Retaining & slopes · Embedded walls & sheeting
Embedded retaining wall on elasto-plastic springs (staged, propped) calculator
A sheet-pile, contiguous or secant wall modelled as a beam on springs that stay between active and passive limits (Rankine) with at-rest initial pressures and the subgrade modulus from Schmitt's formula. Stage 1 excavates as a cantilever, a prop is installed, then stage 2 excavates to formation. Reports deflection, bending moment, prop force and how much passive resistance is used at each stage.
Standard: GEO5 Sheeting Check style · subgrade reaction (Schmitt 1995) · Rankine limits · CIRIA C760 · AS 4678
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Inputs in the worked example
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| Input | Value | Unit |
|---|---|---|
| Wall length | 13 | m |
| Wall bending stiffness EI (per m) | 80000 | kNm²/m |
| Wall moment capacity φMs (per m) | 420 | kNm/m |
| Soil unit weight | 19 | kN/m³ |
| Soil φ′ | 32 | ° |
| Soil c′ | 0 | kPa |
| Passive enhancement for wall friction (× Rankine) | 1.3 | |
| Oedometer modulus | 30 | MPa |
| Subgrade modulus (0 = Schmitt) | 0 | kN/m³ |
| Water table behind the wall (depth) | 4 | m |
| Water table in front, below formation | 0 | m |
| Surcharge behind | 10 | kPa |
| Stage 1 excavation depth (cantilever) | 3 | m |
| Prop depth | 1.5 | m |
| Prop stiffness (per m run) | 60000 | kN/m/m |
| Stage 2 excavation depth (final) | 6.5 | m |
| Required factor on passive resistance | 1.5 |
Worked example — results
| Result | Value | Unit |
|---|---|---|
| Subgrade modulus k | 45,431 | kN/m³ |
| Ka / K0 / Kp | 0.307 / 0.470 / 5.50 | |
| Stage 1: max deflection | 19.4 | mm |
| Stage 1: max moment | 96 | kNm/m |
| Stage 1: passive used | 21 | % |
| Stage 2: max deflection | 28.3 | mm |
| Stage 2: max moment | 213 | kNm/m |
| Prop force (per m run) | 106.1 | kN/m |
| Stage 2: passive used | 62 | % |
| Embedment below formation | 6.50 | m |
- ✓ Bending ≤ wall capacity — 213 kNm/m
- ✓ Stage 1 passive factor ≥ 1.5 — 4.87
- ✓ Stage 2 passive factor ≥ 1.5 — 1.61
- ✓ Both stages converged
Method, formulas and assumptions
- Beam elements every 0.25 m; at each node behind: p = clamp(K0σ′v − k·y, pa, pp), in front below formation: p = clamp(K0σ′v + k·y, pa, pp); net water pressure added. Secant iteration to equilibrium.
- Schmitt (1995): k = 2.1·Eoed^(4/3)/EI^(1/3). Prop installed at the end of stage 1 with stiffness kp; its force = kp × (movement after installation).
- Passive factor = available passive force in front ÷ mobilised (CIRCIA C760 / GEO5 check of passive utilisation).
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For preliminary design and education. Check every result against the current standard and your own engineering judgement before use.