Fluid-Driven Slip on a Three-Dimensional Fault with Rate-and-State Friction: A Finite Element Analysis

A three-dimensional quasi-dynamic finite element method is developed to simulate fluid-induced seismicity on faults governed by rate-and-state friction. The coupled nonlinear hydro-mechanical equations governing both the fault and the surrounding rock matrix are solved simultaneously using the Imperial College Geo-mechanics Tool (ICGT), providing fluid pressure and displacement fields. This work highlights enhancements made to the friction module of ICGT, specifically the implementation of the augmented Lagrangian method to enforce fault surface contact constraints. This approach leverages the strengths of both the penalty method and Lagrange multipliers within the finite element framework. A stick-predictor slip-corrector algorithm is developed for the rate-and-state friction law to improve the convergence of the solution. The proposed numerical model captures the dynamic response of a fault to fluid injection, with the fault represented explicitly as a zero-thickness interface element in the mesh. To account for radiation damping effects and prevent unbounded slip rates within the quasi-dynamic framework, a velocity-dependent cohesion term is introduced into the shear stress formulation. The results emphasize the importance of selecting appropriate spatial mesh sizes and temporal time steps to ensure the convergence of the iterative Newton-Raphson solver. The simulation results show that pore pressure changes initiate an aseismic slip front that propagates along the fault, leading to failure in seismogenic zones. This method successfully captures all stages of the seismic cycle, including the transition from stick to slip behavior.