Modeling brittle fracture, slip weakening, and variable friction in geomaterials with an embedded strong discontinuity finite element.

Abstract

Localized shear deformation plays an important role in a number of geotechnical and geological processes. Slope failures, the formation and propagation of faults, cracking in concrete dams, and shear fractures in subsiding hydrocarbon reservoirs are examples of important effects of shear localization. Traditional engineering analyses of these phenomena, such as limit equilibrium techniques, make certain assumptions on the shape of the failure surface as well as other simplifications. While these methods may be adequate for the applications for which they were designed, it is difficult to extrapolate the results to more general scenarios. An alternative approach is to use a numerical modeling technique, such as the finite element method, to predict localization. While standard finite elements can model a wide variety of loading situations and geometries quite well, for numerical reasons they have difficulty capturing the softening and anisotropic damage that accompanies localization. By introducing an enhancement to the element in the form of a fracture surface at an arbitrary position and orientation in the element, we can regularize the solution, model the weakening response, and track the relative motion of the surfaces. To properly model the slip along these surfaces, the traction-displacement response must be properly captured. This reportmore » focuses on the development of a constitutive model appropriate to localizing geomaterials, and the embedding of this model into the enhanced finite element framework. This modeling covers two distinct phases. The first, usually brief, phase is the weakening response as the material transitions from intact continuum to a body with a cohesionless fractured surface. Once the cohesion has been eliminated, the response along the surface is completely frictional. We have focused on a rate- and state-dependent frictional model that captures stable and unstable slip along the surface. This model is embedded numerically into the element using a generalized trapezoidal formulation. While the focus is on the constitutive model of interest, the framework is also developed for a general surface response. This report summarizes the major research and development accomplishments for the LDRD project titled 'Cohesive Zone Modeling of Failure in Geomaterials: Formulation and Implementation of a Strong Discontinuity Model Incorporating the Effect of Slip Speed on Frictional Resistance'. This project supported a strategic partnership between Sandia National Laboratories and Stanford University by providing funding for the lead author, Craig Foster, during his doctoral research.« less