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.

Highlights

  • Creep models are abstract methods for expressing the creep characteristics of geotechnical materials. e creep behaviour of geotechnical materials can be described using differential, integral, or empirical creep equations, and their creep characteristics can be represented using a theoretical creep curve approximating the real creep curve

  • Erefore, in this paper, we present a new Maxwell creep model based on fractional and elastic-plastic elements to characterise the creep behaviour of rock salt and remolded loess under different stress states. e advantages of the model were identified through validation and sensitivity analysis

  • To further explore the ability of the proposed model to simulate the creep behaviour of geotechnical materials under a 3D stress state, the creep results of remolded loess under triaxial conditions were obtained. e loess samples were collected from the L6 loess layer in the new district of Yan’an city; it belongs to the quaternary middle Pleistocene loess, referred to as the Q2 loess. e undisturbed loess was ground, dried, and sieved through a 2-mm screen to have a moisture content of 10%; it was kept for 24 h without allowing evaporation to allow the water to be uniformly distributed in the loess

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Summary

Introduction

Creep models are abstract methods for expressing the creep characteristics of geotechnical materials. e creep behaviour of geotechnical materials can be described using differential, integral, or empirical creep equations, and their creep characteristics can be represented using a theoretical creep curve approximating the real creep curve. Creep models are abstract methods for expressing the creep characteristics of geotechnical materials. E creep behaviour of geotechnical materials can be described using differential, integral, or empirical creep equations, and their creep characteristics can be represented using a theoretical creep curve approximating the real creep curve. Fractional calculus involves derivative and integration operators that are applied to fractional orders. Because of the long history dependence, or the so-called memory effect, fractional operators are powerful tools for modelling the viscoelastic behaviour of materials, for building a time-dependent constitutive model. Because of the pioneering work of Scott-Blair [1], who proposed a fractional element analogous to the classical Newtonian dashpot, many creep models based on fractional calculus have been developed in recent years. Welch et al [6] proposed a four-parameter creep model to characterise the viscoelastic creep of polymeric

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