Rheology and breakdown energy of a shear zone undergoing flash heating in earthquake-like discrete element models
Authors: Taboada A , Renouf M 
Published: January 2023

We study the initiation and growth of a dry granular shear zone subjected to seismic shearing and flash heating from the perspective of a discrete element method. For this purpose, we created a semi-periodic numerical shear test similar to a rotary shear machine in which a 2 mm ×1.5 mm sample composed of micrometric cohesive disks is sheared in between two rigid walls. The strength of cohesive bonds is defined according to an elasto-brittle contact law calibrated to simulate peak and residual strength envelopes derived from rock mechanics tests. The sample is traversed by a pre-existing fracture and subjected to a vertical confining pressure (e.g. 112.5 MPa) and a velocity step function (e.g. 1 m s–1) applied on the top and bottom walls, respectively. Slip along the fracture induces the growth of a shear zone, which thickens by progressive abrasion of damaged material from cohesive blocks. We carried out two parametric studies to determine the rheology and physical properties of the shear zone for slip velocities and confining pressures characteristic of shallow earthquakes and several flash-heating temperatures. According to parametric studies, the mechanical behavior of the shear zone exhibits three distinct phases. The initial phase of rupture initiation is characterized by the propagation of a shear instability generated by the velocity step (phase 1). During this phase, friction and dilatancy curves are approximated by asymmetric peak functions whose amplitude and geometry are controlled primarily by confining pressure. In the intermediate phase of shear-zone growth, the sample displays an initial transient stage that asymptotically approaches steady state at submelting temperatures (phase 2). According to the inertial number, seismic shearing occurs under quasi-static conditions despite high shear rates. Thus, friction and dilatancy observed in all simulations are roughly constant regardless of slip velocity, confining pressure, and gouge zone thickness. In the final phase of shear weakening, the model evolves toward a new steady state at flash-heating temperatures (phase 3). Average friction and dilatancy are represented by sigmoidal decreasing curves that approach steady-state values lower than for phase 2. Predictably, the thermally weakened friction in steady state (μss ∼ 0.1) is close to the strength of frictionless granular samples sheared in quasi-static conditions. We calculate breakdown energies for the gouge and damage zones and the fracture energy at intermediate and high confining pressures. We show that breakdown energy fundamentally differs from fracture energy commonly used in seismology. The breakdown energy of the damage zones shows long-period damped oscillations weakly correlated with shear-stress fluctuations around average decaying values. Our results suggest that dilatancy is the primary energy sink within the damage zones at steady-state values. The breakdown energy components of the gouge zone follow a similar decaying trend as the average fracture energy but over a longer critical distance. Decohesion and dilatancy are the major energy sinks linked to gouge formation at intermediate pressures. In contrast, dilatancy and debonding frictional energies predominate at high confining pressures. Breakdown energy is equivalent to a fraction of fracture energy that nearly triples when doubling the confining pressure.