Nonlinear creep model and parameter identification of mudstone based on a modified fractional viscous body

To study the evident nonlinear creep characteristics of mudstone, the creep process of rock is regarded as the superposition of linear and nonlinear creep processes. Using an element combination model for reference, we introduce the mechanical element (FC) with a fractional derivative based on fractional calculus theory. Compared with the Newtonian element, the FC can react more effectively to the nonlinear gradual process of rheological problems. The variable viscosity coefficient FC element with fractional calculus is connected to both Kelvin and spring elements in series instead of a Newton body element. In addition, considering the effects of load level and time damage variables, a five-element nonlinear creep damage model is proposed that can simulate the entire process of mudstone creep, particularly the accelerated creep phase of mudstone, and both constitutive and creep equations of the model can be derived. Based on the creep model’s use of multiple parameters under graded loading, this study employs a modified particle swarm optimization algorithm with a genetic crossover factor and least-square method joint inversion algorithm. Using creep experimental data of mudstone, this study identifies the parameters for the proposed five-element fractional creep damage model and derives reasonable parameter values. A parameter sensitivity analysis of the constitutive model is also conducted. The results show that the size of the stress loading level \( \sigma \) determines the length of the stable creep phase of the mudstone and the time to enter the accelerated creep phase. The derivative order \( \gamma \) becomes a direct influence factor on the rock creep rate.