Friction-damage coupled models and macroscopic strength criteria for ice-saturated frozen silt with crack asperity variation by a micromechanical approach

Abstract This paper aims to present physical friction-damage coupled models and derive macroscopic nonlinear strength criteria for ice-saturated frozen silt. Two material scales are considered here. The material at the mesoscale is composed of a frozen silt matrix and embedded mesocracks. At the microscale, the frozen silt matrix is composed of elastic mineral grains and elastic ice crystals. Considering this microstructure, for the ice-saturated frozen silt, the plastic deformation is related to frictional sliding along the mesocracks, and damage is due to the propagation of mesocracks. We obtain the effective elastic properties with a two-step linear Mori-Tanaka homogenization procedure. For the second homogenization step, we deduce the macroscopic stress-strain relations and local thermodynamic forces associated with damage and plasticity. Then, an energy release-based damage criterion is developed to capture the evolution of damage, and a friction sliding criterion with an associated/nonassociated local plastic flow rule is introduced to describe the rate of plasticity. The friction sliding criterion considers the variation of surface asperities of mesocracks as a result of pressure melting and damage evolution. In this context, associated/nonassociated multiscale friction-damage models are established. Furthermore, associated/nonassociated macroscopic nonlinear strength criteria as inherent parts of the corresponding multiscale models are derived under a large range of compressive stresses. For application, a semi-implicit local numerical algorithm of the multiscale models is developed. The accuracy of associated/nonassociated multiscale models is assessed by comparing their numerical simulations with conventional triaxial compression (CTC) tests. Although the associated multiscale model correctly predicts the nonlinear strength behavior and axial deformation of the Lanzhou frozen silt under CTC tests with different temperatures, it fails to quantitatively reproduce volumetric deformation. Nonassociated multiscale model predictions with experimental data of volumetric deformation are significantly improved compared to the associated multiscale model.