Numerical simulation of damage-Permeability relationship in brittle geomaterials
Résumé
Finding a coupling model between a hydraulic parameter such as permeability and a mechanical parameter such as damage is the key element for several recent engineering problems. A review of the technical literature reveals that several mechanical constitutive laws exist which allow determining a damage tensor for a damageable porous material under loading. But the present work develops a method to deduce the permeability change due to the damage propagation. From a phenomenological point of view, a microscopic approach is often used for analyzing the permeability evolution by the fluid flow through cracks. However, a macroscopic approach is appropriate for studying the mechanical characteristics of material such as stress-strain relationship after damage. So, this article illustrates both microscopic and macroscopic damage tensors and establishes a relation between them, then find the permeability change by this relation. Cracks are modeled by a disc-shaped distribution in a three-dimensional space. Geometrical characteristics of each disc (radius, direction and opening) follow the statistical distribution laws, depending on the type of loading (compression or extension). A double porosity method is also employed to simulate the flow through the network of cracks/porosity and to evaluate the equivalent permeability by a homogenization method. The discussed double porosity aspect demonstrates the application of the model for fractured porous materials. The observation of a percolation threshold shows the ability of the model to make a connection between the cracks. The model pays a special attention to the anisotropic aspect of the relation between damage and permeability tensors. Characteristics parameters used in the model, giving the intensity of this coupling must be determined experimentally for each specific material.