yr, the same as the module to the digit shown.
The same model in the other units
In US the boxes show 9.84 ft (the excavation), 65.62 × 98.43 ft and 2.09 ksf, and the cards read −4.11 in, +8.15 in and +12.26 in, which are the same −104.4, +206.9 and +311.3 mm. In SI · tf the pressure box shows 10.2 t/m² and the cards are unchanged in mm.
How each input changes the answer
Each row changes one thing in the example (B × L = 20 × 30 m, qgross = 100 kPa, Dexc = 3 m, zw = 1.5 m, γ and γsat as in the table of the soil profile, OCR method, p = 10 %, Δz = 0.50 m, displacements kept) and runs the module again. The numbers are the ones the module gives, in mm (heave / Sc), so you can reproduce any row.
The example with one change at a time
Change
Heave / Sc mm
Settlement mm
The example The reference
-104.4 / 311.3
206.9
qgross = 50 kPa Below the load that gives virgin compression; no Sv
-104.4 / 124.8
20.4
qgross = 150 kPa
-104.4 / 547.3
442.9
qgross = 200 kPa The heave does not depend on the load
-104.4 / 734.6
630.2
B × L = 10 × 15 m A smaller raft: a shallower zlim; zlim = 28.47 m
-83.4 / 223.9
140.5
B × L = 40 × 60 m A larger raft: a much deeper zlim; zlim = 104.87 m
-122.1 / 381.1
258.9
No excavation Foundation at the surface; the fill is compressed; zlim = 50.94 m
0.0 / 551.7
551.7
Dexc = 1.5 m A shallower excavation; zlim = 52.44 m
-81.1 / 391.2
310.1
Dexc = 5 m A deeper excavation: more heave, less net settlement; zlim = 55.94 m
-121.6 / 224.3
102.7
zw = 0.5 m A higher water table
-89.5 / 385.0
295.5
zw = 5 m A lower water table
-95.2 / 171.3
76.1
OCR = 1 in all layers Normally consolidated: all virgin compression
-104.4 / 616.5
512.1
OCR = 3 in all layers Heavily overconsolidated: no virgin compression
-104.4 / 203.1
98.7
Cc of Clay-2 = 0.60 Twice the virgin index in one layer
-104.4 / 390.2
285.8
Cr of Clay-2 = 0.12 Twice the recompression index in one layer
-104.4 / 344.4
239.9
Cs of Clay-1 = 0.02 Heave and reloading shrink together; the net settlement stays
-67.0 / 274.0
206.9
e0 of Clay-2 = 1.5 A larger void ratio gives a smaller strain
-95.8 / 273.7
177.8
p = 20 % A shallower zlim; zlim = 37.10 m
-103.2 / 307.5
204.3
p = 5 % A deeper zlim; zlim = 76.89 m
-105.0 / 313.2
208.2
Δz = 1 m Coarser slices
-102.7 / 309.4
206.7
Δz = 0.25 m Finer slices
-105.3 / 312.3
207.0
What the rows show: the load moves Sc but not the heave; the excavation and the water table move both, through qremoved and the effective stresses; OCR decides how much of the load is recompression and how much virgin compression; and the size of the raft sets the depth to which the clay is squeezed, so a wider raft reaches deeper layers. Cs changes the heave and the reloading by the same amount and leaves the net settlement as it was. The slice thickness matters little: 1 m and 0.25 m change the settlement by less than 1 mm here.
How fast it settles
Time to 50 % and 90 % of the loading settlement (years)
Change
t50
t90
The example
1.2
17
Cv of Clay-2 = 0.2 m²/yr (instead of 1.0)
2.0
63
Clay-2 with single drainage
1.8
53
B × L = 10 × 15 m
0.8
9.7
B × L = 40 × 60 m
1.8
78
p = 5 %
1.2
20
Bottom of the profile
1.1
12
t90 is governed by the thickest layer: it grows with the square of the drainage path Hdr and falls in proportion to Cv. A deeper calculation depth lengthens the last layer and so t90.
Messages: stops, warnings and notes
Stops
When a value cannot be used, Analyze opens a window titled Cannot analyse — 1 input error (or “N input errors”) with the numbered messages, and nothing is calculated. The bar stays Not analysed. Typing zero in a box that must be positive gives a stop:
A stop: Cc of Clay-1 set to 0.
When
Message
Cc is zero or negative in a layer that is compressed
“Clay-1 (CL, soft): Cc missing — needed below the foundation level.”
e0 or Cr is negative
“Clay-1 (CL, soft): e0 missing — needed below the foundation level.” (or Cr)
With the mv method, mv is zero
“Clay-1 (CL, soft): mv missing — needed below the foundation level.”
γ is zero
“Clay-1 (CL, soft): γ is missing.”
γsat is zero
“Clay-1 (CL, soft): γsat is missing.”
The compressibility is only asked where a layer is compressed, below the foundation level and above zlim; a layer above the foundation level needs only its unit weights.
Warnings
A warning does not stop the analysis. The Warnings window opens by itself after Analyze, the Results and Report tabs show a bar with the first warning and a Warnings (N) button, and the Analyze bar turns to a warning colour and shows the count. The window lists the warnings and then the assumptions of this analysis: the removed load, the excavation plan, the calculation depth, the stress path, where the settlement is measured from, and the time curve.
When
Message
qgross is below qremoved
“The gross pressure is below the removed overburden (qnet < 0): the loading does not bring the stresses back to the initial state.” With 30 kPa the foundation settlement is 0 and the card adds that the ground ends 17.4 mm above its original level.
OCR below 1
“8 slices had σ′p below σ′v0 (OCR < 1): σ′p = σ′v0 was used — under-consolidated clay is outside the scope.”
A laboratory σ′p below σ′v0
“43 slices had σ′p below σ′v0 (laboratory σ′p < σ′v0): σ′p = σ′v0 was used — under-consolidated clay is outside the scope.” (the count follows your values)
γsat not above γw
“Clay-2 (CH, firm): γsat ≤ γw — the effective stress does not grow through this layer.”
The effective stress after the excavation is below 0.1 kPa
“4 slices had σ′exc below 0.1 kPa after the excavation: σ′exc = 0.1 kPa was used (the e – log σ′ law is unbounded near zero stress; the swelling of these slices is a model limit).” For example with γsat just above γw.
Cv missing in a compressed layer
“No time curve: Cv is missing for Clay-2 (CH, firm).” The settlement is calculated; the time columns and the Time view are empty.
The excavation reaches the bottom of the profile
“The excavation reaches the bottom of the soil profile (30.00 m).” With the profile rule a second one follows: “No soil between the foundation level and the calculation depth: nothing to consolidate.” and the results read 0.
Notes on the screen
“Results cleared — the inputs can be edited.” appears after Edit inputs.
“The soil profile ends above zlim: Clay-3 is taken to continue …” is the note under the calculation depth when the profile is shorter than zlim; the report repeats it.
“The soil below zlim is not compressed: the stress increase there is less than 10 % of q.” is the note when the profile is deeper.
“Enter p between 5 % and 50 % and the size of the foundation.” shows instead of the read-outs when p or the size cannot be used.
Good practice and common mistakes
Say where the settlement is measured from. After an excavation, Snet (206.9 mm here) and Sc from the excavation base (311.3 mm) answer different questions; the heave is reported next to them.
Take Cs from the swelling branch of the test. Left empty, Cs = Cr is used and the report says so; a larger Cs raises the heave and the reloading together.
Check σ′p against σ′v0. A laboratory σ′p below the initial stress is replaced by σ′v0 and warned; the slice table shows the regime of every slice.
Decide what lies below the profile. With the influence depth the last layer is extended to zlim (here by 23.94 m); if rock or dense gravel lies there, choose Bottom of the profile.
Keep the slices thin enough. The default 0.50 m is fine for the example; thin layers need a smaller Δz.
Use Cv from the field when you can. The time curve follows Cv and the drainage path; a layer with a sand lens drains differently from the double-drainage assumption.
Read the stop and the warnings. A zero in a required box stops the analysis; a warning does not, but it changes the numbers.
Keep a record. The model is kept in this browser, but a file from Save to file… and the report travel with the project.
Frequently asked questions
What does the Consolidation settlement module calculate?
The primary consolidation settlement of clay layers under a rectangular or strip foundation, slice by slice along the stress path (swelling, reloading, recompression, virgin compression), the excavation heave, and the settlement against time by Terzaghi’s theory. For the example it gives a heave of −104.4 mm, a settlement of the foundation of +206.9 mm and t90 of 17 years.
Why is the settlement of the foundation less than the loading settlement?
The settlement is measured from the original ground by default. The excavation made the clay swell (heave −104.4 mm), and the load first recovers that heave: Snet = Sc + heave = 311.3 − 104.4 = 206.9 mm. Choose Reset to zero before loading to see 311.3 mm measured from the heaved excavation base.
What are Cs, Cr and Cc doing?
Cs governs the swelling on unloading and the reloading back to the initial stress, Cr the recompression from the initial stress to the preconsolidation pressure σ′p, and Cc the virgin compression beyond it. If Cs is empty, Cr is used.
How is the calculation depth chosen?
With the influence depth rule the settlement is summed down to where the stress increase under the centre has fallen to p (5 to 50 %, default 10) of q. For the 20 × 30 m raft that is 50.94 m below the foundation level. With Bottom of the profile it stops at the last layer.
What happens if my profile is shorter than the calculation depth?
The last layer is taken to continue down to the calculation depth with the same properties, and the drawings, the table and the report say so (“continued from 30.00 to 53.94 m (assumed)”). Choose Bottom of the profile if a stiff stratum lies below the profile.
Can I use granular layers or the immediate settlement?
No. Every layer is clay and only primary consolidation is calculated. The immediate settlement is in the two Elastic settlement modules, and Settlement 2D combines both over a profile of clay and sand layers.
What if the load is smaller than the removed overburden?
The module warns that qgross is below qremoved. The load then only brings the clay back part of the way along its swelling line: for 30 kPa the foundation settlement is 0 and the ground ends 17.4 mm above its original level.
Can I drag or move anything on the drawing?
No. The drawings are not interactive apart from the chips that show or hide parts. Every value is typed in the Model tab, and the Section view follows it. After Analyze the inputs are locked until you press Edit inputs.
Does the module remember my inputs?
Yes. Every change is kept in this browser, and the page opens on the model you last worked on, analysed or not. Save to file writes a .json file, Quick Save keeps named versions in the browser, and Reset to defaults returns to the example.
Which units and signs can I use?
SI · kN, SI · tf and US, and the sign convention settlement + (default) or settlement −, all in the header and all changeable after Analyze. The drawings stay in m · kPa · mm. The Calculations tab keeps the classical sign.
How are t50 and t90 found?
Each layer follows Terzaghi’s solution with its Cv and drainage path (Hdr = H/2 for double drainage, H for single); the settlement of the profile is the sum of the layers’ degrees of consolidation times their Sc, and t50 and t90 are the times when that sum reaches 50 % and 90 % of the total.
What does the report contain?
A cover with your project details and a key-information table, then eight parts: introduction and scope, soil profile and parameters, excavation, foundation and calculation depth, stress path and assumptions, consolidation settlement, slice by slice, time-dependent consolidation and a summary, with the drawings. It saves as PDF or Word after Analyze.
Calculate the immediate settlement of a flexible rectangular or strip foundation on layers of clay and silt that deform undrained, with Steinbrenner’s influence factors layer by layer. This manual walks through the screen, every input, the depth rule, the results, the working and the report, with a worked example you can reproduce.
Elastic settlement — cohesive gives the immediate settlement of a flexible foundation on a profile of clay and silt layers that deform undrained, right after the load is applied, at constant volume. The soil is treated as an elastic body: each layer has an undrained modulus Eu and a Poisson’s ratio of ν = 0.5, and the vertical strain is added up layer by layer, slice by slice, with the influence factors of Steinbrenner.
qnet is the pressure that the foundation adds at its own level, α and B′ select the centre or the corner of the foundation, and Is is the shape factor of Steinbrenner, which depends on the length-to-width ratio and on the depth. The settlement is summed from the foundation level down to the calculation depthzlim.
What you can describe
A layered profile of cohesive layers, from the ground surface down, with a name, unit weights and an undrained modulus Eu for each layer.
A rectangular (raft) or strip foundation with its width, length and gross pressure, with or without an excavation before loading.
Groundwater at a depth below the ground, which sets the effective overburden removed by the excavation.
The depth of the calculation: the influence depth, where the stress increase has fallen to a share p of the pressure, or the bottom of the profile (a rigid base below it).
The module gives the settlement at the centre and at the corner (the edge of a strip) of the flexible foundation and for a rigid foundation, the share of every layer, every slice with its stress and strain, the working for any slice, and a PDF or Word report. The stresses, the strain and the settlement are drawn as colour bands over the section.
Which module for what
Clay settles twice: at once, undrained (this module), and later, as the water leaves, by consolidation. For the consolidation of the clay layers and the settlement–time curve use Consolidation settlement.
For one profile that has both kinds of layer, with the immediate and the consolidation settlement added, use Settlement 2D.
If you only need the stress increase under a foundation, the Stresses in a soil mass modules give it at any point. The bearing capacity of the same foundation belongs to the Bearing capacity family.
Before you start: what you need
Have these ready from your investigation and design:
What
Notes
The soil profile
Layer depths from the ground surface, a unit weight γ above the water table and γsat below it for every layer. Every layer is cohesive: the module has no type to choose.
The undrained modulus Eu of each layer
In MPa (or the unit of the system you choose). The settlement is inversely proportional to Eu, so this is the number to think about most. Split a thick layer into several when the stiffness grows with depth. Enter it for the layers below the foundation level.
The groundwater depth zw
Below the ground surface. It matters through the effective overburden that the excavation removes.
The foundation
Width B, length L (or a strip), and the gross pressure qgross at the foundation level.
The excavation
Whether the ground is excavated before the foundation is loaded, and how deep. The foundation level is the base of the excavation.
The depth rule
The influence depth with a share p (10 % is the starting value), or the bottom of the profile when a rigid stratum lies right below it.
Quick start in seven steps
Open the module and choose the units
Open Elastic settlement — cohesive from the Settlement family. In the header pick SI · kN, SI · tf or US, and the sign convention of the displacements (Sign: settlement + is the starting choice). You can change both at any time.
Describe the soil profile
In Soil profile give the depth of the bottom of each layer, its name and its unit weights. Press + Add layer for more layers and × to delete one.
Give the elastic parameters
In Elastic parameters type the undrained modulus Eu of each layer. ν is fixed at 0.50.
Set the water table and the excavation
Enter the groundwater depth in Groundwater. In Excavation choose Yes and the depth, or No.
Describe the foundation
In Foundation choose Rectangle / raft or Strip and enter the width, the length (rectangle only) and the gross pressure. The net pressure is shown below.
Choose how deep to calculate
In Analysis Settings keep Influence depth (Δσ = p · q) with p = 10 %, or choose Bottom of the profile.
Press Analyze
Press Analyze at the foot of the Model tab. The inputs lock and the drawing shows the settlement of the section. The numbers are on the Results tab; Calculations and Report follow.
The screen: three views of the section
The layout is the one every GeoTerva module shares, described in the workspace guide. This module has three views of the section through the centre of the foundation, chosen above the drawing, and five tabs on the right: Model, Results, Calculations, Report and Theory.
The whole window after Analyze. The header carries the sign convention and the units.
Section is the soil profile: the layers with their names, the water table, the excavation, the foundation with its pressure, the depth scale, the calculation slices and the calculation depth zlim. It follows your inputs as you type.
Contours paints one quantity over the section as colour bands, with a legend: Δσz (the stress increase from the net pressure), E (the modulus of the layers), εz (the vertical strain) or S (the settlement of a point at that depth, that is, the compression of the soil between it and the calculation depth).
Settlement shows Settlement S or Strain εz as colour bands, the exaggerated settlement trough of the foundation level, and a bar for every slice on the centre line. After Analyze the module opens on this view.
The Section view of the example, before Analyze.
Contours: the stress increase Δσz.
Settlement: S over the section and the bars of the slices.
Contours: the modulus E of the layers.
The Show chips
Each view has a Show bar of chips that switch parts of the drawing on and off. They change the drawing only, never the calculation, and they can be used before and after Analyze.
Section:Slices, Dimensions, Layer labels.
Contours:Foundation and Layer labels, and the Field buttons Δσz, E, εz, S.
Settlement:Trough, Labels and Slice bars, and the Field buttons Strain εz and Settlement S.
The Show bar of the Section view.
The Field and Show bars of the Contours view.
The Field and Show bars of the Settlement view.
Entering the model, section by section
The Model tab has seven sections. Model data stands on its own and can stay open; the other six are walked through one at a time: opening one closes the previous, and Next and Back at the foot of each move on. Analyze waits below the last section. Boxes show the unit of the system you chose (m · ft, kPa · ksf, and so on); the model itself is kept in SI. When you change the unit system a box may show more digits than before, because it shows the stored value converted.
Model data
Save the model, open another, or start again. Model name is a label for the model. Save to file… writes a .json file (a file window opens, or the file goes to your downloads folder). Open file… reads one. Quick Save… asks for a name and keeps this version in the list under it in this browser; choose it and press Load, or Delete it. Reset to defaults returns to the example.
Every change you make is kept in this browser automatically, so the page opens on the model you last worked on, with the results if it was analysed: a line under the buttons says so. The units and the sign convention are remembered too.
Model data.
Quick Save asks for a name. With no model name it offers “Elastic settlement” and today’s date.
After a Quick Save a line confirms it and the list holds the version.
Soil profile
One row per layer, from the ground surface down: From (read-only, the bottom of the layer above, 0 for the first), To (the depth of the bottom of the layer), Name, the unit weight γ above the water table and the saturated unit weight γsat below it. Changing To moves the From of the next layer, so the profile cannot have a gap or an overlap. A To that is not below its From is ignored and the box returns to its value.
+ Add layer adds a layer below the last one, 2 m thick, named “Layer” and its number, with γ = 19.0 and γsat = 20.0 kN/m³ and Eu = 25 MPa. Change what you need.
× deletes a layer and the layers below move up; the last remaining layer cannot be deleted.
With the influence-depth rule the last layer continues down to the calculation depth when the profile is shorter than that (see Analysis Settings below).
Elastic parameters
The undrained modulus E of every layer that is compressed, in MPa in SI · kN (the unit of the chosen system otherwise), and the Poisson’s ratio ν, fixed and read-only at 0.50. A layer that lies above the foundation level has no boxes: the table says it is removed by the excavation and only its unit weight is used. A layer below the calculation depth says it is not compressed. In the example the fill has no boxes for the first reason and Clay-3 for the second. The ? beside the title opens a help window on the choice of E and ν.
Elastic parameters: only the layers that are compressed ask for a modulus.
Field (unit)
Starting values
E (MPa)
Clay-1 25.0 · Clay-2 15.0 (the fill and Clay-3 take no value in the example; their moduli are 8 and 45 MPa in the stored model)
ν
0.50 for every layer
Groundwater
One number, zw, the depth of the water table below the ground surface. The module uses it for the effective overburden removed by the excavation; the excavation does not change the water table. A negative depth is taken as 0 (the table at the surface), and an empty box keeps the previous value.
Groundwater.
Field (unit)
Starting value
zw (m · ft)
2.50
Excavation
No or Yes. With Yes you give the depth Dexc of the excavation, which is also the foundation level: the foundation load acts at its base, and the soil above is removed (a layer that ends above it takes no part; one that it cuts is used from the foundation level down). The excavation takes off the effective overburden at its base, so the net pressure is smaller than the gross pressure. With No the pressure acts at the ground surface.
Excavation.
Field (unit)
Starting value
Excavation before loading
Yes
Dexc (m · ft)
1.50
Foundation
Rectangle / raft or Strip: a flexible foundation with a uniform pressure at the foundation level. A strip has no length box. Three read-outs follow the inputs: the Foundation level, the removed overburdenqremoved and the net pressureqnet = qgross − qremoved. The settlement follows the net pressure.
Foundation, with the net pressure read-out.
Field (unit)
Starting value
Shape
Rectangle / raft
B, width (m · ft)
4.00
L, length (m · ft)
6.00 (rectangle only)
qgross, gross pressure (kPa · t/m² · ksf)
180
Analysis Settings
Where the compressible zone ends, and the slice thickness. The ? beside the title opens a window that explains the influence depth with a sketch. Influence depth (Δσ = p · q) sums the settlement down to the depth zlim where the stress increase under the centre has fallen to the share p of q; Bottom of the profile sums it down to the last layer, as for a rigid base right below. Three read-outs give the Calculation depthzlim, the depth below the foundation level and where the soil profile ends, and a note under them says what applies.
Analysis Settings.
Field (unit)
Starting value
Depth rule
Influence depth
p (%)
10 (from 5 to 50; a typed value outside is brought back into this range)
Δz (m · ft)
0.50 (from 0.05 to 2)
The slice thickness Δz only sets how finely the layers are divided for the tables and the colour bands. Each layer is cut into the least number of equal slices not thicker than Δz; the settlement of a layer does not depend on it (Δz = 0.25 and 1.0 m give the same 24.1 mm as the starting 0.5 m).
Typed values that are brought into range
Several boxes keep a value inside its range instead of refusing it: p below 5 or above 50 becomes 5 or 50; Δz above 2 becomes 2; a width or length below 0.1 becomes 0.10; a negative pressure becomes 0; a negative water depth becomes 0.00. An empty box takes back its previous value. The inputs of an analysed model are locked until you press Edit inputs.
Choosing the options
Influence depth or bottom of the profile
The stress increase under a foundation falls with depth but never reaches zero, so the sum needs a lower end.
Influence depth (the starting rule) stops where Δσz has fallen to p of q under the centre. A smaller p goes deeper and adds a little more. If the soil profile is shorter than that depth, the last layer is taken to continue down to it with the same properties; if it is longer, the soil below is not compressed.
Bottom of the profile sums the settlement down to the bottom of the last layer. Use it when a rigid stratum (rock, very dense gravel) lies right below the profile: the settlement stops there, whatever the stress increase left at that depth. The note under the read-outs gives that share, for the example 2 % of q.
The ? window of the calculation depth.
Rectangle or strip
Choose Strip for a long foundation (a wall footing, a long raft): the length box disappears and the module uses the plane limit of the factors. Its stress bulb goes deeper, so the influence depth is greater: for the example the strip gives zlim = 26.86 m against 11.69 m, and the profile (25 m) is continued below its bottom with the last layer’s properties. The result card then says Edge instead of Corner.
Excavation yes or no
The excavation lowers the foundation level and takes off the soil weight: with No the whole qgross loads the soil (180 kPa for the example, against a net 152.5 kPa), and the settlement is 29.8 mm against 24.1 mm. Use Yes when the foundation really sits at the base of an excavation.
Centre, corner and rigid
A flexible foundation settles most at the centre and least at the corner. The module gives both, and their difference. A rigid foundation is taken at 0.93 times the flexible centre settlement. Read the one that matches the stiffness of your foundation, or the corner and centre as bounds.
Analyze and read the results
Press Analyze. The bar briefly counts through four steps (net pressure, calculation depth, Steinbrenner factors, layer settlements) and then reads Analysed — 2 layers, 21 slices down to 11.69 m, followed by “The inputs are locked. Edit inputs clears the results; the unit system can still be changed.” A message “Analysed — the settlement of the section; see also Contours and the Results tab.” appears for a moment. The module stays on the Model tab, switches the drawing to the Settlement view, and the numbers are on the Results tab. If the run has a caution, the Warnings window opens by itself (see Messages).
The Results tab of the example.
The cards and the table by layer
Card
Meaning
Example
Centre — flexible foundation
The settlement under the centre of the flexible foundation.
24.1 mm
Corner — flexible foundation (Edge for a strip)
The settlement at the corner, with the differential (centre − corner) beneath.
9.5 mm; differential 14.7
Rigid foundation
0.93 times the flexible centre settlement.
22.4 mm
Under the cards a line gives qgross, qremoved, qnet, the foundation level and the calculation depth with the rule used. The table lists every layer that is compressed: its type, the thickness H compressed (from the foundation level or the top of the layer down to its bottom or zlim), E, ν, the settlement at the centre and at the corner, and its share of the total. A note under the name tells when part of a layer is removed by the excavation (Clay-1: “0.50 m removed by the excavation”), when it is compressed only down to zlim (Clay-2), or when the profile has been continued (“continued from … to … (assumed)”).
In the example Clay-1 gives 9.5 mm (39 %) and Clay-2 14.7 mm (61 %) at the centre.
Slice by slice
Slice by slice: one row for each slice.
The second table gives each slice: its mid-depth z, the layer, Δσz, εz (in %) and the centre settlement ΔS. All columns adds the thickness, E, ν and the corner settlement. Click a row to see the working of that slice on the Calculations tab.
Units and sign
Changing the unit system or the sign convention after Analyze re-states the cards, tables, drawings and report without a new run. With Sign: settlement − every displacement is written with the opposite sign (the vertical displacement positive upward); strains and stresses keep compression positive. In US the starting example gives +0.95 in at the centre, 0.37 in at the corner and 0.88 in for the rigid foundation, the same 24.1, 9.5 and 22.4 mm.
The same example in US units.
The drawing keeps SI units; the cards and tables follow the system.
The Calculations tab, the report and the Theory tab
The Calculations tab writes out the working of one slice at a time. Choose the slice in the Slice list (or click a row in the Results tab). There are five steps, each with its own equations and your numbers; steps 1, 2, 3 and 5 are open and step 4 is closed until you open it:
Net pressure at the foundation level:qremoved = σ′v0(Dexc) and qnet = qgross − qremoved (for the example 27.50 and 152.50 kPa).
The slice: its depths, its Eu and ν = 0.50 (“no volume change”), and its depths below the foundation level, z′top and z′bottom.
Settlement of the slice under the centre:B′, m′ and n′ for the top and bottom of the slice, the terms A0, A1, A2, the factors F1 and F2, Is, and ΔScentre.
Corner of the foundation (Edge for a strip): the same working for the corner, with α = 1 and B′ = min(B, L), or α = 2 for the edge of a strip.
Layer and total: the calculation depth, the layer of the slice with its settlements, and the totals Scentre, Scorner and Srigid = 0.93 × Scentre.
The Calculations tab: steps 1, 2, 4 and 5 are shown open here.
With Sign: settlement − a note says the derivation is written in the classical convention (settlement +) while the results, tables and drawings follow the sign you chose. Before Analyze the tab says “Press Analyze on the Model tab first.”
The report
In Report fill in the cover: Project, Location, Client, Report no., Date, Prepared by (name), Title / qualification, Checked by and optional Notes (printed only when filled in). They are kept in this browser and saved with the model file. After Analyze Save as PDF (it opens a print window: choose “Save as PDF” in the print dialog) and Download Word (.docx) are available; before it they are greyed out. The preview below is the report itself.
The report has eight parts: 1 Introduction and scope, 2 Soil profile and elastic parameters, 3 Foundation, loading and calculation depth, 4 Method and assumptions, 5 Immediate settlement, 6 Slice by slice, 7 Summary and 8 References. When the run carries a caution a part 7 Warnings is added and the last two become 8 and 9. It carries the section and the stress and settlement colour-band drawings and states the units with the conversion constants.
The Report cover form.
The two export buttons.
The cover page of the report preview.
The Theory tab
The Theory tab has thirteen sections, each opened from the contents list at its top: Scope; Theory of elasticity; Steinbrenner’s influence factors; Layered profile; Cohesive layers; Net pressure; Depth of the settlement calculation; Flexible and rigid foundations; Embedment; Colour-band fields; Sign convention and assumptions; Outside the scope; and References.
Worked example: the module’s own example
The module opens on this example, so you can follow the numbers on your screen.
Inputs of the example
Section
Input
Soil profile
Fill 0–1 m (γ 18.0 / γsat 19.0), Clay-1 1–5 m (19.0 / 19.5), Clay-2 5–12 m (18.5 / 19.0), Clay-3 12–25 m (19.5 / 20.0)
The excavation (1.5 m) lies above the water table (2.5 m): qremoved = 18.0 × 1.0 + 19.0 × 0.5 = 27.5 kPa, and qnet = 180 − 27.5 = 152.5 kPa. The fill (0–1 m) and the top 0.5 m of Clay-1 are above the foundation level, so they are not compressed.
Step 2: the calculation depth
For a 4 × 6 m rectangle the stress increase under the centre falls to 10 % of q at z′ = 10.19 m below the foundation level, so zlim = 1.5 + 10.19 = 11.69 m. That is inside Clay-2; Clay-3 below is not compressed. The compressed thickness is 3.50 m of Clay-1 (1.5 to 5.0 m) and 6.69 m of Clay-2 (5.0 to 11.69 m): 21 slices in 2 layers.
Step 3: a slice by hand
For the first slice (1.50–2.00 m) of Clay-1: B′ = B/2 = 2.00 m, m′ = 1.500 and n′ = 0.50 / 2.00 = 0.250 at its bottom; F1 = 0.0116 and F2 = 0.0508, and since ν = 0.5 the term with F2 drops out: Is = 0.0116 (and 0 at its top). So ΔS = 152.5 × 4 × 2.00 × (1 − 0.5²) / 25000 × 0.0116 = +0.425 mm, the first entry of the slice table.
Step 4: the layers and the totals
Adding the slices gives Clay-1 9.5 mm and Clay-2 14.7 mm, a centre settlement of 24.1 mm. The same sums at the corner give 2.0 + 7.5 = 9.5 mm, and the rigid foundation 0.93 × 24.1 = 22.4 mm. These are the numbers on the Results tab. An independent numerical integration of the strains of a point load over the loaded area and the depth gave 9.46 mm and 14.65 mm at the centre for the two layers, the same to the digit shown.
The same model in the other units
Switch to SI · tf: the cards stay in mm (24.1, 9.5, 22.4) and the pressures read qgross 18.4, qremoved 2.8 and qnet 15.6 t/m². In US: +0.95 in, 0.37 in and 0.88 in; qgross 3.76 ksf, qnet 3.19 ksf, the foundation level 4.92 ft and zlim 38.34 ft.
How each input changes the answer
Each row changes one thing in the example (B × L = 4 × 6 m, qgross = 180 kPa, Dexc = 1.5 m, zw = 2.5 m, p = 10 %, Eu = 25 and 15 MPa in the two compressed layers, γ as in the example) and runs the module again. The numbers are the ones the module gives. Settlements in mm.
The example with one change at a time (settlement in mm)
Change
Centre
Corner
The example qnet = 152.5 kPa · zlim = 11.69 m
24.1
9.5
Eu of Clay-2 = 30 MPa (was 15) Clay-2’s share halves. qnet = 152.5 kPa · zlim = 11.69 m
16.8
5.7
Eu of Clay-2 = 7.5 MPa Clay-2’s share doubles. qnet = 152.5 kPa · zlim = 11.69 m
38.8
16.9
Eu of Clay-1 = 50 MPa (was 25) qnet = 152.5 kPa · zlim = 11.69 m
B = 2 m a narrower foundation: shallower influence depth. qnet = 152.5 kPa · zlim = 8.51 m
13.9
5.3
B = 5 m qnet = 152.5 kPa · zlim = 12.92 m
27.5
10.5
L = 4 m (square) qnet = 152.5 kPa · zlim = 9.85 m
19.0
7.5
L = 12 m qnet = 152.5 kPa · zlim = 15.52 m
30.0
10.7
Strip, B = 4 m the last layer is continued below 25 m. qnet = 152.5 kPa · zlim = 26.86 m
32.7
23.2
Excavation: No qnet = 180. qnet = 180.0 kPa · zlim = 10.19 m
29.8
10.7
Dexc = 3 m a deeper excavation removes more weight. qnet = 128.7 kPa · zlim = 13.19 m
22.2
8.1
zw = 0.5 m water above the base of the excavation: less weight is removed. qnet = 161.6 kPa · zlim = 11.69 m
25.5
10.0
zw = 8 m the water table is below the excavation: same answer as 2.5 m. qnet = 152.5 kPa · zlim = 11.69 m
24.1
9.5
p = 20 % qnet = 152.5 kPa · zlim = 8.32 m
19.4
6.4
p = 5 % qnet = 152.5 kPa · zlim = 16.28 m
25.4
10.5
Bottom of the profile down to 25 m. qnet = 152.5 kPa · zlim = 25.00 m
26.3
11.3
Δz = 0.25 m more slices, the same settlement. qnet = 152.5 kPa · zlim = 11.69 m
24.1
9.5
Clay-3 deleted, Clay-2 ends at 9 m Clay-2 is continued to 11.69 m: the same as the example. qnet = 152.5 kPa · zlim = 11.69 m
24.1
9.5
The same, with Bottom of the profile the sum stops at 9 m. qnet = 152.5 kPa · zlim = 9.00 m
20.6
7.1
What the rows show
The modulus divides the settlement of its layer: doubling Eu of Clay-2 takes its part from 14.7 mm to 7.3 mm.
The pressure acts on the net pressure: 100 kPa gives qnet = 72.5 kPa, and the settlement is proportional to it (11.5 mm; 300 kPa gives 43.1 mm).
The size of the foundation changes the stress bulb and so the influence depth as well: a wider or longer foundation settles more and goes deeper.
The excavation and the water table act through the net pressure only: a water table below the base of the excavation (8 m) gives exactly the example’s answer.
The depth rule changes how much of the profile is counted: a smaller p counts more.
The slice thickness does not change the answer.
Messages: stops and cautions
Stop: the module cannot analyse
When an input needed for the calculation is missing, Analyze shows a window titled Cannot analyse — 1 input error (or 2 input errors, and so on) that lists them, and nothing is calculated. The bar stays at Not analysed. Through the boxes of the Model tab the stop that can arise is a missing modulus, because the other boxes are brought into range or keep their previous value:
When
Message and what to do
A layer that is compressed has an empty or zero Eu
“Clay-2 (CH, firm): Eu is missing — needed below the foundation level.” The layer is named; enter the modulus. Each layer gives its own line.
The window that Analyze opens.
Caution: the module analyses and says what to look at
A caution does not stop the analysis. The bar reads Analysed — … — 1 warning (or warnings), the Results and Report tabs show a strip with the first warning and a Warnings (N) button, and the Warnings window opens by itself after Analyze. It lists the warnings and, below them, the assumptions of the analysis. Warnings (N) in the bar opens it again.
The Warnings window (top part): a gross pressure of 20 kPa.
The strip on the Results tab.
When
Message
qgross is not larger than the removed overburden (20 kPa against 27.5 kPa; also 0 kPa)
“The net pressure is not positive (qnet = -7.5 kPa): the foundation does not load the soil beyond the removed overburden, so no immediate settlement develops (a negative value is an elastic rebound).” The settlement is then zero or negative.
The excavation is as deep as the profile or deeper (25 m, 30 m; with one layer left, 1 m)
“The excavation reaches the bottom of the soil profile (25.00 m).” The layers above are removed; the last layer is continued down to the calculation depth.
No soil lies between the foundation level and the calculation depth (excavation 25 m and Bottom of the profile)
“No soil between the foundation level and the calculation depth: nothing settles.”
Assumptions that are stated, not cautions
The assumptions list also says, in words, what the module did with your profile: that a layer above the foundation level was removed by the excavation, that the part of a layer below zlim is left out, and that the last layer was continued when the profile ended above zlim: “The soil profile ends at 9.00 m, above zlim: Clay-2 (CH, firm) is taken to continue down to 11.69 m with the same properties. Choose "Bottom of the profile" when a rigid stratum lies right below the profile.” This also shows in the note of Analysis Settings and in the layer table of the results.
A short profile: the last layer is continued (assumed) down to the calculation depth.
Good practice and common mistakes
Think about Eu first. It sets the answer layer by layer, and a typical range spans a factor of several. Split a layer whose stiffness changes with depth.
This is the immediate settlement. Clay then consolidates; add that from Consolidation settlement, or use Settlement 2D for the total of a profile with clay and sand.
Use this module for clay and silt layers. A layer of sand or gravel in the profile belongs to the granular module or to Settlement 2D, which treat it drained.
Enter the gross pressure at the foundation level, and the excavation depth as the depth of that level. The module takes the net pressure for you.
Check the calculation depth. Read the three read-outs in Analysis Settings. If the profile ends above zlim and you know a rigid stratum is there, choose Bottom of the profile.
Read centre and corner as bounds for a flexible foundation, and the rigid value for a stiff slab.
Keep the sign convention in mind when comparing with other programs’ output: the Sign selector in the header changes every displacement shown.
Save the model with Save to file or Quick Save for the project record; the browser keeps only the last model.
Frequently asked questions
What does this module calculate?
The immediate settlement of a flexible rectangular or strip foundation on clay and silt layers that deform undrained: the vertical strain, with Eu and ν = 0.5, is added up layer by layer with the influence factors of Steinbrenner, down to the calculation depth. It gives the centre, the corner (edge) and the rigid-foundation settlement.
Why is ν fixed at 0.5?
Right after loading a saturated clay deforms without a change of volume, which is ν = 0.5. The later volume change, the consolidation, is not part of this module; Consolidation settlement computes it and Settlement 2D adds the two.
What is the calculation depth?
The depth zlim down to which the settlement is summed. With the influence-depth rule it is where the stress increase under the centre has fallen to p of the pressure (10 % to start with); with Bottom of the profile it is the bottom of the last layer. For the example zlim = 11.69 m.
Why do the first layers get no modulus box?
A layer above the foundation level is removed by the excavation, and a layer below the calculation depth is not compressed, so neither needs a modulus. The table says so in their rows.
What if my profile is shorter than the calculation depth?
With the influence-depth rule the last layer is taken to continue down to zlim with its own properties, and the module says so. If a rigid stratum lies right below your profile, choose Bottom of the profile instead.
How is the rigid foundation value found?
As 0.93 times the settlement at the centre of the flexible foundation. For the example 0.93 × 24.1 = 22.4 mm.
Why does the water table matter if the soil is clay?
It enters through the effective overburden removed by the excavation. With the excavation above the water table, moving the table deeper changes nothing; raising it above the foundation level reduces the removed weight and raises the net pressure.
Can I drag the foundation or the layers on the drawing?
No. The drawings are read-only; change the values in the Model tab. The Show chips and the Field buttons change what is drawn.
Does the module remember my inputs?
Yes. Every change is kept in this browser, and the page opens on the last model, analysed if it was. Reset to defaults returns to the example. Save to file and Quick Save keep versions you can come back to; the units and the sign convention are remembered as well.
Why is the settlement negative or zero in my run?
The gross pressure does not exceed the removed overburden, so the net pressure is not positive. The module warns “The net pressure is not positive” and shows the elastic rebound as a negative value. Check the pressure and the excavation depth.
What does the sign selector do?
It shows settlement as positive (the starting choice) or as negative, the vertical displacement being positive upward. It changes the numbers shown in results, tables, drawings and report, and nothing in the calculation.
What does the report contain?
A cover with your project details and a summary, then eight parts: introduction and scope, soil profile and elastic parameters, foundation and calculation depth, method and assumptions, the immediate settlement, every slice, a summary and references, with the section and the colour-band drawings. It is saved as PDF or Word after Analyze.
Calculate the immediate settlement of a flexible rectangular or strip foundation on layers of sand and gravel that settle drained: the settlement at the centre and the corner, for a rigid foundation, layer by layer, with colour bands over the section. This manual walks through the screen, every input, the results and the report, with a worked example you can reproduce.
Elastic settlement — granular gives the immediate settlement of a flexible foundation that rests on layers of sand and gravel. Granular layers are permeable: the water leaves as fast as the load is applied, so the soil settles drained, with the drained modulus E′ and Poisson’s ratio ν′, and there is no consolidation to add. The settlement is the integral of the vertical strain under the foundation:
S = ∫ εz dz, εz = [Δσz − ν(Δσx + Δσy)] / E
The stresses are those of an elastic half-space (Boussinesq). The integral is evaluated in closed form with the influence factors of Steinbrenner (1934), layer by layer, so that every layer uses its own E′ and ν′. The settlement is summed from the foundation level down to the calculation depth zlim.
What you can describe
A foundation that is a rectangle B × L or a strip of width B, flexible, carrying a uniform gross pressure qgross at the foundation level.
A profile of granular layers from the ground surface down, each with its unit weights, E′ and ν′.
The water table depth, and an excavation whose overburden is taken off the gross pressure.
The calculation depth: the depth where the stress increase has fallen to a share p of q (the influence depth), or the bottom of the profile with a rigid base below it.
The module gives the settlement at the centre and at the corner (the edge of a strip) of the flexible foundation, the settlement of a rigid foundation (0.93 times the centre), the share of each layer and the settlement of every slice, draws the section and colour bands of stress, modulus, strain and settlement, writes out the working and prepares a PDF or Word report.
The bearing resistance of the same foundation: Bearing capacity.
Before you start: what you need
Have these ready from your investigation and your design:
What
Notes
The profile
Layer depths from the ground surface, a name, the unit weight γ above the water table and γsat below it for each layer. Every layer is granular.
E′ and ν′ of each layer
The drained modulus and Poisson’s ratio, from tests or correlations. The help window Choosing E and ν gives ν′ commonly 0.25 – 0.35. Split a thick layer when its stiffness grows with depth.
The foundation
Width B, length L (or a strip), the gross pressure qgross at the foundation level.
The excavation and the water table
The excavation depth Dexc (the foundation level) and the depth zw of the water table below the ground surface.
The depth rule
The share p of q left at the calculation depth (10 % is common practice), or a rigid stratum at the bottom of the profile.
Quick start in seven steps
Open the module and choose the units
Open Elastic settlement — granular from the Settlement family. Pick SI · kN, SI · tf or US in the header, and the sign convention of the settlement beside it.
Describe the soil profile
In Soil profile type the depth of the bottom of each layer, its name and its unit weights. In Elastic parameters type E′ and ν′ of the layers that will be compressed.
Set the water table and the excavation
Type the water table depth in Groundwater and choose No or Yes in Excavation with its depth.
Describe the foundation
In Foundation choose Rectangle / raft or Strip and type B, L and qgross. The net pressure qnet is shown under the boxes.
Choose the calculation depth
In Analysis Settings choose Influence depth (Δσ = p · q) and p, or Bottom of the profile.
Press Analyze
Press Analyze at the foot of the Model tab. The inputs lock, the drawing moves to the Settlement view and the bar reads Analysed.
Read the answer
The Results tab gives the centre, corner and rigid settlement and the table by layer and by slice. Calculations shows the working of any slice; Report saves a PDF or a Word file.
The screen: three views of the section
The layout is the one every GeoTerva module shares, described in the workspace guide. This module has three views of the section through the foundation centre, chosen with the buttons above the drawing. The drawing is a picture of the model: nothing can be dragged, and the drawing has no zoom or pan. You change the model in the Model tab and the drawing follows at once.
Section shows the profile, the water table, the excavation, the foundation with its pressure, the calculation slices on the centre line and the calculation depth zlim (a dashed red line). It is available before and after Analyze.
Contours paints a field over the section, on the plane through the centre: the stress increase Δσz, the modulus E, the strain εz or the settlement S. Until you press Analyze it says “Press Analyze”.
Settlement shows the settlement S of a point at each depth (the compression of the soil between that point and the calculation depth) or the strain εz, the settlement trough of the foundation level and a bar for every slice on the centre line.
Section: the example before Analyze.
Settlement after Analyze: bands, trough and slice bars.
Contours: the stress increase.
Contours: the modulus of the layers.
The Show and Field chips
View
Chips
Section
Show: Slices, Dimensions, Layer labels
Contours
Field: Δσz, E, εz, S · Show: Foundation, Layer labels
The chips only change what is drawn. The (?) beside Show and Field explains each. Pointing at a slice on the Section view or a bar on the Settlement view shows its depth and, after Analyze, its settlement.
The Contours bar.
Colour bands
The stress increase and the modulus are painted in 36 equal bands between the smallest and the largest value of the field, with the legend beside the drawing. The strain and the settlement fall off quickly with depth, so they are painted in classes (1, 1.5, 2, 3, 5 and 7 times a power of ten, from 1/300 of the maximum upward): small values at depth keep colours of their own. The settlement field is zero below the calculation depth.
The workspace after Analyze.
Entering the model, section by section
The Model tab has seven sections. They open one at a time as an accordion (click a title); Next and Back at the foot of a section walk you through them, and Analyze waits at the bottom of the tab. Model data is separate from the inputs. A value is taken when you leave the box or press Enter. The tables give the default of the example, in SI; units follow the unit system chosen in the header (the boxes convert).
Model data
The model is kept in the browser after every change, so the page opens again on the model you last worked on, analysed or not, with a line such as “Opened with the model you last worked on (date and time), analysed. “Reset to defaults” starts again from the example project.” The unit system and the sign convention are remembered as well.
Model name is a free name for the model.
Save to file… writes the model to a .json file; Open file… reads one. A file that is not a model gives “Not a model file: no model inputs found in the file”. A file with a layer of another kind opens with a note, for example “this module takes granular layers only: Clay was read as granular — check E′ and ν′”.
Quick Save… asks for a name and keeps this version in the list beside Load and Delete; a name that exists asks before it is replaced. Load with nothing chosen says “Choose a saved model first.”
Reset to defaults puts the example back and says “The inputs are back at the module defaults, and this is now the model kept in the browser.”
Model data.
Soil profile
One row for each layer, from the ground surface down. From is read-only: it is the bottom of the layer above (0 for the first). You type To, the Name and the unit weights. A To that is not below the layer’s own From is ignored and the box returns to the old value. + Add layer appends a layer starting at the bottom of the last one, 2 m thick, named “Layer 5”, “Layer 6”…, with γ = 19.0 and γsat = 20.0 kN/m³. The × deletes a layer (the only remaining layer cannot be deleted); the layers below move up.
The four layers of the example are Fill, sandy (0–1 m), Sand loose to medium dense (1–5 m, γ 18.5, γsat 19.5), Sand medium dense (5–12 m, 19.0 and 20.0) and Gravelly sand dense (12–25 m, 20.0 and 21.0). A layer is granular by definition here, so there is no Type column.
Soil profile.
Field (unit)
First layer
Range
To m · ft
1.00
below From
γ kN/m³ · t/m³ · pcf
18.0
above zero
γsat kN/m³ · t/m³ · pcf
19.0
above zero
Elastic parameters
One row for each layer with the layer name and depths, the behaviour (granular, drained, E′) and two boxes. Only a layer that lies between the foundation level and the calculation depth has boxes; a layer above the foundation level says “Above the foundation level — removed by the excavation; only its unit weight is used.”, a layer below says “Below the calculation depth zlim = 11.69 m — not compressed.” These notes follow the model as you edit it. The (?) opens Choosing E and ν.
ν′ is limited to 0.49 when you type a larger value. E′ blank or zero stops the analysis (see Messages). The first layer of the example has E′ = 8 MPa and the fourth 70 MPa; they come into play when the foundation level or the calculation depth changes.
Elastic parameters.
Field (unit)
Example
Range
E′ MPa · kg/cm² · ksf
20.0 and 35.0 (layers 2 and 3)
above zero
ν′ —
0.3
0 to 0.49
Groundwater, Excavation and Foundation
Excavation: No puts the foundation at the ground surface; Yes takes the overburden of the excavation off the gross pressure.
Foundation: Rectangle / raft or Strip. A strip has no length box. The water table acts only through the overburden removed by the excavation.
Under the boxes three read-only values show the Foundation level, qremoved (the effective vertical stress at the excavation base) and qnet = qgross − qremoved.
A box left empty keeps its previous value; a value below the limit is raised to it (a width of 0.05 m becomes 0.10 m).
Foundation: the pressure and the net pressure.
Field (unit)
Default
Range
zw Groundwater depth m · ft
2.50
0 or more
Dexc Excavation depth, the foundation level m · ft
1.50 (Yes)
0 or more
B Width m · ft
4.00
0.1 or more
L Length (rectangle only) m · ft
6.00
0.1 or more
qgross Gross foundation pressure kPa · t/m² · ksf
180
0 or more
Analysis Settings
Here you choose the lower end of the settlement sum. Influence depth (Δσ = p · q) sums down to zlim, the depth where the stress increase under the centre has fallen to p of q. Bottom of the profile sums to the bottom of the last layer, as if a rigid base lay right below it. The (?) opens a sketch and a table of the depth z′ below the foundation level for typical shapes. Three read-only values show zlim, the depth below the foundation level and the depth where the profile ends, with a note that explains the case.
Δz sets the slices used for the tables and the fields. The settlement of a layer does not depend on it: 0.25, 0.50 and 1.00 m all give 24.1, 24.1 and 24.1 mm at the centre.
Analysis Settings.
Field (unit)
Default
Range
p stress increase left, as a share of q %
10
5 to 50 (3 becomes 5, 60 becomes 50)
Δz slice thickness m · ft
0.50
0.05 to 2
Choosing the calculation depth and the foundation shape
The stress increase under a foundation falls with depth but never reaches zero, so the sum needs a lower end. There are two choices.
Influence depth (Δσ = p · q) (the starting rule). Use it when the granular soil continues well below the foundation. zlim = Dexc + z′, where z′ is the depth below the foundation level at which Δσz = p · q under the centre. Layers below zlim are not compressed. If the profile ends above zlim, the last layer is taken to continue with the same properties.
Bottom of the profile. Use it when a rigid stratum (rock, very dense gravel) lies right below the last layer. The settlement stops at the bottom of the profile whatever the stress increase there; the module states what share of q is still left.
For the example, with p = 10 %, z′ = 10.19 m and zlim = 11.69 m, inside the medium dense sand. The dense gravelly sand below is not compressed. A smaller p goes deeper and a larger one stops sooner: p = 5 % gives zlim = 16.28 m and 24.9 mm, p = 20 % gives 8.32 m and 21.9 mm, p = 50 % gives 4.99 m and 17.2 mm. The bottom of the profile gives 25.5 mm over 25.00 m.
The (?) window of the calculation depth.
A profile shorter than the influence depth
A strip loads the soil to a much greater depth. The same profile with a strip of width 4 m gives zlim = 26.86 m, below the 25.00 m where the profile ends. The Analysis Settings note then reads “The soil profile ends above zlim: Gravelly sand is taken to continue from 25.00 to 26.86 m with the same properties. Choose Bottom of the profile when a rigid stratum lies below it.” The Section and Settlement views draw a line “profile ends at 25.00 m — the last layer continues (assumed)”, and the Results table marks the layer “continued from 25.00 to 26.86 m (assumed)”.
A strip: the last layer continues down to zlim.
Rectangle or strip
Choose Strip for a long wall footing or embankment foundation where the length is many times the width; the length is then not used and the module gives the settlement at the edge instead of the corner. For a rectangle the corner and the centre differ by the “differential” settlement shown in the Results. With the other inputs of the example the strip gives 31.5 mm at the centre and 21.2 mm at the edge.
The excavation and the net pressure
With an excavation the foundation level is Dexc and the load that settles the soil is the net pressure qnet = qgross − qremoved, where qremoved is the effective vertical stress at the excavation base. The module takes one modulus for unloading and reloading, so the rebound of the excavation and its recovery cancel. For the example qremoved = 18.0 × 1.0 + 18.5 × 0.5 = 27.25 kPa (above the water table) and qnet = 152.75 kPa. Layers that lie wholly above the foundation level only contribute their weight. The water table matters when it lies above the excavation base: zw = 0.5 m gives qnet = 161.6 kPa and 25.4 mm; zw = 10 m leaves the example unchanged at 24.1 mm.
Analyze and read the results
Press Analyze. The bar counts four short steps (net pressure, calculation depth, Steinbrenner factors, layer settlements) and then reads Analysed — 2 layers, 21 slices down to 11.69 m with “The inputs are locked. Edit inputs clears the results; the unit system can still be changed.” The bar then has Warnings (0) and Edit inputs. When the run carries a caution, the bar adds “— 1 warning” and the Warnings window opens by itself (see Messages). The Results tab shows three cards, a line of pressures, the table by layer and the table by slice.
Card
What it is
Example
Centre — flexible foundation
Settlement under the centre of a perfectly flexible foundation.
+24.1 mm
Corner — flexible foundation (Edge for a strip)
Settlement at the corner, with the differential settlement centre − corner.
+8.3 mm; differential +15.8
Rigid foundation
A rigid foundation settles about 0.93 times the flexible centre.
+22.4 mm
Under the cards a line gives qgross, qremoved, qnet, the foundation level and the calculation depth. The layer table lists, for each compressed layer, its type, the thickness H that is compressed, E′, ν′, the settlement at the centre and at the corner and the share of the total. Notes under a layer say how much of it was removed by the excavation, that it was compressed only down to zlim, or that it was continued below the profile.
The layer table of the example.
Below it Slice by slice lists every slice with its depth, layer, Δσz, εz and the settlement at the centre; tick All columns to add the thickness, E′, ν′ and the corner settlement. Click a row to open its step-by-step working in the Calculations tab.
Units and the sign of the settlement
The unit selector in the header switches the boxes, the tables, the cards and the working between SI · kN, SI · tf and US without a new run. The drawings stay in SI (m, kPa, MPa, mm) and say so in the corner. Values you typed are kept unrounded behind the boxes: in SI · tf the unit weights show three decimals (18.0 kN/m³ shows 1.835 t/m³).
The Sign selector beside it chooses Sign: settlement + (the default) or Sign: settlement − (the vertical displacement positive upward). The cards, tables, drawings and report then show settlement as negative: -24.1 mm in place of +24.1. The step-by-step working keeps the classical convention. Strains and stresses keep compression positive.
The first card shows the centre; a net pressure that does not exceed the removed overburden gives a negative value, an elastic rebound.
The Calculations tab, the report and the Theory tab
The Calculations tab writes out the working of one slice, chosen in the Slice box at the top (or by clicking a row of the Results). It has five steps; steps 1, 2, 3 and 5 are open and step 4 opens on a click.
Net pressure at the foundation level — qremoved and qnet = qgross − qremoved with your numbers (27.25 and 152.75 kPa in the example).
The slice — its depths, the type of soil, E′ and ν, and its depths z′ below the foundation level.
Settlement of the slice under the centre — the shape factor Is = F1 + (1 − 2ν)/(1 − ν) · F2 at the top and at the bottom of the slice, with the intermediate terms, and ΔS = qnet · α · B′ · (1 − ν²)/E · (Is bottom − Is top).
Corner (or Edge of a strip) — the same with α = 1 (or 2) and B′ = B.
Layer and total — the calculation depth, the settlement of the layer and the totals at the centre, at the corner and for the rigid foundation.
Calculations: the slice, steps 1 and 2.
Before Analyze the tab says “Press Analyze on the Model tab first.” The working is yours to check: for the first slice of the example, B′ = 2.00 m, m′ = 1.500 and n′ = 0.250 at the bottom give Is = 0.0406, so ΔS = 152.75 × 4 × 2.00 × (1 − 0.30²)/20 000 × 0.0406 = 2.258 mm.
The report
In the Report tab fill in the cover: project, location, client, report number, date (today by default), prepared by, title and qualification, checked by and optional notes. The cover is kept in the browser and saved with the model file. After Analyze the Save as PDF and Download Word (.docx) buttons are active and the report appears below; before it they are greyed and the tab says to press Analyze.
The report has eight parts: 1 Introduction and scope, 2 Soil profile and elastic parameters, 3 Foundation, loading and calculation depth, 4 Method and assumptions, 5 Immediate settlement, 6 Slice by slice, 7 Summary and 8 References. When the run carries a caution a part 7 Warnings is added and the last two become 8 and 9. It carries the section, the stress-increase field and the settlement field as figures and states the units with the conversion constants.
The report cover page.
The Theory tab has thirteen sections: Scope, Theory of elasticity, Steinbrenner’s influence factors, Layered profile, Granular layers, Net pressure, Depth of the settlement calculation, Flexible and rigid foundations, Embedment, Colour-band fields, Sign convention and assumptions, Outside the scope, and References.
Worked example: the module’s own example
The module opens on this example the first time, and Reset to defaults brings it back.
Inputs of the example
Section
Value
Foundation
Rectangle B = 4 m, L = 6 m, qgross = 180 kPa
Excavation, water table
Dexc = 1.5 m, zw = 2.5 m
Layers
Fill 0–1 m (E′ 8 MPa); sand 1–5 m (20 MPa); sand 5–12 m (35 MPa); gravelly sand 12–25 m (70 MPa); every ν′ = 0.30; unit weights as in the section
Calculation depth
Influence depth, p = 10 %
Step 1: the net pressure
The fill (0–1 m, 18.0 kN/m³) and the first half metre of the sand above the water table (18.5 kN/m³) are removed: qremoved = 18.0 × 1.0 + 18.5 × 0.5 = 27.25 kPa, so qnet = 180.00 − 27.25 = 152.75 kPa.
Step 2: the calculation depth
For a 4 × 6 m rectangle the stress increase under the centre falls to 10 % of q at z′ = 10.19 m below the foundation level, so zlim = 1.50 + 10.19 = 11.69 m. The dense gravelly sand lies below it and is not compressed.
Step 3: the slices and the layers
The sand of 1.50–5.00 m is compressed over 3.50 m in seven slices of 0.5 m, the medium dense sand from 5.00 m to 11.69 m over 6.69 m in fourteen: 21 slices. The first slice has ΔS = 2.258 mm (see the Calculations tab), the sum of the first layer is +17.3 mm and of the second +6.8 mm.
Step 4: the totals
Scentre = 17.3 + 6.8 = 24.1 mm, Scorner = 8.3 mm, Srigid = 0.93 × 24.1 = 22.4 mm
The settlement is checked independently by summing the Steinbrenner factors of every slice and by integrating the Boussinesq strains numerically over the loaded area; both agree with these figures (the numerical integration to within 1 %).
The same model in the other unit systems
In SI · tf the module shows qgross = 18.4 t/m², qremoved = 2.8 t/m², qnet = 15.6 t/m², E′ = 204 and 357 kg/cm² and the same 24.1 mm, 8.3 mm and 22.4 mm. In US it shows 13.12 ft × 19.69 ft, qgross = 3.76 ksf, qnet = 3.19 ksf, E′ = 418 and 731 ksf, and the settlement 0.95 in at the centre, 0.33 in at the corner and 0.88 in rigid, which is 24.1 / 25.4 = 0.95 in by hand.
How each input changes the answer
Each row changes one thing in the example (rectangle 4 × 6 m, qgross = 180 kPa, Dexc = 1.5 m, zw = 2.5 m, layers as above with γ and γsat as in the section, p = 10 %) and runs the module again. Values are settlements in mm from the Results tab: the centre and the corner (the edge for the strip) in the second column, the rigid foundation in the third.
The example with one change at a time (settlement in mm; the strip row gives the edge in place of the corner)
Change
Centre · corner
Rigid
The example rectangle 4 × 6 m, qgross = 180 kPa, Dexc = 1.5 m
24.1 · 8.3
22.4
B = 3 m a narrower foundation settles less and the calculation depth is 10.26 m
20.9 · 7.2
19.4
B = 6 m wider: deeper influence, 14.02 m
28.0 · 9.4
26.0
L = 4 m (square) shorter
20.9 · 7.2
19.4
L = 12 m longer
27.8 · 9.3
25.8
Strip, B = 4 m the last layer continues to 26.86 m; corner column is the edge
31.5 · 21.2
29.3
qgross = 120 kPa qnet = 92.8 kPa
14.6 · 5.0
13.6
qgross = 240 kPa qnet = 212.8 kPa
33.5 · 11.5
31.2
No excavation qnet = 180 kPa, foundation at the surface, 10.19 m
39.4 · 12.7
36.6
Dexc = 3 m qnet = 129.4 kPa
17.7 · 6.0
16.4
zw = 0.5 m more overburden removed: qnet = 161.6 kPa, so more settlement
25.4 · 8.7
23.7
E′ of layer 2 = 10 MPa was 20
41.3 · 12.8
38.4
E′ of layer 2 = 40 MPa was 20
15.4 · 6.0
14.3
E′ of layer 3 = 70 MPa was 35
20.7 · 6.4
19.2
ν′ = 0.20 in layers 2 and 3 was 0.30
26.0 · 9.2
24.2
ν′ = 0.40 in layers 2 and 3 was 0.30
21.4 · 7.1
19.9
Bottom of the profile rigid base at 25.00 m
25.5 · 9.5
23.7
p = 5 % zlim = 16.28 m
24.9 · 8.9
23.1
p = 20 % zlim = 8.32 m
21.9 · 6.8
20.4
The modulus: the settlement is inversely proportional to E′ layer by layer, so halving E′ of the upper sand from 20 to 10 MPa raises the centre settlement from 24.1 to 41.3 mm, and the stiffness of the upper layers counts more because the strains are largest there.
ν′ acts through the lateral stresses: a larger value gives a smaller settlement here.
The excavation reduces the net pressure, and so the settlement; a deeper excavation also moves zlim down.
The water table changes the answer only when it lies above the excavation base; at 10 m it equals the example, at 0.5 m it raises qnet.
The unit weight of a layer above the foundation level enters through qremoved: γ = 22 kN/m³ in the fill gives qnet = 148.8 kPa and 23.4 mm.
The depth rule: the settlement grows only slowly beyond p = 10 %, as the added strains are small: 24.1 mm at 10 % and 24.9 mm at 5 %.
Messages: stops and cautions
When the module stops
The module needs a modulus and a Poisson’s ratio for every layer that will be compressed. When one is missing the analysis stops and nothing is calculated: a window Cannot analyse — 1 input error (or “… N input errors”) lists the problems, the bar stays Not analysed, and the inputs stay editable.
Cause
Message
E′ empty, zero or negative in a compressed layer
“Sand (SM, loose to medium dense): E′ is missing — needed below the foundation level.” (the layer’s own name comes first)
ν′ empty in a compressed layer
“Sand (SM, loose to medium dense): ν must be at least 0 and below 0.5 for a granular layer.”
The stop of an empty modulus.
Most other boxes cannot be left wrong: a box left empty returns to its old value and a value outside its range is moved to the limit (see the tables in the model sections).
Cautions
A caution does not stop the run. The Warnings window opens after Analyze with the caution and, below it, the assumptions of the analysis; a bar with the first caution appears at the top of the Results and Report tabs, and the report gets a part Warnings. Warnings (n) in the Analyze bar reopens the window.
Cause
Message
qgross not larger than qremoved (-1.1 mm for qgross = 20 kPa)
“The net pressure is not positive (qnet = -7.3 kPa): the foundation does not load the soil beyond the removed overburden, so no immediate settlement develops (a negative value is an elastic rebound).”
The excavation is deeper than the profile
“The excavation reaches the bottom of the soil profile (25.00 m).” (together with the net-pressure caution)
The Warnings window.
Notes that are not cautions
“The soil below zlim is not compressed: the stress increase there is less than 10 % of q.” — the normal case of the influence-depth rule.
The profile that ends above zlim, described above, and the rigid-base note of Bottom of the profile: “A rigid base is assumed right below the profile; the stress increase at its top is still n % of q.”
Good practice and common mistakes
Put the effort into E′. The settlement is inversely proportional to it layer by layer. Split a thick layer when the stiffness grows with depth, and give each layer the value that suits its depth.
Use this module for drained granular soil only. A clay layer settles undrained and consolidates later; use the cohesive and the consolidation modules, or Settlement 2D for the total.
Read the net pressure.qgross is the pressure at the foundation level; the excavation takes qremoved off it. Check that the foundation level you give is the excavation depth.
Check where the profile ends. If the influence depth lies below it, the last layer is taken to continue with the same properties. Choose Bottom of the profile only when a rigid stratum really lies there.
Rectangle or strip. A footing long compared with its width is a strip; use the rectangle for a pad and the strip for a wall.
Flexible or rigid. The centre and the corner of the flexible foundation bracket the behaviour of a real footing; the rigid value is 0.93 times the centre.
No embedment correction is applied (the factor is taken as 1), a choice that errs on the safe side.
Remember the model is kept in the browser. Use Save to file… to keep it with the project, and Reset to defaults to start again from the example.
Mind the sign. In the minus convention settlements show as negative numbers.
Frequently asked questions
What does this module calculate?
The immediate settlement of a flexible rectangular or strip foundation on sand and gravel layers that settle drained, by the theory of elasticity with Steinbrenner’s influence factors, layer by layer. For the example it gives 24.1 mm at the centre, 8.3 mm at the corner and 22.4 mm for a rigid foundation.
Why is there no consolidation for sand and gravel?
Granular soil is permeable, so the water leaves as fast as the load is applied and the soil settles as the load arrives, with the drained modulus E′ and ν′. Clay layers consolidate over time; see the Consolidation settlement module.
What are the centre, corner and rigid settlements?
The centre is the settlement under the middle of a perfectly flexible foundation, the corner (the edge of a strip) is the settlement at its corner, and a rigid foundation settles about 0.93 times the flexible centre.
How is the calculation depth chosen?
By the influence-depth rule it is the depth zlim where the stress increase under the centre has fallen to p of the applied pressure (5 to 50 %, 10 % by default). Alternatively the sum stops at the bottom of the profile, with a rigid base below it.
What if my profile is shorter than the influence depth?
With the influence-depth rule the last layer is taken to continue with the same properties down to zlim, and the module says so in the notes, the drawings and the Results table. Choose Bottom of the profile when a rigid stratum lies right below the profile.
What is the net pressure?
The gross pressure minus the effective vertical stress that the excavation removes at the foundation level. With the example, 180 − 27.25 = 152.75 kPa.
Does the slice thickness change the settlement?
No. It only sets the slices of the tables and the colour fields; 0.25, 0.5 and 1 m all give the same total.
Can I drag or zoom the drawing?
No. The drawings show the model and follow the boxes; you change the model in the Model tab. After Analyze the inputs are locked until you press Edit inputs.
Does the module remember my inputs?
Yes. Every change is kept in this browser and the page opens again on the model you last worked on, analysed or not, together with the unit system and the sign convention. Save to file, Open file and Quick Save keep versions; Reset to defaults brings the example back.
Which units can I use?
SI · kN, SI · tf and US, switchable at any time, even after Analyze. The drawings stay in SI.
Why does the settlement appear negative?
Either you chose the sign convention “settlement −”, or the net pressure is not positive and the soil rebounds; the second case comes with a warning.
What does the report contain?
A cover with your project details, then the introduction, the soil profile, the foundation and the calculation depth, the method and assumptions, the settlement by layer with the figures, the slice table, the summary and the references (and a Warnings part when there is one). It is saved as PDF or Word after Analyze.
Calculate the total settlement of a flexible rectangular or strip foundation on a layered profile of clay and sand: the immediate settlement of every layer plus the consolidation of the clay along its stress path, with the colour bands over the section and the settlement–time curve. This manual walks through the screen, every input, the results and the report, with a worked example you can reproduce.
Settlement 2D gives the total settlement of a foundation on a layered profile of clay and sand: the immediate (elastic) settlement of every layer plus the consolidation settlement of the cohesive layers, with the settlement–time curve. The foundation is a flexible rectangle or strip, placed at the bottom of an excavation if you enter one. The stresses, the strains and the settlement are drawn as colour bands over the section through the centre of the foundation.
S = Se + Sc
Cohesive layers (clay, silt) settle immediately, undrained, with Eu and ν = 0.5, and then consolidate along their stress path: the excavation unloads and swells them, the foundation reloads them with Cs, Cr up to σ′p and Cc beyond it (or with mv).
Granular layers (sand, gravel) settle immediately and drained, with E′ and ν′; they do not consolidate.
The immediate part uses Steinbrenner’s influence factors layer by layer; the stress increase uses Boussinesq. Both are summed down to the calculation depth: the depth where the stress increase under the centre has fallen to p % of q, or the bottom of the profile.
Results: the settlement of the centre of the flexible foundation, of its corner (edge for a strip) and of a rigid foundation, the excavation heave, the settlement of every layer and every slice, and t50 and t90 of the consolidation.
Which settlement module for which job
Only clay layers, with the full consolidation path and no elastic part: Consolidation settlement.
The module gives the settlement. The bearing capacity of the foundation (see the Bearing capacity family), secondary compression, and the structural effect of differential settlement are checked with your own design checks. The family page lists the four settlement modules.
Before you start: what you need
What
Notes
The profile From: the borehole logs
For each layer the depth of its bottom, the kind (cohesive or granular), γ and γsat. The layers run from the ground surface down without gaps.
The stiffness From: tests and correlations
Eu for each clay layer, E′ and ν′ for each sand or gravel layer, in MPa.
The consolidation data From: oedometer tests
For each clay layer e0, Cc, Cr, optionally Cs, OCR (or σ′p), Cv, and the drainage; or mv for the mv method.
The groundwater From: the borehole logs
The depth zw of the water table below the ground surface.
The excavation and the foundation From: the foundation design
The excavation depth (the foundation level), the width B and length L of the foundation (or a strip), and the gross pressure qgross at the foundation level.
Quick start in eight steps
Open the module and choose the units
Open Settlement 2D from the Settlement family. Pick SI · kN, SI · tf or US in the header; the Sign selector next to it chooses whether settlement is shown positive or negative.
Enter the soil profile
In Soil profile type the bottom of each layer, its kind, name, γ and γsat; + Add layer adds a layer at the bottom.
Enter E and ν, then the consolidation data
In Elastic parameters type E (and ν′ of the granular layers); in Compressibility type the clay data.
Enter the water table, the excavation and the foundation
Type zw in Groundwater; choose Yes or No in Excavation and its depth; in Foundation choose the shape and type B, L and qgross.
Choose the analysis settings
In Analysis Settings choose the compressibility method, the definition of σ′p, the calculation depth, the slice thickness and whether the time curve is wanted.
Press Analyze
Press Analyze at the foot of the Model tab. The inputs lock and the drawing shows the Contours view.
Read the answer
The Results tab gives Se, the consolidation settlement, the total, the heave, the corner and the rigid foundation, then every layer and every slice.
Take the working and the report
The Calculations tab writes out one slice step by step; the Report tab saves a PDF or a Word file.
The screen: five views
The layout is the one every GeoTerva module shares (workspace guide). The drawing has five views, chosen with the buttons above it; the header carries the units and the sign convention.
The header: Sign: settlement +, SI · kN and the account button.
Section is the cross section through the centre of the foundation, drawn to scale: the layers with their kind and parameters, the water table, the excavation, the foundation, the calculation slices and the calculation depth zlim. It follows the inputs as you type; after Analyze it also gives the immediate, consolidation, total and heave values at the top. Show has three chips: Slices, Dimensions and Layer labels.
Contours paints one field over the whole section in colour bands.
Stresses draws the vertical stresses on the centre line against depth, with the stress changes at the right.
Settlement paints the settlement, strain or heave of a point at every depth, with the compression of every slice at the right.
Time draws the settlement against time.
Open the module and the drawing shows Contours, which stays empty until you press Analyze; choose Section to see the profile as you enter it. Edit inputs after an analysis returns the drawing to the Section.
Section view of the default example, before Analyze.
Section view after Analyze: the slices are coloured by regime (the legend is at the foot).
Contours
The Field buttons choose the quantity: σv, u, σ′v0, σ′p, Δσexc, Δσload, σ′exc, σ′final (the default after Analyze) and E. The legend gives the value at the boundary of the bands: 36 equal bands between the minimum and the maximum of the field. The ? beside Field explains the quantities. Show has two chips, Foundation and Layer labels.
Contours, σ′final.
Contours, Δσload.
Stresses
Curves has seven chips: σv, u, σ′v0, σ′p, σ′exc, σ′final and net change. The hatched band at the top is the part removed by the excavation.
Stresses view.
Settlement
The Field buttons are Total S, Immediate Se, Consolidation Sc, Strain εv and Heave. The value at a point is the compression of the soil between that point and the calculation depth, so the value at the foundation level on the centre line is the settlement of the Results tab. The colours are classes (1 · 1.5 · 2 · 3 · 5 · 7 × 10 to the power n, from 1/300 of the maximum up), so that the small movements at depth keep colours of their own. Show has Trough (the exaggerated settlement of the foundation level), Labels and Slice bars (the immediate, heave, swelling-recovery, Cr and Cc parts of every slice).
Settlement, Total S.
Settlement, Heave.
Time
The curves are the total and one per cohesive layer, as the displacement from the original ground (the heave is taken as complete before the loading), with Se drawn as present at once, the final value, and t50 and t90 of the whole profile. Curves has a chip for the total and one for each cohesive layer. Time axis switches between Log and Linear. The view needs the time curve switched on and Cv in the clay layers.
Time view, log axis.
What you can drag
Nothing. The drawings are pictures of the model: change the values in the Model tab and the drawing follows. There are no zoom buttons, the wheel does not zoom and the drawing cannot be panned. A table row in the Results tab opens its calculation (see Calculations).
Entering the model, section by section
The Model tab has eight sections: Model data, Soil profile, Elastic parameters, Compressibility, Groundwater, Excavation, Foundation and Analysis Settings. Click a section title to open or close it; Next and Back at its foot walk you through them. Analyze waits in a bar at the foot of the tab. Units are shown under each label; defaults are shown in SI · kN and convert when you change the units. Emptying most boxes leaves the previous value in the model, so a box cannot be left blank by accident; the exceptions are named below.
Model data
The model name, Save to file… (a .json file in your downloads folder), Open file…, Quick Save… with its list, Load and Delete, and Reset to defaults. Quick Save… asks for a name; an existing name asks “Replace it?”. Delete asks for confirmation. Reset to defaults returns the example without asking and says “The inputs are back at the module defaults, and this is now the model kept in the browser.” A file that is not a model gives “Not a model file: …” in red.
Model data.
Soil profile
One row per layer, from the ground surface down. From is filled in (the bottom of the layer above); you type To. A To that is not below From is not accepted. Type is Cohesive or Granular. + Add layer adds a cohesive layer 2 m thick at the bottom with γ = 18.5 and γsat = 19.0 kN/m³ and clay data (Eu 15 MPa, e0 0.9, Cc 0.3, Cr 0.05, mv 0.0003 1/kPa, Cv 1 m²/yr, OCR 1.2); × deletes a layer (the last one cannot be deleted) and the layers below move up. Changing a layer to cohesive fills in the same clay data if it has none.
With the influence-depth rule the last layer continues down to the calculation depth when the profile ends above it (see Analysis Settings).
Elastic parameters
One row per layer, with the depth range of the layer. A cohesive row says “undrained, Eu” with ν = 0.50 fixed; a granular row says “drained, E′” and takes ν′. A layer entirely above the foundation level shows “Above the foundation level — removed by the excavation; only its unit weight is used.”; a layer below the calculation depth shows that it is not compressed. The ? beside Modulus and Poisson’s ratio opens a note on choosing E.
Elastic parameters.
Field
Default
Limits
E, MPa · kg/cm² · ksf
8 · 35 · 15 · 70 MPa (the compressed layers)
Above 0; empty or 0 gives a stop
ν′ (granular only)
0.3
0 to 0.49
Compressibility
One row per cohesive layer that is compressed; the other rows say why they are not (“Granular layer — it settles elastically only: no consolidation parameters.”). The table fits the width of the panel. The boxes of the method you did not choose are greyed: mv with the e – log σ′ method, and e0, Cc, Cr, Cs with the mv method. Cv is used only when the time curve is on. The OCR column becomes σ′p when you choose the laboratory value.
Compressibility, left part.
Field
Default
Limits
e0
1.05 · 0.85
—
Cc · Cr
0.25, 0.05 · 0.30, 0.06
—
Cs: empty = Cr
empty · 0.04
Emptying it is accepted
mv, 1/kPa
0.00040 · 0.00025
—
Cv, m²/yr
2.00 · 1.00
—
OCR, or σ′p in kPa
1.6 · 1.3 (or 90 · 150 kPa)
OCR from 1
Scrolled to the right: OCR and Drainage.
Drainage is Double (H/2) (water leaves through the top and the bottom of the layer; the default) or Single (H). H is the thickness of the layer below the foundation level, so the drainage path Hdr of the 5 m of Clay-1 below the 2 m excavation is 2.5 m. When Cs is empty the swelling uses Cr and the Warnings window says so (“Cs not given — Cs = Cr = 0.05 is used for the swelling.”). The module changes Cr and Cs together in that case: with Cs empty, Cr = 0.10 instead of 0.05 changes the heave of the default example from −69.1 to −131.6 mm.
Groundwater
One value: the depth zw of the water table below the ground surface. Pore pressure is hydrostatic below it and the water table is not changed by the excavation. A negative value is taken as 0.
Groundwater.
Field
Default
Limits
zw, m · ft
2.00 m
0 or more
Excavation
Yes or No for an excavation before loading; with Yes the excavation base is the foundation level, the removed load qremoved is the initial effective overburden there, and the clay layers swell. A depth of 0 is the same as No. Excavation plan gives the plan that unloads: Same as foundation, Own plan (type Bexc and Lexc) or Wide (I = 1) (the unloading acts fully at every depth). Displacements after the excavation chooses where the settlement is measured from: Kept — from the original ground (the heave is reported separately and the consolidation is Sc + heave) or Reset to zero before loading (the settlement is measured from the heaved base, so it includes the recompression of the heave). A note under the buttons explains the choice you made.
Excavation.
Field
Default
Limits
Dexc, m · ft
2.00 m
0 or more
Excavation plan
Same as foundation
Three buttons
Displacements
Kept — from the original ground
Two buttons
Foundation
Rectangle / raft or Strip; a strip has no length. Three read-outs follow the inputs: the foundation level, qremoved and qnet = qgross − qremoved. qgross is the gross pressure at the foundation level; the immediate settlement uses qnet.
Foundation.
Field
Default
Limits
B, m · ft
10.00 m
At least 0.1 m
L, m · ft
15.00 m
At least 0.1 m
qgross, kPa · t/m² · ksf
120 kPa
0 or more
Analysis Settings
Compressibility method: e – log σ′ (with Cc, Cr, Cs, e0) or mv, a separate linear path. Preconsolidation pressure: OCR (σ′p = OCR · σ′v0) or σ′p from the laboratory. Depth of the settlement calculation: Influence depth (Δσ = p · q) or Bottom of the profile; with the first, type p (5 to 50 %; typed values outside are brought to the limit). Three read-outs give zlim, the depth below the foundation level and the end of the profile, and a note says whether the profile is continued or cut. The ? beside the heading opens a note with a drawing and the depth z′ for common shapes. Slice thicknessΔz (0.05 to 2 m) is the largest thickness of a slice. Time-dependent consolidation: Final settlement only or With settlement–time curve.
Analysis Settings.
Field
Default
Limits
Method · σ′p definition
e – log σ′ · OCR
Two buttons each
Calculation depth · p
Influence depth · 10 %
5 to 50 %
Δz, m · ft
0.50 m
0.05 to 2 m
Time curve
With settlement–time curve
Two buttons
The ? window of the calculation depth.
Slices are made in each layer between the foundation level and zlim, split at the water table, each at most Δz thick. In the default example the water table coincides with the top of Clay-1, so the cohesive layer is cut into 10 slices of 0.50 m and the profile into 51 slices in all. A thinner slice changes the answer very little: Δz = 0.25 m gives 198.1 mm, 2 m gives 197.0 mm.
Choosing the method and the options
Calculation depth
The influence-depth rule sums down to where the stress increase under the centre has fallen to p of q; the default is 10 %. When the profile ends above that depth the last layer is taken to continue with the same properties (the Results table says “continued from 30.00 to 65.40 m (assumed)”, for example for a strip of 10 m); when the profile is deeper the soil below is not compressed. Bottom of the profile stops at the end of the last layer, which suits a stiff stratum right below it: the default example then sums to 30.00 m and gives 198.3 mm against 198.0 mm. A larger p stops earlier (20 %: 194.7 mm; 5 %: 199.0 mm).
Displacements kept or reset
With Kept — from the original ground a load that only restores the removed overburden causes no settlement; with Reset to zero before loading the same load settles by as much as the base had heaved. Use reset when the excavation stays open long enough for the heave to develop before the structure is built. In the default example kept gives S = 198.0 mm and reset gives 267.1 mm; both measures are always shown in the Results table.
Excavation plan
The unloading follows the plan you name. For the default example Same as foundation gives a total of 198.0 mm, Own plan of 20 × 30 m gives 184.5 mm and Wide (I = 1) gives 174.7 mm; the heave grows from −69.1 to −80.4 and −89.6 mm because more of the unloading reaches the clay.
The mv method
With mv the same mv serves the unloading and the reloading; the default example gives 254.8 mm in total (heave −91.3 mm). The method does not use e0, Cc, Cr, Cs or σ′p.
σ′p from the laboratory
With σ′p from the laboratory the module takes the σ′p you type for each clay layer, never below σ′v0. The default values 90 and 150 kPa are below the stress of the deeper slices, so the analysis gives a warning and a total of 248.8 mm; type the values of your tests.
Analyze and read the results
Press Analyze. The bar counts through six steps (initial stresses, excavation unloading, foundation loading, immediate settlement, consolidation, time), then reads “Analysed — 4 layers, 51 slices down to 27.47 m” and shows Warnings (0) and Edit inputs. A toast says “Analysed — the colour bands show the selected field; see also Stresses, Settlement, Time and the Results tab.” The module stays on the Model tab and the drawing changes to Contours; open Results for the numbers. The inputs are locked until you press Edit inputs (“Results cleared — the inputs can be edited.”); the units and the sign can still be changed.
The window after Analyze.
The Total settlement block has six cards. Their values for the default example:
Results tab.
Card
Value
Immediate (elastic) settlement Se, flexible foundation, centre
+41.7 mm
Consolidation settlement of the cohesive layers (from the original ground, Sc + heave)
+156.3 mm
Total settlement S = Se + Sc, centre of the flexible foundation
+198.0 mm
Excavation heave (swelling)
−69.1 mm
Total settlement at the corner of the flexible foundation (the edge, for a strip)
+168.7 mm
Total, rigid foundation: Se ≈ 0.93 × centre, plus Sc
+195.1 mm
A line under the cards repeats qgross, qremoved, qnet, the foundation level, the method, the source of σ′p and the calculation depth. The signs follow the Sign selector: settlement positive and heave negative, or the reverse (the vertical displacement positive upward), in the cards, the tables, the drawings and the report; the Calculations tab keeps the classical signs and says so.
The table of the layers
One row per layer that is compressed, with H (the thickness compressed), E, Se, the heave, Sb (the reloading that recovers the heave, back along Cs), Sr (Cr up to σ′p), Sv (Cc beyond it), Sc = Sb + Sr + Sv, the layer total S, and with the time curve Hdr, t50 and t90. The table is wider than the panel at some sizes: scroll it sideways to reach the last columns. The layer total is Se + (Sc + heave) when the displacements are kept, Se + Sc when they are reset.
Layers table.
Layer
Se · heave · Sc
S · t50 · t90
Clay-1 H 5.00 m, E 8.0 MPa
+20.8 · −62.6 · +198.4
+156.6 mm · 0.62 · 2.7 yr
Sand H 4.00 m, E 35.0 MPa
+5.6 · — · —
+5.6 mm
Clay-2 H 9.00 m, E 15.0 MPa
+14.1 · −6.5 · +27.0
+34.6 mm · 4.0 · 17 yr
Gravelly sand H 7.47 m (to zlim)
+1.2 · — · —
+1.2 mm
Total
+41.7 · −69.1 · +225.4
+198.0 mm · 0.72 · 3.7 yr
Each layer total is in millimetres; the Sc of Clay-1 (+198.4) is larger than its net contribution (+135.8) because the heave of −62.6 mm is recovered first. The Total row gives t50 and t90 of the whole profile: the times when the summed consolidation of the cohesive layers reaches 50 % and 90 % of Sc; the immediate settlement is there at once.
Slice by slice
Below the layers a table lists every slice: z, the layer, σ′v0, σ′p, σ′exc, σ′final, the Regime and Se, heave, Sc and S. All columns adds E, ΔH, σv0, u0, Δσexc, Δσload, Sb, Sr and Sv. The regime says which index carries the loading: Cr → Cc (recompression then virgin), Cr only, Cc only, Cs (heave recovered), Cs (net unloading), mv, or Elastic only for a granular slice. A click on a row opens its calculation.
Slice table.
Warnings
When the analysis finds something to say, the Warnings window opens by itself after Analyze; it lists the warnings and the assumptions of the analysis. A coloured bar at the top of the Results and Report tabs repeats the first warning with a Warnings button, and Warnings (n) in the bar of the Model tab opens the window again.
A warning bar above the cards.
Calculations tab, Report and Theory
Calculations
The tab writes out one slice with your numbers; choose the slice in the Slice list (z, layer and the slice settlement), or click a row of the slice table. The regime of the slice shows at the right. The steps are numbered and open with a click: 1 initial stresses, 2 preconsolidation pressure (clay), 3 excavation — unloading and swelling (clay), 4 foundation loading — Boussinesq, 5 immediate (elastic) settlement of the slice, 6 consolidation compression of the slice (clay), 7 slice, layer and total, and 8 time (for a clay layer with the time curve on). Granular slices have no steps 2, 3, 6 and 8.
Calculations, slice at 3.25 m in Clay-1.
Report
The Report tab has a cover form (Project, Location, Client, Report no., Date, Prepared by (name), Title / qualification, Checked by, Notes), kept in the browser and saved with the model file, and a live preview of the summary report with Save as PDF (opens a print window: choose “Save as PDF”) and Download Word (.docx). The buttons work after Analyze. The report has eleven parts: introduction and scope; soil profile and parameters; excavation, foundation and calculation depth; method and assumptions; immediate settlement; consolidation settlement; total settlement; slice by slice; time-dependent consolidation (when the time curve is on); summary; references. It carries the drawings of the Section, Stresses, Contours, Settlement and Time views.
Report tab.
Theory
The Theory tab has 21 sections: scope; cohesive and granular layers; immediate settlement; Steinbrenner’s influence factors; the layered profile and the net pressure; the stress path of the cohesive layers; slices and initial stresses; preconsolidation pressure; excavation; the stress increase; the depth of the calculation; compression regimes; where the settlement is measured from; the mv method; flexible and rigid foundations; total settlement; time-dependent consolidation; the colour-band fields; sign convention and assumptions; outside the scope; references.
Worked example
The default example: a raft of 10 × 15 m, qgross = 120 kPa, at the bottom of a 2 m excavation; water table at 2 m; Clay-1 from 2 to 7 m (Eu 8 MPa, e0 1.05, Cc 0.25, Cr 0.05, OCR 1.6, Cv 2 m²/yr), sand from 7 to 11 m (E′ 35 MPa), Clay-2 from 11 to 20 m (Eu 15 MPa, e0 0.85, Cc 0.30, Cr 0.06, Cs 0.04, OCR 1.3, Cv 1 m²/yr), gravelly sand from 20 to 30 m (E′ 70 MPa); fill of 18 kN/m³ above. Influence depth with p = 10 %, Δz = 0.5 m, displacements kept.
The depth below the foundation level where the stress increase under the centre falls to 10 % of q is z′ = 25.47 m, so zlim = 2.00 + 25.47 = 27.47 m, above the end of the profile (30 m): Gravelly sand is compressed over 7.47 m only.
Sb = +7.85 mm (back along Cs to σ′v0), Sr = 0.05 × 0.50/2.05 × log(73.98/46.24) = +2.49 mm, Sv = 0.25 × 0.50/2.05 × log(129.6/73.98) = +14.85 mm; Sc = +25.19 mm; net of the heave +17.34 mm.
Immediate: Se = 84.0 × (1 − 0.5²)/8000 × [F(1.50 m) − F(1.00 m)] = +1.42 mm (Steinbrenner’s F of the centre of the raft). S of the slice = 1.42 + 17.34 = 18.76 mm.
These are the numbers of the Calculations tab for that slice (σ′v0 46.24, σ′p 73.98, σ′exc 10.50, heave −7.85, Sc 25.19, S 18.76 mm), and an independent re-computation of the whole profile, written from the same formulas, gives the totals of the Results tab: Se = 41.7, Sc + heave = 156.3, S = 198.0, corner 168.7, rigid 195.1 mm, t50 = 0.72 and t90 = 3.7 years.
Time by hand
Clay-1 has 5.00 m below the foundation level, double drainage, so Hdr = 2.50 m: t50 = 0.197 × 2.50²/2.00 = 0.62 yr and t90 = 0.848 × 2.50²/2.00 = 2.7 yr. Clay-2: Hdr = 4.50 m, t50 = 0.197 × 4.50²/1.00 = 4.0 yr, t90 = 17 yr. The whole profile (0.72 and 3.7 yr) is the sum of the two curves, weighted by their Sc.
The same model in the other unit systems
Switch the units after Analyze and the cards, tables and working convert; the drawings stay in SI. US: Se +1.64 in, consolidation +6.15 in, total +7.80 in (198.0 mm / 25.4), heave −2.72 in, corner +6.64 in, rigid +7.68 in; zlim = 90.12 ft and qremoved = 0.75 ksf. SI · tf: the settlements are the same in mm; qgross = 12.2, qremoved = 3.7 and qnet = 8.6 t/m², and E is shown in kg/cm² (8 MPa reads 82).
The same results in US units.
How each input changes the answer
Each row changes one thing in the default example (total S 198.0 mm, Se 41.7 mm), run on the module. Everything else is as in the worked example.
Change
Se, mm
S, mm
Default
41.7
198.0
qgross 60 kPa qnet = 24 kPa
11.9
36.7
qgross 180 kPa
71.5
350.5
B 5 m (L 15 m) zlim falls to 19.53 m
33.1
158.1
Raft 20 × 30 m zlim rises to 52.94 m
55.2
266.5
Strip of 10 m zlim 65.40 m, profile continued
47.6
219.2
No excavation foundation at the surface
76.2
272.5
Displacements reset
41.7
267.1
Water table 5 m
41.7
155.8
Water table 0.5 m
48.3
288.0
Clay-1 OCR 1.0 normally consolidated
41.7
297.6
Clay-1 OCR 3.0
41.7
110.7
Clay-1 Cc 0.40
41.7
264.6
Clay-1 e0 1.5
41.7
173.6
Clay-1 Eu 16 MPa
31.3
187.6
Sand E′ 70 MPa
38.9
195.2
mv method
41.7
254.8
The immediate settlement follows the stiffness and the net pressure but not the consolidation data; the consolidation follows the clay data, the water table, the excavation and the load. Between the first rows, S rises from 36.7 to 198.0 to 350.5 mm as qgross goes from 60 to 120 to 180 kPa, a more than proportional increase because the clay passes from recompression to virgin compression. The input with the largest effect is not the same for every model: here OCR of Clay-1 (110.7 to 297.6 mm over the range tried) and the water table (155.8 to 288.0 mm) move the answer more than the sand modulus (195.2 to 198.0 mm).
Time
Change
t50, yr
t90, yr
Default (Clay-1 Cv 2 m²/yr, double drainage)
0.72
3.7
Clay-1 Cv 4 m²/yr
0.37
2.1
Clay-1 single drainage
2.6
11
Excavation 8 m (Clay-2 only)
4.0
17
Cv and the drainage change only the time, not the final settlement (198.0 mm in each case).
Messages
Cannot analyse
The window “Cannot analyse — 1 input error” (or 2 and more) lists what is missing; nothing is calculated and the Model tab stays editable. The ones you can reach from the screen:
“Clay-1 (CL, soft): Eu missing — needed below the foundation level.” (the box of E was emptied; the same for E′ of a granular layer, and for the compressibility values the module says which are missing).
“Sand (SM, medium dense): ν′ must be at least 0 and below 0.5 for a granular layer.” (the box of ν′ was emptied).
The stop window.
Warnings
The analysis runs and the Warnings window opens. Each is quoted as the module writes it:
“10 slices had σ′p below σ′v0 (OCR < 1): σ′p = σ′v0 was used — under-consolidated clay is outside the scope.” (an OCR below 1; with the laboratory value the text reads “(laboratory σ′p < σ′v0)”).
“No time curve: Cv is missing for Clay-1 (CL, soft).” (Cv is 0 with the time curve on; the settlements are still given).
“Clay-2 (CH, firm): γsat ≤ γw — the effective stress does not grow through this layer.”
“The net pressure is not positive (qnet = -6.0 kPa): the foundation does not load the soil beyond the removed overburden, so the immediate settlement is not positive (a negative value is an elastic rebound).” followed by “The gross pressure is below the removed overburden (qnet < 0): the loading does not bring the stresses back to the initial state.”
“1 slice had σ′exc below 0.1 kPa after the excavation: σ′exc = 0.1 kPa was used (the e – log σ′ law is unbounded near zero stress; the swelling of these slices is a model limit).”
“The excavation reaches the bottom of the soil profile (30.00 m).”
The Warnings window (the list of assumptions continues below).
The assumptions list always follows: the sum S = Se + Sc, the removed load, the calculation depth, the continuation or cutting of the profile, the displacements, the source of σ′p and a note when Cs is empty. A model with no clay below the foundation level says “Total settlement S = Se”.
Good practice
Check the calculation depth. The influence depth of a large raft or a strip can lie far below the last borehole layer; the profile is then continued with the properties of the last layer. Choose Bottom of the profile when a stiff stratum lies right below it.
Split thick layers where the stiffness or the OCR changes with depth: the module takes one set of values per layer.
Take Eu and E′ from tests or correlations suited to your soil. The immediate settlement is inversely proportional to E; the help beside Modulus and Poisson’s ratio gives the usual ranges.
Decide the reference of the settlement (kept or reset) from how long the excavation stays open, and quote the one you used.
Use the colour bands to look for odd results: a band that jumps at a layer boundary is the stiffness or the compressibility changing; the stress and settlement bands should die out smoothly with depth.
Mind the unit of E: MPa in SI, ksf in US.
Save the model to a file with the project; the quick saves live in this browser only.
Frequently asked questions
What is the difference between the immediate and the consolidation settlement?
The immediate settlement is the elastic deformation as the load is applied: for clay undrained (Eu and ν = 0.5), for sand drained (E′ and ν′). The consolidation settlement is the slow compression of the clay as the pore water leaves. Sand has only the first. The total is S = Se + Sc.
Why does the module ask for an excavation?
The foundation level is the base of the excavation. The excavation removes the effective overburden, so the clay swells; the load first recovers that heave. Choose No for a foundation at the ground surface: the default example then settles 272.5 mm instead of 198.0 mm.
What do “kept” and “reset” mean?
Kept measures the settlement from the original ground: the heave is shown on its own and a load that only restores the removed overburden causes no settlement. Reset measures from the heaved base, so the recompression of the heave counts as settlement. The default example gives 198.0 mm kept and 267.1 mm reset.
Where does the calculation depth come from?
With the influence-depth rule it is the depth where the stress increase under the centre of the foundation falls to p % of q (10 % by default), measured below the foundation level and added to its depth. The Analysis Settings read-outs show it before you analyse.
Why is the corner settlement smaller than the centre?
The foundation is perfectly flexible: its immediate settlement is largest at the centre and smallest at the corner (the edge of a strip). The consolidation is that of the centre line, so the corner total is the corner immediate settlement plus the consolidation of the centre.
What is the rigid foundation value?
A rigid foundation settles uniformly. The module takes the immediate part as 0.93 times the flexible centre value and adds the consolidation of the centre: 195.1 mm for the default example.
The heave is negative. Is that an error?
No. The classical convention shows settlement positive and heave negative. The Sign selector in the header switches to settlement negative and heave positive everywhere except the Calculations tab.
Can I leave Cs empty?
Yes. The swelling then uses Cr and the Warnings window says so. Note that changing Cr then changes the heave too.
Do my inputs survive a reload?
Yes. The page reopens on the last model, analysed if it was analysed. Reset to defaults clears it. Save to file or Quick Save keep versions.
Can I drag or zoom the drawings?
No. The drawings follow the values you type; the views and their chips are the controls.
Why is there no time curve?
The curve needs the time option on, a cohesive layer below the foundation level and Cv above 0 in every clay layer. Otherwise the Time view is empty and, for a missing Cv, a warning names the layer.
What does “continued from 30.00 to 65.40 m (assumed)” mean?
The profile ends above the calculation depth, so the last layer is taken to continue with the same properties. Choose Bottom of the profile if a stiff stratum lies below it.
Three modules design a strutted excavation: Peck’s apparent pressure envelope, the load of every strut, the wales and the sheeting, and the check of the base of the cut. This page helps you choose the module that matches the ground and links to the manual of each.
The Braced Cuts family has three modules for a strutted excavation. All of them draw Peck’s apparent pressure envelope, give the load of every strut, size the wales and the sheeting and check the base of the cut. They differ in the ground. Pick the one that matches the ground inside the cut.
The ground in the cut
Module
Sand, with the water table below or above the base of the cut; the base is checked against piping when the cut is dewatered
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.
Peck’s envelope. Each module draws the apparent pressure envelope on the section.
Struts. The load of every strut comes from the hinged spans, for any number of struts at the levels and spacing you enter.
Sheeting and wales. The sections are sized for the moments, to EN 1993-1-1 or AISC 360-22.
The base of the cut. Sand is checked against piping, clay against bottom heave.
Handles on the drawing. Before Analyze you can drag the struts on the drawing; each manual lists what moves.
What each module takes, side by side
In sand
In clay
Sand over clay
Ground
Sand, γ and φ′
Clay, γ and cu
Sand and clay layers
Envelope
Peck envelope for sand
Peck envelopes, soft to medium or stiff clay from the stability number
Equivalent clay by Peck’s method, then as in clay
Base check
Piping when dewatered
Bottom heave, tension crack at the first strut
Bottom heave
A typical braced-cut design in order
Choose the module
Pick the one that matches the ground inside the cut and open its manual for the fields.
Describe the cut and the ground
Enter the depth and the width of the cut, the soil and the water.
Place the struts
Give the strut levels and the spacing, or drag the struts on the drawing before Analyze.
Choose the steel and the code
Pick the steel grades and the design code for the sheeting and the wales, then press Analyze.
Read and report
Read the envelope, the load of every strut, the sections and the check of the base, then save a report with the cover filled in.
Frequently asked questions
How do I calculate strut loads for a braced excavation with GeoTerva?
Open the module for the ground, Braced cut in sand, Braced cut in clay or Braced cut in sand over clay. Enter the cut, the soil, the water and the strut levels, choose the steel and the code, press Analyze, and read the apparent pressure envelope and the load of every strut.
Which pressure envelope do the modules use?
Peck’s apparent pressure envelope: the one for sand in the sand module, and the soft-to-medium or the stiff clay envelope, chosen from the stability number, in the clay modules.
Which module do I use for sand over clay?
Braced cut in sand over clay. It reduces the sand above the clay to one equivalent clay by Peck’s method and then works as the clay module.
What does the base of the cut check?
The sand module checks the factor of safety against piping when the cut is dewatered. The clay modules check the factor of safety against bottom heave.
Which codes do the sections follow?
The sheeting and the wales are sized to EN 1993-1-1 or AISC 360-22; you choose the code in the module.
Can I move the struts on the drawing?
Yes, before Analyze. Drag a strut on the drawing and its level changes; each manual lists the limits.
Design the bracing of a strutted excavation in sand: Peck’s apparent pressure envelope, the load of every strut, the moments in the sheeting and the wales, the verification of the members to EN 1993-1-1 or AISC 360-22 and the piping check of the base. This manual walks through the screen, every input, the results and the report, with a worked example you can reproduce.
Braced cut in sand designs the bracing of a strutted excavation in sand: sheeting on both sides, wales along the sheeting and struts across the cut. It draws Peck’s apparent pressure envelope, gives the load of every strut for any number of strut levels from 2 to 15, finds the moments in the sheeting and in the wales, and verifies the sheeting, the wales and the struts to EN 1993-1-1 or AISC 360-22. When the water table stands above the base of the cut it adds the hydrostatic pressure on the wall and checks the base against piping.
The envelope is one uniform pressure over the full depth of the cut:
σa = 0.65 Kaσ′v(H), Ka = tan²(45° − φ′/2)
where σ′v(H) is the effective vertical stress at the base of the cut. The sheeting is then treated as a beam on the struts, hinged at the struts according to the hinge convention you choose; each strut load is the reaction per metre of wall times the horizontal spacing, P = R × s.
What you can describe
A cut of depth H and width B, with the sheeting embedded d below the base.
One to ten layers of sand, each with its moist and saturated unit weight and friction angle.
Two to fifteen strut levels at depths you give or drag, at a horizontal spacing s.
The water table below the base or at a depth zw, with the hydrostatic pressure on the wall switched on or off.
A uniform surcharge beside the cut.
The sheeting by its section modulus; the wale and the strut by their numbers or from a catalogue of steel sections; steel grade S235, S275, S355 or typed.
The piping check with the exit gradient from a flow net, from Harr’s charts or given.
The Rankine coefficient on its own: Rankine. A wall held by anchors or by its embedment alone: Sheet-pile walls.
Before you start: what you need
Have these ready:
What
Notes
The sand Boring logs and tests
For each layer from the top: thickness (not the last), moist unit weight, saturated unit weight (needed with a water table) and the friction angle φ′, from 15° to 45°.
The cut Your design
Depth H, width B, the embedment d of the sheeting, and, for the drawing, the plan length L and the depth T to an impervious layer.
The water Groundwater readings
The depth zw of the water table behind the sheeting, or that it lies below the base.
The bracing Your design
The depth of each strut level and the horizontal spacing s.
The members The maker’s tables
Steel grade and section modulus of the sheeting per metre of wall; of the wale; area and weak-axis second moment of the strut, or their catalogue sections.
The piping data, if the water is above the base
Head loss h, Nd and a of a flow net, or a chart value, or the exit gradient itself; the critical gradient icr.
Quick start in eight steps
Open the module and choose the units
Open Braced cut in sand from the Braced Cuts family. Pick SI · kN, SI · tf or US in the header; you can change it at any time, even after Analyze.
Describe the sand
In Soil layers change the first layer, Sand, or fill the New layer form and press + Add layer. The last layer runs on below the cut.
Set the water
In Groundwater choose Below the base or Present and type the depth zw.
Give the cut and the surcharge
In Cut geometry type H, B, d and, if you wish, L and T. In Surcharge add a uniform load if there is one.
Place the struts
In Struts type the spacing s and the depth of each level, or drag the levels on the drawing. + Add a strut level and Remove the last strut change the number.
Give the members
In Sections choose the steel grade and the section of the sheeting, the wale and the strut. In Analysis settings choose the hinge convention and the design code.
Press Analyze
Press Analyze at the foot of the Model tab. The bar reads Analysed — the braced cut calculated and the inputs lock.
Read the answer and take the report
The Results tab gives the diagrams, the strut loads, the moments and the verdict on every member; Calculations writes the working; Report saves a PDF or Word file.
The screen: Section, 3D and the handles
The layout is the one every GeoTerva module shares (workspace guide): the drawing on the left, the tabs Model, Results, Calculations, Report and Theory on the right. The drawing has two views:
Section is the cut with its layers, the sheeting, the struts and wales, the apparent-pressure envelope and the dimensions. It follows your inputs. After Analyze it adds the strut loads, the maximum sheeting moment Mmax and the pressures; a member is green where it carries its force and red where it does not.
3D is an oblique view of the excavation: the sheeting on both sides, the wales and the struts at their spacing, a legend of the sections, and after Analyze the load of each strut level.
Section before Analyze.
Section after Analyze: the strut loads and the moment.
3D after Analyze.
Zoom and Show chips
There are no Show chips: the drawing 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 drag a strut up or down; the field of that strut in the Model tab follows. The drag stops at 0.1 m below the surface and at 0.1 m above the base, so a dragged strut stays inside the cut; a level typed outside it stops the analysis (see Messages).
Press a layer on the drawing and it opens in its form.
After Analyze nothing can be moved and the inputs are locked; Edit inputs unlocks them and clears the results. The unit system can still be changed.
Entering the model, section by section
The Model tab has nine sections: Model data, Soil layers, Groundwater, Cut geometry, Surcharge, Struts, Sections, Piping and Analysis settings. Model data opens and closes on its own; the other eight sections work as an accordion, opening one closes the previous one; Next and Back walk you through them. Where a unit is given twice, such as m · ft, the units are those of SI and US, and the defaults are shown in SI.
Model data
The model name, Save to file…, Open file…, Quick Save… with its list, Load, Delete and Reset to defaults, as in the workspace guide. After Analyze these are locked until you press Edit inputs.
Model data.
Soil layers
A New layer form over a table. Fill the form and press + Add layer: the layer goes to the bottom of the table (up to ten, with a counter). Press a row to change it in the form, which then offers Done and Delete layer; × removes a layer. The thicknesses add up from the ground surface; layers below the base of the cut are not used for the envelope. Several layers are reduced to one Ka by the rule in Analysis settings.
Soil layers.
Field
Default
What to enter
Name optional
automatic
Sand, or Sand-1, Sand-2 … when there are several.
Thickness H m · ft
12 (first layer); 5 (new form)
At least 0.1 m. The last layer has none: it runs on below the cut, and its row shows a dash.
Moist unit weight γ kN/m³ · t/m³ · pcf
17.6
At least 1. Used above the water table.
Saturated unit weight γsat kN/m³ · t/m³ · pcf
20
At least 1; above 9.81 kN/m³ when there is a water table.
Friction angle φ′ °
32
From 15° to 45°.
Two layers.
Groundwater
Water table: Below the base (default) or Present. With Present, type the depth zw (default 3 m, zero or more) below the ground surface; a water table above the base turns on the hydrostatic pressure and the piping check. Below the base the water has no effect on the envelope and the Notes say no piping check is needed.
Groundwater present.
Cut geometry
Impervious layer below the base: At a known depth (default) or None within reach.
Cut geometry.
Field
Default
What to enter
Depth of the cut H m · ft
8
At least 0.5 m. It fixes the envelope.
Width of the cut B m · ft
6
At least 0.5 m. It is the buckling length of the strut unless you type another.
Plan length L m · ft
20
At least 0.5 m; optional. It sets the drawing.
Embedment d m · ft
1.5
Zero or more. The sheeting below the base; it lengthens the seepage path.
Base to impervious layer T m · ft
4
Zero or more; optional, shown with a known depth.
Surcharge
The form offers a Uniform load; Strip and Point stand beside it marked Soon and cannot be pressed. Type the intensity q (kPa, zero or more; the form opens with 10) and press + Add load: one load goes into the table (0 of 1). It acts as its own lateral pressure Kaq over the full depth and is not multiplied by 0.65. × removes it.
Surcharge with a load.
Struts
The horizontal spacing s (default 3 m, at least 0.5 m) and the depth of each level below the ground surface, A from the top (defaults 1.8, 4.6 and 7.3 m; each at least 0.1 m). + Add a strut level adds one up to 15, Remove the last strut takes one away down to 2; a counter shows “3 of 15”. Levels are analysed in order of depth, whatever order you type them in: with the second level typed at 1 m the module treats the struts as 1, 1.8 and 7.3 m (σa 28.12 kPa, Pmax 294.8 kN, Mmax 102.9 kN·m/m). A level at or below the base, or two levels at the same depth, stop the analysis.
Struts.
Sections
Three blocks, Sheeting, Wale (waling beam) and Strut, each with a Steel grade (S235, S275, S355 or Typed) and its fy, which follows the grade until you type your own.
Sheeting: Elastic Wel or Plastic Wpl, and the modulus W per metre of wall (default 600 cm³/m, S275).
Wale: By its modulus W (default, 1,000 cm³, elastic or plastic) or From the catalogue (IPE, HEA, HEB, HEM, UPN or a steel box with Width b, Depth h and Wall thickness t; the catalogue also gives its class and shear).
Strut: By A and I (default A = 65.7 cm², Imin = 3,598 cm⁴, buckling curve c with EN 1993-1-1) or From the catalogue (CHS, SHS, RHS, IPE, HEA, HEB, HEM, UPN; tubes hot finished or cold formed).
Buckling lengthLb (the width of the cut until you type one), effective length factorK (1, from 0.5 to 2) and modulusE (210,000,000 kPa for EN 1993-1-1, 200,000,000 for AISC; from the design code).
Sections.
Piping
For a water table above the base: Check the base against pipingYes or No, and Exit gradient fromFlow net (h, Nd, a), Harr charts (geometry) or Given iexit; each choice has a ? window.
Piping.
Field
Default
What to enter
Head loss h m · ft
5 (from the water table)
The groundwater outside minus the level kept inside; it follows H − zw until you type one.
Potential drops Nd
8
At least 1. Flow net.
Exit element a m · ft
1
At least 0.05 m. Flow net.
Chart value L2 iexit / h
0.5
From 0.05 to 2. Harr.
Exit gradient iexit
0.4
At least 0.01. Given.
Critical gradient icr
1
From 0.5 to 1.5.
Required factor FSreq
1.5
From 1 to 3.
Analysis settings
Layered profile — one Ka from: Weighted φ′ (default), Weighted Ka or Lowest φ′. Hinge convention: Auto, Interior struts, All but the top or Every strut. Design code: EN 1993-1-1 (Eurocode 3) with γF 1.35 (1 to 1.6), γM0 1.00 and γM1 1.00 (1 to 1.3), or AISC 360-22 with LRFD (γH 1.6, 1 to 2) or ASD. With a water table the Hydrostatic pressure on the wall choice also appears: Add γw (z − zw) or Envelope only.
Analysis settings.
Choosing the hinge convention, the code and the water
Hinge convention
The sheeting is cut into pieces at its hinges; each piece is a determinate beam on the struts it holds. Auto and Interior struts hinge the sheeting at every strut except the top and the bottom one, and Auto switches to every strut only if a strut would be in tension. For the example with hinges at B the pieces are 0 to 4.6 m (struts A and B) and 4.6 to 8 m (B and C), and the strut loads are 318.75, 175.53 and 180.60 kN. Every strut gives 89.98, 77.33 and 57.64 kN/m, so the largest load is 270.0 kN; All but the top leaves the largest load at 318.8 kN.
Layered profile
Peck gives one Ka, so a profile is reduced to one value. For a 3 m layer of 16 kN/m³ at 28° over sand of 18.5 kN/m³ at 36°: Weighted φ′ gives σa = 26.92 kPa, Weighted Ka 27.18 kPa and Lowest φ′ 32.97 kPa.
Water above the base
The overburden is taken effective below the water table, with γ′ = γsat − 9.81, and the hydrostatic triangle γw(z − zw) is added to the pressure on the wall. For the example with zw = 3 m: σa = 20.72 kPa, but the largest strut load rises from 318.8 to 376.7 kN. Envelope only leaves the water out; the module then raises a warning, because without the water the wall is loaded for less than ground and water together.
The code
EN 1993-1-1: the working values are factored once by γF, the sheeting and the wale are held to Mc,Rd = Wfy / γM0 and the strut to Nb,Rd = χAfy / γM1. AISC 360-22: LRFD factors the loads by γH and uses φ = 0.90; ASD uses the working loads against Rn / Ω with Ω = 1.67. For the example the section modulus the sheeting asks for is 223.6 cm³/m by EN 1993-1-1, 294.5 by LRFD and 276.6 by ASD.
Analyze and read the results
Press Analyze. The bar reads Analysed — the braced cut calculated, with Notes (n) or Warnings (n) and Edit inputs. The Model tab stays on screen: open Results. A window with warnings does not open by itself after Analyze in a clean case; with a failing member it opens at once.
The bar after Analyze.
The Results tab.
Card
The example
Apparent pressure σa
28.12 kPa
Largest strut load Pmax
318.8 kN (strut A)
Maximum moment in the sheeting Mmax
45.55 kN·m/m
Section modulus the sheeting needs Wreq,sp
223.6 cm³/m
Sheeting ηsp
0.3727 PASS
Wale ηwale
0.5868 PASS
Strut (buckling) ηstrut
0.4112 PASS
With a water table above the base and the piping check on, an eighth card, Factor of safety against pipingFSpiping, is added. The tables are Values, step by step, Beam pieces of the wall (load on the piece and reactions), Strut loads (z, R per metre, P = R × s and the preliminary area) and Wales, level by level (reaction, Mwale = Rs² / 8 and the modulus asked for).
The verdict words
A utilisation reads PASS at 1 or less and FAIL above 1; very close to 1 it reads PASS — near capacity (the wale with only two struts, 0.9761). The piping card can also read NOT COMPARED, when the head loss differs from the one the wall was loaded with. The piping factor reads PASS at or above the required value and FAIL below it.
Members that fail are red on the drawing.
Using the numbers
Strut loads are in kN (tf, kip) per strut; the reactions, and the moments in the sheeting, are per metre of wall; the wale moment is for one span s.
σa and Mmax are working values; the factor of the code is applied once, in the design action.
Changing the unit system re-states the cards, the tables, the working and the Section view (also before Analyze). The 3D view re-states the strut loads but keeps B, H, σa and the section legend in m, kPa and cm.
The Calculations tab, the report and the Theory tab
The Calculations tab starts with Given and what is sought and writes out the steps with your numbers. For the example they are: 1 Build the apparent-pressure envelope; 2 Idealise the sheeting and solve the strut reactions; 3 and 4 one step for each piece of the sheeting; 5 Take the yield strength of each member from its steel grade; 6 Convert the reactions to strut loads; 7 The moment in the sheeting; 8 The moment in the wales; 9 Take the design actions; 10 and 11 the sheeting, the modulus asked for and the section verified; 12 and 13 the same for the wale; 14 and 15 the strut, the area asked for and the buckling check. Notes and assumptions and the Answer close the tab. With the water above the base, steps for the hydrostatic load and for the piping check are added.
The first steps of the Calculations tab.
The Notes window
Notes (n) opens the assumptions of the run: that the sheeting is checked on the modulus given as the modulus of the whole wall; that the wale was verified on its modulus without its shear; that the class of a strut given by A and I was not computed; and that the bracing loads were factored by γF before the code check. With water above the base a note says the flow-net values must come from a net drawn for this cut. Warnings, when there are any, come first.
The report
In Report fill in the cover (project, location, client, report number, date, prepared by, title or qualification, checked by and notes); it is kept in this browser and saved with the model file. Save as PDF and Download Word (.docx) produce the report, which has seven parts: 1 Introduction and scope, 2 Input data, 3 Calculation (3.1 to 3.15; with water above the base two more steps appear: 3.2 Add the hydrostatic pressure and 3.10 Check the base against piping), 4 Results, 5 Assumptions and notes, 6 Summary and 7 References.
The Report tab.
The Theory tab
The Theory tab has sixteen sections: The braced cut and its members; Why the pressure is not Rankine’s; Apparent pressure from measured strut loads; The envelope for sand; Water and a surcharge; Struts: from the envelope to the strut loads; Sheet piles; Wales; The members as they are given; Verifying the steel to EN 1993-1-1; Verifying the steel to AISC 360-22; The envelopes against real cuts; The base of a cut in sand: piping; What the method assumes, and what it leaves out; Worked example; References.
Worked example: the module’s own example
The module opens on this example. Inputs: one layer of sand, γ = 17.6 kN/m³, φ′ = 32°; water below the base; H = 8 m, B = 6 m, d = 1.5 m; struts A, B, C at 1.8, 4.6 and 7.3 m, s = 3 m; S275 members (fy = 275,000 kPa), sheeting Wel = 600 cm³/m, wale Wel = 1,000 cm³, strut A = 65.7 cm², Imin = 3,598 cm⁴; EN 1993-1-1, γF = 1.35.
Hinged at B, piece 1 runs from 0 to 4.6 m: W = 28.12 × 4.6 = 129.35 kN/m acting at 2.30 m, so RB = 129.35 × (2.30 − 1.80) / 2.80 = 23.10 kN/m and RA = 106.25 kN/m. Piece 2 runs from 4.6 to 8 m: W = 95.61 kN/m at 6.30 m, RC = 95.61 × 1.70 / 2.70 = 60.20 and RB = 35.41 kN/m. Strut B collects 23.10 + 35.41 = 58.51 kN/m. With s = 3 m: PA = 318.75 kN, PB = 175.53 kN, PC = 180.60 kN.
Sheeting, wale and strut
The largest sheeting moment is at A, Mmax = 28.12 × 1.8² / 2 = 45.55 kN·m/m. The wale at level A: Mwale = 106.25 × 3² / 8 = 119.53 kN·m. Design actions: NEd = 1.35 × 318.75 = 430.31 kN, MEd = 1.35 × 45.55 = 61.50 kN·m/m. The sheeting asks for Wreq = 61.50 / 275,000 = 223.63 cm³/m, and Mc,Rd = 600×10⁻⁶ × 275,000 = 165.00 kN·m/m gives ηsp = 0.3727. The wale: 1.35 × 119.53 = 161.37 kN·m, Wreq = 586.79 cm³, Mc,Rd = 275.00 kN·m, ηwale = 0.5868. The strut: Lcr = 1.00 × 6.00 = 6.00 m, Ncr = π² × 210,000,000 × 3,598×10⁻⁸ / 6² = 2,071.47 kN, λ̄ = √(65.7×10⁻⁴ × 275,000 / 2,071.47) = 0.9339, curve c gives χ = 0.5791 and Nb,Rd = 1,046.36 kN, so ηstrut = 430.31 / 1,046.36 = 0.4112 (rounded from 0.41125).
The piping check
With the water table at 3 m (everything else as above) the head loss follows H − zw = 5 m, iexit = 5 / (8 × 1) = 0.625 and FS = 1 / 0.625 = 1.600 PASS.
Other unit systems
The default example in US gives σa = 0.5873 ksf, Pmax = 71.65 kip, Mmax = 10.24 kip·ft/ft and Wreq = 4.160 in³/ft with the same utilisations; in SI · tf the same wall gives 2.870 t/m², 32.52 tf and 4.649 tf·m/m, with ηsp = 0.3731. Two checks with values typed in the other systems and recomputed by hand agree to within 0.2 %. In SI · tf the module carries Ka, σ′v and σa at the precision printed in the unit chosen (three digits in t/m²), so the printed numbers reproduce every load and the results differ from SI · kN by about 0.1 % (ηsp 0.3731 against 0.3727); US differs by less than 0.1 %:
US. 112 / 125 pcf at 30°, H = 26 ft, B = 20 ft, s = 10 ft, struts at 6, 15 and 24 ft, 11 in³/ft, 61 in³, 10.2 in² and 86.4 in⁴: by hand σa = 0.6309 ksf, Pmax = 78.87 kip, ηsp = 0.4193; the module gives 0.6304 ksf, 78.80 kip and 0.4190.
SI · tf. 1.8 / 2.0 t/m³ at 32°, geometry as the example: by hand 2.876 t/m², 32.60 tf and ηsp = 0.3737; the module gives 2.880 t/m², 32.64 tf and 0.3744.
How each input changes the answer
Each row changes one thing in the example (γ = 17.6 kN/m³, φ′ = 32°, water below the base, H = 8 m, s = 3 m, struts at 1.8, 4.6 and 7.3 m, S275, EN 1993-1-1 with γF = 1.35) and runs the module again. Each cell gives σa in kPa, Pmax in kN and Mmax in kN·m/m, then the utilisations of the sheeting, wale and strut.
Same pressures and loads; strut 0.8022 (longer buckling length)
Strut Lb = 3 m
Strut 0.2765
Piping rows, water table at 3 m with the defaults otherwise: Nd = 4 gives FS 0.8000 FAIL; icr = 0.9 gives 1.440 FAIL; a given iexit of 0.4 gives 2.500 PASS; a water table at the surface gives 1.00 FAIL. Code rows: AISC LRFD gives utilisations 0.4908, 0.7727, 0.4602; ASD 0.4611, 0.7259, 0.4323. Sheeting grade S355 lowers the sheeting utilisation to 0.2887. The embedment d and the impervious layer T leave every number above unchanged; they enter the piping check (and the drawing) only.
The pattern follows the formulas: σa is proportional to γHKa; strut loads scale with s, the wale moment with s², and water above the base adds a hydrostatic triangle that loads the lower struts. Every row above was recomputed in an independent hand calculation and agrees to the digits shown.
Messages: when the module stops, and what it notes
When a number cannot be used the module stops: nothing is calculated, a window opens and the box is marked.
A stop for an empty modulus.
When
Message
Stop: depth of the cut 0.2 m
“Depth of the cut (H) must be at least 0.5 m.”
Stop: φ′ = 10°
“Friction angle (φ′1) must be at least 15°.”
Stop: a strut at 9 m in a cut of 8 m
“Strut C at z = 9.00 m lies outside the cut. Every strut must sit strictly between the ground surface (z = 0) and the base (z = H = 8.00 m). Move it inside the cut or remove it.”
Stop: two struts at 1.8 m
“Two struts share the depth z = 1.80 m. Coincident struts leave a zero span between supports and the beam statics break down. Merge them into one level or separate them.”
Stop: water present, depth empty
“Water table depth (zw) is missing.”
Stop: saturated weight 9 kN/m³ with water
“Sand layer 1: saturated unit weight must exceed γw. Below the water table the envelope uses γ′ = γsat − γw. Enter the saturated unit weight.”
Stop: Harr charts with an impervious layer
“Harr's charts cannot be used with an impervious layer 4.00 m below the base.” Choose a flow net or a given gradient, or set the layer to None within reach.
Stop: other limits
“Width of the cut (B) must be at least 0.5 m.” · “Horizontal strut spacing (s) must be at least 0.5 m.” · “Wall embedment below the base (d) must be at least 0 m.” · “Yield strength (fy) must be at least 100000 kPa.” · “Thickness (Hi,1) must be at least 0.1 m.” · “Section modulus of the sheeting (W) is missing.”
Where a limit applies, the window opens with Cannot analyse — 1 input error (2, 3 … when several); a condition of the solution 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.”
Warnings
A warning marks a result that is calculated but fails a check; the bar reads Analysed — the braced cut calculated — 1 warning and the window opens at once.
A member fails: “The sheeting given does not carry the design moment: MEd / Mc,Rd = 1.49 …” with the resistance, the demand and the modulus the sheeting asks for (223.63 cm³/m); the wale and the strut have their own messages. The wale message suggests closing the spacing s.
Piping: “Factor of safety against piping FS = 1.14 is below the required 1.50. The upward seepage at the base is close to lifting the sand …” with the remedies: drive the sheeting deeper, lower the head, or add a filter blanket.
Hydrostatic pressure left out: “Water table at z = 3.00 m is above the base and the hydrostatic pressure is left out …”
Head loss different from the wall load: “Hydraulic boundary mismatch: the piping check uses h = 2.00 m, the wall was loaded with the full head 5.00 m …” and the factor of safety is then shown with the word NOT COMPARED. Clear the head-loss box to take the head from the water table.
Notes
The default run carries five notes: that no piping check is needed with the water below the base (re-check if dewatering lowers the water inside the cut below the outside groundwater); the sheeting modulus taken as that of the whole wall; the wale checked on its modulus without shear; the strut class not computed for a strut given by A and I; and the factor γF applied before the code check.
Good practice and common mistakes
Enter the saturated unit weight of every layer when there is a water table; the module stops if it is not above 9.81 kN/m³.
Leave the head loss to follow the water table unless you have a flow net for another seepage picture; a different head gives a factor of safety without a verdict.
Keep struts inside the cut and apart; drag them before Analyze, not after.
The surcharge is not multiplied by 0.65: it acts as Kaq beside the envelope.
Read the strut load per strut and the moment per metre of wall; the wale moment is for one span.
Choose the hinge convention knowingly: every strut lowers the load of A and raises that of B in the example.
Give the sheeting modulus of the whole wall from the maker’s table and take interlocks and shear from the maker’s data.
Name the code once: the factors of EN 1993-1-1 and of AISC are different 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
What is the apparent pressure envelope?
A single uniform pressure over the full depth of the cut, σa = 0.65 Kaσ′v(H), taken from measured strut loads rather than from a Rankine triangle. For the example it is 28.12 kPa.
How are the strut loads found?
The sheeting is cut into pieces at its hinges and each piece is a determinate beam on the struts it holds; the reaction per metre times the spacing s is the strut load. The example gives 318.75, 175.53 and 180.60 kN.
How many struts can I use?
From 2 to 15 levels. Use the buttons Add a strut level and Remove the last strut, then type or drag the depths.
What does the hinge convention change?
Which struts the sheeting is hinged at. Auto and Interior struts hinge every strut except the top and bottom; Every strut hinges all of them. In the example the largest load falls from 318.8 to 270.0 kN with Every strut.
How is water handled?
With the water table above the base the overburden is effective, the hydrostatic pressure is added to the wall, and the piping check is made on the exit gradient. Below the base the water has no effect.
How is the piping factor of safety found?
FS = icr / iexit, with iexit = h / (Nda) for a flow net. With h = 5 m, 8 drops, a = 1 m and icr = 1 it is 1.600, which passes the required 1.5.
Can I add a strip or point surcharge?
The Surcharge section takes a uniform load; Strip and Point are shown marked Soon.
Which members does the module verify?
The sheeting and the wale in bending, and the strut in flexural buckling, to EN 1993-1-1 or AISC 360-22 (LRFD or ASD). The wale and strut can be given from a catalogue of steel sections.
Can I drag things on the drawing?
Before Analyze you can drag the strut levels; the field follows. 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 is remembered. Save to file keeps the model and Quick Save keeps versions in the browser.
Which units does it use?
SI · kN, SI · tf or US, switchable at any time. The default example gives Pmax = 318.8 kN, 32.52 tf or 71.65 kip.
What if a member fails?
It reads FAIL, appears red on the drawing and a warning gives the modulus it asks for. Choose a heavier section or a higher grade, close the spacing, or add a strut level.
Design the bracing of a strutted excavation in undrained clay: the apparent-pressure envelope chosen from the stability number, the load of every strut, the sheeting, the wales and the struts to EN 1993-1-1 or AISC 360-22, the tension crack at the first strut and the bottom heave of the base. This manual walks through the screen, every input, the results and every message, with a worked example you can reproduce.
Braced cut in clay designs the bracing of a strutted excavation in undrained clay. You give the depth of the cut, the clay and the levels of the struts; the module draws the apparent-pressure envelope that Peck derived from measured strut loads, works out the load of every strut, and sizes and verifies the sheeting, the wales and the struts to EN 1993-1-1 or AISC 360-22. It also checks the first strut against the tension crack and the base of the cut against bottom heave.
The clay is analysed in total stress, with the unit weight γ and the undrained shear strength cu. The shape of the envelope is chosen by the stability numberγH/cu, with H the depth of the cut:
Above 4 the clay is soft to medium: the envelope is zero at the surface, rises over the top quarter of the depth and keeps its plateau σa to the base; its resultant is 0.875 σaH.
At or below 4 the clay is stiff: the envelope rises over the top quarter, keeps σa over the middle half and falls over the bottom quarter; its resultant is 0.75 σaH. The coefficient k is yours to set between 0.2 and 0.4 (0.3 by default).
For the default example, γH/cu = 18 × 7 / 35 = 3.60, so the stiff envelope applies with σa = 0.3 × 18 × 7 = 37.80 kPa and a resultant of 0.75 × 37.80 × 7 = 198.45 kN/m.
What you can describe
Clay layers: up to ten, each with its unit weight, saturated unit weight and cu; several layers inside the cut are thickness-averaged into one cu and one γ. The bottom layer runs on below the base.
The cut: depth H, width B, optional plan length L, embedment d of the sheeting below the base and the depth T of a hard stratum.
A water table behind the sheeting, and a uniform surcharge beside the cut.
Struts: from 2 to 15 levels at depths you type or drag, at a horizontal spacing s.
Members: sheeting by its section modulus; wale and strut either by the numbers a profile table prints or from the section catalogue.
The base check against bottom heave with its required factor of safety, and the hinge convention and the design code.
It draws the section and a 3D view, writes the working step by step, and prepares a PDF or Word report.
Which module for which cut
The soil is clay from the surface down: this module.
A wall that is not strutted but anchored or cantilevered, with the embedment worked out, is in the Sheet-pile walls manuals. Loads other than a uniform surcharge are worked out in the Surcharge loads manuals.
Before you start: what you need
Have these ready from your design and your ground investigation:
What
Where from, and notes
The clay
Boring logs, vane or triaxial tests: unit weight, saturated unit weight and undrained shear strength cu (at least 1 kPa) of each layer, and the thickness of each layer except the last.
The cut
Your design: depth H (at least 0.5 m), width B (at least 0.5 m), the plan length if the cut is short, the embedment d of the sheeting below the base, the depth to a hard stratum if there is one.
The struts
The depth of each level below the ground surface, each strictly between the surface and the base, and the horizontal spacing s (at least 0.5 m).
The members
Yield strength from the steel grade; the section modulus of the sheeting per metre of wall; for the wale a modulus (or a catalogue section); for the strut an area and a second moment of area (or a catalogue section).
Loads and water
A uniform surcharge beside the cut, if any; the depth of the water table if it matters for the unit weight.
Quick start in eight steps
Open the module and choose the units
Open Braced cut in clay from the Braced Cuts family. Pick SI · kN, SI · tf or US in the header; you can change it at any time.
Enter the clay
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.
Describe the cut
In Groundwater choose the water table; in Cut geometry type H, B, L, d and the hard stratum; in Surcharge add a uniform load if there is one.
Place the struts
In Struts type the spacing s and the depth of each level; + Add a strut level adds one. Before Analyze you can also drag a strut on the drawing.
Give the members
In Sections choose the steel grade and the section of the sheeting, the wale and the strut; in Base heave the required factor of safety; in Analysis settings the envelope coefficient, the hinge convention and the design code.
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 drawings, the tables of the strut loads and the wales, and the cards: σa, Pmax, Mmax, Wreq, the utilisation of each member and the heave 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 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 cut with its clay, the sheeting, the struts lettered A, B, C … from the top, the dimensions and the hard stratum. After Analyze it adds the envelope with σa, the load of each strut (PA = 162.06 kN …) and Mmax marked on the sheeting; each is green where the member carries its force and red where it does not.
3D is an oblique view of the excavation: the sheeting on both sides, the wales and the struts at their spacing, the clay on the front face, a legend with the steel grade and section of the members, and, after Analyze, the load of every strut level.
Section before Analyze.
Section after Analyze: the envelope, the strut loads and the largest moment.
3D after Analyze.
Dragging, and what is locked
Before Analyze the struts are the only things on the drawing that move: drag a strut up or down, and its depth in Struts follows, in steps of 0.05 m. A strut cannot be taken above 0.1 m, nor lower than 0.1 m above the base. Nothing else on the drawing is dragged: the layers, the water and the cut are changed in the Model tab. After Analyze the model is locked and nothing can be dragged.
There are no Show chips. Each view has −, a percentage and + at the lower right and a button that fits the whole drawing in the pane. The Model tab follows what you type: a value that cannot be used (a strut outside the cut, for example) is reported in the bar at the foot of the tab as Cannot be analysed, before you press Analyze.
Entering the model, section by section
The Model tab has nine sections: Model data, Soil layers, Groundwater, Cut geometry, Surcharge, Struts, Sections, Base heave and Analysis settings. Each opens when you click its title; Next and Back at the foot walk you through them, and Analyze waits in the bar below. A unit shown two or three times, such as m · ft, gives the units of SI · kN, SI · tf and US in turn. 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, 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
A New layer form over a Soil layers table. Fill the form and press + Add layer: the layer goes to the bottom of the table, with a counter (1 of 10). Press a row to change it in the form; × takes it out. Every layer is undrained clay. Several layers inside the cut are thickness-averaged into one cu and one γ for the envelope, and the layer under the base carries the heave check. The bottom layer has no thickness (its row shows a dash): it runs on below the base, to the stratum.
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, or Clay-1, Clay-2 … when there are several.
Thickness H m · ft
5 (form)
At least 0.1 m. Absent on the last layer.
Unit weight γ kN/m³ · t/m³ · pcf
18
At least 1 kN/m³. Used above the water table, or everywhere without one.
Saturated unit weight γsat kN/m³ · t/m³ · pcf
19
At least 1 kN/m³. Used below the water table.
Undrained cohesion cu kPa · kg/cm² · psf
35
At least 1 kPa.
Groundwater
Water table has Below the base (default) and Present. With Present, a box for the depth zw below the ground surface appears (3 m by default, at least 0). The clay envelopes are total-stress: the water is recorded but adds no separate pressure. Its effect is on the unit weight: below the table the clay weighs its saturated unit weight, so γ averaged over the cut rises (with zw = 2 m the example gives σa = 39.29 kPa instead of 37.80 kPa). The module notes that the cut has been computed undrained.
Groundwater.
Cut geometry
Cut geometry.
Cut geometry
Field
Default
What to enter
Depth of the cut H m · ft
7
At least 0.5 m. It fixes the envelope. The module notes when H is below about 6 m, the depth the envelopes were derived for.
Width of the cut B m · ft
6
At least 0.5 m. Feeds the heave check.
Plan length of the cut L m · ft
20 (optional)
At least 0.5 m. Empty means a long cut: the shape term of the heave check is 1.
Wall embedment below the base d m · ft
1.5
0 or more. Drawn, but not credited in the heave check.
Base to hard stratum T m · ft
4
Shown when a hard stratum is At a known depth (the default); None within reach hides it.
Surcharge
The section is the one of the braced-cut family: a New load form (the kind Uniform; Strip and Point stand there marked Soon and the kind stays Uniform) and a table of the loads. Type the intensity q (10 kPa in the form) and press + Add load: the table shows it as a uniform load over the whole surface. One load at most; press × to take it away. The opening model has none. A surcharge is not put inside the envelope; it is added beside it as its own uniform lateral pressure Δpq = q (clay, φ = 0, so Ka = 1) over the full height of the cut, and the struts, the sheeting and the wales all see it. It enters the heave check and the tension-crack depth as well.
Surcharge.
Struts
The horizontal spacings (3 m, at least 0.5 m) and one block per strut, Strut 1, Strut 2 …, each with its depth below the ground surface: zA = 1 m, zB = 3.5 m and zC = 6 m in the example. + Add a strut level and Remove the last strut change the number, from 2 to 15 (the counter reads 3 of 15). The levels are lettered A, B, C … from the top in the order of their depth. At least two struts are needed; each must lie strictly between the surface and the base.
Struts.
Sections
Three blocks, Sheeting, Wale (waling beam) and Strut. Each has a steel grade: S235, S275 (default), S355, or Typed. The yield strength fy follows the grade (275 000 kPa for S275, with the chip “from the grade”) until you type a value of your own; it must be at least 100 000 kPa.
Sheeting: Section modulus given says which catalogue column the value is, Elastic Wel (default) or Plastic Wpl; W per metre of wall (600 cm³/m).
Wale: How the section is given, By its modulus W (default; W = 1 000 cm³, elastic or plastic) or From the catalogue, where a section type (IPE, HEA, HEB, HEM, UPN or a steel box with its width, depth and wall thickness) and a section are chosen; the catalogue gives the class and the shear area.
Strut: By A and I (default; the area A = 65.7 cm², the second moment of area about the weak axis Imin = 3 598 cm⁴ and, with EN 1993-1-1, the buckling curve, default c) or From the catalogue (tube, square or rectangular tube, IPE, HEA, HEB, HEM or UPN). Then the buckling lengthLb (it follows the width of the cut, 6 m, until you type another), the effective length factor K (1) and the modulus of elasticity E (210 000 000 kPa, from the design code).
Sections: the first two blocks.
Base heave
Check the base against bottom heave has Yes (default) and No. With Yes, give the required factor of safetyFSreq (1.5, from 1 to 3). With No the base is not checked and the card is absent. The check compares the resistance of the clay under the base with the weight of the soil beside the cut: see Bottom heave.
Base heave.
Analysis settings
The stiff-clay envelope coefficientk (0.3; 0.2 to 0.4) is used when γH/cu is 4 or less. Hinge convention has Auto (default), Interior struts, All but the top and Every strut: see Strut loads. Verify the steelwork to has EN 1993-1-1 (Eurocode 3), with the partial factor γF on the bracing loads (1.35, from 1 to 1.6) and γM0 (1) and γM1 (1) from 1 to 1.3 on the cross-section and the buckling resistance, or AISC 360-22, with LRFD (the load factor γH on the earth pressure, 1.6, from 1 to 2) or ASD.
Analysis settings.
The envelope: soft to medium, or stiff
The module takes γ and cu (averaged over the depth when there are several layers, and γ weighted with the saturated unit weight below the water table), forms γH/cu and picks the envelope. The plateau pressure σa is the first card.
Soft to medium: γH/c above 4
With cu = 20 kPa the number is 18 × 7 / 20 = 6.3. Then γH − 4cu = 126 − 80 = 46 kPa against 0.3γH = 37.8 kPa, and the larger governs: σa = 46.00 kPa. The resultant is 0.875 × 46 × 7 = 281.75 kN/m, against 198.45 kN/m for the stiff example: a weaker clay loads the struts more, and the module gives Pmax = 338.1 kN (271.3 kN with cu = 35 kPa).
The soft-to-medium envelope: zero at the surface, a plateau from the top quarter to the base.
Stiff: γH/c at most 4
σa = kγH. With k = 0.3 the example gives 37.80 kPa; k = 0.4 gives 50.40 kPa (Pmax = 361.6 kN) and k = 0.2 gives 25.20 kPa (Pmax = 180.8 kN): the loads follow k in proportion. Choose k from the stiffness of the clay; 0.3 is the average of the range.
Near the changeover
At γH/cu = 4 the plateau σa is the same on both sides (0.3γH = 37.8 kPa in the example), but the shapes differ: the soft-to-medium envelope keeps its plateau to the base and has a resultant a sixth larger than the stiff one. The runs show it: cu = 31.5 kPa (ratio 4.00, stiff) gives 271.3 kN for the largest strut and cu = 28 kPa (ratio 4.5, soft to medium) gives 277.8 kN, with the same σa = 37.80 kPa. When γH/cu is between 3.6 and 4.4 the module adds a note that gives the resultant of the branch used and of the other (198.45 and 231.53 kN/m in the example) and advises you to check cu against the tests and, where it is uncertain, to run the other branch and design for the heavier. The default example sits in this band (3.60), so its first note is this one.
Several clay layers, a water table, a surcharge
Several layers: cu and γ are averaged over the depth of the cut with the thicknesses as weights. Two layers, 3 m with cu = 25 kPa over the rest with cu = 45 kPa, average to (25 × 3 + 45 × 4) / 7 = 36.43 kPa; with γ = 18 the ratio is 3.46 and σa = 37.80 kPa.
A water table at 2 m raises the weight of the clay below it to γsat: the average γ is 18.7 kN/m³, the ratio 3.74 and σa = 39.29 kPa.
A surcharge of 20 kPa does not change σa (37.80 kPa): it adds 20 kPa over the 7 m of the cut, 140 kN/m, to the 198.45 kN/m of the envelope. See Strut loads.
Strut loads, sheeting and wales
From the envelope to the strut loads
The sheeting is idealised as hinged at the struts, and each piece between hinges is a determinate beam carrying its share of the envelope. A reaction R per metre of wall comes out at each strut level, and the strut load is P = R × s. A strut at a hinge collects a reaction from the pieces on both sides. The hinge convention says where the hinges are:
Interior struts: hinges at every strut except the top and the bottom ones, the classical arrangement.
All but the top and Every strut: hinges at more levels, which share the load differently (for the example, Pmax = 275.6 and 279.9 kN against 271.3 kN).
Auto (default) takes Interior struts and switches to another convention if that layout would put a strut in tension; the module then says so in a note. The example has the same figures with Auto and with Interior struts.
For the example the two pieces (0 to 3.5 m and 3.5 to 7 m) each carry 99.23 kN/m. Piece 1 is an overhanging beam on A and B: RB = 99.23 × (2.1389 − 1.00) / 2.50 = 45.21 kN/m and RA = 99.23 − 45.21 = 54.02 kN/m. Level B collects 45.21 from each side, 90.42 kN/m, so PA = PC = 54.02 × 3 = 162.1 kN and PB = 90.42 × 3 = 271.3 kN; the module gives 271.3 kN as the largest.
The sheeting and the wales
The largest moment of the sheeting is the largest anywhere in the pieces: 27.03 kN·m/m in the example, at 2.30 m, in piece 1. Each wale is a simple span s loaded by the reaction of its level: Mwale = Rs² / 8 = 90.42 × 3.00² / 8 = 101.72 kN·m at level B. The first card block gives Mmax and the sheeting modulus, and under the cards stand the moment and the modulus of the governing wale.
What the strut layout does
Spacing: with s = 4 m the largest strut load is 361.7 kN and the wale utilisation 0.8878; with s = 2 m, 180.8 kN and 0.2219. The wale moment goes with s², the strut load with s; the sheeting is not affected.
Number of struts: four struts at 1, 2.5, 4 and 5.5 m bring Pmax to 180.3 kN and Mmax to 12.15 kN·m/m.
Depth of the cut: at H = 9 m (struts unchanged) the ratio is 4.63, the soft-to-medium envelope gives σa = 48.60 kPa, and the lowest strut carries 882.1 kN. The module warns that Strut C carries 882.09 kN, 2.3 × the average of the 3 struts and suggests moving the struts so that the tributary heights are similar, or adding a level.
A strut in tension: where a layout would put a strut in tension the module says so (“would be in tension in this layout — it is slack and carries nothing”).
The tension crack and the first strut
A clay face stands unsupported down to the depth where its tension crack closes: zc = 2cu/γ for φ = 0, or (2cu − q)/γ with a surcharge. With several layers or a water table the module finds the depth piece by piece, with the total overburden and the surcharge reaching 2cu. The first strut should go in above this depth, so that the sheeting never relies on an open clay face deeper than the clay itself can hold.
In the example zc = 2 × 35 / 18 = 3.89 m and the first strut is at 1.00 m: the check is passed, and the working shows “first strut A at z = 1.00 m ≤ zc”. The caution appears when the first strut is deeper. With the struts at 4, 5 and 6 m the module warns:
“First strut (A) at z = 4.00 m is deeper than the tensile-crack depth zc = 3.89 m. Below 2c/γ the unsupported clay face is past what it can hold in tension before the strut is installed. Raise the first strut above zc, or justify the temporary unsupported height separately.” The same run also gives, as it must, a heavy first strut: Pmax = 411.1 kN and a sheeting moment of 189.4 kN·m/m, which the sheeting given does not carry (utilisation 1.549).
A surcharge shortens the crack: with 60 kPa the depth is (70 − 60) / 18 = 0.556 m, and a first strut at 1 m triggers the same caution with zc = 0.5556 m. With 20 kPa it is (70 − 20) / 18 = 2.78 m, so the first strut at 1 m passes.
The check of the first strut in the Calculations tab.
Bottom heave of the base
A deep cut in clay can fail by the base bulging up: the clay beneath the excavation is squeezed in under the weight of the soil beside it. The module compares the resistance of the clay along the failure surface with the driving overburden and surcharge:
B′ is B/√2, or the depth T of the hard stratum when that is smaller; B″ = √2 B′. cu under the base gives the bearing term and cside (the cohesion averaged over the height of the cut) the side shear. Without L the cut is taken as long (the shape term is 1), and without a hard stratum B′ = B/√2. The embedment d of the sheeting is not credited, which is on the safe side. The check is made when Check the base is Yes; the card reads PASS at or above FSreq and FAIL below it.
For the example: B/√2 = 4.24 m ≥ T = 4 m, so B′ = 4.00 m and B″ = 5.66 m; 1 + 0.2 × 5.66 / 20 = 1.0566; FSheave = [5.14 × 35 × 1.0566 + 35 × 7 / 4.00] / 126 = 251.33 / 126 = 1.99, above the required 1.5: PASS. The module gives 1.995.
The heave step of the Calculations tab.
What changes the factor of safety
Weaker clay: cu = 20 kPa gives 1.140 (hand: [5.14 × 20 × 1.0566 + 20 × 7 / 4] / 126 = 1.14), FAIL against 1.5, with the warning “Factor of safety against bottom heave FS = 1.14 is below the required 1.50. The clay beneath the base cannot carry the overburden beside the cut with the intended margin. Extend the sheeting below the base, reduce the surcharge beside the cut, narrow the cut or improve the clay under the base.” Stronger clay raises it: 50 kPa gives 2.850 and 80 kPa 4.559.
Width: B = 4 m makes B′ = 2.83 m and gives 2.172; a width of 10 m leaves B′ = T and the factor at 1.995.
Hard stratum and length: with no hard stratum the factor is 1.972; L = 10 m gives 2.075 and an empty L 1.914.
A hard stratum at the base (T = 0): no heave surface can develop, no factor is given, and the module notes “Hard stratum at the base of the cut — bottom heave cannot develop.”
Analyze and read the results
Press Analyze. The bar changes to Analysed — the braced cut calculated, with — n warnings added when there are warnings. 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 window of the warnings does not open by itself.
The Results tab shows, from the top:
Half section — dimensions and struts and Pressure on the sheeting: half the cut to its centre line, with the strut sections, beside the envelope with σa and the envelope resultant and the total on the wall.
Strut loads and Wales — seen from inside the cut: the load of each strut, and the moment and shear of each wale between the struts.
Values, step by step, then the table of the beam pieces of the wall, the strut loads and the wales, level by level.
The cards, last, under Braced cut.
The drawings of the Results tab.
Values, step by step, for the example.
The strut loads.
Card
What it is
The example
Apparent pressure of the envelope σa
The plateau of the envelope chosen from γH/cu.
37.80 kPa
Largest strut load Pmax
The heaviest strut, R × s.
271.3 kN
Maximum moment in the sheeting Mmax
Per metre of wall.
27.03 kN·m/m
Section modulus the sheeting needs Wreq,sp
The number a sheet-pile table is looked up with (the design code is named on the card).
132.7 cm³/m
Utilisation of the sheeting ηsp
Design moment over the resistance of the modulus given; PASS up to 1, FAIL above.
0.2212 PASS
Utilisation of the wale ηwale
The same for the governing wale.
0.4994 PASS
Utilisation of the strut ηstrut
Design load over the buckling resistance (with A and I given).
0.3500 PASS
Factor of safety against bottom heave FSheave
Only when the heave check is on; PASS at or above FSreq.
1.995 PASS
Beneath the cards stand Maximum moment in the governing wale (101.7 kN·m) and Section modulus the wale needs (499.4 cm³).
The cards of the example.
The members and the design code
With EN 1993-1-1 the working loads are multiplied once by γF: NEd = 1.35 × 271.26 = 366.20 kN, MEd = 1.35 × 27.03 = 36.49 kN·m/m for the sheeting, 1.35 × 101.72 = 137.33 kN·m for the wale. Then Wreq = MEdγM0 / fy: 36.49 / 275 000 = 132.7 cm³/m for the sheeting and 137.33 / 275 000 = 499.4 cm³ for the wale. The sections given are held to Mc,Rd = Wfy / γM0: 165.00 kN·m/m for 600 cm³/m (utilisation 36.49 / 165.00 = 0.2212) and 275.00 kN·m for 1 000 cm³ (137.33 / 275.00 = 0.4994). The strut, with A = 65.7 cm² and Imin = 3 598 cm⁴ over 6 m, has Ncr = 2 071 kN, λ̄ = 0.9339, χ = 0.5791 and Nb,Rd = 1 046 kN, so ηstrut = 366.20 / 1 046.36 = 0.3500: buckling governs over the cross-section check (0.2027).
With AISC 360-22 the same cut needs Wreq,sp = 174.7 cm³/m by LRFD (the moment factored by γH = 1.6) and 164.1 cm³/m by ASD, with the sheeting utilisation 0.2912 and 0.2736. The partial factor matters as well: γF = 1.5 gives 147.4 cm³/m. Steel S355 for the three members (with fy = 355 000 kPa) lowers Wreq,sp to 102.8 cm³/m and ηsp to 0.1713; the strut and wale utilisations fall to 0.3107 and 0.3868. The pressure, the strut loads and the heave factor do not depend on the steel.
Catalogue sections
With From the catalogue for the wale (HEB 300) and the strut (HEB 220) the module checks the class of the section, the shear and the flexural buckling of the strut with the section properties of the catalogue; for the example the wale utilisation is 0.6038 and the strut 0.3511. A section given only by a modulus (or by A and I) cannot be classed; the module then notes that the class was not computed and what the check rests on.
Using the numbers
Strut loads are per strut (kN, tf or kip); the sheeting moment is per metre of wall (kN·m/m, tf·m/m, kip·ft/ft) and the wale moment per wale (kN·m).
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.
In SI · tf the default example gives σa = 3.860 t/m², Pmax = 27.66 tf and Mmax = 2.760 tf·m/m; in USσa = 0.7895 ksf, Pmax = 61.02 kip, Mmax = 6.077 kip·ft/ft and Wreq,sp = 2.468 in³/ft (37.80 kPa is 0.7895 ksf; 271.26 kN is about 61 kip). The last digit or two can differ, because the unit weight and cohesion are rounded to the digits printed in the chosen unit before the envelope is built: the heave factor is 1.996 in US, 1.998 in SI · tf and 1.995 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 seventeen numbered steps with your numbers, ending with the notes and the answer:
The first block of the Calculations tab.
Select the apparent-pressure envelope; Idealise the sheeting and solve the strut reactions, with the beam pieces and, for each piece, its own step with the reactions and the shear and moment diagram.
Take the yield strength of each member from its steel grade.
Convert the reactions to strut loads and a preliminary strut area.
The moment in the sheeting; The moment in the wales.
Check the first strut against the tensile-crack depth; Check the base against bottom heave.
Take the design actions from the envelope (γF once).
For each of the sheeting, the wale and the strut, the modulus or the area the code asks for, then the section given verified.
The tab ends with Notes and assumptions and the Answer: “Stiff clay trapezoid, Peck envelope with σa = 37.80 kPa; the heaviest strut is B at P = 271.26 kN …; FS against bottom heave = 1.99 (meets the required 1.50).”
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 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 3.17, one for each step), 4 Results, 5 Assumptions and notes, 6 Summary and 7 References.
The Report tab.
The Theory tab
The Theory tab has seventeen sections: The braced cut and its members; Why the pressure is not Rankine’s; Apparent pressure from measured strut loads; The envelopes for clay; A surcharge, and water in clay; The first strut and the tension crack; Struts: from the envelope to the strut load; Sheet piles; Wales; The members as they are given; Verifying the steel to EN 1993-1-1; Verifying the steel to AISC 360-22; The envelopes against real cuts; The base of a cut in clay: bottom heave; What the method assumes, and what it leaves out; 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.
γH/cu = 18 × 7 / 35 = 3.60 ≤ 4: the stiff envelope. σa = 0.3 × 18 × 7 = 37.80 kPa, resultant 0.75 × 37.80 × 7 = 198.45 kN/m. The module notes that the ratio is close to 4, where the other branch would give 231.53 kN/m.
Step 2: the reactions and the strut loads
Two pieces, 99.23 kN/m each. RA = 54.02 kN/m, RB = 2 × 45.21 = 90.42 kN/m, RC = 54.02 kN/m. With s = 3 m: PA = PC = 162.1 kN, PB = 271.3 kN.
Step 3: the moments and the sections
Mmax = 27.03 kN·m/m in the sheeting; Mwale = 90.42 × 9 / 8 = 101.72 kN·m. With γF = 1.35: Wreq,sp = 132.7 cm³/m (utilisation 0.2212), Wreq,wale = 499.4 cm³ (0.4994), strut 0.3500. All three PASS.
Step 4: the crack and the base
zc = 2 × 35 / 18 = 3.89 m, the first strut is at 1.00 m. FSheave = 251.33 / 126 = 1.99, above 1.5. Every figure above is one the module gives (37.80 kPa, 271.3 kN, 27.03 kN·m/m, 132.7 cm³/m, 0.2212, 0.4994, 0.3500, 1.995).
The same cut in other units
In SI · tf the example gives Pmax = 27.66 tf (271.26 / 9.807) and Mmax = 2.760 tf·m/m; in USPmax = 61.02 kip and Mmax = 6.077 kip·ft/ft. The utilisations agree to within about 0.1 % in all three (sheeting 0.2212, 0.2215 and 0.2212).
How each input changes the answer
Each row changes one thing in the example (clay with γ = 18 kN/m³ (saturated 19) and cu = 35 kPa, H = 7 m, B = 6 m, L = 20 m, d = 1.5 m, T = 4 m, struts at 1, 3.5 and 6 m, s = 3 m, no water, no surcharge, k = 0.3, Auto hinges, S275, EN 1993-1-1) and runs the module again. The numbers are the ones the module gives.
Change
σa kPa Pmax kN
Mmax kN·m/m FSheave
The example (reference)
37.80 271.3
27.03 1.995
cu = 20 kPa (ratio 6.3, soft to medium)
46.00 338.1
32.89 1.140
cu = 28 kPa (ratio 4.5, soft to medium)
37.80 277.8
27.03 1.596
cu = 31.5 kPa (ratio 4.0, stiff)
37.80 271.3
27.03 1.795
cu = 50 kPa
37.80 271.3
27.03 2.850
γ = 20 kN/m³ (saturated 21; ratio 4.0)
42.00 301.4
30.03 1.795
H = 9 m (struts as before)
48.60 882.1
218.7 1.659
H = 5.5 m, struts at 1, 2.5, 4 m
29.70 163.5
12.14 2.406
k = 0.4
50.40 361.6
36.04 1.995
Uniform surcharge 20 kPa
37.80 397.2
37.92 1.721
Water table at 2 m
39.29 281.9
28.10 1.919
s = 4 m
37.80 361.7
27.03 1.995
s = 2 m
37.80 180.8
27.03 1.995
Four struts at 1, 2.5, 4, 5.5 m
37.80 180.3
12.15 1.995
Hinges at every strut
37.80 279.9
28.78 1.995
Struts at 4, 5, 6 m
37.80 411.1
189.4 1.995
d = 3 m
37.80 271.3
27.03 1.995
B = 4 m
37.80 271.3
27.03 2.172
Wale W = 300 cm³
37.80 271.3
27.03 1.995
Strut A = 20 cm², Imin = 500 cm⁴
37.80 271.3
27.03 1.995
cu and γ act through the stability number. Between 31.5 and 80 kPa the envelope does not change (kγH stays 37.80 kPa); only the heave factor rises, from 1.795 to 4.559. Below the changeover the envelope grows as the clay weakens: 338.1 kN at 20 kPa.
H moves everything: from 5.5 to 9 m the largest strut load goes from 163.5 to 882.1 kN and Mmax from 12.14 to 218.7 kN·m/m, so at 9 m the sheeting, the wale and the strut given are all FAIL (utilisations 1.789, 1.624 and 1.138).
The embedment d changes nothing in the strut loads or the heave factor: it is not credited.
The struts given (the last two rows) change only their own utilisation: a wale of 300 cm³ gives 1.665 (FAIL), and a strut of 20 cm² 1.871 (FAIL).
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 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 (○ and ●) 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 bar reads Analysed — the braced cut calculated — 1 warning in that case.
The window Analyze opens when the depth of the cut is 0.2 m.
The window for a strut below the base.
Stops: a value out of range
When
The message
What to do
H below 0.5 m, or empty
“Depth of the cut (H) must be at least 0.5 m.” / “Depth of the cut (H) is missing.”
Enter the depth.
cu below 1 kPa
“Undrained cohesion (cu,1) must be at least 1 kPa.”
Enter cu.
A unit weight below 1
“Unit weight (γ1) must be at least 1 kN/m³.”
Enter the unit weight.
s below 0.5 m
“Horizontal strut spacing (s) must be at least 0.5 m.”
Enter the spacing.
fy below 100 000 kPa
“Yield strength (fy) must be at least 100000 kPa.”
Choose a grade or type fy.
k above 0.4
“Stiff-clay envelope coefficient (k) must be at most 0.4.”
Enter k from 0.2 to 0.4.
FSreq above 3
“Required factor of safety against heave (FSreq) must be at most 3.”
Enter 1 to 3.
A modulus below 1 cm³/m
“Section modulus of the sheeting (W) must be at least 1 cm³/m.”
Enter W.
A thickness below 0.1 m
“Thickness (Hi,1) must be at least 0.1 m.”
Enter a thickness.
A strut area below 0.1 cm²
“Cross-section area (A) must be at least 0.1 cm².”
Enter A.
The layer number is part of the symbol: Hi,1, cu,1 and γ1 belong to layer 1.
Stops: a condition of the solution
When
The message
What to do
A strut at or beyond the base (or the surface)
“Strut C at z = 8.00 m lies outside the cut. Every strut must sit strictly between the ground surface (z = 0) and the base (z = H = 7.00 m). Move it inside the cut or remove it.”
Move it inside the cut or remove it. A shallower cut with the same struts gives the same message.
Two struts at the same depth
“Two struts share the depth z = 1.00 m. Coincident struts leave a zero span between supports and the beam statics break down. Merge them into one level or separate them.”
Merge them or separate them.
Fewer than two struts
“At least two struts are required” (a single level is a propped wall, which the method does not cover); the Struts section counts from 2, so this can arise only from a model opened from a file
Add a second strut.
Warnings
A warning does not stop the analysis; the results are calculated.
When
The warning
What to do
The heave factor is below the required
“Factor of safety against bottom heave FS = 1.14 is below the required 1.50. …” (with cu = 20 kPa; the card reads FAIL)
Deepen the sheeting, reduce the surcharge, narrow the cut or improve the clay.
The first strut is deeper than the crack
“First strut (A) at z = 4.00 m is deeper than the tensile-crack depth zc = 3.89 m. …”
Raise the first strut above zc.
A member does not carry its load
“The wale given does not carry the design moment: MEd / Mc,Rd = 1.66. Mc,Rd = 82.50 kN·m against a design moment of 137.33 kN·m. The wale asks for 499.37 cm³. …” (wale of 300 cm³); likewise for the sheeting (“… the design moment: MEd / Mc,Rd = 1.79 …”) and “The strut section given does not carry the design load: NEd / Nb,Rd = 1.87. Over an effective length of 6.00 m the buckling resistance of this section is 195.73 kN, and the design load is 366.20 kN. …”
A heavier section, a higher grade, a closer spacing for the wale, a shorter buckling length for the strut.
One strut carries much more than the average
“Strut C carries 882.09 kN, 2.3 × the average of the 3 struts (the lightest, B, carries 89.31 kN). …” (with H = 9 m)
Even the layout out: similar tributary heights, the lowest strut nearer the base, or one more level.
The cut is shallower than about 6 m
“Cut depth H = 5.50 m is shallower than the ≈6 m the envelopes were derived for. …” (a note)
Use the result as a preliminary estimate and confirm it by another method or by monitoring.
Notes
The Notes (5) of the example, and their conditions:
The stability number close to 4, with the resultants of the two branches (only when γH/cu lies between 3.6 and 4.4).
The sheeting is checked on the modulus given, as the modulus of the whole wall: a wall of U-sections may have its modulus reduced where the interlocks can slip, a wall of Z-sections carries the full value.
The wale was verified on the modulus given; its shear resistance was not checked (a catalogue section is checked for shear too).
The class of the strut section was not computed for a strut given by A and I; the resistance is on the gross area, correct for a class 1, 2 or 3 section.
With a water table: Computed undrained (no separate hydrostatic pressure on the clay envelope); with a surcharge: Computed with the surcharge q = … added as a uniform lateral pressure; with no hard stratum: Computed with no hard stratum below the base; with several layers: Bottom heave computed layer by layer; and always Computed with the bracing loads factored by γF = 1.35 before the code check (the envelope is an upper bound of measured loads, so the factor turns it into the design action).
Good practice and common mistakes
Check cu against the tests when the ratio is near 4. A few per cent on cu can change the branch and a sixth of the load; run the other branch and design for the heavier.
Choose k on purpose for a stiff clay: the loads follow it in proportion.
Keep the first strut above zc. Where the clay will stand open deeper, justify the temporary unsupported height separately.
Do not rely on the sheeting embedment for the heave check. The module does not credit d; keep the heave check on and give the width and, if there is one, the hard stratum.
Look at the loads of all the struts. An uneven layout puts the lowest strut under the overhang below it; the module says so, and a level more or another hinge convention evens it out.
Give the members. Without a section the member is not verified; with a modulus (or A and I) the class and the shear are not computed, with a catalogue section they are.
The envelope is for a cut of 6 m or more. For shallower cuts treat the result as a preliminary estimate.
Add the surcharge as a load, not by raising γ; it reaches the struts as its own lateral pressure.
Check the long term separately. The clay envelopes are total-stress; if the sheeting stays long enough for the clay to drain, the drained loading is a separate case.
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 choose between the two clay envelopes?
By the stability number γH/cu. Above 4 it takes the soft-to-medium envelope with σa = max(γH − 4cu, 0.3γH); at 4 or below the stiff one with σa = kγH. The example (18 × 7 / 35 = 3.60) is stiff with 37.80 kPa; with cu = 20 kPa it is soft to medium with 46.00 kPa.
What happens when the ratio is close to 4?
The plateau σa is the same on both sides, but the soft-to-medium envelope has a resultant a sixth larger. Between 3.6 and 4.4 the module adds a note with the resultants of both branches and advises running the other branch and designing for the heavier.
How are the strut loads found?
The sheeting is hinged at the struts (the convention is yours; Auto takes the interior struts and switches if a strut would be in tension), each piece between hinges is a determinate beam, the reaction per metre is multiplied by the spacing. The example gives 162.1, 271.3 and 162.1 kN.
What is the tension-crack check?
The first strut should be above zc = 2cu/γ (less a surcharge). In the example zc is 3.89 m and the first strut is at 1 m; at 4 m the module warns.
What does the bottom heave check use, and is the embedment credited?
The bearing resistance of the clay under the base, 5.14cu(1 + 0.2B″/L), plus the side shear of the cut height, against the weight of the soil beside the cut and the surcharge. B′ is B/√2 or the depth of a hard stratum if smaller. The sheeting embedment is not credited. The example gives 1.99.
How is a surcharge treated?
As its own uniform lateral pressure equal to q over the full height, beside the envelope and not inside it. It also enters the heave check and shortens the tension crack. 20 kPa takes the largest strut load from 271.3 to 397.2 kN.
Can I have more than one clay layer?
Yes, up to ten. The layers inside the cut are thickness-averaged into one cu and one γ; the layer under the base carries the heave check; the bottom layer runs on below the base.
Does the water table change anything?
Only the unit weight: the envelope is total-stress, no separate water pressure is added, and below the table the clay weighs its saturated unit weight. A table at 2 m takes σa from 37.80 to 39.29 kPa.
Which codes does it check the steel to?
EN 1993-1-1 with γF, γM0 and γM1, or AISC 360-22 by LRFD or ASD. The sheeting and the wale are checked in bending (the wale in shear too from the catalogue), the strut in compression and flexural buckling.
Can I drag the struts?
Yes, before Analyze: a strut moves in steps of 0.05 m and its depth in the Struts section follows. Keep it above the base. Nothing else on the drawing is dragged, and after Analyze the model is locked until you press Edit inputs.
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.
What does the report contain?
A cover with your project details, then seven parts: introduction and scope, input data, the calculation step by step (3.1 to 3.17), results, assumptions and notes, summary and references, with the drawings, as a PDF or Word file.
Design a strutted excavation in sand over clay: the profile reduced to one equivalent clay by Peck’s method, the apparent-pressure envelope chosen by the stability number, the load of every strut, the moments in the sheeting and the wales, their verification to EN 1993-1-1 or AISC 360-22, and the factor of safety against bottom heave. This manual walks through the screen, every input, the results and every message, with a worked example you can reproduce.
Braced cut in sand over clay designs a strutted excavation in a profile of sand layers above clay layers, with the cut reaching into the clay. Peck’s apparent-pressure envelopes are written for one soil, so the module first reduces the whole profile inside the cut to one equivalent clay, with an average undrained strength cav and an average unit weight γav. The stability numberγavH/cav then chooses the envelope. From the envelope it solves the load of every strut, finds the moment in the sheeting and in the wales, verifies the three members to EN 1993-1-1 or to AISC 360-22, and checks the base of the cut against bottom heave.
The equivalent clay is the average of the shear resistance the soil can mobilise through the cut. With Hs the thickness of the sand inside the cut, Ks its lateral pressure coefficient, φ′ its friction angle, Hc the thickness of a clay layer, qu = 2cu and n′ the progressive-failure coefficient:
cav = [ γsKsHs² tan φ′ + Σ n′quHc ] / 2H, γav = Σ γiHi / H
With γavH/cav above 4 the cut is a soft-to-medium clay: the pressure is zero at the surface, grows to the full value σa at a quarter of the depth and stays there to the base, with σa = γavH − 4cav but not less than 0.3γavH. At or below 4 the clay is stiff: zero at the surface, rising over the top quarter, constant over the middle half and tapering to zero over the bottom quarter (a resultant of 0.75 σaH, against 0.875 σaH for the soft-to-medium shape), with σa = kγavH, k = 0.2 to 0.4 (0.3 by default). The module draws the envelope, solves the struts for any number of levels from 2 to 15 and gives the section modulus the sheeting and the wales need.
What you can describe
Soil layers: up to ten, sand layers first, clay layers below; the bottom layer runs on below the base.
Groundwater: below the base, or present at a depth zw.
The cut: depth H, width B, plan length L, wall embedment d and, if there is one, the depth T from the base to a hard stratum.
A uniform surcharge beside the cut.
Struts: 2 to 15 levels, each by its depth, and one horizontal spacing s.
Three steel members: the sheeting by its section modulus, the wale and the strut by their numbers or from the catalogue, each with a steel grade.
Design code: EN 1993-1-1, or AISC 360-22 by LRFD or ASD.
Which module for which cut
Sand from top to bottom, with the piping check of a dewatered cut: Braced cut in sand.
Sand over clay with the cut reaching the clay: this module. If the sand reaches the base, or the profile has no sand or no clay, the module stops and names the neighbouring module; see Messages.
A wall that is not strutted but held by its embedment and anchors is a sheet-pile wall. A load beside the cut other than a uniform one is worked out in the Surcharge loads manuals.
Before you start: what you need
What
Where from, and notes
The soil profile
Boring logs. Per layer, top down: sand or clay, thickness (not the last layer), unit weight, saturated unit weight; for sand the friction angle φ′, for clay the undrained cohesion cu.
The cut
Your design: depth H, width B, plan length L (optional), the embedment d of the wall below the base and the depth T to a hard stratum, if one is known.
The bracing
Your design: the depth of every strut and the horizontal spacing s.
The steel
The grade and the section properties of the sheeting (modulus per metre of wall), the wale (modulus, or a catalogue section) and the strut (area and weak-axis second moment of area, or a catalogue section).
Quick start in eight steps
Open the module and choose the units
Open Sand over clay from the Braced Cuts family. Pick SI · kN, SI · tf or US in the header; you can change it at any time.
Enter the soil layers
In Soil layers choose Sand or Clay in the New layer form, fill it and press + Add layer, from the top down. Layers are added at the bottom, so enter sand first, then clay; to get a second sand above the clay, edit the type of an existing row. The last layer has no thickness.
Set the water and the cut
In Groundwater choose Below the base or Present; in Cut geometry type H, B, d and, if known, T. Add a surcharge in Surcharge if there is one.
Place the struts
In Struts type the horizontal spacing s and the depth of every strut, or drag the struts on the drawing; + Add a strut level adds one.
Describe the steel
In Sections choose the grade of the sheeting, the wale and the strut and give their sections; in Analysis settings choose the code.
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; the toast says “Analysed — see the Results tab and the Calculations.”
Read the answer
Open Results: the half section, the strut loads, the wales, the values step by step, the tables and, last, the cards.
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 above it:
Section is the cut with its layers, the sheeting, the struts and wales, the apparent-pressure envelope and the dimensions. Before Analyze it follows your inputs; after Analyze it writes the load of every strut and Mmax, green where the member carries its force and red where it does not.
3D is an oblique view of the excavation: the sheeting on both sides, the wales and the struts at their spacing, the layers on the front face. After Analyze each strut level carries its load.
Section before Analyze: it follows the inputs.
Section after Analyze: the loads and the envelope.
3D after Analyze.
Dragging, and what is locked
Before Analyze two kinds of handle move inputs on the Section drawing (the cursor turns to a vertical double arrow); they move in steps of 5 cm and the Model tab follows:
A strut moves up and down and changes its depth. The drag stops at 0.1 m below the surface and at 0.1 m above the base (H − 0.1 m); a depth typed outside the cut makes the analysis stop with the message “lies outside the cut”.
The boundary between two layers moves up and down and changes the thickness of the layer above it (at least 0.1 m).
Nothing else is dragged: the depth H, the width and the water level are typed. After Analyze the handles are gone and nothing on the drawing can be moved. Each view has −, a percentage and + at the lower right and a button that fits the whole drawing in the pane. Before Analyze, pressing a layer on the drawing opens it in its form. There are no Show chips on the drawing.
Entering the model, section by section
The Model tab is an accordion of nine sections: Model data, Soil layers, Groundwater, Cut geometry, Surcharge, Struts, Sections, Base heave and Analysis settings. Model data opens independently of the others; Model data and Soil layers are open when the page loads, and opening any other section closes the previous one. The sections have Back and Next buttons at their foot: Soil layers only Next, Analysis settings only Back, Model data none. Units follow the preset in the header (m, kN, kPa, kN/m³ for SI · kN; the section moduli stay in cm³). After a switch the Section view converts, but the 3D view keeps m, kPa and cm³ in its labels while its strut loads follow the unit; in SI · tf the cohesion is in kg/cm² and in US the sheeting modulus is in in³/ft.
Model data
Save to file…, Open file…, Quick Save…, Load, Delete and Reset to defaults, with the two lines quoted under Before you start. Typed values are not kept after a reload.
Soil layers
The New layer form takes one layer at a time: its name (optional), the Sand or Clay button and the numbers that soil uses. + Add layer puts the form’s values into a new row of the table below it; the counter reads, for the example, “2 of 10”. Press a row (or its layer on the drawing) to edit it in the form; × takes it away. + Add layer appends at the bottom: the previous bottom layer takes its own stored thickness (adding to the default model makes the clay 12 m) and the new bottom row shows a dash. To get a second sand above the clay, edit the type of an existing row. The × buttons are disabled while two layers remain and work while more than two remain (the minimum is two). The form opens with Thickness 5, γ 18, γsat 19, cu 35 (Clay), and with Sand pressed 5, 18, 19, φ′ 30. The default model’s first layer is 3 m of sand (17, 20, 30); its second is a clay (18, 19, 35) with no thickness.
The New layer form over the table of layers.
Field
Default
What to enter
Name —
automatic
Optional. Empty gives Sand, Clay, or Sand-1, Sand-2 … when the profile has several of one soil.
Thickness H m · ft
5 (form); 3 (first row)
The bottom layer has none: its row shows a dash, “it runs on below the base of the cut, to the stratum”.
Unit weight γ kN/m³
18 (form); 17 (first row)
Above the water table.
Saturated unit weight γsat kN/m³
19 (form); 20 (first row)
Below the water table, when the groundwater is present.
Friction angle φ′ °
30 (Sand in the form)
Sand only; clay shows a dash.
Undrained cohesion cu kPa
35 (form)
Clay only; it must be above zero.
Sand above, clay below: a sand layer under a clay layer stops the analysis. The profile is reduced to cav and γav over the depth H of the cut only; whatever lies below the base enters the bottom-heave check.
Groundwater
Below the base or Present; with Present a field asks for the depth of the water tablezw (3 m by default). The module says: “The clay envelopes are total-stress, so it is recorded but adds no separate load.” Water changes the answer only through the unit weight: below the table the soil is taken at γsat. With the table at 2 m the example’s σa goes from 37.75 to 44.75 kPa.
Groundwater.
Cut geometry
When the cut is wide and the stratum is near, T governs the heave surface: with B = 12 m the factor is the same 1.830 as with 6 m, because B′ = T = 4 m in both.
Cut geometry.
Field
Default
What to enter
Depth of the cut H m · ft
7
The depth fixes the envelope. Must be above zero.
Width of the cut B m · ft
6
Feeds the bottom-heave check.
Plan length L m · ft
optional (20)
Feeds the heave check; empty is treated as an infinite length.
Wall embedment d m · ft
1.5
Drawn; the heave check does not credit it.
Base to hard stratum T m · ft
4
Shown when the choice is At a known depth; None within reach hides it.
Surcharge
A uniform load on the ground beside the cut, entered as in the sheet-pile modules: the New load form holds the intensity q (10 kPa in the form), + Add load puts it in the table (the counter reads “0 of 1” until you do), × takes it away. The Strip and Point buttons are marked SOON and cannot be pressed. The load reaches the struts as a uniform lateral pressure over the full height and also enters the heave check: in the example q = 20 kPa raises the largest strut load from 277.5 to 424.5 kN and lowers the heave factor from 1.830 to 1.574.
Surcharge.
Struts
+ Add a strut level adds one (up to 15); Remove the last strut takes the last away. At least two levels are needed. Every strut must lie strictly between the surface and the base. Type the depths or drag the struts.
Struts.
Field
Default
What to enter
Horizontal strut spacing s m · ft
3
Centre to centre along the wall; the load of a strut is P = R × s.
Depth of strut A, B, C … zA m · ft
1, 3.5, 6
Below the ground surface, from the top down.
Sections
Three members, each a steel grade and a section. S235, S275, S355 or Typed sets the yield strength fy: the box follows the grade (275 000 kPa for S275) and may be typed over; clearing it hands it back. In the example all three are S275.
Sheeting: the section modulus per metre of wall (default 600 cm³/m) and which column of the catalogue it is, Elastic Wel or Plastic Wpl.
Wale (waling beam): By its modulus W (default 1 000 cm³, elastic or plastic) or From the catalogue, which also gives its class, its shear area and its shape on the drawings.
Strut: By A and I (default A = 65.7 cm², weak-axis second moment of area 3 598 cm⁴, buckling curve) or From the catalogue; the buckling length Lb follows the width of the cut and the effective length factor K is 1; the modulus of elasticity follows the code (210 000 000 kPa for EN 1993-1-1, 200 000 000 for AISC 360-22).
Sections.
Base heave
Yes or No, and the required factor of safety (1.5), which sets the PASS or FAIL line of the heave card. With No the heave factor is not calculated.
Base heave.
Analysis settings
Field
Default
What to enter
Progressive-failure coefficient n′ —
0.75
Reduces the clay’s qu in cav.
Lateral pressure coefficient of the sand Ks —
1
The sand term of cav is proportional to it.
Stiff-clay envelope coefficient k —
0.3
Used when γavH/cav is 4 or less; the module keeps it between 0.2 and 0.4.
Partial factor on the bracing loads γF —
1.35
EN 1993-1-1. With AISC 360-22 the field is the load factor γH, 1.6.
Partial factors on resistance γM0, γM1 —
1, 1
Cross-section and member buckling resistance (EN 1993-1-1).
The module keeps the values within these ranges: n′ 0.5 to 1, Ks 0.1 to 2, k 0.2 to 0.4 (clamped), γF 1 to 1.6, γM0 and γM1 1 to 1.3, γH 1 to 2, the required heave factor 1 to 3; up to 10 layers, 2 to 15 struts, a strut depth of at least 0.1 m.
Two more choices sit here: the hinge convention and the design code, EN 1993-1-1 (Eurocode 3) or AISC 360-22 with LRFD or ASD.
Analysis settings.
Choosing the method: the envelope and the hinges
The envelope is chosen for you
You do not pick the envelope: the stability number does. In the example cav = 21.31 kPa and γav = 17.57 kN/m³, so γavH/cav = 5.77, above 4: the soft-to-medium envelope, with σa = 37.75 kPa. When the number lies close to 4 the module adds a note: with cu = 60 kPa it is 3.84 and the stiff envelope gives σa = 36.90 kPa, and the note warns that the other branch would give a resultant a sixth larger, so that where cav is uncertain you should run both and design for the heavier.
Two things keep the result from running away. First, the floor of 0.3γavH in the soft-to-medium formula: with φ′ = 36° the formula gives less, the floor governs and σa is 36.90 kPa, the same as with n′ = 1.0. Second, Ks and n′ move cav only through the sand term and the clay term; Ks = 0.5 raises σa to 50.39 kPa because less sand strength is credited.
The hinge convention
Auto (default): the sheeting is hinged at every strut except the top and bottom ones, and the module switches to every strut hinged when that layout would put a strut in tension. It adds the note “Hinge convention switched automatically: hinged at the interior struts this layout would put strut X in tension (R = …), so the sheeting is treated as hinged at every strut instead” and, for a strut that stays slack, the warning “Strut X at z = … would be in tension in this layout — it is slack and carries nothing”.
Interior struts: hinged at every strut except the top and bottom ones. The example solves as two pieces, 0 to 3.5 m on struts A and B and 3.5 to 7 m on B and C.
All but the top and Every strut: hinged at more levels. With every strut hinged the example’s largest strut load is 281.3 kN and Mmax 29.49 kN·m/m, against 277.5 kN and 26.99 kN·m/m.
The design code
EN 1993-1-1 multiplies the working values by γF and verifies the sheeting and the wales in bending and the struts in compression and flexural buckling; AISC 360-22 by LRFD (load factor γH = 1.6, φ = 0.90) or ASD (Ω = 1.67). For the example, AISC by LRFD gives the section modulus the sheeting needs as 174.5 cm³/m and the utilisations 0.2908, 0.6727 and 0.3933 for the sheeting, the wale and the strut.
Analyze and read the results
Press Analyze. The module stays on the Model tab and the bar changes to Analysed — the braced cut calculated, with Notes (5) and Edit inputs; when a run carries warnings, the Warnings window opens by itself; close it and the bar keeps “— 1 warning” and a Warnings button to open it again. The answer is on the Results tab, in this order:
The half section with the dimensions and the strut sections, and the pressure on the sheeting with σa, the area of the envelope and the force it puts on a metre of wall (231.22 kN/m in the example).
The strut loadsPA, PB, PC and the wales seen from inside the cut, with M = Rs²/8 and V = Rs/2 for each level, green where the member carries them and red where it does not.
Values, step by step, then the tables: the layers inside the cut and their strength terms, the beam pieces of the wall, the strut loads and the wales level by level.
The cards: σa, Pmax, Mmax, Wreq,sp, the utilisations ηsp, ηwale and ηstrut, and the heave factor FSheave (eight cards); under them, in plain lines, the moment and the modulus of the governing wale.
The Results tab: the half section, the envelope, the struts and the wales.
The cards of the default example.
The verdict words
Each utilisation and the heave factor carries PASS or FAIL; a utilisation close to 1 reads PASS — near capacity (the wale at cu = 15 kPa, 0.9747). A utilisation is the demand over the resistance, so below 1 passes; the heave factor passes when it reaches the required one: 1.830 is a PASS against 1.5 and a FAIL against 2.0.
The bar after a clean analysis.
The Calculations tab, the report and the Theory tab
Calculations writes the working of the 17 steps of the example with your numbers: the reduction to the equivalent clay (step 1), the choice of the envelope (2), the idealisation of the sheeting and the reactions (3), a step for every piece of the wall (4 and 5), the strength of the members (6), the strut loads (7), the moments in the sheeting and the wales (8 and 9), the bottom heave (10), the design actions (11) and the verification of the sheeting, the wale and the strut (12 to 17). A step opens and closes by its header.
Step 1: the profile reduced to one clay.
Step 10: the bottom heave.
Report has a cover with Project, Location, Client, Report no., Date, Prepared by, Title / qualification, Checked by and Notes (printed only when filled in; the cover details are kept in this browser and saved with the model file). Save as PDF and Download Word (.docx) produce the summary report: a cover and a solution summary, then seven parts: introduction and scope, input data, calculation, results, assumptions and notes, summary, references, with the drawings. The cover says that the warnings appear in its Warnings and notes section.
The Report tab.
Theory has 17 sections: the braced cut and its members; why the pressure is not Rankine’s; apparent pressure from measured strut loads; the envelopes for clay; sand and clay in one cut; a surcharge, and water in clay; struts; sheet piles; wales; the members as they are given; verifying the steel to EN 1993-1-1 and to AISC 360-22; the envelopes against real cuts; the base of a cut in clay; what the method assumes; a worked example; and references.
Worked example: the default cut, by hand
The default model: 3 m of sand (γ = 17, φ′ = 30°) over clay (γ = 18, cu = 35), H = 7 m, B = 6 m, L = 20 m, T = 4 m, struts at 1, 3.5 and 6 m, s = 3 m, Ks = 1, n′ = 0.75, S275 steel, EN 1993-1-1, γF = 1.35. Every figure below is on the Calculations tab and was recomputed independently.
1 The equivalent clay
sand term = 17 × 1 × 3² × tan 30° = 88.33, clay term = 0.75 × 2 × 35 × 4 = 210.00 kN/m
The sheeting is hinged at B, so there are two pieces. Piece 1 (0 to 3.5 m) carries W = 99.09 kN/m acting at 2.139 m: RB = 99.09 × (2.139 − 1.00) / 2.50 = 45.14 and RA = 53.95 kN/m. Piece 2 (3.5 to 7 m) carries 132.13 kN/m acting at 5.25 m: RC = 132.13 × (5.25 − 3.50) / 2.50 = 92.49 and its share of B is 39.64. The total on B is 84.78 kN/m, and the loads P = R × 3 are:
Strut
R (kN/m)
P (kN)
A at 1.0 m
53.95
161.9
B at 3.5 m
84.78
254.3
C at 6.0 m
92.49
277.5
4 Sheeting, wale and strut
The largest moment in the sheeting is Mmax = 26.99 kN·m/m, at 2.30 m in piece 1. The design moment is 1.35 × 26.99 = 36.44 kN·m/m, so Wreq = 36.44 / 275 000 = 132.5 cm³/m; the 600 cm³/m given resists 165.00 kN·m/m, a utilisation of 0.2209. The wale at level C spans 3 m: M = 92.49 × 3² / 8 = 104.05 kN·m, design 140.47, needing 510.8 cm³ against the 1 000 given: 0.5108. The strut takes NEd = 1.35 × 277.47 = 374.58 kN; with λ̄ = 0.9339 and χ = 0.5791 its buckling resistance is 1 046.36 kN: 0.3580.
5 The base
B/√2 = 4.24 ≥ T → B′ = 4.00 m, B″ = √2 B′ = 5.66 m, 1 + 0.2 × 5.66 / 20 = 1.0566
Here 20.00 kPa is the clay’s strength averaged over the height of the cut with sand counted as zero, and 123.00 kPa is ΣγiHi. The same cut in the other unit systems gives slightly different figures, because the module rounds the equivalent unit weight and cohesion to the decimals of the chosen unit before it builds the envelope (17.57 kN/m³, 1.79 t/m³): SI · tf σa = 3.840 t/m², Pmax = 28.23 tf, Mmax = 2.746 tf·m/m and FS 1.825; US σa = 0.7887 ksf, Pmax = 62.40 kip, Mmax = 6.071 kip·ft/ft and FS 1.829; SI · kN FS 1.830. The differences stay within 0.3 %.
How each input changes the answer
Each row changes one value of the default example and reads the module: σa and the largest strut load Pmax; then the heave factor FS and the utilisation of the wale ηwale. The default gives 37.75 kPa and 277.5 kN; 1.830 and 0.5108. The unit weight is 17 kN/m³ in the sand and 18 kN/m³ in the clay, the saturated unit weight 20 and 19 kN/m³, unless the row changes it; the row for the 10 m cut changes H and the struts.
Change
σa · Pmax
FS · wale η
Sand thickness 3 → 1.5 m
37.36 kPa · 274.6 kN
1.913 · 0.5055
Sand thickness 3 → 5 m
36.31 kPa · 266.9 kN
1.716 · 0.4913
Sand φ′ 30° → 36°
36.90 kPa · 271.2 kN
1.830 · 0.4993
Ks 1 → 0.5
50.39 kPa · 370.4 kN
1.830 · 0.6818
n′ 0.75 → 1.0
36.90 kPa · 271.2 kN
1.830 · 0.4993
Clay cu 35 → 60 kPa
36.90 kPa · 264.8 kN
3.137 · 0.4874
Clay cu 35 → 15 kPa
72.03 kPa · 529.4 kN
0.7842 FAIL · 0.9747
Clay γ 18 → 20 kN/m³ (γsat stays 19)
45.73 kPa · 336.1 kN
1.718 · 0.6188
Spacing s 3 → 4 m
37.75 kPa · 370.0 kN
1.830 · 0.9081
Surcharge 20 kPa
37.75 kPa · 424.5 kN
1.574 · 0.7814
Water table at 2 m
44.75 kPa · 328.9 kN
1.731 · 0.6055
Width B 6 → 3 m
37.75 kPa · 277.5 kN
2.043 · 0.5108
Width B 6 → 12 m
37.75 kPa · 277.5 kN
1.830 · 0.5108
No hard stratum
37.75 kPa · 277.5 kN
1.819 · 0.5108
Every strut hinged
37.75 kPa · 281.3 kN
1.830 · 0.5179
Required FS 1.5 → 2.0
37.75 kPa · 277.5 kN
1.830 FAIL · 0.5108
Cut 10 m deep, struts at 1, 3.5, 6, 8.5 m
85.84 kPa · 824.1 kN
1.42 FAIL · 1.517 FAIL
What the rows show:
The sand enters through the average and the floor. With 1.5 m or 5 m of sand the 0.3γavH floor governs, so σa follows the average unit weight (37.36 and 36.31 kPa against 37.75); a stronger sand (φ′ = 36°) changes nothing in the pressure beyond the floor, 36.90 kPa, the same as with n′ = 1.0.
cu acts twice. A stronger clay (cu = 60 kPa) leaves σa at the stiff-envelope value and raises the heave factor from 1.830 to 3.137; a weaker clay (15 kPa) lifts σa to 72.03 kPa and drops the factor to 0.7842, a FAIL.
The spacing scales the loads.s = 4 m multiplies every strut load by 4/3 (277.5 to 370.0 kN) and the wale moment by 16/9: the wale utilisation goes from 0.5108 to 0.9081. The pressure and the heave factor do not move.
The width acts only while it governs. Narrowing the cut to 3 m raises the heave factor to 2.043; widening it to 12 m changes nothing, because the stratum 4 m below the base already limits the failure surface. Without a stratum the cut’s width alone limits it and the factor falls to 1.819.
A deeper cut raises the pressure and every load and lowers the heave factor. At 10 m with a fourth strut the pressure is 85.84 kPa, the largest strut 824.1 kN, the wale and the strut fail (1.517 and 1.063) and the heave factor falls from 1.830 to 1.42.
Messages
Stops
A stop appears in a dialog headed “Cannot analyse — a condition of the solution is not met”, followed by the reason, the instruction, and “Nothing was calculated. Change the inputs marked in red, then press Analyze again.” The stops this module gives:
“Strut C at z = 8.00 m lies outside the cut. Every strut must sit strictly between the ground surface (z = 0) and the base (z = H = 7.00 m). Move it inside the cut or remove it.”
“The cut does not reach the clay (sand 8.00 m ≥ H). With only sand inside the cut the equivalent-clay average has no clay term; the sand module applies. Deepen the cut, thin the sand, or open the sand module.”
“A sand layer lies below a clay layer. The source gives the equivalent-clay rule for sand OVER clay only; clay over sand has no published envelope. Reorder the layers (sand first), or model the cut with the sand or the clay module.”
“No sand layer in the profile. This module is for sand over clay; an all-clay profile belongs to the clay module. Add the sand layer above the clay, or open the clay module.”
“No clay layer in the profile. This module is for sand over clay; an all-sand profile belongs to the sand module. Add the clay layer, or open the sand module.”
An empty box: the dialog reads “Cannot analyse — 2 input errors” and lists, for example, “Depth below the ground surface (zB) is missing.”
The module also stops for a cut depth, unit weight, friction angle, cohesion, strut spacing or yield strength that is not above zero, for fewer than two struts and for two struts at one depth.
A stop: a strut below the base.
Warnings
A warning does not stop the analysis; the Warnings window opens by itself right after Analyze; close it and the bar keeps “— 1 warning” (or “— 3 warnings”) with a Warnings button to open it again. Each warning has its triangle. In the cut 10 m deep (struts at 1, 3.5, 6 and 8.5 m) there are three:
“Factor of safety against bottom heave FS = 1.42 is below the required 1.50.” followed by “The clay beneath the base cannot carry the overburden beside the cut with the intended margin. Extend the sheeting below the base, reduce the surcharge beside the cut, narrow the cut or improve the clay under the base.”
“The wale given does not carry the design moment: MEd / Mc,Rd = 1.52.” with the resistance, the design moment and the modulus the wale asks for.
“The strut section given does not carry the design load: NEd / Nb,Rd = 1.06.” with the buckling resistance, 1 046.36 kN, and the design load, 1 112.49 kN.
The bar with warnings.
Notes
Notes list what the run assumed; the bar of the default example reads “Notes (5)”. Among the notes: “The stability number γavH/cav = 3.92 lies close to 4, where the two clay envelopes change over.” (a cut 4 m deep, with struts at 1, 2.5 and 3.5 m); “Cut depth H = 4.00 m is shallower than the ≈6 m the envelopes were derived for.” (the same cut); and, with the groundwater present, that the run is undrained and the clay envelope carries no separate hydrostatic pressure. A surcharge, the absence of a hard stratum and a switch to AISC 360-22 each add a note that says how the run was computed.
Good practice
Put the sand first and give it its real thickness. Only the sand above the clay enters the reduction; the sand’s φ′ and Ks matter as long as the formula, not the floor, governs.
Read the stability number. Close to 4 the module warns that the two envelopes differ by about a sixth; run the other branch as well and design for the heavier.
Give the real strut depths. The reactions follow the hinged pieces, so a strut moved changes the others.
Check all four verdicts. The sheeting, the wale, the strut and the base are separate cards; one FAIL is enough to change the design.
Give the width and the stratum depth to have the heave check reflect the cut; leaving the stratum out is the safe side.
Keep the model. The page opens on the default model; use Save to file… or Quick Save….
Treat shallow cuts as preliminary. The envelopes were derived for cuts deeper than about 6 m; the module says so.
Frequently asked questions
How does the module treat sand over clay?
It reduces the profile inside the cut to one equivalent clay: cav = [γsKsHs² tan φ′ + Σ n′quHc] / 2H and γav = ΣγiHi/H. The example gives 21.31 kPa and 17.57 kN/m³.
Which envelope is used?
The one the stability number γavH/cav picks: above 4 the soft-to-medium trapezoid with σa = γavH − 4cav, at least 0.3γavH; at or below 4 the stiff trapezoid with σa = kγavH. The example has 5.77 and 37.75 kPa.
How are the strut loads found?
The sheeting is cut into pieces at the hinges; each piece is a determinate beam on its struts, solved by moment and force equilibrium, and a strut at a hinge collects a reaction from both sides. P = R × s: 161.9, 254.3 and 277.5 kN in the example.
Why did the analysis stop with “lies outside the cut”?
A strut must lie strictly between the surface and the base. Dragging a strut below the base does that; move it back or remove it.
Why does the module say the sand reaches the base?
The cut must reach the clay. With only sand inside the cut the average has no clay term, so the module points to the sand module. Deepen the cut or thin the sand.
Does the water table load the wall?
No separate pressure is added: the clay envelopes are total-stress. Below the table the soil is taken at its saturated unit weight, which raises σa: 44.75 kPa instead of 37.75 with the table at 2 m.
What does the bottom-heave check use?
The clay under the base carries the bearing term 5.14c(1 + 0.2B″/L), the layers beside the cut give the side shear csideH/B′ (sand counted as zero) and the overburden ΣγiHi + q drives it. B′ is B/√2 or the depth T to the hard stratum if smaller; the example gives 1.83.
Why does a wider cut not change the heave factor?
When T is smaller than B/√2 the stratum limits the heave surface (B′ = T). With B = 12 m the factor is 1.830, as with 6 m; narrowing to 3 m raises it to 2.043.
Which codes does it check the steel to?
EN 1993-1-1 with γF, γM0 and γM1, or AISC 360-22 by LRFD (γH = 1.6, φ = 0.90) or ASD (Ω = 1.67). The sheeting is checked on its modulus, the wale on its modulus or as a catalogue section, the strut in buckling.
Does the module remember my inputs?
No. It 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.
Can I drag things on the drawing?
Before Analyze, the struts and the boundary between layers. After Analyze nothing; press Edit inputs to unlock the model.
Which units does it use?
SI · kN, SI · tf or US, changed in the header at any time, even after Analyze. For the example: Mmax = 26.99 kN·m/m, 2.746 tf·m/m or 6.071 kip·ft/ft.
Consolidation settlementPrimary consolidation of clay layers with the full stress path.
Elastic settlement, cohesiveImmediate settlement of clay layers, undrained.
Elastic settlement, granularSettlement of sand and gravel layers, drained.
Settlement 2DTotal settlement of a profile of clay and sand layers.
