Shock and Vibration
Volume 2018 (2018), Article ID 2074946, 19 pages
https://doi.org/10.1155/2018/2074946

Research Article

Dynamic Response of a 100,000 m³ Cylindrical Oil-Storage Tank under Seismic Excitations: Experimental Tests and Numerical Simulations

Honghao Li, Wei Zhao, and Wei Wang

Key Lab of Structures Dynamic Behavior and Control of the Ministry of Education, Key Lab of Smart Prevention and Mitigation of Civil Engineering Disasters of the Ministry of Industry and Information Technology, School of Civil Engineering, Harbin Institute of Technology, Harbin 150090, China

Correspondence should be addressed to Honghao Li; lihonghao@hit.edu.cn

Received 4 February 2018; Revised 7 June 2018; Accepted 10 July 2018; Published 10 September 2018

Academic Editor: Roberto Palma

Copyright © 2018 Honghao Li 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.

Considering the disastrous consequences of the oil tank failure, it is of great importance to ensure the safety of the large-scale oil tank under earthquakes. This study sheds light on investigating the dynamic response of a prototype 100,000 m³ cylindrical oil-storage tank under various seismic excitations. The foundation of the tank is also considered in this study so that the obtained results are closer to the reality. Shaking table tests are conducted using a 1/20 scale liquid-tank-foundation system under various seismic excitations. The test results reveal that the dynamic responses such as accelerations and the deformation of the test specimen in the major and minor vibration directions do not differ significantly. Finite element models are constructed for the test specimen and the prototype tank and are validated through comparing the simulation results with the test data. The simulation results suggest that it might be necessary to stiffen the locations on the tank wall where the thickness of the tank wall changes because the stresses at such locations may be close or even exceed the yield strength of the structural steel under severe earthquakes.

1. Introduction

To investigate the seismic response of large-scale liquid storage tanks containing flammable and combustible liquid such as oil is of great importance because damages of such infrastructures under earthquakes can cause large fires, explosion, environmental pollution, and other secondary catastrophes, which may induce huge economic damage and extensive loss of human lives. Although earthquakes have been considered in the design guidelines on liquid storage tanks, damages of liquid/oil-storage tanks were reported in a number of major earthquakes, such as the 1964 Alaska earthquake in the USA (Mw = 9.2), 1978 Miyagi earthquake in Japan (Ms = 7.7), 1999 Kocaeli earthquake in Turkey (Mw = 7.7), 2003 Tokachi-Oki earthquake in Japan (Mw = 8.0), 2008 Wenchuan earthquake in China (Mw = 7.9), and 2011 Tohoku earthquake and the tsunami in Japan (Mw = 9.0). These accidents have highlighted the seriousness of such events, motivated the research in seismic responses of liquid storage tanks, and thus improved the design codes and guidelines of liquid storage tanks against earthquakes.

Research on seismic responses of elevated oil storage started from 1930s, and this topic has drawn a lot of research interest since then. Generally speaking, research in this field typically falls into three categories: (1) theoretical computational models, (2) numerical simulations, and (3) experimental tests. One of the earliest simplified models for investigating the dynamic response of a liquid storage tank was the mass-spring model proposed by Housner [1]. The model considered the tank walls as rigid. The model was then modified to account for the impact of the flexible tank walls on the seismic responses of liquid storage tanks in further studies, such as Velestsos [2], Velestsos and Yang [3], Haroun and Housner [4], and Malhotra et al. [5]. The models mentioned above have been implemented by the seismic design codes and guidelines on liquid storage tanks worldwide, such as API 650 [6] and Eurocode 8 [7]. In recent years, the rapid development of computer technology and availability of powerful software allow numerical simulation become an important technique to investigate seismic behavior of liquid storage tanks in a more sophisticated manner, such as Cho and Lee [8], Virella et al. [9], Livaoglu [10], Liu and Lin [11], Attati and Rofooei [12], Firouz-Abadi et al. [13], Ozdemir et al. [14], Korkmaz et al. [15], Moslemi and Kianoush [16], Matsui and Nagaya [17], and Buratti and Tavano [18]. The shaking table test is the main tool to investigate the dynamic responses of liquid storage tanks under earthquake excitations experimentally. Early examples of such tests could be found in Shih [19], Niwa and Clough [20], Haroun [21], Chiba et al. [22], and Sakai et al. [23]. In more recent years, shaking table tests which were conducted to investigate seismic responses of the liquid storage tanks include Tanaka et al. [24], Pal et al. [25], Nishi et al. [26], De Angelis et al. [27], Maekawa et al. [28], Fang et al. [29], Goudarzi et al. [30], Pal and Bhattacharyya [31], Eswaran et al. [32], Ormeño et al. [33], and Park et al. [34].

Among the mentioned literature, the studies on the seismic behavior of large-scale unanchored liquid storage tanks are rare. In most, if not all, of these shaking table tests mentioned above, only one horizontal component of the ground motion was considered. Furthermore, there is no experimental test considering the seismic response of a coupled liquid-tank-foundation system when all three components (two horizontal and one vertical) of the ground motion are considered. The goal of this study is to address these gaps. The purposes of this study include (1) to investigate the dynamic responses of a large-scale cylindrical unanchored oil-storage tank subjected to earthquake excitations, (2) to examine whether the original design of the tank can sustain major earthquakes and thus to access the seismic vulnerability of such tanks and promote the development of the design code for oil-storage tanks against earthquakes, and (3) to provide experimental data for the validation of numerical models. This study sheds light on the seismic behavior of a 100,000 m³ liquid storage tank considering liquid sloshing and tank-foundation interaction (uplifting). In this study, shaking table tests of a 1/20 scale liquid tank model were firstly conducted under the excitations of various input waves. Then finite element models for the test specimen were created using commercial FEA software ANSYS and validated against experimental data. After showing that the model can represent the dynamic behavior of the test specimen under earthquakes reasonably, similar modeling approaches were used to develop numerical models for a prototype 100,000 m³ oil-storage tank and the dynamic responses of the prototype tank under strong earthquakes were investigated numerically.

2. Shaking Table Tests

2.1. Test Specimen

A 100,000 m³ unanchored cylindrical oil-storage tank which is commonly used in China equipped with a metallic floating roof is selected herein as the prototype structure to investigate its dynamic response under earthquake excitations. The prototype tank was originally designed by Sinopec Engineering incorporation on the basis of Chinese Code for Design of Vertical Cylindrical Welded Steel Oil Tanks (GB 50341-2014). As shown in Figure 1(a), the outer diameter of the prototype tank is 80 m, the diameter of the floating roof is 79.5 m, and the height of the tank is 21.8 m. The filling level of the oil contained by the tank is 18.5 m. The tank wall is comprised of 9 steel shells with different thicknesses ranging from 32 mm to 12 mm, as shown in Figure 1(c). The structural steel used for shell 1 to 7 is SPV490Q ( = 490 MPa), and shells 8 and 9 are fabricated using Q235A ( = 235 MPa). The bottom plate of the tank is also made of structural steel SPV490Q, and the thickness is 20 mm. The tank is placed on a reinforced concrete ringwall (Figures 1(a) and 1(b)). The height and the thickness of the RC ringwall are 2.5 m and 0.8 m, respectively. The ringwall is filled with compacted soil, which acts as the foundation of the tank.

(a)

(b)

(c)

Figure 1: Sketch of the prototype tank. (a) Elevation view. (b) Aerial view. (c) Shell thickness.

Due to the limitation of the shaking table dimension, a reduced scale model with a scaling factor of 1/20 has been designed and fabricated (Figure 2), and the model is a coupled liquid-tank-foundation system. The outer diameter of the test specimen is 4 m, the diameter of the floating roof is 3.975 m, and the height of the test specimen is 1.1 m. The wall of the test specimen was fabricated using structural steel Q235A. Since the thickness of the tank wall and the bottom plate cannot be too small considering the stability issue, the geometrical scaling factor cannot be achieved when designing the wall and bottom plates of the test specimen. Considering the difficulties in fabricating the wall of the test specimen with varied thickness, the wall of the test specimen is set to be 3 mm according to API 650 [6]. The thickness of the bottom plate is 2 mm, which is fabricated using the same structural steel as the tank wall. The bottom plate rests on a reinforced concrete ringwall. The diameter, thickness, and height of the ringwall are 4 m, 150 mm, and 450 mm, respectively. The ringwall is filled with sand. Thus, the foundation of the tank was simulated. The floating roof of the test specimen was made of blockboard with the thickness of 17 mm. In order to simulate the connection between the floating roof and the tank wall, a rubber tube was placed surrounding the blockboard. The test specimen was filled with water with a fill level of 0.88 m. The weight of the liquid is 11t, and the total weight of the tank and floating roof is 650 kg.

(a)

(b)

Figure 2: Test specimen. (a) Overview of the coordinate system. (b) Plan view of the coordinate system.

The scaling factor of the test specimen was selected considering the limitations of the behavior parameters of the shaking table and other specifications of the experimental facilities. Although some insights into the behavior of the test specimen subjected to earthquake excitations can be gained through the shaking table test, the key purpose of the test is to provide experimental data for the validation of finite element models which can be used to investigate the response of the 100,000 m³ cylindrical oil-storage tank, which is planned to be used in China in the near future, under major earthquakes through numerical simulations; thus, the effectiveness of the design method against severe seismic loads which is currently implemented can be assessed. The test results were not directly used to predict whether the prototype tank can survive mega earthquakes. On the other hand, this study only focuses on linear elastic behavior of both the test specimen and the prototype tank. Therefore, the geometric scale factor was set to be 1/20, and the remaining scale factors, including scale factors for density, elastic modulus, time, frequency, acceleration, stress, and strain, were all set to be 1.

2.2. Instrumentation

A virtual coordinate system was defined as shown in Figure 2(a) for convenience. X and Y directions in this coordinate system are the directions of two horizontal components of the ground motion produced by the shaking table, and the Z axis represents the vertical direction. As shown in Figure 2(b), the intersections between the X-Z plane and the tank wall are lines A-A’ and C-C’ (Figure 3). The intersections between the Y-Z plane and the tank wall are lines B-B’ and D-D’. Points A, B, C, and D are located at the top of the tank, and points A’, B’, C’, and D’ are at the bottom of the tank.

(a)

(b)

(c)

Figure 3: Location of measuring instruments. (a) Locations of accelerometers. (b) Locations of string potentiometers. (c) Locations of strain gauges.

Quantities of interest in the response include displacements and accelerations, strains of the tank wall, and water free-surface elevations. These quantities are measured at different locations. The time history of horizontal accelerations at various locations along line A-A’ and line B-B’ on the tank wall was recorded using 8 accelerometers (A-1 to A-4 and A-6 to A-9), as shown in Figure 3(a). The vertical accelerations of points A’ and B’ were measured by two accelerometers (A-5 and A-10). Three accelerometers were placed on the shaking table to record the time histories of the input waves in X, Y, and Z directions, respectively. As shown in Figure 3(b), 10 string potentiometers were used to measure the displacement at various locations of the test specimen, eight of which (D-1 to D-4 and D-6 to D-9) were attached to the tank wall at the same locations with the accelerometers to measure the horizontal displacement of these points. Another two string potentiometers (D-5 and D-10) were used to record the horizontal displacement of the foundation, and thus the deformed profiles of the tank wall could be estimated based on the relative displacement between the tank wall and the foundation. Figure 3(c) shows the strain gauges which were attached to the tank wall and the foundation to measure the time history of the strains at these locations. The strain gauges attached to the tank wall were designated as SW-X, where X represents the number of the strain gauge. The elevations of the water free-surface were measured using displacement sensors.

2.3. Test Setup

The dynamic responses of the test specimen subjected to a series of seismic excitations were tested on the shaking table of the Institute of Engineering Mechanics, China Earthquake Administration. The shaking table is capable of producing six components of motions, including three translations in three directions and three rotations. The earthquake simulator can reproduce a variety of earthquake ground motions within the capacity of the system. The performance parameters of the shaking table are summarized in Table 1.

Table 1: Performance parameters of the shaking table.

Size (m)
5 × 5

Peak horizontal acceleration (g, 9.8 m/s²)
1

Peak vertical acceleration (g, 9.8 m/s²)
0.8

Peak horizontal velocity (cm/s)
60

Peak vertical velocity (cm/s)
60

Peak horizontal displacement (m)
±8

Peak vertical displacement (m)
±5

Maximum gravity payload (t)
30

Maximum overturning moment (kN·m)
750

Frequency bandwidth (Hz)
0.4–40

Two series of input seismic waves were used in these tests, which are obtained by modifying the ground acceleration records of the 1940 El-Centro earthquake (El-Centro wave), which is designated as input wave series 1, and the 2008 Sichuan earthquake (Wolong wave), which is designated as input wave series 2. The ground motion records of these two earthquakes are selected as the input waves because (1) El-Centro earthquake ground motion records were used widely when conducting time history analysis of civil structures and infrastructures, both numerically and experimentally since the response spectrum for El-Centro ground motion is quite close with the standard design spectrum, and (2) the 2008 Sichuan earthquake is the most devastating earthquake that struck China in the past decade. Therefore, it is meaningful to explore the dynamic responses of the test specimen under these two earthquakes.

Figures 4 and 5 illustrate the modified acceleration time histories of the El-Centro earthquake and Sichuan earthquake, which were obtained according to the following equation:

in which represents the modified ground acceleration time history, represents the original ground acceleration time history, and represents the peak ground acceleration of the original ground motion. Therefore, the peak accelerations of the modified ground motion in all three directions were equal to 1.0 g (9.8 m/s²). Then input waves 1-1, 1-2, and 1-3 were obtained by scaling the modified ground acceleration histories of input wave series 1, as shown in Figures 4(a)–4(c). Input waves 2-1, 2-2, 2-3, and 2-4 were obtained by scaling the modified ground acceleration histories of input wave series 2, as shown in Figures 5(a)–5(c). The peak ground accelerations in three directions of all the input waves were tabulated in Table 2. The values of the ground peak accelerations were calculated according to the seismic precautionary intensities (PI) required by the Chinese Code for Design of Buildings (GB 5011-2010), as shown in Table 2, in which seismic PI 6 represents the lowest seismic risk, in which seismic effects are usually not considered, PI 7 represents low seismic risk, PI 8 represents moderate seismic risk, and PI 9 represents high seismic risk. Input waves 2-3 and 2-4 have a PI of 10 or above. Such seismic precautionary intensities are too high to be considered in the design of common civil structures according to GB 5011-2010, which represents mega earthquakes.

(a)

(b)

(c)

(d)

Figure 4: Acceleration time history and power spectrum of the El-Centro wave. (a) X direction. (b) Y direction. (c) Z direction. (d) Power spectrum in the Y direction.

(a)

(b)

(c)

(d)

Figure 5: Acceleration time history and power spectrum of the Wolong wave (2008 Sichuan earthquake). (a) X direction. (b) Y direction. (c) Z direction. (d) Power spectrum in the Y direction.

Table 2: Peak accelerations of input waves in X, Y, and Z directions.

Input wave
Peak accelerations (g)
Seismic precautionary intensity

X
Y
Z

1-1
0.034
0.145
0.014
6

1-2
0.096
0.173
0.026
7

1-3
0.123
0.306
0.075
8

2-1
0.130
0.304
0.161
8

2-2
0.137
0.444
0.138
9

2-3
0.290
0.504
0.298
10 or above

2-4
0.324
0.653
0.439
10 or above

The purpose of using input waves with different peak accelerations which are modified on the basis of the same seismic record is to investigate the behavior of the tank under different seismic intensities as well as the impact of the amount of the energy input to the system on the dynamic behavior of the test specimen.

The power spectrums of the modified ground motions are shown in Figures 4(d) and 5(d), in which the spectral characteristics of these two earthquakes can be explored. According to these two figures, the predominant frequency of the El-Centro earthquake is around 1.5 Hz. However, the Sichuan earthquake has two predominate frequencies: one is around 9 Hz and the other is around 24 Hz.

The dynamic responses of the test specimen were actually evaluated under a number of other seismic records too. However, only the test results under the seismic excitations of these input waves were presented herein due to space limitation.

3. Experimental Results

Dynamic responses of the test specimen, including acceleration time histories and peak accelerations at various locations, the envelope curve of the tank wall deformation, and the elevations of the water free-surface subjected to the series of the input waves were obtained, and the test results are analyzed herein.

3.1. Dynamic Characteristics

The test specimen was firstly subjected to the excitations of white noise to investigate the dynamic characteristics of the test specimen. The natural frequency (1st order) of the test specimen was 14.51 Hz, and the damping ratio was 8.4% according to the Fourier amplitude spectrum of acceleration based on the test results.

3.2. Responses under Input Wave Series 1

The peak accelerations obtained by the accelerometers in the X direction (A-6 to A-9) and Y direction (A-1 to A-4) are shown in Figure 6. It is worthwhile to mention that the test specimen is an unanchored liquid storage tank, which means the tank is placed on the foundation without any anchors; therefore, the peak accelerations recorded by the accelerometers installed at the bottom of the tank (A-4 and A-9) were not equal to the peak ground accelerations of the input waves. Based on the data, the distribution of the peak accelerations at various positions on the tank wall along line A-A’ and B-B’ can be estimated and is also shown in Figure 6. In Figure 6, the dimensional quantity β represents the ratio of the height of the considered spot on the tank wall and the total height of the tank. It can be seen that as the input energy increases, the peak acceleration of a certain point on the tank wall also increases. The largest peak acceleration was typically observed at the top of the test specimen, except the peak acceleration in the X direction under input wave 1-1. The values of the peak accelerations obtained in X and Y directions were fairly close to each other, despite of the difference in the values of the peak accelerations of the two horizontal components of the input wave. Therefore, when designing the oil tank against earthquakes laterally, it is necessary to consider the ground vibrations in both directions. The transmissibility (TR), which is the ratio of the peak acceleration of the tank wall to the peak ground acceleration of the input wave (PGA), is used to represent the amount of magnification on PGA herein. The relationships between the values of TR and the height of the considered spot on the tank wall are shown in Figure 7. It can be seen that in the majority of the cases, the maximum transmissibility is between 2.0 and 2.5, which is coincident with the requirement of Appendix D of GB 50341-2014. The magnification effects in the X direction are more evident than the one in the Y direction. In the Y direction, the largest transmissibility is around 2.0 when the test specimen is subjected to input wave series 1, and in the X direction, the number increased to 8.0. An interesting observation from Figure 7 is that the smaller the peak acceleration of the input wave is, the larger the transmissibility is. The peak vertical accelerations obtained by the accelerometers at points A’ and B’ are shown in Figure 8. The transmissibility for the vertical component of the ground motion at these two points under input waves 1-1, 1-2, and 1-3 are 11.07, 11.04, and 4.139, respectively, which is considerably large. The magnification effect of the vertical seismic component considered in GB 50341-2014 is much smaller than what was observed in this test.

(a)

(b)

Figure 6: Peak acceleration in X and Y directions along the tank wall: input wave series 1. (a) X direction: A-A’. (b) Y direction: B-B’.

(a)

(b)

Figure 7: Transmissibility in X and Y directions: input wave series 1. (a) X direction: A-A’. (b) Y direction: B-B’.

Figure 8: Peak acceleration in the Z direction at points A’ and B’: input wave series 1.

The envelope curve of the tank wall deformation of the test specimen could be obtained on the basis of the readings of the string potentiometers. Figure 9 shows the maximum displacements in positive and negative directions at various locations on the tank wall recorded by the string potentiometers in both X and Y directions relative to the displacement of the foundation under input wave series 1. For unanchored tanks, slippage may occur between the tank and the foundation during earthquakes. Therefore, the displacement at the bottom of the tank wall relative to the foundation is not zero. The negative sign means the deformation is in the negative direction of the coordinate axis. In these figures, the area confined by the two curves represented the range of the deformation of the tank wall under seismic excitations. The deformation of the tank wall under these seismic excitations was very small, which was under 0.1% of the diameter and 0.3% of the height of the test specimen, even when seismic precautionary intensity of 9 was considered. Figure 9 shows that the deformation of the tank wall increases with the increase in the peak acceleration of the input wave. On the other hand, the deformation of the tank wall in the X direction was larger than that in the Y direction, indicating that the damage of the tank in the direction with smaller PGA is more severe than the direction with larger PGA.

(a)

(b)

(c)

(d)

(e)

(f)

Figure 9: The envelop curve of the tank wall deformation of the test specimen: input wave series 1. (a) Input wave 1-1: A-A’. (b) Input wave 1-1: B-B’. (c) Input wave 1-2: A-A’. (d) Input wave 1-2: B-B’. (e) Input wave 1-3: A-A’. (f) Input wave 1-3: B-B’.

The maximum strain on the tank wall when the test specimen was subjected to seismic excitations 1-1, 1-2, and 1-3 were around 800 με, 1000 με, and 1100 με, respectively. The maximum strain was recorded by strain gauge SW-2, which is located near the floating roof, in all these three cases. The numbers were well below the yield strain of the structural steel, which is around 2000 με. The strains obtained by the other strain gauges were much smaller. As the peak acceleration of the input waves increases, the strain gauge readings increase as well, indicating that the internal forces of the tank wall increase with the energy input of the seismic excitations. The strains recorded by the strain gauges attached to the foundation were negligibly small in all these three cases, indicating that the foundation was not affected significantly by the given seismic excitations.

The time histories of the sloshing motion of the liquid are shown in Figure 10. The most severe liquid sloshing was observed when the test specimen was subjected to input wave 1-2. The range of the liquid sloshing was around 350 mm, and the highest water level reached the top of the tank.

(a)

(b)

(c)

Figure 10: Time histories of liquid sloshing motion: input wave series 1. (a) Input wave 1-1. (b) Input wave 1-2. (c) Input wave 1-3.

3.3. Response under Input Wave Series 2

The distributions of the peak acceleration and transmissibility along the tank wall at line A-A’ in the X direction and at line B-B’ in the Y direction are shown in Figures 11 and 12. The maximum peak acceleration and the maximum transmissibility were found at the top of the tank except the case in which both of them in the Y direction were observed at the bottom of the tank under input wave 2-4. The values of the peak acceleration and the transmissibility increased with the increase in seismic precautionary intensity. Similar to the cases when the test specimen was subjected to input wave series 1, the maximum accelerations in X and Y directions were fairly close and the magnification effects in the X direction were much more significant than in the Y direction. The peak vertical accelerations obtained are shown in Figure 13. The peak vertical acceleration reached nearly 2.5 g at point B’, which is 5.7 times of the corresponding PGA of the vertical component of the input wave, indicating that the vertical component of the input wave played a significant role in determining the dynamic response of the test specimen.

(a)

(b)

Figure 11: Peak acceleration in X and Y directions along the tank wall: input wave series 2. (a) X direction: A-A’. (b) Y direction: B-B’.

(a)

(b)

Figure 12: Transmissibility in X and Y directions: input wave series 2. (a) X direction: A-A’. (b) Y direction: B-B’.

Figure 13: Peak acceleration in the Z direction at points A’ and B’: input wave series 2.

The envelope of the tank wall deformation along lines A-A’ and B-B’ subjected to seismic wave series 2 is shown in Figure 14. The deformation of the tank wall under input wave 2-4 was smaller than the deformation of the tank wall under input wave 1-1, although the peak acceleration of the former is around 2 times of the latter. The maximum deformation of the tank wall under this input wave series reached 1.7 mm, which is only 0.04% of the diameter of the test specimen and 0.1% of the height of the test specimen.

(a)

(b)

(c)

(d)

(e)

(f)

(g)

(h)

Figure 14: The envelope curve of the tank wall deformation of the test specimen: input wave series 2. (a) Input wave 2-1: A-A’. (b) Input wave 2-1: B-B’. (c) Input wave 2-2: A-A’. (d) Input wave 2-2: B-B’. (e) Input wave 2-3: A-A’. (f) Input wave 2-3: B-B’. (g) Input wave 2-4: A-A’. (h) Input wave 2-4: B-B’.

The largest strain values according to the strain gauge readings were 650 με, 700 με, 780 με, and 900 με when the test specimen was subjected to input waves 2-1, 2-2, 2-3, and 2-4, respectively, and the largest strain was obtained by strain gauge SW-2 again under these seismic excitations. Therefore, special attention should be paid to the position corresponding to the location of strain gauge SW-2, which is near the floating roof, when designing the tank wall under earthquake. Necessary strengthening strategies could be applied. The strain at the other locations was quite small. As the input energy increased, the strain values at the same location increased. The shapes of the strain histories at the same location were similar subjected to these input waves. However, the tank wall remained elastic in all these four cases. The strain gauge readings at the foundation were negligibly small.

The sloshing motion of the liquid is shown in Figure 15. No evident difference was observed between the sloshing effects under input waves 2-1 to 2-4, and the change in the elevation of the water free-surface did not differ remarkably. The highest water level reached 920 mm, which was 40 mm above the initial filling water level, and the lowest water level was 825 mm, which was 55 mm below the initial filling water level.

(a)

(b)

(c)

(d)

Figure 15: Time histories of liquid sloshing motion: input wave series 2. (a) Input wave 2-1. (b) Input wave 2-2. (c) Input wave 2-3. (d) Input wave 2-4.

4. Numerical Simulations

4.1. Modeling Approaches

Finite element models for the test specimen were firstly constructed using the commercial finite-element code ANSYS. The model is a detailed representation of the test specimen, which accounts for the tank wall, the bottom plate, the reinforced concrete ringwall, the liquid, and the floating roof, as shown in Figure 16. The tank wall and the bottom plate were modeled using shell elements. The liquid was modeled using solid fluid elements, which was a type of element particularly used to model both static liquid and dynamic liquid. The foundation, including the reinforced concrete ringwall and the sand, was represented using solid elements. The floating roof was also modeled using solid elements. The interaction between the liquid and the tank wall was modeled by coupling the degree of freedom in the horizontal directions (X and Y) at the interface. The interaction between the liquid and the floating roof and the bottom plate was modeled by coupling the degree of freedom in the vertical direction at the interface. The contact between the bottom plates and the foundation was represented by contact elements. The stress-strain response of the structural steel and concrete used in this study is shown in Figure 17. Both material and geometric nonlinearity were considered in the modeling process.

Figure 16: Finite element model for the test specimen.

(a)

(b)

Figure 17: Material models. (a) Structural steel. (b) Concrete.

4.2. Validation Studies

In order to evaluate the accuracy and the suitability of the model to represent the dynamic responses of the test specimen under seismic excitations, nonlinear dynamic analyses were performed using the proposed model and the behavior of the numerical model and the test specimen under identical excitations were compared. The model was firstly excited by the white-noise excitations, and the natural frequency of the model was 16.33 Hz, which was about 10% higher than that was obtained from the shaking table tests. Then the dynamic responses of the model subjected to input wave 1-2 were investigated. Figure 18 shows the comparison between the acceleration time histories obtained from the numerical simulation and experimental tests at various locations on the tank wall. The comparisons showed that the model was capable of producing similar acceleration time histories with the shaking table tests. Other comparisons were also made and responses of the model matched well with the shaking table tests. Therefore, it can be concluded that the proposed model is able to represent the behavior of the test specimen under seismic excitations reasonably.

(a)

(b)

(c)

(d)

(e)

(f)

(g)

(h)

(i)

(j)

Figure 18: Comparison between the acceleration time histories obtained from the shaking table tests and the numerical simulations. (a) A-1. (b) A-2. (c) A-3. (d) A-4. (e) A-5. (f) A-6. (g) A-7. (h) A-8. (i) A-9. (j) A-10.

4.3. Numerical Simulations of the Prototype Tank under Seismic Excitations

It has been shown that the proposed model is able to capture reasonable behavior of the liquid storage tank under earthquakes. Thus, identical modeling approaches were used to construct a numerical model for the prototype tank. A new input wave was used herein, which was modified on the basis of “unified” seismic wave 1. The peak accelerations of the new input wave in X, Y, and Z directions are 0.32 g, 0.40 g, and 0.27 g. The new input wave is designated as input wave 1-4. The dynamic responses of the prototype tank subjected to input waves 1-4 and 2-2 were investigated numerically. The reason that these two input waves were selected is that the seismic precautionary intensity 9 was considered once the PGA of the input waves reached 0.4 g, which represented the highest seismic risk according to GB 5011-2010. The exceeding probability of such earthquakes within the design reference period (50 years) is 2%. Thus, the dynamic responses of the prototype tank under such earthquakes can be used to assess whether the current seismic code can protect the oil-storage tanks effectively under major earthquakes.

The same coordinate system described in Section 2.3 was used in this section, and identical designations were used for the intersections between the bottom of the tank wall and the coordinate system. The X direction represents the horizontal direction with smaller PGA, and the Y direction represents the direction with larger PGA.

Figures 19 and 20 show the peak accelerations and transmissibility along the X direction and Y direction when the model was subjected to input waves 1-4 and 2-2. The maximum acceleration always occurred at the bottom of the tank, and the value was large (more than 1.0 g). The responses of the prototype tank with respect to acceleration in the two horizontal directions were similar, which is coincident with the observations from the shaking table tests. In Figure 19, the largest peak acceleration and transmissibility in both horizontal directions under input wave 1-4 were obtained at the bottom of the tank. In the X direction, the maximum peak acceleration and transmissibility were 19.2 m/s² (1.96 g) and 4.90, respectively. In the Y direction, these two values were 20.1 m/s² (2.05 g) and 6.40. In Figure 20, similar observations were made. The maximum peak acceleration and transmissibility were 9.8 m/s² (1.0 g) and 3.89, respectively, under input wave 2-2 in the X direction. In the Y direction, the values were 12.3 (1.26 g) and 3.92, respectively.

(a)

(b)

Figure 19: Numerical simulation: peak accelerations and transmissibility in X and Y directions under seismic input wave 1-4. (a) A-A’ (X direction). (b) B-B’ (Y direction).

(a)

(b)

Figure 20: Numerical simulation: peak accelerations and transmissibility in X and Y directions under seismic input wave 2-2. (a) A-A’ (X direction). (b) B-B’ (Y direction).

The envelope curves of the tank wall deformation along A-A’ and B-B’ under input wave 1-4 are shown in Figure 21. The deformation in the Y direction was larger than that in the X direction. The largest deformation of the tank wall reached 127 mm in the Y direction, which occurred at the lower part of the tank wall, which was 0.59% of the height and only 0.16% of the diameter of the prototype tank. The maximum deformation of the prototype tank wall was also found in the Y direction under input wave 2-2. Therefore, only the envelope curve of the tank wall in this direction was illustrated by Figure 22. Under this seismic excitation, the largest deformation of the tank wall reached 90 mm, which was 29% smaller than the case when the prototype tank was excited by input wave 1-4. This observation indicated that the tank was more vulnerable to the ground motions similar to the El-Centro earthquake than the Wenchuan earthquake. This conclusion was further confirmed by Figures 23 and 24, which illustrate the distributions of the peak stress during the vibration along A-A’ under these two input waves. The peak stress distributions in the other horizontal direction were not shown because they were not as large as the ones along A-A’. As shown in Figure 23, the maximum stress under input wave 1-4 was 484 MPa, which was quite close to the yielding strength of the structural steel (490 MPa). The maximum stress occurred at the location where the thickness of the tank wall changed. According to Figure 24, the maximum stress under input wave 2-2 was 394, which was around 80% of the yielding strength of the structural steel. However, in both cases, the tank behaves elastically. However, the design seems like not conservative enough since the structural steel almost yields when the prototype tank was subjected to seismic wave 1-4. This might be because the magnification effects in the horizontal direction with smaller PGA were underestimated.

(a)

(b)

Figure 21: Numerical simulation: envelope curve of the tank wall deformation under seismic input wave 1-4. (a) A-A’ (X direction). (b) B-B’ (Y direction).

Figure 22: Numerical simulation: envelope curve of the tank wall deformation along B-B’ under seismic input wave 2-2.

Figure 23: Numerical simulation: stress distributions along A-A’ under seismic input wave 1-4.

Figure 24: Numerical simulation: stress distributions along A-A’ under seismic input wave 2-2.

5. Summary and Conclusions

In this study, the dynamic response of a 100,000 m³ cylindrical oil-storage tank under earthquakes was investigated experimentally and numerically. A series of shaking table tests were carried out using a 1/20 scale test specimen with foundation to investigate the dynamic behavior of the liquid-tank-foundation system under seismic excitations. A finite element model was constructed for the test specimen, and validation studies were conducted in order to ensure the accuracy and the suitability of the proposed model to represent the dynamic behavior of the test specimen under earthquakes. Then the proposed modeling approaches were used to create the numerical models for the prototype tank, and the seismic behavior of the prototype tank was investigated numerically. The following conclusions are drawn:

(i)The test specimen behaved elastically under the input wave series 1 and 2. The differences in the accelerations as well as the deformations of the tank wall between the two horizontal directions were not evident. Thus, it is necessary to consider the ground motion in both horizontal directions when designing the oil-storage tank under earthquakes.(ii)The magnification effects in the vertical direction were substantial. It should also be necessary to consider the vertical component of the ground motion, which was underestimated in the design code for the oil-storage tank currently used in China (GB 50341-2014).(iii)Maximum acceleration usually occurred at the top and the bottom of the tank. However, the largest deformation of the tank wall typically occurred nearly 1/3 of the tank height from the bottom of the tank. Therefore, close attention should be paid to these locations.(iv)The numerical simulations for the 100,000 m³ cylindrical oil-storage tank revealed that the prototype tank behaves well under major earthquakes when the highest seismic risk (seismic precautionary intensity 9) was considered according to the Chinese seismic design code. However, in order to further ensure the safety of the tank, more conservative design philosophy needs to be implemented so that the tank can behave elastically under major earthquakes, and special attention should be paid at the locations where the thickness of the tank wall changed.

Data Availability

The data used to support the findings of this study are available from the corresponding author upon request.

Disclosure

Any opinions, findings, conclusions, and recommendations expressed in this paper are those of the authors and do not necessarily reflect the views of the sponsors.

Conflicts of Interest

The authors declare that there are no conflicts of interest regarding the publication of this paper.

Acknowledgments

The presented work was supported by grants from the National Natural Science Foundation of China under Grant no. 50678056.

References

G. W. Housner, “Dynamic pressures on accelerated fluid containers,” Bulletin of the Seismological Society of America, vol. 47, no. 1, pp. 15–35, 1957.

A. S. Veletsos, “Seismic effects in flexible liquid storage tanks,” in Proceedings of 5th World Conference on Earthquake Engineering, vol. 1, pp. 630–639, Rome, Italy, 1974.

A. S. Veletsos and J. Y. Yang, Earthquake Response of Liquid Storage Tanks: Advances in Civil Engineering through Engineering Mechanics, ASCE, Reston, VA, USA, 1977.

M. A. Haroun and G. W. Housner, “Seismic design of liquid storage tanks,” Journal of the Technical Councils of ASCE, vol. 107, no. 1, pp. 191–207, 1981.

P. K. Malhotra, T. Wenk, and M. Wieland, “Simple procedure for seismic analysis of liquid-storage tanks,” Structural Engineering International, vol. 10, no. 3, pp. 197–201, 2000.

American Petroleum Institute (API), Welded Storage Tanks for Oil Storage, American Petroleum Institute Standard, Washington, DC, USA, 2013.

Eurocode 8, Design of Structures for Earthquake Resistance–Part 4: Silos, Tanks and Pipelines, European Committee for Standardization (ECS), Brussels, Belgium, 2006.

J. R. Cho and H. W. Lee, “Non-linear finite element analysis of large amplitude sloshing flow in two-dimensional tank,” International Journal for Numerical Methods in Engineering, vol. 61, no. 4, pp. 514–531, 2004.

J. C. Virella, L. A. Godoy, and L. E. Suarez, “Dynamic buckling of anchored steel tanks subjected to horizontal earthquake excitation,” Journal of Constructional Steel Research, vol. 62, no. 6, pp. 521–531, 2006.

R. Livaglu, “Investigation of seismic behavior of fluid-rectangular tank-soil/foundation systems in frequency domain,” Soil Dynamics and Earthquake Engineering, vol. 28, pp. 132–146, 2008.

D. Liu and P. Lin, “A numerical study of three-dimensional liquid sloshing in tanks,” Journal of Computational Physics, vol. 227, no. 8, pp. 3921–3939, 2008.

N. K. Attari and F. R. Rofooei, “On lateral response of structures containing a cylindrical liquid tank under the effect of fluid/structure resonances,” Journal of Sound and Vibration, vol. 318, no. 4, pp. 1154–1179, 2008.

R. D. Firouz-Abadi, H. Haddadpour, and M. Ghasemi, “Reduced order modeling of liquid sloshing in 3D tanks using boundary element method,” Engineering Analysis with Boundary Elements, vol. 33, no. 6, pp. 750–761, 2009.

Z. Ozdemir, M. Souli, and Y. M. Fahjan, “Application of nonlinear fluid-structure interaction methods to seismic analysis of anchored and unanchored tanks,” Engineering Structures, vol. 32, no. 2, pp. 409–423, 2010.

K. A. Korkmaz, A. Sari, and A. I. Carhoglu, “Seismic risk assessment of storage tanks in Turkish industrial facilities,” Journal of Loss Prevention in the Process Industries, vol. 24, pp. 314–320, 2011.

M. Moslemi and M. R. Kianoush, “Parametric study on dynamic behavior of cylindrical ground-supported tanks,” Engineering Structures, vol. 42, pp. 214–230, 2012.

T. Matsui and T. Nagaya, “Nonlinear sloshing in a floating-roofed oil storage tank under long-period seismic ground motion,” Earthquake Engineering and Structural Dynamics, vol. 42, no. 7, pp. 973–991, 2013.

N. Buratti and M. Tavano, “Dynamic buckling and seismic fragility of anchored steel tanks by the added mass method,” Earthquake Engineering and Structural Dynamics, vol. 43, pp. 1–21, 2014.

C. Shih, “Failure of liquid storage tanks due to earthquake excitation,” Ph.D. thesis, California Institute of Technology, Pasadena, CA, USA, 1981.

A. Niwa and R. W. Clough, “Buckling of cylindrical liquid-storage tanks under earthquake loading,” Earthquake Engineering and Structural Dynamics, vol. 10, no. 1, pp. 107–122, 1982.

M. A. Haroun, “Vibration studies and tests of liquid storage tanks,” Earthquake Engineering and Structural Dynamics, vol. 11, no. 2, pp. 179–206, 1983.

M. Chiba, J. Tani, and N. Yamaki, “Dynamic stability of liquid-filled cylindrical shells under vertical excitation, part I: experimental results,” Earthquake Engineering and Structural Dynamics, vol. 15, no. 1, pp. 23–26, 1987.

F. Sakia, A. Isoe, H. Hirakawa, and Y. Mentani, “Experimental study on uplifting behavior of flat-based liquid storage tanks without anchors,” in Proceedings of Ninth World Conference on Earthquake Engineering, vol. 6, pp. 2–9, Tokyo-Kyoto, Japan, 1988.

M. Tanaka, T. Sakurai, K. Ishida et al., “Proving test of analysis method on nonlinear response of cylindrical storage tank under severe earthquakes,” in Proceedings of 12th World Conference on Earthquake Engineering, pp. 1–8, Auckland, New Zealand, 2000.

N. C. Pal, S. K. Bhattacharyya, and P. K. Sinha, “Experimental investigation of slosh dynamics of liquid-filled containers,” Experimental Mechanics, vol. 41, no. 1, pp. 63–69, 2001.

H. Nishi, M. Yamada, K. Hatayama, and K. Sekine, “Experimental study on the sloshing behavior of the floating roof using a real tank,” Pressure Technology, vol. 46, no. 1, pp. 4–17, 2008.

M. De Angelis, R. Giannini, and F. Paolacci, “Experimental investigation on the seismic response of a steel liquid storage tank equipped with floating roof by shaking table tests,” Earthquake Engineering and Structural Dynamics, vol. 39, no. 4, pp. 377–396, 2010.

A. Maekawa, Y. Shimizu, M. Suzuki, and K. Fujita, “Vibration test of a 1/10 reduced scale model of cylindrical water storage tank,” Journal of Pressure Vessel Technology, vol. 132, no. 5, Article ID 051801, 2010.

Z. Fang, Z. P. Chen, S. J. Yan, G. W. Cao, and J. Wang, “Dynamic experimental investigation on the uplift response of liquid storage tanks under seismic excitations with different characteristics,” Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, vol. 227, no. 7, pp. 1525–1534, 2013.

M. A. Goudarzi, S. R. Sabbagh-Yazdi, and W. Marx, “Seismic analysis of hydrodynamic sloshing force on storage tank roofs,” Earthquake Spectra, vol. 26, no. 1, pp. 131–152, 2010.

P. Pal and S. K. Bhattacharyya, “Sloshing in partially filled liquid containers—numerical and experimental study for 2-D problems,” Journal of Sound and Vibration, vol. 329, no. 21, pp. 4466–4485, 2010.

M. Eswaran, A. Singh, and U. K. Saha, “Experimental measurement of the surface velocity field in an externally induced sloshing tank,” Proceedings of the Institution of Mechanical Engineers, Part M: Journal of Engineering for the Maritime Environment, vol. 225, no. 2, pp. 133–148, 2011.

M. Ormeño, T. Larkin, and N. Chouw, “The effect of seismic uplift on the shell stresses of liquid-storage tanks,” Earthquake Engineering and Structural Dynamics, vol. 44, no. 12, pp. 1979–1996, 2015.

J. H. Park, D. Bae, and C. K. Oh, “Experimental study on the dynamic behavior of a cylindrical liquid storage tank subjected to seismic excitation,” International Journal of Steel Structures, vol. 16, no. 3, pp. 935–945, 2016.