# Experimental Study on Anisotropic Mechanical Characteristics of Shale under Triaxial Loading
## 1 Introduction
[24] proposed the porosity deformation approach (PDA) to the elastic anisotropy of shale under triaxial loading and found that the velocity change due to hydrostatic loading can be used to predict elastic anisotropy under additional axial loading. [PERSON] et al. [25] studied the anisotropy of strength and elastic properties of lower Paleozoic shales from the Baltic basin, Poland, and found that the shale was characterized by VTI type (vertical transverse isotropy) internal anisotropy. [PERSON] et al. [26] adopted a finite-element-based continuum damage mechanics model to capture sample size effects and the influence of intrinsic anisotropy on the stress-strain response of shale and investigated deformation and stiffness anisotropy induced by damage propagation in a rock brittle deformation regime. [PERSON] et al. [27] studied the anisotropic characteristics of the failure mechanism by conducting AE monitoring tests on shale specimens with seven different bedding inclination angles under uniaxial cyclic loading and unloading. [PERSON] et al. [28] explored the anisotropy of the mechanical properties of shale and the energy evolution of its failure through the cyclic loading and unloading experiments of shale specimens with seven different bedding orientations. On the other hand, in terms of dynamic mechanical properties of shale, some efforts had also been conducted to investigate the mechanical properties of shale under dynamic loads with different strain rates, including anisotropic characteristics of strength, elastic modulus, failure mode, etc. [29; 30; 31; 32; 33; 34]. In addition, geologists engaged in the development of unconventional shale gas and shale oil had carried out a lot of research on the anisotropy of elastic wave velocity of shale. [PERSON] et al. [35] implemented ultrasonic velocity and anisotropy measurements on a variety of shale with different clay and kerogen content, clay mineralogy, and porosity at a wide range of effective pressure, and found that the elastic anisotropy of shale increased substantially with compaction. [PERSON] et al. [36] investigated the ultrasonic velocity response of low porosity shale in Western Australia to both isotropic and anisotropic stress fields and to evaluate the velocity response to the changing stress field. [PERSON] et al. [37] conducted real-time ultrasonic and mechanical experiments of Longmaxi formation shale under uniaxial deformation; the results suggest that shale govern the intrinsic P- and S-wave velocity anisotropy, and pronounced bedding planes have a significant influence on the mechanical properties and velocity responses of shale. [PERSON] et al. [38] performed multiple stage triaxial tests of Norwegian Sea shale and evaluated rock strength and the evolution of ultrasonic response during rock deformation. They found that the S-wave anisotropy was significantly affected by the increasing stress anisotropy. [PERSON] et al. [39] studied the velocity and attenuation anisotropy of P- and S-waves in dry Whitby Mudstone samples as a function of stress by ultrasonic experiments and found the degree of anisotropy to be as large as 70% for velocity and attenuation, and the sensitivity of P-wave anisotropy change with applied stress to be more conspicuous than for S-waves. Meanwhile, hydraulic fracturing is the key technology for efficient exploitation of shale gas and oil [40; 41; 42]. In the process of hydraulic fracturing, the initiation and propagation of hydraulic fractures is controlled by the fracture toughness of shale. As an anisotropic material, the fracture toughness of shale varies in different directions. [PERSON] et al. [43] conducted fracture toughness measurements on Mancos shale determined in all three principal fracture orientations using a modified short-rod methodology, and significant anisotropy was observed in shale fracture toughness measurements. [PERSON] et al.