Soil-Structure Interaction Effects on Dynamic Behavior of A Rectangular Water Tank Including Fluid-Structure Interaction T. Cakir Gümüşhane University, Turkey
R. Livaoglu Uludağ University, Turkey
ABSTRACT: A typical dynamic fluid-structure-soil interaction problem for liquid tanks involves a structure supported by an unbounded soil medium, storing fluid.. Dynamic loads have come to be forefront of attention due to a number of events that affected liquid structures all over the world, especially in case of exposure to strong ground motion. In this connection, a seismic evaluation is made of the response to horizontal ground shaking of a rectangular tank considering fluid-structure-soil interaction in this study. The soil foundation is modelled as an elasto-plastic medium with viscous boundary applied on the artificial boundary of soil to simulate the wave energy absorption. On the other hand, the fluid-structure interaction is considered using Lagrangian approach. The parameters varied include the properties of the soil/foundation medium, and four different soil conditions are considered in the analyses. The results show that soil/foundation interaction has major effects on seismic behaviour of rectangular tanks and should be considered in design process. Keywords: Soil-structure interaction, fluid-structure interaction, rectangular tank, viscous boundary
1. INTRODUCTION Liquid storage tanks in seismically active areas are likely to be subjected to dynamic loads that may cause them to deform beyond their safe design limits. Strong earthquakes such as Niigata in 1964, Parkfield in 1966, Coalinga in 1983, Northridge in 1994, and Kocaeli in 1999, some of which are reported by Rai (2002) and Sezen and Whittaker (2006), demonstrated the appropriateness of this statement: some fluid tanks were seen to suffer extensive damage. The widespread damage to liquid structures due to earthquakes may have a substantial impact on the economy of the region in terms of both direct and indirect losses. While direct losses may result from structural and non-structural damage, indirect losses can accrue from business interruption due to damage and loss of utilities (Sezen and Whittaker, 2006). Therefore, in order to consider the economics of design and also mitigation of damage due to strong earthquakes, knowing the seismic behaviour of fluid-tank-foundation/soil system is of great importance. Although plenty of research has been carried out concerning the dynamic behaviour of liquid tanks and a number of methods of varying degrees of accuracy, efficiency and sophistication have been developed for its evaluation, the dynamic response of rectangular water tanks is still among the issues to be well investigated. Most of the investigations carried out on rectangular tanks in the past are well known and summarized in various studies (Dogangun et al., 1997; Livaoglu, 2008; Ghaemmaghami and Kianoush, 2010; Kianoush and Ghaemmaghami, 2011; Cakir and Livaoglu, 2012), and need not be repeated herein. On the other hand, some of the analytical, numerical and experimental works carried out in recent years related to rectangular tanks will be briefly summarized in the ensuing to reflect the current state-of-technology. Ghaemmaghami and Kianoush (2010) investigated the wall flexibility and fluid-structure interaction (FSI) effects on seismic behaviour of rectangular tanks, and concluded that the wall flexibility and fluid damping properties have a major effect on behaviour. Jeong (2011) developed an analytical method based on the Rayleigh-Ritz approach for calculating natural frequencies of rectangular tanks, and 1
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ment with finnite elementt analysis reesults. Livaogglu et al. verified the method by observinng an agreem b interraction effectts on seismicc behavior off rectangularr tanks by peerforming (2011) innvestigated backfill parametrric analysess. Kianoush and Ghaem mmaghami (2011) exam mined the effect e of eaarthquake frequenccy content on n dynamic behaviour b of rectangular tanks, and stated that the behaviour is highly sensitivee to frequenccy characteristics of the earthquake e rrecord. Cakirr and Livaogglu (2012) prroposed a simplifieed analyticall method forr seismic an nalysis of recctangular tan nks. Furtherm more, more recently, effects oof liquid slosshing in rectaangular tanks were invesstigated by Ansari A et al. (2011), ( Gouddarzi and Sabbaghh-Yazdi (2012) and Chernn et al. (2012 2). m the literaturre that even though t a few w investigatioons were carriied out on rectangular It is clearrly seen from tanks, liimited researrch has beenn done on the t effects of o soil-structture interactiion (SSI) onn seismic responsee of them. This T observaation providded the initial motivatioon for the herein-reporte h ed work. Accordinngly, two maain purposes have been selected s for this t paper. One of them is to present details of the probllem and finitte element model m (FEM) of fluid-recttangular tankk system, and d to verify thee validity of FEM under fixedd-base assum mption throug gh the propoosed analyticcal model. The other is to t further mic behaviorr of the recctangular tannk considerin ng the effeccts of soil/fooundation investigaate the seism interactioon.
TER STORA AGE TANK UNDER IN NVESTIGAT TION 2. WAT i investigateed in this A reinfoorced concrette rectangulaar tank withh a containerr capacity off 10000 m3 is study. T The tank hass two main divisions. d Based on the in-situ inveestigations of o the authorrs, it was determinned that thee roof of thhe tank was constructedd as a two-w way beam slab s supportted by 6 m-height-slender collumns which have 0.3 m x 0.3 m plan geometry, annd the roof slab had a thickness of Furthermore, the depth of water within w the coontainer wass measured as a 2.8 m. The T other 0.3 m. F geometriical characteeristics are shhown in Fig. 2.1. Moreovver, the Younng’s moduluss, Poisson’s ratio, r and unit weigght of the co oncrete were considered as 30000 MP Pa, 0.2 and 25 2 kN/m3, reespectively. There T are several pparts in a recctangular tankk since thesee structures were w constru ucted as segm mental in practice. So, each parrt of the struccture is subjeected to diffeerent loads, and a exhibits different beh haviors. In thhis study, only the exterior wall of the rectangular tank which w interaccts with both h the soil and the fluid wass tackled.
Figuree 2.1. Geometrrical propertiees of rectangu ular tank
3. FEM OF THE SY YSTEM AN ND ANALYT TICAL VER RIFICATIO ON m the fluiid-rectangulaar tank systeem and to The ANSYS (2006) finite elemeent program is used to model s The FEM F of the system is sh hown in Fig. 3.1. The obtain thhe frequenciees of modes and mode shapes. system iss considered to be fixed at a the base. Th he rectangulaar tank is discretized by solid s elementts defined by eightt nodes haviing three traanslational deegrees of freeedom in eaach node, annd the roof system s is assumedd as additionaal mass whicch is modeleed with quaddrilateral shelll element lo ocated on topp of wall. The fluidd elements are a also definned by eight nodes with three t translattional degreees of freedom m at each node. FS SI is taken into i accountt by using Lagrangian L a approach so that fluid ellements are specially formulatted to model fluid withinn container haaving no net flow rate.
Figure 3.1. 3 The FEM of the fluid-reectangular tannk system
Fig. 3.2 shows the mode m shapes of the FEM M with fixed base b assumpption. Only th he first two vibration modes, w which have the ability too represent almost a all syystem behav viour based on o mass partticipation ratios or effective mo odal masses, were taken into considerration.
Figure 3..2. The mode shapes and freequencies of the t system
The use of analyticaal models seeems to set a reverse r trendd. Simplified d analytical procedures p reelying on carefullyy chosen app proximations, in fact, cannnot be renouunced to undderstand the complex c behhaviour of structurees. Thus, a siimplified moodel is introdduced in Fig. 3.3 to demo onstrate the accuracy a of the t FEM. Housnerr’s two-mass representatioon (Housnerr, 1963) is useed to model fluid-wall in nteraction in this t study since it has h been com mmonly prefeered in the litterature and//or recommended by currrent major eaarthquake codes. Housner’s H sim mplified anallysis proceduure takes intoo account the fluid which h is separateed into an impulsivve mass mi thhat is rigidly connected c with the tank w walls and a convective mass mc that iss attached to the walls using stiiffness of sprring (kc). Thhe heights off the convectiive mass (hc) and impulssive mass m m1 consiists of the (hi), depeending on deepth of the fluuid h, are alsoo provided by Housner (11963). The mass summatiion of impulsive mass (m mi), mass of wall w (mw) annd effective mass m of the roof r (mr) which is the correspoonding part of o the roof mass m acting onn the exteriorr wall of the rectangular tank except for those carried by b columns and a the interrior wall. Thhe mass m2 iss directly eq qual to conveective mass (m ( c). The 3 lateral sttiffness of thee exterior waall, k1, can reaadily be deterrmined as k1=12EI = oof slab is ort /Hw since the ro rigid. Thhe stiffness k2 is directly equal e to convvective stiffneess (kc). The modal propeerties such as effective
modal m masses ( M 1* , M 2* ), heightts ( h1* , h2* ) annd stiffnessees ( k1* , k 2* ) caan be determ mined by utillizing the modal annalysis technnique (Choprra, 2007).
(a)
(b) Figure 33.3. a) Schemee of the fluid-tank system, b) b The mathem matical modell and modal prroperties of thhe system
As Fig. 3.3 demonsttrates, the moode frequenccies were caalculated as 0.184 0 and 12 2.54 Hz, resppectively. d beetween the slloshing stiffnness and the stiffness s of thhe supportingg system, Due to thhe absolute differences it is worrth mentioning here thatt the first annd second modes m represeent the convvective and impulsive modes, respectively. r When a com mparison is made m for the first f structuraal mode, it iss seen that thee trend of the preseent numericaal result agreees well with analytical a vaalue so that th he mode freq quency is com mputed as 12.54 Hzz from the annalytical moddel while thee same quantiity is calculaated as 11.91 Hz from thee FEM. In fact, thiss reflects succcessful estim mation and the t analyticaal verificationn provides strong s support for the FEM forr use in furthher investigattions.
MIC ANAL LYSIS 4. SEISM
v of thee FEM throuugh the analyytical model, the versatiliity of the FEM M allows After verrifying the validity the treatm ment of somee more realisstic situationss. Therefore, the modellinng was extennded to accouunt for the soil/founndation interaaction effectss and elasto-pplastic behavviour of soil, thus the soill/foundation system is modelledd with 3-D D structural solid elements definedd by eight nodes withh three trannslational degrees--of-freedom in each node too. Whenn modelling a dynamic problem p inclluding SSI, pparticular attentionn must be giv ven to the sooil boundary conditions. A As the subsooil is modelleed by a finitee element grid which will be tru uncated by artificial grid boundaries, there is a neeed for using absorbing booundaries r to rad diation of ennergy away from f the stru ucture. Thereefore, the in order to minimizee the errors related b mo odel developped by Lysm mer and Kuhleemeyer (1969) is used foor three dimeensions to viscous boundary considerr radiational effect of thhe seismic waves w througgh the soil medium. m Maathematical details d of modelingg of the fluidd and boundeed media can be found in Livaoglu L andd Dogangun (2007). The proposed FEM of the fluid-recctangular tankk-soil/foundaation system m is shown in Fig. 4.1. o soil properrties were carrried out emp ploying the suggested s A series of dynamic analyses witth variation of To evaluate the t variation of the dynam mic responsee of the rectaangular tank supported onn flexible model. T foundation, three diff fferent foundaation soil typpes were connsidered in thhe analyses, as a shown in T Table 4.1.
In the seismic analysses, North-Soouth componnent of the groound motionn recorded duuring August 17, 1999 Kocaeli Earthquake in Yarimca station in Tuurkey is usedd. Furthermoore, Rayleigh h damping was w taken into connsideration in n the seism mic analyses. The dampiing values for f both struucture and soil s were presumeed to be 5%.
Figure 4.1. 4 The FEM of the fluid-reectangular tannk-soil/foundaation interactioon system Table 4.11. Properties of o The Considdered Soil Typpes Soil typess γ (kN/m3) E (kN/m m2) S1 18 0.40 75000 S2 19 0.35 1500000 5000000 S3 20 0.30
G (kN N/m2) 26786 55556 192308
5. RESU ULTS AND DISCUSSIO ONS
Computaational resultts obtained bby applying thhe proposed procedure arre presented in terms of the t lateral displacem ments, sloshhing displacements and sttresses. Tablle 5.1 summarizes the peeak responsees and the correspoonding timess. The table clearly indiicates the efffects of SS SI since the maximum values v of displacem ments and sttresses changged significaantly. These effects e on seeismic respon nse of tank are a shown graphicaally, and disccussed compaaratively below. Table 5.11. Seismic An nalysis Resultss Soil typess S1 t (s) Value ur (m) 5.0 0.0022 us (m) 4.95 -0.43488 Sze (MPa)) 5.0 -0.42900 Sye (MPa)) 5.0 -0.0831 Sxe (MPa)) 5.0 -0.03455 Szi (MPa) 5.0 0.4717 Syi (MPa) 5.0 0.1005 Sxi (MPa) 5.0 0.0470
S2 t (s) 5.0 4.9 4.95 4.95 4.95 5.0 5.0 5.0
Value 0.0011 -0.4027 -0.4859 -0.0949 -0.0404 0.5333 0.1134 0.0530
S3 S t (s) 4 4.95 4 4.9 4 4.95 4 4.95 4 4.95 4 4.95 4 4.95 4 4.95
Vallue 0.00009 -0.3 3559 -0.6 6172 -0.1 1224 -0.0 0544 0.66607 0.13383 0.06639
FIXED D t (s) 4.9 4.85 4.9 4.9 4.9 4.9 4.9 4.9
Value 0.0006 -0.3432 -0.6559 -0.1435 -0.0670 0.6858 0.1480 0.0720
ur : Maxim mum lateral rooff displacement of exterior walll; us : Maximum m sloshing displlacement of fluiid; Sze, Sye and Sxe : Stresses esstimated on the exterior face off the wall in z, y and x directions, respectively; Szi, Syi and Sxi : Stresses estimaated on the inteerior face (fluid d side) of the waall in z, y and x directions, resppectively.
5.1. Lateral Displacements The lateral displacement responses throughout the height of the tank wall are depicted in Fig. 5.1. It is worth mentioning that these displacements represent the relative displacements of the wall with respect to the ground level. The most important point arising from the comparisons is that the variation of soil stiffness notably affects the displacement response of the system so that the displacement response of the exterior wall increases while the soil stiffness decreases. 7 6
Height (m)
5 4 3 S1
2
S2 S3
1
FIXED
0 0.0000
0.0005
0.0010
0.0015
0.0020
0.0025
Lateral displacement (m) Figure 5.1. The variation of lateral displacement throughout the height of rectangular tank
Roof displacement (m)
The time history of the lateral top displacements of the rectangular tank is shown in Fig. 5.2 in order to clarify the changes of the lateral top displacement values due to flexible foundation conditions. It can be clearly noted from Fig. 5.2 that the response amplification/reduction has occurred depending on the soil/foundation conditions. For example, while the maximum lateral displacement is estimated as 0.0006 m for fixed-base case, the same quantity is calculated as 0.0022 m for S1 soil type. Thus, it can be highlighted that SSI affects the tank behaviour so much so that the dramatic increment in the displacement response is almost at a level of 267% between S1 soil type and fixed-base case. 0.003
t= 5 s ur= 0.0022 m (S1) t= 5 s ur= 0.0011 m (S2) t= 4.95 s ur= 0.0009 m (S3)
0.002 0.001
0.000
S1 S2 S3 FIXED
-0.001 -0.002
t= 4.9 s ur= 0.0006 m (FIXED-BASE)
0
4
8
12
16
20
24
28
32
Time (s) Figure 5.2. Time histories of roof displacements for rectangular tank
5.2. Sloshing Displacements SSI effects on sloshing displacement can be easily observed from Table 5.1. Furthermore, the time histories of the sloshing displacements are illustrated in Fig. 5.3. It is a well known fact that SSI has a negligible effect on the convective component of the fluid inside the tank (Veletsos and Tang, 1990; Livaoglu, 2008), whereas many investigation in the literature showed for laterally excited liquid storage tanks, this may significantly change the impulsive component of response. On the other hand, as Fig. 5.3 demonstrates, the sloshing response due to relatively low water level in tank is magnified, and the response tends to increase with decreasing of the soil stiffness.
Sloshing displacement (m)
0.4 0.2 0.0 -0.2
S1
t= 4.85 s us = -0.3432 m (FIXED-BASE) t= 4.9 s us = -0.3559 m (S3) t= 4.9 s us= -0.4027 m (S2) t= 4.95 s us= -0.4348 m (S1)
-0.4 -0.6 0
4
8
12
16 Time (s)
20
S2 S3 FIXED
24
28
32
Figure 5.3. Time histories of sloshing displacement for different soil conditions
5.3. Stresses The computed stress responses and their variations throughout the strong ground motion at the exterior and interior faces of the tank wall can also be compared to make clear the SSI effects. The comparison of time history responses of the stress in z direction at the exterior face of the wall is shown in Fig. 5.4. As this figure depicts, the maximum stresses obtained at the critical sections of the wall change with varying soil conditions. For example, while the peak stress, as compression, has the value of 0.6559 MPa for fixed-base case, it was decreased to 0.4290 MPa for S1 soil type. This reflects a stress decrement of about 35% due to the variation of soil conditions. If similar comparisons are made in x direction from Fig. 5.5, it can also be seen that the results are as expected, and the stresses decrease with decreasing the stiffness of soil/foundation system. 600000
t= 4.95 s Sze = -0.4859 MPa (S2)
Sze (N/m2)
400000
200000 0 -200000
S1
-400000
t= 5 s Sze = -0.4290 MPa (S1)
S2
-600000
t= 4.95 s Sze = -0.6172 MPa (S3)
S3 FIXED
t= 4.9 s Sze = -0.6559 MPa (FIXED)
-800000 0
4
8
12
16
20
24
28
32
2
Sxi (N/m )
Time (s) Figure 5.4. Variation of stresses in time in z direction at the exterior face of the tank wall 100000 80000 60000 40000 20000 0 -20000 -40000 -60000 -80000
t= 4.9 s Sxi = 0.0720 MPa (FIXED) t= 4.95 s Sxi = 0.0639 MPa (S3) t= 5 s Sxi = 0.0470 MPa (S1)
S1 S2 S3 FIXED
t= 5 s Sxi = 0.0530 MPa (S2)
0
4
8
12
16
20
24
28
32
Time (s) Figure 5.5. Variation of stresses in time in z direction at the interior face (fluid side) of the tank wall
6. CONCLUSIONS The paper utilizes a three-dimensional finite element method to study the effects of SSI on seismic behaviour of rectangular tanks. First, modelling FSI, the numerical results are shown to have good agreement with the proposed analytical solution under fixed-base assumption. Thanks to the versatility of the FEM, the modelling is then extended to account for SSI effects. Effects of SSI on the dynamic response of the system are investigated by comparing the results among four different soil/foundation conditions. The results are presented in terms of the lateral displacements, sloshing displacements and stresses in the wall obtained from nonlinear time history analyses. It is concluded that the seismic response of liquid structures is a complex SSI problem, and the magnitudes of exterior wall movements and stresses in the wall induced by horizontal ground shaking are quite sensitive to the response of the subsoil. It should be stated that more analytical, numerical and experimental works and well documented case histories may be needed not only to further develop methods of analysis that are consistent with the actual dynamic behaviour of these systems but also to generalize the results from the procedure presented here. Furthermore, the results of the numerical investigations are expected to be useful for the better understanding and the optimization of seismic design of this particular type of liquid tanks. REFERENCES Ansari, M.R., Firouz-Abadi, R.D. and Ghasemi, M. (2011). Two phase modal analysis of nonlinear sloshing in a rectangular container. Ocean Engineering. 38:1277-1282. Ansys 10. (2006). ANSYS Inc., Canonsburg, PA. Cakir, T. and Livaoglu, R. (2012). Fast practical analytical model for analysis of backfill-rectangular tank-fluid interaction systems. Soil Dynamics and Earthquake Engineering. 37:24-37. Chern, M.J., Vaziri, N., Syamsuri, S. and Borthwick, A.G.L. (2012). Pseudospectral solution of three-dimensional nonlinear sloshing in a shallow water rectangular tank. Journal of Fluids and Structures. 35:160-184. Chopra, A.K. (2007). Dynamics of Structures: Theory and Applications to Earthquake Engineering, Prentice Hall, New Jersey. Dogangun, A., Durmus, A. and Ayvaz, Y. (1997). Earthquake analysis of flexible rectangular tanks by using the Lagrangian fluid finite element. European Journal of Mechanics, A/Solids. 16:1,165-182. Ghaemmaghami, A.R. and Kianoush, M.R. (2010). Effect of wall flexibility on dynamic response of concrete rectangular liquid storage tanks under horizontal and vertical ground motions. Journal of Structural Engineering. 136:4,441-451. Goudarzi, M.A. and Sabbagh-Yazdi, S.R. (2012). Investigation of nonlinear sloshing effects in seismically excited tanks. Soil Dynamics and Earthquake Engineering. 43:355-365. Housner, G.W. (1963). Dynamic behavior of water tanks. Bulletin of the Seismological Society of America. 53:381-387. Jeong, K.H. (2011). Hydroelastic vibration analysis of liquid-contained rectangular tanks. Structural Engineering and Mechanics, An International Journal. 40:5,665-688. Kianoush, M.R. and Ghaemmaghami, A.R. (2011). The effect of earthquake frequency content on the seismic behavior of concrete rectangular liquid tanks using the finite element method incorporating soil-structure interaction. Engineering Structures. 33:2186-2200. Livaoglu, R. and Dogangun, A. (2007). Effect of foundation embedment on seismic behavior of elevated tanks considering fluid-structure-soil interaction. Soil Dynamics and Earthquake Engineering. 27:855-863. Livaoglu, R. (2008). Investigation of seismic behavior of fluid-rectangular tank-soil/foundation systems in frequency domain. Soil Dynamics and Earthquake Engineering. 28:132-146. Livaoglu, R., Cakir, T., Dogangun, A. and Aytekin, M. (2011). Effects of backfill on seismic behavior of rectangular tanks. Ocean Engineering. 38:1161-1173. Lysmer, J. and Kuhlemeyer, R.L. (1969). Finite dynamic model for infinite media. Engineering Mechanics Division Journal. 95:859-877. Rai, D.C. (2002). Seismic retrofitting of R/C shaft support of elevated tanks. Earthquake Spectra. 18:4,745-760. Sezen, H. and Whittaker, A.S. (2006). Seismic performance of industrial facilities affected by the 1999 Turkey earthquake. Journal of Performance of Constructed Facilities. 20:1, 28-36. Veletsos, A.S. and Tang, Y. (1990). Soil-structure interaction effects for laterally excited liquid storage tanks. Earthquake Engineering and Structural Dynamics. 19:474-496.
