## 1 Introduction  
Liquid storage tanks form part of the essential infrastructure of our modern society and industries because they hold various fluids, such as water, oil, LNG and others, which are indispensable for human life. If they become damaged due to an earthquake, they can also have negative effects on the environment and bring serious losses to society and industry. Such damage can result in a loss of life in the worst cases. Therefore, the seismic safety of these tanks is very important. However, the experiences of the Alaska earthquake of 1964, the San Fernando earthquake of 1971, the Kobe earthquake of 1995, and the Chi-Chi earthquake of 1999 demonstrated that liquid storage tanks can be damaged heavily by earthquake ground motions [1]. Based on these observations, many studies have sought to reveal the dynamic behaviors of these tanks and to improve their seismic safety. Various studies of the dynamic behaviors of liquid storage tanks induced by earthquakes have been conducted. Simplified theories were proposed by [PERSON] to calculate the hydrodynamic pressure, which is composed of impulsive and convective components, on cylindrical or rectangular water tanks [2, 3, 4]. [PERSON] and [PERSON] conducted a study of the dynamic responses of liquid storage tanks considering the flexibility of the walls and simulated the impulsive and convective modes of vibration of a tank-fluid system [5]. Moreover, [PERSON] et al. presented a means of evaluating the impulsive and convective components of the hydrodynamic pressure in a liquid storage tank [6]. [PERSON] and [PERSON] [7, 8] and [PERSON] and [PERSON] [9] investigated the effects of the flexibility of the tank wall when estimating the behaviors of these types of tanks. [PERSON] undertook theoretical and experimental investigations of the dynamic behaviors of an anchored, ground-supported, cylindrical tank [10]. Based on these pioneering studies, advanced studies have been done with sophisticated approaches to reveal various dynamic characteristics of fluid-structure interaction systems. [PERSON] et al. evaluated the dynamic responses of 2D and 3D rectangular liquid containers using an analytical solution based on the Rayleigh-Ritz method and compared their solution with that from a coupled boundary element/finite element method [11]. Furthermore, the effect of wall flexibility on sloshing was investigated by [PERSON] et al. [11]. [PERSON] and [PERSON] investigated the dynamic response of a concrete rectangular tank, including the effects of vertical acceleration and flexibility of the tank wall [12]. [PERSON] and [PERSON] investigated the dynamic responses of concrete rectangular tanks using a generalized SDOF system [13]. [PERSON] and [PERSON] studied the effects of lateral loading on the nonlinear behavior of liquid storage tanks by means of the FEM [14]. [PERSON] et al. [15] and [PERSON] et al. studied the dynamic behaviors of rectangular tanks using coupled boundary-element and finite-element methods [16]. [PERSON] and [PERSON] presented a quasi-static approach for liquid-filled storage tanks under earthquake excitation using a nonlinear finite element procedure [17]. [PERSON] and [PERSON] investigated the seismic behavior of rectangular tanks on a flexible soil foundation using the FEM [18]. [PERSON] and [PERSON] assessed storage tanks considering of a nonlinear material and the corresponding geometry properties under seismic force using the FEM [19]. [PERSON] et al. studied nonlinear sloshing behavior in 2D containers [20]. Following this work, [PERSON] and [PERSON] investigated nonlinear sloshing inside a partially filled rectangular storage tank [21], and [PERSON] and [PERSON] conducted numerical and experimental studies of the effects of various conditions on sloshing behavior and characteristics, finding that the amplitude of the sloshing depends on the tank geometry, the liquid depth, and the amplitude and frequency of ground motion [22]. [PERSON] and [PERSON] [23] and [PERSON] et al.