Abstract Microseismicity associated with fluid pressurization in the subsurface occurs during fluid injection but can also be triggered after injection shut‐in. Understanding the extent and duration of the post‐injection microseismicity is critical to limit the risk of fluid‐induced seismicity and insure the safe utilization of the subsurface. Using theoretical and numerical techniques, we investigated how aseismic slip on a fault plane evolves and stops after a fluid pressurization event. We found that the locking mechanisms controlling the arrest of aseismic slip highly depend on the initial fault stress criticality and the pressurization duration. The absolute arrest time of fault aseismic slip after injection shut‐in is proportional to the pressurization duration and increases significantly with the initial fault stress criticality. Given that microseismicity can be triggered by aseismic slip, these results provide insights into the mechanics controlling the arrest of microseismicity after fluid pressurization as a milestone toward induced seismicity mitigation strategies.
Abstract The brittle‐ductile transition is a domain of finite extent characterized by high differential stress where both brittle and ductile deformation are likely to occur. Understanding its depth location, extent, and stability through time is of relevance for diverse applications including subduction dynamics, mantle‐surface interactions, and, more recently, proper targeting of high‐enthalpy unconventional geothermal resources, where local thermal conditions may activate ductile creep at shallower depths than expected. In this contribution, we describe a thermodynamically consistent physical framework and its numerical implementation, therefore extending the formulation of the companion paper Jacquey and Cacace (2020, https://doi.org/10.1029/2019JB018474 ) to model thermo‐hydro‐mechanical coupled processes responsible for the occurrence of transitional semi‐brittle, semi‐ductile behavior in porous rocks. We make use of a damage rheology to account for the macroscopic effects of microstructural processes leading to brittle‐like material weakening and of a rate‐dependent plastic model to account for ductile material behavior. Our formulation additionally considers the role of porosity and its evolution during loading in controlling the volumetric mechanical response of a stressed rock. By means of dedicated applications, we discuss how our damage poro‐visco‐elasto‐viscoplastic rheology can effectively reconcile the style of localized deformation under different confining pressure conditions as well as the bulk macroscopic material response as recorded by laboratory experiments under full triaxial conditions.
Abstract. Theoretical approaches to earthquake instabilities propose shear-dominated instabilities as a source mechanism. Here we take a fresh look at the role of possible volumetric instabilities preceding a shear instability. We investigate the phenomena that may prepare earthquake instabilities using the coupling of Thermo-Hydro-Mechano-Chemical reaction-diffusion equations in a THMC diffusion matrix. We show that the off-diagonal cross-diffusivities can give rise to a new class of waves known as cross-diffusion waves. Their unique property is that for critical conditions cross-diffusion waves can funnel wave energy into a quasi-stationary wave focus from large to small-scale. The equivalent extreme event in ocean waves and optical fibres leads to the appearance of rogue waves and high energy pulses of light in lasers. In the context of hydromechanical coupling, a rogue wave would appear as a sudden fluid pressure spike on the future fault plane. This is here interpreted as a trigger for the ultimate (shear) seismic moment release.
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 fracture–solid 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 Newton–Krylow 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).
<p>We present the hypothesis that material instabilities based on multiscale and multiphysics dissipative waves hold the key for understanding the universality of physical phenomena that can be observed over many orders of scale. The approach is based on an extended version of the thermodynamic theory with internal variables (see related abstract by Antoine Jacquey et al. for session EMRP1.4 entitled: &#8220;Multiphysics of transient deformation processes leading to macroscopic instabilities in geomaterials&#8221;). The internal variables can, in many cases, shown to be related to order parameters in Lev Landau&#8217;s phase-transition theory. The extension presented in this contribution consists of replacing the jump condition for the symmetry-breaking order parameter at the critical point (e.g., density difference at the liquid-gas transition) through considering a second-order phase transition, where the internal variables change continuously from the critical point due to the propagation of material-damaging dissipative waves. This extension to the first-order theory allows assessing the dynamics of coupling the rates of chemical reactions, failure and fluid-flow as well as thermo-mechanical instabilities of materials. The approach gives physics-based insights into the processes that are commonly described by empirical relationships. Here, we present a first analytical model extended by numerical analyses and laboratory and field observations that show the existence of these precursor phenomena to large-scale instabilities. In the event that the propagating waves lead to a large-scale instability, the dissipation processes are predicted to leave tell-tale multi-scale structures in their wake, which can be used to decipher the dynamic processes underpinning the event.</p><p>First analyses from a laboratory analogue experiment are presented, illustrating the slow speed of the waves and their peculiar dispersion relationships and reflection from boundaries. An idealized 1-D (oedometric) compaction experiment of a highly porous (45% porosity) carbonate rock investigates the emergence of localized compaction bands proposed to be formed by long-term resonant collision of the transient dissipation waves. Complementary numerical models of the phenomenon allow in-depth analysis of the dynamics and illustrate the physics of the formation of dissipative waves.</p><p>For field application, we propose that a multiscale analysis - from the grain- over the outcrop- up to the lithospheric scale - can be used to extract quantitative information directly from natural deformation bands, fractures, and fault zones on, for example, the state of stress, the size of the underlying earthquakes, the flow and mechanical properties of the host rock, and the spatiotemporal evolution of fluid and mechanical pressure associated with faulting. The experimental investigation of the fundamental instability has broader applications in the fields of industrial processing of multiphase materials, civil, mechanical, and reservoir engineering and solid mechanics.</p>
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.
Abstract. We propose a non-local, meso-scale approach for coupling multiphysics processes across scale. 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. For extreme conditions, cross-diffusion waves can lead to an energy cascade connecting large and small-scales and cause solid-state turbulence.
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