Analysis of Dynamics in Multiphysics Modelling of Active Faults

Abstract

Instabilities in Geomechanics appear on multiple scales involving multiple physical processes. They appear often as planar features of localised deformation (faults), which can be relatively stable creep or display rich dynamics, sometimes culminating in earthquakes. To study those features, we propose a fundamental physics-based approach that overcomes the current limitations of statistical rule-based methods and allows a physical understanding of the nucleation and temporal evolution of such faults. In particular, we formulate the coupling between temperature and pressure evolution in the faults through their multiphysics energetic process(es). We analyse their multiple steady states using numerical continuation methods and characterise their transient dynamics by studying the time-dependent problem near the critical Hopf points. We find that the global system can be characterised by a homoclinic bifurcation that depends on the two main dimensionless groups of the underlying physical system. The Gruntfest number determines the onset of the localisation phenomenon, while the dynamics are mainly controlled by the Lewis number, which is the ratio of energy diffusion over mass diffusion. Here, we show that the Lewis number is the critical parameter for dynamics of the system as it controls the time evolution of the system for a given energy supply (Gruntfest number).

Episodic mineralising fluid injection through chemical shear zones

“…using Gr as the continuation parameter) for various values of Le, as well as some continuation analyses along Le for various values of Gr. Figure 1A shows that both series lead to the determination of the same boundary for the zone of oscillations and contribute to refine the original picture shown on Figure 1B, originally obtained (Alevizos, et al, 2016) with a limited series of continuations for = 0.6, 0.7, 0.8, 0.9, 1.0.…”

“…A stability analysis with respect to Gr showed a steady-state response of the system in the shape of an "S-curve", with a lower branch representing the steady-state response of the fault creeping at geological strain rate, and an upper branch characterising fast slip events, either in the form one continuous slip or as episodic stick-slip events. A further study (Alevizos, et al, 2016) showed the importance of Le, whose values affect strongly the shape and stability regime of the S-curve. In particular, that work showed the existence of a critical value Lec below which oscillations can't exist, regardless of the value of Gr.…”

“…Previous studies have shown that the response of the system is strongly dependent on the values of two parameters: the Gruntfest number (Gr) which represents the ratio of characteristic time scales of heat production over energy transfers , and the Lewis number (Le) expressed as the ratio of heat diffusion over mass diffusion (Alevizos, et al, 2016). In this contribution, we focus now on the effect of chemical reactions and present some results about the influence of two of the dimensionless numbers characterising those reactions: the Arrhenius number (Arc) defining the activation enthalpy of the effective chemical reaction, and Damköhler number (Da) that quantifies the reaction rate with respect to the convective transport rate.…”