# A Coupled Darcy-Forchheimer Flow Model in Fractured Porous Media
## 7 Conclusions  
Based on the finite volume method, the discrete scheme of the Darcy flow equation in porous media and the Forchheimer flow equation in the fracture is derived, and the solution method of the coupled flows is proposed. Based on this method, the nonlinear seepage law of buried fractured surrounding rock tunnel with rich water depth is studied, and the main conclusions are as follows:  
1. The results of the new method are compared with those of [PERSON] et al. (2008) for intersecting fracture cases. The pressure and fracture velocity distributions calculated by the new method are consistent with those calculated by [PERSON] et al. (2008). When the mesh size is less than 0.02 m, the calculation error is less than 1%. Therefore, the new method can accurately describe the nonlinear seepage behavior in fractured and porous media.
2. The water pressure gradient of the surrounding rock in the fractured tunnel presents the characteristics of \"large at the bottom and small at the top\", which indicates that the flow at the bottom of the tunnel is higher than that at the top. In addition, the fracture flow along the flow direction is large, the vertical flow direction is small, and the maximum flow is 60 times the minimum flow.
3. The random fracture uniformity affects the hydraulic characteristics of the tunnel surrounding the rock. The more the fracture direction is concentrated in the direction of the hydraulic gradient, the stronger the conductivity of the surrounding rock is and the greater the water inflow is.
4. Fracture density is another important factor affecting the conductivity of the tunnel surrounding the rock. The greater the fracture density, the greater the water pressure gradient and the greater the tunnel flow. The main reason is that the larger the fracture density is, the more fractures there are, and the more likely it is to intersect with the tunnel, resulting in more fractures with high flow. It is also noted that although the generation of fractures is based on the Monte Carlo method, the influences originate from several fracture network models. Hence, the new insights are applicable to flow in fractured rock tunnels.  
Conceptualization, F.X. and Y.J.; methodology, L.T.; software, Y.W.; validation, F.X., H.C. and C.Z.; formal analysis, C.Z.; investigation, F.X.; resources, C.Z.; data curation, H.C.; writing--original draft preparation, F.X.; writing--review and editing, Y.J.; visualization, L.T.; supervision, L.T.; project administration, L.T.; funding acquisition, Y.J. All authors have read and agreed to the published version of the manuscript.  
This research was funded by the Supported by Open Research Fund of State Key Laboratory of Geomechanics and Geotechnical Engineering, Institute of Rock and Soil Mechanics, Chinese Academy of Sciences (Grant No. SKLGME021009), the Fundamental Research Funds for the central Universities, CHD (Grant No. 300102212523), the National Natural Science Foundation of China (Grant No. 52209148), the National Natural Science Foundation of Shandong Province, China (Grant No. ZR2022 ME188) and National Key Research and Development projects of China (Grant No. 2021 YFB2600402).  
Not applicable.  
The data presented in this study are available on request from the corresponding author.  
**Acknowledgments:** This work was supported by the Supported by Open Research Fund of State Key Laboratory of Geomechanics and Geotechnical Engineering, Institute of Rock and Soil Mechanics, Chinese Academy of Sciences (Grant No. SKLGME021009), the Fundamental Research Funds for the central Universities, CHD (Grant No. 300102212523), the National Natural Science Foundation of China (Grant No. 52209148), the National Natural Science Foundation of Shandong Province, China (Grant No. ZR2022 ME188) and National Key Research and Development projects of China (Grant No. 2021 YFB2600402). This support is gratefully acknowledged.  
**Conflicts of Interest:** The authors declare no conflict of interest.