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A Semi-empirical Failure Criterion for Brittle Rocks

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Abbreviations

\(\varvec{\delta }\) :

Second-order symmetric unit tensor

\({\mathbb {I}}\) :

Fourth-order symmetric unit tensor

\({\mathbb {C}}^{\mathrm{m}}\) :

Isotropic elasticity tensor of the matrix phase

\(E^{\mathrm{m}}\) :

Young’s modulus of the matrix phase

\(\nu ^{\mathrm{m}}\) :

Poisson’s ratio of the matrix phase

\(k^{\mathrm{m}}\) :

Bulk modulus of the matrix phase

\(\mu ^{\mathrm{m}}\) :

Shear modulus of the matrix phase

\(\varvec{\sigma }\) :

Macroscopic stress tensor

\(\varvec{\varepsilon }\) :

Macroscopic strain tensor

\(\varvec{\varepsilon }^{\mathrm{p}}\) :

Total plastic strain induced by microcracks

\(\varvec{\sigma }^{\mathrm{p}}\) :

Thermodynamic force associated with \(\varvec{\varepsilon }^{\mathrm{p}}\)

d :

Isotropic internal damage variable

\(\alpha \) :

Generalized friction coefficient

\({\mathcal {R}}(d)\) :

Material resistance to damage evolution

\(d_{\mathrm{c}}\) :

Critical damage corresponding to material failure

\(r_{\mathrm{c}}\) :

Maximum damage resistance

b :

Kinetic parameter involved in failure functions

\(\sigma _{\mathrm{t}}\) :

Uniaxial tensile strength

\(\sigma _{\mathrm{c}}\) :

Uniaxial compressive strength

\(\sigma _{\mathrm{s}}\) :

Intersection with the \(\sigma _3\)-axis

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Funding

Funding was provided by National Key Research and Development Program of China (2017YFC1501100), National Natural Science Foundation of China (51679068).

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Authors and Affiliations

  1. Key Laboratory of Ministry of Education for Geomechanics and Embankment Engineering, Hohai University, Nanjing, China

    Qi-Zhi Zhu & Jian-Fu Shao

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  1. Qi-Zhi Zhu
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  2. Jian-Fu Shao
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Correspondence to Qi-Zhi Zhu.

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Zhu, QZ., Shao, JF. A Semi-empirical Failure Criterion for Brittle Rocks. Rock Mech Rock Eng 53, 4271–4277 (2020). https://doi.org/10.1007/s00603-020-02125-z

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