Constitutive and computational aspects of localized and diffuse instabilities in geomaterials

A rich variety of failure patterns in geomaterials arise from the instability of otherwise uniform states, establishing a connection between well-known phenomena such as liquefaction, dilatancy, localization and fracture. While in geotechnical engineering, instability is a misnomer and rather refers to problems of limit equilibrium analysis, by contrast, the notion of instability in mechanics usually refers to two broad categories: material (constitutive) and geometrical (structural). The type of instability discussed in this dissertation is of the material type since it results from the interaction of particles with their neighbours at the microscale and has its origins in the strong dependence of material behaviour on stress, density and plastic strain softening. Thus, the proper understanding of material behaviour is essential to the formulation of realistic constitutive models and to the capturing of various failure patterns and instabilities in geomaterials. This dissertation studies failure as a bifurcation problem and discusses localized and diffuse instabilities, the two most ubiquitous types of material instability in geomaterials. These material instabilities are examined through a newly developed elastoplastic constitutive model endowed with appropriate attributes such as stress, density and fabric dependencies. The analyses reveal the possibility of having diffuse instability in the absence of any localized deformations within the plastic limit surface. The resulting analysis gives rise to the existence of a domain of bifurcation that encompasses the intrinsic effects of stress-strain history, direction of loading, type of loading, and fabric. The computations start at a material point level (mesoscale) and are later on extended to initial boundary value problem settings (macroscale) where both localized and diffuse failures are examined. The boundary value problems involved focus on real geomaterial aspects, such as material heterogeneity and drainage conditions. In all simulations, the correlation between nonpositive values of the second-order work and regions of impeding unstable deformation are found to be strong and evident. One of the consequences of such an observation is that conventional analysis of failure based on Mohr-Coulomb plastic limit may not be sufficient to examine the safety of a geostructure. Rather, other criteria such as based on second-order work and the existence of a bifurcation surface within the plastic limit must also be checked. As a consequence, FEM-codes need to be equipped with robust constitutive law with softening, non-associated plastic flow along with the second-order work instability criterion to capture the proper physics of material behaviour and the proper failure modes.;This dissertation examines contemporary approaches to failure analysis of geomaterials as a bifurcation problem, and hence presents a paradigm shift from current methods of analysis.