Abstract
The crack initiation stress (CI), a threshold stress at which brittle rock starts to become damaged during compression, has been widely studied. It can be used to estimate the spalling strength of tunnels in brittle rock masses. Many methods based on stress–strain curves and acoustic emission data have been proposed to identify the CI, and these methods have good statistical consistency. In the present study, the influence of varying the Poisson's ratio on the value of the CI is analyzed using the crack volumetric strain (CVS) method, and the physical meaning of the lateral strain response (LSR) method is explained. Based on the LSR method, a more stable lateral strain interval response (LSIR) method is proposed to determine the CI. We analyzed the CI of granite samples from two deep boreholes in the Beishan area, the site of China’s underground research laboratory (URL). The results show that the mean CI values determined by our proposed method are in good agreement with the results from the LSR method. The standard deviation and correlation analysis show that the CI values obtained by the proposed method have a smaller dispersion and a higher independence than those from the LSR method.
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Abbreviations
- \(\sigma_{1}\) :
-
Maximum principal stress
- \(\sigma_{3}\) :
-
Minimum principal stress
- E :
-
Elasticity modulus
- \(v\) :
-
Poisson's ratio
- ΔV :
-
Olume increment
- V :
-
Volume of rock
- (ΔV/V)el :
-
Elastic volumetric strain
- (ΔV/V)cr :
-
Crack volumetric strain
- ΔV/V :
-
Total volumetric strain
- \(\varepsilon_{1}\) :
-
Axial strain
- \(\varepsilon_{3}\) :
-
Lateral strain
- \({\Delta }\varepsilon_{1}\) :
-
Axial strain increment
- \({\Delta }\varepsilon_{3}\) :
-
Lateral strain increment
- \(E_{3}\) :
-
Lateral stiffness of elastic stage
- \(\varepsilon_{{{\text{e}}1}}\) :
-
Axial elastic strain
- \(\varepsilon_{{{\text{e}}3}}\) :
-
Lateral elastic strain
- \(\varepsilon_{3}^{{\text{c}}}\) :
-
Relative compression strain
- \(\varepsilon_{3}^{{\text{d}}}\) :
-
Lateral strain corresponding to the crack damage stress
- \(\sigma_{{{\text{cd}}}}\) :
-
Crack damage stress
- CC:
-
Crack closure stress
- CI:
-
Crack initiation stress
- CD:
-
Crack damage stress
- CVS:
-
Crack volumetric strain
- LSR:
-
Lateral strain response
- RCSR:
-
Relative compression strain response
- CAEH:
-
Cumulative AE hit
- UCS:
-
Uniaxial compressive strength
- URL:
-
Underground research laboratory
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Acknowledgements
This work was supported by the Key Projects of the National Natural Science Foundation of China [Grant Number 51234004]; the Project of Decommissioning of Nuclear Facilities and Radioactive Waste Management; and the National Key Research and Development Program of China (NO. 2017YFC0804601, 2018YFC0808403). The authors are sincerely grateful to Professor Jaak J Daemen, Mackay School of Earth Sciences and Engineering, University of Nevada, for his thoughtful proofreading of this paper.
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Tang, M., Wang, G., Chen, S. et al. An Objective Crack Initiation Stress Identification Method for Brittle Rock Under Compression Using a Reference Line. Rock Mech Rock Eng 54, 4283–4298 (2021). https://doi.org/10.1007/s00603-021-02479-y
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DOI: https://doi.org/10.1007/s00603-021-02479-y