Instability of a periodic system of faults

SUMMARY To investigate the effect of heterogeneity of resistance on a fault, we present an analysis of the behaviour of a canonical model, namely a periodic system of coplanar faults that can slip under a slip‐weakening friction law. The friction on the sliding patches is characterized by a weakening rate α. We present a stability analysis based on the decomposition of the solution on a set of eigenfunctions of increasing periodicities that are multiples of the natural period of the system. We discuss the structure of the discrete spectrum of the static solution. For a given geometry, we show that there exists a transition value α 0 of weakening rate defining two distinct regimes. When α is smaller than α 0 , the system is stable, while when α is larger than α 0 , unstable modes with exponential growth are present. This stability limit can be regarded as a non‐local criterion of sliding. A somehow surprising result is the fact that a system with infinite extension can exhibit a stable behaviour. Specifically, we show that even a fault with weakening almost everywhere can be stable. An infinite homogeneous fault, on the contrary, is always unstable as soon as weakening is assumed. To understand this apparent paradox, we refer to the concept of the effective friction law, which describes the large scale behaviour of the fault system, and more precisely here to the effective weakening rate. The results presented here indicate that the effective friction law of a periodic fault system with weakening on the sliding parts can be either a weakening or strengthening law depending on the geometry of the surface of sliding.