Fault orientation in damage failure under compression

The Mohr-Coulomb criterion is widely used in geosciences to relate the state of stress at failure to the observed orientation of the resulting faults. This relation is based on the assumption that the fault occurs along a plane that maximizes the Coulomb stress. Here, we test this hypothesis using an elastic, progressive damage model that implements the Mohr-Coulomb criterion at the local scale. We find that the orientation of the fault is not given by the Mohr-Coulomb criterion. Instead, for minimal disorder, it corresponds to the most unstable mode of damage in the model, which we determine through a linear stability analysis of the homogeneously damaged state. Our simulations show that microstructural disorder significantly affects the orientation of the fault, which, however, remains always far from the Mohr-Coulomb prediction.