Anisotropy in elastic modulus of fault materials: Insights from the discrete element method

The potential for earthquakes triggered by modulus softening in fault cores has been extensively documented, with a particular emphasis on calculating and characterizing the modulus within fault gouges. Traditionally, the modulus is treated as an average parameter of the entire assembly, and its anisotropic nature is often overlooked. This study derives and verifies formulae to calculate the anisotropy of the elastic modulus of fault material in ellipsoidal assemblies of different shapes using the discrete element method. It defines the anisotropy of the elastic modulus on an irreducible tensor basis in the normal direction of contact forces between particles. The findings indicate that shape-induced anisotropy significantly affects the elastic modulus. Given the consistency between the elastic modulus and wave velocity, the process of elastic wave propagation is simulated. The wave velocity is estimated using the time-of-flight method, which validates the accuracy of the anisotropic decomposition. The relationship between velocity and shape, ascertained by the time-of-flight method, is consistent with that derived from the anisotropic decomposition of the elastic modulus. In contrast, the global average modulus, which disregards anisotropy, fails to acknowledge this relationship. This study highlights the critical importance of considering modulus anisotropy in fault gouges. It evidences the efficacy and universality of this approach, which can be readily applied to other physical properties with orientation dependencies, such as polarization, magnetization, principal axes of stress or strain, and crystallographic axes, among others.