Temporary works & site · Platforms & excavations
Temporary cut batter: safe height (Culmann) calculator
The critical height of a temporary cut by Culmann's planar wedge for a soil with cohesion and friction, the factor of safety for the planned depth, and the batter needed for a target factor of safety. Section to scale with the critical wedge.
Standard: Culmann planar wedge · WHS Excavation Work Code of Practice (benching/battering > 1.5 m) · FS ≥ 1.5 temporary
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Inputs in the worked example
The live calculator starts with these values; change any of them and every result, check and diagram updates instantly.
| Input | Value | Unit |
|---|---|---|
| Excavation depth | 4 | m |
| Batter angle from horizontal | 60 | ° |
| Cohesion c' | 8 | kPa |
| Friction angle φ' | 28 | ° |
| Unit weight | 19 | kN/m³ |
| Required FS | 1.5 |
Worked example — results
| Result | Value | Unit |
|---|---|---|
| Critical height Hc | 8.48 | m |
| Factor of safety Hc/H | 2.12 | |
| Critical plane angle | 44.0 | ° |
| Batter for FS = 1.5 | 60.0 | ° |
- ✓ FS ≥ required — 2.12
- ✓ Depth > 1.5 m needs benching, battering or shoring (WHS code) — required
Method, formulas and assumptions
- Culmann: Hc = 4c/γ · sinβ cosφ / (1 − cos(β − φ)), critical plane at (β + φ)/2. Planar mechanism; ignores tension cracks, water and surcharge — keep spoil and plant back from the crest.
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For preliminary design and education. Check every result against the current standard and your own engineering judgement before use.