Strength and deformation behaviour of the isotropic rock under triaxial stress state has been studied extensively, but the studies on the behaviour of the anisotropic rock under true triaxial stress state are scant. The experimental study conducted on the anisotropic rocks are not conclusive due to limited experimental data. In reality, construction of any underground opening results in the application of true triaxial stress state on surrounding geomaterial even the isotropic rocks behave anisotropically due to the presence of the geological structures. In this study, a theoretical strength criterion is proposed for anisotropic rocks and jointed rock mass. The proposed criterion is an extension of Jaeger two-dimensional (2D) anisotropic criterion into three-dimension (3D) using Mogi-Coulomb strength criterion. It is concluded from the study that the most critical anisotropic plane is at angle β = (45+ϕ/2)° and ω = 90°. For all the other orientations, the strength is observed to be more than this critical orientation. It is also observed that intermediate principal stress enhances the strength and its influence on foliation or joint is negligible when its orientation is perpendicular to the foliation or joint plane.


The strength behaviour of anisotropic rocks has been extensively studied under the triaxial stress state (Jaeger, 1960; Hoek, 1964; Donath, 1964; Chenevert and Gatlin, 1965; Rao 1984; Ramamurthy et al., 1988, 1993; Singh, 1988; Singh et al., 1989; Behrestaghi et al., 1996; Nasseri et al., 2003; Saroglou and Tsiambaos, 2008; Saeidi et al., 2014 among others). These studies on the anisotropic behaviour of rocks consider the plane of anisotropy perpendicular to the intermediate principal stress (σ2) and hence neglecting its influence on the strength behaviour. However, it is experimentally confirmed that the strength of rock and rock mass is also a function of intermediate principal stress (Mogi, 1971; Kwa'sniewski and Mogi, 1990; Haimson and Chang, 2000; Chang and Haimson, 2000; Tiwari and Rao, 2006; Tiwari and Rao, 2007; Oku et al., 2007; Lee and Haimson, 2011; Singh and Singh, 2012; Sriapai et al., 2013; Ma and Haimson, 2016; Rukhaiyar and Samadhiya, 2017; Li et al. 2018 among others). Hence, various 3D criteria are proposed for isotropic rocks some of them are theoretical criteria such as:

  • time-dependent 3D strength criterion (Aubertin et al., 2000),

  • an explicit yield criterion coupled with anisotropic damage in Cauchy stress space for materials initially obeying J2 plasticity (Yang et al. 2005),

  • 3D criterion based on fracture mechanics (Zuo et al., 2008),

  • non-linear failure criterion considering the penny shaped micro cracks (Zhou et al., 2014), which was later extended to dynamic loads (Zhou et al., 2015) and for creep (Zhou et al., 2017),

  • Drucker-Prager (Drucker and Prager, 1952), modified Wiebols-Cook criterion (Zhou, 1994), modified Lade criterion (Ewy, 1999) using simple triaxial compression test parameters among others. However, the majority of the criteria mentioned above are complex involving a larger number of non-conventional material parameters. Other simple empirical or semi-empirical for isotropic rocks are Mogi criterion (Mogi, 1971), 3D Hoek-Brown (1988) (Pan and Hudson, 1988), Mohr-Coulomb extension in 3D by (Yu et al., 2002), Mogi-Coulomb criterion (Al-Ajmi and Zimmerman, 2005), 3D Hoek-Brown (2007) (Zhang and Zhu, 2007), Ramamurthy criterion (2007) (Ramamurthy, 2007), Modified Hoek-Brown analogues to Yu et al. (2002) by Zhou et al. (2010), Singh and Singh (2011) gave non-linear Mohr-Coulomb criterion. Singh (2018) concluded that Mogi-Coulomb criterion is relatively modest criterion among others and predict the strength fairly good in 3D stress condition.

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