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Shear expression derivation and parameter evaluation of Hoek-Brown criterion

Chen Yifan, Lin Hang, Li Su, Cao Rihong, Yong Weixun, Wang Yixian, Zhao Yanlin

Archives of Civil and Mechanical Engineering

2022

Vol. 22, no. 2

art. no. e77, 1--9

Hoek-Brown criterion is one of the most widely used strength criteria in the field of rock engineering, which can reflect the nonlinear empirical relationship between the ultimate principal stresses in rock failure, while the determination of Hoek-Brown parameters is still controversial. The evaluation of Hoek-Brown parameters according to geological strength index (GSI) classification of rock mass involves engineering experiences and subjectivity, and the fitting method of Hoek-Brown parameters based on laboratory triaxial experimental results of multiple fractured rocks is also not going to be easy. Besides, the majority of previous studies were still carried out through the triaxial tests of intact rocks. In this study, the shear expression of Hoek-Brown criterion was derived, and an approximate method for determining Hoek-Brown parameters basedon shear tests was established. Primarily, Hoek-Brown criterion was briefly reviewed and the variations of Hoek-Brown parameters with the change of GSI was analyzed. When GSI decreases from 100 to 50, the reduction of a is only 0.006.While s shows almost no change and approximates to 0 when GSI decreases from 50 to 0. On this basis, the existing shear expression of Hoek-Brown criterion for intact rock (GSI = 100) was extended to the fractured rock mass with 50 < GSI < 100. In addition, the approximate shear expression of Hoek-Brown criterion for fractured rock mass in the range of 0 < GSI < 50 was deduced by assuming s = 0. Then, Hoek-Brown parameters can be calculated through shear tests and MATLAB programing. Finally, based on the structural plane occurrence information of Tangdan copper mine, a random fracture network was generated by Monte Carlo method to prepare random fractured rock mass samples for compression-shear experiments, which were employed to verify the proposed method.

Statistical damage constitutive model based on the Hoek-Brown criterion

Chen Yifan, Lin Hang, Wang Yixian, Xie Shijie, Zhao Yanlin, Yong Weixun

Archives of Civil and Mechanical Engineering

2021

Vol. 21, no. 3

556--564

The constitutive models of rock are essentially the general depictions of the mechanical responses of rock mass under complex geological environments. Statistical distribution-based constitutive models are of great efficacy in reflecting the rock failure process and the stress–strain relation from the perspective of damage, while most of which were achieved by adopting Drucker–Prager criterion or Mohr–Coulomb criterion to characterize microelement failure. In this study, underpinned by Hoek–Brown strength criterion and damage theory, a new statistical damage constitutive model, which is simple in terms of model expression and capable of reflecting the strain softening characteristics of rock in post-peak stage, was established. First, the rock in the failure process was divided into infinite microelements including elastic part satisfying Hooke’s law and damaged part retaining residual strength. Based on strain equivalence hypothesis, the relation between rock microelement strength and damage variable was derived. By assuming the statistical law of microelement strength obeying Weibull distribution and the microelement failure conforming to Hoek–Brown criterion, the new statistical damage constitutive model based on Hoek–Brown criterion was, therefore, gained. The mathematical expressions of the corresponding model parameters were subsequently deduced in accordance with the geometric characteristics of the deviatoric stress–strain curve. Last, the existing conventional triaxial compression test data of representative rock samples under different confining stresses were employed to compare with the theoretical curves by proposed model, the consistency between which was quantified by utilizing the correlation factor evaluation method. The result indicated that the proposed model could well describe the entire stress–strain relationship of rock failure process and manifest the characteristics of rock residual strength. It is of great significance to the researches on rock damage and softening issues and rock reinforcement treatments.