Damage hardening creep model based on viscoelastic–plastic strain separation

Recently, with the increase in tunnel construction, mining, and other projects, it is of great significance to conduct research on rock-creep characteristics. This paper investigates the viscoelastic and viscoplastic strain characteristics of red sandstone under different stress levels by conducting cyclic loading and unloading creep tests. The study separates the viscoelastic and viscoplastic strains and establishes a damage-hardening creep constitutive model. The results show that rock creep is a dynamic process in which internal stress is continuously adjusted, and viscoelastic and viscoplastic strains continue to develop and transform into each other. As the stress level increases, the decelerated creep rate of viscoelastic strain in the rock sample increases, while the steady-state creep rate remains relatively unchanged; in contrast, both the decelerated creep rate and the steady-state creep rate of viscoplastic strain increase significantly. Under constant stress, the viscoelastic strain of the rock sample remains relatively stable over time, exhibiting characteristics of elastic stability; although viscoplastic strain continues to increase, its increment gradually decreases, reflecting the hardening characteristic in the plastic deformation process of the rock sample. To accurately describe this complex creep behavior, this paper introduces elastic damage and plastic hardening functions and constructs a nonlinear creep constitutive model based on the effective stress principle. Through the introduction of an equivalent nonlinear viscous element, the model was analytically investigated and compared with the traditional Nishihara model, thereby demonstrating its enhanced accuracy and superior performance. The model developed in this paper effectively describes this complex creep-deformation behavior at various stages, providing a theoretical basis for further understanding rock-creep behavior and its engineering applications.