A triaxial creep model for salt rocks based on variable-order fractional derivative
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A triaxial creep model for salt rocks based on variable-order fractional derivative Wu Fei1 · Liu Jie1 · Zou Quanle1 · Li Cunbao2 · Chen Jie1 · Gao Renbo1
Received: 8 May 2020 / Accepted: 16 September 2020 © Springer Nature B.V. 2020
Abstract This paper intend to describe the entire creep process of a salt rock under triaxial loading, especially the creep characteristics in the accelerated creep stage, by replacing the Newtonian dashpot in the Maxwell model with the variable-order fractional derivative component and extending it from one to three dimensions. The experimental data were obtained from the creep of salt rock under multistage loading for approximately five months to examine the applicability of the new model. The fitting results show that the new model can accurately describe the creep behavior of the salt rock and can fully reflect the accelerative rheological property of the salt rock. Compared with the traditional nonlinear rheological model, the new model has fewer parameters and increased accuracy of the fitting results, and is anticipated to have an increased application area. Keywords Salt rock · Triaxial creep model · Variable-order fractional derivative · Multistage loading
1 Introduction Salt rock, as a medium with rheological behavior, low porosity, and permeability, is recognized as an ideal rock for energy storage in underground salt rock caves, as shown in Fig. 1 (Xie et al. 2011). Nowadays, the research on the rheological models of salt rock has gradually become the focus of the research on salt rock (Shao et al. 2003; Jia et al. 2007; Bourgeois et al. 2002; Jia et al. 2020; Zhang et al. 2020). The rheological models mainly consider the long-term strength, creep, and relaxation of salt rock, among which the longterm strength and creep are the two most important parameters. In recent decades, a large
B Z. Quanle
[email protected]
B L. Cunbao
[email protected]
1
State Key Laboratory for the Coal Mine Disaster Dynamics and Controls, Chongqing University, Chongqing 400044, China
2
Institute of Deep Earth Sciences and Green Energy, Shenzhen University, Shenzhen 518060, China
Mech Time-Depend Mater Fig. 1 Underground salt cave
number of creep models have been proposed to describe the creep behavior of rocks (Jin and Cristescu 1998; Hou and Lux 1999; Hou 2003; Li et al. 2009; Zhang et al. 2012; Jiang et al. 2013; Xu et al. 2017b; Zhang et al. 2019). Based on the creep experimental results for salt rock under different stress levels, (Wang 2004; Wang et al. 2014) analyzed the damage evolution of the entire process of salt rock creep. Based on the failure theory of continuous media, Kang et al. (2015) considered the damage effect of coal in the accelerated creep stage and expressed it through a damage parameter. Through a uniaxial creep experiment under different axial pressures, a viscoelasticplastic nonlinear model describing the creep behavior of coal was established. By connecting the nonlinear viscoplastic body (NVPB) model and five-component viscoplastic model in series
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