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Fractional-order visco-elastoplastic constitutive model for rock under cyclic loading

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Abstract

The creep property of rock under cyclic loading is very important in civil engineering. In order to establish a novel constitutive equation for rock under cyclic loading, a fractional-order viscoplastic body under cyclic loading was constructed based on fractional-order viscous element. A fractional-order visco-elastoplastic model (FVEPM) for rock was established by connecting constructed fractional-order viscoplastic body with Burgers model. The model was a Burgers model when the maximum value of cyclic loading was less than the critical strength of rock; otherwise, it was a FVEPM which can be used to reflect the transient, steady-state, and tertiary creep phases of rock. The cyclic loading was decomposed into a static load and a cyclic loading with a zero average stress. According to rheological mechanics theory, the rheology constitutive equation of rock under the static load can be derived. According to viscoelastic mechanics theory, the constitutive equation under cyclic loading with a zero average stress was established by introducing the variation parameters of energy storage and energy dissipation compliance caused by rock damage and fracture. Finally, a new dynamic constitutive equation of rock cyclic loading can be obtained by superimposing the constitutive equation under static load and cyclic loading with a zero average stress. Compared with existing test results of rock under cyclic loading, the proposed constitutive model can be used to describe the creep characteristics of rock under cyclic loading and reflect the presented fluctuation of strain curve of rock under cyclic loading.

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Acknowledgments

The authors express their deep gratitude to Dr. Jiufu Zhang for his help during the research. We are also grateful to the Arabian Journal of Geosciences editor and reviewers for their constructive suggestion and kind help in improving the quality of the manuscript.

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Authors and Affiliations

  1. School of transportation, Southeast University, Nanjing, 211196, Jiangsu, China

    Shaoyun Pu, Zhiduo Zhu, Lei Song & Weilong Song

  2. Key Laboratory of Urban Underground Engineering and Environmental Safety in Jiangsu Province, Southeast University, Nanjing, 211196, Jiangsu, China

    Shaoyun Pu, Zhiduo Zhu, Lei Song & Weilong Song

  3. Wuxi Metro Group Co., Ltd, Wuxi, 214000, Jiangsu, China

    YuYi Peng

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  1. Shaoyun Pu
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  2. Zhiduo Zhu
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  3. Lei Song
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  4. Weilong Song
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Correspondence to Shaoyun Pu or Zhiduo Zhu.

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Responsible Editor: Zeynal Abiddin Erguler

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Pu, S., Zhu, Z., Song, L. et al. Fractional-order visco-elastoplastic constitutive model for rock under cyclic loading. Arab J Geosci 13, 326 (2020). https://doi.org/10.1007/s12517-020-05288-9

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  • DOI: https://doi.org/10.1007/s12517-020-05288-9

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