A new constitutive model is proposed based on the generalized three-dimensional (3D) Hoek-Brown strength criterion, which was proposed by Zhang and Zhu [1, 2]. The constitutive model involves a 3D multi-segment plasticity flow rule that can not only consider the effect of the different confining stresses on the plasticity flow rule and volumetric deformation but also need no addition uncertain parameter such as dilatancy angle. The constant volume flow rule is applied at the high confining stress condition. With the specific mathematical treatment and derivation, a new interpolation and radial flow rule is prescribed at the low confining stress and the tension condition respectively, and the continuity of plastic potential function at the principal stress space is ensured. Then the new constitutive model is implemented in the three-dimensional finite element software (GeoFBA3D). A set of numerical true triaxial compressive tests are carried out and compared with analytical solutions. Finally, a real engineering example of a highway tunnel excavated in rock masses is given for validation and application.


In order to determination the strength of the rock and rock masses in rock mechanics and rock masses engineering, the Hoek–Brown strength criterion was developed for intact rock originally [3, 4] and then extended to rock masses[5, 6]. Hoek and Brown derived their strength criterion for intact rock with one of pure trial and error, and for rock masses with considering the geological condition from the field. The Hoek–Brown criterion has been used most widely in rock engineering that was due to the adequacy of its predictions of the observed rock fracture behavior, and the convenience of its application to a range of typical engineering problems. However, a major limitation for the Hoek–Brown strength criterion was that it cannot consider the effect of the intermediate principal stress. To overcome the limitation, several three-dimensional (3D) versions of the Hoek–Brown strength criterion have been proposed by Pan and Hudson, Singh, Priest, Zhang and Zhu, and Melkoumian et al. [1-2, 7-11]. Among these 3D Hoek–Brown type criteria, the criterion of Zhang and Zhu can entirely inherit the advantages of the original Hoek–Brown strength criterion and has the same expression at both the triaxial and the biaxial states. The criterion was considered as a true 3D version of the generalized Hoek–Brown strength criterion and validated by numerous test data of intact rocks and jointed rock masses. The criterion of Zhang and Zhu was named as GZZ strength criterion commonly [12] and has been accepted by other researchers on rock masses.

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