A phase-field model for quasi-dynamic nucleation, growth, and propagation of rate-and-state faults

TL;DR

This paper introduces a phase-field model for simulating fault nucleation, growth, and propagation in earthquakes, offering a unified, mesh-convergent approach that captures complex fault behaviors without sophisticated geometry algorithms.

Contribution

It presents a novel phase-field formulation for fault dynamics that simplifies modeling complex fault evolution and off-fault damage within a single framework.

Findings

Model results align with established fault surface methods.

The approach avoids mesh convergence issues in traditional methods.

Demonstrates potential for studying complex earthquake processes.

Abstract

Despite its critical role in the study of earthquake processes, numerical simulation of the entire stages of fault rupture remains a formidable task. The main challenges in simulating a fault rupture process include complex evolution of fault geometry, frictional contact, and off-fault damage over a wide range of spatial and temporal scales. Here, we develop a phase-field model for quasi-dynamic fault nucleation, growth, and propagation, which features two standout advantages: (i) it does not require any sophisticated algorithms to represent fault geometry and its evolution; and (ii) it allows for modeling fault nucleation, propagation, and off-fault damage processes with a single formulation. Built on a recently developed phase-field framework for shear fractures with frictional contact, the proposed formulation incorporates rate- and state-dependent friction, radiation damping, and their impacts on fault mechanics and off-fault damage. We show that the numerical results of the phase-field model are consistent with those obtained from well-verified approaches that model the fault as a surface of discontinuity, without suffering from the mesh convergence issue in the existing continuous approaches to fault rupture (e.g. the stress glut method). Further, through numerical examples of fault propagation in various settings, we demonstrate that the phase-field approach may open new opportunities for investigating complex earthquake processes that have remained overly challenging for the existing numerical methods.