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Terramechanics and off-road mobility
Undrained bearing capacity of clay
Pressure at which saturated clay under a loaded area fails in bearing, taken as the undrained strength times a bearing factor.
- Ref
- TER-20
- Rev
- v1
- Field
- Terramechanics and off-road mobility
- Result
- qf [kPa]
The pressure at which saturated clay fails in bearing under a loaded area is qf = cuNc, the undrained shear strength times a bearing factor. This is a total-stress, undrained approximation (φu ≈ 0). The lecture uses Nc = 5.7 for a strip idealisation and 7.4 for a square or circular one. These are model-specific bearing factors, not universal soil constants. Do not mix undrained total-stress parameters with drained effective-stress parameters in the same calculation.
Pressure at which saturated clay under a loaded area fails in bearing, taken as the undrained strength times a bearing factor. The factor depends on the idealised shape of the loaded area.
Calculator
- Same clay with Nc = 7.4 (square or circular contact)296 kPa
- Allowable bearing pressure with a factor of safety of 376 kPa
What drives the result
Each variable is moved across its typical range while the others stay at the values above. The longest bar is the key driver.
- A clay of 40 kPa strength fails in bearing at 228 kPa with the strip factor, or 296 kPa with the square factor. A track exerting a mean pressure of 50 kPa has a factor of safety of 4.56, although sinkage and motion resistance would already be large.
- The failure pressure is directly proportional to the strength, so a clay softened to 20 kPa by remoulding carries only 114 kPa.
Chart data as tables
Ranked variables
| Variable | Typical range | Lowest result | Highest result | Swing (kPa) | Local step | Change in result |
|---|---|---|---|---|---|---|
| cu Undrained shear strength | 5 to 200 kPa | 28.5 | 1,140 | 1,112 | +10% | +10 % |
| Nc Bearing factor (5.7 for a strip, 7.4 for a square or circle) | 5 to 8 | 200 | 320 | 120 | +10% | +10 % |
Sweep of Undrained shear strength
| Undrained shear strength (kPa) | Bearing capacity (kPa) |
|---|---|
| 5 | 28.5 |
| 29.38 | 167.4 |
| 53.75 | 306.4 |
| 78.13 | 445.3 |
| 102.5 | 584.3 |
| 126.9 | 723.2 |
| 151.3 | 862.1 |
| 175.6 | 1,001 |
| 200 | 1,140 |
Sweep one variable
Variables and how each one contributes
Bearing capacity
What the equation gives you. Everything else feeds it.
Undrained shear strength
The undrained shear strength of the clay, in kPa. Soft clay is about 10 to 40 kPa and stiff clay above 100 kPa. Raises the bearing capacity in proportion. Raising it by 10 % (to 44) moves the result by +10 %, from 228 to 250.8 kPa.
Bearing factor (5.7 for a strip, 7.4 for a square or circle)
The bearing factor, a plain number: 5.7 for a strip, 7.4 for a square or circle. Raises the bearing capacity in proportion. Raising it by 0.5 (to 6.2) moves the result by +8.77 %, from 228 to 248 kPa.
Worked example with the values above
- Multiply the strength by the factor: cu Nc = 40 × 5.7.
- qf = 228 kPa.
- With a factor of safety of 3 the allowable pressure is 76 kPa.
Assumptions and limits
- Saturated clay loaded quickly enough to remain undrained (φu ≈ 0).
- The bearing factor suits the contact shape: strip or square/circular.
Common mistakes
- Using effective-stress strength parameters with this total-stress formula.
- Quoting the bearing factor as a universal constant.
Statistics and uncertainty
Undrained strength varies by ±30 % even within one site, and the bearing factor is a model choice, not a measurement, so the capacity is uncertain by at least that amount. A bearing factor of safety of 3 is typical for this reason.
Where it is used
- Checking whether a wheel or track can carry its load on soft clay.
- Estimating the load at which a vehicle sinks in.
Maths you need
- Undrained shear strength: strength of clay loaded without drainage
- Bearing factor: depends on the shape of the loaded area