New Maxwell Creep Model Based on Fractional and Elastic-Plastic Elements

Abstract

Creep models are mainly used to describe the rheological behaviour of geotechnical materials. An important research focus for studying creep in geotechnical materials is the development of a model with few parameters and good simulation performance. Hence, in this study, by replacing the Newtonian dashpot and spring in the classical Maxwell model with fractional and elastic-plastic elements, a new Maxwell creep model based on fractional derivatives and continuum damage mechanics was developed. One- and three-dimensional (1D/3D) creep equations of the new Maxwell creep model were derived. The 1D creep equation of the new model was used to fit existing creep data of rock salt, and the 3D creep equation was used to fit the creep data of remolded loess. The model curves matched the creep data very well, showing considerably higher accuracy than other models. Furthermore, a sensitivity study was carried out, showing the effects of the fractional derivative order β and exponent α on the creep strain of rock salt. This new model is simple with few parameters and can effectively simulate the complete creep behaviour of geotechnical materials.