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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.

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 [

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 [

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 [

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.

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 [

When the soil is in the inelastic stage, the shear modulus

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 [

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 [

Hertz-damp pounding model.

The pounding occurs on the left:

The pounding occurs on the right:

The pounding occurs on the left:

The pounding occurs on the right:

After two objects collide with each other, the reasonable COR greatly influences the rationality of the model. For most pounding problems of engineering structures, the range of CORs is 0.5–0.75 [

When the sliding base-isolated liquid-storage structure with moat wall (Figure

Sliding base-isolated concrete rectangular liquid-storage structure with moat wall.

It is assumed that the liquid-storage structure may collide with both sides of the moat wall during the action of a horizontal earthquake, and the Hertz-damp model is used to simulate the nonlinear pounding problem. The simplified mechanical model of the sliding base-isolated rectangular liquid-storage structure considering the SSI and pounding is shown in Figure

Simplified model of a sliding isolation rectangular liquid-storage structure that considers the SSI and pounding.

The foundation parameters of the simplified model can be obtained by (

The dynamic equation of the system shown in Figure

As seen from Figure

Inserting (

The liquid sloshing height is a characteristic dynamic response of liquid-storage structures and should be considered in studies of this type of structures; it can be solved by using [

The energy balance equation can be obtained by using (

The earthquake input energy of the system can be obtained by further equivalent conversion of the right side of (

For the sliding base-isolated structure, the earthquake input energy is mainly dissipated by damping, friction, and pounding. The energies

The size of the rectangular liquid-storage structure is 6 m × 6 m × 4.8 m, the liquid height is 3.6 m, the wall thickness is 0.2 m, and the moat wall thickness is 0.2 m. The damping ratio ^{9} N/m. The impact damping

A large number of studies show that a soft soil causes more significant changes to the structural dynamic responses. To study the influence of the foundation effect on the dynamic responses of the sliding base-isolated liquid-storage structure, a soft soil site is assumed to be the foundation based on the Uniform Building Code (UBC2007). The material parameters of this soft soil are shown in Table

Parameters of the foundation.

Soil profile type | Shear wave velocity | Soil density^{3}) | Poisson’s ratio | Modulus of elasticity | Damping ratio |
---|---|---|---|---|---|

Soft soil | 150 | 1900 | 0.30 | 6.12 | 5 |

The near-field pulse-like Chi-Chi earthquake and far-field Imperial Valley-06 earthquake are chosen to conduct time history analyses. The seismic waves are from the PEER strong earthquake observation database (

Seismic waves.

Earthquake | Station | PGA (g) | PGV (cm/s) | PGD (m) | Pulse duration |
---|---|---|---|---|---|

Chi-Chi | TCU036 | 0.13381 | 11.50826 | 0.02336 | 5.341 |

Imperial Valley-06 | Westmorland Fire Sta | 0.07605 | 4.24472 | 0.00838 | — |

Seismic waves.

Chi-Chi

Imperial Valley-06

The initial gap is 0.10 m, the friction coefficient is 0.06, and the other parameters are mentioned previously. To study the influences of the SSI on the dynamic responses of a liquid-storage structure, the structural dynamic responses are calculated with and without the SSI. The liquid sloshing height, structural acceleration

Effect of SSI on structural dynamic responses considering pounding.

Liquid sloshing height

Structural acceleration

Impact force

Structural displacement

As shown in Figure ^{2} and 17.59 m/s^{2}, respectively, and the maximum impact forces are 7.02 × 10^{6} N and 1.70 × 10^{6} N, respectively. From this analysis, we can conclude that near-field pulse-like Chi-Chi earthquake causes more serious damage to a sliding base-isolated structure than far-field Imperial Valley-06 earthquake and that the former will greatly influence the function of the sliding isolation structure.

A remarkable characteristic of sliding isolation is that the friction effect will consume a large amount of energy when the structure moves. In addition, the damping of the system will dissipate a portion of the energy, and the pounding effect can dissipate another portion of the energy when pounding occurs. In addition, in order to validate the motion equations derived from Hamilton’s principle, the input energy of the earthquake and the total dissipated energy considering the SSI effect are shown in Figure

Comparison of input energy and total dissipated energy.

Effects of SSI on energy dissipation.

Friction energy dissipation

Pounding energy dissipation

Damping energy dissipation

As seen from Figure

As seen in Figure

By comparing the corresponding energy responses for the actions of the near-field pulse-like Chi-Chi earthquake and far-field Imperial Valley-06 earthquake, we found that

Pounding dynamic responses corresponding to different gap sizes.

Liquid sloshing height

Structural acceleration

Impact force

As shown in Figure

Friction coefficient

Pounding dynamic responses corresponding to different friction coefficients.

Liquid sloshing height

Structural acceleration

Impact force

As seen in Figure

Slippage is an important characteristic dynamic response of a sliding isolation structure. Although the amount of slippage has little effect on the liquid-storage structure in theory, when taking into account some practical problems, especially liquid-storage structures in the petroleum chemical industry and nuclear industry, once the slippage exceeds a critical limit, the accessory pipelines will be damaged, and liquid may leak out. This result is as serious as failure of the structure itself. If we ignore the problem, the loss of a sliding isolation structure will outweigh the gain. To have a more comprehensive understanding of the slippage of the sliding isolation structure, the correlation effect of the friction coefficient and initial gap on the maximum horizontal displacement of a liquid-storage structure is studied considering the SSI. The calculated results are shown in Figure

Correlation effects of the friction coefficient and initial gap on the maximum horizontal displacement of the structure.

Chi-Chi earthquake

Imperial Valley-06 earthquake

As seen in Figure

Based on the calculated results of Figure

The SSI and the pounding possibility between a sliding isolation liquid-storage structure and its moat wall are considered in this paper. A simplified mechanical model of the sliding base-isolated liquid-storage structure is established, and the pounding dynamic responses of the system under the action near-field Chi-Chi earthquake and far-field Imperial Valley-06 earthquake are studied. The effects of the SSI, initial gap, and friction coefficient on the dynamic responses of a liquid-storage structure are discussed. The main conclusions are as follows:

The liquid sloshing height of a sliding isolation liquid-storage structure increases when the SSI is considered because the SSI increases the period of the isolation structure and the difference between the isolation period and liquid sloshing period becomes small. When the liquid-storage structure collides with the moat wall, the structural dynamic responses due to a pulse phenomenon will appear, but the structural acceleration and impact force are reduced because of the buffer effect of the foundation.

The friction energy dissipation and pounding energy dissipation of the system are reduced when the SSI is considered. The friction energy dissipation and damping energy dissipation gradually increase as the time increases, whereas the pounding energy dissipation is only affected by each pounding and shows a ladder-type growth phenomenon as the time increases. The friction energy dissipation, pounding energy dissipation, and damping energy dissipation for near-field pulse-like Chi-Chi earthquake are far greater than far-field Imperial Valley-06 earthquake. To ensure that the structure continues to work properly under some strong earthquakes, the near-field pulse-like Chi-Chi earthquake affects the design process more for each part of the structure.

After considering the SSI, the dynamic responses of a sliding isolation liquid-storage structure with different initial gaps for near-field Chi-Chi earthquake are generally larger than far-field Imperial Valley-06 earthquake.

Increasing the friction coefficient can reduce the pounding dynamic responses of the structure to a certain extent. However, when the friction coefficient is large, this type of isolation structure will not slide, so it will lose the designed shock absorption during some earthquakes. Therefore, the selection of the friction coefficient of a sliding isolation structure should be considered comprehensively and an intermediate value for the friction coefficient is ideal.

When the friction coefficient is small, the initial gap greatly affects the slippage of a sliding isolation liquid-storage structure. When the initial gap is large, the friction coefficient greatly affects the slippage of the sliding isolation liquid-storage structure.

The authors declare that there is no conflict of interests regarding the publication of this paper.

This paper is supported in part by the National Natural Science Foundation of China (Grant nos. 51368039 and 51478212), the Education Ministry Doctoral Tutor Foundation of China (Grant no. 20136201110003), and the Plan Project of Science and Technology in Gansu Province (Grant no. 144GKCA032).