Statistical damage constitutive model based on energy conversion for rocks

The nonlinearity of the constitutive relation for rocks becomes more prominent with a more complex physical-mechanical environment and mechanical behavior. The accurate establishment of the constitutive relation affects the determination of rock deformation and damage state from physical features. In this study, a novel statistical damage constitutive model for rocks is proposed based on quantified energy conversion. The novelty of the model is that the nature of rock damage before and after damage stress is considered. In the constitutive model, the evolution characteristics of energy conversion show a five-stage evolution with a ‘spoon’ form and correspond to the rock deformation and damage process, which can be fitted with the modified GaussAmp function; the damage variable is deduced by the Weibull distribution with energy conversion as the distribution variable, which presents a monotonic decrease caused by initial defects before the σcd and shows a ‘S’ shape caused by nascent cracks after the σcd. Furthermore, triaxial test data of three types of rocks under different confining pressures were used to verify the proposed model, and the results were in good agreement with the test data in most cases. The characteristics of the crack closure stage, peak stress, residual strength, and stress drop process are controlled by the model parameters, which can be determined using experimental data. As these parameters definitely have a physical meaning and a relation to the confining pressure, the proposed model has the potential to be used in rock engineering.