# Simplified Calculation Method for Active Anti-Floating of Elliptical Basements by Relief Wells
## 1 Introduction
The total flow rate is consistent on both sides and is then unified appropriately at the cut-off wall. The calculation of the seepage field on the outer side is relatively straightforward, with the focus being on the inner measurement of the seepage field [18; 19]. Currently, numerical methods are typically employed for analysis, and there is a noticeable absence of practical simplified calculation methodologies. The fundamental concept of simplified calculation for IDPR anti-floating primarily involves three stages. First, the pressure reduction target, which is the average anti-floating water level within the basement floor, is established. The determination of this water level should factor in the characteristics of the structure and the site, the environmental impact of the drainage, the durability of the drainage structure, as well as the volume of the drainage, among other elements. Once the water level is set, the active anti-flooding structure can be designed. In the simplified calculation approach presented in this paper, the anti-floating water level is treated as a known input parameter. Next is the calculation of the drainage volume. In the simplified calculation of a multi-well system, the superposition principle is commonly used. When there is no impermeable boundary, the drawdown at any point in the multi-well system is the sum of the drawdowns caused by each well at that point [20; 21]. Based on the principle of superposition, [PERSON] [22] proposed a method to solve the water depth drop at any point in a pressurized and unpressurized multi-well system under arbitrary arrangement: the group of wells is virtualized as a \"big well\" and the \"big well formula\" is used for calculation. The water depth and flow rate can be obtained when the group of wells is approximately circularly distributed. However, in an IDPR environment with cut-off wall to intercept seepage, the big well formula is no longer applicable. In addition, [PERSON] [23] proposed the mirror superposition method to solve the seepage field of a pit with a completely watertight cut-off wall boundary. In fact, the cut-off wall of the pit is not a completely water-insulated boundary, and there is both bypass seepage and through seepage. [PERSON] [24] used the conformal transformation method to find the head and flow in the case of bypass seepage when the thickness of the cut-off wall is taken into account. [PERSON] [25] carried out both approximate calculations and numerical simulations for comparative verification of the mirror superposition method in the case of permeability. However, the above studies did not consider the working conditions of relief wells. Under the condition of cut-off wall, the arrangement of relief wells mainly affects the pressure distribution on the inner side of the cut-off wall, while the influence on the flow rate on the outer side of the cut-off wall is smaller, so the inner and outer seepage flow fields can be decoupled, which provides the feasibility for simplifying the proposed calculation method. For seepage calculations in multi-well systems with the presence of a cut-off wall, a coefficient of resistance method is used which takes the cut-off wall into account; This method was proposed by [PERSON] [26] in 1957 on the basis of the theory of [PERSON]'s segmentation method and the theory of [PERSON]'s calculations of rapidly changing seepage zones, and is an approximation of constant seepage in the non-rocky foundations of a lock and dam. It can be used to determine seepage elements at various points in a seepage zone, including the seepage pressure, seepage gradient, and seepage flow rate. [PERSON] et al. [18] obtained the discharge by solving the seepage field on the inside of the cut-off wall by solving the resistance coefficient. [PERSON] et al.