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Nuclear Engineering and Design 217 (2002) 120

Non-linear seismic response of base-isolated liquid storagetanks to bi-directional excitation

M.K. Shrimali, R.S. Jangid *

Department of Ciil Engineering, Indian Institute of Technology Bombay, Powai, Mumbai 400 076, India

Received 21 May 2001; received in revised form 8 January 2002; accepted 6 March 2002

Abstract

Seismic response of the liquid storage tanks isolated by lead-rubber bearings is investigated for bi-directional

earthquake excitation (i.e. two horizontal components). The biaxial force-deformation behaviour of the bearings is

considered as bi-linear modelled by coupled non-linear differential equations. The continuous liquid mass of the tank

is modelled as lumped masses known as convective mass, impulsive mass and rigid mass. The corresponding stiffness

associated with these lumped masses has been worked out depending upon the properties of the tank wall and liquid

mass. Since the force-deformation behaviour of the bearings is non-linear, as a result, the seismic response is obtained

by the Newmarks step-by-step method. The seismic responses of two types of the isolated tanks (i.e. slender and

broad) are investigated under several recorded earthquake ground to study the effects of bi-directional interaction.

Further, a parametric study is also carried out to study the effects of important system parameters on the effectiveness

of seismic isolation for liquid storage tanks. The various important parameters considered are: (i) the period ofisolation, (ii) the damping of isolation bearings and (iii) the yield strength level of the bearings. It has been observed

that the seismic response of isolated tank is found to be insensitive to interaction effect of the bearing forces. Further,

there exists an optimum value of isolation damping for which the base shear in the tank attains the minimum value.

Therefore, increasing the bearing damping beyond a certain value may decrease the bearing and sloshing displace-

ments but it may increase the base shear. 2002 Elsevier Science B.V. All rights reserved.

www.elsevier.com/locate/nucengdes

1. Introduction

Liquid storage tanks are strategically very im-

portant structures, since they have vital uses inindustries, nuclear power plants and are con-

nected to public life. There has been a number of

reports on damage to liquid storage tanks such as

in the Chilean earthquake (Steinbrugge and Ro-

drigo, 1963), California, Livermore earthquake

(Niwa and Clough, 1982) and San Juan earth-

quake (Manos, 1991). The earthquake motionexcites the liquid contained in the tank. A part of

the liquid moves independent of tank wall mo-

tion, which is termed as sloshing, while another

part of the liquid which moves in unison with the

rigid tank wall is known as impulsive mass. If the

flexibility of the tank wall is considered then the

part of the impulsive mass moves independently

* Corresponding author. Tel.: +91-22-576-7346; fax: +91-

22-578-3557

E-mail address: [email protected] (R.S. Jangid).

0029-5493/02/$ - see front matter 2002 Elsevier Science B.V. All rights reserved.

PII: S 0 0 2 9 - 5 4 9 3 ( 0 2 ) 0 0 1 3 4 - 6
mailto:[email protected]

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M.K. Shrimali, R.S. Jangid/Nuclear Engineering and Design 217 (2002) 1 20 3

the seismic response of liquid storage tanks. This

is achieved by comparing the seismic response of

the tanks to bi-directional excitation with consid-

eration of interaction between the restoring forces

to the corresponding response without interaction

and (iii) to investigate the influence of important

system parameters on the effectiveness of isolation

systems. The important parameters included are:isolation period, damping and yield strength of

the lead-rubber bearings.

2. Structural model of liquid storage tank

Fig. 1 shows the idealised structural model of

liquid storage tank mounted on isolation system.

The lead-rubber bearings are installed between the

base and foundation of the tank for isolation. Thecontained continuous liquid mass is lumped as

convective, impulsive and rigid masses referred as

mc, mi and mr, respectively. The convective and

impulsive masses are connected to the tank wall

by corresponding equivalent spring having stiff-

ness kc and ki, respectively. The damping constant

of the convective and impulsive masses are cc and

ci, respectively. The system has six-degrees-of-free-

dom under bi-directional earthquake ground mo-

tion, two-degrees-of-freedom of each lumped

mass in two horizontal x- and y-directions. These

degrees-of-freedom are denoted by (ucx, ucy), (uix,

uiy) and (ubx, uby) which denote the absolute dis-

placement of convective, impulsive and rigid

masses in x- and y-directions, respectively. The

tank model is assumed to have a deformable

circular cylindrical shell. The parameters of the

tanks considered are liquid height H, radius, Rand average thickness of tank wall, th. The effec-

tive masses are defined in terms of liquid mass m,

from the parameters are expressed (Haroun, 1983)

as

Yc=1.013270.87578S+0.35708S2

0.06692S3+0.00439S4 (1)

Yi=0.15467+1.21716S0.62839S2

+0.14434S30.0125S4 (2)

Yr=0.01599+0.86356S0.30941S2

+0.04083S3 (3)

where S=H/R is the aspect ratio (i.e. ratio the

liquid height to radius of the tank) and Yc, Yi,

and Yr are the mass ratios defined as

Yc=mc

m (4)

Yi=

mi

m (5)

Yr=mr

m (6)

m=R2Hw (7)

where w is the mass density of liquid.

The natural frequencies of sloshing mass, cand impulsive mass, i are given by following

expressions (Haroun, 1983) as

i=

P

HE

s (8)

c=

1.84g

R

tanh

1.84

H

R

(9)

where E and s are the modulus of elasticity and

density of tank wall, respectively; g is the acceler-

ation due to gravity; and P is a dimensionless

parameter expressed asFig. 1. Structural model of base-isolated liquid storage tank.

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where q is the yield displacement; xb and yb are

the relative velocities of isolation bearings in the

x- and y-directions, respectively; and , and A

are the non-dimensional parameters which control

the shape and size of force-deformation loop of

the bearing. The parameters are selected such that

the predicted response from the model matches

with experimental results. It is to be noted thatthe off diagonal terms of the matrix [G] provide

the coupling or interaction between the restoring

forces of the lead-rubber bearings in two orthogo-

nal directions. It will be interesting to investigate

the effects of this interaction on the seismic re-

sponse of base-isolated tanks. This interaction

effect is ignored if the isolated tank is analyzed

under two-dimensional (2-D) idealisation in two

horizontal directions independently.

4. Governing equations of motion

The equations of motion of isolated liquid stor-

age tank subjected to earthquake ground motion

are expressed in the matrix form as

[m ]{z}+ [c ]{z }+ [k]{z }+{F}= [m][r]{ug}

(14)

where {z}={xc,xi,xb,yc,yi,yb}T and {F}=

{0, 0, (1)FyZx, 0, 0, (1)FyZy}Tare the dis-

placement and restoring force vectors,

respectively; xc=ucxubx and yc=ucyuby are

the displacements of the convective mass relative

to bearing displacements in x and y-directions,

respectively; xi=uixubx and yi=uiyuby are

the displacements of the impulsive mass relative

to bearing displacements in x- and y-directions,

respectively; xb=ubxugx and yb=ubyugy are

the displacements of the bearings relative to

ground in x- and y-directions, respectively; [m],

[c ] and [k] are the mass, damping and stiffness

matrix of the system, respectively; [r] is the influ-

ence coefficient matrix; and {ug}={ugx,ugy}T is

the earthquake ground acceleration vector, the ugxand ugy are the earthquake accelerations in x - and

y-directions, respectively.

The matrices [m], [c], [k] and [r] are expressed

as

[m]=

mc 0 mc 0 0 0

0 mi mi 0 0 0

mc mi M 0 0 0

0 0 0 mc 0 mc

0 0 0 0 mi mi

0 0 0 mc mi M

(15)

[c]=diag[cc,ci,cb,cc,ci,cb] (16)

[k]=diag[kc,ki,kb,kc,ki,kb] (17)

[r]=0 0 1 0 0 0

0 0 0 0 0 1

nT(18)

whereM=mc+mi+mr is the total effective mass

of the tank.

The equivalent stiffness and damping constants

of the convective and impulsive masses are ex-pressed as

kc=mc c2 (19)

ki=mi i2 (20)

cc=2cmcc (21)

ci=2imii (22)

where c and i are the damping ratios of the

convective and impulsive masses, respectively.

5. Incremental solution of equations of motion

The governing equations motion of the isolated

liquid storage tank cannot be solved using the

classical modal superposition technique due to (i)

the damping in the isolation system and liquid

storage tank is different in nature because of

material characteristics and (ii) the force-deforma-

tion behaviour of the lead-rubber bearings is non-

linear. As a result, the governing equations of

motion are solved in the incremental form using

Newmarks step-by-step method assuming linear

variation of acceleration over small time interval,

t. The equations of motion in incremental form

are expressed as

[m]{z}+ [c]{z }+ [k]{z }+{F}

= [m][r]{ug} (23)

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M.K. Shrimali, R.S. Jangid/Nuclear Engineering and Design 217 (2002) 1 206

where {z}={xc, xi, xb, yc, yi, yb}T is

the incremental displacement vector; and {F} is

the incremental hysteretic force vector of the lead-

rubber bearing expressed by

{F}={0, 0, (1)FyZx, 0, 0, (1)FyZy}T

(24)

where Zx and Zy are the incremental hysteretic

displacement components in x- and y-directions,

respectively.

The incremental acceleration and velocity vec-

tors {z} and {z } over the time interval, t are

expressed as

{z}=a0{z}+a1{z }t+a2{z}

t (25)

{z }=b0{z}+b1{z }t+b2{z}

t (26)

where a0=6/(t2); a1=(6/(t

2)); a2=3;

b0=3/t ; b1=3; b2=t/2; and the super-script t denotes time.

The final equations of the motion in the incre-

mental form are expressed as

[keff]{z}={Peff}{F} (27)

where [keff] is the effective stiffness matrix; and

{Peff} is the effective excitation vector.

The matrix [keff] and vector {Peff} are explicitly

given by

[keff]=a0[m]+b0[c]+ [k] (28)[Peff]= [m]{r}{ug} [m](a1{z }

t+a2{z}t)

[c](b1{z }t+b2{z}

t) (29)

The incremental restoring force vector involves

the incremental hysteretic displacement compo-

nents, Zx and Zy, which depends on the bear-

ing velocities at time, t+t. As a result, an

iterative procedure is required to obtain the re-

quired solution. The steps of the procedure are as

follows:

1. Assume Zx=Zy=0 for iteration j=1 in

Eq. (24) and solve for {z} by Eq. (27).

2. Calculate the incremental velocity vector using

the Eq. (26) and find the velocity vector at

time, t+t by {z }t+t={z }t+{z }. This

velocity vector will provide the velocity of the

base mass or rigid mass in x - and y -directions,

respectively (i.e. xbt+t and yb

t+t).

3. Knowing the velocity of the mass in both the

horizontal directions at time t+t, compute

the revised incremental displacements compo-

nent, Zx and Zy using the third order

RungeKutta method.

4. Iterate further, until the following convergence

criteria is satisfied for the incremental hys-

teretic displacements component of the bear-ing i.e.

Zxj+1 ZxjZm

(30a)

Zyj+1 ZyjZm

(30b)

where is the small tolerance parameter; the

superscript denotes the iteration number; and

Zm is the maximum value of hysteretic dis-

placement of the bearing is expressed by

Zm= A+

(31)

The final acceleration vector is obtained from

the direct equilibrium of Eq. (14) instead of using

Eq. (25) to avoid any unbalanced forces generated

in the numerical integration scheme.

After obtaining the final acceleration vector, the

absolute acceleration of convective and impulsive

mass in both thex - andy -directions are obtained.

The total base shear generated due to earthquake

ground motion in x- and y-directions, respec-

tively, is expressed as

Fsx=mcucx+miuix+mrubx (32)

Fsy=mcucy+miuiy+mruby (33)

6. System parameters

The damping, stiffness and yield level of the

bearing are designed to provide the desired valueof three parameters, namely the Tb, b and F0expressed as

Tb=2Mkb

(34)

b= cb

2Mb(35)

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F0=Fy

W (36)

where b=2/Tb is the isolation frequency; and

W=Mg is the effective weight of the liquid stor-

age tank.

The parameters, which characterize the model

of liquid storage tank, are height of liquid in thetank (H), aspect ratio (S), damping ratio of the

convective mass (c) and damping ratio of the

impulsive mass (i). The isolator parameters for

the tank with lead-rubber bearings require the

specification of the parameters such as the period

of isolation (Tb), damping ratio of the bearing

(b) and yield strength level of the bearing (F0).

The other parameters of the lead-rubber bearing

are the yield displacement (q) and parameters of

hysteresis loop of the bearing such as A, and .

However, these parameters are held constant and

values taken are: q=25 mm, A=1, =0.5 and

=0.5. The damping ratios for the convective

mass (c) and the impulsive mass (i) and are

taken as 0.5 and 2%, respectively. For the tanks

Table 1

Properties of earthquake ground motion

PGA (g) PGA (g)ComponentEarthquake Component

S90W 0.2144 S00E 0.3486Imperial Valley, 1940 (El-Centro)

0.5704Loma Prieta, 1989 (Los Gatos Presentation Center) 0.6079N90E N00E

N90E 0.6297 N00EKobe, 1995 (JMA) 0.8345

Fig. 3. Time variation of response of the slender tank in x-direction due to Imperial Valley earthquake (Tb=2 s, b=0.1 and

F0=0.05).

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Fig. 4. Time variation of response of the slender tank in y-direction due to Imperial Valley earthquake (Tb=2 s, b=0.1 and

F0=0.05).

with steel wall the modulus of elasticity is taken asE=200 MPa and the mass density, s=7900 kg

m3. The ratio of post- to pre-yielding stiffness is

computed using following expression =b2Mq/

Fy.

7. Numerical study

The seismic response of base-isolated liquid

storage tanks is investigated under two horizontal

components of earthquake ground motion. The

bi-directional interaction between the restoring

forces of the lead-rubber bearings is duly consid-

ered. The earthquake ground motions considered

are of Kobe (1995), Loma Prieta (1989) and Im-

perial Valley (1940). The peak acceleration of

different components of these ground motions is

given in Table 1. The components S90W, N90E

and N90E of Kobe, Loma Prieta and ImperialValley earthquake ground motions, respectively,

are applied in x-direction. The other orthogonal

components of the above mentioned ground mo-

tions are applied in the y-direction. The response

quantities of interest are base shear (Fsx, Fsy),

displacements of convective mass (xc, yc), impul-

sive mass (xi, yi) and isolation bearings (xb, yb).

The response of base-isolated liquid storage tank

is analyzed to study the influence of bi-directional

interaction and system parameters on the effec-

tiveness of seismic isolation. Two different typesof tanks namely the broad and slender tanks are

considered for detailed parametric study from

Malhotra (1997a). The properties of these tanks

are: (i) aspect ratio (S) for slender and broad

tanks is 1.85 and 0.6, respectively; (ii) the height,

H, of water filled in slender and broad tanks is.

11.3 and 14.6 m, respectively; (iii) ratio of tank

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wall thickness to its radius (th/R) is taken 0.004

for both the tanks and (iv) the natural frequencies

of convective mass and impulsive mass for the

broad and slender tank are 0.123, 3.944 Hz and

0.273, 5.963 Hz, respectively.

The time variation of various response quanti-

ties of slender and broad tanks are shown in Figs.

36 under Imperial Valley, 1940 earthquake

ground motion. The response is shown for both

non-isolated and isolated tanks with and without

interaction of the bearing forces. The parameters

of the isolation system considered are Tb=2 s,

b=0.1 and Fy/W=0.05. It is observed from the

figures that the isolation is quite effective in re-

ducing the base shear and impulsive displacement

of liquid storage tank significantly. This implies

that the seismic isolation is quite effective in re-

ducing the earthquake response of liquid storagetanks. The sloshing displacement in the isolated

slender tank is marginally increased while in

broad tank it is reduced slightly in comparison to

corresponding non-isolated tanks. Further, it is

also observed that all the seismic response quanti-

ties of slender and broad tanks with the interac-

tion of bearings forces follow the same pattern as

without interaction condition. Also, there is no

significant difference in the peak response of the

isolated tanks obtained by interaction and no

interaction conditions. Thus, the interaction of

the restoring forces of the bearing does not have

significant effect on the seismic response of iso-

lated tanks. The similar effects of bi-directional

interaction on the corresponding force-deforma-

tion behaviour of the lead-rubber bearing for

slender and broad tanks are depicted in Figs. 7

and 8, respectively.

The peak response quantities for the broad andslender tanks under different earthquake ground

Fig. 5. Time variation of response of the broad tank in x-direction due to Imperial Valley earthquake (Tb=2 s, b=0.1 and

F0=0.05).

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Fig. 6. Time variation of response of the broad tank in y-direction due to Imperial Valley earthquake (Tb=2 s, b=0.1 and

F0=0.05).

motion inx - andy -directions are shown in Tables2 and 3, respectively. The parameters of bearings

considered are: Tb=2 s, b=0.1 and Fy/W=

0.05. The percentage reduction in base shear due

to isolation of the broad tank with interaction

effect is 66.28, 74.41; 67.50, 57.96 and 65.13, 66.39

under Imperial Valley, Loma Prieta and Kobe

earthquake ground motions in x- and y-direc-

tions, respectively. The corresponding reduction

in slender tank is 68.97, 80.04; 82.23, 67.05 and

74.07, 67.16. This indicates that reduction of base

shear in slender tank is more in comparison tobroad tank. This is due to the fact that the total

base shear is mainly contributed from impulsive

component and seismic isolation is quite effective

in reducing the impulsive response of the tanks.

As the slender tanks have more impulsive mass as

compared with broad tanks, the seismic isolation

will be more effective. Further, there is significant

increase in the sloshing displacement of liquidmass due to isolation of the slender tank. The

effect of bi-directional interaction on the peak

response is not quite significant as observed ear-

lier. However, the base shear and impulsive dis-

placement are reduced marginally due to

interaction of bearing forces in comparison to no

interaction condition.

In Fig. 9, variation of peak response of slender

tank is plotted against the period of isolation, Tb.The bearing damping is considered to be 10% and

normalized yield strength as 0.05. It is observedfrom the figure that the increase of flexibility of

isolation system reduces the peak base shear (the

reduction is more in y-direction compared to

x-direction). The base displacement initially de-

creases due to increase in flexibility of isolation

system; thereafter it increases with increase of

time period in x-direction (while in y-direction

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increase in base displacement is significant with

time period due to Loma Prieta earthquake). The

sloshing displacement is marginally decreased

with the increase of time period in both direc-

tions. Fig. 10 shows the effect of flexibility of

isolation system on the peak response of broad

tank. The variation of base shear and base dis-

placement with time period of isolation system in

both the directions i.e. x- and y-directions, shows

similar trends as shown in Fig. 9. The sloshing

displacements in both the directions are not sig-

nificantly influenced with increase in the time

Fig. 7. Force-deformation behaviour of isolation system of the slender tank under Imperial Valley earthquake ( Tb=2 s, b=0.1 and

F0=0.05).

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Fig. 8. Force-deformation behaviour of isolation system of the broad tank under Imperial Valley earthquake (Tb=2 s, b=0.1 and

F0=0.05).

period (except due to Kobe earthquake). This is

due to the fact that sloshing period of broad tank

is 8.13 s, which is well separated from the varia-

tion of the period considered from 1.5 to 4 s.

Hence, the seismic isolation system should be

design such that its time period is well separated

from sloshing period.

The effects of isolation damping on the peak

response of liquid storage tank are shown in Figs.

11 and 12 for both slender and broad tanks,

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respectively. The period of isolation considered is

2 s and Fy/W=0.05. The physical significance of

damping is to dissipate seismic energy and hence

reduces bearing displacement but as a result the

acceleration transmitted to structure increases,

hence increase in base shear. The base shear first

decreases and attains minimum value and then

increases with increase of the isolation damping.

This indicates that there exists optimum value of

isolation damping for which base shear is mini-

mum. The minimum value of base shear observed

inx -direction for slender tank at damping ratio of

0.09, 0.15 and 0.19 for Kobe, Loma Prieta and

Imperial Valley ground motions, respectively.

Similarly, damping ratio for minimum value of

base shear in y-direction for the slender tank

under the corresponding ground motions is 0.19,

0.33 and 0.19. The minimum value of base shear

observed in x-direction for broad tank at damp-

ing ratio of 0.09, 0.21 and 0.23 for Kobe, Loma

Prieta and Imperial Valley ground motions, re-

spectively. Similarly, damping ratio for minimum

value of base shear in y-direction for the broad

tank for the corresponding ground motions is

0.17, 0.25 and 0.17. For slender tanks the base

and sloshing displacements inx - andy -directions,

respectively, decrease as damping of the isolation

system increases. The variation of base displace-

Table 2

Peak response of broad and slender tanks in x-direction

Imperial Valley (1940)Earthquake Loma Prieta (1989) Kobe (1995)

BroadSlenderBroadSlender BroadTank Slender

xc (cm) 36.14Non-isolated 17.50 52.05 30.4741.54 53.08

Isolated Interaction 53.80 54.00 47.38 23.65 64.77 25.43

No interaction 54.84 53.56 45.44 23.66 62.21 26.42

Non-isolated 0.390 1.280xi (cm) 0.960 2.370 0.660 1.870

0.5360.1430.424Isolated 0.1280.2710.082Interaction

No interaction 0.088 0.293 0.130 0.410 0.150 0.580

0.319 0.258 0.771 0.440 0.594 0.476Fsx/W Non-isolated

Isolated Interaction 0.099 0.087 0.137 0.143 0.154 0.166

No interaction 0.107 0.093 0.155 0.144 0.164 0.182

13.9212.3111.7211.896.35xb (cm) 7.22InteractionIsolated14.1312.6910.8012.166.107.87No interaction

Table 3

Peak response of broad and slender tanks in y-direction

Imperial ValleyEarthquake Loma Prieta Kobe

Slender Broad SlenderTank Broad Slender Broad

Non-isolated 23.71 42.29yc (cm) 142.77 55.31 37.85 23.76

44.20Isolated 195.04 64.18 57.32 34.69Interaction 31.95

31.20 43.78 194.71 63.97No interaction 58.19 34.870.740 3.530Non-isolated 0.910yi (cm) 2.9501.5301.950

Isolated 0.7330.2560.790Interaction 0.3340.2780.083

No interaction 0.088 0.292 0.335 0.790 0.260 0.760

1.056 0.609Fsy/W 0.883Non-isolated 0.7440.491 0.340

0.2500.2900.2560.3480.0870.098InteractionIsolated

No interaction 0.103 0.093 0.349 0.258 0.298 0.256

Isolated 20.62yb (cm) 25.4922.7930.946.3107.468Interaction

21.1326.0822.3230.966.3207.470No interaction

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Fig. 9. Effect of time period on peak response of the base-isolated slender tank (b=0.1 and F0=0.05).

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ment with isolation damping for the broad tank

has trends similar to the slender tank as shown in

Fig. 11. The sloshing displacement for broad tank

is not significantly affected by variation of isola-

tion damping (except for Kobe earthquake in

y-direction).

Fig. 10. Effect of time period on peak response of the base-isolated broad tank (b=0.1 and F0=0.05).

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Fig. 11. Effect of damping on peak response of the base-isolated slender tank (Tb=2 s and F0=0.05).

The effects of yield strength of isolation system

on the peak response of slender and broad tank

are shown in Figs. 13 and 14, respectively. The

figures indicate that the base shear initially de-

creases and then increases with the increase of the

yield strength of the bearings, implying that there

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exists an optimum value of bearing yield strength

for which the base shear is minimum. This is

expected that the yielding of the bearing adds the

hysteretic damping in the system and at higher

damping there is a tendency for the base shear to

increase, as observed in Figs. 12 and 13. Further,

Fig. 12. Effect of damping on peak response of the base-isolated broad tank (Tb=2 s and F0=0.05).

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Fig. 13. Effect of yield strength of isolation system on seismic response of the base-isolated slender tank ( Tb=2 s and b=0.1).

both the bearing and sloshing displacements de-

crease with the increase of bearing yield

strength.

8. Conclusions

The seismic response of base-isolated liquid

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storage tank is investigated under two horizontal

components of real earthquake ground motions.

The bi-directional interaction between the restor-

ing forces of the lead-rubber bearings is duly

considered. The response of base-isolated liquid

storage tank is analyzed to study the influence of

Fig. 14. Effect of yield strength of isolation system on seismic response of the base-isolated broad tank (Tb=2 s and b=0.1).

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bi-directional interaction and system parameters

on the effectiveness of seismic isolation. The fol-

lowing conclusions are drawn from the trends of

the results of the limited parametric study:

1. Base isolation system is quite effective in re-

ducing the seismic response of the liquid stor-

age tanks.

2. The base isolation is found to be more effec-tive for the slender tanks in comparison to the

broad tanks.

3. The peak response of base-isolated liquid stor-

age tank is not much influenced by the bi-di-

rectional interaction of restoring forces of the

lead-rubber bearings.

4. The effectiveness of seismic isolation of the

liquid storage increases with the increase of the

flexibility of isolation systems. However, the

bearing displacement also increases with the

increase of isolator flexibility.5. An optimum value of the isolation damping

exists for which the base shear in the tank

attains the minimum value. Thus, the increase

of bearing damping beyond the optimum

value will decrease the bearing and sloshing

displacement but it will increase the base

shear.

6. The bearing and sloshing displacements of the

isolated liquid storage tank decreases with the

increase of the yield strength of the bearing.

However, the base shear may get increased for

higher bearing yield strength.

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