## 4 Micro-Cracking Behaviors of Shale under Different Bedding Parameters
### The Difference Between Bedding Strength and Its Shear-to-Tensile Strength Ratio  
Both the variation of bedding strength and the shear-to-tensile strength ratio of beddings can change the UCS, crack type and complexity of the micro-cracking morphology in shale formation. However, the difference of their contributions has not been discussed. This section will comparatively analyze their effects and identify their difference using the indicators of JSR and STR. Both the JSR and the STR are taken as 1.0 for the datum case, where the tensile strength (\(\overline{\sigma}_{c}^{sj}\)) and shear strength (\(\overline{\tau}_{c}^{sj}\)) of beddings are taken as 15 MPa, and other parameters are taken the same as those parameters in Tables 1 and 2. Another two cases are used to compare their different influences between the JSR and STR. Increasing the tensile and shear strength of beddings simultaneously (\(\overline{\sigma}_{c}^{sj}\) = 18 MPa and \(\overline{\tau}_{c}^{sj}\) = 18 MPa) represents the influence of the JSR (JSR = 1.2). Increasing the shear strength of beddings only (\(\overline{\sigma}_{c}^{sj}\) = 15 MPa and \(\overline{\tau}_{c}^{sj}\) = 18 MPa) represents the influence of the STR (STR = 1.2). The UCS at these bedding parameters is shown in Figure 15. When the JSR increases from 1.0 to 1.2, the UCS increases linearly at the dip angle of \(60^{\circ}\). If the shear strength of the beddings is kept unchanged (\(\overline{\tau}_{c}^{sj}\) = 18 MPa), the variation of the STR does not affect the UCS of the shale specimen. Therefore, the bedding strength contributes more greatly to the UCS of shale. The shear strength of beddings is the essential factor affecting the UCS, especially when the shear failure of beddings becomes the dominant fracture pattern. Further, the percentages of matrix cracks and tensile cracks with different bedding strength parameters are presented in Figure 16a,b, respectively. Compared to the datum case in Figure 16a, both the increase of the JSR (\(\overline{\sigma}_{c}^{sj}\) = 18 MPa and \(\overline{\tau}_{c}^{sj}\) = 18 MPa) and STR (\(\overline{\sigma}_{c}^{sj}\) = 15 MPa) can improve the percentage of the matrix cracks (Pbt+Pbs). The JSR induces a slightly higher percentage of matrix failure than the STR. In addition, increasing the JSR (\(\overline{\sigma}_{c}^{sj}\) = 18 MPa and \(\overline{\tau}_{c}^{sj}\) = 18 MPa) and STR (\(\overline{\sigma}_{c}^{sj}\) = 15 MPa and \(\overline{\tau}_{c}^{sj}\) = 18 MPa) can increase the percentage of tensile cracks (Pbt+Sjt) (see Figure 16b). Figure 15: Variation of uniaxial compressive strength with dip angle at three bedding strength parameters. For constant shear strength of beddings (\(\overline{\tau}_{c}^{sj}=18\) MPa), a larger STR plays an even more significant role in the increase of tensile cracks in most circumstances. Generally, the increase of bedding strength has a greater impact on the increase of the percentage of matrix cracks, while the increase of shear-to-tensile strength ratio of beddings has a greater impact on the increase of percentage of tensile cracks. The fractal dimensions of the final fracture morphology of shale formation with different bedding strength parameters are shown in Figure 17. Compared to the datum case, the effects of the JSR (\(\overline{\sigma}_{c}^{sj}=18\) MPa and \(\overline{\tau}_{c}^{sj}=18\) MPa) and STR (\(\overline{\sigma}_{c}^{sj}=15\) MPa and \(\overline{\tau}_{c}^{sj}=18\) MPa) on the crack fractal dimension has a close relationship with the dip angle of the bedding. When the dip angle is \(0^{\circ}\), most of the micro-cracks occur in the rock matrix. Under this condition, the micro-cracking morphology becomes more complex with a higher STR. When the dip angle is \(60^{\circ}\), most of the micro-cracks occur in the beddings.