Augmented virtual internal bond considering micro Mohr-Coulomb criterion

The augmented virtual internal bond (AVIB) is a multiscale constitutive model developed from the virtual internal bond (VIB). VIB considers solid materials to consist of randomized ‘material particles’ in a micro scale. The material particles are connected with VIB. AVIB uses the Xu-Needleman potential function to simultaneously account for the energy contribution of normal and shear deformations of a micro bond. Because the micro fracture mechanism has been implicitly embedded into the constitutive relation of AVIB, AVIB presents many advantages in simulating the fracture propagation of materials. Although the AVIB can successfully simulate the tensile fracture propagation, it cannot simulate the compressive-shear failure behaviors of geomaterials. The underlying reason lies in that the Xu-Needleman potential function cannot describe the micro contact properties of granular materials. To break this limitation of AVIB, a Mohr-Coulomb type of rupture criterion is introduced for compressive bond. Through the micro Mohr-Coulomb criterion, AVIB can capture the key failure mechanism of geo-materials subjected to compression and shear. Through numerical simulation, it is found that the micro cohesive strength governs the macro cohesive strength of geomaterials and the micro friction angle governs the macro friction angle. A linear relationship exists between the micro and macro cohesive strengths, and the micro and macro friction angles. There is no correlation between the micro cohesive strength and macro friction angle, and the micro friction angle and macro cohesive strength. The simulation example suggests that the triaxial strength of rock is linear with the confining pressure, which agrees with the observation in experiment. This demonstrates that the proposed method is valid. It may provide a new micro mechanics constitutive model for geomaterials.