## 3 Experimental Results
### Hydraulic Fracturing
Therefore, the 3 DEC (3-Dimensional Distinct Element Code) software (Version 7.00) [20] was utilized to simulate the fluid diffusion along the joined fractures, aiming to qualitatively illustrate the correspondence between the fluid pressure variation curve and the damage behavior of the sample. The proposed model has dimensions of 40 \(\times\) 40 \(\times\) 40 cm\({}^{3}\). Considering its symmetry, half of it is taken as shown in the three-dimensional model on the left side of Figure 8. The injection wellbore is located at the center of the model, which is the center on the right side of the half-model. A compressive stress of 12.5 MPa was applied to the top of the model, while fixed displacement boundary conditions were assigned to the other five surfaces. For the 3 DEC simulation of the fracturing process, it is necessary to predefine the location of the fracture planes. Specifically, the y-z plane passing through  
Figure 7: The curves of fluid pressure within the wellbore, the injection rate, and the sample temperatures with time in each experiment, (**a–d**) correspond successively to the four cases H1–H4. The numbers in the figure, such as (i), represent some specific time points during the injection. the midpoint of the \(x\)-axis is designated as the predefined fracture plane, also known as the flowplane in 3 DEC. To enhance the visualization of fluid boundary conditions, the flowplane is translated and displayed separately on the right side of Figure 8. The three peripheral edges of the flowplane are configured as free fluid boundaries. Additionally, the right-side partial edge of the flowplane is designated for constant flow injection, with a specified flow rate of 7.5 mL/min. Initially, the predefined fracture plane was joined, but it was allowed to open under hydraulic action. The rock matrix is assumed to be elastic, with an elastic modulus of 80 GPa, and a Poisson's ratio of 0.23, and its permeability is neglected. The parameters of the fracture plane and fluid are detailed in Table 2.  
From the moment fluid injection commences until it fully penetrates the fracture, the fluid injection pressure at different time points within the wellbore is illustrated in Figure 9. When the fracture initiation begins, there is a notable drop in fluid pressure. As the fracture propagates stably, the fluid pressure gradually becomes stable. Finally, when the fluid fully traverses the fracture to reach a free boundary, the fluid pressure accelerates its decline once again, subsequently stabilizing at a lower level. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Parameter Name** & **Parameter Value** & **Parameter Name** & **Parameter Value** \\ \hline Normal stiffness (N/m) & \(10\times 10^{9}\) & Initial/max aperture (m) & \(1\times 10^{-5}/1\times 10^{-4}\) \\ Shear stiffness (N/m) & \(10\times 10^{9}\) & Fluid bulk modulus (Pa) & \(2\times 10^{5}\) \\ Cohesion (Pa) & \(1\times 10^{9}\) & Fluid density (kg/m\({}^{3}\)) & 1000 \\ Tensile strength (Pa) & \(1\times 10^{4}\) & Viscosity (pa-s) & \(1\times 10^{-3}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: The parameters of the fracture plane and the fluid. Figure 8: The 3 DEC model and the boundary conditions. The three-dimensional half-model on the left represents the simulated rock mass itself, with stress and fixed displacement boundary conditions. The two-dimensional plane on the right is the separately displayed flowplane, with free and constant flow boundary conditions. Based on the simulation results, it can be inferred that for sample H1, cracks initiated at point 1, followed by continuous crack propagation, with the fluid pressure gradually stabilizing. When the injection rate increased to 20 mL/min, cracks continued to propagate stably. As the injection rate further increased, the decrease in the fluid pressure accelerated suddenly, indicating that the cracks had permeated the entire sample. For sample H2, cracks also initiated at point 1.