## 5 Discussion
### Reasons for the Relationship between K\({}_{IC}\) and \(\sigma_{t}\)  
The mechanical parameters of rock may not be isolated, as they are, to an extent, related to each other. In underground energy development, rock masses are often in complex stress states. For example, tunnels, engineering slopes, underground engineering chambers, and roadways are in a state of tensile stress, while other parts of the system are in a state of compressive stress. Since the tensile strength of the rock is much lower than the compressive strength, the rock always begins to be damaged in zones under tensile stress. Cracks change their propagation direction, and fracture surfaces separate because the tensile stress exceeds the bonding force between the atoms, leading to rock failure, that is, mode-I fracture. Some research [45; 46] has been carried out into the properties of tensile crack extension under compressive shear stress conditions. It is believed that cracks always undergo mode-I fracturing by turning. When rock in compression is damaged, shearing and stretching are mainly caused by tensile cracks induced by tensile stress. This is one of the reasons why tensile, shear, and compressive strength are interrelated. Tensile damage may also occur when rock is in a compressed state. Rocks are brittle materials, and tensile stress can easily cause damage. Some scholars have studied microscopic fracturing in a compressed state. The results show that stress-induced microcracks in the rock are caused by tensile failure, not by shear failure. Crack propagation in the axial direction is caused by tensile failure and has hysteresis [47; 48; 49]. The above results indicate that the tensile strength and compressive strength of rock are correlated and that compressive and tensile failure has similar fracture mechanisms at microscopic scales, so one of the root causes of rock failure is the generation and expansion of microcracks. The generation and expansion of microcracks occurs due to tensile stress and, ultimately, tensile failure [38; 39; 40]. However, it has been argued that the tensile strength of axial cracks is the primary control over compression damage [47] and that the characteristics of macro-cracks in brittle rock-like materials are not solely determined by the nature of micro-cracks. In the SCB test, the stress resulting from compression is concentrated at the loading point and the tip of the artificial notch. Tensile stress causes a new crack or an existing axial crack to spread gradually from the notch tip. Eventually, the SCB sample is broken into two halves along the main tensile crack, as shown in Figure 12a. In the Brazilian splitting test, the loading point of the Brazilian disc is compressed, causing tensile stress on both sides of the center of the disc. The tensile action caused by the tensile stress between the two points causes tensile cracking at the fracture surface. The expansion and penetration of the main tensile crack eventually lead to the destruction of the rock, breaking it into two halves as shown in Figure 12b. After being heat-treated at temperatures between 20 \({}^{\circ}\)C and 600 \({}^{\circ}\)C, it was observed that all of the SCB and BD samples were broken into two halves. This means that differences in the temperature of heat-treatment did not affect this characteristic of failure along a main central tensile crack. Figure 12: Broken specimens. (**a**) Broken sample of SCB; (**b**) Broken sample of BD  
The fracture morphology is related to the loading process and is ultimately determined by the properties of fracturing. The similarity of the SEM-detected fracture morphology under the two testing methods is due to their failure properties being the same. The characteristics of cracks in SCB specimens and Brazilian splitting specimens are similar [18]. This similarity indicates that the mechanical process by which the damage occurs is the same. The tensile toughness of the rock can be estimated by testing the tensile strength of the sample, which will greatly simplify fracture toughness evaluation.