Understanding Frictional Equilibrium in the Brittle Crust through Stochastic Frictional Slips

Abstract:

Fault slip relaxes crustal stresses. Assuming frictional equilibrium achieved by distributed, local slips, the classic Coulomb frictional failure theory allows for the estimation of crustal stress with an empirical frictional coefficient. However, natural variability of fault friction and slip uncertainty exist in the Earth’s crust. To what extent it influences crustal stress and its evolution is intriguing. Here we established a quasi-static, 2D model to simulate the stress evolution due to Coulomb frictional slips in the crustal rock masses. The model simply features randomly-oriented fractures with heterogeneous frictional coefficients. We emphasize the global stress response by summing the contribution of cascades of local frictional slip under specific boundary conditions. An iterative process regulates the slip cascading and timely updates the global stress that, in turn, influences local fracture criticality. We illustrated the stress evolution in a normal faulting stress regime, considering differently distributed fracture frictional coefficients. Common to all scenarios, the decrease in stress difference manifests as a self-organized process that ultimately leads to frictional equilibrium of the 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 frictional equilibrium of a stochastic system can depart substantially from a deterministic estimation via an empirical frictional coefficient. Although the model quantitatively corroborates the notion of frictional equilibrium in places where fracture slip is the dominant mechanism for stress release, it reveals far more profound influence of system heterogeneity on the local and global stress evolution.