A damage constitutive model of carbonaceous shale containing a single crack under drying-weting cycles and triaxial compression

To describe the deformation and strength characteristics of carbonaceous shale containing a single fracture under triaxial compression after dry–wet cycles, a segmented damage constitutive model combining dry–wet damage and fracture damage is proposed. Firstly, based on phenomenological theory, the damage variable subjected to dry–wet cycles and fissure angle is obtained. Secondly, a coupled damage variable for fractured carbonaceous shale is derived based on the Lemaitre strain equivalence hypothesis and Weibull statistical damage model. Then, considering the initial compaction stage and the residual strength characteristics, a segmented damage constitutive model of carbonaceous shale containing a single fracture under dry–wet cycles and triaxial compression was established. The rationality and accuracy of the model were compared and verified through the experimental stress–strain curves. The results show that the model can well describe the deformation and failure process of carbonaceous shale under dry–wet cycles, fissure angle and confining pressure. The damage evolution shows an S-shaped change characteristic. The dry–wet cycles promote the damage and failure, confining pressure inhibits the damage and failure, and the fissure angle controls the anisotropy of the damage. The research results have important reference value for revealing the mechanism of rock damage and deterioration under the coupling of multiple factors.