# Optimization of Uplift Piles for a Base Plate Considering Local Anti-Floating Stability
## 1 Introduction  
With the development of underground space due to human activity, many underground structures have been buried increasingly deeper. Moreover, increasing groundwater levels have been observed in major cities all around the world due to water resources conservation policies. Many underground structures are subjected to high buoyancy nowadays, and the issue of anti-floating should be considered seriously in structure design and project construction [1; 2; 3; 4; 5; 6; 7; 8; 9]. Usually, anti-floating measures are divided into active anti-floating measures and passive anti-floating measures. Active anti-floating measures reduce the hydraulic head at the base plate by means of drainage. Passive anti-floating measures resist buoyancy by increasing the weight of structures or setting uplift piles (anchors) [1; 10]. Among those anti-floating measures, uplift piles are widely used in various structures due to their advantages of convenient construction, long service life, and good economic benefits [11; 12; 13]. Figure 1 shows uplift piles used as anti-floating measures for an underground structure. Uplift piles provide pulling forces to offset buoyancy. In order to improve the mechanical performance of the uplift piles, most researchers focus on enhancing the ultimate pulling force of the pile by changing the pile structure. These piles include root piles, screw piles, belled piles, etc. [14; 15; 16; 17; 18; 19; 20; 21]. Higher buoyancy can be resisted by setting these special piles. Most of the abovementioned research focuses on the overall anti-floating stability of underground structures. However, under the influence of multiple forces (buoyancy, pulling force, and column loads), the base plate will generate a large deformation and increase the risk of failure, which is the issue of local anti-floating stability. The design parameters of uplift piles include pile length, pile diameter, and pile spacing. Most ofthe current designs use the overall anti-floating stability as the verification condition, and arranged the pile according to equal length, equal diameter, and uniform distribution. It is clear that, this design method ignores the local anti-floating stability. For the anti-floating design of the structure, in addition to satisfying the overall stability, the local anti-floating stability of the base plate should also be considered. Therefore, it is necessary to study the reasonable design parameters of uplift piles, so that the deformation degree of the base plate can be reduced under the premise of satisfying the overall anti-floating stability. In recent years, with the development of a soft computing technique, topology optimization theory has been widely used in geotechnical engineering, which provides new ways to solve traditional problems and provides the reference for structural design [22; 23; 24; 25]. Topological optimization theory refers to finding the optimal distribution form of materials in the design domain under specific constraints. The bi-direction evolutionary structural optimization (BESO) method is one of the topological optimization methods. The basic principle of the BESO method is to discretize the structures into finite elements, add materials to the elements with high sensitivity, and remove materials from the elements with low sensitivity. Due to its concise theory and high efficiency combined with numerical calculation, the BESO method has been widely used in searching for the optimal layouts of structures. [PERSON] et al. [17] combined the method with the limit equilibrium method to predict the critical failure surface of the anti-dip bedding rock slope. [PERSON] et al. [19] used this method for reinforcement design around the tunnel. [PERSON] [26] used finite element software ANSYS and wrote a BESO topology optimization program using APDL language to propose a bridge shape that satisfies functionality, economy, environmental protection, and aesthetics.