Ground engineering · Tunnels & shafts
Tunnelling settlement trough (Peck) calculator
Maximum surface settlement, trough width i = K z0 and settlement at an offset for a volume loss.
Standard: Peck (1969) Gaussian trough · O'Reilly & New (1982) K
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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 |
|---|---|---|
| Tunnel diameter | 6 | m |
| Axis depth | 18 | m |
| Volume loss | 1 | % |
| Trough width parameter K | 0.5 clay | |
| Offset of interest | 10 | m |
Worked example — results
| Result | Value | Unit |
|---|---|---|
| Settlement volume VL π D²/4 | 0.283 | m³/m |
| i = K z0 | 9.00 | m |
| Smax = Vs/(√(2π) i) | 12.53 | mm |
| S(x) | 6.76 | mm |
| Max slope 0.61 Smax/i | 0.001 |
- ✓ Smax ≤ 25 mm
- ✓ Max slope ≤ 1/500
Method, formulas and assumptions
- Settlement volume VL π D²/4 = 1/100*PI()*6^2/4 = 0.28274 m³/m
- i = K z0 = 0.5*18 = 9 m
- Smax = Vs/(√(2π) i) = 0.28274/(SQRT(2*PI())*9)*1000 = 12.533 mm
- S(x) = 12.533*EXP(-(10^2)/(2*9^2)) = 6.7605 mm
- Max slope 0.61 Smax/i = 0.61*12.533/1000/9 = 8.495e-4
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For preliminary design and education. Check every result against the current standard and your own engineering judgement before use.