Engineering
Mohr-Coulomb Soil Shear Strength & Infinite-Slope Factor of Safety
Calculate a drained Mohr–Coulomb shear-strength example and, separately, an ideal dry cohesionless infinite-slope ratio.
Use consistent strength parameters and separate the two models
The first example uses effective-stress parameters c′ and phi′ with compressive effective normal stress sigma′. Its result is an idealized drained shear-strength envelope. Setting phi′ to zero makes the arithmetic equal c′; it does not by itself turn effective-stress inputs into an undrained total-stress clay analysis.
The second example is independent: a dry, cohesionless infinite slope with a planar failure surface parallel to its surface and no surcharge or seismic loading. Its ratio tan(phi)/tan(beta) uses the separate slope friction angle in B6 and ignores B2/B3. The nonzero cohesion in the first example must not be treated as part of this second model.
A ratio below 1 indicates insufficient resistance under these assumptions, not proof of active movement or its timing. A ratio above 1 is not a design approval. Required margins and appropriate models depend on site conditions and governing criteria. This worksheet does not assess a real slope.
| Geotechnical Shear Metric | Formula | Strength: c′=15 kPa, sigma′=80 kPa, phi′=32°; separate dry slope: phi=32°, beta=24° | Over-Steepened beta = 36° |
|---|---|---|---|
| Mohr-Coulomb Shear Strength | B2 + B3 * TAN(RADIANS(B4)) | 15 + 49.99 = 64.99 kPa | 64.99 kPa |
| Zero effective friction angle | tau = c′ when phi′ = 0 | 15.00 kPa (arithmetic limiting case) | Not an undrained analysis |
| Independent dry-slope ratio | TAN(RADIANS(B6))/TAN(RADIANS(B5)) | 1.40 (model ratio) | 0.86 (model ratio) |
Mohr-Coulomb Drained Shear Strength tau_f (kPa)
Sums cohesive intercept B2 and frictional resistance B3 * TAN(RADIANS(B4)).
=IF(COUNT(B2:B4)<>3,"Invalid inputs",IF(OR(B2<0,B3<0,B4<0,B4>=90),"Invalid inputs",ROUND(B2+B3*TAN(RADIANS(B4)),2)))Dry Cohesionless Infinite-Slope Factor of Safety (FS)
Use a positive slope angle below 90 degrees and a friction angle from 0 to below 90 degrees. B6 is the independent dry-slope friction angle. The rounded display is not suitable for deciding a near-threshold design margin.
=IF(OR(NOT(ISNUMBER(B5)),NOT(ISNUMBER(B6))),"Invalid inputs",IF(OR(B5<=0,B5>=90,B6<0,B6>=90),"Invalid inputs",ROUND(TAN(RADIANS(B6))/TAN(RADIANS(B5)),2)))Try the example
Use the original values or change them to test your understanding.