## 1 Introduction  
In the construction of water-rich areas, whether in tunnels or shafts, water gushing is always the most difficult problem to deal with, and accidents such as sudden flooding of tunnels and shaft flooding occur frequently, causing great damage to property and casualties. In the construction of water-rich areas, whether in tunnels or shafts, water gushing is always the most difficult problem to deal with, and accidents such as sudden flooding of tunnels and shaft flooding occur frequently, causing great damage to property and casualties. Generally, the number of over-bored holes is one. However, the parameters of each hole are not the same in the actual rock project. Therefore, how to choose a suitable parameter about the grouting judgment is a very important issue. When excavating the aquifer, if only the ideal geological conditions are considered, there may be a large error in the prediction of water inflow. When the predicted value is small, the excavation without grouting may exceed the drainage capacity of the shaft and cause flooding. Therefore, there is an urgent need to develop mathematical models for different geologies and to form a grouping judgment system in combination with advance exploration to prevent accidents and ensure the safety of the project. Now there are many methods of predicting influx of water, including precipitation infiltration method, subsurface runoff modulus method, groundwater dynamics method, comparison method, fuzzy mathematical method, numerical simulation method, etc. On the groundwater dynamics method in the normal influx of stable flow problems, [PERSON] based on [PERSON]'s law proposed Dupuit hypothesis. People based on the assumption of semi-infinite aquifer, improve the ground water head above the surface of the horizontal tunnel steady-state flow, transient flow of water prediction formulae and the ground water head below the surface of the water inlet formula [1; 2; 3; 4; 5]. Furthermore, some people proposed their own equations based on different mathematical models [6; 7; 8; 9; 10; 11; 12; 13; 14; 15; 16; 17]. However, all of them have some errors or are incomplete. For example, the formula of [PERSON] ignores the water inlet at the top of the cave when the water level is higher than the surface [15; 16], while the rest of the formulas all ignore the water surge at the palm surface. A number of Chinese scholars improved the previous formulas to some extent based on mathematical methods such as angle-preserving mapping and mirroring method [18; 19; 20; 21; 22; 23]. Although now has proposed a lot of water surge analytical formula, but all of them are based on different mathematical simplification model proposed. These formulas are more suitable for isotropic geological excavation, but there are still few formulas suitable for fractured rock mass such as anisotropic medium excavation. In addition, double porosity is not considered in many formulas. With the development of calculation technology, various numerical simulation software have high accuracy in water inflow prediction. Among the available studies, COMSOL Multiphysics [24; 25], FLAC3D [26; 27; 28; 29] and MODFLOW [30; 31; 32] and other software verified to be better able to simulate the engineering water surges in excavations under complex geological conditions. Therefore, the analysis of the water surge in recent years has focused on numerical means of research, and less research on theoretical aspects. Although the numerical simulation method can take into account the actual situation of the project, including geology, excavation profile, flow-solid coupling, etc., to some extent, it has its own limitations. As stated by [PERSON] and [PERSON] [33] numerical model are tedious, time-consuming, and expensive for tunnel engineers in practice. For example, their assumptions are mostly small deformations and have great reliance on the ground investigation data.