# Study on Composite Fracture Characteristics and Hydraulic Fracturing Behavior of Hard Rock
## 3 Composite Fracture Characteristics in Hard Rock  
### The CSTBD Splitting Test and Results  
The lithology of this test specimen is metamorphic granite porphyry. Considering the processing cost of the specimen and the applicability of mechanical analysis, the central straight-crack Brazilian disc (CSTBD) specimen was selected for the splitting test. The size of the specimen is \(\phi\)\(\times\)\(h\) = 25 mm \(\times\) 25 mm, and a crack with half-length (\(a\)) of 5 mm and width (\(b\)) of 1 mm is prefabricated on the central axis of the specimen. In this experiment, six specimens were designed, and the central straight-crack angle (\(\beta\)) increased from 0\({}^{\circ}\) to 28.7\({}^{\circ}\). The basic physical and mechanical parameters measured are shown in Table 1. For example, the cohesive force \(c\) and the internal friction angle of rock \(\varphi\) were determined by the triaxial compression test. The compressive strength \(\sigma_{\mathrm{P}}\), the modulus of elasticity \(E\), and the Poisson's ratio \(v\) were determined by the uniaxial compression test. The tensile strength \(\sigma_{\mathrm{t}}\) was determined by the Brazilian splitting test.  
The load-displacement curves of specimens under different central direct crack angles (\(\beta\)) were obtained through the splitting test, as shown in Figure 2. According to the analysis in Figure 2, it can be seen that under a certain crack angle (\(\beta\)), CSTBD specimens can withstand a load of more than 8.9 kN, such as specimen C02. In the initial loading stage, the internal micro-cracks of the specimen were compacted and showed a certain plastic deformation, which then developed linearly. When the peak load is reached, the strength of the sample decreases rapidly, showing obvious brittle failure. This trend is consistent across different beta values.  
The peak loads obtained from each set of numerical simulation experiments were used to calculate the values of \(K_{\mathrm{I}}\), \(K_{\mathrm{II}}\), and \(T\) at the failure of each specimen using Equations (7)-(9), as shown in Table 2.  
\begin{table}
\begin{tabular}{c c} \hline \hline \multicolumn{1}{c}{**Parameter**} & **Value** \\ \hline \multicolumn{1}{c}{Cohesive force \(c\)} & 24.44 MPa \\ Internal friction angle of rock \(\varphi\) & 40.7\({}^{\circ}\) \\ Compressive strength \(\sigma_{\mathrm{P}}\) & 155.81–210 MPa \\ Tensile strength \(\sigma_{\mathrm{t}}\) & 7.5–13.5 MPa \\ Modulus of elasticity \(E\) & 82.3–92.5 GPa \\ Poisson’s ratio \(v\) & 0.17–0.3 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Basic physical and mechanical parameters.  
Figure 2: Load–displacement curve of the CSTBD specimen in the splitting test.  
The crack path of the specimen is shown in Figure 3. The red crack represents the primary crack generated from the prefabricated crack tip, while the yellow crack represents the secondary crack generated from contact with the loading plate. When \(\beta\) = 0, the crack appears as a pure type I fracture, and the direction of main crack propagation is consistent with the original crack's direction. When \(\beta\) > 0, the crack occurs in the I-II composite fracture and deviates from the original direction. As the crack spreads to the boundary of the specimen, the crack path shifts to the central axis of the specimen to a certain extent. In addition, the loading will be maintained for a short time after the failure of the specimen in the laboratory test, leading to secondary cracks in the specimen.