Ground engineering · Tunnels & shafts
Tunnel lining & rock load calculator
Overburden, lining hoop thrust and stress, ovalisation moment, and rock support pressure.
Standard: Thin-ring thrust · Muir Wood · Terzaghi rock load · Barton Q
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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 |
|---|---|---|
| Radius to lining centroid R | 3 | m |
| Depth to axis | 20 | m |
| Ground γ | 20 | kN/m³ |
| Surface surcharge | 10 | kPa |
| K0 | 0.6 | |
| Lining thickness | 300 | mm |
| Lining f'c | 40 | MPa |
| Terzaghi rock condition | Very blocky & seamy | |
| Rock γ | 25 | kN/m³ |
| Barton Q value | 1 | |
| Joint roughness Jr | 1.5 | |
| Excavation support ratio ESR | 1 |
Worked example — results
| Result | Value | Unit |
|---|---|---|
| σv at axis (full overburden) | 410 | kPa |
| σh = K0 σv | 246 | kPa |
| Hoop thrust N = p̄R | 984 | kN/m |
| Hoop stress N/t | 3.28 | MPa |
| Ovalisation M = (σv − σh)R²/6 | 246 | kNm/m |
| Stress with bending | 19.68 | MPa |
| Allowable 0.45 f'c | 18.0 | MPa |
| Terzaghi rock load height Hp | 13.2 | m |
| Terzaghi support pressure | 330 | kPa |
| Barton roof support pressure | 133 | kPa |
| Equivalent dimension B/ESR | 6.0 | m |
- ✓ Hoop stress ≤ 0.45 f'c
- ✗ Combined stress ≤ 0.45 f'c
Method, formulas and assumptions
- σv = γH + q (full overburden, conservative; arching ignored)
- Thin ring under mean pressure p̄ = (σv + σh)/2: N = p̄ R, σ = N/t
- Ovalisation with ground reaction (Muir Wood 1975): M = (σv − σh) R²/6
- Terzaghi (1946): Hp = factor × B or × (B + Ht) for the rock class (upper bound of range), p = γr Hp
- Barton et al. (1974): Proof = 0.2 Q^(−1/3) / Jr MPa
- Tunnel linings are designed to project specifications and AS 5100 / AS 3600 with numerical analysis; this is a first estimate.
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For preliminary design and education. Check every result against the current standard and your own engineering judgement before use.