Experimental study and micromechanics-based general constitutive theoretical framework for cold-region rocks under triaxial compression

This study establishes a general multiscale constitutive model by integrating micromechanics, thermodynamics, and fractional calculus theory for cold-region rocks under triaxial compression. Conventional triaxial compression tests are conducted on frozen and freeze-thawed rock samples to investigate the macroscopic mechanical properties under the influence of freezing temperature and freeze-thaw (F-T) cycles. Additionally, scanning electron microscopy (SEM) and nuclear magnetic resonance (NMR) analyses provide deeper insights into the intrinsic microscale physical mechanisms. Experimental observations reveal that, at the mesoscale, cold-region rocks can be conceptualized as a composite medium composed of a porous matrix interspersed with cracks. At the microscale, the porous matrix itself consists of mineral grains, pore ice, and unfrozen pore water. By quantitatively characterizing the relevant microstructural variables, a two-step homogenization procedure is employed to derive the effective elastic properties of rocks: the self-consistent scheme (SCS) at the microscale and the Mori–Tanaka (M-T) method at the mesoscale. After rigorously deducing the system’s free energy and corresponding state equations, we systematically establish specific criteria of the model: the loading damage evolution associated with crack initiation and propagation, state-dependent friction-cohesive-type yielding induced plastic distortion, and open cracks closure deformation caused nonlinear and Poisson effect. To accurately capture the characteristics of plastic deformation, the non-orthogonal plastic flow rule (NPFR) formulated via fractional differential calculus is adopted. For efficient numerical implementation, a robust stress integration algorithm is developed by combining the line search method (LSM) with conventional return mapping (RM) algorithm. The predictive performance of the proposed model is thoroughly validated through the frozen and F-T red sandstone and granite.