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 elasticplastic 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. e 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. e 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.is new model is simple with few parameters and can effectively simulate the complete creep behaviour of geotechnical materials.

Creep Properties and Constitutive Model of Salt Rock

“…Chen et al [133] considered that when c > 1, the constant coefficient Abel dashpot is transformed into a super Abel dashpot that can be used to reflect the nonlinear accelerated creep characteristic of rock during the creep process. By replacing the Newton body in the Maxwell model and in viscoplastic body, respectively, with constant coefficient Abel dashpot and super Abel dashpot and then combining these two modified models in series, the creep constitutive model of salt rock based on fractional derivatives theory can be obtained (as shown in Figure 13(b)) [134].…”

Nonlinear Viscoelastic‐Plastic Creep Model of Rock Based on Fractional Calculus

“…Rock rheology is a process in which the rock mineral structure is constantly adjusted with time, resulting in the continuous change of stress and strain state with time [1][2][3][4][5][6][7].…”

A Test Method for Creep Characteristics of Loess Based on the One‐Dimensional Consolidator

“…e total area of loess in China is about 640000 km 2 , accounting for 6.3% of the total land area, of which loess is the most widely distributed in Western China, accounting for 50%-60% of the total area in the western region. e creep behavior of loess is one of the most important problems to be studied [1][2][3][4][5][6][7].…”