The Deviation of Semi-Theoretical and Semi-Empirical Water Inflow Prediction Formula Based on Sphere Coordinate Conversion and a Grouting Excavation Evaluation Method

The water in the rock medium is exchanged with the confined aquifer through the fracture, which leads to the water inflow line in the confined aquifer is no longer horizontal. This paper assumes that the aquifuge is a kind of semi-isolation layer, while the first-order derivative of the total head slope line function within the influence of precipitation approaches the slope of the line connecting the top plate of the aquifuge with the spherical center. This hypothesis demonstrates the relationship between the bottom of the well water inflow and the complete well gushing water. Laplace’s equation for the spherical coordinate transformation is used to find the analytical solution of the water inflow for stable flow. The calculation results are in line with reality through actual engineering and numerical simulation methods. The current numerical simulation methods and theoretical methods mostly consider the aquifer in the ideal state, which is difficult to simulate the fractured rock mass. The theoretical formula proposed in this paper can more effectively reflect the actual seepage situation of fractured rock mass than other formulas. In addition, the combination of theoretical derivation, numerical simulation and field measurement can predict the water inflow more accurately than unilateral research. At the same time, for the question of whether the face excavation is grouted or not, this paper using the subjective and objective assignment weight method combined with analytic hierarchy process method and entropy-weight method to take the weight calculation and giving a slurry excavation judgment method based on the proposed formula. Theoretical support is given for the selection of permeability coefficients for each hole in the overrun exploration and this method is validated by different projects, which has some degree of reference value.