Shock and Vibration

Volume 2017 (2017), Article ID 8594051, 14 pages

https://doi.org/10.1155/2017/8594051

## Pounding Dynamic Responses of Sliding Base-Isolated Rectangular Liquid-Storage Structure considering Soil-Structure Interactions

^{1}Key Laboratory of Disaster Prevention and Mitigation in Civil Engineering of Gansu Province, Lanzhou University of Technology, Lanzhou 730050, China^{2}Western Engineering Research Center of Disaster Mitigation in Civil Engineering of Ministry of Education, Lanzhou University of Technology, Lanzhou 730050, China

Correspondence should be addressed to Xuansheng Cheng and Wei Jing

Received 18 August 2016; Revised 19 December 2016; Accepted 4 January 2017; Published 31 January 2017

Academic Editor: Ivo Caliò

Copyright © 2017 Xuansheng Cheng et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

The soil-structure interaction (SSI) is simulated by an artificial boundary, the pounding that occurs between the sliding base-isolated rectangular liquid-storage structure (LSS) and the surrounding moat wall is considered, the instantaneous pounding is simulated using the Hertz-damp model, and a simplified mechanical model with two particles and four degrees of freedom is established. Dynamic equation is obtained using Hamilton principle; effects of SSI, initial gap, and friction coefficient on the pounding responses under the action of near-field pulse-like Chi-Chi earthquake and far-field Imperial Valley-06 earthquake are studied. The results show that SSI will amplify liquid sloshing height but that structural acceleration and impact force will be reduced because of SSI. The responses caused by Chi-Chi earthquake are far greater than those of Imperial Valley-06 earthquake. Initial gap has a small effect on liquid sloshing height; structural acceleration and impact force first increase as the initial gap increases and then begin to decrease; in the design of moat wall of sliding isolation LSS, a certain gap exists that will more adversely affect the pounding responses of structure. Liquid sloshing height is less affected by coefficient of friction, but structural acceleration and impact force decrease as friction coefficient increases in general.

#### 1. Introduction

In lifeline engineering, liquid-storage structures play irreplaceable roles in the development of a national economy, but many earthquakes have caused different degrees of damage to the liquid-storage structures. Because of the uniqueness of this type of structure, failure causes some types of disaster, such as a fluid leakage, fire, or environment pollution. An effective means to improve the seismic capacity for this structure is a special base isolation structure that has been used widely. One of the main shock absorption measures is rubber isolation, which can reduce dynamic responses, such as base shear, overturning moment, and wall internal force, of the liquid-storage structure, but its effect on liquid sloshing is very limited and may even produce the opposite effect [1–4]. However, some new types of sliding isolation methods can achieve independence of the isolation period and liquid sloshing period [5] and avoid the resonance phenomenon, which can reduce both the structural dynamic responses and liquid sloshing simultaneously [6, 7]. Therefore, if this design is reasonable, the effect of this sliding base-isolated technology will be better than rubber base isolation [8, 9].

Although the sliding isolation measure can effectively reduce the structure dynamic responses, one characteristic of a sliding isolation structure is that it will suffer a large horizontal displacement during an earthquake. For normal use and structural safety, it is very necessary to use a corresponding limiting displacement method. At present, a common method, the moat wall, is widely used in various types of base-isolated structures. Although the moat wall can control the base-isolated structure displacement [10], the pounding between the isolation structure and moat wall greatly affects the system dynamic responses. In recent years, some scholars have paid attention to the pounding problem of the base-isolated structure caused by an earthquake and have achieved certain results. Nagarajaiah and Sun [11] assessed the dynamic responses of a base-isolated structure used for a fire control command, which was destroyed because of structure and moat wall pounding during the 1994 Northridge earthquake. The results showed that the pounding increased the base-isolated structure dynamic responses. Matsagar and Jangid [12] assumed that pounding occurred only between the bottom of the structure and the moat wall and studied the pounding dynamic responses of a building with various isolation systems. Komodromos [13] concluded that the dynamic responses caused by pounding increased as the impact stiffness and isolation system stiffness increased based on numerical simulations. Fu et al. [14] determined that the dynamic responses caused by pounding could change the basic mode of the base-isolated structure and excite a higher mode of the structure. Masroor and Mosqueda [15] considered the moat wall flexibility in a pounding model of an isolated structure and found that the moat wall characteristics greatly influenced the amplification of the dynamic response and degree of damage. Pant and Wijeyewickrema [16] considered different earthquake excitations and found that the pounding effect had a significant effect on the performance of an isolated structure. Fan et al. [17] studied the vulnerability of an isolation structure with a moat wall and determined that the structure mass and mechanical parameters of an isolation bearing had a greater effect on the maximum base displacement. Khatiwada and Chouw [18] noted that the impact stiffness and coefficient of restitution were the main factors influencing the pounding responses.

The foundation effect is not considered in the above studies when the base-isolated structure collides with the moat wall, but the SSI has a significant effect on the vibrational frequency [19], the system damping ratio and rotational displacement of the foundation [20], the structural dynamic responses [21], and the reasonable choice of the isolation bearing [22] of an isolation structure. Currently, studies of the SSI on the pounding dynamic responses of a structure are very limited [23]. Chau et al. [24] noted that the vibrational response of the structure could be amplified but that the SSI could suppress the vibrational response caused by pounding. Mahmoud and Gutub [25] found that the SSI effect had a more significant effect on isolated buildings located on a soft soil, and the SSI effect could increase the number of collisions between the structure and surrounding moat wall. Shakya and Wijeyewickrema [26] used the gap element and Kelvin-Voigt model to simulate the pounding problem and found that the dynamic responses of the structure will be reduced when the foundation is considered.

In summary, the effect of the SSI on the structural dynamic responses is obvious. Although the probability of pounding of the sliding base-isolated structure with the moat wall is larger than the rubber isolation, studies on the dynamic responses of a sliding isolation structure that consider the SSI have not been performed. The spring-mass model is used to simulate the coupling problem of the sliding base-isolated liquid-storage structure, and the 2D viscoelastic artificial boundary is used to simulate the foundation effect. A simplified mechanical model and the corresponding dynamic equations of the sliding isolation rectangular liquid-storage structure that consider the SSI and pounding are established, and the dynamic responses of the rectangular liquid-storage structure experiencing near-field pulse-like Chi-Chi earthquake and far-field Imperial Valley-06 earthquake are studied. Sliding isolation has a certain advantage in the shock absorption of a liquid-storage structure, and theoretical research on this type of damping method is helpful to its future application.

#### 2. Calculation Model

##### 2.1. Foundation Model

To consider the foundation effect, the lumped parameter model is used to simulate the elastic foundation and the discrete model, which is based on the theory of a homogeneous, isotropic, and elastic half space. Translation and rotation of the foundation are simulated using the spring element and damping element, respectively, and the corresponding parameters can be calculated by using the following equations [27]:where is Poisson’s ratio; is the shear modulus; and and are the constants to correct the translation and rotation of the spring, respectively. and have strong relationships with the foundation length-width ratio, and according to the existing literature [27], the approximate values of and are equal to 1, and are the foundation length and width, respectively, and and are parallel and perpendicular to the direction of earthquake, respectively. is soil density, and and are equivalent radii of the foundation that correspond to translation and rotation, respectively. The maximum shear modulus is only suitable when the soil is in the low strain condition, and it can be expressed as a function of the shear wave velocity and soil density

When the soil is in the inelastic stage, the shear modulus is significantly reduced. The shear modulus will be changed when the shear strain is beyond the range of the elastic state because of a dynamic effect. To realistically simulate the ground effect, the shear modulus needs to be reduced by introducing the shear modulus reduction curve () [27], and the shear strain can be expressed aswhere is the horizontal shear force and is the overturning moment.

##### 2.2. Pounding Calculation Model

Sliding base-isolated liquid-storage structures will suffer large amounts of slippage under the action of some strong earthquakes. Thus, the pounding dynamic responses caused by pounding between the liquid-storage structure and moat wall are important subjects to study. The contact element method is an effective technique to simulate pounding problems; common pounding models include the linear model, Kelvin model, Hertz model, and Hertz-damp model [24, 28–31]. Muthumar and Desroches [29] concluded that, for the same parameters, the differences in the displacements and acceleration calculated by the different models are within 12%. Chau et al. [24] and Jankowski [31] systematically compared the numerical and experimental results of the pounding models for different materials and showed that both the linear and nonlinear pounding models could satisfy the precision requirements for engineering.

Previous experimental studies have shown that the energy loss during the pounding process is mainly concentrated when the two objects are approaching each other but is relatively small during the recovery phase [32]. The modified Hertz model (Hertz-damp model), which is composed of nonlinear springs and a nonlinear damping element (Figure 1), is chosen to simulate the pounding. The model does not consider the energy loss in the pounding recovery phase and assumes that all of the energy loss caused by pounding occurs as the two objects approach each other [31]. The contact forces during the pounding and recovery phases can be expressed as (4) and (5), respectively.