Rheology based on damage mechanics: Toward a new view of modeling the upper crustal deformation

Abstract

The deformation of the brittle upper crust is primarily accompanied by displacements on faults. Nevertheless, it has often been found that continuum fluid models, usually based on a non-Newtonian viscosity, are applicable. I provide a new view of rheology for upper crustal deformation, using the fiber-bundle model, a model of damage mechanics. In my analyses, a yield stress σy was introduced. Below this stress, I assumed that no fiber failure occurs, and the crust behaves elastically without earthquakes. Above the yield stress, I hypothesized that the fibers begin to fail and a failed fiber is replaced by a new fiber. This replacement is analogous to an earthquake rupture. The deformation above the stress σy under a constant strain rate ε for a suffcient time can be modeled as an equation similar to that used for a non-Newtonian viscous flow. There is a power-law relation between mean stress in the crust σ and the strain rate ε with ε∝(σ — σy)n where n is constant. I derived the modified Omori’s law (Omori-Utsu’s law) for aftershock decay using a viscoelastic version of my model and got good agreement with observations taking n=5-13. I point out that further development of my model can contribute to fully understanding the upper crustal deformation.