Mohr–Coulomb Shear Strength

Coulomb wrote the friction half of this in 1773 while working on the retaining walls of Martinique; Mohr supplied the stress-circle framework a century later. The idea is that soil resists shear in two ways: a cohesion intercept that exists at zero normal stress, and a frictional part proportional to the effective normal stress squeezing the grains together. A silty clay with c′ = 15 kPa and φ′ = 25° on a plane carrying σ′ = 100 kPa can resist τ = 15 + 100 × tan 25° = 15 + 46.6 = 61.6 kPa.

The trap is primed: this must be written in effective stress. Raise the pore pressure and σ′ falls, taking the frictional term with it, which is precisely how a stable slope fails after a week of rain without a single grain being removed. The second trap is c′ itself. For a normally consolidated clay or a clean sand the true effective cohesion is essentially zero, and a c′ of 10 or 20 kPa fitted to a scattered triaxial dataset is an artefact of the regression that will quietly carry a large fraction of your slope's factor of safety. Skempton's 1964 work on progressive failure in London Clay showed that long-term strength drifts down to a residual with no cohesion at all.