## 1 Introduction  
With the acceleration of urbanization, problems of traffic congestion and urban land shortages are becoming increasingly serious [1, 2]. Therefore, underground traffic development has become an important way for large and medium-sized cities to relieve traffic congestion [3, 4]. The shield tunneling method has gradually become mainstream due to its high automation, safety, ground adaptability, and low impact on the environment in metro construction [5, 6]. However, metro construction inevitably produces ground movement, which may cause a negative impact on the nearby surface and subsurface structures in urban areas, and even lead to security incidents. Metro construction in coastal cities faces higher security risks than in other areas. Major security accidents have occurred in Shanghai, Tianjin, Nanjing, Wuhan, Nanning, and Foshan (Figure \(1\)[7]). For example, the water inrush and mud gushing in Wuhan Metro Line 3 claimed two lives and injured five people, with direct economic losses worth close to 30 million yuan. In addition, with the increasing intensity of underground development, the planned metro lines will inevitably go below the groundwater level in the future. This situation demonstrates that the safety of shield tunneling in water-rich stratum has become a key problem restricting urban metro construction. Therefore, proper modelling of the ground deformation characteristics because of shield tunneling in water-rich soft stratum is critical. Numerous research works based on empirical formulas, theoretical predictions, model tests, and numerical analyses have been conducted to study the ground settlement caused by shield tunneling. [PERSON] [8] proposed a calculation formula to predict surface settlement by analyzing a large number of measured data. Many studies have adapted [PERSON]'s formula to fit different geological conditions [9; 10; 11], but there are relatively few site-measured data analyses on the ground settlement of shield tunneling in water-rich soft stratum. Furthermore, numerous theoretical analyses have been employed to examine the ground settlement caused by shield tunneling [12]. Based on elastic theory, [PERSON] et al. [13] presented analytic solutions for the strain field due to near-surface ground loss. [PERSON] et al. [14] developed a closed form solution used to assess the displacement field around the tunnel. Based on elastic-plastic theory, [PERSON] et al. [15] put forward analytical solutions for estimating ground movements caused by shallow tunneling in soft ground. Due to the inherent complexities of the ground conditions, the ground settlements obtained by these methods are only suitable for specific conditions. The ground settlement caused by shield tunneling can also be simulated and predicted by the centrifuge model test [16; 17; 18]. However, because of its high cost and restricted applicability, the development of this method is limited. Numerical investigation is the most commonly used method in the study of ground responses to shield tunneling [19]. Several numerical models were proposed to simulate the complete construction process. [PERSON] et al. [20; 21] proposed a three-dimensional finite element model for simulations of shield-driven tunnels in soft stratum. The model was used for systematic numerical studies in mechanized tunneling. The model improved the overall behavior of the simulation, but it was still incapable of capturing the real shield movement. [PERSON] et al. [22; 23] investigated the effect of mechanical and hydraulic boundary conditions on pore water pressure at the tunnel face with and without filter cake formation. [PERSON] et al. [24] developed a three-dimensional finite element model  
Figure 1: Safety incidents caused by water [7]. (**a**) Shanghai Metro Line 4 (2003). (**b**) Nanjing Metro Line 2 (2007). (**c**) Tianjin Metro Line 3 (2009). (**d**) Wuhan Metro Line 3 (2013). (**e**) Nanning Metro Line 1 (2014). (**f**) Foshan Metro Line 2 (2018). considering shield conicity and construction process. [PERSON] et al.