Shear Strength of Soils

In geotechnical engineering, the safety of structures like foundations, retaining walls, and slopes depends on the soil's ability to resist shear failure. Shear strength is the internal resistance per unit area that the soil mass can offer to resist failure and sliding along any plane inside it.

Soil failure is typically not a tensile or compressive yielding, but rather a shear sliding of soil grains past one another.

Mohr-Coulomb Failure Criterion

The most widely used framework to describe soil shear strength is the Mohr-Coulomb failure criterion, which states that the shear strength of a soil ($\tau_f$) on any failure plane is a linear function of the normal stress ($\sigma$) acting on that plane.

The general equation is:

Cohesion ($c$) represents the shear strength of the soil when no normal stress is applied (common in clays and cemented soils). Angle of internal friction ($\phi$) represents the frictional resistance generated between soil grains as normal stress increases (common in sands and gravels).

Effective Stress Principle in Shear Strength

Because soil is a multi-phase material containing water, its true shear strength depends on the effective stresses transmitted directly between the soil grains, not the total stress.

When the Mohr-Coulomb criterion is modified for effective stress, it becomes:

For saturated coarse-grained soils (like clean sand), $c'$ is approximately zero, making the shear strength purely frictional: $\tau_f = \sigma' \tan(\phi')$

Engineering Checks

In clays under rapid loading conditions (where water cannot drain quickly), total stress (undrained) shear strength parameters are used instead of effective parameters. Engineers must always exercise caution in selecting the correct parameters ($c', \phi'$ vs $c_u, \phi_u$) to match the actual drainage conditions in the engineering project.