Soil Mechanics / module 11
Shear strength of soils
Why and how soil fails in shear: friction and interlocking, the Mohr–Coulomb criterion on effective stress, peak, critical and residual states, and drained versus undrained strength.
What you will understand
- Explain shear strength as friction, mobilised on the effective stress
- State and apply the Mohr–Coulomb failure criterion τf = c′ + σ′·tanφ′
- Use the Mohr circle and derive the principal-stress form σ′1f = σ′3·Kp + 2c′√Kp
- Locate the failure plane at 45 + φ′/2 to the major principal plane
- Distinguish peak, critical-state and residual strength
- Distinguish drained (c′, φ′) from undrained (su, φu = 0) strength and know when each governs
Lessons
What gives soil its strength
Friction on the effective stress, interlocking and dilation, and the peak–critical–residual sequence.
The Mohr–Coulomb criterion
The failure line, the Mohr circle tangent to it, and the principal-stress form.
Drained and undrained strength
Why the same clay has two strengths, and when each governs.
Module summary
- Soil strength is frictional and mobilised on the effective stress, so pore pressure is central to it.
- Mohr–Coulomb τf = c′ + σ′·tanφ′; principal form σ′1f = σ′3·Kp + 2c′√Kp; failure plane at 45 + φ′/2.
- Dense soils dilate and show a peak above the critical-state strength; residual is lower still on pre-sheared clay surfaces.
- Drained (c′, φ′, long-term) versus undrained (su, φu = 0, short-term); loading on clay is short-term critical, unloading long-term critical.
Teaching basis and review status
These are educational models and exercises. Check their assumptions before using the results. The full technical content and every diagram have not yet been independently verified.
Concrete and steel calculations retain their stated first-generation Eurocode teaching basis. Use the standards and amendments specified for your project; do not mix generations without an appropriate design basis.
Read the lesson register and outstanding review notesCheck your understanding
Practice
A drained triaxial test on sand (c′ = 0, φ′ = 35°) is run at σ′3 = 60 kPa. What is the axial effective stress at failure, in kPa? (Kp = tan²(45 + 35/2).)
Check yourself
A rise in porewater pressure, with no change in total stress, does what to the available shear strength?
Practice
For a cohesionless soil at failure with σ′1 = 180 kPa and σ′3 = 60 kPa, what is the mobilised (here, peak) friction angle, in degrees? (sinφ′ = (σ′1 − σ′3)/(σ′1 + σ′3).)