Fast Boundary Element Methods for fault mechanics and earthquake control

Earthquakes due to either natural or anthropogenic sources cause important human and material damage. In both cases, the presence of pore fluid influence the triggering of seismic instabilities. Preliminary results, done in the context of the European Research Council CoQuake’s project (www.coquake.eu), show that the earthquake instability could be avoided by active control of the fluid pressure [Stefanou, (2019)].
In this contribution, we propose to study the ability of Fast Boundary Element Methods (Fast BEMs) [Chaillat and Bonnet (2013)] to provide a multi-physic large-scale robust model required for modeling earthquake processes, pore-fluid-induced seismicity and their control.
The main challenges concern:

•  the modelling of a realistic on-fault behaviour as well as hydro-mechanical couplings;
• the extension of Fast Boundary Element methods to fault mechanic problems incorporating the effect of fluid injection of the on-fault behaviour;
• the simulation of both small and large time scales corresponding to earthquakes and fluid diffusion respectively by using a single advance in time algorithm.

The main methods used for numerical modeling of earthquake ruptures at a planar interface between two elastic half-spaces are spectral BEMs as in [Lapusta and al. (2000)]. As a first step, we consider this method for a simple problem in crustal faulting. A rate-and-state friction law is considered and different adaptive time stepping algorithms inspired from the literature are tested to take into account both small and large time scales with the correct resolution in time. These solving methods are compared on different benchmarks and convergence studies are conducted on each of them.
Then, poroelastodynamic effects are considered. To this aim, a dimensional analysis of generic poroelastodynamic equations [Schanz (2009)] is performed. It allows determining which of the poroelastodynamics effects are predominant depending on the observation time of the fault. The obtained equations corroborate and justify simplified multiphysics models from the literature, for example [Heimisson and al. (2021)]. A first multi-physics test using Fast BEMs to solve a simplified crustal faulting problem with fluid injection is considered. The objective of this project is to provide a viable efficient tool to explore the advantages and limitations of novel strategies of earthquake control using fluid injection to drive the fault from an unstable state of high potential energy to a stable state of lower potential energy.

References:

S. Chaillat, M. Bonnet. Recent advances on the fast multipole accelerated boundary element method for 3D time-harmonic elastodynamics, Wave Motion, 1090-1104, 2013
E. R. Heimisson, J. Rudnicki, N. Lapusta. Dilatancy and Compaction of a Rate-and-State Fault in a Poroelastic Medium: Linearized Stability Analysis., Journal of Geophysical Research: Solid Earth, 126(8), 2021
N. Lapusta, J. Rice and al.. Elastodynamic analysis for slow tectonic loading with spontaneous rupture episodes on faults with rate- and state-dependent friction, Journal of Geophysical Research: Solid Earth, 23765-23789, 2000.
M. Schanz. Poroelastodynamics: Linear Models, Analytical Solutions, and Numerical Methods., Applied Mechanics Reviews, 62(3)., 2009.
I. Stefanou. Controlling Anthropogenic and Natural Seismicity: Insights From Active Stabilization of the Spring‐Slider Model, Journal of Geophysical Research: Solid Earth, 8786-8802, 2019.