MohrCoulombkriteriet

Mohr-Coulomb criterion is a mathematical model used to describe the failure of materials under complex stress states. It is named after Christian Otto Mohr and Charles-Augustin de Coulomb, who contributed to the understanding of material failure. The criterion is widely used in geotechnical engineering and soil mechanics to predict the failure of soils and rocks under various loading conditions.

The Mohr-Coulomb criterion is based on the concept of shear strength, which is the maximum shear stress that a material can withstand before failure. It assumes that the shear strength of a material is a linear function of the normal stress acting on the plane of failure. This relationship is described by the equation:

τ = c + σ tan(φ)

where τ is the shear stress, c is the cohesion, σ is the normal stress, and φ is the angle of internal friction. The cohesion represents the shear strength of the material when the normal stress is zero, while the angle of internal friction describes the increase in shear strength with increasing normal stress.

The Mohr-Coulomb criterion can be represented graphically on a Mohr's circle, which is a graphical representation of the stress state at a point in a material. The failure envelope, which is a straight line on the Mohr's circle, represents the maximum shear stress that the material can withstand before failure. The slope of the failure envelope is equal to the angle of internal friction, and the intercept on the shear stress axis is equal to the cohesion.

The Mohr-Coulomb criterion is a simple and widely used model for describing material failure, but it has limitations. It assumes that the shear strength of a material is independent of the stress history and that the failure envelope is linear. In reality, the shear strength of a material may depend on factors such as the stress history, the rate of loading, and the presence of cracks or other defects. Despite these limitations, the Mohr-Coulomb criterion remains an important tool for engineers and scientists working in the fields of geotechnical engineering and soil mechanics.