Global Frictional Equilibrium via Stochastic, Local Coulomb Frictional Slips

Based on the assumption that fault slip dominates in the stress relaxation in the brittle crust, Coulomb theory allows for the crustal stress estimation with an empirical frictional coefficient. However, natural variability of fault friction and slip uncertainty exist in the Earth's crust. To address the extent to which heterogeneous frictional slips influence crustal stress and its evolution, we establish a quasi-static, 2D model to represent the fractured crustal rock mass. The model consists of randomly oriented fractures with heterogeneous distribution of frictional coefficients. The global mechanical response is quantitatively related to the cascades of local frictional slips under specific boundary conditions. The temporal evolution of stress is explicitly modeled by an iterative process where a simple slip law is assumed for critical fractures. We particularly illustrate the stress evolution in a normal faulting stress regime, considering different distributions of frictional coefficients. All cases indicate that the decrease in differential stress manifests as a self-organized process, eventually leading to the frictional equilibrium of the fractured rock mass. The final stress state upon equilibrium jointly depends on the orientation and frictional coefficient of all fractures therein. The model informs that the global stress state of a stochastic system can depart substantially from a deterministic estimation via an empirical frictional coefficient. This model quantitatively corroborates and extends the notion of frictional equilibrium, and reveals far more profound influence of system heterogeneity on the local and global stress evolution.ISSN:2169-9313ISSN:0148-0227ISSN:2169-935