Three modules check a retaining wall for stability and bearing, in the static case and in an earthquake: a reinforced-concrete cantilever wall, a gravity wall and a reinforced-soil wall. This page helps you choose the module that matches your wall and links to the manual of each.
The Retaining Walls family has three modules. All of them check a wall against sliding, overturning and bearing, in the static case and in an earthquake. They differ in the kind of wall. Pick the one that matches the wall you are designing.
Your wall
Module
A reinforced-concrete wall with a stem, a toe and a heel, with an optional shear key or pressure-relief shelf; stability, bearing and the actions in the stem and the slabs
A wall of granular fill reinforced by strips, geotextile or geogrid behind a facing; the tension of every level, rupture, pullout and the stability of the block
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.
Static and seismic cases. Each module checks the wall under its own weight, the soil, the water and the surcharges, and again in an earthquake.
The stability checks. Sliding, overturning, eccentricity and bearing, each against its required factor.
Pick the one that matches the wall and open its manual for the fields.
Draw the wall
Enter the dimensions of the wall, or of the reinforced block.
Describe the soil and the loads
Enter the backfill and the foundation soil, the water, the surcharges and the earthquake.
Analyze and read the checks
Press Analyze. Read the factors of safety, the bearing pressure and the actions, then save a report with the cover filled in.
Frequently asked questions
How do I check a retaining wall with GeoTerva?
Open the module for the wall: Cantilever RC wall, Gravity wall or MSE wall. Draw the wall, enter the soil, the water, the surcharges and the earthquake, press Analyze, and read the factors of safety for sliding, overturning and bearing.
Which module do I use for a reinforced-soil wall?
MSE wall. It checks the tension, the rupture and the pullout of every reinforcement level and the stability of the reinforced block.
Do the modules include an earthquake?
Yes. Each module checks the wall in the static case and in the seismic case.
Where do the earth pressures come from?
From the methods described in the Lateral earth pressure manuals, such as Rankine, Coulomb and Mononobe–Okabe, depending on the module.
Do the cantilever and gravity modules give the forces in the wall?
The cantilever module gives the shear and moment in the stem and the slabs. The gravity module lists every force in a ledger.
Check a reinforced-concrete cantilever wall for sliding, overturning, eccentricity and bearing in the static and the seismic cases, with a shelf, a key, water and surcharges, and read the shear and moment in the stem and slabs. This manual walks through the screen, every input, the options, the results and the report, with a worked example you can reproduce.
Cantilever RC wall checks a reinforced-concrete cantilever retaining wall, a stem on a base slab with a toe and a heel, for sliding, overturning, eccentricity and bearing pressure, in the static case and in the seismic cases, and gives the shear force and bending moment in the stem, the toe and heel slabs, the shelf and the key. Every force is drawn and listed, so each factor of safety can be followed by hand.
The earth pressure acts on the vertical plane through the heel edge, soil against soil, so the thrust is parallel to the backfill surface. The sliding factor is:
Neff is the vertical force on the base with the uplift taken off, Hdrive the horizontal force that pushes the wall, and Ptoe and Pkey the passive resistance of the soil in front of the base and of the key, used in sliding only. Overturning is taken about the front bottom corner of the base slab (the toe edge, point O), and the eccentricity and the bearing pressure are referred to the base underside about the same point.
What you can describe
A stem of constant or tapered thickness (the back face or the front face stays vertical), a toe, a heel and a base slab, with an optional pressure-relief shelf on the back of the stem and an optional shear key under the base.
A flat or inclined backfill (β above −45° and below 45°), a passive-side fill over the toe, and one soil for the backfill, the front fill and the foundation.
Uniform, strip and point surcharges (up to six loads), groundwater on the retained side and on the front side, and base uplift.
Rankine or Coulomb static earth pressure and Mononobe–Okabe seismic earth pressure, with the hydrodynamic water pressure and the inertia of the wall and of the soil that moves with it.
Which module for which wall
A gravity wall in stone masonry or plain concrete on a stepped footing: Gravity wall.
The pressure of a surcharge on its own, or the earth pressure of a layered or sloping ground behind a wall of your own: the modules of Surcharge loads and Lateral earth pressure.
A bearing capacity with depth, shape and inclination factors: Bearing capacity. Here the bearing pressure under the base is compared with the allowable pressure qall that you enter.
Have these ready from your design and your ground investigation:
What
Notes
The wall section From: Your design
Retained height H, stem thickness at the top and at the base, toe and heel projections, base slab thickness; a shelf or a key if you use them.
The soil From: Boring logs and tests
Moist and saturated unit weight, the effective friction angle φ′ (cohesion is taken as zero), the base friction coefficient μb and the allowable bearing pressure qall.
The backfill and the front fill From: Your design
The slope angle β of the backfill and the height hp of the soil in front of the wall above the base top.
Loads and water From: Your design loading, groundwater readings
Surcharges, the depth of the water table behind the wall and, if any, the water height in front of it.
The earthquake From: Your seismic study
The horizontal and vertical coefficients kh and kv; the module does not derive them.
The required factors From: Your design basis
Minimum sliding and overturning factors for the static and the seismic case.
Quick start in seven steps
Open the module and choose the units
Open Cantilever RC wall from the Retaining Walls family. Pick SI · kN, SI · tf or US in the header; you can change it at any time.
Draw the wall
In Geometry type H, the stem thickness (constant or variable), the toe, the heel and the base slab. In Optional geometry switch the shelf and the key on or off and size them.
Describe the ground
Set the backfill in Backfill Slope, the front fill in Passive-Side Fill and the soil in Soil Definition.
Add loads, water and the earthquake
Add surcharges in Surcharge Load, the water table in Groundwater and, if needed, choose Yes in Earthquake and enter kh and kv.
Set the criteria and the method
Check the minimum factors in Stability criteria, and the static method and the passive resistance in Analysis Settings.
Press Analyze
Press Analyze in the bar at the foot of the Model tab. A window reports the outcome, the inputs lock, and the drawing and the four cards below it fill in.
Read the answer
The Results tab gives the checks, the forces and the structural actions. Pressure and Forces show them on the wall; Calculations writes out the working and Report saves a PDF or a Word file.
The screen: four views and four cards
The layout is the one every GeoTerva module shares, described in the workspace guide. The drawing on the left has four views, chosen with the buttons above it:
2D View is the section of the wall as you have modelled it, with the dimensions in the unit system you chose, the soil label, the groundwater lines, the shelf, the key, the surcharges and the ringed overturning pivot O. It changes as you type.
3D View shows the wall as a solid. Drag to rotate, double-click to reset (the hint is on the drawing).
Pressure is available after Analyze: the pressure diagrams on the wall, with the resultants and their heights.
Forces is available after Analyze: the free body of the weights, the pressures, the uplift and the passive resistances, with the lever arms from O.
2D View before Analyze, with the four cards still grey.
2D View after Analyze: the cards carry the values.
3D View, rotated by dragging.
The four cards
Under the drawing, Sliding, Overturning, Bearing capacity and Eccentricity each show a Static and a Seismic value with its requirement. Before Analyze they are grey; after it they turn green or red, and pressing a card opens the Results tab. Seismic reads “not analysed” until the earthquake is on. The overturning card names the pivot.
The four cards after Analyze.
The Pressure and Forces bars
Each of these two views has a bar of its own, and it lists only what the model contains. In Pressure, Surface chooses the plane: Virtual back always, Stem back face with a shelf, Front resistance, Key resistance and Base uplift when they exist; Layers shows or hides Soil, Hydrostatic water and Resultant, with Surcharge, Strip & point loads, Seismic increment, Seismic total and Hydrodynamic water added when the model has them; with the earthquake on, Load case switches between the static case and the seismic cases. In Forces, Load case and Layers (Weights, Earth pressure, Water & uplift, Front resistance, and Surcharge and Seismic when present) do the same. The (?) beside each group says that the layers are display only: the checks always use every component.
Pressure view: the virtual back.
Forces view: the free body of the wall.
Entering the model, section by section
The Model tab has twelve sections: Model data, Geometry, Optional geometry, Backfill Slope, Passive-Side Fill, Soil Definition, Surcharge Load, Groundwater, Earthquake, Concrete & reinforcement, Stability criteria and Analysis Settings. Model data opens and closes on its own; of the others one is open at a time, so opening one closes the previous one. Next and Back at the foot walk you through them, and Analyze waits in the bar at the bottom. Where a unit is shown twice or three times, such as m · ft, the units are those of SI · kN, SI · tf and US in turn. Defaults are shown in SI; a unit switch converts the boxes (the 4 m wall reads 13.12 ft).
Model data
The first section holds the model name, Save to file…, Open file…, Quick Save… with its (?), the list of quick saves with Load and Delete, and Reset to defaults. A line under the buttons says what was restored when the page opened. Save to file writes a .json file named after the model; Quick Save keeps a version in this browser, with its inputs, its analysed state and the report cover.
Model data.
Geometry
Stem thickness has Constant (one thickness t, default 0.50 m) and Variable, the default, with a top thickness tt and a base thickness tb. With Variable, Thickening direction (Toward front, the default, or Toward backfill) says which face of the stem stays vertical; the (?) opens a sketch of both. Four read-only cards give the derived base widthB = Lt + tb + Lh, its definition, the stem profile and the analysis strip (1.0 m: all forces are per metre of wall).
Geometry.
Geometry fields
Field
Default
What to enter
Retained height H m · ft
4.00
From the base top to the wall top.
Stem top thickness tt m · ft
0.30
With Variable.
Stem thickness at base tb m · ft
0.70
With Variable; at least the top thickness.
Constant stem thickness t m · ft
0.50
With Constant.
Front projection (toe) from stem base front face Lt m · ft
1.25
Measured from the front face of the stem at its base. Zero or more.
Backfill-side projection (heel) from stem base back face Lh m · ft
1.50
Measured from the back face of the stem at its base. Zero or more.
Base slab thickness tf m · ft
0.75
Greater than zero.
The (?) window of Thickening direction.
Geometry with a constant stem.
Optional geometry
Two switches, each with an Include toggle and a (?), both on in the example. Pressure-relief shelf: a horizontal slab on the back of the stem. Below its underside the self-weight pressure of the soil restarts and is reduced by a relief ratio R = min(Ls / bkr, 1); the surcharge and the water are not reduced. Shear key: a downward projection under the base that adds passive resistance in sliding.
Optional geometry.
Shelf and key fields
Field
Default
What to enter
Shelf elevation above base top hs m · ft
2.00
The mid-height of the shelf. The whole shelf must lie within the stem height.
Shelf projection Ls m · ft
1.00
Greater than zero.
Shelf thickness ts m · ft
0.40
Greater than zero.
Key width bk m · ft
0.40
Greater than zero.
Key depth below base dk m · ft
0.60
Greater than zero.
Key offset from toe edge xk m · ft
1.00
From 0 to B − bk: the key must lie under the base.
The (?) window of Shear key.
Backfill Slope
Flat or Inclined, the default. With Inclined, enter the angle β of the backfill surface, above −45° and below 45° (default 10°); a positive angle rises away from the wall. Flat sets β = 0. The uniform surcharge follows the ground line. Two read-only cards state the surface mode and the slope. The size of β must also stay smaller than φ′, for a negative angle as well (see Messages).
Backfill Slope.
Backfill slope field
Field
Default
What to enter
Backfill slope angle β deg
10.0
Used with Inclined.
Passive-Side Fill
The soil in front of the wall above the base top. It rests on the toe slab and moves with the wall: its weight is a vertical load, and its lateral resistance on the vertical plane at the toe edge is credited in sliding at the passive state chosen in Analysis Settings. Enter hp = 0 if the front fill may be removed. The (?) opens a sketch of how hp is measured.
Passive-Side Fill.
Passive-side fill field
Field
Default
What to enter
Fill height above base slab on passive/front side hp m · ft
1.00
From 0 to H.
Soil Definition
One soil serves the backfill, the front fill and the foundation. Cohesion is taken as zero. The name is only a label on the drawing.
Soil Definition.
Soil fields
Field
Default
What to enter
Soil label shown in the drawing —
Soil
Text shown in the drawing.
Moist unit weight γ kN/m³ · t/m³ · pcf
18.0
Greater than zero. Above the water table.
Saturated unit weight γsat kN/m³ · t/m³ · pcf
20.0
Above the unit weight of water.
Effective friction angle φ′ deg
30.0
Above 0° and below 60°.
Base friction coefficient μb —
0.55
Greater than zero. Friction on the base underside: μbNeff; no adhesion is used.
Allowable bearing pressure qall kPa · t/m² · ksf
200
Greater than zero. The limit for the largest base pressure.
Surcharge Load
The form is the one of the sheet-pile modules. Choose the kind of load by its picture, enter its values and press + Add load: it goes into the Surcharge loads table (Load, Kind, Magnitude, Position). Press a row to edit it in the form (the form then says “Changes apply as they are entered.”, Done brings back the form for a new load and Delete load removes the load); × removes a row. Up to six loads (the form counts “2 of 6”). A strip or point load is measured from the back face of the wall at its top, and its lateral pressure is taken by the elastic solutions for a rigid wall. The uniform loads of the table add up into one uniform surcharge q. A point load closer than 0.30 m to the wall is calculated as if it stood at 0.30 m.
Surcharge Load with a strip and a point load.
What a new load form starts with
Field
Default
What to enter
Uniform surcharge on the retained surface q kPa · t/m² · ksf
10
The value a new uniform load starts from. Zero or more.
Strip load qs kPa · t/m² · ksf
20
Zero or more.
Near edge from the wall x1 m · ft
1
Zero or more.
Far edge from the wall x2 m · ft
3
Greater than the near edge.
Point load Q kN · tf · kip
empty
Zero or more; enter it before Add load.
Distance from the wall x m · ft
empty
Zero or more; enter it before Add load.
The loads on the drawing.
The example has no surcharge: the table is empty and the surcharge is off.
Groundwater
Retained side water (Include, on in the example): the water table at the depth zw below the wall top and the unit weight of water. Front-side water (off in the example): a water level in front of the wall, as a height hwf above the base top; the (?) shows how it is measured. Front water is assumed present in every load case as a favourable load.
Groundwater.
Groundwater fields
Field
Default
What to enter
GWT depth below the wall top zw m · ft
1.50
Zero or more.
Water unit weight γw kN/m³ · t/m³ · pcf
9.81
Below the saturated unit weight.
Water height above base top hwf m · ft
0.50
Zero or more; the box is enabled with front-side water.
Earthquake
No (the default) or Yes. With Yes the two boxes open and the module adds the seismic cases. The seismic earth pressure is always Mononobe–Okabe on the same plane as the static method.
Earthquake switched on.
Earthquake fields
Field
Default
What to enter
Horizontal seismic coefficient kh —
0.15
From 0 to below 1.
Vertical seismic coefficient kv —
0.10
From 0 to below 1. With kv above zero two cases are run, the vertical acceleration upward and downward; the lower factor governs.
Concrete & reinforcement
Four values. Only the concrete unit weight enters the weights of the concrete parts. The strength f′c, the yield strength fy and the cover are kept with the model and do not change any result (changing them leaves every number of the example as it was).
Concrete & reinforcement.
Concrete fields
Field
Default
What to enter
Concrete unit weight γc kN/m³ · t/m³ · pcf
24.0
Greater than zero.
Concrete compressive strength f′c MPa
30
Kept with the model.
Reinforcement yield strength fy MPa
420
Kept with the model.
Nominal concrete cover cn mm
50
Kept with the model.
Stability criteria
The minimum factors the checks are compared with. They appear on the cards and in the report as “required”.
Stability criteria.
Stability criteria fields
Field
Default
What to enter
Minimum sliding FS, static FSs —
1.50
Greater than zero.
Minimum overturning FS, static FSo —
2.00
Greater than zero.
Minimum sliding FS, seismic FSse —
1.10
Greater than zero.
Minimum overturning FS, seismic FSoe —
1.10
Greater than zero.
Analysis Settings
Described in the next section: the static method, the seismic pressure, the passive resistance and the base uplift.
Choosing the method and the passive resistance
Static earth pressure is Rankine (the default) or Coulomb. Both act on the vertical plane through the heel edge, soil against soil, with the wall friction angle equal to β; for that plane the Coulomb Ka equals the Rankine Kaβ exactly, and the example gives the same answer with either (2.05, 2.10, 94.72 kPa). The Seismic earth pressure is Mononobe–Okabe, used when Earthquake is Yes; its increment acts at 0.6 h above the bottom of the plane.
Then the passive resistance, which is used in the sliding check only:
Analysis Settings.
Setting
Default
What it does
Passive state w Full Passive, 2/3 Passive + 1/3 Rest, 1/3 Passive + 2/3 Rest, Full Rest
1/3 Passive + 2/3 Rest
Kmob = wKp + (1 − w) K0, with Kp = tan²(45° + φ′/2) and K0 = 1 − sin φ′. For 30° that is Kp = 3.0000, K0 = 0.5000 and Kmob = 1.3333 in the example. The passive pressure is Kmob times the effective vertical stress.
Include toe passive resistance toe
On
Adds Ptoe = ∫ Kmobσ′v dz over the soil in front of the base slab. Off: the weight of the front fill still counts, its lateral resistance does not.
Unreliable top layer hignore
0.00 m
The passive stresses start from the front ground lowered by this depth (frost, erosion, future trenches).
Seismic passive credit factor ηp,E
0.00
Between 0 and 1: the share of Ptoe and Pkey credited in the seismic cases. At 0 the seismic sliding rests on base friction alone.
Shear key overturning pivot Base slab front bottom corner (default), Shear-key front bottom corner
Base slab front bottom corner (default)
For a key at the toe edge, the choice of the shear-key front bottom corner as the pivot adds the key depth to every horizontal arm and gives a lower FSo.
Include active earth pressure on rear face of heel shear key
Off
For a key at the heel edge, includes the active earth pressure on the rear face of the key.
Base uplift / buoyancy
Include (on)
The pore pressure under the base is a linear head field between the retained and the front water levels, and reduces Neff. Under the earthquake the hydrodynamic water pressure is always included.
The (?) window of the passive state.
The (?) window of the pivot.
How the options change the answer
Passive state moves FSs only: 1.58 at Full Rest, 2.05 at the default, 2.98 at Full Passive. Overturning and bearing stay at 2.10 and 94.72 kPa.
Toe passive off gives FSs = 1.63; hignore = 0.5 m gives 1.76.
A shelf and a key both help sliding; see the table of what-ifs below.
Analyze and read the results
Press Analyze. A progress bar steps through reading the model, earth pressure and stability, the detailed sheet, the summary sheet, the results and the report; then a window states the outcome and the bar at the foot reads Analysed — all checks satisfied or Analysed — N warnings, with the message “The inputs and the analysis settings are locked. Edit inputs clears the results; the unit system can still be changed.” Edit inputs asks “The results will be cleared. Edit the inputs?” and then unlocks the model. The module stays on the Model tab, so press Results to see the numbers.
The window after a clean analysis.
The bar after Analyze.
When the run carries warnings the window is titled Attention — N warnings, says “Review these points before the results are used.” and lists each one with the reason and what to do; Show results and Stay on the model follow. A Warnings (N) button in the bar and in the tabs reopens the list. The warnings are the module’s own cautions, listed in Messages below.
The warnings window, for the example with H = 5 m.
The Results tab
Blocks from the top:
Design checks: a line (All checks satisfied or the count of checks not satisfied and their names), then one row per check, Sliding, Overturning, Bearing and Eccentricity, with a column for the static case and one for each seismic case. Each cell gives the value, the requirement or limit, a bar of demand over capacity with a tick at 1.0, and OK or NOT OK; the governing case is outlined. qmin ≥ 0 is information only, the same condition as |e| ≤ B/6. A check that cannot be evaluated (the resultant outside the base) reads “cannot be evaluated”.
Pressure resultants: the horizontal resultant of each pressure component and its height above the base underside (and the uplift and its distance from the toe); the front and key resistance are shown “reference”, not added in the checks.
Weights, lever arms and moments: every concrete part and soil zone with area, weight, centroid and moment, with a polygon check and a check of the soil weight against the force ledger.
Shear key and Relief shelf blocks, with the factors with and without them and the stem moment with and without the shelf.
The cards of Earth pressure (Ka, Kae, the forces), Static stability, Seismic stability and RC design actions: the stem moment and shear, the toe and heel moments, the shelf and key demand.
The Results tab of the example.
The Results tab when checks are not satisfied.
The structural actions
The RC design actions give, for each member, the largest bending moment at its critical section over the load cases and the shear force with it, per metre of wall: the stem at the base top (with the axial force), the toe at the stem front face, the heel at the stem back face, the shelf at its root and the key at its root. The stem is loaded on its own back face. In the example the stem gives M = 69.62 kN·m/m with V = 55.14 kN/m, the toe 42.18 and the heel 30.47 kN·m/m, the shelf 18.92 and the key 20.90. The module gives the actions; the reinforcement is designed from them.
With the earthquake
With Earthquake Yes the cards and the table gain a column for each seismic case, Seismic kᵥ↑ and Seismic kᵥ↓ (one Seismic column when kv is zero). The example with kh = 0.15 and kv = 0.10 gives, for sliding, 0.62 and 0.75, against a requirement of 1.10; sliding, bearing and eccentricity are not satisfied in either seismic case and are marked NOT OK and the Pressure and Forces views draw the seismic total, its increment, the hydrodynamic pressure and the inertia.
The Results tab with the earthquake on.
Forces view, seismic case.
The Calculations tab, the Report and the Theory tab
The Calculations tab has two levels, Summary and Detailed, chosen with the buttons at the top, and a contents list whose sections open and close (open all, close all). Summary has seven sections: Geometry and weights, Earth-pressure coefficients, one section for each load case, Relief shelf, Shear key, Structural actions and Summary of checks. Detailed has twelve and 42 steps: Input data, Geometry and concrete components, Soil weights, Earth-pressure coefficients and stresses, Pressures for each case, Stability, Relief shelf, Shear key, Structural actions, the internal forces, Summary of checks, and Assumptions and warnings. Each step shows the equation, the numbers substituted and the result. Before Analyze the tab says “Press Analyze on the Model tab to calculate this wall.”
Calculations, Summary level.
Calculations, Detailed level.
The Report
The Report tab has a cover form (project, location, client, report number, date, prepared by, title or qualification, checked by and optional notes), kept in the browser and saved with the model file. After Analyze, Save as PDF (it opens a print window: choose Save as PDF there) and Download Word (.docx) are available; before it they are greyed out. The preview is the summary report.
It has thirteen parts: 1 Purpose and scope, 2 Design basis and assumptions, 3 Geometry and section, 4 Soil, material and load parameters, 5 Resisting forces, 6 Lateral earth pressure coefficients, 7 Driving forces, 8 Overturning check, 9 Sliding check, 10 Eccentricity and base pressure, 11 Relief shelf and shear key, 12 Design actions for the RC members and 13 Summary of results, with the drawings and the tables. When the run carries cautions, a part with them is added.
The Report tab: the cover form and the first page.
The Theory tab
The Theory tab explains the method in 21 sections: Overview; The wall system; Coordinates and signs; Geometry decomposition; Soil moving with the wall; Effective stress; Rankine; Coulomb; At-rest and passive resistance; Surcharge; Hydrostatic water and uplift; Mononobe–Okabe; Hydrodynamic water; Inertia of wall and soil; Relief shelves; Shear keys; Sliding, overturning, bearing; Structural actions; Worked example; Variables; References.
Worked example: the module’s own example
The module opens on this example; you can follow every number on your own screen (values from the Calculations tab, SI · kN).
Inputs of the example
Section
Inputs
Geometry
H = 4.00 m; stem 0.30 m at the top and 0.70 m at the base, thickening toward the front; toe 1.25 m, heel 1.50 m, slab 0.75 m
Optional geometry
Shelf: hs = 2.00, Ls = 1.00, ts = 0.40 m. Key: 0.40 m wide, 0.60 m deep, 1.00 m from the toe edge
Retained side zw = 1.50 m below the wall top; no front water; uplift included
Settings
Rankine; 1/3 Passive + 2/3 Rest; toe passive on; no earthquake; required FSs = 1.50, FSo = 2.00
Step 1: the coefficients
The Rankine coefficient for β = 10° and φ′ = 30° is Kaβ = 0.3495 along the slope, and the horizontal part is Ka = 0.3495 cos 10° = 0.3442, the value the module shows. Kp = tan²60° = 3.0000, K0 = 1 − sin 30° = 0.5000, Kmob = ⅓ · 3.0000 + ⅔ · 0.5000 = 1.3333.
Step 2: weights and forces
ConcreteWc = 24.00 × 5.2275 = 125.46 kN/m; soil moving with the wallWs = 134.47 kN/m; their sum 259.93 kN/m.
Water on the plane: the water column from the water table to the base underside is 3.25 m, so Pw = ½ · 9.81 · 3.25² = 51.81 kN/m. Soil thrustPa,H = 36.77 kN/m (it is relieved by the shelf, R = 0.789). Hdrive = 36.77 + 51.81 = 88.58 kN/m.
These are the numbers of the Results tab. The soil weights and the uplift are read from the module; the rest follow from them by the formulas above.
A plain wall, checked by hand
Switch the shelf, the key, the water, the front fill and the uplift off and choose Flat: the wall is a plain 4 m wall on a 3.45 m base. Then Ka = ⅓; the plane is 4.75 m high, so Pa = ½ · ⅓ · 18 · 4.75² = 67.69 kN/m at 1.583 m; the weights are 218.10 kN/m (concrete and the soil over the heel); the toe passive is 1.3333 · 18 · 0.75² / 2 = 6.75 kN/m. Sliding: (0.55 × 218.10 + 6.75) / 67.69 = 1.872; overturning: 479.68 / 107.17 = 4.476; |e| = 0.017 m and qmax = 65.09 kPa. The stem at its base carries V = ½ · ⅓ · 18 · 4² = 48.00 kN/m and M = 48.00 × 4/3 = 64.00 kN·m/m. The module gives the same numbers. An independent calculation also agrees with the module for a sloping backfill, a different soil, a uniform surcharge, the front fill, hignore, the passive states, the toward-backfill and the constant stem, and the seismic cases below.
The seismic cases of the plain wall
Add the earthquake with kh = 0.15 and kv = 0.10 (η = 0, so no passive credit). Mononobe–Okabe with ψ = arctan(kh / (1 ∓ kv)) gives Kae = 0.4459 (vertical acceleration upward) and 0.4227 (downward); PAE = ½ γ (1 ∓ kv) Kaeh² = 81.49 and 94.41 kN/m. With the inertia khW = 32.72 kN/m the horizontal force is 114.21 and 127.12 kN/m, the normal force (1 ∓ kv) W is 196.29 and 239.91 kN/m, and sliding is 0.55 × 196.29 / 114.21 = 0.945 and 0.55 × 239.91 / 127.12 = 1.038. The module gives the same.
The same wall in the other unit systems
In SI · tf the example gives qmax = 9.66 t/m² against a limit of 20.39 t/m², the earth thrust 3.75 tf/m, the water force 5.28 tf/m and the concrete unit weight 2.45 t/m³; in US, qmax = 1.98 ksf against 4.18 ksf, 2.52 and 3.55 kip/ft, and H reads 13.12 ft. The factors 2.05 and 2.10 are the same in the three systems; the eccentricity reads 0.324 m, 0.324 m and 1.062 ft, against a limit of 0.575 m and 1.886 ft.
How each input changes the answer
Each row changes one thing in the example (H = 4 m, β = 10°, γ = 18, γsat = 20 kN/m³, φ′ = 30°, μb = 0.55, shelf, key, water at 1.5 m and uplift as in the Worked example). The second column gives the static sliding factor and the static overturning factor, the third the largest base pressure in kPa and the eccentricity in m. The numbers are the ones the module gives, so you can reproduce any row.
The example with one change at a time
Change
FSs / FSo
qmax kPa / |e| m
The example Rankine; Coulomb gives the same
2.05 / 2.10
94.72 / 0.324
Flat backfill β = 0
2.26 / 2.17
87.64 / 0.299
β = 20°
1.79 / 2.01
106.18 / 0.356
φ′ = 35°
2.43 / 2.25
85.73 / 0.246
φ′ = 25° overturning below 2.00
1.73 / 1.95
105.98 / 0.419
γ = 20, γsat = 21 kN/m³
2.11 / 2.13
99.14 / 0.316
H = 3 m
3.36 / 3.07
58.26 / 0.057
H = 5 m three checks not satisfied
1.38 / 1.52
163.08 / 0.756
Heel 2.00 m
2.27 / 2.41
86.22 / 0.233
Heel 1.00 m
1.82 / 1.75
109.70 / 0.460
Toe 0.50 m partial contact
1.95 / 1.72
160.25 / 0.543
Base slab 0.50 m
2.03 / 2.22
78.52 / 0.236
Stem thickening toward the backfill
2.04 / 2.13
105.91 / 0.354
Constant stem, 0.50 m
2.04 / 2.03
108.24 / 0.376
Shelf off
1.58 / 1.90
109.39 / 0.448
Key off
1.69 / 2.10
92.83 / 0.320
Shelf and key off
1.31 / 1.90
107.50 / 0.446
Water off
4.45 / 6.01
78.18 / 0.018
Water table at the wall top, zw = 0
1.21 / 1.34
160.34 / 0.948
Uplift off
2.40 / 4.09
96.02 / 0.140
Front water 0.50 m overturning below 2.00
1.88 / 1.94
81.92 / 0.284
No front fill, hp = 0
1.40 / 2.04
75.26 / 0.229
μb = 0.45 only sliding changes
1.81 / 2.10
94.72 / 0.324
Full Rest passive state
1.58 / 2.10
94.72 / 0.324
Toe passive off
1.63 / 2.10
94.72 / 0.324
Water has the largest effect among the rows above: with the water switched off the sliding factor is 4.45 and the overturning factor 6.01; with the water table at the wall top they fall to 1.21 and 1.34, and the eccentricity reaches 0.948 m, outside B/6 = 0.575 m. The uplift acts the same way.
Height matters steeply: the thrust grows with H². From 3 m to 5 m the sliding factor goes from 3.36 to 1.38.
The heel helps overturning and eccentricity more than sliding: 1.00 m to 2.00 m raises FSo from 1.75 to 2.41. A longer toe lowers the largest base pressure: 160.25 kPa with a 0.50 m toe, 94.72 kPa with 1.25 m.
Only sliding responds to μb, the passive state, the toe switch and hignore: the overturning, the eccentricity and the bearing pressure do not use the passive resistance.
The concrete strength, the yield strength and the cover change nothing; γc changes the weights (2.08 for 25 kN/m³).
qall changes only the verdict: with 100 kPa the pressure of 94.72 kPa still passes, with 50 kPa it does not.
Messages: when the module stops, and what it warns about
Stops
When an input cannot be used, Analyze opens a window and nothing is calculated. A missing or out-of-range value gives Check the inputs, a bullet list of every message that applies, and the button Back to the model. A geometry or method that has no solution gives The wall could not be analysed with one message. The bar stays on Not analysed.
The window for a height of zero.
The window for a geometry without a solution.
When
Message
H is zero or empty
“The retained height H must be greater than zero.” (with it, the shelf and hp messages below usually follow)
Stem thickness is zero, or the base thinner than the top
“The stem thickness must be greater than zero.” / “The stem base thickness tb must be at least the top thickness tt.”
Toe, heel or slab out of range
“The toe projection Lt must be zero or more.” / “The heel projection Lh must be zero or more.” / “The base slab thickness tf must be greater than zero.”
β outside −45° to 45°
“The backfill slope β must lie between −45° and 45°.”
hp above H
“The passive-side fill height hp must lie between 0 and H.”
Unit weights
“Enter a positive moist unit weight γ.” / “Enter a positive saturated unit weight γsat.” / “γsat must exceed the water unit weight γw.” / “Enter a positive concrete unit weight γc.”
φ′ outside 0° to 60°
“The friction angle φ′ must lie between 0° and 60°.”
μb or qall not positive
“The base friction coefficient μb must be greater than zero.” / “The allowable bearing pressure must be greater than zero.”
A required factor not positive
“The stability criteria must be positive.”
Water
“The groundwater depth zw must be zero or more.” / “The front water height hwf must be zero or more.”
Shelf
“The shelf projection Ls and thickness ts must be greater than zero.” / “The shelf must lie within the stem height: hs − ts/2 > 0 and hs + ts/2 < H.”
Key
“The key width bk and depth dk must be greater than zero.” / “The key must lie under the base: 0 ≤ xk and xk + bk ≤ B.”
Earthquake
“kh must lie between 0 and 1.” / “kv must lie between 0 and 1.”
Passive settings
“The seismic passive credit factor ηp,E must lie between 0 and 1.” / “The unreliable top layer hignore must be zero or more.”
A surcharge load is not usable
“Strip load 1: the load q must be zero or more.” / “Strip load 1: the near edge x₁ must be zero or more.” / “Strip load 1: the far edge x₂ must be greater than the near edge x₁.” / “Point load 2: the load Q must be zero or more.” / “Point load 2: the distance x from the wall must be zero or more.” (the number is the place of the load in the table). When you press Add load on an incomplete form, the form itself says, for example, “The new load: the far edge x₂ must be greater than the near edge x₁.”
The backfill falls below the base slab at the heel
“The backfill surface must stay above the base slab at the heel.”
The size of β not below φ′ (Rankine)
“No real Rankine inclined-backfill solution for the entered β and φ′ (β must be smaller than φ′).”
Where several values are wrong, all their messages are listed together. An empty box in a required field gives the message of that field.
Warnings
Analysis runs, and the cautions are listed in the Attention window, in the Warnings (N) list and at the top of the Results tab. Each has a reason and a remedy:
Warning
Reason and remedy
Sliding or overturning factor of safety below the requirement (static or the seismic case) for example “FS = 1.38 < 1.50.”
Remedy: “Add or deepen a shear key, widen the base or increase the front resistance.” for sliding; “Lengthen the heel or the toe.” for overturning. A factor that is below its requirement never prints equal to it: when both round to the same two decimals, more decimals are shown, so for H = 4.7675 m in the example the text reads “FS = 1.4996 < 1.5000.” and the Sliding card shows 1.4996 / 1.5000.
Partial base contact
“The resultant lies outside the middle third, so part of the base lifts off.” Remedy: “Lengthen the base or the heel, or reduce the lateral load.”
Bearing pressure exceeds the allowable value
The largest pressure is above qall. Remedy: “Widen the base or reduce the loads.”
The seismic load cases are not evaluated
“No real Mononobe–Okabe equilibrium solution: the thrust has no maximum …” for kh = 0.6, for example. Remedy: “Change the soil and seismic parameters under Analysis Settings. The static case below is unaffected.”
Load case “Static” is not covered by the design envelope
“Its resultant falls outside the base, so it has no contact pressure and no design actions …” The case has no bearing value (“cannot be evaluated” in the Results tab).
The shelf tip reaches beyond the external pressure plane
“The relief shelf is wider than the heel, which the relief method does not cover.” Remedy: shorten the shelf or lengthen the heel.
Front water height exceeds the passive-side soil height
“The water in front of the wall stands above the front fill.”
The retained groundwater table is above the ground
“The groundwater table lies above the backfill surface at the heel, so free water would stand on the ground.”
The bar with warnings.
The cards when checks fail.
Good practice and common mistakes
Know what the plane is. The earth pressure acts on the vertical plane through the heel edge, and the soil between the stem and that plane is counted as weight. The thrust is parallel to the backfill, so a sloping backfill adds a vertical part Pa,V to the normal force.
Use the passive resistance with care. It is credited in sliding only. Start from the default state (1/3 passive), switch the toe off if the front soil may be removed (or enter hp = 0), and use hignore for frost, erosion or a future trench.
Give the water its real level. Water behind the wall raises the thrust and the uplift; in the example it lowers the sliding factor from 4.45 to 2.05.
Check the shelf against the heel. The relief method assumes the shelf is no wider than the heel; the module warns when it is.
Choose the earthquake coefficients yourself. The module applies the kh and kv you enter and runs both vertical directions; the passive credit ηp,E is 0 until you decide otherwise.
Read the governing case. On the cards and in the table the governing case of each check is outlined.
Use the actions for the reinforcement. The stem, toe, heel, shelf and key moments and shears are the inputs of the section design.
Enter loads in the unit system you chose. A strip or point load is measured from the back face of the wall at its top.
Keep a record. The report, a saved model file or a Quick Save keep what an analysis was based on.
Frequently asked questions
What does the Cantilever RC wall module check?
Sliding, overturning, eccentricity and bearing pressure of a reinforced-concrete cantilever wall, static and seismic, and the shear and moment in its stem, toe, heel, shelf and key. The example gives sliding 2.05, overturning 2.10, a largest base pressure of 94.72 kPa and an eccentricity of 0.324 m.
Why is the earth pressure taken on a vertical plane through the heel?
The wall is treated with the soil over the heel as one body: the thrust acts on the vertical plane through the heel edge, soil against soil, parallel to the backfill surface, and that soil is counted as weight. For this plane Rankine and Coulomb give the same coefficient.
Is there a difference between Rankine and Coulomb here?
No: for a vertical plane with the wall friction angle equal to β the Coulomb coefficient equals the Rankine one, and the example gives the same factors with either choice.
What is the pressure-relief shelf and what does the module do with it?
A horizontal slab on the back of the stem. Below its underside the soil self-weight pressure restarts and is reduced by R = min(Ls / bkr, 1). The relieved pressure is used on the stem and on the external plane; the surcharge and the water are not reduced. In the example R = 0.789 and the stem base moment falls from 84.63 to 69.62 kN·m/m.
What does the shear key add?
The passive resistance Pkey of the soil in front of the key is added to the sliding resistance. In the example the sliding factor is 2.05 with the key and 1.69 without it; the key weight still counts in the weights.
Is the passive resistance used in overturning and bearing?
No, in sliding only. That is why the passive state, the toe switch and hignore change the sliding factor and nothing else.
Do f′c, fy and the cover change the results?
No. They are kept with the model; only the concrete unit weight enters the weights. The stem and slab actions are given for your reinforcement design.
How does the earthquake work?
With Earthquake Yes the module runs Mononobe–Okabe for the soil, the hydrodynamic water pressure and the inertia of the wall and the soil that moves with it, for the vertical acceleration upward and downward, and reports each case; the lower factor governs. The seismic passive credit is ηp,E, 0 by default.
What values does the module accept?
For example H above zero, the size of β above −45° and below 45° and below φ′, φ′ from above 0° to below 60°, hp from 0 to H, kh and kv from 0 to below 1; the full list is in Messages. A missing or out-of-range value stops the analysis with a message that names it.
Can I drag the wall or the loads on the drawing?
No dragging of the section: change the values in the Model tab. The 3D View rotates by dragging, and double-clicking resets it. After Analyze the inputs are locked until you press Edit inputs.
Does the module remember my inputs?
Yes. Every change is kept in the browser and the page opens on the model you last worked on, analysed if it was. Reset to defaults brings back the example; Save to file and Quick Save keep copies.
What does the report contain?
A cover with your project details, then thirteen parts from the purpose and the design basis to the summary of results, with the drawings, saved as a PDF or a Word file after Analyze.
Check a gravity wall in stone masonry or plain concrete: sliding, overturning, eccentricity and bearing, static and seismic, with every force in a ledger you can follow. This manual walks through the screen, every input, the choice of method, the results and the report, with a worked example you can reproduce.
Gravity wall checks the external stability of a wall that holds the soil back by its own weight: a trapezoidal body on a stepped footing, in stone masonry or plain concrete. You draw the section with eight dimensions, describe one backfill soil, add surcharges, water and an earthquake if they apply, and the module works out every force on the wall per metre run, then checks four things:
Sliding along the base: FSs = (μb·Neff + Ptoe) / ΣHdrive.
Overturning about the toe, the front bottom corner of the footing: FSo = ΣMresisting / ΣMoverturning.
Bearing: the largest base pressure qmax against the allowable pressure qall.
Eccentricity of the base resultant against B/6, which keeps the whole base in contact.
The earth pressure acts on the vertical plane through the back edge of the footing; the soil between that plane and the back of the wall is counted as part of the wall. You choose Rankine or Coulomb for the static pressure, and the earthquake always uses Mononobe–Okabe with the horizontal and vertical coefficients you give. Groundwater on both sides, base uplift, uniform, strip and point surcharges, and passive resistance in front of the footing (sliding only) are optional.
Which retaining-wall module is for what
This module is for a wall that works by weight and is not reinforced: the body is treated as one rigid block, and its external stability is checked.
The Cantilever RC wall is for a reinforced-concrete wall with a stem, a toe and a heel, and gives the actions in the stem and the slabs.
The MSE wall is for reinforced soil, checked level by level.
Total height H from the underside of the base to the top, the top width Wu, the batter offsets on the front and back of the body, the footing projections and the footing heights, front and back.
The wall material
Stone masonry or plain concrete and its unit weight γm.
One soil
Moist and saturated unit weights, the effective friction angle φ′ (the soil is cohesionless: c′ = 0), the friction coefficient μb of the base on the foundation, and the allowable bearing pressure qall. The same soil is used behind the wall, in front of it and under the base.
The ground in front
The height Df of the ground above the underside of the base, and whether it may be removed (then enter zero).
Loads and water
Surcharges behind the wall, the groundwater depth behind the wall, a water level in front, and, for an earthquake, kh and kv.
The required factors
Four minimum factors of safety: sliding and overturning, static and seismic.
Quick start in eight steps
Open the module and choose the units
Open Gravity wall from the Retaining Walls family. Pick SI · kN, SI · tf or US at the top right; you can change it at any time, even after Analyze.
Draw the wall
In Geometry enter H, Wu, the batter offsets Wdl and Wdr, the footing projections Wbl and Wbr and the footing heights Hfl and Hfr. The drawing follows every change and the section shows the base width B.
Describe the ground
Set the backfill surface (Backfill Slope), the ground in front (Passive-Side Fill) and the soil (Soil Definition).
Add loads, water and the earthquake
In Surcharge Load add uniform, strip or point loads; in Groundwater switch the water on each side on; in Earthquake choose Yes and enter kh and kv.
Choose the material and the criteria
Pick Stone masonry or Plain concrete in Wall material and check the four required factors in Stability criteria.
Choose the method
In Analysis Settings choose Rankine or Coulomb, the passive state and the other options.
Press Analyze
Press Analyze. A window reports All checks satisfied or lists the warnings. Show results opens the Results tab; Stay on the model (offered with warnings) keeps the Model tab.
Read the answer and take the report
Results gives the four checks for the static case and each seismic case; Calculations shows the working; Report saves a PDF or a Word file.
The screen: four views of the wall
The layout is the one every GeoTerva module shares, described in the workspace guide. The drawing on the left has four views, chosen with the buttons above it, and a row of four summary cards below it.
2D View
A section of the wall with all its dimensions, the soil with its name, unit weights and friction angle, the backfill slope β, the ground in front, the water tables (dashed lines marked GWT) and the surcharges. The ringed mark pivot O is the toe, the point the overturning moments are taken about. The 2D view follows your inputs before Analyze and after it.
Strip and point loads appear on the drawing with their values and distances from the back face of the wall at its top. The drawing is scaled so that the farthest strip or point load stands on the drawn ground, and the labels of a uniform, a strip and a point load are stacked so that they do not overlap.
Nothing on the drawing is dragged to change a value. A strip or point load is pressed on the drawing to open it in the load form of the Surcharge Load section.
2D View with a strip load and a point load.
3D View
The wall extruded along its length, a picture of the section you entered. Drag to rotate · double-click to reset: dragging turns the wall, and a double-click returns the starting angle. The 3D view shows the wall only: loads, water and results are not drawn in it.
3D View.
Pressure and Forces
Both views are available after Analyze; before it they say “Not analysed — press Analyze on the Model tab”. They are drawings of the same results, with chips above them:
Pressure draws the pressures on the Virtual back (the plane x = B through the back edge of the footing), on the Front resistance of the footing, or the water pressure under the base (Base uplift). The last two are offered when the model has them, and in those two views the Layers group gives way to a Shown note, because their content is fixed. Load case switches between Static and the seismic cases; Layers shows or hides each component: soil, surcharge, strip and point loads, seismic increment, seismic total, hydrostatic and hydrodynamic water, and the resultant.
Forces draws the free body of the wall: every wall part (C1, C2 …) and soil zone (S1, S2 …) with its weight and lever arm, the thrusts, the uplift, the inertia forces, the pivot O, the totals ΣMo, ΣMr and the factor FSo. Its Load case and Layers chips (Weights, Earth pressure, Surcharge, Water & uplift, Seismic, Front resistance) work as in the Pressure view.
The (?) beside each chip group explains it. The chips change only what is drawn; the checks always use every component.
Pressure view, static case with groundwater behind the wall.
Forces view, static case.
Pressure view on Base uplift.
Forces view, seismic case with kv upward.
The summary cards
Four cards under the drawing: Sliding, Overturning, Bearing capacity and Eccentricity. Each shows the Static value against its limit and the Seismic value, the governing seismic case. Before Analyze every value is a dash. Afterwards a card is green when its checks pass and red when one fails; without an earthquake the Seismic side reads a dash and “not analysed”.
The summary cards.
Entering the model, section by section
The Model tab is a column of sections. Each opens when you click its title and the others close; Next and Back walk you through. Analyze waits in the bar at the bottom. Units are shown beside the boxes: where two or three are given, they are SI · kN, SI · tf and US in turn. Defaults are the SI · kN values; in US the same example shows, for instance, 9.84 ft for H, 114.59 pcf for γ and 4.177 ksf for qall. The module stops the analysis for values outside the limits named in the field tables; the messages are listed in Messages.
Model data
The first section holds the model itself, not a calculation input. Every change is kept in this browser, so the page opens again with the wall you last modelled, analysed or not. The unit system and the Calculations level of detail are remembered too.
Model name: a label for the model; it is offered when you save.
Save to file… writes the model to a .json file (the browser’s Save window where it has one, otherwise a download); 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, or Delete. A name that exists asks whether to replace it. A Quick Save holds every input, whether the model was analysed, and the report cover, and lives only in this browser; use a file to move a model.
Reset to defaults returns every input to the example without a question (the unit system stays) and says “The inputs are back at the module defaults, and this is now the model kept in the browser.”
Model data.
Geometry
A trapezoidal body on a stepped footing. H is the total height from the underside of the base to the top of the wall; the batter offsets and the footing projections and heights are set separately on the front (toward the toe) and on the back (toward the backfill). The section shows the derived base widthB = Wbl + Wdl + Wu + Wdr + Wbr and says the analysis strip is 1.0 m (all forces are per metre run).
Geometry.
Field
Default
What to enter
H total wall height
3.00 m · ft
Greater than zero. The two footing heights must be smaller than H.
Wu top width
1.00 m · ft
Greater than zero.
Wdl, Wdr batter offsets, front and back
0.50 m · ft each
Zero or more; zero gives a vertical face.
Wbl, Wbr footing projections, front and back
0.50 m · ft each
Zero or more.
Hfl, Hfr footing heights, front and back
0.50 m · ft each
Greater than zero and smaller than H.
Backfill Slope
Flat (the default) or Inclined. For Inclined enter the slope angle β in degrees; it rises away from the wall when positive and falls away when negative. The uniform surcharge follows the same ground line, and a readout shows the surface mode and the slope.
Backfill Slope.
Field
Default
What to enter
β backfill slope angle
0.0°
Between −45° and 45°, the limits themselves refused; the box arrows run over the same range, −44.5° to 44.5°. The magnitude must also stay below φ′ (see Messages). A flat backfill sets β = 0.
Passive-Side Fill
The height Df of the ground in front of the wall above the underside of the base. Where it stands above the top of the front footing (Hfl), the fill over the footing moves with the wall and its weight is a vertical load. The lateral resistance on the front face of the footing, from the front ground (less hignore) down to the base, is credited at the state chosen in Analysis Settings. Enter Df = 0 if the front soil may be removed.
Passive-Side Fill.
Field
Default
What to enter
Df front ground height
0.00 m · ft
From 0 to H.
Soil Definition
One soil for the backfill, the ground in front and the foundation. The soil is cohesionless (c′ = 0).
Soil Definition.
Field
Default
What to enter
Name
Soil
The label shown on the drawing.
γ moist unit weight
18.0 kN/m³ · t/m³ · pcf
Greater than zero.
γsat saturated unit weight
20.0 kN/m³ · t/m³ · pcf
Greater than zero and greater than γw. Used below the water table.
φ′ effective friction angle
30.0°
Greater than 0° and smaller than 60°.
μb base friction coefficient
0.55
Greater than zero. The base resists sliding by μb·Neff; no adhesion is used.
qall allowable bearing pressure
200 kPa · t/m² · ksf
Greater than zero.
Surcharge Load
Up to six loads on the ground behind the wall, of three kinds. Choose the kind in New load, fill its boxes and press + Add load: it joins the table (“0 of 6”, “1 of 6” … counts them). Press a row, or the load on the drawing, to edit it (Done returns to a new load; Delete load removes it; × removes a row). Several uniform loads add up.
The lateral pressure of a strip or point load is taken by the elastic solutions for a rigid wall, as the section says. A load with a zero value is left out of the calculation.
Surcharge Load with three loads in the table.
Field
Default
What to enter
q uniform surcharge
10.0 kPa · t/m² · ksf in the form
Zero or more; acts over the whole retained surface. The table starts empty, so the example has no surcharge until you press Add load.
qs strip load; x1, x2 edges
empty
Load zero or more; near edge x1 zero or more; far edge x2 greater than x1 (the box stops at 0.1). Distances run from the back face of the wall at its top.
Q point load; x distance
empty
Load zero or more; distance zero or more. A point load closer than 0.30 m is calculated at 0.30 m.
Groundwater
Two independent switches, both off in the example. Retained side water: zw is the depth of the water table below the top of the wall, and γw the unit weight of water. Front-side water: hwf is the height of water above the underside of the base in front of the wall. Below the retained water table the soil is taken at γsat, with the pore pressure as a force of its own.
Groundwater with both sides switched on.
Field
Default
What to enter
zw water depth below the wall top
1.50 m · ft
Zero or more.
γw water unit weight
9.81 kN/m³ · 1.00 t/m³ · 62.45 pcf
Greater than zero; γsat must exceed it.
hwf front water height
0.30 m · ft
Zero or more.
Earthquake
No (the default) or Yes. With Yes the module adds the seismic cases: Mononobe–Okabe thrust on the same pressure plane, the inertia of the wall and of the soil that moves with it, and hydrodynamic water. kv is taken upward and downward, and both cases are checked; with kv = 0 there is a single case.
The module takes kh and kv as you enter them.
Earthquake.
Field
Default
What to enter
kh horizontal coefficient
0.15
From 0 up to, not including, 1.
kv vertical coefficient
0.10
From 0 up to, not including, 1.
Wall material
Stone masonry (the default, 22 kN/m³) or Plain concrete (24 kN/m³). Choosing a material sets its usual unit weight; the value in the box can then be changed.
Wall material.
Field
Default
What to enter
γm unit weight of the wall
22.0 kN/m³ · 2.24 t/m³ · 140.05 pcf
Greater than zero.
Stability criteria
The minimum factors of safety the checks are compared with. The eccentricity limit B/6 and the allowable pressure are not entered here.
Stability criteria.
Field
Default
What to enter
FSs sliding, static
1.50
Greater than zero.
FSo overturning, static
2.00
Greater than zero.
FSse sliding, seismic
1.10
Greater than zero.
FSoe overturning, seismic
1.10
Greater than zero.
Analysis Settings
The method and the options of the passive resistance and the uplift. They are described in Choosing the method.
The passive state offers Full Passive, 2/3 Passive + 1/3 Rest, 1/3 Passive + 2/3 Rest (the default) and Full Rest.
Analysis Settings.
Field
Default
What to enter
Static earth pressure
Rankine
Rankine or Coulomb.
w passive state
1/3 Passive + 2/3 Rest
Four choices, listed below the table.
toe: include toe passive resistance
on
A switch.
hignore unreliable top layer
0.00 m · ft
Zero or more.
ηp,E seismic passive credit
0.00
From 0 to 1.
Base uplift: Include
on
A switch.
Choosing the method and the options
Static earth pressure: Rankine or Coulomb
Both act on the vertical plane through the back edge of the footing (x = B), soil against soil, so no wall friction is used: the thrust is parallel to the backfill surface (δ = β). For this plane the Coulomb thrust equals the Rankine thrust exactly. With a flat backfill the two give the same Ka; with a sloping backfill the Rankine card shows the horizontal coefficient and the Coulomb card the coefficient along the surface, and the forces are identical. In the example with β = 10° the module gives Ka = 0.3442 for Rankine and 0.3495 for Coulomb, and the same sliding factor of 2.75, overturning factor of 8.53 and qmax of 61.80 kPa in both.
Seismic earth pressure: Mononobe–Okabe
Always Mononobe–Okabe, on the same plane. The module finds θ = tan⁻¹(kh / (1 ± kv)), the thrust PAE and the increment ΔPAE = PAE − PA over the static thrust, which acts at 0.6 of the plane height above its bottom. The static thrust keeps its static diagram. Hydrodynamic water is always included when the earthquake is on and water is present.
Passive resistance in front of the footing
The soil in front adds a resistance to sliding only (never to overturning or bearing): Ptoe = ∫Kmob·σ′v dz over the front face of the footing, with Kmob = w·Kp + (1 − w)·K0, Rankine Kp, Jaky K0. The passive statew chooses how much of the full passive resistance is relied on. The weight of the fill over the front footing is used whether the toe switch is on or off.
The table gives the resistance and the sliding factor of the example with Df = 0.8 m (nothing else changed; the foundation is the same soil):
Option
Ptoe kN/m
FSs
Full Passive (w = 1)
17.28
3.74
2/3 Passive + 1/3 Rest
12.48
3.56
1/3 Passive + 2/3 Rest (the default)
7.68
3.38
Full Rest (w = 0)
2.88
3.21
Toe switch off
0.00
3.10
hignore lowers the ground the passive stresses start from, for soil that may be lost to frost, erosion or a trench. With hignore = 0.3 m the example gives Ptoe = 3.00 kN/m and FSs = 3.21.
ηp,E is the share of Ptoe credited in the seismic cases; the default 0 gives friction only. With Df = 0.8 m and an earthquake, 0 gives a seismic sliding factor of 1.36 (kᵥ upward) and 0.5 gives 1.43.
The (?) beside the passive-resistance options opens a window with a sketch of each option and its formula; it is a reading aid and changes nothing.
The (?) window of the passive resistance (its small heading says Geometry help).
Base uplift
With water present, the pore pressure under the base is a linear head between the retained and the front water levels, and its resultant U reduces the effective normal force. It is a drainage assumption about the foundation; a blocked drain or an artesian layer needs its own head. In the example with the retained water on, U = 22.07 kN/m at x = 2.000 m from the toe, and switching the uplift off changes the sliding factor from 2.01 to 2.36.
Analyze and read the results
Press Analyze. A progress bar runs, the model locks, and a window opens:
All checks satisfied with “Every stability check of this model is satisfied and the calculation raised no warning.” and Show results.
Attention — N warnings with “Review these points before the results are used.”, the warnings, Show results and Stay on the model.
The bar then reads Analysed — all checks satisfied (or Analysed — N warnings) with Edit inputs and, with warnings, a Warnings (N) button that opens the list again. Edit inputs asks “The results will be cleared. Edit the inputs?” and unlocks the model. The unit system can still be changed while the model is locked; the cards and tables convert. The analysed state is kept in the browser with the model.
The window after Analyze with warnings.
The Results tab
Opened by Show results, or by the tab. Design checks is a table of the four checks (and the information line qmin ≥ 0) for the static case and for each seismic case. Each cell gives the value, the limit and the verdict, with a bar of demand over capacity (FS: required / FS; qmax / qall; |e| / (B/6)) and a tick at 1.0. The case that governs each check is outlined and marked GOVERNING. A banner above says All checks satisfied or, for example, 1 check not satisfied, naming the check.
Design checks of the example.
Check
Limit
The example
Sliding FSs
required 1.50
3.04
Overturning FSo
required 2.00
9.68
Bearing qmax
limit 200.00 kPa
56.75 kPa
Eccentricity |e|
limit 0.500 m
0.070 m
qmin (information)
full contact
42.75 kPa
Verdicts are OK and NOT OK; qmin is marked info (a negative qmin says the base is only partly in contact, the same condition as |e| > B/6). Where the resultant falls outside the base the bearing and eccentricity cells say cannot be evaluated with the reason.
Design checks with an earthquake: sliding fails in the governing case.
Below the checks the tab gives the pressure resultants (the horizontal resultant and height of each component, the uplift, the seismic total and increment, the hydrodynamic water and the inertia), the weights, lever arms and moments of the wall parts and the soil zones with a polygon check, and cards for the earth pressure (Ka, Kae, Pa, the water force) and for the static and seismic stability.
Pressure resultants.
Reading a failing check
When a check fails, its cell shows NOT OK in red, the card under the drawing turns red, and the warnings name the cause and a remedy, for example “Widen the base or increase the front resistance.”
A model with two failing checks.
The Calculations tab, the report and the Theory tab
Calculations
Two levels, chosen with Summary and Detailed above the working; the choice is kept in the browser. A contents list opens each section, with open all and close all.
Summary has one short step per result with the formula and your numbers: Geometry and weights, Earth-pressure coefficients, one Load case section for the static case and each seismic case (resultants, sliding, overturning, bearing), and a Summary of checks. Four sections for a static model, six with the two seismic cases.
Detailed is the full working in eight sections: Input data (every value the calculation uses), Geometry and wall components (each part with area, centroid, weight and moment), Soil weights, Earth-pressure coefficients and stresses, Pressures, Stability (the force ledger, sliding, the moments about the toe, the base pressure), Summary of checks, and Assumptions and warnings. With an earthquake each seismic case adds its own Seismic case, Pressures and Stability sections: fourteen sections with both kv directions.
Calculations, Summary level.
Calculations, Detailed level.
Report
Fill the Report cover (project, location, client, report number, date, prepared by, title or qualification, checked by, and optional notes printed only when filled in). It is kept in the browser and saved with the model file. Save as PDF and Download Word (.docx) are greyed out until the model is analysed. The module offers one report, the Summary report, and the preview below the buttons is that report.
Its parts follow the model: for the example, 1 Purpose and scope, 2 Design basis and assumptions, 3 Geometry and section, 4 Soil, material and load parameters, 5 Resisting forces, 6 Lateral earth pressure coefficients, 7 Driving forces, 8 Overturning check, 9 Sliding check, 10 Eccentricity and base pressure, 11 Summary of results. With an earthquake, Seismic parameters is added and the driving forces and the overturning check gain the seismic cases (12 parts).
The Report tab: the cover form and the first page.
Theory
The Theory tab explains the model in sections that open one by one: an overview and the wall system, the coordinates and free body, the geometry decomposition, the soil moving with the wall, effective stress, Rankine, Coulomb, at-rest and passive resistance, surcharge, hydrostatic water and uplift, Mononobe–Okabe, hydrodynamic water, the inertia of the wall and the soil, sliding, overturning and bearing, the scope of the checks, a worked example, the variables and the references. The internal stresses of the masonry or concrete body (compression, tension, shear along joints) belong to the structural design of the wall.
Worked example: the module’s own example
The module opens on this wall. All values are per metre run of wall.
H = 3.00 m, Wu = 1.00 m, Wdl = Wdr = 0.50 m, Wbl = Wbr = 0.50 m, Hfl = Hfr = 0.50 m, so B = 3.00 m
Soil
γ, φ′, μb, qall
18.0 kN/m³, 30°, 0.55, 200 kPa
Material
γm
stone masonry, 22.0 kN/m³
Others
flat backfill, Df = 0, no loads, no water, no earthquake
Rankine, passive state 1/3 Passive + 2/3 Rest
Weights
Five wall parts: the front block 11.00 kN/m at x̄ = 0.500 m, the front batter 13.75 at 0.833, the core 66.00 at 1.500, the back batter 13.75 at 2.167 and the back block 11.00 at 2.500: Wm = 115.50 kN/m with a moment of 173.25 kN·m/m about the toe. The soil that moves with the wall (1.875 m² × 18) is Ws = 33.75 kN/m at x̄ = 2.611 m, moment 88.13. N = 115.50 + 33.75 = 149.25 kN/m.
Earth pressure
Ka = (1 − sin 30°) / (1 + sin 30°) = 0.3333; the pressure is 0 at the top and Ka·γ·H = 18.00 kPa at the base, so Pa = ½ · 0.3333 · 18 · 3.00² = 27.00 kN/m, at H/3 = 1.000 m above the base. Passive resistance is zero (Df = 0).
xR = (261.375 − 27.00) / 149.25 = 1.5704 m from the toe, so e = B/2 − xR = 1.5000 − 1.5704 = −0.0704 m (the Results tab shows 0.070 m), which is inside B/6 = 0.500 m. qmax = 149.25 / 3 · (1 + 6 · 0.0704 / 3) = 56.75 kPa and qmin = 42.75 kPa, against qall = 200 kPa. These are the numbers of the Results tab, the Calculations tab and the report.
The same wall with an earthquake
Switch Earthquake to Yes (kh = 0.15, kv = 0.10). With kv upward, θ = tan⁻¹(0.15 / 0.90) = 9.46°; Mononobe–Okabe gives PAE = 32.51 kN/m, an increment of 5.51 acting at 1.800 m, and the inertia of the wall and soil is 0.15 × 149.25 = 22.39 kN/m. Sliding: FSs = 0.55 × 134.325 / (32.51 + 22.39) = 1.35. Overturning: the upward kv·W adds to the overturning moment, Mo = 93.79 kN·m/m, so FSo = 261.375 / 93.79 = 2.79; qmax = 67.37 kPa and |e| = 0.252 m. With kv downward, θ = 7.77° and the factors are 1.50 (sliding), 3.74 (overturning) and qmax = 78.51 kPa. All against 1.10, 1.10 and 200 kPa: OK. The Results tab marks the kᵥ upward case as governing for sliding and overturning.
The same kind of wall in US units and in SI · tf
In US, enter H = 12 ft, Wu = 3 ft, the batter offsets, the footing projections and the footing heights 1.5 ft each, γ = 115 pcf, γsat = 125 pcf, φ′ = 32°, μb = 0.5 and qall = 4 ksf (the wall unit weight stays at its default, 140.05 pcf). The module gives FSs = 2.21, FSo = 5.85, qmax = 1.33 ksf and |e| = 0.100 ft. In SI · tf with H = 4 m, γ = 1.9, γsat = 2.1 and γm = 2.3 t/m³, φ′ = 32° and qall = 25 t/m² (other values as in the example), it gives FSs = 2.42, FSo = 5.83 and qmax = 7.29 t/m². A hand calculation of the same walls in SI units with the converted values gives the same factors.
How each input changes the answer
Each row changes one thing in the example (H = 3 m, Wu = 1 m, batters, projections and footing heights 0.5 m, γ = 18 kN/m³, γsat = 20 kN/m³, φ′ = 30°, μb = 0.55, γm = 22 kN/m³, flat backfill, no loads, no water, no earthquake, Rankine) and runs the module again; a remark under the change names anything else that is set. The numbers are the ones the module gives, so you can reproduce any row.
The example with one change at a time (static case unless stated)
γ = 20 kN/m³ the backfill is heavier · qmax = 58.78 kPa
2.81
9.04
H = 4 m all other dimensions as in the example · qmax = 72.92 kPa
2.24
5.41
H = 5 m all other dimensions as in the example · qmax = 119.08 kPa
1.78
3.45
Wu = 1.5 m B = 3.5 m · qmax = 61.35 kPa
3.71
13.51
Wbr = 1.0 m the back footing is longer, B = 3.5 m · qmax = 58.08 kPa
3.61
13.05
Wbl = 1.0 m the toe is longer, B = 3.5 m · qmax = 63.59 kPa
3.15
12.50
μb = 0.40 only sliding changes · qmax = 56.75 kPa
2.21
9.68
β = 10° (Inclined) Rankine; the Coulomb option gives the same · qmax = 61.80 kPa
2.75
8.53
A uniform surcharge of 10 kPa added in Surcharge Load · qmax = 52.75 kPa
2.22
6.22
Retained water on, zw = 1.5 m uplift on (default) · qmax = 44.89 kPa
2.01
3.52
Retained water on, uplift off zw = 1.5 m · qmax = 55.41 kPa
2.36
8.52
Retained water on, zw = 0.5 m uplift on; the module warns · qmax = 54.07 kPa
1.28
2.25
Df = 0.8 m passive state 1/3 Passive + 2/3 Rest, toe on · qmax = 55.35 kPa
3.38
9.71
Earthquake, kᵥ upward kh = 0.15, kv = 0.10; the governing case · qmax = 67.37 kPa
1.35
2.79
What the rows show:
Height has a large effect. Raising H to 5 m while the base stays 3 m wide takes FSo from 9.68 to 3.45 and qmax from 56.75 to 119.08 kPa: the thrust grows with H², the moment with H³.
A longer toe raises overturning and sliding but also the toe pressure: Wbl = 1 m gives qmax = 63.59 kPa and qmin = 24.84 kPa, against 56.75 and 42.75 for the example.
Water behind the wall costs a great deal: FSo falls from 9.68 to 3.52 with zw = 1.5 m, and to 2.25 with zw = 0.5 m. The uplift is a large part of it: with the uplift off FSo is 8.52.
μb changes sliding only.FSs goes from 3.04 to 2.21 and nothing else moves.
A sloping backfill, a surcharge and the friction angle act through the thrust: φ′ = 25° raises Pa from 27.00 to 32.88 kN/m, φ′ = 35° lowers it to 21.95.
The earthquake takes sliding to 1.35 and overturning to 2.79 in the governing case; the seismic requirement is lower (1.10), and the retained water with zw = 0.5 m gives lower factors still.
Messages: when the module stops and when it warns
Stops
When a value cannot be used, Analyze opens a window titled Check the inputs with the problems in a list and the button Back to the model. Nothing is calculated; the bar keeps Not analysed. Correct the values and press Analyze again. A combination of values that has no solution opens a window of its own, listed in the table.
The stop window for H = 0.
When
Message
H is zero or empty
“The wall height H must be greater than zero.” (with H = 0 the two footing heights are reported as well: “The front footing height Hfl must lie between 0 and H.” and “The back footing height Hfr must lie between 0 and H.”)
Wu is zero
“The top width Wu must be greater than zero.”
A batter offset is negative
“The batter offsets Wdl and Wdr must be zero or more.”
A footing projection is negative
“The footing projections Wbl and Wbr must be zero or more.”
A footing height is zero or not below H
“The front footing height Hfl must lie between 0 and H.” or “The back footing height Hfr must lie between 0 and H.”
β outside −45° to 45° (or at a limit)
“The backfill slope β must lie between −45° and 45°.”
β not smaller than φ′ in magnitude
A different window, titled The wall could not be analysed: “No real Rankine inclined-backfill solution for the entered β and φ′ (β must be smaller than φ′).” With Coulomb: “No real Coulomb solution for the entered β and φ′.”
Df above H
“The front ground height Df must lie between 0 and H.”
γ or γsat not positive; γsat not above γw
“Enter a positive moist unit weight γ.” · “Enter a positive saturated unit weight γsat.” · “γsat must exceed the water unit weight γw.”
φ′ zero or 60° and above
“The friction angle φ′ must lie between 0° and 60°.”
μb or qall not positive
“The base friction coefficient μᵦ must be greater than zero.” · “The allowable bearing pressure must be greater than zero.”
γm not positive; a required factor not positive
“Enter a positive unit weight of the wall material.” · “The stability criteria must be positive.”
Water on and zw or hwf negative
“The groundwater depth zw must be zero or more.” · “The front water height hwf must be zero or more.”
Earthquake on and kh or kv not below 1
“kₕ must lie between 0 and 1.” · “kᵥ must lie between 0 and 1.”
ηp,E outside 0 to 1; hignore negative
“The seismic passive credit factor ηp,E must lie between 0 and 1.” · “The unreliable top layer hignore must be zero or more.”
A strip or point load is incomplete
For example “Strip load 2: the far edge x₂ must be greater than the near edge x₁.” When you press Add load with such values, the form says “The new load: the far edge x₂ must be greater than the near edge x₁.”
When several values are wrong the messages are listed together.
Warnings
The module calculates and reports, and the window Attention — N warnings lists what to review, each with a remedy. The messages, as the module words them:
“Sliding factor of safety below the requirement (static). FS = 0.99 < 1.50. Widen the base or increase the front resistance.” (also for each seismic case, written “(seismic +kₕ, kᵥ upward)” or “downward”).
“Overturning factor of safety below the requirement (static). FS = 1.75 < 2.00. Widen the footing (Wbl, Wbr) or the body of the wall.”
“Bearing pressure exceeds the allowable value (static). qmax = 56.75 kPa > qall = 40.00 kPa. Widen the base or reduce the loads.”
“Partial base contact (seismic +kₕ, kᵥ upward). The resultant lies outside the middle third, so part of the base lifts off. Widen the base or reduce the lateral load.”
“The retained groundwater table is 0.176 m above the ground at the top of the pressure plane (Static): the water column is taken to the plane bottom (hw = 3.000 m) and only its part below the plane top loads the plane.” followed by “The groundwater table lies above the backfill surface behind the wall, so free water would stand on the ground. Check the groundwater depth zw and the backfill slope β.”
“The seismic load cases are not evaluated. No real Mononobe–Okabe equilibrium solution: the thrust has no maximum — it keeps growing as the failure plane approaches the backfill surface (θ = 37.87° > φ′ − β = 30.00°). Change the soil and seismic parameters under Analysis Settings. The static case below is unaffected.” (shown, for example, with φ′ = 30°, kh = 0.70 and kv = 0.10).
“Front water height exceeds the passive-side soil height.” followed by “The water in front of the wall stands above the front fill. Check the front water height hwf against the front ground height Df.”
Where the resultant falls outside the base, the bearing and eccentricity cells read cannot be evaluated with “The resultant falls outside the base — the wall overturns.”
Good practice and common mistakes
Enter Df = 0 when the soil in front may be removed. Then no fill weight and no passive resistance are credited. If you keep the front soil, consider hignore for the top layer that frost, erosion or a trench can take away.
Treat water honestly. Behind the wall it cuts FSo by a large factor in the example; a wall with no drain needs the water switched on. Switch the uplift off only when the base is drained.
Read the dynamic card as the governing seismic case. Look at both kv directions in the Results tab; the weaker one governs.
Mind the sign of β. A positive angle rises away from the wall and raises the thrust; a negative one falls away.
Use the passive state you can rely on. The default 1/3 Passive + 2/3 Rest credits a modest part of the passive resistance; the seismic credit ηp,E is 0 unless you decide otherwise.
Add loads one by one and check the table. Up to six; strip and point loads are measured from the back face of the wall at its top.
The checks are external. The module treats the body as one rigid block; the internal stresses of the masonry or concrete are for the structural design.
Keep a record. Use Save to file for the project; the browser keeps the last model, and Quick Saves live in this browser only.
Frequently asked questions
What does the module check?
Sliding along the base, overturning about the toe, the largest base pressure against the allowable pressure, and the eccentricity of the base resultant against B/6, for the static case and, with an earthquake, for kv upward and downward. The example gives 3.04, 9.68, 56.75 kPa and 0.070 m.
On what plane is the earth pressure calculated?
On the vertical plane through the back edge of the footing, soil against soil, with the thrust parallel to the backfill surface. The soil between that plane and the back of the wall is counted as weight that moves with the wall. For this plane Coulomb and Rankine give the same thrust.
Which earth-pressure theory does the earthquake use?
Mononobe–Okabe, always, on the same plane, with the kh and kv you enter; the increment over the static thrust acts at 0.6 of the plane height above its bottom. kv is applied upward and downward and both cases are checked.
Does passive resistance help overturning or bearing?
No. The resistance of the soil in front of the footing is added to sliding only. Its state (w), the toe switch, hignore and, for the earthquake, ηp,E control how much is credited.
What if the front soil may be removed?
Enter Df = 0. Then there is no fill over the front footing and no passive resistance in the checks.
How many surcharges can I add, and how are they placed?
Up to six: uniform (over the whole surface), strip (near and far edge) and point (distance from the wall). Distances are measured from the back face of the wall at its top. A point load closer than 0.30 m is calculated at 0.30 m.
Can I move the wall or a load by dragging on the drawing?
No. Values are entered in the boxes. The only actions on the drawings are pressing a load to open it in the form, and, in the 3D view, dragging to rotate and double-clicking to reset.
Does the module remember my inputs?
Yes. Every change is kept in this browser, including whether the model was analysed, the unit system and the level of detail of the Calculations tab. The page opens on the last model; Reset to defaults returns to the example. Save to file and Quick Save keep versions.
Why does the Analyze window show warnings when every card is green?
Warnings also cover input conditions, for example a groundwater table above the ground behind the wall, or front water standing above the front fill. They are listed in the window and under Warnings in the bar.
Why is the overturning factor so much larger than the sliding factor in the example?
The weight acts about 1.5 m from the toe while the thrust acts about 1 m above the base, so the restoring moment is large; sliding depends on friction alone. Both are computed from the same forces, which you can follow in the force ledger of the Detailed calculation.
How do I change the unit system?
Choose SI · kN, SI · tf or US at the top right, before or after Analyze. Boxes, cards, tables and drawings convert; the calculation is the same. The module notes the unit beside every box.
What does the report contain?
A cover with your project details, then parts for the purpose and scope, the design basis and assumptions, the geometry, the soil, material and load parameters, the resisting forces, the earth-pressure coefficients, the driving forces, the overturning check, the sliding check, the eccentricity and base pressure, and a summary of results. It is saved as a PDF or a Word file after Analyze.
Check a mechanically stabilized earth wall of granular fill reinforced by galvanized steel strips, geotextile sheets or geogrids: the tension, the rupture and the pullout of every level, the connection to the facing, and the overturning, eccentricity, sliding and bearing of the reinforced block, static and under an earthquake. This manual walks through the screen, every input, the two procedures, the results, the working and the report, with a worked example you can reproduce.
MSE wall checks a mechanically stabilized earth wall: a wall of free-draining granular fill with galvanized steel strips, geotextile sheets or geogrids laid in it level by level behind a facing. The fill takes the compression, the reinforcement the tension, and the friction between them holds the two together. The module gives the tension of every reinforcement level and checks each level for rupture, for pullout beyond the failure surface and, if you give its strength, for the connection to the facing. It then checks the reinforced block as a gravity wall for overturning, the eccentricity of the resultant, sliding on the base and bearing of the foundation soil on Meyerhof’s effective width, and repeats the checks under an earthquake.
Two procedures are offered. The simplified method (FHWA / AASHTO) raises the lateral stress for steel strips (Kr = 1.7 Ka at the top falling to 1.2 Ka at 6 m) and uses a bilinear failure surface 0.3 H behind the facing in the upper half of the wall; for a geosynthetic it takes Ka and the Rankine surface. Rankine at every depth (the source) takes Ka at every depth and the Rankine wedge from the toe for every kind of reinforcement.
Ka = tan²(45° − φ′1/2), T = σ′hSVSH (a strip), T = σ′hSV (a sheet, per metre of wall)
What you can describe
A wall heightH, a reinforcement lengthL (the same at every level, from the back of the facing) and the vertical spacingSV; for strips also the horizontal spacingSH.
Galvanized steel strips (width, thickness, yield strength, corrosion per year and design life), geotextile sheets or a geogrid (ultimate strength, three reduction factors, and for a geogrid the coverage ratio).
The pullout resistance factorF* and the scale effect correctionα, which the module fills in and you can type over from pullout tests.
The reinforced fill, the retained fill behind the block and the foundation soil.
One uniform surcharge on the whole surface, taken as a live load.
A horizontal seismic coefficientkh.
The five required factors of safety, and optionally the strength of the connection to the facing.
The module gives the internal and the external checks of the wall. Combine them with a slope stability analysis of the whole wall and the ground below it, which the module reminds you of in every run (see Messages).
Before you start: what you need
Have these ready from your design and your ground investigation:
What and source
Notes
The wall Your design
Height H (1 to 30 m), reinforcement length L and the spacings SV (0.2 to 2 m) and, for strips, SH. The practice takes L not less than 0.7 H and not less than 2.4 m; the module cautions you when it is shorter.
The reinforcement The maker’s data
For strips: width, thickness as placed, yield strength, the loss of thickness per year and the design life. For a geosynthetic: the ultimate tensile strength from the wide-width test, the reduction factors for installation damage, creep and chemical and biological degradation, and for a geogrid the coverage ratio.
Pullout data Pullout tests, if you have them
The factors F* and α fill themselves; type over them with the values of your tests.
The soils Your ground investigation
Unit weight and friction angle of the reinforced fill and of the retained fill; unit weight, friction angle and cohesion of the foundation soil.
The loads Your design loading
A uniform surcharge on the surface, and the seismic coefficient kh if the earthquake governs.
The required factors Your design basis
Rupture, pullout, overturning, sliding and bearing; the module opens on 1.8 (strips) or 1.5 (sheets), 1.5, 2, 1.5 and 2.5. The strength of the connection per strip or per metre of wall, if it is known.
Quick start in eight steps
Open the module and choose the units
Open MSE wall from the Retaining Walls family. Pick SI · kN, SI · tf or US in the header; you can change it at any time, also after Analyze.
Choose the procedure and describe the wall
In Wall and reinforcement layout choose Simplified method (FHWA / AASHTO) or Rankine at every depth (the source) and enter H, L, SV and, for strips, SH.
Choose the reinforcement
In Reinforcement press Galvanized steel strips, Geotextile sheets or Geogrid and enter its data. Pullout resistance has F* and α, already filled in.
Describe the soils
In Fills and Foundation soil enter the unit weights and the strength. The retained fill follows the reinforced fill until you type over it.
Add the surcharge and the earthquake
In Surcharge enter q and press + Add load; in Earthquake enter kh (0 means no earthquake).
Set the required factors
In Required factors check the five factors and, if you know it, enter the strength of the connection.
Press Analyze
Press Analyze at the foot of the Model tab. The bar reads Analysed, the inputs lock and the drawing colours every level by its factors. If the run has warnings, a Warnings window opens by itself. A mistake in the inputs opens Cannot analyse with what to correct.
Read the results and take the working
The Results tab gives the cards, the tension and the length the checks ask for and the table of the levels; Calculations writes out every step with your numbers; Report saves a PDF or a Word file.
The screen: views, chips and zoom
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 four views, chosen above it:
Section is the wall in section: the facing, the reinforcement levels with their length L, the retained fill, the foundation soil, the failure surface of the chosen procedure, the surcharge and the dimensions H, SV and L. Before Analyze it follows your inputs. After Analyze every level is coloured by its factors (green passes, amber is within 10 % of the required value, red fails), a red tick marks the length the pullout check asks for, and a small box lists the checks as value / required.
Stresses (after Analyze) draws the vertical stress, the lateral stress and the tension of every level against what it can carry, part by part: the fill and the surcharge.
Levels (after Analyze) draws one bar per level: the factor against rupture, the factor against pullout, each with a dashed line at the factor required, and the length each level has against the length it needs.
Block (after Analyze) draws the reinforced block as a gravity wall: the thrust of the retained fill and where it acts, the weight, the resultant on the base with its eccentricity, the bearing pressure on the effective width and the factors against the required ones; with an earthquake the seismic forces and factors stand beside them.
The module on its default model, analysed.
Section before Analyze (a 10 kPa surcharge added).
Section after Analyze.
Section after Analyze with a surcharge: the levels that fail are red.
Stresses.
Levels.
Block.
Show chips
The Section view has two chips, Failure surface and Required length, both on when the module opens. The first draws the failure surface; the second draws the red ticks of the length the pullout check asks for after Analyze. The other views have no chips.
Zoom
Each view has −, a percentage and + at the lower right and a button that fits the whole drawing in the pane.
Picking, dragging and locking
Nothing on the drawing can be dragged: the wall is entered in the Model tab. With a surcharge added, the load on the Section drawing can be picked before Analyze: pressing it opens the Surcharge section with the load in the form (Editing · Load 1), the same as pressing its row in the table. After Analyze the inputs are locked: the bar says “The inputs are locked. Edit inputs clears the results; the unit system can still be changed.” Edit inputs unlocks the model, clears the results and takes the drawing back to the inputs.
Units
Switching to US or SI · tf converts the boxes, the cards, the tables, the working and the drawings (for example H = 32.8 ft and the eccentricity 1.893 ft in US). A value typed in one system is converted in the boxes of another and may show unrounded, for example H = 32.8084 ft for 10 m.
Entering the model, section by section
The Model tab has nine sections: Model data, Wall and reinforcement layout, Reinforcement, Pullout resistance, Fills, Foundation soil, Surcharge, Earthquake and Required factors. Each opens when you click its title; Next and Back at the foot walk you through them, and Analyze waits below the last one. Model data and Wall and reinforcement layout are open when the module opens; the others open when you click their title. A value that the module fills in itself carries a small tag beside its label (from the fill, default or same as the fill). Where a unit is written twice, such as m · ft, the units are those of SI · kN, SI · tf and US in turn. Defaults are given in SI.
Model data
The first section holds the model name, Save to file…, Open file…, Quick Save… with its list and Load and Delete, and Reset to defaults. Quick Save… asks for a name for the version and puts it in the list with the date; Reset to defaults brings the default model back at once. The workspace guide describes them: workspace guide.
Model data.
Wall and reinforcement layout
Procedure has Simplified method (FHWA / AASHTO) (the default) and Rankine at every depth (the source). The four fields below describe the wall; SH appears for strips only. The levels lie at SV, 2 SV, … down to the base; when H is not a multiple of SV the last level is placed at the base and still carries the fill of the height SV (the module notes it).
Wall and reinforcement layout.
Wall fields
Field
Default
What to enter
Height of the wall H · m · ft
10
From 1 to 30 m.
Length of the reinforcement, the same at every level L · m · ft
7.5
Measured from the back of the facing; at least 0.5 m. The practice asks for 0.7 H and not less than 2.4 m.
Vertical spacing of the reinforcement SV · m · ft
0.6
From 0.2 to 2 m, and not more than H.
Horizontal spacing of the strips (centre to centre) SH · m · ft
1
At least 0.1 m; the strip width must be less than it. Strips only.
Reinforcement
Reinforcement has Galvanized steel strips (default), Geotextile sheets and Geogrid; the fields below it change with the choice. A strip is checked on its section after the corrosion of the design life, a sheet on its long-term strength. Changing the kind also changes the values the module fills in: F*, α and the required factor against rupture.
Reinforcement: strips.
Strips
Field
Default
What to enter
Width of a strip w · mm · in
75
At least 5 mm; less than SH.
Thickness of a strip as placed t · mm · in
6
At least 0.5 mm.
Yield strength of the strip steel fy · MPa · kg/cm² · ksi
240
At least 10 MPa.
Corrosion: loss of thickness per year r · mm · in
0.025
Zero or more. The thickness lost over the design life, r × n, is taken off the strip before it is checked.
Design life, years n
50
From 0 to 200.
The long-term strength is Tult / (RFidRFcrRFcbd) per metre; with the defaults 150 / (1.2 × 2.5 × 1.25) = 40 kN/m. A geogrid level carries that strength times Cr per metre of wall: 40 × 0.8 = 32 kN/m.
Reinforcement: geotextile sheets (the geogrid adds the coverage ratio).
Reduction factor for chemical and biological degradation RFcbd
1.25
From 1 to 3.
Coverage ratio of the geogrid Cr
0.8
From 0.05 to 1; the part of the plan area a level of geogrid covers. Geogrid only.
Pullout resistance
The resistance of a level to being pulled out of the fill beyond the failure surface is F*ασ′v on each of its two faces over its effective length. F* is filled in with the tag from the fill and α with the tag default; type over them with the values of pullout tests. If you clear F*, the module fills it in again.
Pullout resistance.
Pullout fields
Field
Default
What to enter
Pullout resistance factor F*
0.727 (strips) · 0.484 (sheets)
From 0.01 to 3. Filled in as tan φ′1 for a strip and ⅔ tan φ′1 for a geosynthetic.
Scale effect correction α
1 (strips) · 0.8 (geogrid) · 0.6 (geotextile)
From 0.1 to 1.
Fills
The reinforced fill is a free-draining granular soil. The retained fill behind the block pushes on it with its own Rankine thrust. It fills itself with the values of the reinforced fill; type over it for another soil. When you change φ′1, the retained fill’s φ′b, F* and the pullout values follow, unless you have typed over them.
Fills.
Fill fields
Field
Default
What to enter
Unit weight of the reinforced fill γ1 · kN/m³ · t/m³ · pcf
16.5
From 10 to 25 kN/m³.
Friction angle of the reinforced fill φ′1 · °
36
From 20° to 45°.
Unit weight of the retained fill behind the block γb · kN/m³
16.5
From 10 to 25. Follows the reinforced fill.
Friction angle of the retained fill φ′b · °
36
From 15° to 45°. Sets the thrust on the back of the block. Follows the reinforced fill.
Foundation soil
The soil under the block. Its friction angle and cohesion give the bearing capacity; the lesser of its friction angle and that of the reinforced fill gives the friction on the base, taken as ⅔ of it with no cohesion.
Foundation soil.
Foundation fields
Field
Default
What to enter
Unit weight of the foundation soil γ2 · kN/m³
17.3
From 10 to 25.
Friction angle of the foundation soil φ′2 · °
28
From 0° to 45°.
Cohesion of the foundation soil c′2 · kPa · kg/cm² · psf
50
Zero or more.
Surcharge
The section is a form over a table. Kind of load shows Uniform; Strip and Point are shown faded with the tag SOON. Enter q and press + Add load: the load goes into the table (Load 1 · Uniform surcharge · q = 10 kPa · whole surface), and the counter reads 1 of 1; there is one load. The New load form starts at q = 10 kPa, and the model starts with no load. Press the row or the load on the drawing to change it (Editing · Load 1, with Done and Delete load; changes apply as they are entered); × takes it away.
The load is taken as a live load: it adds q to the vertical stress and Kr q to the lateral stress at every depth and Ka q H to the thrust on the back of the block, and its weight is not counted as resisting, nor in the pullout resistance.
Surcharge: the load added.
Surcharge field
Field
Default
What to enter
Surcharge on the surface q · kPa · t/m² · ksf
10 (the form)
Zero or more. Acts on the whole surface above the reinforced and the retained fill.
A load picked: it is edited in the form.
Earthquake
A horizontal seismic coefficient adds, to the static checks, the dynamic thrust of Mononobe–Okabe on the retained fill, the inertia of the reinforced block and the dynamic increment of the levels; the checks are then made against 75 % of the required factors. The module takes the vertical coefficient as zero.
Earthquake with kh = 0.2.
Earthquake field
Field
Default
What to enter
Horizontal seismic coefficient (0: no earthquake) kh
0
From 0 to 0.6. Zero means no earthquake. It must be less than tan φ′b (see Messages).
Required factors
The factors the design requires are global factors of safety on the resistances (allowable stress design), one for each check. The strength of the connection is optional; without it the connection is not checked, and the Results card says not checked.
Required factors (strips).
Required factors
Field
Default
What to enter
Required factor of safety against rupture FSB
1.8 (strips) · 1.5 (sheets)
From 1 to 10. Fills itself when you change the kind of reinforcement.
against pullout FSP
1.5
From 1 to 10.
against overturning FSot
2
From 1 to 10.
against sliding FSsl
1.5
From 1 to 10.
against bearing failure FSbc
2.5
From 1 to 10.
Strength of the connection of a strip to the facing (optional) Tac · kN · tf · kip
empty
At least 0.1. Per strip. Strips only.
Strength of the connection to the facing per metre of wall (optional) Tac · kN/m
empty
At least 0.1. Sheets only. The long-term strength from connection tests.
Required factors for a geosynthetic.
A value outside the range shown stops the analysis (see Messages). The five required factors work as limits on the cards: a check reads OK at or above its required value and NOT OK below it.
Choosing the procedure and the reinforcement
The two procedures
The procedure decides the lateral stress in the fill and the failure surface. On the default wall (strips, H = 10 m) the simplified method gives the largest tension Tmax = 30.84 kN and the factors against rupture and pullout 2.772 and 1.909; Rankine at every depth gives Tmax = 25.70 kN and the factors 3.327 and 1.898. The block checks (6.500 · 1.952 · 11.32) are the same in both, because the thrust on the back of the block is Rankine in both. In the table, Simplified is the simplified method (FHWA / AASHTO) and Rankine is Rankine at every depth.
Simplified
Rankine
Lateral stress, strips
Kr = 1.7 Ka at the top, falling to 1.2 Ka at 6 m, then constant
Ka at every depth
Lateral stress, sheets
Ka
Ka
Failure surface, strips
La = 0.3 H down to H/2, then 0.6 (H − z)
La = (H − z) / tan(45° + φ′1/2)
Failure surface, sheets
The Rankine surface
The Rankine surface
Here z is the depth of the level and La its distance from the facing to the failure surface; the effective length Le = L − La is the part that resists pullout.
Section with Rankine at every depth.
The kind of reinforcement
Strips are checked for rupture on wtefffy with teff = t − rn; with the defaults 0.075 × 0.00475 × 240 000 = 85.50 kN per strip. The Results then give the thickness the required factor asks for, with the corrosion allowance.
Geotextile sheets are checked on Tall = Tult / (RFidRFcrRFcbd) per metre. The Results then give the vertical spacing the required factor allows at the level of the largest tension, and the lap length at the facing.
Geogrid is checked on TallCr per metre of wall. The Results give the vertical spacing the required factor allows.
Changing only the kind of reinforcement on the default wall (everything else as it opened) gives the factors against rupture and pullout 1.556 and 10.11 for geotextile sheets and 1.245 and 10.78 for the geogrid; the geogrid reads NOT OK against its 1.50 required, and the Warnings window opens (see Messages). Both kinds of sheet take F* = 0.484 (⅔ tan φ′1), with α = 0.6 for the geotextile and 0.8 for the geogrid, which is why their pullout factors differ from the strips’.
Levels, geotextile sheets on the default wall.
Analyze and read the results
Press Analyze at the foot of the Model tab. The module stays on the Model tab: the bar reads Analysed — the MSE wall calculated (with the number of warnings, if any), the inputs lock and the drawing shows the results; open the Results tab to read them. A mistake in the inputs opens Cannot analyse instead. When the run has warnings the Warnings window opens by itself; a run with notes only does not open it, and the notes are behind the Notes button of the bar.
The cards
The first card block gives the static checks; each card shows the value, OK or NOT OK with the required value, and the name of the check:
Rupture of the reinforcementFSB: the least over the levels, against the factor required (FSB,req ).
Pullout of the reinforcementFSP: the least over the levels.
Overturning of the blockFSot.
Eccentricity of the resultant on the basee: OK when it is within L/6.
Sliding of the block on its baseFSsl.
Bearing of the foundation soilFSbc.
Connection to the facingFSc: not checked until you give the strength of the connection; then it is judged against the factor required for rupture.
Results with the earthquake (kh = 0.2) and a connection strength of 40 kN: a warnings bar, then the static and the earthquake cards.
With a seismic coefficient the cards add Rupture under the earthquakeFSB,s , Pullout under the earthquakeFSP,s , Overturning under the earthquake, Eccentricity under the earthquake (within L/3) , Sliding under the earthquake and Bearing under the earthquake, each against 75 % of its required factor.
The lines below the cards
Largest tension in a levelTmax (per strip for strips, per metre for sheets); with an earthquake also Tmax,s .
Strips: the thickness the required factor asks for, with the corrosiontreq. Sheets: the vertical spacing the required factor allowsSV,req at the level of the largest tension, and, for a geotextile, the lap length at the facing.
The length the required pullout factor asks forLreq: compare it with the L provided.
The active thrust on the back of the blockPa in kN/m.
The Values, step by step table gives the key value of every step of the working, and The reinforcement levels table lists every level: depth z, Kr/Ka, the vertical and lateral stress, the tension T, FSB, the distances La and Le, the pullout resistance Pr, FSP and Lreq. With an earthquake a second table lists the dynamic increment Tmd, the total Ttot and the earthquake factors of every level.
Warnings and notes
Warnings (a △ mark) say what does not reach its required value and what to do about it; notes (○ and ●) state what the run assumes. The window lists them all.
For the default wall with a 10 kPa surcharge the first warning reads: “The reinforcement does not reach the required factor against pullout at level 1. FS(P) = 0.95 against 1.50 required; the level needs 10.11 m. Lengthen the reinforcement to Lreq.”
The Warnings window.
Calculations, Report and Theory
Calculations
The Calculations tab writes the working with your numbers. It opens with Given and what is sought, then the steps:
The wall and the reinforcement levels: the number of levels, Ka, and for the simplified method the failure surface and the active zone.
The stresses in the fill: σ′v, Kr and σ′h at the base.
What a level can carry: Tcap for a strip after the corrosion, or Tall and Tcap for a sheet, and the pullout resistance Pr.
Internal stability, level by level: the tension, the factors against rupture and pullout, the lengths, the thickness or the spacing the factors ask for, and the table of the levels.
The connection to the facing (only when its strength is given).
External stability of the reinforced block: the thrust Pa, the moments about the toe, overturning with the eccentricity, sliding and bearing on the effective width L′ = L − 2e.
The earthquake (only when kh is given): Mononobe–Okabe, the inertia of the block, the factors and the levels under the earthquake.
Notes and warnings close the tab. Every step has its equations, then your numbers inserted.
A step of the working: your numbers in the equations.
Report
The Report tab has the Report cover (project, location, client, report number, date, prepared by, title or qualification, checked by and optional notes; kept in this browser and with the model file) and Save as PDF and Download Word (.docx). The report has the parts 1. Introduction and scope, 2. Input data, 3. Calculation (the steps of the Calculations tab), 4. Results, 5. Assumptions and notes, 6. Summary and 7. References. The summary lists the checks that do not reach their required value, in words.
The Report tab.
Theory
The Theory tab explains how the module checks the wall in fourteen sections: A reinforced-soil wall, The stresses in the fill, The failure surface and the lengths, The tension of a level, Rupture, Pullout, The reinforced block: overturning, Sliding, Bearing, The earthquake, Reading the results, A worked example, What the module assumes, and what it does not do and References. Open one section or all.
Worked example: the default wall
The module opens on this wall: H = 10 m, L = 7.5 m, SV = 0.6 m, SH = 1 m, steel strips 75 × 6 mm with fy = 240 MPa, r = 0.025 mm/year over 50 years, F* = 0.727 and α = 1, reinforced and retained fill γ = 16.5 kN/m³ and φ′ = 36°, foundation soil γ = 17.3 kN/m³, φ′ = 28°, c′ = 50 kPa, the simplified method, no surcharge, no earthquake, and the required factors 1.8, 1.5, 2, 1.5 and 2.5. There are 17 levels.
Internal stability
Quantity
Working
Module
Ka
tan²(45° − 36°/2)
0.2596
Kr/Ka at 6 m and below
1.2
1.20
σ′v at the base
16.5 × 10
165.0 kPa
σ′h at the base
1.2 × 0.2596 × 165.0
51.40 kPa
Tmax (level 17)
51.40 × 0.6 × 1
30.84 kN per strip
Tcap
0.075 × (0.006 − 0.025 × 50/1000) × 240 000
85.50 kN
FSB
85.50 / 30.84
2.772
La at the top
0.3 × 10
3.00 m
Pr at level 1
2 × 0.075 × 0.727 × 1 × 9.9 × (7.5 − 3.0)
4.858 kN
FSP at level 1
4.858 / 2.544
1.909
Lreq at level 1
3.00 + 1.5 × 2.544 / (2 × 0.075 × 0.727 × 9.9)
6.535 m
External stability
Quantity
Working
Module
Pa
½ × 0.2596 × 16.5 × 10²
214.2 kN/m
Mo
214.18 × 10/3
713.9 kN·m/m
Weight
16.5 × 10 × 7.5
1237.5 kN/m
FSot
(1237.5 × 3.75) / 713.9
6.500
e
7.5/2 − (4640.6 − 713.9) / 1237.5
0.5769 m
FSsl
1237.5 × tan(⅔ × 28°) / 214.18
1.952
Pressure on L′ = 7.5 − 2 × 0.577
1237.5 / 6.346
195 kPa
FSbc (the lesser of the two factors governs)
(50 × 25.80 + ½ × 17.3 × 6.346 × 16.72) / 195
11.32
Every value above agrees with an independent hand calculation from the formulas the Calculations tab states (the stated F* = 0.727 is tan 36° rounded to three places, so a hand value of FSP from tan 36° differs in the last figure: 1.908). All six checks read OK; the connection reads not checked because its strength is not given. The warnings window does not open: the run has notes only (five of them).
US and SI · tf: the same wall
Switching the units does not change a factor. The cards give the same FSB, FSP, FSot, FSsl and FSbc; the quantities with a dimension convert:
Quantity SI · kN
US
SI · tf
e 0.5769 m
1.893 ft
0.5769 m
Tmax (per strip) 30.84 kN
6.934 kip
3.145 tf
treq 4.334 mm
0.1706 in
4.334 mm
Lreq 6.535 m
21.44 ft
6.535 m
Pa 214.2 kN/m
14.68 kip/ft
21.84 tf/m
In US the default boxes show H = 32.8084 ft, L = 24.6063 ft, SV = 1.9685 ft, SH = 3.28084 ft, w = 2.95276 in, t = 0.23622 in, fy = 34.8091 ksi, γ = 105.037 pcf and c′ = 1044.27 psf for the foundation soil. In SI · tf: fy = 2447.32 kg/cm², γ = 1.68253 t/m³, c′ = 0.509858 kg/cm².
The same wall under an earthquake, kh = 0.2
With kh = 0.2 and a connection strength of 40 kN per strip, the static cards stay as above and the earthquake adds the figures below (retained fill φ′ = 36°). ψ = tan⁻¹ 0.2 = 11.31° and KAE = 0.3814.
Quantity
Working
Module
Dynamic increment ΔPAE
½ × 16.5 × 10² × (0.3814 − 0.2596)
100.45 kN/m
Inertia of the block PIR
½ × 0.2 × 16.5 × 10²
165.00 kN/m
Ps
214.18 + 0.5 × 100.45 + 165.00
429.41 kN/m
FSot,s
4640.6 / 1840.3
2.522 (1.50 required)
es
1.487 m (L/3 = 2.500 m)
FSsl,s
1237.5 × tan(⅔ × 28°) / 429.41
0.9736 (1.13 required): NOT OK
FSbc,s
7.112 (1.88 required)
FSB,s
2.315 (1.35 required)
FSP,s
0.6273 (1.13 required): NOT OK
Connection FSc
40 / 30.84
1.297 (1.80 required): NOT OK
Block under the earthquake.
Levels under the earthquake.
The warnings window then lists three warnings: the connection (“The connection to the facing does not reach the required factor at level 17. FSc = 1.30 against 1.80. Use a stronger connection, or bring the levels closer.”), the block under the earthquake and the level under the earthquake.
How each input changes the answer
Each row changes one input of the default wall and leaves the rest as the module opened (strips 75 × 6 mm, simplified method, H = 10 m, L = 7.5 m, SV = 0.6 m, SH = 1 m, γ1 = 16.5 kN/m³, φ′1 = 36°, φ′b = 36°, foundation γ = 17.3 kN/m³, φ′2 = 28°, c′2 = 50 kPa, no surcharge, no earthquake). The values are read from the module after Analyze. The middle column lists the least FSB (rupture) and the least FSP (pullout) over the levels, one under the other (required 1.80 and 1.50); the last column lists overturning, sliding and bearing, one under the other (required 2.00, 1.50 and 2.50).
One change at a time
Change
Rupture Pullout
Overturning Sliding Bearing
Default wall
2.772 1.909
6.500 1.952 11.32
L = 5 m (instead of 7.5)
2.772 0.8486
2.889 1.301 6.986
L = 9 m
2.772 2.546
9.360 2.342 13.28
L = 3 m
2.772 0
1.040 0.7808 0.3046
SV = 0.4 m
4.158 2.835
6.500 1.952 11.32
SV = 1 m
1.663 1.169
6.500 1.952 11.32
SH = 0.5 m
5.544 3.819
6.500 1.952 11.32
Strip width w = 100 mm
3.696 2.546
6.500 1.952 11.32
Strip thickness t = 4 mm
1.605 1.909
6.500 1.952 11.32
Corrosion r = 0.05 mm/year
2.043 1.909
6.500 1.952 11.32
Yield strength fy = 355 MPa
4.100 1.909
6.500 1.952 11.32
φ′1 = 32° (F*, φ′b follow)
2.342 1.387
5.492 1.649 10.79
φ′1 = 40° (F*, φ′b follow)
3.310 2.631
7.761 2.330 11.80
φ′b = 30° only
2.772 1.909
5.063 1.520 10.51
γ1 = 19 kN/m³ (γb follows)
2.407 1.909
6.500 1.952 9.832
φ′2 = 20°
2.772 1.909
6.500 1.369 5.320
φ′2 = 35°
2.772 1.909
6.500 2.492 25.35
c′2 = 0
2.772 1.909
6.500 1.952 4.706
F* typed as 1.0
2.772 2.626
6.500 1.952 11.32
α = 0.8
2.772 1.527
6.500 1.952 11.32
Surcharge q = 10 kPa
2.614 0.9498
5.500 1.741 10.36
Surcharge q = 20 kPa
2.472 0.6322
4.767 1.571 9.543
H = 14 m (L stays 7.5 m)
1.980 1.400
3.316 1.394 6.191
H = 6 m (L stays 7.5 m)
4.620 2.418
18.06 3.253 22.08
What the rows show
The length L works on pullout and on the block, not on rupture: at 5 m the pullout factor falls to 0.8486 and the eccentricity 0.8654 m exceeds L/6; at 3 m the top levels reach no further than the failure surface (their effective length is zero) and the least pullout factor reads 0.
The spacing SV and SH set the area each level carries, so they scale the tension: halving SH to 0.5 m doubles the rupture factor, 5.544. They do not enter the block checks.
The strip (w, t, r, fy) sets the rupture factor; the width also enters the pullout resistance (2 w …), the thickness does not.
φ′1 changes the tension, the failure surface, the weight and the pullout factor at once, and moves F* and φ′b with it, so the row combines several effects; φ′b alone changes only the thrust on the block.
The foundation soil works on sliding (through φ′2, the lesser friction angle) and on bearing (φ′2, c′2); overturning does not change.
A surcharge adds to the tension and the thrust but not to the pullout resistance or the resisting weight, because it is taken as a live load: the pullout factor falls to 0.9498 with 10 kPa.
Messages
The messages are quoted as the module shows them. A stop message appears in the Cannot analyse window; warnings and notes are in the Warnings window and the bar.
Stop: Cannot analyse
A value is outside its range or empty: Cannot analyse — 1 input error, then, for example, “Vertical spacing of the reinforcement (SV) must be at most 2 m.” or “Height of the wall (H) is missing.”
The corrosion takes the whole strip: Cannot analyse — a condition of the solution is not met, “The corrosion eats the whole thickness of the strip within its design life. The thickness lost, r × n = 10.00 mm, is not less than the thickness as placed. Thicken the strip, or shorten the life or the rate. Nothing was calculated. Change the inputs marked in red, then press Analyze again.” (r = 0.2 mm/year, n = 50, t = 6 mm).
Strips wider than their spacing: “The strips are wider than their spacing. Strips side by side would overlap. Enter w < SH.” (w = 1200 mm, SH = 1 m).
A seismic coefficient beyond the retained fill: “The seismic coefficient is beyond what the retained fill can stand: no Mononobe–Okabe wedge is in equilibrium. With atan kh ≥ φ′b the dynamic thrust has no finite value. Enter kh < tan φ′b.” (φ′b = 20°, kh = 0.4).
The Cannot analyse window.
Cautions of the practice
“The reinforcement is shorter than the least the practice allows, 0.7 H and 2.4 m.” FHWA and AASHTO take L ≥ 0.7 H, and never less than 2.4 m, whatever the checks give; the checks say whether the length holds. (Lengthen the reinforcement.) It appears for H = 14 m with L = 7.5 m, and for L = 5 m and 3 m.
“A level has less than 0.9 m beyond the failure surface.” The practice asks for at least 0.9 to 1 m of reinforcement in the resisting zone. It appears for L = 3 m.
Warnings: a check does not reach its required value
Rupture: “The reinforcement does not reach the required factor against rupture at level 17. FS(B) = 1.60 against 1.80 required. Thicken or widen the strips, or bring the levels closer.” (t = 4 mm). For a sheet the advice is “Choose a stronger geosynthetic, or bring the levels closer.”
Pullout: “The reinforcement does not reach the required factor against pullout at level 1. FS(P) = 1.17 against 1.50 required; the level needs 8.77 m. Lengthen the reinforcement to Lreq.” (SV = 1 m).
Connection: “The connection to the facing does not reach the required factor at level 17. FSc = 1.30 against 1.80. Use a stronger connection, or bring the levels closer.” (Tac = 40 kN).
Sliding: “The block does not reach the required factor against sliding. FS = 1.37 against 1.50. Lengthen the reinforcement, or improve the fill or the foundation soil.” (φ′2 = 20°). The same form appears for overturning (“Lengthen the reinforcement: the block gets heavier and wider.”).
Earthquake: “The block does not stand the earthquake with the factors required. Overturning 2.52, e = 1.49 m, sliding 0.97, bearing 7.11 against 75 % of the static requirements. Lengthen the reinforcement.” and “A level does not stand the earthquake with the factors required. FS(B)s = 2.32, FS(P)s = 0.63 against 75 % of the static requirements. Strengthen or lengthen the reinforcement.”
Notes
“The height is not a multiple of SV: the last level is placed at the base.” The base level is then closer to the one above than SV and still carries SV of fill. The default wall (10 m at 0.6 m) shows it; 10 m at 0.4 m or 0.5 m does not.
“The fill drains and carries no water pressure; the facing carries no load of its own.”
“The global (deep-seated) stability is not part of this module.”
“The connection to the facing is not checked: the strength of the connection is not given.” (until it is given).
“The simplified method of FHWA / AASHTO is used for the stresses and the failure surface.” (or the Rankine one).
Good practice
Start from the length. Try L = 0.7 H first and read Lreq in the Results: the pullout check asks for that length at its most demanding level.
Read the least factors with the levels. The cards give the least over the levels; the Levels view and the table show which level governs and whether the top or the base is critical.
Take F* and α from tests when you have them. The values the module fills in are lower bounds.
Choose SV so that it divides H if you want even levels.
Mind the surcharge. It is taken as a live load: it loads the reinforcement but gives no resistance. A strip or point load stands in the form marked SOON; account for them in your own checks.
Enter the earthquake as the coefficient your design takes and read the earthquake cards against 75 % of the required factors.
Keep the model with the project. Use Save to file; Quick Save keeps versions in this browser only.
Add the checks the notes name: the global stability of the wall and the ground below it. The run assumes a draining fill and a facing that carries no load of its own; check both for your wall.
Frequently asked questions
Which procedure should I choose?
The Simplified method (FHWA / AASHTO) is the one the module opens with and the practice of the design codes; for steel strips it takes a higher lateral stress near the top and a failure surface closer to the facing. Rankine at every depth (the source) takes the plain Rankine pressure and wedge. On the default wall the simplified method gives FSB 2.772 against 3.327 for Rankine.
Why does the module say the pullout factor is 0.00 for a short wall?
When L is not longer than the distance La to the failure surface, a level has no effective length Le and no pullout resistance. At L = 3 m on the default wall the pullout card reads 0 NOT OK.
What do F* and α mean, and why are they filled in?
F* is the friction a level mobilises on the soil per unit of the vertical stress, α a scale effect correction. The module fills F* as tan φ′1 for a strip and ⅔ tan φ′1 for a geosynthetic and α as 1, 0.8 or 0.6 by the kind; they are lower bounds, and you can type over them with the values of pullout tests.
Why is the surcharge not counted in the pullout resistance?
The module takes the surcharge as a live load: it adds to the tension and the thrust, but its weight is not counted as resisting nor in the pullout resistance, which is the safe side. On the default wall a 10 kPa surcharge cuts the pullout factor from 1.909 to 0.9498.
Can I enter a strip load or a point load?
The form shows Strip and Point faded and tagged SOON. The module takes one uniform surcharge.
What does “not checked” on the connection card mean?
The connection to the facing is checked only when you give its strength, per strip or per metre of wall, in Required factors. Then the card shows FSc against the factor required for rupture.
How does the module treat the earthquake?
Enter kh. The module adds the Mononobe–Okabe thrust of the retained fill (half the increment, at 0.6 H), the inertia PIR of the block and the dynamic increment of every level, and judges every check against 75 % of its required factor; the resultant may fall out to L/3. With atan kh not less than φ′b the analysis stops.
Why does the module keep my model when I reload the page?
Model data says that every change is kept in this browser. The page opens on the model you last worked on, and an analysed model comes back analysed and locked; Edit inputs unlocks it. The model is not shared with another computer: use Save to file… for that.
Can I change the units after Analyze?
Yes. The bar says the unit system can still be changed while the model is locked; the cards, tables, working and drawings convert.
Why did the Warnings window open by itself?
It opens after Analyze when the run has warnings, that is, when a check does not reach its required value or the practice’s cautions apply. A run with notes only does not open it; the Notes button of the bar lists them.
Why is a level placed at the base when H is not a multiple of SV?
The levels are at SV, 2 SV, …; the last one sits at the base, closer to the one above than SV, and still carries SV of fill. The module notes it. Choose SV to divide H for even levels.
Does the module design the facing or check the global stability?
It checks the reinforcement of every level, the connection when its strength is given, and the block. The facing is taken to carry no load of its own, the fill free-draining; the global stability is for a slope stability analysis, which the module reminds you of in every run.
Cantilever RC wallStability, bearing and stem actions of a reinforced-concrete cantilever wall.
Gravity wallA stone masonry or plain concrete gravity wall on a stepped footing.
MSE wallA reinforced-soil wall: every level checked for rupture and pullout, the block for sliding, overturning and bearing, with the earthquake.
