Numerical simulation of multiscale fault systems with rate- and state-dependent friction

TL;DR

This paper develops a comprehensive mathematical model for simulating multiscale fault systems with complex friction laws, employing advanced numerical methods to efficiently solve the resulting non-smooth optimization problems.

Contribution

It introduces a unified model encompassing classical friction laws and implements an efficient numerical scheme for large-scale fault system simulations.

Findings

Model captures complex fault behaviors with large displacements.

Numerical methods demonstrate high efficiency and reliability.

Simulations illustrate realistic fault system dynamics.

Abstract

We consider the deformation of a geological structure with non-intersecting faults that can be represented by a layered system of viscoelastic bodies satisfying rate- and state-depending friction conditions along the common interfaces. We derive a mathematical model that contains classical Dieterich- and Ruina-type friction as special cases and accounts for possibly large tangential displacements. Semi-discretization in time by a Newmark scheme leads to a coupled system of non-smooth, convex minimization problems for rate and state to be solved in each time step. Additional spatial discretization by a mortar method and piecewise constant finite elements allows for the decoupling of rate and state by a fixed point iteration and efficient algebraic solution of the rate problem by truncated non-smooth Newton methods. Numerical experiments with a spring slider and a layered multiscale system illustrate the behavior of our model as well as the efficiency and reliability of the numerical solver.