Constructing a three-dimensional creep model for rocks and soils based on memory-dependent derivatives: A theoretical and experimental study

Creep characteristics of rocks directly determine the long-term safety of deep rock mass engineering. In the present proposed framework of memory-dependent (M-D) derivative theory, different M-D elements are constructed and combined to be a memory-dependent derivative creep (MDDC) model with four single elements in this paper. In accordance with the generalized plastic mechanics theory, the one-dimensional MDDC model is extended to a three-dimensional MDDC model. The instantaneous deformation is described by the Hooke body, while the attenuation creep and steady state creep are described by the M-D Kelvin body, and the accelerated creep by the strain-triggered M-D dashpot. The creep test data of sandstone, coal rock, clay, and strongly weathered sandstone are fitted by the MDDC model, Riemann-Liouville type fractional model, Caputo type fractional model, and Burgers model. The results showed that the MDDC model has the highest accuracy and broadest applicability in characterizing the creep of rocks and soils under different stress paths. The MDDC model has a good capacity to describe the creep at the nonlinear accelerated creep stage without detrimentally impacting the memory effect over time. It is thus far more superior to the element combination model and the fractional model.