A phenomenological constitutive model considering crack closure effect of thermally damaged rock

Crack closure behavior is an important part in stress-strain curve of brittle rock; however, the crack closure effect is seldom described in previous constitutive models. This study proposes a phenomenological constitutive model which can consider crack closure effect of thermally damaged rock. First, a phenomenological constitutive model is deduced by substituting Drucker-Prager failure criterion into a damage mechanics based constitutive model. The model is then modified from being multiplied using a Sigmoid function to model the complete stress-strain curve of rock from crack closure to post-peak under uniaxial compression. Second, two sets of test data of rock experiencing different degrees of thermal damage are used to verify the proposed model. It is found that the complete stress-strain relations of the two thermally damaged rocks under different thermal treatments can be well captured using the proposed model. At last, the model parameters are comprehensively discussed from sensitivity analysis. The crack closure behavior is mainly affected by parameters b and c while parameters a and m affects the strength and deformation behavior beyond crack closure stage.