A micro-macro constitutive model for compressive failure of rock by using 4D lattice spring model

Abstract

In this work, a micro-macro mechanics-based constitutive model is developed to describe the compressive failure process of rock. A micromechanics model is first developed based on the conceptual model of a micro cracked spring bond, where two micro parameters with clearly geometric meanings are introduced. By using the micromechanics model, it is possible to reproduce the whole nonlinear failure process of the rock under compressive loading, however, it fails to predict the reasonable quantitative relation between the crack initiation stress (σCI) and the direct tensile strength (DTS) that is commonly observed in laboratory tests. Therefore, a macroscopic failure criterion is introduced to determine the failure state of the spring bond instead of the spring deformation used in the micromechanics model. The numerical results indicate that the 4D-LSM with the micro-macro constitutive model can not only fully reproduce the whole nonlinear behavior of rock under different confining pressures, but also reproduce the quantitative relation between σCI and the DTS and the overall macroscopic nonlinear failure strength criterion defined by Hoek and Brown. The micro-macro constitutive model not only provides a feasible solution for better describing the complex nonlinear compressive failure process of rock but helps to better understand the internal failure mechanism of rock.