## 1 Introduction
When the unit grouting quantity and the water permeability of rock strata are used to judge the development characteristics of cracks in the grouted rock strata, it is considered that there are two kinds of combination relationships: (i) The unit grouting quantity and the water permeability of rock strata are relatively small if the results show that the groutability and water permeability of rock strata are poor, indicating that the development of rock cracks is weak. (ii) The unit grouting quantity and the water permeability of rock strata are relatively large if the results show that the groutability and water permeability of rock strata are relatively good, indicating that cracks in rock strata are relatively well developed. As far as karstification strata are concerned, they belong to strongly permeable strata, and their water paths and slurry paths are mainly wide karst fissures. In the combination relationship between the water permeability of rock strata and the unit grouting quantity, the combination of high water permeability of rock strata and large unit grouting quantity often appears, which is the reason why karstification strata must adopt grouting method to plug natural karst cracks in order to achieve the purpose of seepage control. In the area far away from the development of karst in the deep part of the rock strata, there will also be a combination of low water permeability of rock strata and small unit grouting quantity, indicating that the rock strata are slightly permeable, do not absorb slurry, and there is no need for grouting. It can be seen that the water permeability of rock strata is large, the unit grouting quantity is also large, the water permeability of rock strata is small, and the unit grouting quantity is also small. This shows that there is a positive correlation between the unit grouting quantity and the water permeability of rock strata. The above analysis shows that there is a nonlinear positive correlation between the unit grouting quantity and the water permeability of rock strata in karst curtain grouting. From a mathematical point of view, this dependency between the two physical quantities can be expressed by a certain functional relationship. Establishment of Theoretical Relationship between the Unit Grouting Quantity and the Water Permeability of Rock Strata  
The water permeability of rock strata is one of the most commonly used indexes in hydraulic anti-seepage design and construction. In the karst curtain grouting project, not only the permeability of the grouted rock strata is directly expressed by the water permeability of rock strata, but also it is regarded as an important index for the quality inspection and evaluation of the curtain grouting. The current regulations and codes for hydraulic design and construction in China [27; 28] clearly stipulate that the anti-seepage standard of rock mass of dam foundation (or reservoir bank) of large reservoir dam is that the water permeability of single hole in the water-pressure test of inspection hole is less than 5 Lu. The water permeability of rock strata is obtained directly by the water-pressure-test method, which is the main achievement index of the water-pressure test [13; 18]. The water-pressure test is also known as the Lugeon test [13; 29]. The current regulations and codes for hydraulic design and construction in China [27; 28] specify that the international Lugeon test is adopted as the basic method for obtaining the water permeability of rock strata (Lugeon Value). It is widely used in grouting engineering. The basic definition of the water permeability of rock strata is the amount of water that is pressed into the rock strata by the grouting hole per meter, per unit time, under the full pressure acting on the grouting hole section.