Three-dimensional creep constitutive model of sandstone based on damage statistics

MethodsThe Nishihara model in the classical elastoplastic model was selected and the damage was introduced to make up for the shortcomings that it could not reveal the nonlinear creep characteristics of the rock, and the Weibull distribution function was used as the damage statistical function, and the SMP criterion was used as the strength criterion of sandstone to deduce the damage variables under three-dimensional conditions. The conventional triaxial compression test was carried out on the MTS-815 rock rigidity testing machine, and the applicability of the damage statistical model was verified by comparing the compression test results with the damage evolution curve. The yield function was used to fit the yield surface of the sandstone to determine the yield stress under each confining pressure, and a fracture plastic body was added to represent the plastic deformation of the primary fracture, and the components of each part of the model were integrated to derive the constitutive equation according to the mechanical boundary. The STAC600-600 rock rheology testing machine was used to carry out the rock classification rheological test, and the fitting results of the creep model were analyzed, and the model parameters were optimized to improve the fitting accuracy. Finally, the fitting results of this model were compared with other models to analyze the advantages and disadvantages of the model.Results and DiscussionsThe damage variables established by the SMP criterion and Weibull distribution function are highly consistent with the rock deformation law under conventional triaxial compression conditions, and the damage does not develop in the early stage of loading, and the deviator stress is higher than the yield stress and will develop rapidly until the rock fails. The damage evolution trend shows that the fracture unit of the rock will accumulate rapidly after the deviator stress reaches the yield limit, and the speed of damage accumulation is different under different confining pressure conditions, and the lower the confining pressure, the faster the accumulation rate. The improved Nishihara model was used to fit the creep deformation curve, and good results could be obtained, but the fitting results of the accelerated creep curve under the conditions of 8MPa, 12MPa and 20MPa confining pressure all shifted forward, and the Poisson's ratio μ was refitted as a function related to the confining pressure, and the accuracy was significantly improved. There is an algebraic relationship between the important parameters of the model u and m and the confining pressure, and the constitutive parameters under each confining pressure can be obtained after obtaining the relation. Compared with the fitting results of the other two models, the fitting accuracy of the model is better than that of the other two, and the variable t that is easy to cause errors does not participate in the process of calculating the parameters of the model, and the damage parameters are directly related to stress and strain, which improves the accuracy to a certain extent.ConclusionsThe results show that the damage statistical creep constitutive model fits the creep deformation characteristics of rocks under three-dimensional conditions, enriches the influencing factors of constitutive parameters, and has a certain guiding role.