A 3-D Theoretical Derivation of the Hoek-Brown Criterion



A Hoek-Brown rock failure criterion is derived by a three-dimensional crack model based on the linear elastic fracture theory. We believe that when macro-failure occurs, the failure characteristic factor needs to exceed the critical value. This factor is a product of the micro-failure orientation angle and the changing rate of the angle with respect to the major principal stress. And the factor mathematically leads to the empirical Hoek-Brown rock failure criterion is further discussed. Thus, the proposed factors can successfully relate the evolution of micro-damage crack characteristics to macro-failure. A quantitative relationship between the brittle-ductile transition point and confining pressure is proposed based on the above theoretical development, which is consistent with experimental observations.


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© Springer Nature Singapore Pte Ltd. 2020

Authors and Affiliations

  1. 1.School of Mechanics and Civil EngineeringChina University of Mining & Technology-BeijingBeijingChina
  2. 2.Institute of Port, Coastal and Offshore EngineeringZhejiang UniversityHangzhouChina

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