# A Coupled Darcy-Forchheimer Flow Model in Fractured Porous Media
## 6 Result and Discussion  
Based on the numerical method of nonlinear flow in dual media, the influences of fracture heterogeneity and density on the evolution of inrush flow in fractured surrounding rock tunnels are studied. (1) The effects of heterogeneity of fracture  
To investigate the influence of fracture orientation inhomogeneity, the simulated fracture parameters \(\kappa\) are 0, 1, 2, 4, and 8. The larger \(\kappa\) is, the more non-homogenous the fracture distribution is. Other parameters are as follows: the aperture of all fractures is set at 0.1 mm, the length of fracture is between [10; 80] m, and the exponential distribution is \(\lambda=1\). The average fracture angle is 90\({}^{\circ}\). Figure 6: Geometry model of tunnel. Figure 7 is the cloud map of water pressure distribution in a tunnel surrounding rock with different \(\kappa\) values. As can be seen, the water head of the whole flow field expands outward in concentric circles with the tunnel. The water pressure nephogram of surrounding rock with different \(\kappa\) values is slightly different, which indicates that the uniformity of fracture affects the water pressure distribution of surrounding rock in the tunnel. To better illustrate this difference, the water pressure in \(y=\)[30; 50] sections of the tunnel centerline at \(x=40\) was taken, and the water pressure distribution with different \(\kappa\) values was plotted as shown in Figure 8. The water pressure near the bottom of the tunnel changes greatly, with an average gradient of 8300 Pa/m, while the water pressure near the top of the tunnel changes less, with an average gradient of 3300 Pa/m. This suggests that the flow at the bottom of the tunnel is higher than at the top. In addition, the greater the \(\kappa\) value is, the greater the water pressure gradient around the tunnel is. But the influence on the surrounding rock at the bottom of the tunnel is less than that at the top of the tunnel. This indicates that the more the fracture direction is concentrated in the direction of the hydraulic gradient, the larger the tunnel flow will be. Figure 9 shows the flow distribution of the fracture network with different \(\kappa\) values. As can be seen, the fracture flow distribution has obvious heterogeneity: the fracture flow along the flow direction (Y-axis) is large, the fracture flow along the vertical flow direction (X-axis) is small, and the maximum flow is about 60 times the minimum flow. The maximum fracture flow is distributed near the tunnel, ranging from 1 \(\times\) 10\({}^{-6}\) to 2 \(\times\) 10\({}^{-6}\) m\({}^{3}\)/s/m. The main reason is that there is a large hydraulic gradient at the tunnel exit, which is consistent with the analysis results of the above water pressure distribution. Figure 7: Water pressure distribution of fractured rock tunnel under different \(\kappa\) values. The effects of fracture density  
The influence of the number of fractures on the seepage field of the tunnel surrounding rock is analyzed by changing the number of fractures. The number of fractures is 10, 50, 100, 150, 200, and 300. The other parameters are the same as in section (1). Figure 10 shows the distribution of water pressure and velocity of surrounding rock under different \(N\) values. The water pressure distribution around the tunnel is less affected by the number of fractures. Similarly, the water pressure at \(y=\)[30, 50] of the tunnel centerline with \(x=40\) was taken, and the water pressure distribution with different \(N\) values were drawn, as  
Figure 8: Water pressure distribution of tunnel rock at [30, 50] range under different \(\kappa\) values. Figure 9: Fracture flow rate distribution under different \(\kappa\) values. shown in Figure 11. The greater the value of \(N\), the greater the water pressure gradient around the tunnel. However, the influence of \(N\) value change on the surrounding rock at the tunnel bottom is less than that at the tunnel top.