## 4 Result of Numerical Modeling
### Parameter Sensitivity Analysis  
During fracture propagation, several factors can influence the propagation of hydraulic fracture in a discrete fracture network system, such as intensity of discrete fracture (fracture number, and  
Figure 11: (a) the failure morphology of the sample; (b) the simulated fracture. Figure 10: The dimensions of the sample. marked with \(n\)), fracture length (marked with \(l\)), and dip angle (marked with \(\alpha\)). In this section, the weighted value of hydraulic fracture is used to explore how these parameters influence the hydraulic fracture propagation. Here, the DFN is a two-dimensional horizontal section of a rock with 4 m length and 4 m width. Assuming that the DFN is static, partially connected and randomly distributed. The maximum principal stress direction keeps in line with the \(x\)-axis, and many groups of fractures are repeated computing for eliminating the influence of randomness. Figures 12-15 show quantitative comparison of the behavior of the models based on different parameters. Figure 12: The influence of fracture number (\(n\)) on the hydraulic fracture weighted value. Here, \(\alpha=30^{\circ}\), \(l=0.2\) m, and the angle between two groups fracture remains orthogonal. Eight kinds of fracture numbers (175, 200, 225, 250, 275, 300, 325 and 350) have been analyzed, with 150 groups of randomly generated fractures for each kind of fracture number. (**a**) scatter distribution of the the hydraulic fracture weighted value with different values of \(n\); (**b**) average of the hydraulic fracture weighted value with different values of \(n\). Figure 13: The influence of fracture length (\(l\)) on the hydraulic fracture weighted value. Here, \(\alpha=35^{\circ}\), \(n=250\), and the angle between two groups fracture keeps orthogonal. In addition, eight kinds of fracture lengths (0.15 m, 0.2 m, 0.25 m, 0.3 m, 0.35 m, 0.4 m, 0.45 m and 0.5 m) have been analyzed, with 150 groups of randomly generated fractures for each kind of fracture length. (**a**) scatter distribution of the hydraulic fracture weighted value with different values of \(l\); (**b**) average of the hydraulic fracture weighted value with different values of \(l\). Firstly, the influence of fracture number on the weight value of hydraulic fracture is shown in Figure 12. The trends of scatter distribution and average distribution are consistent with each other, and the weight value of hydraulic fracture decreases with the increasing of fracture number. That also means that the greater the fracture, the better for the hydraulic fracture propagation. Then, Figure 13 shows that the weight value of hydraulic fracture decreases with increasing of fracture length. It also indicates that as the fracture length is growing, the weight value of the hydraulic fracture is reducing. Longer fracture length will benefit the hydraulic fracture propagation. Finally, as demonstrated in Figure 14, it has little influence on the weight value of hydraulic fracture for different values of \(\alpha\) when the angle between two groups of fracture keeps orthogonal. Hence, the influence of different values of \(\alpha\) on the weight value of hydraulic fracture will also be studied under two groups of fractures are not orthogonal. Figure 15 shows the weight value of the hydraulic fracture firstly decreases and then increases with the increase of \(\alpha\) when the angle between two groups of fractures are \(20^{\circ}\). That being said, the farther away from the maximum stress direction, the larger the weight value of the hydraulic fracture. Figure 14: The influence of dip angle (\(\alpha\)) on the hydraulic fracture weighted value when the angle between two groups fracture remains orthogonal. Here, \(n=250\) and \(l=0.2\) m. The realizations belong to fifteen kinds of \(\alpha\) (\(0^{\circ},6^{\circ},11^{\circ},17^{\circ},22^{\circ},28^{\circ},34^{\circ}, 40^{\circ},46^{\circ},52^{\circ},57^{\circ},63^{\circ},69^{\circ},74^{\circ}\) and \(80^{\circ}\)), with 150 groups of randomly generated fractures for each kind of \(\alpha\).