# Seismic Response of Foundation Settlement for Liquid Storage Structure in Collapsible Loess Areas
## 1 Introduction  
When water-immersed, collapsible loess undergoes significant subsidence, which can easily lead to structural foundation failure. This will cause settlement and deformation in LSS, significantly affecting the dynamic response of LSS. During seismic events, such structures are more prone to damage. Both domestic and international scholars have conducted extensive research on the dynamic response of various structures, such as shear wall structures and bridges, under foundation failure conditions. However, there has been relatively little research on the dynamic response of LSS under such conditions. The study of LSS problems began in 1933 when [PERSON] first introduced the concept of fluid-solid coupling vibration, followed by the proposal of a non-simplified analytical model. This laid the groundwork for gradually expanding research on the dynamic response of fluids. With the advancement and application of computer technology, simplified analytical models have been increasingly applied to practical engineering problems, enabling effective analysis and the resolution of LSS issues [1; 2; 3; 4; 5]. [PERSON] and [PERSON] [6] used the combination of the boundary element method and finite element program to study the dynamic response of LSSs under seismic excitation, including hydrodynamic interaction and verified the accuracy of the results through numerical examples. [PERSON] et al. [7] used ANSYS software to carry out tank wall deformation under horizontal and vertical earthquakes. [PERSON] et al. [8] studied the dynamic response of the storage tank under three-dimensional seismic load. The study shows that the dynamic response of the three-dimensional ground motion to the storage tank is more obvious than that of the one-dimensional ground motion. [PERSON] and [PERSON] [9] found that the tank wall deformation would not occur without considering liquid-solid interaction. [PERSON] andZhou [10] studied the natural vibration characteristics of the model tank with liquid inside by conducting a large-scale seismic simulation test on the unanchored cylindrical steel liquid storage model tank. [PERSON] et al. [11] analyzed the response of an oil storage tank during an earthquake by ADINA. [PERSON] et al. [12] studied the dynamic characteristics of tanks by nonlinear time-history dynamic analysis. [PERSON] et al. [13] compared the dynamic response of the LSS with and without free surface sloshing. [PERSON] et al. [14] analyzed the dynamic response of different CRLSS during an earthquake. [PERSON] et al. [15] studied the dynamic response of rectangular concrete storage tanks during near-field, far-field, and long-period earthquakes using a shaking table test. [PERSON] et al. [16] predicted the sloshing wave height of tanks of different sizes by using the theoretical formula of the simplified mechanical model and the two-way interaction method. [PERSON] et al. [17] found that the effect of different seismic waves on the effective stress of the tank wall is different. [PERSON] et al. [18] used a shaking table to test a low-density polyethylene tank with two different supporting foundation conditions: rigid and flexible. [PERSON] et al. [19] studied the soil-structure group dynamic interaction system by a shaking table test. [PERSON] and [PERSON] [20] found that the effectiveness of isolation systems with different stiffness characteristics depends on the soil type, tank slenderness ratio, and ground motion type. [PERSON] et al. [21] considered the nonlinear effects of tank foundation, soil flexibility, and mooring system. [PERSON] et al. [22] analyzed the influence of various parameters on the seismic response of storage tanks. The above research, based on the finite element method, analyzed the impact of seismic on the dynamic response patterns of LSS. It concluded that under horizontal loads, the wall is more prone to deformation. However, the research did not take into account the influence of foundation failure on the dynamic response patterns.