International Journal of Application or Innovation in Engineering & Management (IJAIEM)
Web Site: www.ijaiem.org Email: editor@ijaiem.org, editorijaiem@gmail.com
Volume 2, Issue 2, February 2013
ISSN 2319 - 4847
Seismic Response of Isolated Liquid Storage
Tanks with Elastomeric Bearings
Pravin B. Waghmare1, Dr. P.S.Pajgade2 and Dr. N.M.Kanhe3
1
Ph.D Candidate, Department Of Civil Engineering,
Rashtrasant Tukadoji Maharaj Nagpur University Nagpur
2
Professor & H.O.D Civil Engineering Dept
Prof. Ram Meghe Institute of Technology and Research, Badnera
3
Principal Guru Nanak Institute
of Technology & Management, Nagpur
ABSTRACT
The conventional seismic design and rehabitation approach are to strengthen a structure traditionally leads to uneconomical
design, as a design of large design forces generated by amplified ground acceleration transferred to the structure. An
alternative approach is to install the energy absorption devices in between the base plate and foundation to decouple the
structure from ground. This is achieved by using elastomeric bearing. Liquid storage tanks are important components of
lifeline and industrial facilities. They are critical elements in water supply scheme and firefighting system, and extensively
used for storage and processing of variety of liquid like material such as petroleum product, liquefied natural gas,
chemical fluid and wastage of different forms. These types of structures are also used in nuclear power plant for storage,
which are strategically very important. The tanks come under variety of configuration; it may be ground supported, elevated or
partly buried. Depending upon the nature of the stored product, failure of the tanks of their accessories may lead to fires,
pollution or contamination of surrounding areas, or may impede firefighting effort at critical times. Because of their use and
their vulnerability to earthquake, incidences of damage to tanks have been reported. In recent years, the number, size and
importance of these structures have been increased and there is need to understand their seismic behavior and to formulate
rational and efficient method of their analysis and design to resist earthquake ground motion. In the present study, research
work had done in area of seismic analysis of liquid storage tanks with framed staging. Different isolation techniques are
developed. Comprehensive parametric studies on elevated (with framed staging cylindrical liquid storage) tanks seismically
isolated by elastomeric bearings are developed. The parameters considered are isolation time period, damping, yield strength of
bearing. In addition to the above study, modal responses of elevated tank are carried out. The isolation tank models are to be
considered by placing the base isolation system at the bottom of the supporting tower structure. MATLAB software has been
used for analysis and solving all dynamic equations of motion.From the above study it is concluded that the isolation is very
effective in reducing the seismic response of liquid storage tanks.
Keywords: seismic design, ground acceleration, energy absorption devices, elastomeric bearing, aspect ratio, time
period, peak response.
1. INTRODUCTION
Liquid storage tanks are important components of lifeline and industrial facilities. They are critical elements in water
supply scheme and firefighting system, and extensively used for storage and processing of variety of liquid like
material such as petroleum product, liquefied natural gas, chemical fluid and wastage of different forms. These types
of structures are also used in nuclear power plant for storage, which are strategically very important. The tanks come
under variety of configuration; it may be ground supported, elevated or partly buried. Depending upon the nature of the
stored product, failure of the tanks of their accessories may lead to fires, pollution or contamination of surrounding
areas, or may impede firefighting effort at critical times. Because of their use and their vulnerability to earthquake,
incidences of damage to tanks have been reported. In recent years, the number, size and importance of these structures
have been increased and there is need to understand their seismic behavior and to formulate rational and efficient
method of their analysis and design to resist earthquake ground motion. In the present study, research work had done in
area of seismic analysis of liquid storage tanks with framed staging. Different isolation techniques are developed.
Comprehensive parametric studies on elevated (with framed staging cylindrical liquid storage) tanks seismically
isolated by elastomeric bearings are developed. The parameters considered are isolation time period, damping, yield
strength of bearing.
In addition to the above study, modal responses of elevated tank are carried out. The isolation tank models are to be
considered by placing the base isolation system at the bottom of the supporting tower structure.MATLAB software has
been used for analysis and solving all dynamic equations of motion.
1.1 Mathematical modeling of seismically isolated liquid storage tank
Volume 2, Issue 2, February 2013
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International Journal of Application or Innovation in Engineering & Management (IJAIEM)
Web Site: www.ijaiem.org Email: editor@ijaiem.org, editorijaiem@gmail.com
Volume 2, Issue 2, February 2013
ISSN 2319 - 4847
The structural model of the isolated liquid storage tanks considered is as shown in fig.1,in which isolation bearing are
placed at the bottom of the base and the foundation of the tank. The contained liquid is considered as incompressible,
in viscid and has irrotationalflow. During the excitation the entire liquid mass vibrates in three distinct patterns such as
 Sloshing or convective mass (i.e. top liquid mass which changes the free liquid surface).
 Impulsive mass (intermediate liquid mass vibrating along with tank wall.
 Rigid mass (i.e. the lower liquid mass which rigidly moves with the tank wall
 .e. the lower liquid mass which rigidly moves with the tank wall
Fig.1 (a) 3-D Model (b) Tank with LRB (c) Mathematical Model of Tank
The various equivalent masses and associated natural frequencies of the tank liquid are expressed as [1]
mC = mYc--------------------------------------mi = m Yi-------------------------------------mr = mY-------------------------------------------
-
- (1.1)
---(1.2)
--(1.3)
Where, liquid mass,m= Π R3Hρw
R-radius of tank, H-height of tank,ρw-mass density of tank liquid
Yc ,Yi ,Yr -----------------are non dimensional parameters
Natural frequencies of convective and impulsive mass are as below [1]
ωi=
------------------------------
ω c=
---------------------
--(1.4)
------(1.5)
Where P-Non –dimensional parameters associated with frequency of impulsive mass
E-modulus of elasticity of tank wall.
-Density of tank wall, S- aspect ratio=H/R,
Yc ,Yi ,Yr,non dimensional parameters for th/R =0.004
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Volume 2, Issue 2, February 2013
ISSN 2319 - 4847
=
(1.6)
The centroid of the equivalent massesmC,mi,mr are at a height HC,Hi,Hr from bottom of the tank are as below[1]
=
(1.7)
The effective heights HC,Hi,Hr in terms of liquid height, H are expressed as
HC, = H
Hi ,= H
Hr = H
(2)
The equivalent stiffness and damping of the convective and impulsiveness masses are expressed as [1]
kc=mc ω2c
(2.1)
ki=mi ω2i
(2.2)
Cc=2ξcmcωc
(2.3)
Ci=2ξi miωi
(2.4)
(1.8)
(1.9)
1.2 Governing equation of motion
The equation of motion of elevated liquid storage tank subjected to unidirectional earthquake ground motion are
expressed in the matrix form[1].
[r]
(2.5)
Where {x} is the displacement vector. [m]-mass matrix, [c] damping matrix, [k] - stiffness matrix,[r]-influence
coefficient vector, üg-earthquake acceleration.
1.3 Displacement vector for non isolated tank
The displacement vector for non isolated tank is given by
{x} = {xc,xi,xt}T
(2.6)
Where,xc=uc- ut-------------------displacement of convective mass.
xi=ui- ut-------------------displacement of convective mass.
xt=ut- ug-------------------displacement relative to ground (i.e. tower drift).
The [m]-mass matrix, [c] damping matrix, [k] - stiffness matrix, [r]-influence coefficient vector, for the non isolated
tank are expressed as [1].
[m] =
(2.7)
[C]=diag [Cc,Ci,Ct](2.8)[k] =diag [kc,ki,kt]
(2.9)
{r} = {0,0,1}T (3)
Where, the effective mass of the tank, M=mc+mi+mr also it is assume that mb = 0.05m
The stiffness,kt and damping Ct of the tower structure based on the assumption of single-degree of freedom system are
given as below [1].
kt =
Ct = 2ξt(M +0.05m)ωt
(3.2)
Where, Tt,ξt are time period and damping ratio of the tower structure.
1.4 Displacement vector for isolated tank
The displacement vector for isolated tank is given by
{x} = {xc,xi,xt,xb }T
Where,xc=uc- ut-------------------displacement of convective mass.
xi=ui- ut-------------------displacement of convective mass.
xt=ut- ub-------------------displacement relative to ground (i.e. tower drift).
Volume 2, Issue 2, February 2013
(3.1)
(3.3)
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International Journal of Application or Innovation in Engineering & Management (IJAIEM)
Web Site: www.ijaiem.org Email: editor@ijaiem.org, editorijaiem@gmail.com
Volume 2, Issue 2, February 2013
ISSN 2319 - 4847
xb=ub- ug-------------------bearing displacement relative to ground.
The [m]-mass matrix, [c] damping matrix, [k] - stiffness matrix, [r]-influence coefficient vector, for the non isolated
tank are expressed as [1].
[m] =
(3.4)
[C]=diag [Cc,Ci,Ct,Cb,]
[k] =diag [kc,ki,kt,kb]
{r} = {0,0,0,1}T (3.7)
Where, the effective mass of the tank, M=mc+mi+mr also it is assume that mb = 0.05m
The stiffness,kb and damping Cbof the isolation system are given as below [1].
(3.5)
(3.6)
Kb=
(3.8)
Cb = 2ξb(M +0.15m)ωb
(3.9)
Where, Tb,ξbare time period and damping ratio of the isolation system.
The base shear which is directly proportional to earthquake forcestransmitted to the tank wall is expressed as as [1]
Fs = mcüc+ miüi+ ( mr+0.05m)üt(for non isolated tank)
(4)
Fs = mcüc+ miüi+( mr+0.05m)üt+2 mbüb(for isolated tank) (4.1)
1.5 Numerical study
Earthquake response of elevated isolated R.C.C. Tank of capacity 284.79kl is investigated under real earthquake
ground motion. The various responses obtained are predicted as below.
Table 1.1 Properties of Tank [1],[2],[3],[4],[5],[6],[7]
Aspect
ratio
S= H/R
Height of
tank (H)
(meter)
0.61
15
Ratio of Tank
wall thickness/radius
0.004
Natural
frequency
of
convective
mass ωc
(HZ)
0.61
Natural
frequency
of impulsive
mass ωi
(HZ)
2.84
Modulus of
elasticity of wall
E
(kn/m2)
6
22.36x10
Mass
density of tank
wall
(kn/m3)
25
Table 1.2 Properties of earthquake ground motion [3]
Earthquake
Magnitude
Record/Component
PGA
Kern-Country (1952/07/21
M(7.5)
KERN/HOL-UP
0.022(g)
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International Journal of Application or Innovation in Engineering & Management (IJAIEM)
Web Site: www.ijaiem.org Email: editor@ijaiem.org, editorijaiem@gmail.com
Volume 2, Issue 2, February 2013
ISSN 2319 - 4847
Fig.3 time variation of elevated liquid tank response under kern-country (1952/07/21) earthquake
Fig. 4 Elastic restoring forces of elevated liquid tank response under kern-country (1952/07/21) earthquake
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International Journal of Application or Innovation in Engineering & Management (IJAIEM)
Web Site: www.ijaiem.org Email: editor@ijaiem.org, editorijaiem@gmail.com
Volume 2, Issue 2, February 2013
ISSN 2319 - 4847
Fig. 5 variation of various responses of elevated liquid tank against aspect ratio
2. CONCLUSION
Performance of elevated liquid storage tank is investigated by putting the base isolation system at the bottom of the
supporting tower under real earthquake ground motion. The earthquake response of isolated tank is compared with
non-isolated tank to measure the effectiveness of the isolation. It is observed that the base shear of elevated liquid
storage tank is significantly reduced due to isolation. The peak earthquake response predicted by the isolation system is
slightly more also it is concluded that seismic isolation increase with increase of bearing flexibility and damping.
REFERENCES
[1] IS 3370-1967-PART I, “Code of practice for concrete structure for storage of liquids” Bureau of Indian standards,
New Delhi.
[2] IS 3370-1967-PART II, “Code of practice for concrete structure for storage of liquids” Bureau of Indian standards,
New Delhi.
[3] IS 3370-1967-PART III, “Code of practice for concrete structure for storage of liquids” Bureau of Indian standards,
New Delhi.
[4] IS 3370-1967-PART IV, “Code of practice for concrete structure for storage of liquids” Bureau of Indian standards,
New Delhi.
[5] IS 1893-1984-PART II, “Criteria for earthquake resistant design of structures” Bureau of Indian standards, New
Delhi.
[6] IS: 11682-1985, “Criteria for design Of RCC staging for overhead water tanks” Bureau of Indian standards, New
Delhi.
[7] Jain S.K., Jaiswal O. R. IITK-GSDMA Guidelines for seismic design of liquid storage tanks
[8] MATLAB version R200a.
[9] Shrimali M. K. And Jangid R.S. Earthquake response of isolated elevated liquid storage steel tanks, Dept.Of Civil
Engg. IIT, Bombay.
AUTHOR
Pravin B. Waghmare, Ph.D Candidate, Department of Civil Engineering, Rashtrasant Tukadoji Maharaj
Nagpur, University Nagpur
Volume 2, Issue 2, February 2013
Page 87