dynamic response of a 100,000m3 cylindrical oil...

Research ArticleDynamic Response of a 100,000m3 Cylindrical Oil-StorageTank under Seismic Excitations: Experimental Tests andNumerical 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 andMitigation 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; [email protected]

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. (is 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.

Considering the disastrous consequences of the oil tank failure, it is of great importance to ensure the safety of the large-scale oil tankunder earthquakes. (is study sheds light on investigating the dynamic response of a prototype 100,000m3 cylindrical oil-storagetank under various seismic excitations. (e foundation of the tank is also considered in this study so that the obtained results arecloser to the reality. Shaking table tests are conducted using a 1/20 scale liquid-tank-foundation system under various seismicexcitations. (e test results reveal that the dynamic responses such as accelerations and the deformation of the test specimen in themajor and minor vibration directions do not differ significantly. Finite element models are constructed for the test specimen and theprototype tank and are validated through comparing the simulation results with the test data. (e simulation results suggest that itmight be necessary to stiffen the locations on the tank wall where the thickness of the tank wall changes because the stresses at suchlocations 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 liquidstorage tanks containing flammable and combustible liquidsuch as oil is of great importance because damages of suchinfrastructures under earthquakes can cause large fires,explosion, environmental pollution, and other secondarycatastrophes, which may induce huge economic damage andextensive loss of human lives. Although earthquakes havebeen considered in the design guidelines on liquid storagetanks, damages of liquid/oil-storage tanks were reported ina number of major earthquakes, such as the 1964 Alaskaearthquake in the USA (Mw � 9.2), 1978 Miyagi earthquakein Japan (Ms � 7.7), 1999 Kocaeli earthquake in Turkey(Mw � 7.7), 2003 Tokachi-Oki earthquake in Japan(Mw � 8.0), 2008Wenchuan earthquake in China (Mw � 7.9),and 2011 Tohoku earthquake and the tsunami in Japan(Mw � 9.0). (ese accidents have highlighted the seriousnessof such events, motivated the research in seismic responses

of liquid storage tanks, and thus improved the design codesand guidelines of liquid storage tanks against earthquakes.

Research on seismic responses of elevated oil storagestarted from 1930s, and this topic has drawn a lot of researchinterest since then. Generally speaking, research in this fieldtypically falls into three categories: (1) theoretical compu-tational models, (2) numerical simulations, and (3) exper-imental tests. One of the earliest simplified models forinvestigating the dynamic response of a liquid storage tankwas the mass-spring model proposed by Housner [1]. (emodel considered the tank walls as rigid.(emodel was thenmodified to account for the impact of the flexible tank wallson the seismic responses of liquid storage tanks in furtherstudies, such as Velestsos [2], Velestsos and Yang [3],Haroun and Housner [4], and Malhotra et al. [5]. (emodels mentioned above have been implemented by theseismic design codes and guidelines on liquid storage tanksworldwide, such as API 650 [6] and Eurocode 8 [7]. In recentyears, the rapid development of computer technology and

HindawiShock and VibrationVolume 2018, Article ID 2074946, 19 pageshttps://doi.org/10.1155/2018/2074946

mailto:[email protected]

http://orcid.org/0000-0002-8854-9879

https://doi.org/10.1155/2018/2074946

availability of powerful software allow numerical simulationbecome an important technique to investigate seismic be-havior of liquid storage tanks in a more sophisticatedmanner, such as Cho and Lee [8], Virella et al. [9], Livaoglu[10], Liu and Lin [11], Attati and Rofooei [12], Firouz-Abadiet al. [13], Ozdemir et al. [14], Korkmaz et al. [15], Moslemiand Kianoush [16], Matsui and Nagaya [17], and Buratti andTavano [18]. (e shaking table test is the main tool to in-vestigate the dynamic responses of liquid storage tanksunder earthquake excitations experimentally. Early exam-ples of such tests could be found in Shih [19], Niwa andClough [20], Haroun [21], Chiba et al. [22], and Sakai et al.[23]. In more recent years, shaking table tests which wereconducted to investigate seismic responses of the liquidstorage tanks include Tanaka et al. [24], Pal et al. [25], Nishiet al. [26], De Angelis et al. [27], Maekawa et al. [28], Fanget 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 theseismic behavior of large-scale unanchored liquid storagetanks are rare. In most, if not all, of these shaking table testsmentioned above, only one horizontal component of theground motion was considered. Furthermore, there is noexperimental test considering the seismic response of a cou-pled liquid-tank-foundation system when all three compo-nents (two horizontal and one vertical) of the ground motionare considered. (e goal of this study is to address these gaps.(e purposes of this study include (1) to investigate thedynamic responses of a large-scale cylindrical unanchored oil-storage tank subjected to earthquake excitations, (2) to ex-amine whether the original design of the tank can sustainmajor earthquakes and thus to access the seismic vulnerabilityof such tanks and promote the development of the designcode for oil-storage tanks against earthquakes, and (3) toprovide experimental data for the validation of numericalmodels. (is study sheds light on the seismic behavior ofa 100,000m3 liquid storage tank considering liquid sloshingand tank-foundation interaction (uplifting). In this study,shaking table tests of a 1/20 scale liquid tank model werefirstly conducted under the excitations of various input waves.(en finite element models for the test specimen were createdusing commercial FEA software ANSYS and validated againstexperimental data. After showing that the model can rep-resent the dynamic behavior of the test specimen underearthquakes reasonably, similar modeling approaches wereused to develop numerical models for a prototype 100,000m3

oil-storage tank and the dynamic responses of the prototypetank under strong earthquakes were investigated numerically.

2. Shaking Table Tests

2.1. Test Specimen. A 100,000m3 unanchored cylindrical oil-storage tank which is commonly used in China equipped witha metallic floating roof is selected herein as the prototypestructure to investigate its dynamic response under earth-quake excitations. (e prototype tank was originally designedby Sinopec Engineering incorporation on the basis of ChineseCode for Design of Vertical Cylindrical Welded Steel OilTanks (GB 50341-2014). As shown in Figure 1(a), the outer

diameter of the prototype tank is 80m, the diameter ofthe floating roof is 79.5m, and the height of the tank is21.8m. (e filling level of the oil contained by the tank is18.5m. (e tank wall is comprised of 9 steel shells withdifferent thicknesses ranging from 32mm to 12mm, asshown in Figure 1(c). (e structural steel used for shell 1 to 7is SPV490Q (σy � 490MPa), and shells 8 and 9 are fabricatedusing Q235A (σy � 235MPa). (e bottom plate of the tank isalso made of structural steel SPV490Q, and the thickness is20mm. (e tank is placed on a reinforced concrete ringwall(Figures 1(a) and 1(b)).(e height and the thickness of the RCringwall are 2.5m and 0.8m, respectively.(e ringwall is filledwith compacted soil, which acts as the foundation of the tank.

Due to the limitation of the shaking table dimension,a reduced scale model with a scaling factor of 1/20 has beendesigned and fabricated (Figure 2), and the model isa coupled liquid-tank-foundation system. (e outer di-ameter of the test specimen is 4m, the diameter of thefloating roof is 3.975m, and the height of the test specimen is1.1m. (e wall of the test specimen was fabricated usingstructural steel Q235A. Since the thickness of the tank walland the bottom plate cannot be too small considering thestability issue, the geometrical scaling factor cannot beachieved when designing the wall and bottom plates of thetest specimen. Considering the difficulties in fabricating thewall of the test specimen with varied thickness, the wall ofthe test specimen is set to be 3mm according to API 650 [6].(e thickness of the bottom plate is 2mm, which is fabri-cated using the same structural steel as the tank wall. (ebottom plate rests on a reinforced concrete ringwall. (ediameter, thickness, and height of the ringwall are 4m,150mm, and 450mm, respectively.(e ringwall is filled withsand. (us, the foundation of the tank was simulated. (efloating roof of the test specimen was made of blockboardwith the thickness of 17mm. In order to simulate theconnection between the floating roof and the tank wall,a rubber tube was placed surrounding the blockboard. (etest specimen was filled with water with a fill level of 0.88m.(e weight of the liquid is 11t, and the total weight of thetank and floating roof is 650 kg.

(e scaling factor of the test specimen was selectedconsidering the limitations of the behavior parameters of theshaking table and other specifications of the experimentalfacilities. Although some insights into the behavior of thetest specimen subjected to earthquake excitations can begained through the shaking table test, the key purpose of thetest is to provide experimental data for the validation offinite element models which can be used to investigate theresponse of the 100,000m3 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 severeseismic loads which is currently implemented can beassessed. (e test results were not directly used to predictwhether the prototype tank can survive mega earthquakes.On the other hand, this study only focuses on linear elasticbehavior of both the test specimen and the prototype tank.(erefore, the geometric scale factor was set to be 1/20, andthe remaining scale factors, including scale factors for

2 Shock and Vibration

density, elastic modulus, time, frequency, acceleration,stress, and strain, were all set to be 1.

2.2. Instrumentation. A virtual coordinate system was de-�ned as shown in Figure 2(a) for convenience. X and Y

directions in this coordinate system are the directions of twohorizontal components of the ground motion produced bythe shaking table, and the Z axis represents the verticaldirection. As shown in Figure 2(b), the intersections betweenthe X-Z plane and the tank wall are lines A-A’ and C-C’(Figure 3). e intersections between the Y-Z plane and the

80 m

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

XY

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

Shock and Vibration 3

tank wall are lines B-B’ and D-D’. Points A, B, C, and D arelocated at the top of the tank, and points A’, B’, C’, and D’ areat the bottom of the tank.

Quantities of interest in the response include displace-ments and accelerations, strains of the tank wall, and waterfree-surface elevations. ese quantities are measured atdi�erent locations. e time history of horizontal acceler-ations at various locations along line A-A’ and line B-B’ onthe tank wall was recorded using 8 accelerometers (A-1 toA-4 and A-6 to A-9), as shown in Figure 3(a). e verticalaccelerations of points A’ and B’ were measured by twoaccelerometers (A-5 and A-10). ree accelerometers wereplaced on the shaking table to record the time histories of theinput waves in X, Y, and Z directions, respectively. As shownin Figure 3(b), 10 string potentiometers were used tomeasure the displacement at various locations of the testspecimen, eight of which (D-1 to D-4 and D-6 to D-9) wereattached to the tank wall at the same locations with theaccelerometers to measure the horizontal displacement ofthese points. Another two string potentiometers (D-5 and

D-10) were used to record the horizontal displacement of thefoundation, and thus the deformed pro�les of the tank wallcould be estimated based on the relative displacement be-tween the tank wall and the foundation. Figure 3(c) showsthe strain gauges which were attached to the tank wall andthe foundation to measure the time history of the strains atthese locations. e strain gauges attached to the tank wallwere designated as SW-X, where X represents the number ofthe strain gauge. e elevations of the water free-surfacewere measured using displacement sensors.

2.3. Test Setup. e dynamic responses of the test specimensubjected to a series of seismic excitations were tested on theshaking table of the Institute of Engineering Mechanics,China Earthquake Administration. e shaking table iscapable of producing six components of motions, includingthree translations in three directions and three rotations.eearthquake simulator can reproduce a variety of earthquakeground motions within the capacity of the system. e

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


performance parameters of the shaking table are summa-rized in Table 1.

Two series of input seismic waves were used in thesetests, which are obtained by modifying the ground accel-eration records of the 1940 El-Centro earthquake (El-Centrowave), which is designated as input wave series 1, and the2008 Sichuan earthquake (Wolong wave), which is desig-nated as input wave series 2. (e ground motion records ofthese two earthquakes are selected as the input waves be-cause (1) El-Centro earthquake ground motion records wereused widely when conducting time history analysis of civilstructures and infrastructures, both numerically and ex-perimentally since the response spectrum for El-Centroground motion is quite close with the standard designspectrum, and (2) the 2008 Sichuan earthquake is the mostdevastating earthquake that struck China in the past decade.(erefore, it is meaningful to explore the dynamic responsesof the test specimen under these two earthquakes.

Figures 4 and 5 illustrate the modified acceleration timehistories of the El-Centro earthquake and Sichuan earth-quake, which were obtained according to the followingequation:

€u(t) �€ug(t)

€ug0, (1)

in which €u(t) represents the modified ground accelerationtime history, €ug(t) represents the original ground acceler-ation time history, and €ug0 represents the peak groundacceleration of the original ground motion. (erefore, thepeak accelerations of the modified ground motion in allthree directions were equal to 1.0 g (9.8m/s2). (en inputwaves 1-1, 1-2, and 1-3 were obtained by scaling themodified ground acceleration histories of input wave series1, 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 ac-celeration histories of input wave series 2, as shown inFigures 5(a)–5(c). (e peak ground accelerations in threedirections of all the input waves were tabulated in Table 2.(e values of the ground peak accelerations were calculatedaccording to the seismic precautionary intensities (PI) re-quired by the Chinese Code for Design of Buildings (GB5011-2010), as shown in Table 2, in which seismic PI 6represents the lowest seismic risk, in which seismic effectsare usually not considered, PI 7 represents low seismic risk,PI 8 represents moderate seismic risk, and PI 9 represents highseismic risk. Input waves 2-3 and 2-4 have a PI of 10 or above.Such seismic precautionary intensities are too high to beconsidered in the design of common civil structures accordingto GB 5011-2010, which represents mega earthquakes.

(e purpose of using input waves with different peakaccelerations which are modified on the basis of the sameseismic record is to investigate the behavior of the tankunder different seismic intensities as well as the impact of theamount of the energy input to the system on the dynamicbehavior of the test specimen.

(e power spectrums of the modified ground motionsare shown in Figures 4(d) and 5(d), in which the spectralcharacteristics of these two earthquakes can be explored.According to these two figures, the predominant frequency

of the El-Centro earthquake is around 1.5Hz. However, theSichuan earthquake has two predominate frequencies: one isaround 9Hz and the other is around 24Hz.

(e dynamic responses of the test specimen were ac-tually evaluated under a number of other seismic recordstoo. However, only the test results under the seismic exci-tations of these input waves were presented herein due tospace limitation.

3. Experimental Results

Dynamic responses of the test specimen, including accel-eration time histories and peak accelerations at variouslocations, the envelope curve of the tank wall deformation,and the elevations of the water free-surface subjected to theseries of the input waves were obtained, and the test resultsare analyzed herein.

3.1. Dynamic Characteristics. (e test specimen was firstlysubjected to the excitations of white noise to investigate thedynamic characteristics of the test specimen. (e naturalfrequency (1st order) of the test specimen was 14.51 Hz, andthe damping ratio was 8.4% according to the Fourier am-plitude spectrum of acceleration based on the test results.

3.2. Responses under Input Wave Series 1. (e peak accel-erations obtained by the accelerometers in the X direction(A-6 to A-9) and Y direction (A-1 to A-4) are shown inFigure 6. It is worthwhile tomention that the test specimen isan unanchored liquid storage tank, which means the tank isplaced on the foundation without any anchors; therefore, thepeak accelerations recorded by the accelerometers installedat the bottom of the tank (A-4 and A-9) were not equal to thepeak ground accelerations of the input waves. Based on thedata, the distribution of the peak accelerations at variouspositions on the tank wall along line A-A’ and B-B’ can beestimated and is also shown in Figure 6. In Figure 6, thedimensional quantity β represents the ratio of the height ofthe considered spot on the tank wall and the total height ofthe tank. It can be seen that as the input energy increases, thepeak acceleration of a certain point on the tank wall alsoincreases. (e largest peak acceleration was typically ob-served at the top of the test specimen, except the peakacceleration in the X direction under input wave 1-1.(e values of the peak accelerations obtained in X and Ydirections were fairly close to each other, despite of the

Table 1: Performance parameters of the shaking table.Size (m) 5× 5Peak horizontal acceleration (g, 9.8m/s2) 1Peak vertical acceleration (g, 9.8m/s2) 0.8Peak horizontal velocity (cm/s) 60Peak vertical velocity (cm/s) 60Peak horizontal displacement (m) ±8Peak vertical displacement (m) ±5Maximum gravity payload (t) 30Maximum overturning moment (kN·m) 750Frequency bandwidth (Hz) 0.4–40


difference in the values of the peak accelerations of the twohorizontal components of the input wave. (erefore, whendesigning the oil tank against earthquakes laterally, it isnecessary to consider the ground vibrations in both di-rections. (e transmissibility (TR), which is the ratio of thepeak acceleration of the tank wall to the peak ground ac-celeration of the input wave (PGA), is used to represent theamount of magnification on PGA herein. (e relationshipsbetween the values of TR and the height of the consideredspot on the tank wall are shown in Figure 7. It can be seenthat in the majority of the cases, the maximum trans-missibility is between 2.0 and 2.5, which is coincident withthe requirement of Appendix D of GB 50341-2014. (emagnification effects in the X direction are more evidentthan the one in the Y direction. In the Y direction, the largesttransmissibility is around 2.0 when the test specimen issubjected to input wave series 1, and in the X direction, thenumber increased to 8.0. An interesting observation fromFigure 7 is that the smaller the peak acceleration of the inputwave is, the larger the transmissibility is. (e peak verticalaccelerations obtained by the accelerometers at points A’ andB’ are shown in Figure 8. (e transmissibility for the verticalcomponent of the ground motion at these two points underinput waves 1-1, 1-2, and 1-3 are 11.07, 11.04, and 4.139,respectively, which is considerably large. (e magnification

effect of the vertical seismic component considered in GB50341-2014 is much smaller than what was observed in thistest.

(e envelope curve of the tank wall deformation of thetest specimen could be obtained on the basis of the readingsof the string potentiometers. Figure 9 shows the maximumdisplacements in positive and negative directions at variouslocations on the tank wall recorded by the string potenti-ometers in both X and Y directions relative to the dis-placement of the foundation under input wave series 1. Forunanchored tanks, slippage may occur between the tank andthe foundation during earthquakes. (erefore, the dis-placement at the bottom of the tank wall relative to thefoundation is not zero. (e negative sign means the de-formation is in the negative direction of the coordinate axis.In these figures, the area confined by the two curves rep-resented the range of the deformation of the tank wall underseismic excitations. (e deformation of the tank wall underthese seismic excitations was very small, which was under0.1% of the diameter and 0.3% of the height of the testspecimen, even when seismic precautionary intensity of 9was considered. Figure 9 shows that the deformation of thetank wall increases with the increase in the peak accelerationof the input wave. On the other hand, the deformation of thetank wall in the X direction was larger than that in the Y

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


direction, indicating that the damage of the tank in thedirection with smaller PGA is more severe than the directionwith larger PGA.

e maximum strain on the tank wall when the testspecimen was subjected to seismic excitations 1-1, 1-2, and1-3 were around 800 με, 1000 με, and 1100 με, respectively.e maximum strain was recorded by strain gauge SW-2,which is located near the �oating roof, in all these threecases. e numbers were well below the yield strain of thestructural steel, which is around 2000 με. e strains ob-tained by the other strain gauges were much smaller. As thepeak acceleration of the input waves increases, the straingauge readings increase as well, indicating that the internal

forces of the tank wall increase with the energy input of theseismic excitations.e strains recorded by the strain gaugesattached to the foundation were negligibly small in all thesethree cases, indicating that the foundation was not a�ectedsigni�cantly by the given seismic excitations.

e time histories of the sloshingmotion of the liquid areshown in Figure 10. e most severe liquid sloshing wasobserved when the test specimen was subjected to inputwave 1-2. e range of the liquid sloshing was around350mm, and the highest water level reached the top of thetank.

3.3. Responseunder InputWave Series 2. e distributions ofthe peak acceleration and transmissibility along the tankwall at line A-A’ in the X direction and at line B-B’ in the Ydirection are shown in Figures 11 and 12. e maximumpeak acceleration and the maximum transmissibility werefound at the top of the tank except the case in which both ofthem in the Y direction were observed at the bottom of thetank under input wave 2-4. e values of the peak accel-eration and the transmissibility increased with the increasein seismic precautionary intensity. Similar to the caseswhen the test specimen was subjected to input wave series1, the maximum accelerations in X and Y directions were

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

Input wavePeak accelerations (g) Seismic precautionary

intensityX Y Z1-1 0.034 0.145 0.014 61-2 0.096 0.173 0.026 71-3 0.123 0.306 0.075 82-1 0.130 0.304 0.161 82-2 0.137 0.444 0.138 92-3 0.290 0.504 0.298 10 or above2-4 0.324 0.653 0.439 10 or above

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


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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’.

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

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


fairly close and the magnification effects in the X directionwere much more significant than in the Y direction. (epeak vertical accelerations obtained are shown in Figure 13.(e peak vertical acceleration reached nearly 2.5 g at pointB’, which is 5.7 times of the corresponding PGA of thevertical component of the input wave, indicating that thevertical component of the input wave played a significant

role in determining the dynamic response of the testspecimen.

(e envelope of the tank wall deformation along linesA-A’ and B-B’ subjected to seismic wave series 2 is shown inFigure 14. (e deformation of the tank wall under inputwave 2-4 was smaller than the deformation of the tank wallunder input wave 1-1, although the peak acceleration of the

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ght (

m)β

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(f )

Figure 9: (e envelop curve of the tank wall deformation of the test specimen: input wave series 1. (a) Input wave 1-1: A-A’. (b) Input wave1-1: 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’.


former is around 2 times of the latter. e maximum de-formation of the tank wall under this input wave seriesreached 1.7mm, which is only 0.04% of the diameter of thetest specimen and 0.1% of the height of the test specimen.

e largest strain values according to the strain gaugereadings were 650 με, 700 με, 780 με, and 900 με when thetest specimen was subjected to input waves 2-1, 2-2, 2-3, and

2-4, respectively, and the largest strain was obtained bystrain gauge SW-2 again under these seismic excitations.erefore, special attention should be paid to the positioncorresponding to the location of strain gauge SW-2, which isnear the �oating roof, when designing the tank wall underearthquake. Necessary strengthening strategies could beapplied. e strain at the other locations was quite small. As

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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.

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(a)

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(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’.




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(b)

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

0.5

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Input wave 2-1 Input wave 2-2 Input wave 2-3 Input wave 2-4

Acc

eler

atio

n (g

)

Accelerometers at B’Accelerometers at A’

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

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(b)

Figure 14: Continued.


the input energy increased, the strain values at the samelocation increased. (e shapes of the strain histories at thesame location were similar subjected to these input waves.However, the tank wall remained elastic in all these fourcases. (e strain gauge readings at the foundation werenegligibly small.

(e sloshing motion of the liquid is shown in Figure 15.No evident difference was observed between the sloshingeffects under input waves 2-1 to 2-4, and the change in theelevation of the water free-surface did not differ remarkably.(e highest water level reached 920mm, which was 40mmabove the initial filling water level, and the lowest water level

was 825mm, which was 55mm below the initial filling waterlevel.

4. Numerical Simulations

4.1.ModelingApproaches. Finite element models for the testspecimen were firstly constructed using the commercialfinite-element code ANSYS. (e model is a detailed rep-resentation of the test specimen, which accounts for thetank wall, the bottom plate, the reinforced concrete ringwall,the liquid, and the floating roof, as shown in Figure 16. (etank wall and the bottom plate were modeled using shell

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(c)

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(d)

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(e)

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(f )

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eigh

t (m

)

β

Deformation (mm)

(h)

Figure 14: (e envelope curve of the tank wall deformation of the test specimen: input wave series 2. (a) Input wave 2-1: A-A’. (b) Inputwave 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’.


elements. (e liquid was modeled using solid fluid ele-ments, which was a type of element particularly used tomodel both static liquid and dynamic liquid. (e foun-dation, including the reinforced concrete ringwall and thesand, was represented using solid elements. (e floatingroof was also modeled using solid elements.(e interactionbetween the liquid and the tank wall was modeled bycoupling the degree of freedom in the horizontal directions(X and Y) at the interface. (e interaction between theliquid and the floating roof and the bottom plate wasmodeled by coupling the degree of freedom in the verticaldirection at the interface. (e contact between the bottomplates and the foundation was represented by contact el-ements. (e stress-strain response of the structural steeland concrete used in this study is shown in Figure 17. Bothmaterial and geometric nonlinearity were considered in themodeling process.

4.2.ValidationStudies. In order to evaluate the accuracy andthe suitability of the model to represent the dynamic re-sponses of the test specimen under seismic excitations,nonlinear dynamic analyses were performed using theproposed model and the behavior of the numerical modeland the test specimen under identical excitations were

compared. (e model was firstly excited by the white-noiseexcitations, and the natural frequency of the model was16.33Hz, which was about 10% higher than that was ob-tained from the shaking table tests. (en the dynamic re-sponses of the model subjected to input wave 1-2 wereinvestigated. Figure 18 shows the comparison between theacceleration time histories obtained from the numerical

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

Floating roof

Tankwall

Foundation

Figure 16: Finite element model for the test specimen.


fy

εyε

σ

(a)

fc

ε0 εcuε

σ

(b)

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

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/s2 )

Test resultsSimulation

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0.00.51.01.52.02.5

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/s2 )

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Time (s)


(d)

Figure 18: Continued.


simulation and experimental tests at various locations on thetank wall. (e comparisons showed that the model wascapable of producing similar acceleration time histories withthe shaking table tests. Other comparisons were also made

and responses of the model matched well with the shakingtable tests. (erefore, it can be concluded that the proposedmodel is able to represent the behavior of the test specimenunder seismic excitations reasonably.

Acc

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atio

n (m

/s2 )

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(h)

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0 5 10 15 20 25–1.2–1.0–0.8–0.6–0.4–0.2

0.00.20.40.60.81.01.21.41.6

Time (s)


(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 underSeismic Excitations. It has been shown that the proposedmodel is able to capture reasonable behavior of the liquidstorage tank under earthquakes. (us, identical modelingapproaches were used to construct a numerical model for theprototype tank. A new input wave was used herein, whichwas modified on the basis of “unified” seismic wave 1. (epeak accelerations of the new input wave in X, Y, and Zdirections are 0.32 g, 0.40 g, and 0.27 g. (e new input waveis designated as input wave 1-4. (e dynamic responses ofthe prototype tank subjected to input waves 1-4 and 2-2 wereinvestigated numerically. (e reason that these two inputwaves were selected is that the seismic precautionary in-tensity 9 was considered once the PGA of the input wavesreached 0.4 g, which represented the highest seismic riskaccording to GB 5011-2010. (e exceeding probability ofsuch earthquakes within the design reference period (50years) is 2%. (us, the dynamic responses of the prototypetank under such earthquakes can be used to assess whetherthe current seismic code can protect the oil-storage tankseffectively under major earthquakes.

(e same coordinate system described in Section 2.3 wasused in this section, and identical designations were used forthe intersections between the bottom of the tank wall and thecoordinate system.(e X direction represents the horizontaldirection with smaller PGA, and the Y direction representsthe direction with larger PGA.

Figures 19 and 20 show the peak accelerations andtransmissibility along the X direction and Y direction whenthe model was subjected to input waves 1-4 and 2-2. (emaximum acceleration always occurred at the bottom of thetank, and the value was large (more than 1.0 g). (e re-sponses of the prototype tank with respect to acceleration inthe two horizontal directions were similar, which is co-incident with the observations from the shaking table tests.In Figure 19, the largest peak acceleration and trans-missibility in both horizontal directions under input wave

1-4 were obtained at the bottom of the tank. In the X di-rection, the maximum peak acceleration and transmissibilitywere 19.2m/s2 (1.96 g) and 4.90, respectively. In the Y di-rection, these two values were 20.1m/s2 (2.05 g) and 6.40. InFigure 20, similar observations were made. (e maximumpeak acceleration and transmissibility were 9.8m/s2 (1.0 g)and 3.89, respectively, under input wave 2-2 in the X di-rection. In the Y direction, the values were 12.3 (1.26 g) and3.92, respectively.

(e envelope curves of the tank wall deformation alongA-A’ and B-B’ under input wave 1-4 are shown in Figure 21.(e deformation in the Y direction was larger than that inthe X direction. (e largest deformation of the tank wallreached 127mm in the Y direction, which occurred at thelower part of the tank wall, which was 0.59% of the heightand only 0.16% of the diameter of the prototype tank. (emaximum deformation of the prototype tank wall was alsofound in the Y direction under input wave 2-2. (erefore,only the envelope curve of the tank wall in this direction wasillustrated by Figure 22. Under this seismic excitation, thelargest deformation of the tank wall reached 90mm, whichwas 29% smaller than the case when the prototype tank wasexcited by input wave 1-4. (is observation indicated thatthe tank was more vulnerable to the ground motions similarto the El-Centro earthquake than theWenchuan earthquake.(is conclusion was further confirmed by Figures 23 and 24,which illustrate the distributions of the peak stress duringthe vibration along A-A’ under these two input waves. (epeak stress distributions in the other horizontal directionwere not shown because they were not as large as the onesalong A-A’. As shown in Figure 23, the maximum stressunder input wave 1-4 was 484MPa, which was quite close tothe yielding strength of the structural steel (490MPa). (emaximum stress occurred at the location where the thick-ness of the tank wall changed. According to Figure 24, themaximum stress under input wave 2-2 was 394, which wasaround 80% of the yielding strength of the structural steel.

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(b)

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


However, in both cases, the tank behaves elastically.However, the design seems like not conservative enoughsince the structural steel almost yields when the prototypetank was subjected to seismic wave 1-4. (is might be be-cause the magnification effects in the horizontal directionwith smaller PGA were underestimated.

5. Summary and Conclusions

In this study, the dynamic response of a 100,000m3 cylin-drical oil-storage tank under earthquakes was investigatedexperimentally and numerically. A series of shaking table testswere 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 finiteelement model was constructed for the test specimen, andvalidation studies were conducted in order to ensure theaccuracy and the suitability of the proposed model to rep-resent the dynamic behavior of the test specimen underearthquakes. (en the proposed modeling approaches wereused to create the numerical models for the prototype tank,and the seismic behavior of the prototype tank was in-vestigated numerically. (e following conclusions are drawn:

(i) (e test specimen behaved elastically under theinput wave series 1 and 2. (e differences in theaccelerations as well as the deformations of the tank

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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).

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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).


wall between the two horizontal directions were notevident. (us, it is necessary to consider the groundmotion in both horizontal directions when de-signing the oil-storage tank under earthquakes.

(ii) (e magnification effects in the vertical directionwere substantial. It should also be necessary toconsider the vertical component of the groundmotion, which was underestimated in the designcode for the oil-storage tank currently used in China(GB 50341-2014).

(iii) Maximum acceleration usually occurred at the topand the bottom of the tank. However, the largestdeformation of the tank wall typically occurrednearly 1/3 of the tank height from the bottom of thetank. (erefore, close attention should be paid tothese locations.

(iv) (e numerical simulations for the 100,000m3 cy-lindrical oil-storage tank revealed that the prototypetank behaves well under major earthquakes when thehighest seismic risk (seismic precautionary intensity9) was considered according to the Chinese seismicdesign code. However, in order to further ensure thesafety of the tank, more conservative design phi-losophy needs to be implemented so that the tank canbehave elastically under major earthquakes, andspecial attention should be paid at the locationswhere the thickness of the tank wall changed.

Data Availability

(e data used to support the findings of this study areavailable from the corresponding author upon request.

Disclosure

Any opinions, findings, conclusions, and recommendationsexpressed in this paper are those of the authors and do notnecessarily reflect the views of the sponsors.

Conflicts of Interest

(e authors declare that there are no conflicts of interestregarding the publication of this paper.

Acknowledgments

(e presented work was supported by grants from theNational Natural Science Foundation of China under Grantno. 50678056.

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0.0

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21.8

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0.2

0.4

0.6

0.8

1.0

–45 –30 –15 0 15 30 45 60 75 90

Hei

ght (

m)

β

Deformation (mm)

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

0.00 0.20 0.40 0.60 0.80 1.00

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Stress/yield strength

Hei

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

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Stress/yield strength

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ght (

m)

β

Stress (MPa)

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


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