Damage constitutive model considering nonlinear fracture closure of rock under freezing-thawing cycles

It is difficult to reflect the nonlinear characteristics of rock compaction by directly applying the damage statistical distribution of rock micro-elements during the establishment of freezing-thawing rock damage constitutive models, which show better agreements with those stress-strain curves with inapparent compaction stage. To remedy this, a new piecewise constitutive relation consisting of damage constitutive relation and compaction constitutive relation is proposed in this paper. First, the freezing-thawing damage was characterized by the change of rock deformation modulus, the improved Harris distribution was used to reflect the microscopic damage of rock under loading, and the damage statistical constitutive relation of freezing-thawing rock was founded based on the generalized equivalent strain theory. According to the geometric characteristics of the peak point on the stress-strain curve, the solution methods of relevant parameters were deduced. For the rock compaction relation, the rock material was divided into framework component and void component, and the corresponding compressive deformation was, respectively, calculated by Hooke's law and true strain analysis method. Then the stress-strain relation of rock compaction containing void equivalent deformation modulus and void factor was derived. Through combining the damage statistical constitutive relation and the compaction constitutive relation, the piecewise expression of the full stress-strain curve of rock subjected to freezing-thawing cycles and uniaxial compression can be achieved. Ultimately, the correctness and applicability of this expression were validated by repeatedly comparing the theoretical curves and the experimental curves of different experiment results.