## 2 Study on the Compressive and Tensile Mechanical Properties of Shale
### Study on the Compressive Strength of Shale  
Figure 2 displays the crack characteristics and stress-strain curves of uniaxial compression tests on parallel bedding shale samples (designated as sc-H-1, sc-H-2, and sc-H-3). It can be observed that each rock specimen contains cracks. In the initial stage of loading, the curves slightly bend upwards, exhibiting a concave shape downward, which is indicative of the compaction phase. During this phase, the micro-cracks within the shale are compressed and closed. The length of each compaction phase varies due to the different distributions of natural cracks in the samples. As the load increases, the samples transition into the linear elastic stage, where the stress-strain curves show a good linear increase and the elastic compressive modulus of the samples is calculated at this stage. Subsequently, the samples enter the failure stage, where cracks propagate, micro-cracks gradually develop, and macroscopic cracks form. The stress-strain curves of the samples deviate from the linear section, and failure occurs at the peak of the curve, which was followed by a rapid decline in the stress-strain curve. The stress-strain curves of samples sc-H-1, sc-H-2, and sc-H-3 exhibit minor fluctuations in the linear elastic stage, which are caused by the natural cracks in the shale. The post-peak stress in the shale samples shows a serrated or stepped decline. This phenomenon is similar to the experimental results of [PERSON] et al. (2016), [PERSON] et al. (2017), and [PERSON] et al. (2018), mainly due to the influence of natural cracks in the rock samples on the characteristics of crack initiation, propagation, and penetration; that is, the stress reduction on the stress-strain curve corresponds to the crack propagation behavior of the samples. The more noticeable serrated stress-strain curve in the sc-H-3 test is due to the greater number of natural cracks within the shale sample, which also indicates that the compressive strength of the sc-H-3 sample is lower than that of samples sc-H-1 and sc-H-2. The results of the uniaxial compression tests on the parallel bedding shale samples are shown in Table 2, from which it can be seen that the elastic compressive modulus of the parallel bedding shale samples from 22.42 to 32.74 GPa with an average value of 28.13 GPa; the Poisson's ratio ranges from 0.11 to 0.15 with an average value of 0.13; and the compressive strength ranges from 127.82 to 223.21 MPa with an average value of 191.08 MPa. Figure 2: Uniaxial compression stress–strain curve of shale with parallel bedding. Figure 3 presents the crack characteristics and stress-strain curves of uniaxial compression tests on vertical bedding shale samples (designated as sc-V-1, sc-V-2, and sc-V-3). It can be observed that the failure patterns of the vertical bedding shale samples are essentially the same as those of the parallel bedding shale samples. During the initial loading compaction phase and the linear elastic phase, the stress-strain curves of the vertical bedding shale samples are similar to those of the parallel bedding shale samples. The stress-strain curve of sample sc-V-3 exhibits more serrated behavior, which is due to the greater number of natural cracks present in the shale sample. This corresponds to the more serrated stress-strain curve observed in the uniaxial compression test for sc-V-3 and indicates that the compressive strength of sc-V-3 is lower than that of the samples sc-H-1 and sc-H-2. The results of the uniaxial compression tests on the vertical bedding shale samples are shown in Table 3, from which it can be seen that the elastic compressive modulus of the vertical bedding shale ranges from 25.56 to 31.90 GPa with an average value of 28.57 GPa; the Poisson's ratio ranges from 0.13 to 0.18 with an average value of 0.15; and the compressive strength ranges from 83.53 to 158.22 MPa with an average value of 123.00 MPa.