## 4 Numerical Results and Discussion
### Tensile Strength of the Rock and Cementing Strength of Natural Fractures  
The influence of the tensile strength of the rock \(\sigma_{t}\) and the cementing strength natural fractures \(\sigma_{c}\) on hydraulic fracture propagation were investigated. The in situ stress difference was kept at 5 MPa. In the cases of the sensitivity analysis of the rock tensile strength, \(\sigma_{t}\) ranged from 3 MPa to 9 MPa, and \(\sigma_{c}\) was 1 MPa. In the case of the sensitivity analysis of the cementing strength of the natural fractures, \(\sigma_{c}\) was from 0.5 MPa to 3 MPam and \(\sigma_{t}\) was 3 MPa. The simulation cases are listed in Table 2, and the results are represented in Figures 13-16.  
Figure 14: Schematic diagram of fracture morphology in different tensile strength of rock. (**a**) 3 MPa. (**b**) 6 MPa. (**c**) 9 MPa.  
Figure 15: The extracted morphology of hydraulic fractures under different cementing strengths of natural fractures.  
Figure 13 shows the extracted hydraulic fractures' morphology under different rock tensile strengths. It indicates that the bifurcations and secondary fractures were diminished when the rock tensile strength was higher. To understand the propagation pattern of the hydraulic fractures, we analyzed the step-by-step fracture development when the rock tensile strength was 3 MPa, 6 MPa, and 9 MPa, as shown in Figure 14. When the tensile strength was 3 MPa, hydraulic fracturing produced a long left-sloping main fracture and a right-sloping secondary fracture. The secondary fracture propagated for a short distance and stopped. When the tensile strength of the rock was 6 MPa and 9 MPa, only the main fracture occurred, and the main fracture propagated in a zigzag fashion in the natural fracture network and rock matrix. The smaller the differences between the tensile strength of the rock and the natural fractures, the greater the possibility of hydraulic fracture propagated along the natural fractures. It can be seen from Figure 13 that when the tensile strength of rock was relatively small, the phenomenon of fracture bifurcation was more obvious, forming a secondary fracture and more bifurcations. This is because when the tensile strength of rock was higher, greater resistance was needed to overcome it to break up the rock, and fewer bifurcations occur, with a smaller fissured area.  
The morphology of hydraulic fracturing fractures with different natural fracture mechanic properties is demonstrated in Figure 15. It can be seen from the figure that the hydraulic crack initiated from the perforation and formed a tri-wing fracture along the  
Figure 16: Schematic diagram of fracture morphology in different interface cementing strengths of natural fractures. (**a**) 0.5 MPa. (**b**) 1 MPa. (**c**) 3 MPa.  
direction of the natural fracture. To understand the propagation pattern of the hydraulic fractures, we analyzed the step-by-step fracture development when the rock tensile strength was 0.5 MPa, 1.0 MPa, and 3.0 MPa, as shown in Figure 16. With the increase in the cementing strength of natural fractures, the length of the hydraulic crack on the lower side of perforation became shorter, and the number of bifurcated fractures turning to the rock matrix along the main fractures became larger.