Macroscopic friction response of rotational and non-rotational lattice solid gouge models in 2D and 3D

Traditionally, 2D Discrete Element Models (DEMs) have been preferred over 3D models, for fault gouge simulations, because of the computational cost of solving 3D problems. In order to realistically simulate fault gouge processes it is important to characterize differences between 2D and 3D models and be able to assess whether 2D models are adequate for approximating 3D gouge dynamics. In this paper, 2D and 3D fault gouges are simulated as two rectangular elastic blocks of bonded particles, separated by a region of randomly sized non-bonded spherical gouge particles, sheared in opposite directions by normally-loaded driving plates. The dynamic behavior of multiple model parameterizations is analyzed by examining instantaneous macroscopic fault friction (μ _I) statistics. The response of the mean macroscopic friction is characterized for varying values of inter-particle (microscopic) friction μ _P in 2D and 3D and for non-rotational and rotational particle dynamics. In the non-rotational models, realistic angular gouge mean macroscopic friction values (E[μ _I] ≈ 0.6) are obtained in the simulations for a 2D inter-particle friction value of μ _P = 0.3 and 3D value of μ _P = 0.2. The rotational models exhibit mean macroscopic friction values of E[μ _I] = 0.3 (in 2D) and E[μ _I] = 0.38 (in 3D) for inter-particle friction values μ _P ≥ 0.3. The 2D rotational macroscopic friction values are in close agreement with comparable 2D glass-rod (E[μ _I] ≈ 0.3) laboratory experiments. In the 3D case, the simulated mean macroscopic friction values are lower than those of 3D spherical bead laboratory experiments where 0.4 > E[μ _I] ≤ 0.45.