Multiscale coupling and multiphysics approaches in earth sciences: Applications

Abstract

Geoscientists are confronted with the challenge of assessing nonlinear phenomena that result from multiphysics coupling across multiple scales from the quantum level to the scale of the earth and from femtosecond to the 4.5 Ga of history of our planet. We neglect in this review electromagnetic modelling of the processes in the Earth's core, and focus on four types of couplings that underpin fundamental instabilities in the Earth. These are thermal (T), hydraulic (H), mechanical (M) and chemical (C) processes which are driven and controlled by the transfer of heat to the Earth's surface. Instabilities appear as faults, folds, compaction bands, shear/fault zones, plate boundaries and convective patterns. Convective patterns emerge from buoyancy overcoming viscous drag at a critical Rayleigh number. All other processes emerge from non-conservative thermodynamic forces with a critical critical dissipative source term, which can be characterised by the modified Gruntfest number Gr. These dissipative processes reach a quasi-steady state when, at maximum dissipation, THMC diffusion (Fourier, Darcy, Biot, Fick) balance the source term. The emerging steady state dissipative patterns are defined by the respective diffusion length scales. These length scales provide a fundamental thermodynamic yardstick for measuring instabilities in the Earth. The implementation of a fully coupled THMC multiscale theoretical framework into an applied workflow is still in its early stages. This is largely owing to the four fundamentally different lengths of the THMC diffusion yardsticks spanning micro-metre to tens of kilometres compounded by the additional necessity to consider microstructure information in the formulation of enriched continua for THMC feedback simulations (i.e., micro-structure enriched continuum formulation). Another challenge is to consider the important factor time which implies that the geomaterial often is very far away from initial yield and flowing on a time scale that cannot be accessed in the laboratory. This leads to the requirement of adopting a thermodynamic framework in conjunction with flow theories of plasticity. This framework allows, unlike consistency plasticity, the description of both solid mechanical and fluid dynamic instabilities. In the applications we show the similarity of THMC feedback patterns across scales such as brittle and ductile folds and faults.

Thermo‐poro‐mechanics of chemically active creeping faults: 3. The role of serpentinite in episodic tremor and slip sequences, and transition to chaos

“…Within the framework of the solid mechanical instabilities, this thickness emerges as a solution depending on the microstructure [ Muhlhaus and Vardoulakis , ; Papanicolopulos and Veveakis , ], as well as the hydraulic and thermal ambient conditions [ Sulem et al , ; Veveakis et al , , ]. In the field, these solid mechanical failure instabilities extend the laboratory‐scale derivations of centimeter‐thick shear bands, appearing as meter‐wide fault zones [ Regenauer‐Lieb et al , ].…”

Conditions for the localisation of plastic deformation in temperature sensitive viscoplastic materials

“…These concepts gave rise to the proposition of an energy based localisation theory in which instabilities emerge when the mechanical input rate rises significantly leading to a departure from the near isothermal limit towards the near adiabatic limit [Cherukuri and Shawki 1995b;1995a]. Since the energy equation can provide information about the time evolution of the system, this regime has been extensively studied in earth sciences [Regenauer-Lieb et al 2013a;Regenauer-Lieb et al 2013b] for one-dimensional failure patterns seen in landslides [Veveakis et al 2007] and fault mechanics [Veveakis et al 201 0].…”

Cnoidal waves in solids

“…(43) we may calculate the number of stress singularities, N S , as a function of λ (Regenauer-Lieb et al, 2013b, 2013a: ince the stress singularities are cnoidal waves, they are periodic in space (Fig. 2).…”