# Experimental Study on Mechanical Properties of Anisotropic Slate under Different Water Contents
## 4 Analysis of Anisotropic Properties of Slate Parameters
### Elastic Modulus Anisotropy  
Figure 12 depicts the elastic modulus variation with bedding angle under different water contents and confining pressures. It illustrates that the elastic modulus's variation curves with the bedding angle form a U shape. When the bedding angle is between 30\({}^{\circ}\) and 60\({}^{\circ}\), the elastic modulus of the slate reaches a minimum, but the overall change in amplitude remains small. However, as the bedding angle nears 90\({}^{\circ}\), the elastic modulus of slate increases sharply. The elastic modulus rises with confining pressure and falls with water content. This is because the increase in confining pressure compacts the bedding's weak plane, enhancing the slate's resistance to deformation. Conversely, exposure to water dissolves some mineral particles, and the lubrication from the water film between grains reduces friction, resulting in slate softening and a diminished resistance to deformation. Researchers lack a unified understanding of the trend in the variation of the elastic modulus of anisotropic rock masses with \(\beta\). Some scholars [28; 31; 32] observe that the rock masses' elastic modulus increases with \(\beta\); others [10; 33] note that the elastic modulus of slate varies in a U-shaped pattern with increasing \(\beta\), akin to the findings from the tests in this study. From a microscopic perspective, this can relate to the mineral composition and the arrangement of microfractures between slate beddings. Macroscopically, the former group attributes the change in elastic modulus to the compaction effect: The bedding plane of the 0\({}^{\circ}\) sample is perpendicular to the axial compression direction, causing significant compaction of the fractures between bedding planes and large rock deformation; the 30\({}^{\circ}\), 45\({}^{\circ}\), and 60\({}^{\circ}\) samples exhibit partial compaction of fractures; the axial pressure exerts the least compacting effect on the 90\({}^{\circ}\) sample, so as the compaction effect weakens, the elastic modulus gradually increases. The latter group argues that although the axial compaction of the 0\({}^{\circ}\) sample is the most substantial, the strength of the 30\({}^{\circ}\), 45\({}^{\circ}\), and 60\({}^{\circ}\) samples at failure is lower than that of the 0\({}^{\circ}\) and 90\({}^{\circ}\) samples, resulting in a relatively small elastic modulus; the 90\({}^{\circ}\) sample supports the load through both the matrix and the bedding plane, thereby improving resistance to deformation. In this scenario, the strain caused by axial pressure is minimal, and the elastic modulus is at its highest. Figure 11: Compressive strength anisotropy curve. The depiction of a transversely isotropic body within the global coordinate system is illustrated in Figure 13. In this representation, the \(z\)-axis is perpendicular to the bedding plane, while the \(x^{\prime}\)-\(y^{\prime}\)-\(z^{\prime}\) coordinate system results from rotating the \(x\)-\(y\)-\(z\) coordinate system clockwise by an angle \(\beta\), using the \(y\)-axis as the axis of rotation. According to the generalized Hooke's law, the stress-strain relationship for a transversely isotropic body is articulated in Equation (7). Here, \(\sigma\) and \(\varepsilon\) represent normal stress and strain, respectively, while \(\tau\) and \(\gamma\) denote shear stress and strain. The elastic compliance matrix comprises five independent parameters. \(E_{1}\) and \(\upsilon_{1}\) are the elastic modulus and Poisson's ratio in the transversely isotropic plane, respectively. \(E_{2}\) and \(\upsilon_{2}\) similarly represent the elastic modulus and Poisson's ratio in the plane perpendicular to the transversely isotropic plane. \(G_{12}\) is the shear modulus on this perpendicular plane [34]. \[\left\{ \begin{array}{c}\varepsilon_{x}\\ \varepsilon_{y}\\ \varepsilon_{z}\\ \gamma_{xy}\\ \gamma_{yz}\\ \gamma_{zx}\end{array} \right\}=\left\{