Study on the weakening of mechanical properties and damage constitutive model of pre-cracked cyan sandstone after freeze–thaw cycles

Water-bearing fractured rock masses are prone to geological hazards due to freeze–thaw (FT) damage, which brings adverse effects on the stability of rock engineering. In order to study the FT damage characteristics of rocks, the intact and pre-cracked cyan sandstone samples were taken as the research objects, with pre-crack inclination angles β of 0°, 45°, and 90°, respectively. The effects of FT cycle on stress–strain curve, peak strength, apparent stiffness and FT coefficient of cyan sandstone samples were studied by uniaxial compression test. Based on macroscopic damage variables, a damage constitutive model of cyan sandstone is proposed combined with strain equivalence hypothesis and Weibull distribution hypothesis. Considering that the strain equivalence hypothesis is difficult to reflect the compaction effect of microcracks, the damage constitutive equation is modified by taking the ratio of the secant modulus of the actual stress–strain curve to that of the classical Lemaitre damage constitutive curve as the correction coefficient. The application results show that the modified constitutive model can well describe the stress–strain relationship of cyan sandstone before the peak strength, which verifies the reliability of the model parameters derived from the test data, and the practicability of the damage characterization method and correction coefficient. The results can provide theoretical reference for the study of FT damage of rocks in cold regions.