Study on creep model of rock based on internal variables and strain energy density

•In the framework of Rice’s irreversible internal variable thermodynamics, two sets of internal variables are introduced to represent the adjustment of the internal structure of the material during viscoelastic and viscoplastic deformation.•The creep constitutive equation is established by giving specific complementary energy functions, internal variable evolution equation, and strain energy density function. The existing traditional creep models have obvious shortcomings when describing the accelerated creep properties of the viscoplastic stage of rock. As a way to describe the whole process of rock creep and different creep stages and characterize the deformation characteristics of the accelerated creep stage, the creep damage during the creep loading process can be considered to be caused by the development of internal defects in the rock and soil materials. According to the theory of internal variable thermodynamics, the internal variable evolution equation in the form of self-consistent differential equations is established. The creep curve of rock under different temperatures is in good agreement with the model curve. But there are some errors. This is due to the inevitable differences between the samples. However, the changing trend of strain and creep time is the same. Therefore, the rock creep model established in this paper is reasonable and feasible to describe the creep characteristics under different stresses and different temperatures. The variation of the rock creep model curve under different parameters is analyzed. Then, the clear physical meaning of different parameters is obtained. Finally, the established rock creep model can predict the creep deformation under different temperatures and stress. It has theoretical significance for practical engineering.