Evolution of Frictional Strength of Dry Sheared Granular Porous Media During Slip-Rate Weakening

Abstract

Using the discrete-element method, we study loss of shear strength at frictional asperity contacts, induced by flash heating, in a granular fault gouge. The magnitude of the reduction in the shear stress and the local friction coefficients are computed over a wide range of shear velocities V_s. For small strain rates, there is negligible difference between the frictional stress for packings with and without frictional weakening that arises due to flash heating. As strain rate increases, however, the difference between the two becomes significant. The results indicate a clear transition in the shear stress-shear strain response corresponding to V_s > 0.3 m/s and those with V_s ≤ 0.3 m/s. Specifically, the stress–strain diagrams at lower V_s exhibit a pronounced decreasing strength over small distances, whereas they indicate a progressive increase in the shear stress at higher V_s, which is reminiscent of a transition from ductile behavior at high velocities to brittle response at low velocities. Only a small fraction of the contacts experience lower friction, with the majority having friction coefficients closer to 0.5, hence suggesting that fast slip is accommodated only at a few contacts, with the rest either not sliding at all, or sliding very slowly. Moreover, if we define an effective macroscopic friction coefficient, µe = τ/P, where τ is the shear stress, and P is the pressure, and the inertial number I by, I = γD√(ρ/P), where γ is the strain rate, and D is the average size of the particles, we find that the weakening packing follows a nonlinear friction law, well approximated by, µe ≈ I^3/4. Thus, the model with flash heating deviates from linear friction law even at smaller, albeit not too small, values of I, which is intriguing and novel. The implications of the results for earthquake physics and the principal slip planes in fault z ones are discussed.