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Mathematics 2016, 4(4), 57; doi:10.3390/math4040057

Analysis of Dynamics in Multiphysics Modelling of Active Faults

1
School of Petroleum Engineering, University of New South Wales (UNSW), Sydney, NSW 2052, Australia
2
CSIRO Mineral Resources Flagship, North Ryde, NSW 2113, Australia
*
Author to whom correspondence should be addressed.
Academic Editor: Reza Abedi
Received: 30 April 2016 / Revised: 9 September 2016 / Accepted: 14 September 2016 / Published: 22 September 2016
(This article belongs to the Special Issue Applied Mathematics and Mechanics)
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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). View Full-Text
Keywords: homoclinic bifurcation; fault dynamics; multiphysics processes homoclinic bifurcation; fault dynamics; multiphysics processes
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Alevizos, S.; Poulet, T.; Veveakis, M.; Regenauer-Lieb, K. Analysis of Dynamics in Multiphysics Modelling of Active Faults. Mathematics 2016, 4, 57.

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