Abstract
Crack initiation stress (\({\sigma }_{ci}\)) can be used to estimate the spalling strength of rock mass for engineering applications. Its accurate identification is of great significance for analyzing the long-term stability and brittle failure mechanism of rocks. This paper presented an error analysis of various crack initiation stress determination methods and proposed a new method for the identification of crack initiation stress by the expansion rate of axial crack strain. The comparison of the crack initiation stresses calculated by this method with those calculated by the crack volumetric strain method, lateral strain response method, and lateral strain interval response method through tests on three types of rocks showed that the results for marble obtained by all four methods were similar. However, the crack initiation stresses of granite and sandstone calculated by the lateral strain response method were significantly smaller, While the results obtained by the other three methods were similar. The results showed that the \({\sigma }_{ci}\) determined by the method proposed by this paper is accurate. This method can accurately identify the crack initiation stress and its application in engineering practice is convenient.
Highlights
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Various crack initiation stress determination methods were analyzed to provide reference for the selection of crack initiation stress calculation.
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A new method for the identification of crack initiation stress by the expansion rate of axial crack strain is proposed.
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The applicability of the new method was analyzed by uniaxial compression tests on marble, sandstone, and granite.
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Abbreviations
- \({\upsigma }_{1}\) :
-
Major principal stress
- \({\sigma }_{2}\) :
-
Medium principal stress
- \({\upsigma }_{3}\) :
-
Minor principal stress
- \({\sigma }_{\mathrm{cc}}\) :
-
Crack closure stress
- \({\sigma }_{\mathrm{ci}}\) :
-
Crack initiation stress
- \({\sigma }_{cd}\) :
-
Crack damage stress
- E :
-
Young’s modulus
- \(\mu\) :
-
Poisson’s ratio
- \({\varepsilon }_{1}\) :
-
The strain in the direction of the maximum principal stress
- \({\varepsilon }_{2}\) :
-
The strain in the direction of the medium principal stress
- \({\varepsilon }_{3}\) :
-
The strain in the direction of the minor principal stress
- \({\varepsilon }_{1}^{e}\) :
-
The elastic strain in the direction of the maximum principal stress
- \({\varepsilon }_{2}^{e}\) :
-
The elastic strain in the direction of the medium principal stress
- \({\varepsilon }_{3}^{e}\) :
-
The elastic strain in the direction of the minor principal stress
- \({\varepsilon }_{1}^{c}\) :
-
Axial crack strain
- \({\varepsilon }_{3}^{c}\) :
-
Relative compressive strain
- \({\varepsilon }_{3}^{d}\) :
-
The lateral strain corresponding to the crack damage stress
- \({\varepsilon }_{v}\) :
-
Overall volumetric strain
- \({\varepsilon }_{v}^{c}\) :
-
Crack volumetric strain
- \({v}_{1}^{c}\) :
-
Axial crack expansion rate
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Acknowledgements
This work was funded by the Science and Technology Fundamental Resources Investigation Project (2018FY100103), the National Natural Science Foundation of China (Nos.41572297). Specially, the authors highly appreciate the anonymous reviewers and editors for their critical and constructive comments to improve the quality of this article.
Funding
The Science and Technology Fundamental Resources Investigation Project,2018FY100103, Xinzhi Wang, National Natural Science Foundation of China, 41572297, Xinzhi Wang.
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DW proposed the idea of this research and performed data collection, data analysis, and the first draft; XW supervised the structure, revised the first draft and provided suggestions for improvement; HD performed material preparation. ZF put forward some useful suggestions for the revision of the manuscript. All authors give their final approval of the manuscript version to be submitted and any revised version of it.
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Wen, D., Wang, X., Ding, H. et al. Estimation of Crack Initiation Stress Based on Axial Crack Strain Expansion Rate. Rock Mech Rock Eng 56, 1025–1041 (2023). https://doi.org/10.1007/s00603-022-03113-1
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DOI: https://doi.org/10.1007/s00603-022-03113-1