## 4 Shape Effects of Shale  
The International Society of Rock Mechanics (ISRM) recommends that uniaxial compression tests utilize cylindrical specimens with a diameter exceeding 50 mm and a height-to-diameter ratio between 2 and 3. The identical cylindrical specimens used in uniaxial compression are suitable for conventional triaxial tests, while true triaxial tests require cubic specimens. In this study, cylindrical specimens with a diameter of 50 mm and a height of 100 mm were employed for uniaxial compression tests. In contrast, rectangular specimens with a base of 50 mm and a height of 100 mm were utilized for triaxial compression tests to simulate uniaxial stress conditions. Considering that the specimen shape influences the stress transfer paths and the stress distribution states, the effect of the cross-sectional shape on the uniaxial test results warrants further discussion. Table 2 compares the anisotropy of mechanical parameters between cylindrical and prismatic specimens. The data reveal notable differences in the anisotropy of compressive strength and peak strain between the two specimen types, although their elastic modulus remains nearly identical. Figure 17 illustrates the uniaxial strength of cylindrical and prismatic shale specimens tested in this study. The figure highlights that the uniaxial strength of shale varies based on the cross-sectional shape, classifying the specimens into two distinct types. The strength difference between cylindrical and prismatic specimens is minimal when the bedding angles are \(0^{\circ}\) and \(90^{\circ}\). This is especially true at a bedding angle of \(90^{\circ}\), where the strengths are nearly equivalent. Regarding isotropic rocks, previous studies have examined the influence of cross-sectional shapes on mechanical properties [36; 37; 38]. For instance, [PERSON] et al. [39] conducted uniaxial compression tests on rock-like materials with various cross-sectional shapes (cylinders, triangular prisms, quadrangular prisms, etc.) and found that while the cross-sectional shape affects failure modes, it does not significantly impact the uniaxial strength. [PERSON] et al. [40], through adjacent sampling methods used to minimize rock heterogeneity, reported that granite's cross-sectional shape had little effect on the uniaxial compressive strength, with parameters such as crack initiation stress, crack damage stress, and crack closure stress showing minimal variation. [PERSON] et al. [41] suggested that strength differences between prismatic and cylindrical specimens might arise from the larger cross-sectional area of prismatic specimens. However, these differences disappeared when the prismatic specimen's dimensions were converted to an equivalent diameter. These findings collectively suggest that, for isotropic rocks, a cross-sectional shape has a negligible impact on strength, provided that heterogeneity is controlled. This explains the minimal strength differences observed at bedding angles of \(0^{\circ}\) and \(90^{\circ}\) in the present study. However, at inclined bedding angles, the strength of cylindrical specimens is significantly lower than that of prismatic specimens. This phenomenon may be attributed to the influence of the bedding weak plane and the uneven stress distribution caused by differences in the cross-sectional shape. During crack propagation, circumferential stress \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Anisotropy Index** & **Compressive Strength** & **Elastic Modulus** & **Peak Strain** \\ \hline Column specimen & 1.420 & 1.094 & 1.523 \\ Rectangular & 1.239 & 1.083 & 1.318 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Anisotropy index of mechanical parameters of cylindrical and cuboid specimens. emerges, as shown in Figure 18a. While [PERSON] et al. [41] posited that circumferential tension has minimal impact on the strength of cylindrical and prismatic specimens, this conclusion primarily applies to isotropic rocks and does not account for bedding effects.