Particle Dynamics Simulations of Rate and State Dependent Frictional Sliding of Granular Fault Gouge

Particle dynamics methods (PDM) have proven very valuable in the study of fault processes, fault mechanics, and associated deformation. Such discrete numerical techniques capture the heterogeneity and discontinuous nature of earth materials, and can reproduce many behaviors and geometries observed in natural and experimentally-generated shear zones. These include strain localization and delocalization, stick-slip sliding, and characteristic fracture arrays. However, several fundamental experimental results thought to be important in the earthquake generation process, have not been well represented by PDM models: 2D simulations conducted on idealized assemblages of particles using simple elastic-frictional contact laws, generally yield friction values much lower than natural materials, and lack second-order time- and velocity-dependent changes in strength that influence dynamic fault slip. In efforts to reconcile these differences between experimental and numerical friction, new simulations using the discrete element method (DEM) have been carried out using more realistic particle motions conditions and interparticle contact laws: (a) particle rotations are restricted as a proxy for grain roughness, interlocking, and out-of-plane contacts that resist rolling, and (b) time-dependent contact healing is introduced to capture temporal strengthening of granular assemblages. The resulting mechanical behavior qualitatively reproduces the scale and phenomenology of empirically based rate and state constitutive laws for friction. Frictional strength is increased, and in the absence of interparticle rolling, can attain values comparable to those observed in the lab. Even though interparticle contact strength depends only on time of static contact in these models, the bulk assemblage shows velocity- and slip-dependent behavior associated with changes in deformation mechanism, particle configuration and packing, and contact orientation. These results demonstrate the complexity of, and range of factors that control, granular deformation under dynamic conditions. The DEM results bring us one step closer to building a consistent, physics-based description of fault friction phenomena that can be extrapolated to natural faults and an understanding of their seismogenic behavior.