## 3 Experimental Results
### Subcritical Crack Growth Parameters  
The colinear flaw geometries of 45-0-2a and 60-0-2a and the non-colinear flaw geometries of 45-a-a and 45-2a-2a were employed for the determination of subcritical crack growth parameters. In the 45-0-2a and 60-0-2a specimens, coalescence occurred by the propagation of internal shear cracks, and then external wing cracks propagated until the specimen failed under monotonic and cyclic loading. In the 45-a-a and 45-2a-2a specimens, coalescence occurred through a vertical or quasi-vertical tension crack. For the 45-0-2a and 60-0-2a specimens, the fracture strength was determined when the coalescence occurred through the propagation of internal shear cracks. For the 45-a-a and 45-2a-2a specimens, the fracture strength was determined when a vertical or quasi-vertical tension crack occurred to coalesce the flaws. Two tests were performed for the loading rate of 0.02 MPa/s, and three tests were carried out for the loading rate of 50 MPa/s. The relationship between the loading rate and fracture strength is presented in Figure 12. The subcritical crack growth parameter \(n\) values for the 45-0-2a and 60-0-2a specimens, which were coalesced by shear cracks, were 34 and 36, respectively. The subcritical crack growth parameter \(n\) values for the 45-a-a and 45-2a-2a specimens, which were coalesced by vertical tension cracks, were 30 and 37, respectively. Stress intensity factors are needed to determine the subcritical crack growth parameter \(m\) under cyclic loading. The specimens coalesced by shear cracks used the shear crack model to determine the stress intensity factor [26]. A schematic illustration of the shear crack model is shown in Figure 13a. The shear crack model assumed that the cracks grew in their own plane. The stress intensity factor is expressed as:  
\[K=\tau^{*}\sqrt{na} \tag{6}\]  
where a is half of the crack length and \(\tau^{*}\) is the effective shear stress. \(\tau^{*}\) is given by:  
\[\tau^{*}=\sigma_{1}(\sin\beta\cos\beta-\mu\cos^{2}\beta)-\sigma_{3}(\sin\beta \cos\beta+\mu\sin^{2}\beta) \tag{7}\]  
where \(\beta\) is the crack inclination angle, and \(\mu\) is the friction coefficient between the crack surfaces. In this study, only a uniaxial compression was applied, and the cracks remained open under compression; Equation (7) can be simplified as:  
\[\tau^{*}=\sigma_{1}(\sin\beta\cos\beta) \tag{8}\]  
and the stress intensity factor of Equation (6) yields:  
\[K=\sigma_{1}(\sin\beta\cos\beta)\sqrt{\pi a} \tag{9}\]  
The specimens coalesced by a vertical tension crack employed the sliding crack model to determine the stress intensity factor [28]. A schematic illustration of the sliding crack model is shown in Figure 13b. Figure 12: Relationship between the loading rate and fracture strength for determining the subcritical crack growth parameter under monotonic loading. Figure 13: Schematic illustration of the crack model (**a**) shear crack mode; (**b**) sliding crack model. The sliding crack model predicted that the failure of the rock would occur by axial splitting. The stress intensity factor solution for this configuration was given as:  
\[K=\frac{2a\tau^{*}\cos\beta}{\sqrt{\pi b}}-\sigma_{3}\sqrt{nb} \tag{10}\]  
where \(b\) is the wing crack length and \(\tau^{*}\) is given in Equation (7). Additionally, only a uniaxial compression was applied and Equation (10) is reduced to:  
\[K=\frac{2a\sigma_{1}\sin\beta\cos^{2}\beta}{\sqrt{\pi b}} \tag{11}\]  
The stress intensity factor equations of the shear crack model and sliding crack models developed while containing one crack and did not consider the interaction of the two cracks. The specimens used in this study included two existing cracks, but they were separated by more than half of the length of the crack; consequently, the interactions between the two cracks would be negligible when new cracks grew from the exiting crack tip. Therefore, Equations (9) and (11) were assumed to be valid even under conditions with two exiting cracks.