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Generalized crack damage stress thresholds of hard rocks under true triaxial compression

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Abstract

The rock failure process can be characterized by several distinct stress thresholds: the crack closure stress σcc, crack initiation stress σci, crack damage stress σcd and peak stress σp. Seventy-one true triaxial compression tests were conducted to investigate the crack damage stress σcd, which is the stress at the onset of unstable crack development and dilation. Two empirical models are developed to predict the crack damage stress σcd using the intermediate principal stress σ2 and the minimum principal stress σ3. In addition, the proposed models are validated by ten results derived from the German Continental Deep Drilling Program (KTB) deep hole amphibolite. A comparison with other failure criteria also indicates the accuracy and simplicity of the proposed models. The proposed composite models show that the crack damage stress σcd gradually increases with increasing intermediate principal stress σ2 and minimum principal stress σ3. The physical meanings and ranges of six material parameters are analyzed and explained. Both the influence of the tangent Young’s modulus E and strain characteristics on the crack damage stress σcd and the inhomogeneity of the tested specimens are discussed in this paper.

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Abbreviations

σ1, σ2 and σ3 :

Maximum, intermediate and minimum principal stresses, respectively

σ c :

Uniaxial compression strength

σcc, σci, σcd and σp :

Crack closure stress, crack initiation stress, crack damage stress and peak stress, respectively

σ m,2 :

Effective mean stress

σ oct :

Octahedral normal stress

τ oct :

Octahedral shear stress

\( \varTheta \) :

Lode angle

ε1, ε2 and ε3 :

Maximum, intermediate and minimum principal strains, respectively

εv and εvcd :

Volumetric strain and volumetric strain at σcd, respectively

ε 1p :

Maximum principal strain at σp

E :

Tangent Young’s modulus

ρ :

Dry bulk density

v :

P-wave velocity

γ1, γ2 and γ :

Anisotropic indexes based on the P-wave velocity

c0 and ϕ0 :

Cohesion and the internal friction angle of the rock material, respectively

θ :

Failure angle between the failure plane and the maximum principal stress applied plane

a, b, A, B, C, D, L1, L2, P1, P2, T1, T2, U1 and U2 :

Material constants

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Acknowledgements

The authors sincerely acknowledge the financial supports from the Key Research Program of Frontier Sciences, CAS, under Grant No. QYZDJ-SSW-DQC016, the 111 Project under Grant No. B17009 and the National Natural Science Foundation of China under Grant No. 51621006. The first author would like to thank the Chinese Scholarship Council for financial support [(2018)3101] to the joint PhD study at the University of British Columbia, Canada. The authors would also like to thank Mr. Zhao-Feng Wang at Institute of Rock and Soil Mechanics, Chinese Academy of Sciences, and Mr. Yong Han and Mr. Rui Kong at Key Laboratory of Ministry of Education on Safe Mining of Deep Metal Mines, Northeastern University, China, for their work and assistance in the laboratory tests. The authors declare that they have no conflict of interest as far as the authors are concerned.

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Authors and Affiliations

  1. State Key Laboratory of Geomechanics and Geotechnical Engineering, Institute of Rock and Soil Mechanics, Chinese Academy of Sciences, Wuhan, 430071, China

    Yaohui Gao & Xia-Ting Feng

  2. Key Laboratory of Ministry of Education on Safe Mining of Deep Metal Mines, Northeastern University, Shenyang, 110819, China

    Xia-Ting Feng, Xiwei Zhang, Yangyi Zhou & Yan Zhang

  3. University of Chinese Academy of Sciences, Beijing, 100049, China

    Yaohui Gao

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  1. Yaohui Gao
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Correspondence to Xia-Ting Feng.

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Gao, Y., Feng, XT., Zhang, X. et al. Generalized crack damage stress thresholds of hard rocks under true triaxial compression. Acta Geotech. 15, 565–580 (2020). https://doi.org/10.1007/s11440-019-00900-z

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