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Step-variable-order fractional viscoelastic-viscoinertial constitutive model and experimental verification of cemented backfill

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Abstract

The focus of this study will be on the order of a fractional dashpot with 1 < β < 2, which has the angible physical meaning of a viscoinertial element. The creep constitutive model based on fractional calculus shows its unique advantages in describing the creep characteristics and can well describe the creep mechanical behavior under different load conditions. The viscoelastic properties of the fractional dashpot have been well studied in the literature for the order 0 < β < 1, and the viscoinertial element (1 < β < 2) extends the theoretical content of the fractional dashpot. With the theoretical framework of the viscoinertial property, the disadvantages of the fractional constitutive model in describing the nonlinear acceleration stage can be circumvented without adding a new element. Based on the step-variable-order fractional dashpot (SVOFD), the creep constitutive models depending on different variables are constructed. Drawing support from the UGO algorithm of 1stOpt software, the parameters of the fractional constitutive models are determined by fitting with the graded loading and unloading creep tests. Summing up, it may be stated that the proposed variable-order fractional constitutive models can better describe the loading and unloading creep characteristics of cemented backfill.

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Data availability

The datasets used and/or analyzed during the current study are available from the corresponding author on reasonable request.

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Funding

This work was supported by the National Natural Science Foundation of China (52004272, 52122404, 52061135111, 52174092, 51734009, 41977238, 51904290, 51974296), Natural Science Foundation of Jiangsu Province, China (BK20200660, BK20220157).

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Authors and Affiliations

  1. State Key Laboratory for Geomechanics and Deep Underground Engineering, China University of Mining and Technology, Xuzhou, 221116, Jiangsu, China

    Yiming Wang, Hai Pu, Qian Yin & Jiangyu Wu

  2. School of Mechanics and Civil Engineering, China University of Mining and Technology, Xuzhou, 221116, Jiangsu, China

    Yiying Feng

  3. College of Mining Engineering and Geology, Xinjiang Institute of Engineering, Urumqi, 830091, Xinjiang, China

    Hai Pu

  4. State Key Laboratory of Coal Resources and Safe Mining, School of Mines, China University of Mining & Technology, Xuzhou, 221116, Jiangsu, China

    Dan Ma

  5. Key Laboratory of Deep Coal Resource Mining of Ministry of Education, China University of Mining & Technology, Xuzhou, 221116, Jiangsu, China

    Dan Ma

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  1. Yiming Wang
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Contributions

Yiming Wang: Conceptualization, Methodology, Writing—original draft, and Software. Yiying Feng: Data curation and Writing—review & editing. Hai Pu: Visualization and Investigation. Qian Yin: Polishing. Dan Ma: Software. Jiangyu Wu: Editing.

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Correspondence to Jiangyu Wu.

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Wang, Y., Feng, Y., Pu, H. et al. Step-variable-order fractional viscoelastic-viscoinertial constitutive model and experimental verification of cemented backfill. Acta Mech 234, 871–889 (2023). https://doi.org/10.1007/s00707-022-03416-y

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  • DOI: https://doi.org/10.1007/s00707-022-03416-y

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