Abstract
Rock damage model is of great significance to the forecast of rock failure in engineering design such as tunnel, drilling, stability of slope, and mine. However, the applicability of statistical damage constitutive models and efficient model selection criteria of rock have not been fully investigated, which leads to difficulties in resolving issues practice via employing models. In the paper, we developed a rock damage constitutive model based on power law distribution and investigated the corresponding applicability in describing rock damage behavior. The uniaxial compression tests for different rocks (e.g., sandstone, granite, mudstone, shale, and marble) are carried out to verify the applicability of the model, and the criterion for model selection is proposed based on the rock porosity strain ratio. The results show that the proposed model exhibits better performance in predicting variation for the brittle rock damage compared with the common damage model based on Weibull distribution. Besides, the applicability of the proposed model can be extended to elastic–plastic rock by adopting the sigmoid function. The research in this study provides an effective model to describe rock damage behavior for brittle and elastic–plastic and presents a criterion for model selection.
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Abbreviations
- D :
-
Damage variables
- \({D}_{{\text{AE}}}\) :
-
Damage variable of the acoustic emission
- \({E}_{d}\) :
-
Cumulative energy changing with strain
- \({E}_{0}\) :
-
Final cumulative energy value when the uniaxial compression is completed
- \(N\) :
-
Total number of meso-units
- \({N}_{{\text{f}}}\) :
-
The number of failed meso-units
- \(P\left(x\right)\) :
-
Probability density function
- \(m\) :
-
Shape parameter
- \(x\) :
-
Random distributed variable
- \({\upvarepsilon }_{0}\) :
-
Proportional parameter
- \({\varepsilon }_{f}\) :
-
Strain value corresponding to the peak point
- \({\sigma }_{f}\) :
-
Peak stress value
- \({\varepsilon }_{v}\) :
-
Initial pore strain
- \(\lambda\) :
-
Ratio of initial pore strain to peak strain
- \({R}_{M}^{2}\) :
-
R2 of the proposed model
- \(a\) :
-
Parameter of the modified model
- \(b\) :
-
Parameter of the modified model
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Acknowledgements
The work investigated in this paper was supported by the National Natural Science Foundation of China (Grant No. 41302124): Open Funding by Hubei Intelligent Geological Equipment Engineering Technology Research Center (Grant No. DZZB202002), Open Funding by Engineering Research Center of Rock Soil Drilling & Excavation and Protection, and Postdoctoral research fund of Central South University (Grant No. 140050062). We are also grateful to all the editors and reviewers for their invaluable comments.
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HC contributed to conceptualization, supervision, and project administration. DZ performed investigation, formal analysis, data curation, and writing—original draft preparation. TB contributed to supervision and resources. PS was involved in conceptualization and project administration. JL performed investigation and writing—review and editing. HE performed writing—review and editing.
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Cao, H., Zhu, D., Bao, T. et al. Applicability of rock damage model based on power law distribution. Acta Geophys. (2024). https://doi.org/10.1007/s11600-023-01260-9
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DOI: https://doi.org/10.1007/s11600-023-01260-9