MohrCulomb

Mohr-Coulomb is a widely used failure criterion in geotechnical engineering that describes when soils and rocks fail under combined normal and shear stresses. It combines Coulomb’s friction law with Mohr’s circle to provide a simple, empirical envelope for shear strength on a potential failure plane.

The primary form of the criterion states that the shear stress at failure on a plane with normal stress sigma_n is tau = c + sigma_n tan(phi), where c is the material’s cohesion and phi is the angle of internal friction. Both parameters are material properties that are typically determined from laboratory tests such as direct shear or triaxial compression, and may depend on confining pressure and moisture. In practice, the model is often applied in terms of principal stresses or through a two-dimensional failure envelope in design calculations.

Applications of Mohr-Coulomb are widespread in geotechnical design and analysis. It is used for slope stability assessments, bearing capacity evaluations for shallow foundations, design of retaining structures, and various aspects of tunneling and earthworks. The criterion provides a simple, first-order approximation of strength under typical stress states encountered in soils and some rocks.

Limitations include its simplifications: it assumes rate-independent, monotonic loading with constant c and phi, and may not capture post-peak behavior, pore-water pressure effects, or complex 3D stress and anisotropy in real soils and fractured rock masses. For more complex behavior, alternatives like the Drucker-Prager model or advanced constitutive laws may be used.