## 1 Introduction  
Liquefied natural gas (LNG), renowned for its ability to only cause low levels of pollution, as well as its cleanliness, safety, and efficiency, stands as a widely embraced energy source across the globe [1]. Among the prevalent categories of large LNG storage tanks are aboveground vertical tanks, semi-buried tanks, and fully buried underground tanks [1]. Due to their comparatively thin walls, aboveground tanks are susceptible to damage during seismic events. Earthquakes not only jeopardize the costly tank structure but also amplify the severity of secondary disasters such as fires and environmental contamination stemming from LNG leakage. The vulnerabilities of vertical tanks during past seismic incidents have resulted in instances of bottom uplift, wall buckling, liquid spillage, dome rupture, pipeline failure, and foundational damage [2, 3]. In contrast, fully buried underground tanks, lauded for their robust seismic resistance and enhanced safety, have found extensive applications in nations like Japan and South Korea. The research on liquid storage tanks encompasses seismic damage surveys, theoretical explorations, numerical simulation studies, and experimental investigations [4]. In the 1930s, seismic studies on vertical storage tanks, primarily those rigidly anchored to the base, commenced. Acknowledging the complexity of this issue and the technological constraints of the era, [PERSON] developed a classic theoretical model [5] based on previous research. [PERSON] assumed that the tank's internal liquid was an ideal, incompressible, and non-viscous fluid, while the tank walls were regarded as rigid. The seismic impact of the liquid on the rigid walls was simulated using a mass-spring system to represent the impulsive and convective pressures induced by earthquakes. [PERSON] [6] further simplified the tank as a cantilever beam structure with one end fixed, calculating elastic tank pulse pressures under horizontal seismic forces using the assumed mode method. [PERSON] [7] integrated the theories of [PERSON] and [PERSON], formulating the three-mass-point flexible wall model (Haroun-Housner model), incorporating the convective and pulsating pressures of the liquid. In 2000, [PERSON] et al. [8] proposed practical theoretical calculations for tanks with flexible steel or concrete walls. [PERSON] [9] and [PERSON] et al. [10], who considered the foundation soil to be a system of translational and rotational spring-damping elements, established a simplified equivalent mechanical model to study whether the seismic response of tank structures was influenced by the elastic properties of the foundation soil. However, these methods either neglected the role of the foundation soil or oversimplified it as a spring-damping element, leading to imprecise results. Through the proliferation and optimization of numerical methods such as finite element analysis and finite difference methods, scholars have effectively employed numerical software (e.g., Abaqus, Ansys, etc.) to simulate the combined effects of fluid-structure-soil systems. Currently, the most prevalent multi-material fluid-solid coupling algorithms include the Euler method, the [PERSON] method, the Arbitrary Lagrangian-Eulerian (ALE) method, the Volume of Fluid (VOF) method, and the Coupled Eulerian-Lagrangian (CEL) method. [PERSON] [11] extensively investigated the oscillations of liquid within tanks under seismic loads. The study of the free and forced oscillations of an elastically rotating shell partially filled with an ideal incompressible fluid has also been explored. [PERSON] [12] utilized Ansys to analyze the response patterns of steel tanks containing nanocomposite materials under seismic conditions. [PERSON] et al. [1] compared the displacements and stresses of aboveground water tanks and underground tanks under seismic loads, revealing that underground tanks have fewer displacements and stresses, indicating their relative safety.