On the relation between the coefficient of friction of a fault and the variation of damage degree on the host rock: a numerical approach

We present a study on the dependence of the frictional properties of a fault rock on its degree of damage. The purpose is therefore to gain insight into frictional sliding, the governing force that controls earthquake nucleation, propagation and arrest. The focus on this topic is to try to find a reason for the experimental evidence that the friction coefficient seems to be almost independent on lithology. A possible explanation to investigate through the numerical modelling could be that the frictional properties of a realistic fault rock depend mostly on the concentration of micro- to macroscopic cracks and/or of lamellar phyllosilicates in the host rock, rather than on the composition of its bulk materials. The formalism of the Linear Elastic Fracture Mechanics (LEFM) can quantitatively reproduce the stresses and the strains on the interface propagating frictional rupture. The purpose is to use a Finite Element Method (FEM) numerical code in order to simulate the plane strain elastic deformation of a two-dimensional medium crossed by elliptical fractures and weak anisotropic inclusions. The analysis of the distribution and orientation of the stresses resulting from the interaction of a system of randomly oriented elliptical fractures under different loading conditions could provide information on the onset and propagation of frictional ruptures, such as real contact area reduction, slip velocity, number and length of global sliding precursors. The magnitude and orientation of the principal stresses around the tips of elliptical voids are crucial for the understanding of fracture coalescence and frictional reactivation of shear cracks in an elastic rock, which in turn is one of the main factors that govern the seismic cycle of natural faults.