Retaining & slopes · Slope stability
Anti-slide (stabilising) piles in a slope calculator
Force each pile must provide to raise the slope factor of safety, the moment and shear at the slip surface, and the embedment below the slip (Broms, stiff clay or weak rock) needed to develop it.
Standard: Force deficit from the slope analysis · Broms (1964) cohesive soil below the slip surface
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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 |
|---|---|---|
| Driving force on slip surface (per m) | 900 | kN/m |
| Resisting force (per m) | 950 | kN/m |
| Required factor of safety | 1.5 | |
| Pile spacing | 2 | m |
| Depth of slip surface at piles | 6 | m |
| Pile diameter | 1 | m |
| Undrained strength below slip | 120 | kPa |
| Embedment below slip surface | 9 | m |
| Pile moment capacity φMu | 3500 | kNm |
Worked example — results
| Result | Value | Unit |
|---|---|---|
| Current FS = R/D | 1.06 | |
| Required stabilising force FSr·D − R | 400.0 | kN/m |
| Force per pile | 800.0 | kN |
| Load eccentricity above slip (triangular load, H/3) | 2.00 | m |
| Depth to max moment below slip 1.5D + P/(9cuD) | 2.24 | m |
| Maximum moment P(e + 1.5D + 0.5f′) | 3,096 | kNm |
| Remaining length for fixity √(M/(2.25cuD)) | 3.39 | m |
| Required embedment f + g | 5.63 | m |
- ✓ Embedment ≥ required
- ✓ Moment capacity ≥ maximum moment
Method, formulas and assumptions
- Current FS = R/D = 950/900 = 1.0556
- Required stabilising force FSr·D − R = MAX(0,1.5*900-950) = 400 kN/m
- Force per pile = 400*2 = 800 kN
- Load eccentricity above slip (triangular load, H/3) = 6/3 = 2 m
- Depth to max moment below slip 1.5D + P/(9cuD) = 1.5*1+800/(9*120*1) = 2.2407 m
- Maximum moment P(e + 1.5D + 0.5f′) = 800*(2+1.5*1+0.5*(2.2407-1.5*1)) = 3096.3 kNm
- Remaining length for fixity √(M/(2.25cuD)) = SQRT(3096.3/(2.25*120*1)) = 3.3864 m
- Required embedment f + g = 2.2407+3.3864 = 5.6271 m
- Assumes the sliding mass loads the pile with a triangular distribution and that soil arching between piles holds the force (spacing about 2–4 D). Check flow of soil between piles and the structural shear capacity.
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For preliminary design and education. Check every result against the current standard and your own engineering judgement before use.