Toward the formulation of a realistic fault governing law in dynamic models of earthquake ruptures

Dynamic earthquake models can help us in the ambitious understanding, from a deterministic point of view, of how a rupture starts to develop and propagates on a fault, how the excited seismic waves travel in the Earth crust and how the high frequency radiation can damage a site on the ground. Since analytical solutions of the fully dynamic, spontaneous rupture problem do not exist (even in homogeneous conditions), realistic and accurate numerical experiments are the only available tool in studying earthquake sources basing on Newtonian Mechanics. Moreover, they are a credible way of generating physics– based ground motions. In turn, this requires the introduction of a fault governing law, which prevents the solutions to be singular and the crack tip and the energy flux to be unbounded near the rupture front. Contrary to other ambits of Physics, Seismology presently lacks knowledge of the exact physical law which governs natural faults and this is one of the grand challenges for modern seismologists. While for elastic solids it exists an equation of motion which relates particle motion to stresses and forces through the material properties (the scale–free Navier–Cauchy’s equation), for a region undergoing inelastic, brittle deformations this equation is presently missed and scientists have yet to fully decipher the fundamental mechanisms of friction. The traction evolution occurring during an earthquake rupture depends on several mechanisms, potentially concurrent and competing one with each other. Recent laboratory data and field observations revealed the presence, and sometime the coexistence, of thermally–activated processes (such as thermal pressurization of pore fluids, flash heating of asperity contacts, thermally–induced chemical reactions, melting of rocks and gouge debris), porosity and permeability evolution, elasto–dynamic lubrication, etc. In this chapter we will analyze, in an unifying and comprehensive sketch, all possible chemico–physical mechanisms that can affect the fault weakening and we will explicitly indicate how they can be incorporated in a realistic governing model. We will also show through numerical simulations that simplified constitutive models that neglect these phenomena appear to be inadequate to describe the details of the stress release and the consequent high frequency seismic wave radiation. In fact, quantitative estimates show that in most cases the incorporation of such nonlinear phenomena has significant effects, often dramatic, on the dynamic rupture propagation, that finally lead to different damages on the free surface. Given the uncertainties in the relative weight of the various competing processes, the range of variability of the value of some parameters, and the difference in their characteristic time and length scales, we can conclude that the formulation of a realistic governing law still requires multidisciplinary efforts from theoretical models, laboratory experiments and field observations