## 1 Introduction  
Throughout the history of subway construction, the open excavation method and the cover excavation method have been the most widely used methods for subway stations construction [1], especially for shallow underground tunnels, which have advantages in terms of cost, time, and safety. However, with the continuous development of engineering technology and the economic level, the pile-beam-arch (PBA) method has been widely used for the construction of subway stations [2; 3; 4] because of its good surface settlement control, convenient excavation mode [5], no need for large area excavation and filling, and no impact on the normal operation of road traffic. PBA is a technique based on the traditional concealed undercutting method, which integrates the characteristics of cover excavation method and forms a perfect frame bearing system of arch-beam-column before most of the soil has been excavated. The essence of the PBA method is to attempt to quickly form the overall framework, consisting of side piles (or side columns), steel pipe piles supporting the arch section, and then, under the protection of the arch structure, to excavate the sections [6; 7]. The pile-beam-arch method of construction has lower ground disturbance and higher structural safety [8], which is particularly suitable for the construction of metro stations with heavy ground traffic, concentrated underground pipelines and high ground settlement requirements [9; 10]. The overturning resistance of the side piles, the compression and bending resistance of the steel pipe pile and the stability of the ground at the top of the arch are the keys to structural safety. Although the pile-beam-arch method construction technology is widely used all over the world. The excavation of underground structures inevitably disturbs the initial stress field, redistributes the stress of the surrounding rock and leads to layer settlement or uplift. A number of problems need to be solved, such as the complex structural mechanics system conversion [8; 11; 12] of the pile-beam-arch method and tunnel instability in soft surrounding rocks and ground settlement [13; 14]. Research methods on the mechanical properties and ground settlement of pile-beam-arch method subway stations mainly include model tests [10; 15; 16], numerical analysis [17; 18; 19], and field tests [20]. The pile-beam-arch method is used for large underground space projects. The advantage of this method is that it can minimize the ground loss caused by excavation and mitigate the damage to nearby buildings, and the pile-beam-arch method needs to be constructed inside the cavity, making the load-bearing structure inside the subway station particularly important. Therefore, the control of surface settlement is an important control factor for the construction of the pile-beam-arch method, for example, in the existing studies, the surface settlement of the excavation of the pilot tunnels and the construction of the arch structure in the construction of pile-beam-arch method accounts for about two-thirds of the total settlement [21; 22], and even the value of this settlement reaches 90% [20]. There are, of course, many factors that affect the surface settlement, among which the maximum surface settlement is linearly related to the pile spacing. As the pile spacing increases, the maximum settlement increases; the maximum settlement decreases as the pile cross-section increases, and the economic cost should be reasonably controlled while the ground settlement is reasonably controlled [23]. In the case of unfavourable surrounding rock conditions, surface settlement can be effectively controlled by reducing the spacing of the side piles. When constructing the pile method of the double-connected arch cave with three pilot tunnels, the middle pilot tunnel can be constructed first, which can reduce the amount of surface settlement [24].