## 6 Conclusions  
The roughness and tortuosity of rough fractures affect the seepage behavior of fluids in the rock mass. In this study, the influence of fracture roughness and tortuosity on seepage flow was studied through fluid seepage tests under load conditions. By analyzing the relationship between the friction resistance coefficient, the tortuous resistance coefficient, and the Reynolds number, a frictional resistance coefficient model considering fracture roughness and tortuosity was established, which can be used to more accurately analyze the head loss in the fluid seepage process. The conclusions were as follows.  
1. Normal pressure, hydraulic pressure, and fracture roughness affected the seepage behavior of the fluid in the rough fracture. The seepage flow of the fluid decreased with the increase in normal pressure, while increasing with the increase in hydraulic pressure. Under constant hydraulic pressure and normal pressure, the seepage flow of a fluid decreased with the increase in fracture roughness, and showed a trend of a nonlinear decrease. The greater the decreased range of fluid seepage flow, the more pronounced was the influence of normal pressure on the fluid seepage flow.
2. For rough fractures under normal pressure, the frictional resistance coefficient decreased with the increase in the Reynolds number. The roughness of the fracture affected the relationship between the frictional resistance coefficient and the Reynolds number. The relationship among the friction resistance coefficient, the Reynolds number, and the roughness was established. The calculation of the friction resistance coefficient based on the roughness coefficient and the Reynolds number provided a reliable experimental basis for analyzing the decrease in seepage flow.
3. The influence of the tortuosity of the rough fracture seepage path on fluid seepage behavior cannot be ignored. Under normal pressure conditions, the tortuous resistance coefficient of a rough fracture decreased with the increase in the Reynolds number. The tortuosity of rough fractures affected the relationship between the tortuous resistance coefficient and the Reynolds number. The relationship among the tortuosity, the frictional resistance coefficient, and the tortuous resistance coefficient was thus established. The tortuous resistance coefficient model considering fracture tortuosity can be used to analyze seepage flow loss in the local range of the seepage paths.
4. The existing frictional resistance coefficient model was modified, considering the frictional resistance and local resistance of fluid seepage. The modified frictional resistance coefficient model, considering the tortuosity and roughness, was thus established. Experimental data were applied to the modified model and the existing model to verify its rationality. The modified model was closer to the results of the practical application and more in line with the external environment of the fracture. The total head loss of the fluid was obtained based on the modified friction coefficient model. The influence of fracture roughness and tortuosity on fluid seepage behavior can be researched in more detail and more accurately by analyzing the changes in fluid seepage flow and head loss.  
Conceptualization, Y.X. and Y.Z.; methodology, Q.Y.; software, L.W.; writing--original draft preparation, S.W. All authors have read and agreed to the published version of the manuscript.  
This work was financially supported by the National Natural Science Foundation of China, grant number (51574060 and 51774138), and the Fundamental Scientific Research Business Expenses of the Colleges and Universities in Hebei Province, grant number (JQN2020039), and the Tangshan Science and Technology Project (19130216g). The authors are grateful to all study participants.  
Not applicable.  
Informed Consent Statement: Informed consent was obtained from all subjects involved in the study.