Investigations on mechanical responses of frozen soil–rock mixture under cyclic loading: experiments and binary-medium-based multiscale constitutive model

In cold regions, the frozen soil–rock mixture (FSRM) is subjected to cyclic loading coupled with freeze–thaw cycles due to seismic loading and ambient temperature changes. In this study, in order to investigate the dynamic mechanical response of FSRM, a series of cyclic cryo-triaxial tests were performed at a temperature of −10 °C on FRSM with different coarse-grained contents under different loading conditions after freeze–thaw cycles. The experimental results show that the coarse-grained contents and freeze–thaw cycles have a significant influence on the deformation properties of FSRM under cyclic loading. Correspondingly, a novel binary-medium-based multiscale constitutive model is firstly proposed to describe the dynamic elastoplastic deformation of FSRM based on the coupling theoretical framework of breakage mechanics for geomaterials and homogenization theory. Considering the multiscale heterogeneities, ice-cementation differences, and the breakage process of FSRM under external loading, the relationship between the microscale compositions, the mesoscale deformation mechanism (including cementation breakage and frictional sliding), and the macroscopic mechanical response of the frozen soil is first established by two steps of homogenization on the proposed model. Meanwhile, a mixed hardening rule that combines the isotropic hardening rule and kinematic hardening is employed to properly evaluate the cyclic plastic behavior of FSRM. Finally, comparisons between the predicted results and experimental results show that the proposed multiscale model can simultaneously capture the main feature of stress–strain (nonlinearity, hysteresis, and plastic strain accumulation) and volumetric strain (contraction and dilatancy) of the studied material under cyclic loading.