Global Frictional Equilibrium via Stochastic, Local Coulomb Frictional Slips

Abstract

A simple quasi-static 2D model simulates the global stress relaxation of fractured rock mass due to local frictional slips • The fractures in the rock mass are stochastically assigned with varying frictional coefficients, representing the system heterogeneity • Global stress evolution of the stochastic case differs from its deterministic counterpart, extending the notion of frictional equilibrium Supporting Information:

How Does In Situ Stress Rotate Within a Fault Zone? Insights From Explicit Modeling of the Frictional, Fractured Rock Mass

“…When θ < 45°, the mean stress becomes less compressive with increasing fracture density, and it is more compressive when θ > 45° (Figures 7e–7h). As a result, the principal stresses would rotate to be at 45° to the fault strike direction for all values of θ , except for 0° and 90° in which differential stress still relaxes but in the absence of stress rotations, that is, contracting Mohr circles with one end fixed (see Zhang & Ma, 2021). These results are in good consistency with those predicted by Casey's (1980) model but substantiated by physics‐based mechanisms.…”

“…In this section, the mechanical behavior of frictional fractures under plane strain condition (Zhang and Ma, 2020) is extended to include elastic deformation. In particular, complete constitutive relationship for frictional fracture is derived considering loading and unloading conditions, respectively, used to calculate the stress changes inside the multilayer model induced by fracture deformation in Section 3.…”

“…Therefore, the additional strain in the y-direction contributed by fractures entails the adjustment of strain in the elastic matrix. Equivalently, σyy should be modified to accommodate the strain increments (Zhang and Ma, 2020). Specifically, bisection method (see Appendix B) is used to search for the stress change in σyy, which gives an updated state of stress of each layer.…”

“…Therefore, the additional strain in the y ‐direction contributed by fractures entails the adjustment of strain in the elastic matrix. Equivalently, σ yy should be modified to accommodate the corresponding strain increments (Zhang & Ma, 2021). The interplay between local fracture deformation and specific boundary conditions of the model drives the stress variations in a self‐regulated manner.…”

Impoundment‐Associated Hydro‐Mechanical Changes and Regional Seismicity Near the Xiluodu Reservoir, Southwestern China

“…This correlation corroborates the primary control of fault criticality on seismicity occurrence, but there remain some obstacles to predict the regional seismicity evolution. The fault criticality is a conditional scalar index based on the assumed probabilistic distributions of in‐situ stress field, fault geometry, and frictional coefficient, which are quite heterogeneous and difficult to constrain (Ma et al., 2020; Shen et al., 2019; Snee & Zoback, 2018; Walsh & Zoback, 2016; Zhang & Ma, 2021). Despite the possible deviation of the assumed parameter distributions from the realistic in‐situ conditions, the first‐order quantification of fault criticality is rather informative to estimate the faults' susceptibility to reactivation, particularly in the context of nearby reservoir impoundment.…”