A Nonlinear Visco-Elasto-Plastic Bingham Fatigue Model of Soft Rock Under Cyclic Loading

The fatigue constitutive model under cyclic loading is of vital importance for studying the fatigue deformation characteristics of soft rocks. In this paper, based on the classical Bingham model, a modified Bingham fatigue model for describing the fatigue deformation characteristics of soft rocks under cyclic loading was developed. Firstly, the traditional constant-viscosity component was replaced by an improved nonlinear viscoelastic component related to the number of cycles. The elastic component was replaced by an improved nonlinear elastic component that decays as the number of cycle loads increases. Meanwhile, by decomposing the cyclic dynamic loads into static loads and alternating loads, a one-dimensional nonlinear viscoelastic-plastic Bingham fatigue model was developed. Furthermore, a rock fatigue yield criterion was proposed, and by using an associated flow rule compatible with this criterion, the one-dimensional fatigue model was extended to a three-dimensional constitutive formulation under complex stress conditions. Finally, the applicability of the developed Bingham fatigue model was verified through fitting with experimental data, and the parameters of the model were identified. The model fitting results show high consistency with experimental data, with correlation coefficients exceeding 0.978 and 0.989 under low and high dynamic stress conditions, respectively, and root mean square errors (RMSEs) below 0.028. Comparative analysis between theoretical predictions and existing soft rock fatigue test data demonstrates that the developed Bingham fatigue model more effectively captures the complete fatigue deformation process under cyclic loading, including the deceleration, constant velocity, and acceleration phases. With its simplified component configuration and straightforward combination rules, this model provides a valuable reference for studying fatigue deformation characteristics of rock materials under dynamic loading conditions.