A damage-mechanics model for crustal deformation

The deformation of the brittle upper crust is primarily associated with displacements on faults. Nevertheless, it has often been found that continuum fluid models, usually based on a non-Newtonian viscosity, are applicable. We derive a continuum rheology for crustal deformation using damage mechanics. It is hypothesized that when a constant strain rate ˙ {ɛ } is applied to a solid material the stress σ and damage increase until failure occurs, which is analogous to an earthquake. We further assume that this process is repeated, in analogy to the repetitive occurrence of earthquakes on a fault. Our model assumes that the crust behaves elastically below a yield stress σ _y. Above this stress the continuum deformations can be modeled as a non-Newtonian viscous flow with ˙ {ɛ } ∼ (σ -σ _y)^{ n} where n is constant. We derive the modified Omori's law for aftershock decay using a viscoelastic version of our model and get good agreement with observations taking n = 6. Using parameter values appropriate for aftershocks, we obtain a continuum crustal rheology that can explain major orogenies such as the Indian-Asian collision.