# Deformation and Stress Analysis of Pile-Supported Immersed Tunnels under Seismic Loads
## 1 Introduction  
Immersed tunneling is an engineering technology used to construct tunnels underwater. There have been numerous cases of the application of immersed tunnels for water resources development and energy transportation [1; 2; 3]. Horizontal and vertical loads acting on the tunnel structure by seismic waves cause deformation, stress concentration, and possible injury to the tunnel structure. It is important to analyze the fundamental frequency of the tunnel structure and the interaction with the frequency of seismic waves when analyzing the structural response of immersed tunnels [4; 5], the nature of the undersea foundation geological layer, and the seismic wave load characteristics. Therefore, great attention should be paid to the dynamic response to earthquakes under tunnel foundation-seawater interaction [6; 7].  
When seismic waves are transmitted to the seabed and seawater, the effect of the presence of seawater on the propagation of seismic waves and energy absorption leads to a change in the vertical frequency of the structure, which attenuates the amplitude of seismic waves during propagation [8; 9]. The ability of the seabed to enhance the seismic defenses of tunnels has been demonstrated when seismic SV waves are incident at different angles on the multilayered seabed [10], and the single-layered seabed [11]. The ambient temperature of seawater affects the tunnel stresses during earthquakes [12]. This shows the extent of the seismic response of immersed tunnel-piled foundations is related to seawater. The effect of seawater changing the vertical frequency of the tunnel on the stress and deformation needs to be further investigated.  
Sand compaction pile (SCP) can effectively improve the rigidity and densification of the seabed and increase the bearing capacity and stability, which is well evidenced in existing studies [13; 14; 15; 16; 17; 18]. [PERSON] et al. [19], [PERSON] et al. [20], and [PERSON] et al. [21] showed the relationship between the SCP arrangement and the deformation of the foundation. Moreover, the piles can significantly improve the lateral bearing capacity of the foundation and effectively increase the foundation densification and the effective stress of the soil around the piles [22; 23; 24; 25]. A large number of analysis methods show that the pile-soil interaction under dynamic loads is similar to that of Euler-Bernoulli beams and Pasternak foundations [26; 27; 28; 29; 30; 31]. However, the relationship between the injury at the piled foundation-tunnel connection and the replacement rate and slenderness ratio of the piled foundation in seismic analysis is not clear.  
In this paper, seismic effects are simulated by time history analysis within a sand compaction pile-immersed tunnel-seawater pressure (SIS) system. Numerical simulations (ABAQUS version 2020) were conducted to investigate pile-soil interaction, the connection between foundation piles and the tunnel, as well as the stress and deformation of the tunnel wall. Furthermore, the numerical simulations are validated by the established physical model experiment of the SIS system. The key influencing factors of seawater pressure, direction of the tunnel, replacement rate of the piled foundation, and slenderness ratio of the pile are parametrically analyzed. The optimum replacement rate and range of the slenderness ratio of the pile are determined. The positive and negative effects of seawater pressure on the seismic performance of the tunnel are evaluated. A more detailed basis for the seismic design of pile-supported immersed tube tunnels is provided.