SheetPileCalc

1. Enter project geometry, soil strata, groundwater, surface surcharge, anchors or props, and construction stages.
2. Choose a method family that matches the question: limit-equilibrium methods estimate required embedment; subgrade-reaction methods model wall movement against soil springs.
3. Review the selected earth-pressure theory, wall friction, design factors and water assumptions before running the calculation.
4. Analyse each stage and inspect the pressure, wall-deflection, shear and bending-moment plots, support actions and result grid.
5. Use the tutorial and verification examples to understand the calculation route and compare the output with reference cases.

• Limit-equilibrium methods assume active/passive pressures are mobilised and provide classical embedment and action checks; they do not predict wall movement.
• Subgrade-reaction methods represent the wall as a beam on horizontal soil springs; the capped variant limits spring reactions by active/passive pressure bounds.
• Coupled flexibility methods shown as planned are not available in this version.
• Verification examples are method-specific and compare calculated values against reference results; they support checking but do not validate a project model automatically.

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.

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".

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.

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.

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:

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.

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.

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).

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.

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.

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.

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.

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.

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.

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.

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

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.

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

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

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

Peak comparison uses the embedded PFC reference where present.

Calculated and reference ordinates are matched by elevation where possible.

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

Load verification / regression example for the selected method

Use these sections to locate the inputs, checks and results shown in the app:

• Project Data
• Soil Types
• K Design
• Soil Profile
• Water
• Surcharges
• Ties / Anchors
• Stages
• Summary
• Result Grid
• Output
• Tutorial