MohrCoulombmodellen

The Mohr-Coulomb model is a widely used mathematical model in soil mechanics and rock mechanics to predict the shear strength of a material. It describes the failure of brittle materials under shear stress. The model is based on the work of Otto Mohr and Charles Augustin de Coulomb.

The Mohr-Coulomb model assumes that failure occurs when the shear stress on a plane within the material reaches a critical value. This critical value is dependent on two material properties: the cohesive strength (c) and the angle of internal friction (phi). Cohesion represents the shear strength of the material when the normal stress is zero, while the angle of internal friction accounts for the increase in shear strength with increasing normal stress.

Mathematically, the failure criterion can be expressed as: tau = c + sigma * tan(phi), where tau is the shear stress at failure, sigma is the normal stress acting on the failure plane, c is the cohesion, and phi is the angle of internal friction. The model is often represented graphically using a Mohr's circle diagram, where the failure envelope is a straight line tangent to the Mohr's circles representing stress states within the material.

While the Mohr-Coulomb model is a simplification of real material behavior, it provides a reasonable approximation for many engineering applications, such as the stability analysis of slopes, foundations, and retaining walls. Its simplicity and intuitive parameters have contributed to its widespread adoption in geotechnical engineering. However, it has limitations, particularly in predicting the behavior of materials under complex stress paths or cyclic loading.