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A new three-dimensional Hoek-Brown strength criterion

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Abstract

The Hoek-Brown (HB) strength criterion has been widely applied to the estimation of strength of intact rock and rock mass, while evolving ever since. However, negligence of the effect of the intermediate principal stress still remains in the criterion’s latest version. At the same time, several three-dimensional (3D) HB strength, which can takes into account the influence of the intermediate principal stress, have already been proposed, among which the 3D HB criterion proposed by Zhang and Zhu seems to be the most reasonable one. However, the Zhang 3D HB criterion may have problems with some stress path close to triaxial extension state because of the non-convexity characteristic of its failure surface. In this paper, a new 3D HB strength criterion is presented based on a generalized form of the HB criterion, which also considers the effect of the intermediate principal stress and inherits all the merits of the original version of the HB criterion. In addition, this new criterion can remedy to some extent the shortcomings observed in the Zhang 3D HB criterion. Polyaxial tests for five different rocks from published literatures are used for evaluating this new criterion and comparing it with the Zhang 3D HB criterion. The results show that this new criterion may over-predict or under-predict the polyaxial strength of rocks but the errors are relatively small, and similar results are also found for the Zhang 3D HB criterion, which one is better depends on the type of the rock under estimation.

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Abbreviations

σ′ i :

Effective principal stresses with i = 1, 2, 3

σ ci :

Uniaxial compressive strength of the intact rock material

m i :

Petrographic constant of the intact rock material

m b :

Petrographic constant of rock mass

s and a :

Parameters depend on the nature and the degree of fracturing of the rock mass

D :

Disturbance of rock mass

I GS :

Geological strength index

σ′m :

Hydrostatic stress

J′2 :

Second invariant of deviator stress tensor

η :

Similarity angle (Eq. (4))

A and B :

Constants of yield function of 3D HB criterion (Eq. (8))

k :

Parameter determines shape on the octahedral plane of 3D HB criterion (Eq. (14))

n :

Number of test series for certain type of rock

y test i and y calc i :

Test and calculated data

y test :

Mean value of the test sample

R :

Maximum correlation coefficient (Eq. (25))

R SS and R MS :

Residual sum of squares and mean square of residual, respectively

σ′1test and σ′1calc :

Mayor test and calculated principal stress

ɛ i :

Error between σ′1test and σ′1calc

\(\bar \varepsilon _{abs}\) :

Average absolute prediction error

\(\bar \varepsilon _{ave}\) :

Average prediction error

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Authors and Affiliations

  1. Key Laboratory for Bridge and Tunnel of Shaanxi Province, Chang’an University, 710064, Xi’an, China

    Hua Jiang & Yong-Li Xie

Authors
  1. Hua Jiang
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  2. Yong-Li Xie
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Correspondence to Hua Jiang.

Additional information

The project was supported by Western Transportation Technology Funds of China (200731800038), and the Special Fund for Basic Scientific Research of Central Colleges, Chang’an University (CHD2011JC175).

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Jiang, H., Xie, YL. A new three-dimensional Hoek-Brown strength criterion. Acta Mech Sin 28, 393–406 (2012). https://doi.org/10.1007/s10409-012-0054-2

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