A microcrack-based continuous damage model for brittle geomaterials

Abstract

A new microcrack-based continuous damage model is developed to describe the behavior of brittle geomaterials under compression dominated stress fields. The induced damage is represented by a second rank tensor, which reflects density and orientation of microcracks. The damage evolution law is related to the propagation condition of microcracks. Based on micromechanical analyses of sliding wing cracks, the actual microcrack distributions are replaced by an equivalent set of cracks subjected to a macroscopic local tensile stress. The principles of the linear fracture mechanics are used to develop a suitable macroscopic propagation criterion. The onset of microcrack coalescence leading to localization phenomenon and softening behavior is included by using a critical crack length. The constitutive equations are developed by considering that microcrack growth induces an added material flexibility. The effective elastic compliance of damaged material is obtained from the definition of a particular Gibbs free energy function. Irreversible damage-related strains due to residual opening of microcracks after unloading are also taken into account. The resulting constitutive equations can be arranged to reveal the physical meaning of each model parameter and to determine its value from standard laboratory tests. An explicit expression for the macroscopic effective constitutive tensor (compliance or stiffness) makes it possible, in principal, to determine the critical damage intensity at which the localization condition is satisfied. The proposed model is applied to two typical brittle rocks (a French granite and Tennessee marble). Comparison between test data and numerical simulations show that the proposed model is able to describe main features of mechanical behaviors observed in brittle geomaterials under compressive stresses.