Mohr-Coulomb Failure Criterion in Soil Mechanics

The Mohr-Coulomb failure criterion is a fundamental concept in soil mechanics used to predict shear failure in soils under applied stresses. It defines shear strength ($\tau$) as a linear function of normal effective stress ($\sigma'$), cohesion ($c$), and the internal friction angle ($\phi$) through the formula $\tau = c + \sigma' \tan\phi$. Cohesion represents soil's inherent shear strength independent of normal stress, often due to bonding or cementation, while the friction angle reflects resistance from interparticle friction and interlocking. Failure occurs when the Mohr stress circle tangentially meets the failure envelope, which is depicted by a linear line on a shear stress versus normal stress plot. The effective stress concept accounts for pore water pressure effects, which influence soil strength. The internal friction angle varies by soil type, being generally higher in granular soils and lower in clays. This criterion is critical in designing geotechnical structures such as foundations, slopes, and retaining walls, predicting failure conditions, guiding soil improvement methods, and supporting numerical stability analyses.