The strengths of many sedimentary and metamorphic rocks varies considerably with the loading direction and the manifested feature in the variation of strength is often transversely isotropic. Therefore, when planning excavations in rock formations exhibiting periodic planar microstructures such as bedding and foliation, it is important to accurately define the condition at failure in the framework of transverse isotropy. In view of this, this work focuses on the formulation of a transversely isotropic rock failure condition, which is an extension of the isotropic Mohr-Coulomb (M-C) criterion by appealing to the assumption that the friction angle and cohesion of a plane can be evaluated as a function of relative orientation of the plane referred to the weakness plane. The implication of the employed spatial distribution function is that the M-C parameter value of a plane is the smallest when a plane is parallel to the weakness plane, while it is the largest when the plane is perpendicular to the weakness plane. The formulation takes into consideration of the general 3-D stress state, so that the proposed criterion can capture the salient failure characteristics of transversely isotropic rock in true triaxial stress condition. In order to validate the performance of the proposed failure condition, a series of conventional and true triaxial compression tests on inclined rock samples is simulated. Based on these numerical experiments, the influence of the relative orientation of weakness planes to loading direction on the failure behavior of transversely isotropic rocks is discussed.
Many transversely isotropic rocks exhibiting periodic weak planar structures, such as bedding and foliation, show a strong directional dependence in their failure strength. In general, the strength is the highest when the load is applied in the direction parallel or perpendicular to the weak plane, while it is the lowest when the loading direction is 30° ∼ 45° to the weak plane. According to the experimental research (Ramamurthy, 1993; Saroglou and Tsiambaos, 2008), the ratio of the maximum to the minimum strength of the transversely isotropic rock is about 1.0∼2.0 for shale, 2.0∼6.0 for slate and phyllite, and 2.0∼4.0 for gneiss. As such, it is important to incorporate the strength and failure characteristics of transversely isotropic rocks in the stability analysis of rock excavations, including tunnels and slopes. Therefore, considering that the failure criteria of materials define not only the onset of failure but also the orientation of associated fracture plane, the establishment of accurate failure condition for transversely isotropic rocks in 3-D stress state is important for understanding and reproducing the failure phenomena observed in many sedimentary and metamorphic rocks.
Since the 1960s, a number of transversely isotropic failure criteria have been proposed along with the accumulation of laboratory data on transversely isotropic rock samples. An extensive review of several well-known criteria is given by Duveau et al. (1998). Among the existing criteria the single plane of weakness (SPW) theory proposed by Jaeger (1960) is the simplest and assumes the respective sets of M-C strength parameters for failure along the weakness and failure across the weakness plane. Jaeger also proposed a criterion where cohesion is a continuous function of sample inclination. McLamore and Gray (1967) extended the Jaeger's theory by postulating that the friction angle also varies with the orientation of the weaknesss plane. Similar formulations of transversely isotropic failure conditions in the context of the nonlinear Hoek-Brown (H-B) criterion can be found in Hoek (1983) and Saroglou and Tsiambaos (2008). However, these kinds of criteria are fully empirical in their derivation nature and suffer from a lack of physical and mathematical background. Examples of mathematically more rigorous formulations include Pariseau (1972), Cazacu and Cristescu (1999), Pietruszcak and Mroz (2001) and Lee and Pietruszczak (2008), which employ the general 3-D stress state, although these approaches, in general, require more material parameters to be identified from an extensive experimental program. The main advantage of 3-D formulation lies in the fact that the resulting criteria enable the assessment of the response of the failure strength to the orientation of the weakness plane in true triaxial stress condition, which is more realistic than the laboratory triaxial compression condition.