A statistical damage constitutive model under freeze-thaw and loading for rock and its engineering application

The freeze-thaw damage of rock is a critical problem to study rock engineering in cold regions. When water is frozen in pores, 9% volume expansion will induce damage in rock for a huge ice pressure. Thus, rock will be deteriorated and softened after freeze-thaw. Besides, loading damage produces when the inner stress exceeds the bearing capacity of rock. So it's crucial to establish a damage constitutive model under freeze-thaw and loading in order to evaluate the stability of rock engineering in cold regions. The freeze-thaw damage of rock is expressed by static elastic modulus in this paper, which can be accurately and simply predicted by damage evolution equation using P-wave velocity or compression strength proposed by Liu et al., 2015. Loading damage can be obtained by statistical theory assuming that micro-unit strength satisfies the Weibull distribution and the maximum-tensile-strain yield criterion. Then the final statistical damage constitutive equation under freeze-thaw and loading is derived, in which unknown parameters can be determined through carrying out compression experiment on rock after different freeze-thaw cycles. This developed model is validated by a previous experiment and applied to analyze the stability of a tunnel under coupled thermo-hydro-mechanical condition in cold regions. The results show that the proposed constitutive model is very suitable for rock suffering freeze-thaw cycles and it is of high accuracy and good practicality.