A statistical meso-damage mechanical method for modeling trans-scale progressive failure process of rock

Abstract

Starting from the concept of Representative Volume Element (RVE) at the mesoscopic scale, a statistical meso-damage mechanical method (SMDMM) is developed to model the trans-scale progressive failure process of rock, based on the statistical and continuum damage mechanics theory and the finite element method (FEM). The proposed mesoscopic constitutive law of RVE is established within the framework of elastic–brittle-damage theory in which the double damage functions correspond to a tensile and compressive damage surface. A statistical approach is employed to describe the mesoscopic heterogeneity of rock material. The damage evolution and accumulation of mesoscopic RVEs is used to reflect the macroscopic failure characteristics of rock. The global stress and strain fields are solved by the FEM. An element represents a RVE, the initiation and propagation of meso-macroscopic trans-scale cracks and their interaction are manifested by removing the failed elements. Numerical analyses are carried out on a few groups of laboratory-scale rock specimens and the effects of RVE size, material homogeneity and quasi-static loading step length are investigated. Finally, a full-scale Atomic Energy of Canada Limited (AECL) Mine-by test tunnel is simulated. The proposed SMDMM is calibrated and validated for its trans-scale modeling capability to reproduce the shape and size of excavation damage zone profile around the tunnel. Accordingly, the simulation results are compared with experimental observations and numerical results predicted by other models. It is shown that the SMDMM has good performance for modeling the rock failure process from meso- to engineering/field-scale.