Site investigation · Laboratory: strength & consolidation
Residual strength: ring shear calculator
Residual friction angle from a regression through the origin and a free-intercept fit.
Standard: ASTM D6467 · BS 1377-7
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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 |
|---|---|---|
| Stages: σn (kPa), τr (kPa) | 100, 22.1 200, 41.8 300, 63.0 400, 82.5 |
Worked example — results
| Result | Value | Unit |
|---|---|---|
| φr through origin | 11.76 | ° |
| φr (free fit) | 11.44 | ° |
| Intercept c′r | 1.75 | kPa |
- ✓ Intercept small (≤ 5 kPa)
Method, formulas and assumptions
- φr through origin = DEGREES(ATAN(SUMPRODUCT([t.s],[t.tr])/SUMPRODUCT([t.s],[t.s]))) = 11.763 °
- φr (free fit) = DEGREES(ATAN(SLOPE([t.tr],[t.s]))) = 11.442 °
- Intercept c′r = INTERCEPT([t.tr],[t.s]) = 1.75 kPa
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For preliminary design and education. Check every result against the current standard and your own engineering judgement before use.