# Simplified Calculation Method for Active Anti-Floating of Elliptical Basements by Relief Wells
## 1 Introduction  
In recent years, with the development of the city, increasing attention has been paid to the development of underground space, and a series of large-scale, complete functional systems of underground complexes, underground facilities, urban renovation, and new construction areas has emerged. The construction of these super-large and super-deep basements inevitably faces the problem of calculating the flotation resistance of the underground structure and selecting anti-floating measures. [PERSON] et al. [1] pointed out that when a sudden high-water level occurs, a single anti-buoyancy measure cannot actively reduce the water load on the underground structure, and the basement will suffer from wall cracking and floor arching. [PERSON] et al. [2] investigated the risk of impact instability of the structure caused by the buoyancy force of groundwater due to the increase in head in the pressurized aquifer in the Shanghai area. [PERSON] et al. [3] conducted acomprehensive study on the design of shield tunnel cover thickness from the aspects of working surface and anti-buoyancy stability. [PERSON] et al. [4] introduced the failure reasons and laws of anti-buoyancy structure through engineering examples of anti-buoyancy accidents. [PERSON] et al. [5] ensured that the large air shafts between the Olympic Sports Centre Station and the Century Avenue Station of Lanzhou Metro Line No. 1 were fitted with anti-float safety devices. The traditional anti-floating measures for underground structures mainly use anti-draft piles or anti-floating anchors, which provide a tensile force to resist the water load acting on the structural base plate. [PERSON] [6] discussed various methods of passive flotation resistance and explained the conditions applicable to each method. [PERSON] et al. [7] designed a composite pile with a lower expanded section applicable to engineering flotation resistance, analyzed the mechanism of its resistance to pull-out, and proposed a theoretical model of single pile pull-out capacity and calculation parameters for this type of pile. [PERSON] et al. [8] conducted field pile pull-out tests of bored and grouted piles and proposed an MMF growth curve model that accurately describes the pull-out load-displacement curve of pull-out resistant piles and predicts the ultimate capacity of piles for underground engineering. [PERSON] et al. [9] investigated the shear stress distribution of the anchor in geotechnical soil through destructive tests of pull-out anchors, and pointed out that increasing the length of the anchor has a limited effect on the shear stress of the anchor in the geotechnical soil, while increasing the length of the anchor has only a limited effect on improving its bearing capacity. However, there exists an alternative to this passive'resistance' based approach--an active 'drainage' based approach to decompression and flotation [10; 11]. In this method, the design water level is lowered and the water load on the bottom of the structure is reduced by installing a hydrophobic layer, a drainage ditch, a relief well below the bottom of the structure or a drainage corridor around the structure to drain the water. By reducing or eliminating the water load, most (or all) of the anti-draft piles or anti-floating anchors can be omitted, and the thickness and reinforcement of the floor slab can be reduced, while the drainage water from the system can be used for other purposes. This is sufficient to offset the cost of long-term pumping. Therefore, compared to conventional passive anti-floating, active drainage relief anti-floating has great economic advantages [12; 13; 14; 15; 16; 17]. The design of the IDPR anti-floating system primarily addresses four crucial issues: the arrangement of drainage structures, water discharge, pressure distribution on the bottom plate, and environmental impact. To tackle these challenges, the seepage field is divided into inner and outer sections, with the cut-off wall serving as the boundary.