Shear Strength

A steel bar has one yield stress wherever it is. A sand has a different strength at every depth, because its resistance is friction and friction depends on the normal stress. That single difference is what makes soil mechanics its own subject.

Mohr-Coulomb: τ = c′ + σ′tan φ′. The cohesion intercept is strength at zero confining stress, from electrochemical bonding between clay particles — which is why a clay trench face stands vertically and a sand one collapses immediately.

For a purely frictional soil, the driving force down a slope and the frictional resistance both scale with weight — so weight cancels and the stable angle is φ′ regardless of height. A sand pile and a hundred-metre dune stand at the same angle.

Dense sand must dilate — grains ride over one another — so it shows a peak strength and then falls away. Loose sand contracts and rises to the same value with no peak. Both converge on the same critical state.

Peak strength is mobilised once and lost as soon as a slip surface forms, so design uses the critical state — or, on a pre-existing shear surface, the residual, which in a stiff plastic clay can be under half the peak. That is why old landslips reactivate at angles that look safe.

The test must match the field loading rate, or it answers the wrong question. Only the triaxial lets drained or undrained conditions be chosen deliberately.

In an undrained saturated clay, additional confining stress goes entirely into the pore water, so σ′ is unchanged and the strength does not vary with confinement — a horizontal envelope. Short-term analysis then needs a single parameter c_u, which is why a field vane test is so useful.

Bearing capacity, slope stability and earth pressure — and each is analysed twice, undrained for end of construction and drained for the long term. Whichever gives the lower factor of safety governs.