Fractional derivative in the elastic-viscoplastic stress-strain state model describing anisotropic creep of soft clays
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Fractional derivative in the elastic-viscoplastic stress-strain state model describing anisotropic creep of soft clays Li-ye Wang1 · Feng-xi Zhou1,2
Received: 9 April 2020 / Accepted: 16 November 2020 © The Author(s), under exclusive licence to Springer Nature B.V. part of Springer Nature 2020
Abstract A fractional elastic-viscoplastic (F-EVP) creep model describing the anisotropy of soft soil is established. A nonlinear viscoplastic creep expression is obtained by a fractional derivative and the Laplace transformation, which is extended by the definition of the reference yield surface. On this basis, the anisotropy of soil is considered in the model by a rotating hardening criterion, and the effect of anisotropic parameters on the stress-dilatancy ratio is discussed. The scalar multiplier in the form of stress ratio is described, and a critical friction angle is used to unify the modeling parameter. The validity of the model is examined by the existing triaxial creep results. The results indicate that the rotational anisotropy induces coaxial rotation as the result of the stress-dilatation relationship. The fractional viscoplastic model can reasonably describe the plastic behavior of soil before yielding, and accurately characterize the creep behavior of soil. From the comparison between the test results and the model calculation results, it is found that the model calculation results are basically consistent with the test results. Keywords Fractional derivative · Rotational anisotropy · Elastic-viscoplastic behavior · Deformation model · Soft clays
1 Introduction The characteristics of geotechnical materials due to their correlation with time and stress paths make them inherently rheological, showing stress-dilatancy, anisotropic, etc. (Buisman 1936; Rowe 1962; Wheeler et al. 2003), resulting in a highly non-linear strain-stress relationship. Among them, in order to predict the evolution mechanism of the “viscosity” of soft clays over time (creep), the elastic-viscoplastic (EVP) model is developed based on the elastoplastic model. The core theory three-dimensional EVP models are categorized as
B F.-x. Zhou
[email protected]
1
School of Civil Engineering, Lanzhou University of Technology, Gansu, 730050, China
2
School of Civil Engineering, HeXi University, Gansu, 734000, China
Mech Time-Depend Mater
overstress theory, boundary surface theory, unsteady flow surface theory, and others. Overstress theory is based on the consideration of both reference yield surface and dynamic yield surface, it has achieved an effective description of elastic deformation and viscoplastic deformation (Perzyna 1963). The representative models include Adachi and Oka (1982); Fodil et al. (1997); Yin et al. (2002); Hinchberger and Rowe (2005); Kelln et al. (2008); and Yin et al. (2010, 2015). The boundary surface model is based on the overstress theory and combines the concept of hysteresis deformation with viscous and plastic deformation. The overstress theory has been used to calculate the viscous deformation instead of viscopl
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