| Localized deformation in the form of slip surfaces and shear bands appears naturally in geomaterials such as soil and rock. Concurrent with the appearance of localized deformation is the loss of overall strength of the geomaterial body. Typically, rate-independent strain-softening plasticity models have been used to represent this overall 'softening' behavior in geomaterials. It is well-known, however, that rate-independent strain-softening plasticity models lead to mesh-dependent finite element solutions. This thesis discusses an approach which leads to mesh-independent finite element solutions of geomaterial behavior when localized deformation is present.; Many attempts have been made to numerically model localized deformation using rate-independent, strain-softening plasticity models, but, in the absence of a material 'length scale', adaptive remeshing, or other regularization technique, these attempts typically do not satisfy two necessary criteria for a finite element solution to be meaningful (i.e., mesh-independent): objectivity with respect to mesh refinement and insensitivity to mesh alignment. A previously-developed model which meets these two criteria without introducing a material length scale and without requiring special mesh alignment strategies represents localized deformation as a strong discontinuity (jump in displacement field). This model is adopted to formulate a rate-independent, non-associated strain-softening Drucker-Prager plasticity model in the context of strong discontinuities and to implement this plasticity model along with an enhanced quadrilateral element within the framework of an assumed enhanced strain method. The formulation and implementation are carried out for small deformations and rotations and for the drained condition, whereby the effect of pore-fluid is neglected.; Numerical simulations of the load-displacement behavior of soft rock under plane strain loading demonstrate the ability of the model to approximate, in a mesh-independent manner, the experimentally-observed failure surface orientation, stress level at which onset of localization occurs, and post-localization 'softening' behavior. In addition, numerical simulations of strain localization occurring in more complex model problems like slope stability and top-down sequential excavation demonstrate near mesh-independence of finite element solutions resulting from the strong discontinuity approach. |
