Abstract. Theory and numerical implementation describing groundwater flow and the transport of heat and solute mass in fully saturated fractured rocks with elasto-plastic mechanical feedbacks are developed. In our formulation, fractures are considered as being of lower dimension than the hosting deformable porous rock and we consider their hydraulic and mechanical apertures as scaling parameters to ensure continuous exchange of fluid mass and energy within the fracturesolid matrix system. The coupled system of equations is implemented in a new simulator code that makes use of a Galerkin finite-element technique. The code builds on a flexible, object-oriented numerical framework (MOOSE, Multiphysics Object Oriented Simulation Environment) which provides an extensive scalable parallel and implicit coupling to solve for the multiphysics problem. The governing equations of groundwater flow, heat and mass transport, and rock deformation are solved in a weak sense (either by classical Newton-Raphson or by free Jacobian inexact NewtonKrylow schemes) on an underlying unstructured mesh. Nonlinear feedbacks among the active processes are enforced by considering evolving fluid and rock properties depending on the thermo-hydro-mechanical state of the system and the local structure, i.e. degree of connectivity, of the fracture system. A suite of applications is presented to illustrate the flexibility and capability of the new simulator to address problems of increasing complexity and occurring at different spatial (from centimetres to tens of kilometres) and temporal scales (from minutes to hundreds of years).

Abstract. We propose a multiscale approach for coupling multi-physics processes across the scales. The physics is based on discrete phenomena, triggered by local thermo-hydro-mechano-chemical (THMC) instabilities, that cause cross-diffusion (quasi-soliton) acceleration waves. These waves nucleate when the overall stress field is incompatible with accelerations from local feedbacks of generalized THMC thermodynamic forces that trigger generalized thermodynamic fluxes of another kind. Cross-diffusion terms in the 4×4 THMC diffusion matrix are shown to lead to multiple diffusional P and S wave equations as coupled THMC solutions. Uncertainties in the location of meso-scale material instabilities are captured by a wave-scale correlation of probability amplitudes. Cross-diffusional waves have unusual dispersion patterns and, although they assume a solitary state, do not behave like solitons but show complex interactions when they collide. Their characteristic wavenumber and constant speed define mesoscopic internal material time–space relations entirely defined by the coefficients of the coupled THMC reaction–cross-diffusion equations. A companion paper proposes an application of the theory to earthquakes showing that excitation waves triggered by local reactions can, through an extreme effect of a cross-diffusional wave operator, lead to an energy cascade connecting large and small scales and cause solid-state turbulence.

Rock Mechanics and Rock Engineering manuscript No.

The long-term strength of the lithosphere is controled by two different modes of deformation: a brittle-like, effective pressure-sensitive behavior at shallow crustal depth, which gradually transits to a thermally activated ductile flow rheology with increasing depth. All applications dealing with long-term tectonics therefore share the necessity to describe in a consistent way the multiphysics coupling among the different deformation mechanisms controlling the bulk behavior of the lithosphere. We describe an efficient numerical implementation of a consistent visco-elasto-plastic rheology suitable to describe the first-order aspects of continental rock masses. Different from typical long-term geodynamics numerical frameworks, we explicitly account for both volumetric and deviatoric response of lithospheric rocks to applied loads. Plastic correction to a viscoelastic stress state is introduced via a non-associative Drucker-Prager model, without resorting to the assumption of a plastic limiter. The transient behavior of crustal and lithospheric rocks is accounted for by an overstress (rate-dependent) viscoplastic rheology, which additionally helps solving for numerical issues related to plastic strain accumulation even in the absence of energetic feedbacks. When applied to the study of the dynamics of plume-lithosphere interactions, our implementation is able to reproduce a surface topography with complex multiharmonic wavelength patterns in agreement with observations. In the final chapter, we discuss main limitations of the current rheological description when applied to the study of transient semi-brittle rock behavior. These aspects are tackled in a companion paper, where a thermodynamically consistent formulation extending the current numerical description is presented.