## 5 Conclusions  
In order to overcome the lack of theoretical research on the prediction of the unit grouting quantity in karst curtain grouting and to seek a reasonable and applicable prediction method of the unit grouting quantity, in this paper, a theoretical study on the prediction of the unit grouting quantity in karst curtain grouting was carried out. On this basis, a prediction method of the unit grouting quantity in karst curtain grouting based on the water permeability of rock strata was proposed. The following main conclusions can be drawn:  
1. The theoretical relationship between the unit grouting quantity and the water permeability of rock strata in karst curtain grouting can be expressed in the form of power function. The theoretical equation contains only the parameter \(K\), which is the comprehensive characterization of the characteristics of slurry fluid, the characteristics of grouted rock strata, and the technical factors of grouting in karst curtain grouting, and its value is determined by field tests and data fitting.
2. Based on the theoretical relationship between the unit grouting quantity and the water permeability of rock strata in karst curtain grouting, the proposed method can be used to reasonably predict the required unit grouting quantity in karst curtain grouting construction. The procedure is as follows: (i) According to the hydrogeological conditions of the construction area of karst curtain grouting, the suitable curtain grouting test section is selected to carry out the field test, and the data of the unit grouting quantity and the water permeability of rock strata obtained in the test are recorded. (ii) Using the test data and nonlinear function fitting, the comprehensive coefficient of karst curtain grouting is determined; and (iii) according to the theoretical relationship equation between the unit grouting quantity and the water permeability of rock strata in karst curtain growating, the required unit grouting quantity is predicted by using the water permeability of rock strata obtained in the main project.
3. The relationship equation between the unit grouting quantity and the water permeability of rock strata in the karst curtain grouting obtained by theory (Equation (16)) is consistent with the fitting equation obtained in the typical case of karst curtain grouting project (Equations (17) and (18)), indicating that the theoretical equation can be effectively applied to predict the unit grouting quantity in the karst curtain grouting.
4. In the engineering case, it is obtained that the comprehensive coefficient of karst curtain grouting is 24.37 in the area of strong karst development and 16.51 in the area of weak karst development. It can be applied respectively to predict the unit grouting quantity in the main project of karst curtain grouting in the area of strong karst development and the area of weak karst development.  
Conceptualization, J.-D.N.; data curation, J.-D.N.; formal analysis, J.-D.N.; investigation, B.W.; methodology, B.W.; supervision, K.C. and G.-J.C.; validation, B.W.; visualization, K.C. and G.-J.C.; writing--original draft, J.-D.N. and B.W.; writing--review and editing, K.C. and G.-J.C.  
This research received no external funding.  
This research was supported by the School of Civil Engineering, Central South University, China. The authors would also like to thank the China Hunan Water Resources and Hydropower Survey and Design Research Institute for field test data of the trial grouting boreholes.  
The authors declare no conflicts of interest.