Seismic Response_rc Tank

KSCE Journal of Civil Engineering (2012) 16(3):366-376DOI 10.1007/s12205-011-1104-1

366

www.springer.com/12205

Structural Engineering

Seismic Response Evaluation of the RC Elevated Water Tank withFluid-Structure Interaction and Earthquake Ensemble

F. Omidinasab* and H. Shakib**

Received January 9, 2010/Revised October 6, 2010/Accepted February 18, 2011

Abstract

In this paper, a reinforced concrete elevated water tank, with a capacity of 900 cubic meters and height of 32 meters, has beenutilized and subjected to an ensemble of earthquake records. Finite element model has been employed to model elevated water tanksystem. Fluid-structure interaction for modeling is considered by Eulerian method. Also the behaviors of concrete and steel materialwere considered to be nonlinear. Seismic responses of the elevated water tank such as base shear force, overturning moment,displacement and hydrodynamic pressure have been assessed for ensemble earthquake records. The obtained result revealed thatscattering of responses in range of the mean minus standard deviation and mean plus standard deviation are approximately 60 to 70percents. Also, responses of elevated water tank are dependent with earthquake characteristics and frequency of elevated water tank.The maximum response of base shear force, overturning moment, displacement and hydrodynamic pressure occurred in differentcase of vessel filling. Keywords: elevated water tank, seismic response, ensemble earthquake records

1. Introduction

Elevated liquid tanks and particularly the elevated water tanksare considered as an important city services in the many flatareas, and accordingly, their serviceability performance duringand after strong earthquakes is of crucial concern. The failure ofthese structures may cause some hazards for the health of thecitizens due to the shortage of water or difficulty in putting outfire during the earthquake golden time. Although many studieshave been investigated on analysis and design of ground watertanks in the past decade, only a few studies have been conductedon the elevated water tanks. During the recent earthquakes,elevated tanks did not exhibit favorable seismic performance andhave been suffered notable damage. Due to the failure of thislifeline element, the emergency services such as fire fighting havebeen delayed [e.g., 1960 Chile (Steinbrugge and Rodrigo, 1963),1978 Izu-Oshima and Miyagi (Minowa, 1980), 1971 San Fernando,and 1987 Whittier earthquakes (Knoy, 1995)]. Elevated watertanks are heavy structures in the sense that a greater portion oftheir weight is concentrated at an elevation much about its base.Critical parts of the system are the columns and braces throughwhich the loads are transmitted to the foundation and on theother hand, if the water storage of the system is cracked it willnot function properly. The physical nature of the system is so thatit is highly sensitive to the structural as well as the earthquake

loading characteristics.The effect of fluid interaction on the seismic response of water

tanks was the subject of many studies in the past years (Attariand Rofooei, 2008; Damatty et al., 2005; Sezen et al., 2008;Livaoglu and Dogangun, 2006; Livaoglu, 2005; Livaoglu andDogangun, 2007; Koh et al., 1998; Anghileri et al., 2005).However, most of them focused on the effect of fluid interactionon the cylindrical ground water tanks, but a small number ofthem have concentrated on the evaluation of effect of fluid interac-tion on the seismic response behavior of the elevated watertanks. Most of these studies used a simplified fluid interactionmodel (Housner, 1963; Housner, 1957; Westergaard, 1931; Bartonand Parker, 1987; Dogangun et al., 1966), however a few of themused the finite element method as well. Livaoglu and Dogangun(2006) proposed a simple analytical procedure for seismicanalysis of fluid-elevated tank-foundation-soil systems, and theyused this approximation in the selected tanks. Haroun andEllaithy (1985) developed a model considering fluid sloshingmodes and it assesses the effect of tank wall flexibility on theearthquake response of the elevated tanks. Marashi and Shakib(1997) carried out an ambient vibration test for the evaluation ofthe dynamic characteristics of elevated tanks. Resheidat andSunna (1986) investigated the behavior of a rectangular elevatedtank. They neglected the sloshing effects on the seismic behaviorof the elevated tanks. Haroun and Temraz (1992) analyzed

*Assistant Professor, Faculty Engineering Department, Khorramabad Branch, Islamic Azad University, Khorramabad, Lorestan 6818615865, Iran (Corre-sponding Author, E-mail: [email protected])

**Professor, Civil Engineering Department, Tarbiat Modares University, Tehran 14115-111, Iran (E-mail: [email protected])

Seismic Response Evaluation of the RC Elevated Water Tank with Fluid-Structure Interaction and Earthquake Ensemble

Vol. 16, No. 3 / March 2012 367

models of two-dimensional x-braced elevated tanks supportedon the isolated footings to investigate the effects of dynamicinteraction between the tower and the supporting soil-foundationsystem. They also neglected the sloshing effects. Livaoglu andDogangun (Livaoglu, 2005; Livaoglu and Dogangun, 2007) con-ducted a comparative study of seismic behavior of the elevatedtanks considered fluid-structure-soil on elevated tanks.

Due to the high sensitivity of the elevated water tanks to theearthquake characteristics such as frequency contents, peakground acceleration and the effective duration of the earthquakerecords, it seems necessary to consider the earthquake loading asa non-stationary random process. A number of the authors haveinvestigated the different view point on steel and reinforced con-crete elevated water tanks by using a single earthquake record(Attari and Rofooei, 2008; Sezen et al., 2008; Livaoglu andDogangun, 2007; Shrimali and Jangid, 2003; Dutta et al., 2001;Shekari et al., 2008). However, a few number of the researcherssuch as Livaoglu (2005) considered two earthquake records forground rectangular tank and also Panchal and Jangid (2008)considered six earthquake records in their investigation on theseismic behavior of the steel elevated water tanks.

The nonlinear behavior of reinforced concrete elevated watertanks supported on frame type staging is studied by Dutta et al.(2001). They observed the effect of strength deterioration of thereinforced concrete members of the tank staging under cyclicloading. Dutta et al. (2001) also investigated how the inelastictorsional behavior of the tank system with accidental eccentricityvaries with increasing number of panels. Dutta et al. (2000a,2000b) studied the supporting system of elevated tanks withreduced torsional vulnerability and they suggested approximateempirical equations for the lateral, horizontal and torsionalstiffness for different frame supporting systems. Omidinasab andShakib (2008) had been studied a reinforced concrete elevatedwater tank under an ensemble of earthquake records using per-formance based-design method, and the obtained results reveal-ed the vulnerability of tanks designed in accordance with currentcodes.

According to the literature review, it has been realized that alimited number of studies have been carried out on the fluid-structure interaction and nonlinear behavior of elevated watertanks considering the effect of earthquake characteristics. Due tothe uncertainty of the earthquake loading and some importantphenomena such as fluid-structure interaction and the nonline-arity effects on the system response, this study has been made.This research is aimed at evaluating the effects of fluid-structureinteraction and concrete nonlinear behavior of the elevated watertanks subjected to an ensemble of earthquake records.

2. Description of the Elevated Tank

Reinforced concrete elevated tank with different elevation ofsupport systems have been employed in this study. These elevatedtank is placed on framed structure have capacity of 900 cubicmeters and height of 32 m. Detail of tank is shown in Figs. 1 and

2. Since the tank vessel is Intze, hence, there is a symmetric inthe loading and shape of the vessel. It should be noted that thestaging and vessel is designed according to the latest standardsand codes. Also, detail specifications of these tank and mechani-cal properties considered for the steel, concrete and water areprovided in Table 1.

3. Modeling of Elevated Water Tank

Finite element model has been employed to model elevatedwater tank system. The behavior of concrete material was consi-dered to be nonlinear. Also the tank fluid and staging system aremodeled as finite element. More details are as follows.

3.1. Fluid-Structure System ModelingAs shown in Fig. 3, columns and beams in the support system

were modeled as beam elements (with three nodes and with sixdegrees-of-freedom per node). There is likely that the potentialof forming plastic joint in each point of the element. In order to

Fig. 1. Details and Elevation of the Tank

Fig. 2. (a) Arrangement of the Columns and Beams under theTank Container, (b) Arrangement of the Columns and Beamson the First Storey

F. Omidinasab and H. Shakib

368 KSCE Journal of Civil Engineering

ensure the probability of plastic hinge formation in the middle ofbeam, each beam and column of the staging was modeled withthree elements. In addition, the truncated cone and containerwalls were modeled with triangle and quadrilateral shell elements(with three and four nodes and six degrees-of-freedom per node).Water was modeled with acoustic cubic elements (with eightnodes and three degrees-of-freedom per node).

Fluid-structure interaction problems can be investigated byusing different techniques such as Added Mass (AM) (Housner,

1957, 1963; Westergaard, 1931; Barton and Parker, 1987; Dogangunet al., 1966), Lagrangian (LM) (Zienkiewicz and Bettes, 1978),Eulerian (EM) (Wilson and Khalvati, 1983; Olson and Bathe,1983; Dogangun et al., 1996b; Dogangun and Livaoglu, 2004),and Lagrangian-Eulerian (L-E M) (Donea et al., 1982) approachesin the Finite Element Method (FEM) or by the analytical methodslike Housners two-mass (Housner, 1963) representation ormulti-mass representations of Bauer (Bauer, 1964) and EC-8(Eurocode-8, 2001). In this study, displacement based Lagrangianapproach was used to model the fluid-elevated tank interaction.The fluid elements were defined by eight nodes with threetranslational degrees-of-freedom at each node. It should be notedthat, due to the lack of a geometrical capability in the LagrangianFEM with brick shaped elements considered here, Intze-typewas idealized as a cylindrical vessel that has the same capacitywith the Intze type. Each brick fluid element includes specialsurface effects, which may be thought of as gravity springs usedto hold the surface in place. This was performed by addingsprings to each node, with the spring constants being positive onthe top of the element. For an interior node, the positive andnegative effects were canceled out. The positive spring stiffnesscan be expressed as (Livaoglu and Dogangun, 2007):

(1)

Where is the mass density, Af is the area of the face of theelement, gi and Ci are acceleration in the i direction and ithcomponent of the normal to the face of the element, respectively.Expressions for mass (Mf) and rigidity matrices (Kf) of fluid aregiven below (Livaoglu and Dogangun, 2007):

(2)

(3)

Where, J is the Jacobian matrix, Qijk is the interpolation func-tion, i, j, k are the weight functions, and B is the strain-dis-placement matrix obtained from =Bu, where kinetic (T) andpotential energy equations (U) can be written as (Livaoglu andDogangun, 2007):

(4)

(5)

If the expressions for the kinetic and potential energies aresubstituted into Lagrange equation, then:

(6)

Where uj is the jth displacement component and Fj is the appliedexternal load. Then the governing equation can be written as:

(7)

Where, is the acceleration and R is a general time varying load

Ks Af gxCx gyCy gzCz+ +( )=

Mf QTv QdV ijkQijkT QijkJijk

k

j

i= =

Kf BTv EBdV ijkBijkT EBijkdetJijk

k

j

i= =

U U 12---uTKfu= =

T 12---vTMf v=

ddt---- Tu j------- T

uj-------Uuj-------+ Fj=

Mf u Kf Ks+( )u+ R=u

Table 1. Tank and Material Properties

Tank vessel property Tanks staging property

Parameter Dimensions(m) Parameter Dimensions

(m)Vessel volume 900 m3 Columns dimensions 1.20 1.20Inner diameter 12 Columns height 7+7+6 = 20

Height 10.6 Staging inner diameter in top 8.60

Top Ring Beam 0.6 0.6 Staging inner diameter in bottom 12.75

Bottom Ring Beam 0.8 0.6 Beams dimensions in first floor 1.20 0.60

Roof thickness 0.20 Beams dimension in second floor 1.20 0.60

Vessel thickness 0.40 Beams dimension in third floor 1.20 1.0

Bottom slab thickness 0.50Material property

ConcreteE (MPa) 2.6 10 4

fc ' (MPa) 30Weight of volume unit (KN/m3) 25

SteelE (MPa) 2.1 10 5

fy (MPa) 240Weight of volume unit (KN/m3) 78.5

WaterDensity (KN/m3) 10Bulk module (GPa) 2.10

Fig. 3. Finite Element Model of the Fluid-Elevated Tank System


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vector.Figure 4 shows modeling of vessel in different cases of tank

fullness percent and Fig. 5 shows the final model of tank withstaging for different levels of fluid.

3.2 Modeling of the Materials Nonlinear BehaviorConcrete is a material whose tension and compression behavior

have significant difference. Many researchers have attempted topresent a mathematical model of this type of material on thebasis of experimental results and, as such, different models havebeen proposed. In this study, Park and Kent model is considered(ABAQUS / Standard Users Manual, Ver. 6.7-1, 2008). Kentand Park (Park, Kent and Sampton, 1972) proposed a model inwhich a mathematical relation on the stress-strain behavior ofconcrete was considered. This model was later developed byScott et al. in 1982 (Scott et al., 1982) and employed by manyresearchers in the bending frames (Scott et al,, 1982; Kwak andFilippou, 1990). In this paper, the values of uniaxial compressivestress (fc'), modulus of elasticity (EC) and Poissons ratio () wereassumed to be equal 300 kg/cm2, 26.15 GPa and = 0.20,respectively. Therefore, the stress-strain curves of concrete forconfinement and non-confinement cases were obtained andillustrated in Fig. 6. In this figure, uniaxial compressive yieldstress and the tensile yield stress versus strain is plotted. Also, thefigure describing the evolution of the tensile yield stress versusthe strain is shown. The plastic strain associated with a total lossof load-carrying capacity of the material in tension was about0.0035. An elasto-perfectly plastic constitutive law by Von-

Mises was assumed to model the reinforcement behavior withES = 210 GPa, = 0.3 and fyd = 387 (yield stress) respectively.Bond-slip between concrete and reinforcement is neglected.Rayleigh damping was used in the analyses. For columns, theconcrete confinement model and for the beams and shells, theun-confinement concrete model was used.

4. Ground Motions

To evaluate the dynamic response of the elevated tanks, threecases of empty, half-full, and full filling levels were considered.The time history analyses were carried out by using the above-mentioned system and equations. For performing nonlinear timehistory analysis, the tank was assumed to be located in soil typeC according to UBC-97 soil category. An ensemble of earthquakerecords that contains seven pairs of earthquake records was usedto investigate the response behavior of the system. The specifi-cations of each record are shown in Table 2. In order to scale therecords, the UBC-97 procedures was used and scaled on thebasis of the structures period between 0.2 T and 1.5 T; where Tis the fundamental period of the structure. The original andscaled spectra of horizontal components of Landers earthquakeare shown as an example in the Fig. 7. As it is shown in Table 2,the maximum PGA and PGV values of the selected earthquakerecords are related to Duzce ground motion and are equal to 822cm/s2 and 62.1 cm/s, respectively.

5. Free Vibration Analysis

To define the dynamic characteristics of the elevated watertank and determine the seismic behavior of the system, first, freevibration analysis has been carried out. The dynamic characteris-tics of tank including period and the effective modal mass ratioare shown in Table 3. The table shows sum of the first eightmodes covers more than 90% of the total mass of the system. Forexample, the main modes in full case for tank is shown in Fig. 8.By this analysis, sum of the structures first eight modespartnership is more than 90%. The first and second modes arerelated to convective and third to eighth modes associated withthe structures modes.

Fig. 4. Modeling of the Tank Vessels in Finite Element Software:(a) Empty Case, (b) Half-Full Case, (c) Full Case

Fig. 5. Modeling of the Tank in Finite Element Software (ABAQUS/Standard Users Manual, Ver. 6.7-1, 2008)

Fig. 6. Concrete Strain-Stress Curves in the Obtained Strain andStress Behaviors Based on Kent and Park Relation



6. Seismic Response Evaluation

In this study, nonlinear time history analysis was used to deter-mine seismic behavior of the elevated water tank. It was assumedthat earthquake acceleration is simultaneously applied to the tank

in two perpendicular horizontal directions. The system wasexamined in three cases, i.e., empty, half-full and full filling tank.The results are discussed in the following paragraphs.

Table 4 shows the maximum responses of the system for theabove-mentioned cases. These responses include base shear, over-turning moment, bottom slab displacement and hydrodynamicpressure of the system. The maximum response is determined fordifferent parameters of the elevated water tank subjected toseven pair of the acceleration earthquake records.

Table 2. Details of Ground Motions Selected for the Study

Number Record Year Component Station PGA (g)PGV

(cm/s)PGD (cm)

Duration (sec)

Closest to fault rupture (Km) M

1 Duzce, Turkey 1999BOL - 00 Bolu 0.728 56.4 23.07 55.90 17.60 7.1BOL - 90 Bolu 0.822 62.1 13.55 55.90 17.60 7.1

2 Landers 1992YER - 270 Yermo Fire 0.245 51.5 43.81 44.98 24.90 7.3YER - 360 Yermo Fire 0.152 29.7 24.69 44.98 24.90 7.3

3 Loma Prieta 1989G04 - 00 Gilroy Array #4 0.417 38.8 7.09 40.95 16.10 6.9G04 - 90 Gilroy Array #4 0.212 37.9 10.08 40.95 16.10 6.9

4 Morgan Hill 1984G02 - 00 Gilroy Array #2 0.162 5.1 1.42 30.98 15.10 6.2G02 - 90 Gilroy Array #2 0.212 12.6 2.1 30.98 15.10 6.2

5 Northridge 1994CNP - 106 Canoga Park -Topanga Can 0.356 32.1 9.13 25.98 15.80 6.7CNP - 196 Canoga Park -Topanga Can 0.420 60.8 20.17 25.98 15.80 6.7

6 Superstitn Hills 1987B-CAL - 225 Calipatria Fire 0.18 15.5 3.3 23.24 28.30 6.7B-CAL - 315 Calipatria Fire 0.247 14.6 3.1 23.24 28.30 6.7

7 Whittier Narrows 1987A-CAS - 00 Compton - Castlegate Street 0.332 27.1 5.04 32.16 16.90 6.0A-CAS - 270 Compton - Castlegate Street 0.333 14.1 1.48 32.16 16.90 6.0

Fig. 7. Response Spectra of Landers Earthquake Horizontal Com-ponents in 5% Damping, Scaling and UBC Spectrum

Fig. 8. Mode Shapes of Elevated Water Tank in the Full Case

Table 3. Period and Modal Partnership Mass Ratio of Tank

ModeNo.

Full Case Half-Full Case Empty CaseT (sec) UX UY RZ T (sec) UX UY RZ T (sec) UX UY RZ

1 3.678 0.043 0.040 0.000 4.035 0.022 0.057 0.000 2 3.678 0.040 0.043 0.000 4.035 0.057 0.022 0.000 3 1.016 0.338 0.504 0.000 0.941 0.346 0.492 0.000 0.908 0.391 0.515 0.0004 1.015 0.504 0.339 0.000 0.940 0.492 0.346 0.000 0.907 0.515 0.391 0.0005 0.715 0.000 0.000 0.862 0.714 0.000 0.000 0.862 0.713 0.000 0.000 0.8626 0.196 0.021 0.006 0.000 0.190 0.026 0.007 0.000 0.192 0.024 0.008 0.0007 0.195 0.007 0.022 0.000 0.189 0.008 0.027 0.000 0.191 0.009 0.026 0.0008 0.156 0.000 0.000 0.115 0.156 0.000 0.000 0.115 0.156 0.000 0.000 0.115

Sum 0.953 0.954 0.977 0.951 0.951 0.977 0.939 0.94 0.977 First and second modes in full and half-full mode are related to convective modes.


Vol. 16, No. 3 / March 2012 371

7. Effects of the Frequency Content

The effects of frequency content of the earthquake records areinvestigated on the system responses. Fig. 9 shows the Fourieramplitude versus frequency for longitudinal and transverse earth-quake records of Duzce. In order to shows the systems the rangeof the frequency content, the natural frequencies of empty andfull cases of the elevated water tank are also presented. The resultsshowed that the frequency content of the Duzce earthquake was

high within the frequency range of natural system, causingresonance in the responses. While, for Morgan Hill earthquakerecord, due to the low amplitude of the frequency content withinthe frequency range of natural system, the responses wereconsiderably reduced (Fig. 10).

8. Dispersion of the Seismic Response of Tankfor the Earthquake Records

The tank seismic responses including base shear force, over-turning moment, slab displacement and hydrodynamic pressureof the system subjected to seven pair of earthquake records havebeen investigated. In order to show the despersion of the results,mean plus standard deviation and mean minus standard deviationof the responses are calculated. Therefore, mean, mean plusstandard deviation and mean minus standard deviation of theresponses calculated. Also, maximum and minimum values of theresponses are shown in the Figs. 11-14.

8.1 Base ShearTime histories of base shear in full and half-full cases for

Duzce and Morgan Hill earthquake records are shown in Figs. 11and 12 respectively. Also, responses of base shear forces versus

Fig. 9. Frequency Content of Duzce Record and FrequencyDomain of the Tank in Full, Half Full and Empty Cases

Fig. 10. Frequency Content of Morgan Hill Record and FrequencyDomain of the Tank in Full, Half Full and Empty Cases

Table 4. Results of Evaluation of Seismic Demand of Tanks

Number RecordBase Shear (KN) Overt. Moment (KN.m) Slab Displa. (cm) Hydr. Pressure (KPa)

Hwater/Hvessel Hwater/Hvessel Hwater/Hvessel Hwater/Hvessel1.0 0.5 0.0 1.0 0.5 0.0 1.0 0.5 0.0 1.0 0.5 0.0

1 Duzce 6627 5602 1770 28065 60984 14315 39.41 27.51 20.38 24.27 22.93 0.002 Landers 5548 5511 1822 28910 49413 13850 33.14 27.47 19.87 22.63 21.16 0.003 Loma Prieta 3570 4349 2755 26797 18764 21299 23.32 29.04 23.61 12.61 11.94 0.004 Morgan Hill 1471 2168 830 15681 10633 7681 14.05 9.67 9.31 7.01 6.39 0.005 Northridge 2581 4655 1498 26797 30648 12104 19.72 23.00 14.80 11.18 8.65 0.006 Superstitn Hills 4010 4009 2511 19020 51289 14548 22.63 19.54 22.46 17.50 16.51 0.007 Whittier Narrows 5132 4506 2253 31108 50038 23743 27.84 22.09 21.55 15.74 14.05 0.00

Average - Standard Deviation 2352 3253 1267 19558 19902 9899 17.23 15.96 13.79 9.66 8.38 0.00Average 4134 4401 1920 25197 38824 15363 25.73 22.62 18.85 15.85 14.52 0.00

Average + Standard Deviation 5916 5547 2573 30835 57746 20827 34.24 29.28 23.92 22.04 20.66 0.00Hwater : Water height in vessel; Hvessel : Vessel height

Fig. 11. Time History of Base Shear in Full Case for Duzce Earth-quake Record



the percentage of the storage tank filling are presented forensemble earthquake records in the Fig. 13. The variation of themaximum, minimum, mean and one plus and one minus standarddeviation values of base shear forces versus the percentage of thestorage tank filling are presented in the Fig. 14 for the system. Asit can be seen clearly, in the event of empty storage tank, disper-sion of base shear is small. The dispersion is increased when thepercentage of the filling in the storage tank are increased. Theincreased dispersion is not linear with the amount of the fillingpercentage. This increase mainly depends to the system charac-teristics. According to Figs. 13 and 14, the maximum dispersionoccurs for the case when the storage tank is half-full filling.

However, as it can be seen from the Figs. 13 and 14, the maxi-mum dispersion is happened when the storage tank are full. It isof interest to mention that dynamic characteristics of the systemand hydrodynamic effects are considerably affecting the amountof base shear forces.

8.2 Overturning MomentTime histories of overturning moment in half-full and empty

cases for Northridge and Loma Prieta earthquake records are shownin Figs. 15 and 16 respectively. Also, responses of overturningmoment versus the percentage of the storage tank filling arepresented for ensemble earthquake records in the Fig. 17. The

Fig. 12. Time History of Base Shear in Half-Full Case for MorganHill Earthquake Record

Fig. 13. Responses of Base Shear Based on Fullness PercentTank for Ensemble Earthquake Records

Fig. 14. The Variation Distribution of Base Shear Based on Full-ness Percent Tank

Fig. 15. Time History of Overturning Moment in Half-Full Case forNorthridge Earthquake Record

Fig. 16. Time History of Overturning Moment in Empty Case forLoma Prieta Earthquake Record

Fig. 17. Responses of Overturning Moment Based on FullnessPercent Tank for Ensemble Earthquake Records


Vol. 16, No. 3 / March 2012 373

variation of the maximum, minimum, mean and one plus andone minus standard deviation values of overturning momentversus the percentage of the storage tank filling are presented inthe Fig. 18 for the system. The dispersion of overturning momentis small for the systems when the storage tank is empty case aswell as full case. The maximum dispersion was related to thehalf-full storage tank. The pattern of overturning moment variationis almost same for the systems with different characteristics.However, it should be noted that fluid-structure interaction con-siderably influence the dispersion when the tank are half-full.

8.3 DisplacementTime histories of displacement in full and half-full cases for

Whittier Narrows and Landers earthquake records are shown inFigs. 19 and 20 respectively. Also, responses of displacement versusthe percentage of the storage tank filling are presented for ensembleearthquake records in the Fig. 21. The variation dispersion of slabdisplacement versus the percentage of the filling is shown in theFig. 22 for the system. As it can be seen, dispersion increaseslinearly with the increase in the percentage of the filling. How-ever, Figs. 21 and 22 show that maximum dispersion occurred inthe full storage tank.

8.4 Hydrodynamic Pressure Time histories of hydrodynamic pressure in half-full case for

Whittier Narrows and Landers earthquake records are shown in

Figs. 23 and 24 respectively. Also, distribution of hydrodynamicpressure vessel in full case for Landers and Superstitn Hillsearthquakes are shown in Figs. 25 and 26 respectively. Responsesof hydrodynamic pressure versus the percentage of the storagetank filling are presented for ensemble earthquake records in theFig. 27. The variation of hydrodynamic pressure versus the per-centage of the storage tank filling is presented in the Fig. 28 forthe system. The dispersion increases linearly as the percentage ofthe filling in the storage tank increases. However, as it can beseen from the Fig. 28 the maximum dispersion is happened whenthe storage tank is full.

The above figures show that the major system responses suchas base shear, overturning moment, slab displacement and hydro-

Fig. 18. The Variation Distribution of Overturning Moment based onFullness Percent Tank

Fig. 19. Time History of Roof Displacement in Full Case for WhittierNarrows Earthquake Record

Fig. 20. Time History of Roof Displacement in Half-Full Case forLanders Earthquake Record

Fig. 21. Responses of Displacement Based on Fullness PercentTank for Ensemble Earthquake Records

Fig. 22. The Variation Distribution of Displacement Based on Full-ness Percent Tank



Fig. 23. Time History of Hydrodynamic Pressure in Half-Full Casefor Loma Prieta Earthquake Record

Fig. 24. Time History of Hydrodynamic Pressure in Half-Full Casefor Duzce Earthquake Record

Fig. 25. Distribution of Hydrodynamic Pressure Vessel in Full Casefor Landers Earthquake (t=18 sec)

Fig. 26. Distribution of Hydrodynamic Pressure Vessel in Full Casefor Superstitn Hills Earthquake (t=15.56, 15.84 sec)

Fig. 27. Responses of Hydrodynamic Pressure Based on FullnessPercent Tank for Ensemble Earthquake Records

Fig. 28. The Variation Distribution of Hydrodynamic Pressurebased on Fullness Percent Tank


Vol. 16, No. 3 / March 2012 375

dynamic pressure are highly scattered. The maximum of scatter-ing for base shear, overturning moment, slab displacement andhydrodynamic pressure are about 4.5, 5.7, 4.6, and 4 respectively.This shows that the system is vastly influenced by the character-istics of the earthquake records. For the design of such systemone, should not be considered as an ergodic random process andthe earthquake records must be considered as the non-stationaryrandom process.

9. Conclusions

In this paper, elevated water tank supported by moment resist-ing frame was considered and subjected to seven pair of theselected earthquake records. The seismic responses of the elevat-ed water tank were determined using the nonlinear time historyanalysis for the empty, half-full and full filling containers. Thefollowing conclusions are drawn from the results of this study:1. The maximum response does not always occur in the full tank.

This result may be due to the fact that the hydrodynamic pres-sures of container in half-full case compared with the full fill-ing case are higher. In addition, it can be also assigned to theeffect of the frequency content of earthquake records.

2. The system predominant frequencies are located on the rangeof high amplitude of frequency content of some of the selectedearthquake records and causes amplification of responses.However, in the other earthquake records, this phenomenon isnot visible as the system frequencies predominant are locatedon the low amplitude range of frequency content.

3. Scattering of the mean plus and minus standard deviation cov-ers approximately 60 to 70 percents of the responses.

4. The increase in the percentage of container filling shows thatthe value of base shear force, overturning moments, displace-ment and hydrodynamic pressure increase in the range ofmean plus and minus standard deviation.

5. Evaluation of the convective pressure revealed that the earth-quake records with low predominant frequency causes excita-tion in the oscillating modes with relatively high period andconsequently result in high hydrodynamic pressure at fluidfree surface. Excitation in the impulsive modes causesincrease in hydrodynamic pressure at low levels and the bot-tom of the tank for records with higher predominant fre-quency.

6. Examination of maximum hydrodynamic pressure resultingfrom the convective and impulsive modes showed that themaximum pressure occurs at the lower levels of water freesurface. Since impulsive pressure is dominant in these levels,maximum pressure occurs at the bottom of full tank.

References

ABAQUS (2008). Standard users manual, Ver. 6.7-1.Anghileri, M., Castelletti, L. M. L., and Tireli, M. (2005). Fluid-struc-

ture interaction of water filled tanks during the impact with theground. International Journal Impact Engineering, Vol. 31, No. 3,

pp. 235-254.Attari, N. K. A. and Rofooei, F. R. (2008). On lateral response of

structures containing a cylindrical liquid tank under the effect offluid/structure resonances. Journal of Sound and Vibration, Vol.318, Nos. 4-5, pp. 1154-1179.

Barton, D. C. and Parker, J. V. (1987). Finite element analysis of theseismic response of anchored and unanchored liquid storage tanks.Earthquake Engineering and Structural Dynamics, Vol. 15, pp. 299-322.

Bauer, H. F. (1964). Fluid oscillations in the containers of a spacevehicle and their influence upon stability. NASA TR R 187.

Dogangun, A., Durmus, A., and Ayvaz, Y. (1966a). Finite elementanalysis of seismic response of rectangular tanks using added massand Lagrangian approach. Proceedings of the Second InternationalConference on Civil Engineering Computer Applications Researchand Practice, Bahrain, April 6-8, Vol. I, pp. 371-379.

Dogangun, A., Durmus, A., and Ayvaz, Y. (1996b). Static and dynamicanalysis of rectangular tanks by using the Lagrangian fluid finiteelement. Computers & Structures, Vol. 59, No. 3, pp. 547-552.

Dogangun, A. and Livaoglu, R. (2004). Hydrodynamic pressures actingon the walls of rectangular fluid containers. Structural Engineeringand Mechanics, Vol. 17, No. 2, pp. 203-214.

Donea, J., Gluliani, S., and Halleux, J. P. (1982). An arbitrary Lagran-gian-Eulerian finite element method for transient dynamic fluid-structure interaction. Computer Methods in Applied Mechanics andEngineering, Vol. 33, Nos. 1-3, pp. 689-723.

Dutta, S. C., Jain, S. K., and Murty, C. V. R. (2000a). Alternate tankstaging configurations with reduced torsional vulnerability. SoilDynamics and Earthquake Engineering, Vol. 19, No. 3, pp. 199-215.

Dutta, S. C., Jain, S. K., and Murty, C. V. R. (2000b). Assessing theseismic torsional vulnerability of elevated tanks with RC frame-typeStaging, Soil Dynamics and Earthquake Engineering, Vol. 19, No.3, pp. 183-197.

Dutta, S. C., Jain, S. K., and Murty, C. V. R. (2001). Inelastic seismictorsional behavior of elevated tanks. Journal of Sound andVibration , Vol. 242, No. 1, pp. 151-167.

El Damatty, A. A., Saafan, M. S., and Sweedan, A. M. I. (2005). Ex-perimental study conducted on a liquid-filled combined conical tankmodel. Thin-Walled Structures, Vol. 43, Issue 9, pp. 1398-1417.

European Committee for Standardization (2001). Eurocode-8, and part4: Silos, tanks and pipelines, Final PT.

Haroun, M. A. and Ellaithy, M. H. (1985). Seismically induced fluidforces on elevated tanks. Journal of Tech. Top Civil Engineering,Vol. 111, No. 3, pp. 1-15.

Haroun, M. A. and Termaz, M. K. (1992). Effects of soil-structureinteraction effects on seismic response of elevated tanks. SoilDynamics Earthquake Engineering, Vol. 11, No. 2, pp. 37-86.

Housner, G. W. (1957). Dynamic pressures on accelerated fluid con-tainers. Bulletin Seismology Society American, Vol. 47, No. 1, pp.15-35.

Housner, G. W. (1963). Dynamic behavior of water tanks. BulletinSeismology Society American, Vol. 53, No. 2, pp. 381-387.

Knoy, C. E. (1995). Performance of elevated tanks during recentCalifornia seismic events. AWWA Annual Conference & Exhibi-tion.

Koh, H. M., Kim, J. K., and Park, J. H. (1998). Fluid-structure inter-action analysis of 3-D rectangular tanks by a variationally coupledBEM-FEM and comparison with test results. Earthquake Engi-neering Structutre Dynamic, Vol. 27, No. 3, pp. 109-124.

Kwak, H. G. and Filippou, F. C. (1990). Finite element analysis of



reinforced concrete structures under monotonic loads, ReportNo.UCB/SEMM-90/14, University of California, Berkeley (CA).

Livaoglu, R. (2005). Investigation of the earthquake behavior ofelevated tanks considering fluid-structure-soil interactions, PhDThesis, Karadeniz Technical University, Trabzon (in Turkish).

Livaoglu, R. and Dogangun, A. (2006). Simplified seismic analysisprocedures for elevated tanks considering fluid-structure-soil inter-action. Journal of Fluids Structure, Vol. 22, No. 3, pp. 421-439.

Livaoglu, R. and Dogangun, A. (2007). Effect of foundation embed-ment on seismic behavior of elevated tanks considering fluid-struc-ture-soil interaction. Soil Dynamics and Earthquake Engineering,Vol. 27, No. 9, pp. 855-863.

Marashi, E. S. and Shakib, H. (1997). Evaluations of dynamic charac-teristics of elevated water tanks by ambient vibration tests. Pro-ceedings of the 4th International Conference on Civil Engineering,Tehran, Iran, Vol. I, pp. 367-373.

Minowa, C. (1980). Dynamic analysis for rectangular water tanks.Recent Adv. Lifeline Earthquake Engineering Japan, Vol. 12, No. 3,pp. 135-142.

Olson, L. G. and Bathe, K. J. (1983). A study of displacement-basedfluid finite elements for calculating frequencies of fluid and fluid-structure systems. Nuclear Engineering and Design, Vol. 76, No. 3,pp. 137-151.

Omidinasab, F. and Shakib, H. (2008). Seismic vulnerability ofelevated water tanks using performance based-design. The 14thWorld Conference on Earthquake Engineering, Beijing, China.

Panchal, V. R. and Jangid, R. S. (2008). Variable friction pendulumsystem for seismic isolation of liquid storage tanks. Nuclear Engi-neering and Design, Vol. 238, No. 6, pp. 1304-1315.

Park, R., Kent, D. C., and Sampton, R. A. (1972). Reinforced concrete

members with cyclic loading. Journal of the Structural Division,ASCE, Vol. 98, No. 4, pp. 1341-1360.

Reshidat, R. M. and Sunna, H. (1986). Behavior of elevated storagetanks during earthquake. Proceeding of the 3rd US National Conf-erence on Earthquake Engineering, pp. 2143-2154.

Scott, B. D., Park, R., and Priestley, M. J. N. (1982). Stress-strainbehavior of concrete confined by overlapping hoops at low and highstrain rates. ACI Strucural Journal, ACI, Vol. 79, No. 3, pp. 13-27.

Sezen, H., Livaoglu, R., and Dogangun, A. (2008). Dynamic analysisand seismic performance evaluation of above-ground liquid-con-taining tanks. Engineering Structures, Vol. 30, No. 3, pp. 749-803.

Shekari, M. R., Khaji, N., and Ahmadi, M. T. (2008). A coupled BE-FE study for evaluation of seismically isolated cylindrically liquidstorage tanks considering fluid-structure interaction. Journal ofFluids and Structures, doi: 10.1016/j.jfluidstructs.2008.07.005.

Shrimali, M. K. and Jangid, R. S. (2003). Earthquake response ofisolated elevated liquid storage steel tanks. Journal of Construc-tional Steel Research, Vol. 59, No. 10, pp. 1267-1288.

Steinbrugge, K. V. and Rodrigo, F. A. (1963). The Chilean earthquakesof May 1960: A structural engineering viewpoint. Bulletin SeismologyAmerican, Vol. 53, No. 2, pp. 225-307.

Westergaard, H. M. (1931). Water pressures on dams during earthquakes.Proceedings of the ASCE, Vol. 57.

Wilson, E. L. and Khalvati, M. (1983). Finite elements for the dynamicanalysis of fluid-solid systems. International Journal of NumericalMethods in Engineering, Vol. 21, No. 6, pp. 1657-1668.

Zienkiewicz, O. C. and Bettes P. (1978). Fluid-structure dynamic inter-action and wave forces an introduction to numerical treatment.International Journal of Numerical Methods in Engineering, Vol.13, No. 3, pp. 1-16.

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