Numerical Analyses of Frictional Sliding on Rate-and-State Interfaces: Fluid Effects, Dynamic Weakening, and Potential-Based Formulation Through Machine Learning

Citation

Liu, Shengduo (2025) Numerical Analyses of Frictional Sliding on Rate-and-State Interfaces: Fluid Effects, Dynamic Weakening, and Potential-Based Formulation Through Machine Learning. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/1tzb-pn69. https://resolver.caltech.edu/CaltechTHESIS:08142024-141724425

Abstract

Rate-and-state friction formulations have been widely used to reproduce a number of observations on faulting in the earth's crust, including earthquake nucleation, creeping fault segments, dynamic earthquake rupture, aftershock sequences, and episodic slow slip events. The formulations have also been used to explain the motion of landslides and glaciers. In this thesis, we use numerical simulations to study various factors that can affect the stability of fault slip with rate-and-state friction, including poroelastic bulk properties and dilatation/compaction of the fault material in the presence of fluids, fault healing, injection rate when there is fluid injected into the fault, as well as dynamic weakening of the fault gouge. We also seek to optimize simulations with rate-and-state friction by developing a potential-based formulation using machine learning.

First, we study the stability of frictional fault slip in the presence of fluids, with a focus on fault loading due to fluid injection into the fault as done in many field and laboratory experiments. In Chapter 2, we present a boundary-integral approach on simulating frictional fault slip in a permeable shear layer surrounded by poroelastic bulk. The approach is then used to explore the effects of poroelasticity and inelastic dilatancy on the stability of frictional fault slip in a fluid-injection problem. We find that the diffusion into and poroelastic properties of the bulk can significantly stabilize fault slip, with the stabilization by bulk diffusion and poroelastic properties comparable to the well-known stabilizing effects of the dilatancy mechanism.

In Chapter 3, we further develop the boundary integral code to allow for purely elastic bulk with the same fluid transport properties as the poroelastic bulk material and consider the effect of fault healing and fluid injection rate on fault slip. We show that the poroelastic bulk effects can be very closely captured by using the undrained value of Poisson’s ratio in an elastic bulk model with the same fluid mass diffusivity of the bulk. We find that fault healing significantly delays the onset of dynamic slip events and restricts their spatial extent, making the initial response of the fault to fluid injection much different than its longer-term response. While this is an expected conclusion, fault healing is not typically accounted for in fluid injection modeling which often uses simpler slip-dependent friction laws. We also find that faster or intermittent injection rates lead to more frequent but more spatially constrained dynamic slip events, for the same injected fluid mass, motivating further investigations into injection strategies that would optimize fault stability.

Second, in Chapter 4, we numerically simulate a laboratory experiment of spontaneous dynamic rupture by developing a 3D finite-element model of the experiment with rate-and-state friction. In the experiment, a dynamic rupture is initiated on a Homalite-100 interface and then produces an intermittent slip in the rock gouge embedded into a part of the interface. Our simulations show that the laboratory findings are consistent with rock gouge which is rate-strengthening at low slip rates but dynamically weakening at high slip rates through the mechanism similar to flash heating. However, to fit the experimental results, the traditional flash-heating formulation needs to be substantially modified, potentially due to effects of localization and delocalization of slip in the rock gouge.

The third part of the thesis focuses on identifying a potential-based formulation for the rate-and-state friction laws. Due to their empirical derivation, the rate-and-state friction laws cannot be written as the gradients of a potential, which leads to difficulties in implicit solution of dynamic frictional problems. In Chapter 5, we present a potential-based formulation for the rate-and-state friction law through Neural Network approximation and training on datasets generated by a one-degree of-freedom spring-slider system with the rate-and-state friction law. The learnt potential is able to reproduce the results with rate-and-state friction law, and indeed facilitates an implicit solution of dynamic problems. However, the training of the potential requires a much larger dataset than fitting the original rate-and-state friction law.

Overall, our modeling significantly advances our understanding of the factors that control stability of frictional sliding on natural faults and suggests promising machine-learning directions in replacing the empirical rate-and-state formulations with the ones based on thermodynamic potentials.

Thesis Files