Site investigation · Laboratory: strength & consolidation
Stress paths (MIT p′–q) and strength fit calculator
Total and effective stress paths from triaxial data, with the Kf line fitted to give c′ and φ′.
Standard: MIT stress path · Kf line → c′, φ′
Open the live calculator → All site investigation calculators
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 |
|---|---|---|
| Points at failure: σ3 (kPa), deviator Δσ (kPa), Δu (kPa) | 100, 165, 42 200, 290, 88 400, 520, 170 |
Worked example — results
| Result | Value | Unit |
|---|---|---|
| Kf intercept a | 12.86 | kPa |
| Kf slope tan α | 0.5058 | |
| φ′ = asin(tan α) | 30.39 | ° |
| c′ = a/cos φ′ | 14.91 | kPa |
| R² of fit | 0.9996 |
Method, formulas and assumptions
- p = (σ1 + σ3)/2, q = (σ1 − σ3)/2, p′ = p − u
- Kf line q = a + p′ tan α; sin φ′ = tan α; c′ = a/cos φ′
Related site investigation calculators
- Oedometer consolidation test — Lab sheet: e–log σ' curve, Cc, Cr, Casagrande preconsolidation pressure, mv per stage and cv by Taylor's…
- Triaxial test (UU / CU / CD) — Mohr circles and failure envelope from triaxial specimens: su for UU, c′ and φ′ for CU (with pore pressure)…
- Unconfined compression test — Stress–strain with area correction, peak qu, su = qu/2 and E50 secant modulus.
- Direct shear test — Peak (and residual) failure envelopes from shear box results.
- Permeability (constant / falling head) — Hydraulic conductivity from constant- or falling-head tests, corrected to 20 °C.
- Coefficient of consolidation (root-time & log-time) — cv from Taylor's t90 and Casagrande's t50, with permeability from k = cv·mv·γw.
- Collapse potential (oedometer) — Collapse potential from the strain on wetting at constant stress, with the usual severity classes.
- Free swell & swell pressure (oedometer) — Free swell strain under seating load and swell pressure from the constant-volume or load-back method.
- Residual strength: ring shear — Residual friction angle from a regression through the origin and a free-intercept fit.
- Vane shear (lab / field) — Undrained strength from peak and remoulded torque, sensitivity and Bjerrum's plasticity correction.
For preliminary design and education. Check every result against the current standard and your own engineering judgement before use.