Library / Terramechanics and off-road mobility / TER-23
Terramechanics and off-road mobility
Undrained strength from cone index
Rough empirical estimate of the undrained shear strength of clay from a cone penetrometer reading, with both quantities in the same pressure units.
- Ref
- TER-23
- Rev
- v1
- Field
- Terramechanics and off-road mobility
- Result
- cu [kPa]
For clay, the lecture takes cu ≈ CI/10 as an empirical estimate, with both quantities in the same pressure units: a cone index of 400 kPa gives a strength of about 40 kPa. It is a rough rule for field use, not a substitute for a laboratory test. The strength it gives feeds the bearing and wheel-resistance estimates for clay.
Rough empirical estimate of the undrained shear strength of clay from a cone penetrometer reading, with both quantities in the same pressure units.
Calculator
- Cone index in psi58.02 psi
- Bearing capacity with Nc = 5.7228 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 cone index of 400 kPa (58.02 psi) suggests a strength of 40 kPa, which with Nc = 5.7 puts the bearing capacity near 228 kPa. The factor of 10 depends on the soil and the cone, so treat it as a first guess.
- A soft clay with a cone index of 100 kPa gives cu of 10 kPa, and a firm one with 600 kPa gives 60 kPa.
Chart data as tables
Ranked variables
| Variable | Typical range | Lowest result | Highest result | Swing (kPa) | Local step | Change in result |
|---|---|---|---|---|---|---|
| CI Cone index | 50 to 1,500 kPa | 5 | 150 | 145 | +10% | +10 % |
Sweep of Cone index
| Cone index (kPa) | Undrained shear strength (kPa) |
|---|---|
| 50 | 5 |
| 231.3 | 23.13 |
| 412.5 | 41.25 |
| 593.8 | 59.38 |
| 775 | 77.5 |
| 956.3 | 95.63 |
| 1,138 | 113.8 |
| 1,319 | 131.9 |
| 1,500 | 150 |
Sweep one variable
Variables and how each one contributes
Undrained shear strength
What the equation gives you. Everything else feeds it.
Cone index
The cone index from a penetrometer test in clay, in kPa. Raises the strength estimate in proportion, one tenth as fast. Raising it by 10 % (to 440) moves the result by +10 %, from 40 to 44 kPa.
Worked example with the values above
- Divide by 10: 400 / 10.
- cu ≈ 40 kPa.
- That feeds the bearing estimate: 5.7 × 40 = 228 kPa.
Assumptions and limits
- Saturated clay, with the cone index measured in the undrained condition.
- Cone index and strength in the same pressure units.
Common mistakes
- Mixing psi and kPa between the two quantities.
- Applying it to sand or other soils without clay behaviour.
Statistics and uncertainty
The ratio of cone index to undrained strength varies with soil type, typically between 8 and 16, so the estimate may be off by ±40 %. Where a result matters, run a laboratory or vane shear test.
Where it is used
- Getting a clay strength from a quick field penetrometer reading.
- Feeding the bearing and wheel-resistance estimates when no laboratory test exists.
Maths you need
- Cone penetrometer: a probe pushed into soil
- Undrained strength: strength of clay under quick loading