National Conference on Recent Advances in Civil and Structural Engineering (RACSE-'14)
ISBN: 978-81-927554-1-0
FLUID-STRUCTURE INTERACTION APPROACHES FOR SEISMIC
BEHAVIOR OF ELEVATED WATER TANK
1
2
3
Jay J. Patel , Chirag N. Patel and H. S. Patel
Abstract: In the 21st Century, with the expansion of cities, it is required to store and distribute
water to areas far away from water reservoirs. RC elevated water tank is a feasible alternate for
distributing water under natural head to the maximum possible area. It is very important for
water tank to remain in function later to any natural calamity like earthquake. Seismic behaviour
of them has to be investigated in depth. It can be seen from the literature that fluid-structure
interaction plays an important role on seismic behaviour of elevated tanks. The main aim of this
study is to analyse water tank in SAP 2000 considering fluid-structure interaction and compute
structural response such as base shear, overturning moment, top displacement and sloshing
displacement under response spectrum seismic analysis. Result shows dynamic response of SAP
2000 can be used for further analysis and fluid-structure interaction can be assigned using
alternate approach.
Keywords: Fluid-Structure Interaction, Impulsive Mass, Convective Mass.
INTRODUCTION
Water supply is a lifeline facility that must remain operational following a disaster hence, we
should think of what will happen to elevated tank in case of seismic loads, cyclone etc. The
Indian sub - continent is highly vulnerable to natural disasters like earthquake, droughts,
floods, cyclones etc. These natural disasters are causing many casualties and innumerable
property losses each year. Of all the natural calamities, earthquakes occupy first place in
vulnerability. An earthquake occurs when two tectonic plates move or slip from its position
and produces energy that is transferred to the earth’s surface. This energy transforms into a
seismic wave causing vibration of the ground. History signifies the failure of major
reinforced concrete (RC) elevated water tank have occurred because of earthquakes.
According to seismic code IS: 1893 (Part I): 2000 as in, more than 60% of India is prone to
earthquakes. As elevated tanks are not completely filled, a two-mass idealization as proposed
by Housner (1963) is more appropriate than single mass model and is commonly used as
shown in Fig. 1.
Fig. 1: Two mass model for Elevated Water Tank.
1. Jay J. Patel, P. G. Student, Applied Mechanics Department, L. D. College of Engineering, Ahmedabad.
jayjagdish90@gmail.com. 2. Chirag N. Patel, Assistant Professor, Applied Mechanics Department, L. D. College of
Engineering, Ahmedabad. cnpatel.693@gmail.com 3. Dr. H. S. Patel Principal, Government Engineering College,
Patan. dr.hspatel@yahoo.com .
Organized by ADIT and BVM on 25th - 26th April, 2014
Vol.-I Page No.: 274
National Conference on Recent Advances in Civil and Structural Engineering (RACSE-'14)
ISBN: 978-81-927554-1-0
In multi mass model mass in the container is divided into two parts, impulsive and convective.
The liquid in the lower region of tank behaves like a mass that is rigidly connected to tank wall
termed as impulsive mass and liquid mass in the upper region undergo sloshing motion is termed
as convective mass. When tank containing liquid with a free surface is subjected to horizontal
earthquake ground motion, tank wall and liquid are subjected to horizontal acceleration exerting
impulsive and convective hydrodynamic pressure on tank wall and base causing sloshing. This is
termed as fluid-structure interaction. Under seismic loads, supporting structure acts as a
cantilever of uniform rigidity along the height generating overturning moment. History signifies
failure occurred due to unawareness of seismic behavior of elevated tank and due to lack of its
incorporation in design. The primary aim of this paper is to analyze RC Elevated Water Tank in
SAP 2000 Software considering Fluid-Structure Interaction and thereby understanding behavior
of the Tank responses i.e. base shear, overturning moment, top displacement and sloshing
displacement under seismic analysis.
PROBLEM DESCRIPTION
An intz shape water container of 250 m3 capacity is supported on RC staging of 6 columns
with horizontal bracings of 300 x 600 mm at three levels. Details of staging configuration are
shown in Fig. 2. Staging conforms to ductile detailing as per IS 13920. Grade of concrete and
steel are M20 and Fe415, respectively. Tank is located on hard soil in seismic zone IV.
Density of concrete is 25 kN/m3. Design and other required data for modeling in SAP 2000 is
as shown below (all dimensions are in mm).
Fig. 2: Details of tank geometry.
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Vol.-I Page No.: 275
National Conference on Recent Advances in Civil and Structural Engineering (RACSE-'14)
ISBN: 978-81-927554-1-0
MODEL IN SAP2000
Above stated reinforced concrete elevated water tank is modeled in FE software SAP2000
and structural response i.e. Base shear, Base Moment, Top Displacement and Sloshing
Displacement are computed considering fluid-structure interaction under response spectrum
seismic analysis.
Fig. 3: RC Elevated Water Tank model in SAP 2000.
FLUID-STRUCTURE INTERACTION ASSIGNMENT
There are different ways to handle the fluid–structure interaction problems that can be
investigated by the added mass approach (Westergaard, 1931; Barton and Parker, 1987), the
Eulerian approach (Zienkiewicz and Bettes, 1978), the Lagrangian approach (Wilson and
Khalvati, 1983; Olson and Bathe, 1983) or the Eulerian– Lagrangian approach (Donea et al.,
1982) with the finite-element method. The simplest method of these is the added mass
approach; can be investigated using some of conventional FEM software such as SAP2000,
STAAD Pro and LUSAS as other approaches require special programs that include fluid
elements and sophisticated formulations. Present research is based on GSDMA guidelines
and westergaard added mass approach. Also alternate approach is explored for fluid-structure
interaction assignment.
Westergaard Added Mass Approach
Westergaard added mass approach is the simplest approach among the other added mass
approach; it can be investigated using some of conventional FEM software such as SAP2000,
STAAD Pro and LUSAS. In present study we considered FE Software SAP2000 for fluid –
structure modeling.
The general equation of motion for a system subjected to an earthquake excitation can be
written as,
Mü + Cu + Ku = -Müg (1)
In which M, C and K are mass, damping and stiffness matrices, ü, u and u are the
acceleration, velocity and displacement respectively, and g is the ground acceleration.
In the case of added mass approach the form of above equation becomes as below:
M̽ü + Cu + Ku = -M̽üg (2)
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Vol.-I Page No.: 276
National Conference on Recent Advances in Civil and Structural Engineering (RACSE-'14)
ISBN: 978-81-927554-1-0
In which M* is the new mass matrix after adding hydrodynamic mass to the structural
mass, while the damping and stiffness matrices are same as in equation 1.
Fig. 4: FEM Model for fluid-structure interaction added mass approach.
Westergaard added mass approach was originally developed for the dams but it can be
applied to other hydraulic structure, under earthquake loads i.e. tank. In this study the
impulsive mass has been obtained according to GSDMA guideline technique and is added to
the tanks walls according to Westergaard Approach as shown in Fig. 5 using equation 3
where, ρ is the mass density, h is the depth of water and Ai is the area of curvilinear surface.
Fig. 5: (a) Westergaard added mass concept (b) normal and Cartesian directions.
⎡7
⎤
mai = ⎢ ρ h(h − yi ⎥ Ai (3)
⎣8
⎦
Alternate Approach for Mass Distribution
Analysis of hydrodynamic structure such as elevated concrete water tank is quite complicated
when compared with other structures. As well as dynamic fluid-structure interaction (FSI)
plays an important effects in this complexity for which research suggests solution by using
different methods. Algreane Gareane A. I.et al (2009) suggested the dynamic behavior of
elevated concrete water tank with alternative impulsive masses configurations. The suggested
model is to distribute the impulsive mass, by different alternative configurations which are
easier than Westergaard technique. The impulsive mass is considered to be acting at the level
of gravity center of empty container tank walls, and distributed into 4, 8, 16, 24 and 48
masses, as shown in the figure 6.
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Vol.-I Page No.: 277
National Conference on Recent Advances in Civil and Structural Engineering (RACSE-'14)
ISBN: 978-81-927554-1-0
Fig. 6: Alternate approach for mass assignment.
Comparative Study for Mass Assignment
A study is done for analyzing the behavior of tank under Westergaard approach and Alternate
approach. For the study, above stated problem is considered and structural response from
SAP 2000 software in both the case is compared and studied. Mass is applied at centre of
gravity of empty container level to wall which is divided into 24 panels.
Results show that the effect of alternative mass distribution has a minor effect on the dynamic
response of elevated tank. It also proves that, the mass could be distributed by any of two
methods. In present research alternate approach is used for fluid-structure interaction
assignment.
Response
Westergaard Approach Alternate Approach
% Variation
Base Shear (kN)
278.099
278.557
0.16
Base Moment (kN-m)
5189.45
5238.59
0.94
Top Displacement
(mm)
19.9
19.9
0.00
Table 1: Structural response comparison for Westergaard Approach and Alternate
Approach
RESULTS
Response spectrum analysis for tank is done in FE Software SAP 2000 and structural
response is computed and compared with manual calculations. Following is the comparison
of response.
Response
Base Shear (kN)
Base Moment (kN-m)
Top Displacement(mm)
Sloshing Displacement (mm)
SAP 2000 Manual Calculations % Variation
278.6
5307.6
19.9
17.9
277
5381
-
0.576
1.364
-
Table 2: Structural response comparison for SAP2000 and Manual Calculations.
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Vol.-I Page No.: 278
National Conference on Recent Advances in Civil and Structural Engineering (RACSE-'14)
ISBN: 978-81-927554-1-0
CONCLUSIONS
Based on the above mentioned analysis procedure and results, following conclusions can be
drawn.
Results show that there is a minor effect in the dynamic response of elevated tank compared
to both the approaches i.e. westergaard approach and alternate approach. Also dynamic
response from SAP2000 and manual calculations shows minor effect. It also proves that, the
model is verified and SAP2000 can be used for further analysis. Also distribution of water
mass in container is done in the form of impulsive mass and convective mass considering
fluid-structure interaction by alternate approach method is acceptable.
REFERENCES
Gareane A. I. Algreane, S. A. Osman, Othman A. Karim, and Anuar Kasa, (2011). Dynamic
Behavior of Elevated Concrete Water Tank with Alternate Impulsive Mass Configurations,
Proceedings of the 2nd WSEAS International Conference on ENGINEERING MECHANICS,
STRUCTURES and ENGINEERING GEOLOGY.
IITK-GSDMA Guidelines for Seismic Design of Liquid Storage Tanks Provisions with
commentary and explanatory examples, 2003.
I.S 1893-2002, Criteria for earthquake resistant design of structures, Reinforced Concrete
Structures.
Jay J. Patel, Chirag N. Patel, H. S. Patel, (2014). Seismic Performance of RC Elevated Water
Tank-State of Art Literature Review, National Conference on Immerging and Engineering
Technologies, SRPEC, 2014.
Structural Analysis Program SAP2000. User’s manual, Computers and Structures, Inc., Berkeley,
Calif.
Ramazan Livaoglu and Adem Dogangün, (2006). Evaluation of Seismic Models for FluidElevated Tanks Systems Suggested in Codes, 7th International Congress on Advances in Civil
Engineering, 6-8 October 2006, Yildiz Technical University, Istanbul, Turkey.
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