MohrCoulomblikningen

MohrCoulomblikningen, known in geotechnical engineering as the Mohr–Coulomb criterion, is a widely used constitutive model for predicting the shear strength of soils and rocks. It states that the shear strength on a plane is a linear function of the normal stress: tau = c + sigma_n tan(phi), where tau is shear stress, sigma_n is the normal stress on the plane, c is cohesion, and phi is the internal friction angle. Under effective-stress conditions, such as saturated soils, the criterion is written as tau = c' + sigma_n' tan(phi'), with c' and phi' defined for effective stress and sigma_n' representing the normal effective stress.

In principal-stress terms, failure occurs when the Mohr circle for the state of stress just touches the Mohr–Coulomb envelope. The corresponding relation between the major and minor principal stresses at failure in a triaxial state is sigma1 = sigma3 (1 + sin(phi)) / (1 - sin(phi)) + 2 c cos(phi) / (1 - sin(phi)). When cohesion is zero (c = 0), this reduces to sigma1 = sigma3 (1 + sin(phi)) / (1 - sin(phi)). The parameters phi and c are typically determined from direct shear or triaxial compression tests.

Limitations of the Mohr–Coulomb model include its empirical nature, its assumption of isotropy and rate independence, and its limitations in capturing behavior under large deformations, strain hardening/softening, or highly noncohesive soils. It remains a first-order, widely adopted criterion in many engineering applications, with variants and extensions such as pore-pressure considerations, the Drucker–Prager criterion, and critical-state soil models providing alternatives or refinements.

Historically, the criterion combines Mohr’s circle concept with Coulomb’s friction law and was developed and popularized during the 19th and 20th centuries for soil mechanics. It remains a cornerstone in slope stability, bearing capacity, and earth-fill design, valued for its simplicity and physical transparency.

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