## 4 Discussion
### Local Stress Characteristics under Crack Initiation Stress
According to the elastic mechanics, the maximum principal stress (\(\sigma_{1}\)) and the minimum principal stress (\(\sigma_{3}\)) at different locations of the flaw are calculated by the detected stress components to further understand the change of local stress around the flaw under the crack initiation stress. In order to keep up with the traditional geotechnical engineering field, the compressive stress is positive and the tensile stress is negative in this section. Figure 12 shows the distribution maps of the maximum and minimum principal stresses around the flaw under different model initiation stresses. The distribution patterns of \(\sigma_{1}\) and \(\sigma_{3}\) around the flaws are quite different at different flaw inclination angles. When the flaw inclination angle \(\beta=15^{\circ}\), \(\sigma_{1}\) and \(\sigma_{3}\) on the upper surface of the flaw are greater than those on the lower surface of the flaw due to the stress-shielding effect. The maximum value of \(\sigma_{1}\) and \(\sigma_{3}\) appears in M1 and M7 (flaw tip); \(\sigma_{1}\) of the 12 measuring circles are all positive values, the \(\sigma_{1}\) in the middle part of the upper and lower surfaces of the flaw is positive at a low level, and the lowest value of \(\sigma_{1}\) appears in M4 and M10. The \(\sigma_{3}\) measured at the flaw tip is a positive value, and the \(\sigma_{3}\) measured on the upper and lower surfaces of the flaw is negative. When \(\beta=30^{\circ}\), the stress-shielding effect is still obvious; the greatest values of \(\sigma_{1}\) and \(\sigma_{3}\) also appear in M1 and M7 and the lowest value of \(\sigma_{1}\) appears in M5 and M11. When \(\beta=45^{\circ}\), the stress-shielding effect is weakened, and the least value of \(\sigma_{1}\) appears in M6 and M12. When \(\beta=60^{\circ}\), the stress-shielding effect almost disappears; the greatest values of \(\sigma_{1}\) and \(\sigma_{3}\) appear in M2 and M8, which is different from the above results; the distribution of \(\sigma_{3}\) is in a round shape. When \(\beta=75^{\circ}\), the difference between the values of \(\sigma_{1}\) is small, and the distribution \(\sigma_{3}\) at \(\beta=75^{\circ}\) is similar to that at \(\beta=60^{\circ}\). In a word, when the flaw inclination angle \(\beta\) increases from \(15^{\circ}\) to \(75^{\circ}\), the shape of the maximum principal stress \(\sigma_{1}\) changes from a flat to a proximal circular shape; the greatest value moves from the flaw tip to the adjacent position in a counter-clockwise direction, but it is still near the flaw tip; the lowest value moves from the middle of the flaw to the flaw tip in a counter-clockwise direction; the distribution 1 change of the minimum principal stress \(\sigma_{3}\) is similar to that of \(\sigma_{1}\). It shows that with the increase of flaw inclination angle, the concentration effect of tensile stress and compressive stress around the flaw decreases gradually. According to the experimental results of [PERSON] et al. [16], the initial flaw of rock or rock-like material with defects is usually tensile cracking, which is essentially caused by tensile stress. As shown in Figures 10 and 12, the tensile stress concentration occurs on both sides of the flaw, and the initial crack initiation is in the tensile stress zone. To further analyze the influence of flaw inclination angle on crack initiation, the variation graphs of maximum tensile stress of samples with different flaw inclination angles were plotted, as shown in Figure 13. The maximum tensile stress decreases gradually with the increase of flaw inclination angle, which is opposite to the change of crack initiation stress. This shows that the larger the flaw inclination angle, the lower the concentration of tensile stress, and the more difficult the cracking at the flaw tip is.