Creep Constitutive Model of Rock Considering Gradient Damage

Aiming at the problem of structural instability caused by creep in deep rocks, by introducing the gradient damage theory, a constitutive model that accurately describes the vermic‐damage evolution of rocks is constructed. Assuming that the rock is an isotropic continuous medium, the internal damage is mainly caused by the initiation and propagation of microcracks, and the total strain includes elastic, viscoelastic, and viscoplastic strains. The damage gradient term is introduced to describe the damage effect of adjacent micro‐units, solving the singularity of strain localization in traditional theories. Meanwhile, based on the first and second laws of thermodynamics, the total free energy and damage driving force are derived, and the bidirectional coupling effect of creep and damage is quantified. A rock creep damage model considering gradient damage is constructed. The creep constitutive model of rock considering gradient damage is in good agreement with the experimental curve, and the correlation coefficient is above 0.95. The core reason is that the model accurately fits the physical properties and creep‐damage evolution law of rock. On the one hand, the gradient damage hypothesis fully considers the nature of natural heterogeneity of rock and can truly describe the gradient expansion process of internal defects from local to global. The material is not simplified as a uniform damage body. On the other hand, the model effectively quantifies the two‐way coupling effect of creep promoting damage and damage accelerating creep. It avoids the limitation of the traditional model to separate the two. Through parameter sensitivity analysis, the physical meanings of the model parameters are made clear.