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Theoretical models of fracture deformation based on aperture distribution

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Abstract

The theory of rock fracture deformation is mainly based on the test, and the empirical formula has the parameters differences and inadequate theoretical logicality. Based on the processes of the fracture closure under normal stress and the fracture aperture distribution models including the power function form and normal function, the applied force causes the increase of the fracture contact area and the deformation modulus. Thus, we obtain the theoretical expression of force versus the deformation. We also propose a method that can predict the closure of the rock fracture contact area. The incremental area of fracture closure generated under each normal stress can be considered as the aperture increase effect corresponding to each displacement change amount to obtain the aperture distribution frequency corresponding to each stage load. The curves calculated by the theoretical models can fit well with the existing theoretical and experimental results, indicating that the proposed fracture deformation theory is reasonable. This paper expounds the fracture deformation theory, which has an important theoretical value for the rock mass engineering stability and the fracture seepage theory.

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The data that support the findings of this study are available from the corresponding author upon reasonable request.

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Acknowledgements

This work was supported by the National Natural Science Foundation of China (Grant Nos. 41831289, 41772250, and 41877191). The authors also thank the anonymous reviewers for their helpful comments and suggestions.

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Authors and Affiliations

  1. School of Resources and Environmental Engineering, Hefei University of Technology, Hefei, 230009, China

    Haichun Ma, Peichao Feng, Jiazhong Qian, Xiaohui Tan, Jingping Wang, Lei Ma & Qiankun Luo

  2. Hydraulic Fracturing and Oil-Gas Migration Development Center, Hefei University of Technology, Hefei, 230009, China

    Haichun Ma, Peichao Feng & Jingping Wang

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  1. Haichun Ma
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Ma, H., Feng, P., Qian, J. et al. Theoretical models of fracture deformation based on aperture distribution. Eur. Phys. J. Plus 137, 898 (2022). https://doi.org/10.1140/epjp/s13360-022-03129-0

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