## 1 Introduction  
Along with the development of underground engineering construction, layered rock mass is the most familiar type of rock mass due to the existence of directional structural planes. The failure modes and deformation behaviors of transversely isotropic rocks are very different from those of isotropic rock mass under the uniform loading of an arbitrary angle. Therefore, the influence of the mechanical properties of rock materials, particularly under transverse isotropic conditions, is a notably important problem for describing the deformation and failure characteristics of rock masses. The issues with respect to transversely isotropic rocks are often encountered in mining engineering. Uniaxial and triaxial cyclic tests were sensitive to being strongly influenced by the inclination of loading with respect to the isotropy planes [1]. The direct tensile strength of the initial bedding plane was quantified through laboratory experiments, and the influence of weak planes on the mechanical behaviors of transversely isotropic rocks under uniaxial compression was studied [2, 3]. In addition, the fracture mode and failure strength of the rock samples tested in Brazil were characterized with different foliation-loading angles [4, 5], of which the digital image correlation (DIC) method was used to study crack initiation and propagation with various anisotropy angles [6]. The relationship among the tensile strength, specimen size, and loading slice angle of the transversely isotropic rocks was revealed from the perspective of size effect, which together control the failure mechanism of transversely isotropic rocks in the Brazilian test [7,8]. The isotropic materials' response curve was defective because of the neglect of the orthotropic and transversely isotropic cases, and the classical criteria for isotropic materials were generalized for the case of orthotropy as well as transverse isotropy [9]. These laboratory studies have provided a great deal of insight and many valuable results. In order to identify the distribution of the stress and strength of rock mass affected by the transversely isotropic laminated layers, a number of physical models have been reported [10, 11, 12, 13]. Moreover, the wave phase velocity [14] and ultrasonic response [15] across the transversely isotropic layers were employed and analyzed, creating an effective constitutive model that was capable of describing the bedding plane elastic-plastic matrix equation [16]. The evolution of the mechanical parameters of bedding planes with the internal variable was determined, including the isotropic plane direction and dip angle [17], and the magnitude of the anisotropic elastic constant [18] and its influence under non-uniform action [19]. The studies revealed that the in situ stress ratio and the orientation of the bedding plane significantly affected the load distribution. Theoretical derivation of the anisotropic damage model was given [20], both in the elastic [21] as well as in the post-failure phases [22]. [PERSON] et al. [23] and [PERSON] et al. [24] proposed a calculation of p-wave travel time marching in a three-dimensional transversely isotropic medium wave step by step. Anisotropic damage models considering loading were induced [25], continuum damage ([26]) was analyzed, and some suggestions were put forward. The experiments in the lab and the implementations on the worksite [27] showed that according to the structure in the direction of principal stress test [28], assembling produced a set of devices for carrying out an experiment in parallel and perpendicular to the direction of the bedding, analyzing its influence on tunnel convergence [29], and determining the influence of the stratification plane directivity on the supporting structure [30]. Meanwhile, shale stability depended on the direction between the borehole axis and the stratification at the drilling site [31,32].