Rock Mechanics and Rock Engineering

, Volume 50, Issue 3, pp 733–749 | Cite as

Multi-Physics Modelling of Fault Mechanics Using REDBACK: A Parallel Open-Source Simulator for Tightly Coupled Problems

  • Thomas Poulet
  • Martin Paesold
  • Manolis Veveakis
Original Paper


Faults play a major role in many economically and environmentally important geological systems, ranging from impermeable seals in petroleum reservoirs to fluid pathways in ore-forming hydrothermal systems. Their behavior is therefore widely studied and fault mechanics is particularly focused on the mechanisms explaining their transient evolution. Single faults can change in time from seals to open channels as they become seismically active and various models have recently been presented to explain the driving forces responsible for such transitions. A model of particular interest is the multi-physics oscillator of Alevizos et al. (J Geophys Res Solid Earth 119(6), 4558–4582, 2014) which extends the traditional rate and state friction approach to rate and temperature-dependent ductile rocks, and has been successfully applied to explain spatial features of exposed thrusts as well as temporal evolutions of current subduction zones. In this contribution we implement that model in REDBACK, a parallel open-source multi-physics simulator developed to solve such geological instabilities in three dimensions. The resolution of the underlying system of equations in a tightly coupled manner allows REDBACK to capture appropriately the various theoretical regimes of the system, including the periodic and non-periodic instabilities. REDBACK can then be used to simulate the drastic permeability evolution in time of such systems, where nominally impermeable faults can sporadically become fluid pathways, with permeability increases of several orders of magnitude.


Fault mechanics Mutliphysics Modelling Permeability evolution Finite element method 

List of Symbols


Arrhenius number


Forward Arrhenius number


Reverse Arrhenius number


Endothermic Damköhler number


Exothermic Damköhler number


Gruntfest number

\(\bar{\Lambda }\)

Thermal pressurization coefficient


Lewis number


Chemical Lewis number


Péclet number

\(.^{\star }\), [\(t^{\star }\), \(x^{\star }\), \(T^{\star }\), \(\Delta p^{\star }\), \(\sigma ^{\star }_{ij}\)]

Normalized variables [time, space, temperature, pore pressure increase, stress]


The thermal conductivity (W m−1 K−1)

\(\beta\), [\(\beta _s\), \(\beta _f\)]

Compressibility [solid, fluid phase] (Pa−1)

\(\Delta h\)

Enthalpy of the reaction (J mol−1)

\(\epsilon _{ij}\)

Strain tensor

\(\dot{\epsilon }_0\)

Reference strain rate (s−1)

\(\dot{\epsilon }^{p}_{d}\)

Deviatoric plastic strain rate (s−1)

\(\dot{\epsilon }^{p}_{v}\)

Volumetric plastic strain rate (s−1)

\(\lambda\), [\(\lambda _s\), \(\lambda _f\)]

Thermal expansion coefficient [solid, fluid phase] (K−1)

\(\mu _f\)

Fluid viscosity (Pa s)

\(\nu\), [\(\nu _{1}\), \(\nu _{2}\), \(\nu _{3}\)]

Stochiometric coefficients [of species AB, A, B] from Eq. 8

\(\dot{\Pi }\)

Plastic multiplier (scalar) (s−1)

\(\rho\), [\(\rho _{AB}\), \(\rho _{A}\), \(\rho _{B}\), \(\rho _{s}\), \(\rho _{f}\)]

Density [of species AB, A, B, solid, fluid] (kg m−3)

\(\sigma _{ij}\), [\(\sigma '_{ij}\)]

Stress tensor [effective stress] (Pa)

\(\phi\), [\(\phi _0\), \(\Delta \phi _{chem}\), \(\Delta \phi _{mech}\)]

Porosity [initial, chemical component, mechanical component]


Taylor-Quinney coefficient

\(\omega\), [\(\omega _{AB}\), \(\omega _{A}\), \(\omega _{B}\), \(\omega _{F}\), \(\omega _{R}\)]

Molar reaction rates [of species AB, A, B, forward, reverse] (mol m−3 s−1)

\(A_{\phi }\)

Interconnected porosity coefficient


Elasticity tensor (Pa)


Specific heat capacity (m2 K−1 s−2 )


Activation energy (J mol−1)


Ratio of forward over reverse pre-exponential constants

M, [\(M_{AB}\), \(M_{A}\), \(M_{B}\)]

Molar mass [of species AB, A, B] (kg mol−1)

Q, [\(Q_{F}\), \(Q_{R}\), \(Q_{mech}\)]

Activation enthalpy [forward chemical reaction, reverse, of micro-mechanical processes] (J mol−1)


Universal gas constant (J K−1 mol−1)


Temperature (K)

V, [Vs, \(V_{\rm f}\), \(V_{\rm A}\), \(V_{\rm B}\), \(V_{\rm AB}\), \(V_{\rm act}\)]

Volume [of solid phase, fluid phase, component A, B, AB, activation volume] (m3)


Thermal diffusivity (m2 s−1)

k, [\(k_{F}\), \(k_{A}\), \(k_{B}\)]

Pre-exponential factor [of forward chemical reaction, for species A, B] (s−1)

\(k_{\pi }\)

Permeability (m2)

p, [\(p_Y\)]

Volumetric mean stress [value at yield] (Pa)


Pore fluid pressure (Pa)

q, [\(q_Y\)]

Equivalent stress [value at yield] (\(\mathbb {R}^9 \longrightarrow \mathbb {R}\))


Yield function


Solid ratio

v, [\(v^s\), \(v^f\)]

Velocity [solid, fluid phase] (m s−1)



This work was supported by resources provided by the Pawsey Supercomputing Centre with funding from the Australian Government and the Government of Western Australia.


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Copyright information

© Crown Copyright 2016

Authors and Affiliations

  1. 1.CSIRONorth RydeAustralia
  2. 2.School of Petroleum EngineeringUNSWKensingtonAustralia
  3. 3.School of Mathematics and StatisticsUWACrawleyAustralia

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