In this paper, three three-dimensional (3D) versions of the Hoek-Brown strength criterion, respectively proposed by Pan and Hudson [1], Priest [2] and Zhang and Zhu [3], are briefly reviewed and evaluated. The evaluation shows that neither the Pan-Hudson criterion nor the Priest criterion will reduce to the form of the Hoek-Brown criterion at triaxial or biaxial stress state. Compared with the Hoek-Brown criterion, the Pan-Hudson criterion under-predicts the strength at triaxial stress state but overpredicts the strength at biaxial stress state. The Priest criterion predicts the same strength as the Hoek-Brown criterion at triaxial stress state but over-predicts the strength at biaxial stress state. The Zhang-Zhu criterion reduces to the form of the Hoek-Brown criterion at both triaxial and biaxial stress states and thus can be considered a true 3D version of the Hoek-Brown criterion. The three 3D strength criteria are also applied to analyze true triaxial compression test data of intact rocks collected from the published literature. Predictions of the Zhang-Zhu criterion are in good agreement with the test data for a range of different rock types, but the Pan-Hudson tends to under-predict and the Priest criterion tends to over-predict the strength of rocks.
1. INTRODUCTION
The Hoek-Brown strength criterion has been widely used in rock mechanics and rock engineering because (1) it has been developed specifically for rock materials and rock masses; (2) its input parameters can be determined from routine unconfined compression tests, mineralogical examination and discontinuity characterization; and (3) it has been applied for over 20 years by practitioners in rock engineering, and has been applied successfully to a wide range of intact and fractured rock types [2, 3]. The original Hoek-Brown strength criterion is defined by [4]:
(mathematical equation available in full paper)
where sc is the unconfined compressive strength of the intact rock; s1 and s3 are, respectively, the major and minor effective principal stresses; and m and s are material constants, where m = mi and s = 1 for intact rock. Mi depends only upon the rock type (texture and mineralogy) and can be selected from [5, 6]. This criterion was later updated [7] and modified [8] to the current generalized form as follows:
(mathematical equation available in full paper)
where mb is the value of constant m for the rock mass; and s and a are constants that depend on the characteristics of the rock mass. The parameters mb, s and a can be estimated from the Geological Strength Index (GSI) as follows [9]:
(mathematical equation available in full paper)
where D is a factor that depends on the degree of disturbance due to blast damage and stress relaxation. Values of D range from 0 for undisturbed in situ rock masses to 1 for very disturbed rock masses. The Hoek-Brown strength criterion, either in the original or the current generalized form, does not take account of the influence of the intermediate principal stress. Much evidence, however, has been accumulating to indicate that the intermediate principal stress does influence the rock strength in many instances [10-16].
