A finite-element (FE) model of localized deformation in soft rock taking a strong discontinuity approach is presented. The model is formulated within the context of rate-independent, nonassociated DruckerPrager plasticity with nonlinear cohesion hardening/softening. Strain localization is modeled as a jump in the displacement field and simulated within the framework of the FE method using the standard Galerkin approximation. The model is used to simulate the load-displacement behavior of Gosford sandstone deforming in plane strain, focusing on the prediction of the stress levels necessary to initiate strain localization, based on the strong and weak discontinuity criteria (jumps in displacement and strain, respectively), and on the demonstration of mesh-independence of the FE solutions in the bifurcated state. For the sandstone, the onset of weak discontinuity is detected first, before the onset of strong discontinuity, suggesting a possible coupling of the two types of discontinuities in the strain-softening regime.
Abstract:The mechanical response of a solid continuum changes drastically as the deformation evolves from a diffuse state to a highly localized state. For this reason the subject of strain localization has received much research attention lately. This paper investigates the impact of strain localization in the form of strong discontinuity, or displacement jump, on the limit strengths of retaining walls supporting an elastoplastic backfill. The analysis focuses on the propagation of strong instability in active and passive loading using a recently developed strong discontinuity finite element model where the elements are enhanced to accommodate the presence of displacement jumps. Specifically, the analysis applies to dilative frictional material that is susceptible to shear banding. For the retaining wall problem, strong instability is shown to initiate at the ground surface and propagate downward at an angle that depends on the state of stress at the onset of localization.
SUMMARYThis paper presents the results of finite element (FE) analyses of shear strain localization that occurred in cohesionless soils supported by a geosynthetic-reinforced retaining wall. The innovative aspects of the analyses include capturing of the localized deformation and the accompanying collapse mechanism using a recently developed embedded strong discontinuity model. The case study analysed, reported in previous publications, consists of a 3.5-m tall, full-scale reinforced wall model deforming in plane strain and loaded by surcharge at the surface to failure. Results of the analysis suggest strain localization developing from the toe of the wall and propagating upward to the ground surface, forming a curved failure surface. This is in agreement with a well-documented failure mechanism experienced by the physical wall model showing internal failure surfaces developing behind the wall as a result of the surface loading. Important features of the analyses include mesh sensitivity studies and a comparison of the localization properties predicted by different pre-localization constitutive models, including a family of three-invariant elastoplastic constitutive models appropriate for frictional/dilatant materials. Results of the analysis demonstrate the potential of the enhanced FE method for capturing a collapse mechanism characterized by the presence of a failure, or slip, surface through earthen materials.
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