Distributed damage, faulting, and friction

We present a formulation for mechanical modeling of geological processes in the seismogenic crust using damage theology. The seismogenic layer is treated as an elastic medium where distributed damage, modifying the elastic stiffness, evolves as a function of the deformation history. The model damage rheology is based on thermodynamic principles and fundamental observations of rock deformation. The theoretical analysis leads to a kinetic equation for damage evolution having two principal coefficients. The first is a criterion for the transition between strength degradation and recovering (healing), and is related to friction. The second is a rate coefficient of damage evolution which can have different values or functional forms for positive (degradation) and negative (healing) evolution. We constrain these coefficients by fitting model predictions to laboratory data, including coefficient of friction in sawcut setting, intact strength in fracture experiments, first yielding in faulting experiments under three-dimensional strain, onset and evolution of acoustic emission, and dynamic instability. The model damage rheology accounts for many realistic features of three-dimensional deformation fields associated with an earthquake cycle. These include aseismic deformation, gradual strength degradation, development of process zones and branching faults around high-damage areas, strain localization, brittle failure, and state dependent friction. Some properties of the model damage rheology (e.g., cyclic stick-slip behavior with possible accompanying creep) are illustrated with simplified analytical results. The developments of the paper provide an internally consistent framework for simulating long histories of crustal deformation, and studying the coupled evolution of regional earthquakes and faults. This is done in a follow up work.