Damage creep model of viscoelastic rock based on fractional derivative and experimental verification

Exploring the creep law of sandstone provides a theoretical basis for evaluating the long-term stability of geotechnical engineering projects in red beds. Based on a conventional triaxial test of sandstone, a progressive loading triaxial creep test is conducted. The deformation characteristics and laws of each sample in different deformation stages are summarized, and the laws relating steady creep rate, stress and time are analyzed. On this basis, a nonlinear viscoelastic‒plastic creep model based on fractional derivative theory and damage theory is established. According to the nonlinear fitting results, the parameter sensitivities are analyzed. The results verify the rationality of the model; this model has a good fitting effect for each creep deformation stage, especially for the accelerated creep stage. The constitutive relationship of the model is simple, clear and easily applicable. The research results provide a reference for studying the long-term stability of geotechnical engineering projects.