An implementation of smoothed particle hydrodynamics for large deformation, history dependent geomaterials with applications to tectonic deformation

The deformation of a wide range of materials in geology can be described by fluid behavior, whether of mass wasting, cooling lava or crustal flows. These "geophysical flows" can be problematic to model numerically as they can involve the significant deformation of heterogeneous, history-dependent material. The large deformation can become increasingly troubling when it is highly localized in shear bands or on discrete failure plains such as with the brittle deformation along faults in the upper crust. Traditional, grid-based numerical schemes have difficulty capturing this faulting behavior. An alternative approach is to use a numerical scheme that does not rely on a grid. In this dissertation, a mesh-free formulation, based on the Smoothed Particle Hydrodynamics (SPH) method, is developed for the significant deformation of creeping, visco-plastic material as applied to the brittle failure of the continental crust in tectonic deformation.; To apply the SPH scheme to creeping, viscous flows, several modifications are needed. The first modification is an improved treatment of the Laplacian operator, particularly near the surface of the flow where the standard SPH discretization fails. Secondly, a means of enforcing the incompressibility constraint is developed. In the course of these efforts, an improved treatment of boundary conditions is implemented. Finally, to simulate the deformation of crustal material, a Mohr-Coulomb rheology is added along with modifications to improve the localization of strain. The numerical model is then applied to two tectonic environments: a doubly-vergent wedge and a symmetric rift.; The SPH model with these modifications performs well for creeping, viscous, incompressible flow and thermal diffusion. The Mohr-Coulomb implementation performs satisfactorily (convergence is slow), however, due to the width of the SPH discretization, the shear bands do not result in strain more localized than with grid-based methods. As such, the SPH method as presented is well suited for modeling coupled thermo-mechanical flows of history-dependent material, such as the rolling advance of cooling lava. Brittle deformation can be approximated, however it is not clear that the influence of the width of the SPH discretization can be overcome efficiently, particularly in comparison with other mesh-free methods.