SheetPileCalc v26

Project Data

Parameter	Value	Unit

Design method checks

LE 1.x - Limit Equilibrium. Classical preliminary checks solving for embedment from pressure equilibrium. 1.1 Cantilever uses Blum's simplified rotation-point method with reverse resistance collapsed to a lumped reaction. 1.2 Single-propped FES uses free-earth-support equilibrium about the prop. These methods report embedment, reactions, M/V actions; they do not predict deflection or ground movement.

SR 2.x - Subgrade Reaction. Approximate Winkler soil-structure interaction. The wall is a beam on independent horizontal springs; SR 2.2 caps the springs at active/passive pressure limits. This is not a coupled continuum analysis and should be benchmarked for final design use.

Coupled 3.x - Coupled Flexibility. Planned methods will use interconnected flexibility terms to approximate soil continuity below excavation level. Not available in this version.

Verification examples are loadable per method via the Load Example dropdown - each carries its own reference result block so the Summary tab Diff column auto-validates against published data.

Learning mode. The Tutorial tab walks the method ladder (LE → SR → Coupled) in eight lessons, each one click from a solved verification example. The K Design tab derives earth pressure coefficients (Rankine, Coulomb, Lancellotta lower bound), Ko, cohesion terms and EC7 DA1 / BS 8002 design values from φ′, δ and c′, and writes them into the soil types of either case.

Legal notice. The full StructCalc.online terms and legal notice are provided on the StructCalc home page. These tools are for independent verification by qualified engineers and are not a primary design tool.

Blank on open. Use the Examples dropdown to populate a method-specific verification dataset.

Soil Types

#	ID	Name	γ	Eh	Ko	Ka	Kp	c	Kac	Kpc	dEh/dy	ν	Del

γ kN/m³, Eh/kh kN/m² or kN/m³ style stiffness input. Ka/Kp may be entered directly, or derived from φ′, δ and c′ (with EC7 / BS 8002 factoring) on the K Design tab.

Earth Pressure Coefficient Designer

1. Characteristic soil parameters

Peak friction angle φ′k		deg
Effective cohesion c′k		kN/m²
Wall friction ratio δ/φ′		-
Wall adhesion ratio cw/c′		-
OCR (for Ko)		-
Partial factor set

2. Coefficients — vertical wall, level ground, horizontal components

Theory	Ka	Kp	Kac	Kpc

Coulomb Kp overestimates passive resistance once δ exceeds about φ′/3 (planar wedge on a curved failure surface) — prefer the Lancellotta lower bound or Kerisel–Absi tables for design. Cohesion terms: Kac / Kpc = 2·√(K·(1 + cw/c′)). Undrained total-stress design is the φ = 0 case: Ka = Kp = 1, Kac = Kpc = 2 with c = cu.

3. Adopt into the model

Active-side theory (Ka, Kac)
Passive-side theory (Kp, Kpc)
Target soil type (SLS case)

Writes Ka, Kp, Kac, Kpc, Ko and c′ (design value) into the selected row of the current case.

4. Unplanned excavation allowance — EC7 9.3.2.2

Governing height h

m

h = retained height for a cantilever wall, or the depth below the lowest support for a propped wall. ΔH = min(10% of h, 0.5 m) and applies to ULS verification only.

Adjusts the ULS case formation level. Press once only.

Educational design helper: closed-form coefficients for a vertical wall with level retained ground and drained parameters, reported as horizontal components to match the solver. Verify adopted values against Kerisel–Absi / EC7 Annex C for final design. See Tutorial lessons 2 and 6.

Soil Profile

#	Top elev	Active type	Passive type	Del

Layer tops are elevations. Soil type IDs refer to the Soil Types table.

Water Conditions

Parameter	Value	Unit

Water profile support is stored in the data file; the current solver uses water levels and pressure interpolation where available. Effective stress mode = 1 applies K to σ′v = σv − u and adds u separately (the strict effective-stress form); mode 0 keeps the legacy total-stress behaviour that the built-in reference examples were benchmarked against — see Tutorial lesson 3.

Surcharges

#	ID	Elev	Side	Dist	Length	Width	Near	Far	Active	Del

Side = active/passive. Near/Far are kN/m².

Ties / Anchors

#	ID	Elev	Spacing	Area	E	Free L	Incl.	Prestress	Active	Del

Horizontal stiffness is derived from EA/L/spacing × cos²θ.

Construction Stages

#	No.	Action	Value / ID	Elev	Side	Analyse	Del

Actions currently parsed: changeEI, applySurcharge, excavate, fill, installStrut, applyWaterProfile, changeSoil.

Summary

Quantity	Calc	Reference	Diff

Peak comparison uses the embedded PFC reference where present.

Result Grid

Elev.	y mm	rot	M	V	p	kh	Soil R	Tie R	Ref M	Ref V	Ref p

Calculated and reference ordinates are matched by elevation where possible.

Output

Result Data

Run the selected analysis first, then copy the complete result grid as comma-separated data for pasting into Excel or another spreadsheet.

One row per analysis node.

CSV columns

Column	Contents
elev	Node elevation
disp_mm / rotation	Wall displacement and rotation
moment / shear	Calculated wall actions
net_pressure / kh	Net pressure and spring stiffness
soil_reaction / tie_reaction	Soil and tie reactions
spring_state	Current soil-spring state where applicable

Output commands are kept on this tab to match the FrameCalc workflow.

Tutorial — Embedded Wall Analysis From First Principles

Lesson 1 — The three earth pressure states

Soil pushes on a wall with a pressure that depends on how much the wall moves. With no movement the ground sits at rest. If the wall yields away from the retained soil, pressure falls to the active limit — reached after small movements, of the order of 0.1–0.5% of the wall height in granular soils. If the wall is pushed into the soil, resistance climbs toward the passive limit, but mobilising it takes far more movement, typically 2–10% of the height.

Ka·σ′v ≤ σh ≤ Kp·σ′v at rest: σh = Ko·σ′v, Ko ≈ 1 − sin φ′ (Jaky)

That asymmetry drives this whole app. LE methods (1.x) assume both limits are fully mobilised everywhere and answer "how deep must the wall go". SR methods (2.x) start the buried soil near rest and only approach the limits as the wall deflects, so they can answer "how far will it move".

Look at: switch the plot to Pressure Limits and identify the Ka and Kp envelopes either side of formation.

Lesson 2 — Where Ka and Kp come from

Rankine (1857) assumes a smooth wall: simple, conservative on Kp. Real walls are rough — wall friction δ inclines the soil thrust, trimming Ka slightly and raising Kp a lot. Coulomb's wedge (1776) includes δ but assumes a planar failure surface: fine for Ka, but it overestimates Kp badly once δ exceeds about φ′/3, because the true passive surface is curved. Curved-surface solutions — the Kerisel–Absi tables or Lancellotta's closed-form lower bound — give safe passive values with wall friction, which is why K Design adopts Lancellotta for the passive side by default.

Rankine: Ka = (1 − sin φ′)/(1 + sin φ′), Kp = 1/Ka
with cohesion: pa = Ka·σ′v − Kac·c′, pp = Kp·σ′v + Kpc·c′, Kac/Kpc = 2·√(K·(1 + cw/c′))
undrained (φ = 0): Ka = Kp = 1, Kac = Kpc = 2, c = cu — watch for tension cracks near the top

Typical design wall friction: δ ≈ ⅔·φ′ for steel sheet piles, up to φ′ for rough cast-in-place concrete; adhesion cw ≈ 0.5·c′. Try φ′ = 32°, δ/φ′ = 0.67 in K Design and compare the three theories — Coulomb's Kp will sit well above Lancellotta's.

Lesson 3 — Water: usually the biggest load

On most embedded walls the largest single pressure is water, not soil. Both sides carry hydrostatic pressure below their water tables; excavation lowers the passive-side table, so the wall carries the unbalanced head. The effective stress principle says soil strength acts on σ′v = σv − u:

pa = Ka·(σv − u) + u pp = Kp·(σv − u) + u

This app's legacy mode multiplies K by the integrated total stress and adds u — conservative on the active side, but it overstates passive resistance below water by roughly Kp·u. Two remedies: enter buoyant unit weights (γ′ = γsat − 10) for layers below the water table, or set Effective stress mode = 1 on the Water tab, which subtracts u before applying K. The built-in reference examples were benchmarked in legacy mode, so leave them as loaded. Steady seepage around the toe modifies these pressures and can cause piping or base heave in granular soils — that check sits outside this app, which assumes hydrostatic conditions.

Experiment: add an active water table 2 m below the wall top on the Water tab, re-solve, and watch net pressure and Mmax jump. Then set effective stress mode = 1 and compare again.

Lesson 4 — Cantilever walls: Blum's method

An unpropped wall stands by rotating about a pivot near its toe: passive resistance in front above the pivot, and a reversed pressure block behind, below it. Blum's simplification replaces everything below the pivot with a lumped reaction R: solve moment equilibrium for the depth d₀ to the pivot, then extend the toe to d ≈ 1.2·d₀ so the reversed block can actually develop — that is the app's d₀ factor, a mechanism correction rather than a safety factor.

Maximum moment occurs where net shear crosses zero, below formation. Because both the net thrust and its lever arm grow with retained height H, cantilever moments grow roughly with H³ — the reason cantilevers stop being economic beyond about 4–5 m retained and you add a prop.

Look at: embedment, d₀, R and where Mmax sits in the Summary tab — then the Moment plot to see the reversal near the toe.

Lesson 5 — Propped walls: free vs fixed earth support

Add one prop and the wall becomes a propped beam with two unknowns: embedment and prop force. Free Earth Support (FES) assumes the toe can translate and rotate — take moments about the prop for the minimum embedment, then horizontal equilibrium for the prop force. Shortest wall, largest bending moment. Fixed Earth Support (FixES) assumes deeper embedment fixes the toe; Blum's equivalent beam splits the wall at the contraflexure point — longer wall, smaller span moments. Rowe showed flexible sheet piles arch and shed moment, so stiff-wall FES moments are on the safe side.

Multi-prop walls (LE 1.4) are statically indeterminate, so LE distributes pressure span-by-span as a preliminary check only — confirm prop loads and moments with an SR run (Lesson 7).

Compare LE-1.2 against LE-1.3: note the trade of embedment against Mmax between free and fixed earth assumptions.

Lesson 6 — Design codes: SLS, ULS and partial factors

UK practice designs embedded walls to EC7 Design Approach 1, verifying two combinations. Combination 1 factors actions (γG = 1.35) with unfactored soil strength (set M1). Combination 2 uses γG = 1.0 but factors the soil — tan φ′ and c′ divided by 1.25, cu by 1.4 — and usually governs embedment. BS 8002 instead applies a mobilisation factor M = 1.2 to drained strength (1.5 on cu), giving working-state pressures with the margin built in.

This app carries the pair as its SLS and ULS cases: put characteristic parameters in SLS, then use the K Design factor preset to write the factored set into the ULS soil types. EC7 9.3.2.2 additionally requires an unplanned excavation allowance ΔH = min(10% of the governing height, 0.5 m) on ULS checks — K Design block 4 computes and applies it.

Exercise: derive unfactored and EC7 Comb.2 coefficients for φ′k = 32° and apply them to the SLS and ULS cases of the same model. Solve both and compare embedment demand.

Lesson 7 — Subgrade reaction: how WALLAP-class analysis works

SR methods swap rigid limit equilibrium for a wall that bends: an Euler–Bernoulli beam FE loaded by the active-side pressure, restrained below formation by horizontal Winkler springs of stiffness kh (from Eh and its depth gradient) plus any tie stiffness EA·cos²θ/(L·s). SR 2.1 keeps every spring elastic. SR 2.2 is elastic–perfectly-plastic: an active-set iteration caps any spring whose reaction reaches the passive (or active) limit and re-solves, so the pressure diagram redistributes the way real soil does. SR 2.3 carries spring states stage by stage.

You gain what LE cannot give — deflections, prop loads with real stiffness, redistributed pressures. The answer leans hard on kh, the least certain number in the model: always bracket it (halve it, double it) and confirm the results stay tolerable across the range. Springs remain independent — no load spread between levels. Fixing that is the coupled tier's job.

Look at: the Result Grid spring-state column in SR 2.2 (which levels hit their limits), and the Pressure Limits plot with deflection overlaid.

Lesson 8 — Coupled methods and the continuum: toward FREW and PLAXIS

Winkler's flaw: push one spring and its neighbours feel nothing, but real soil is continuous — load spreads and pressures arch between supports. Oasys FREW fixes this with full flexibility matrices (from Mindlin's elastic solutions or pre-computed plane-strain FE soil blocks) so every node's reaction depends on the whole displacement field, still capped at the Ka/Kp limits. This app's CP 3.x methods currently approximate that continuity by smoothing the SR solution across neighbouring levels — a clearly-labelled prototype for comparison, not a validated coupled solver yet.

Beyond the wall line sits full 2D FEM (PLAXIS-class; FEMSoilCalc in this suite), which meshes the ground itself and adds what no wall-line model can: ground movements behind the wall, stress paths and global stability. A working rule for temporary works: LE sizes the wall, SR checks movement and prop loads, and coupled or continuum analysis earns its keep when neighbouring assets are movement-sensitive.

Compare CP-3.1 against SR-2.1 on the same geometry: the smoothed reactions hint at what genuine coupling does to sharp Winkler peaks.

Where to read next

CIRIA C760 (Gaba et al., 2017), Guidance on embedded retaining wall design — the current UK reference, superseding C580. BS EN 1997-1 with the UK National Annex for the DA1 factor sets. BS 8002:2015 for the mobilisation approach. CIRIA R104 (Padfield & Mair, 1984) for the classical LE hand methods behind modes 1.x. Kerisel & Absi, Tables for the calculation of passive pressure, active pressure and bearing capacity, for curved-surface coefficients. Lancellotta (2002), Géotechnique 52(8), for the lower-bound Kp used in K Design. The WALLAP and FREW technical manuals are excellent free method references even without a licence.

Work the lessons in order — each loads a verification example one click from a solved state. Educational content for qualified engineers; it does not replace project-specific design checks.