A nonlinear fractional-order damage model of stress relaxation of net-like red soil

Mingwu Wang,Fengqiang Shen,Xinyu Xu,Qiuyan Liu,Yingxun Ding

doi:10.1038/s41598-021-02317-9

Mingwu Wang, Fengqiang Shen + Show 3 more

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https://doi.org/10.1038/s41598-021-02317-9

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Abstract

It is essential to precisely describe the nonlinear characteristics of the stress relaxation behavior to ensure the long-term stability of geotechnical structures in the net-like red soil. A novel damage model of variable fractional-order was discussed here to accurately analyze the progress of stress relaxation for the net-like red soil. Moreover, unsaturated triaxial experiments on stress relaxation under a step-loading mode were performed to identify model parameters and investigate the nonlinear relaxation characteristics of the net-like red soil. The feasibility and validity of the proposed model were furthermore verified by comparisons with the experimental results and fitting curves obtained from the Nishihara model and the generalized Kelvin model. Results show that the analytical result by the proposed model is consistent with the measured data, and the proposed model can better depict the nonlinear characteristics of stress relaxation relative to other analytical models. It can better exhibit the relaxation evolution of soil compared with the conventional models.

Highlights

It is essential to precisely describe the nonlinear characteristics of the stress relaxation behavior to ensure the long-term stability of geotechnical structures in the net-like red soil
A deep insight into stress relaxation behavior by numerical analysis can bring about a thorough comprehension of the rheological properties of the net-like red soil
The element rheology models with a capability to account for the elastic-viscoplastic behavior were verified by some researchers[13,14,15]

Summary

Introduction

It is essential to precisely describe the nonlinear characteristics of the stress relaxation behavior to ensure the long-term stability of geotechnical structures in the net-like red soil. The element rheology models (such as the generalized Kelvin model, Burgers model, and Nishihara model) with a capability to account for the elastic-viscoplastic behavior were verified by some researchers[13,14,15] Those conventional element models sometimes have difficulties precisely describing the nonlinear characteristics of soil stress relaxation because the parameters of the viscous element cannot change with time at a ll[16]. The fractional derivative model was recently employed to construct a time-dependent constitutive model[17,18,19,20,21,22], and some beneficial progress has been made These fractional constitutive models mainly focused on rock mass creep and stress relaxation behaviors, little on soil stress relaxation, let alone variable-order fractional derivative relaxation model that could reflect the whole stress relaxation process. Zhou et al.[25] and Liu et al.[26] proposed constitutive damage models of rock based

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