A Novel Staged Cyclic Damage Constitutive Model for Brittle Rock Based on Linear Energy Dissipation Law: Modelling and Validation

In practical engineering, rocks are often subjected to repeated loading and unloading caused by natural or artificial actions. In this study, a novel staged cyclic damage constitutive model for brittle rock is proposed and verified. Firstly, aiming at the pre-peak deformation characteristics, the damage variable of brittle rock defines as the ratio of dissipation strain energy to constitutive strain energy is developed. Based on the linear energy dissipation law, a new damage variable characterization including compressive energy dissipation coefficient and strain energy parameters is deduced. Secondly, a power function correction coefficient of strain is introduced to modify the traditional damage model based on the strain equivalence hypothesis. Finally, the novel staged cyclic loading–unloading damage constitutive model considering the accumulation effect of plastic strain is established by using the iteration relationship. The established model includes basic parameters such as compressive dissipation coefficient, strain energy and plastic strain, and the feasibility of this model are verified through the experimental data of three brittle rocks (including shale, green sandstone, and red sandstone). The comparison results show that the established model can accurately reflect the cyclic loading–unloading behaviours and hysteresis process of brittle rocks, which provide an important reference for studying rock damage and constitutive model for brittle rocks.