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Statistical damage constitutive model based on the Hoek–Brown criterion

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Abstract

The constitutive models of rock are essentially the general depictions of the mechanical responses of rock mass under complex geological environments. Statistical distribution-based constitutive models are of great efficacy in reflecting the rock failure process and the stress–strain relation from the perspective of damage, while most of which were achieved by adopting Drucker–Prager criterion or Mohr–Coulomb criterion to characterize microelement failure. In this study, underpinned by Hoek–Brown strength criterion and damage theory, a new statistical damage constitutive model, which is simple in terms of model expression and capable of reflecting the strain softening characteristics of rock in post-peak stage, was established. First, the rock in the failure process was divided into infinite microelements including elastic part satisfying Hooke’s law and damaged part retaining residual strength. Based on strain equivalence hypothesis, the relation between rock microelement strength and damage variable was derived. By assuming the statistical law of microelement strength obeying Weibull distribution and the microelement failure conforming to Hoek–Brown criterion, the new statistical damage constitutive model based on Hoek–Brown criterion was, therefore, gained. The mathematical expressions of the corresponding model parameters were subsequently deduced in accordance with the geometric characteristics of the deviatoric stress–strain curve. Last, the existing conventional triaxial compression test data of representative rock samples under different confining stresses were employed to compare with the theoretical curves by proposed model, the consistency between which was quantified by utilizing the correlation factor evaluation method. The result indicated that the proposed model could well describe the entire stress–strain relationship of rock failure process and manifest the characteristics of rock residual strength. It is of great significance to the researches on rock damage and softening issues and rock reinforcement treatments.

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Data availability

Some or all data, models, or code that support the findings of this study are available from the corresponding author upon reasonable request.

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Acknowledgements

This paper gets its funding from project (51774322) supported by National Natural Science Foundation of China; Project (2018JJ2500) supported by Hunan Provincial Natural Science Foundation of China. The authors wish to acknowledge these supports. The anonymous reviewer are gratefully acknowledged for his valuable comments on the manuscript.

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Authors and Affiliations

  1. School of Resource and Safety Engineering, Central South University, Changsha, 410083, Hunan, China

    Yifan Chen, Hang Lin & Shijie Xie

  2. School of Civil Engineering, Hefei University of Technology, Hefei, 230009, China

    Yixian Wang

  3. School of Energy and Safety Engineering, Hunan University of Science and Technology, Xiangtan, 411201, Hunan, China

    Yanlin Zhao

  4. Kunming Prospecting Design Institute of China Nonferrous Metals Industry Co., Ltd, Kunming, 650051, Yunan, China

    Weixun Yong

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  1. Yifan Chen
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  2. Hang Lin
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Correspondence to Hang Lin.

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Chen, Y., Lin, H., Wang, Y. et al. Statistical damage constitutive model based on the Hoek–Brown criterion. Archiv.Civ.Mech.Eng 21, 117 (2021). https://doi.org/10.1007/s43452-021-00270-y

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