T.C. 

İSTANBUL KÜLTÜR UNIVERSITY 

INSTITUTE OF GRADUATE STUDIES 

 

 

 

 

 

 

 

 

 

SEISMIC RESPONSE OF LIQUID STORAGE TANKS ON BASE ISOLATED 

STRUCTURES WITH TRIPLE FRICTION PENDULUM SYSTEM  

 

 

 

 

 

Master of Applied Science Thesis 

 

 

HAMZA HASSAN NUH 

 

1800005586 

 

 

 

 

 

Department: Civil Engineering 

 

Programme: Structural Engineering 

 

 

 

Supervisor: Assist. Prof Dr. Gökhan YAZICI 

 

 

 

 

January 2022



  

T.C. 

İSTANBUL KÜLTÜR UNIVERSITY 

INSTITUTE OF GRADUATE STUDIES 

 

 

 

 

 

SEISMIC RESPONSE OF LIQUID STORAGE TANKS ON BASE ISOLATED 

STRUCTURES WITH TRIPLE FRICTION PENDULUM SYSTEM 

 

 

Master of Applied Science Thesis 

 

 

HAMZA HASSAN NUH  

 

1800005586 

 

Department: Civil Engineering 

 

Program: Structural Engineering 

 

 

Supervisor and Chairperson: 

Assist. Prof Dr. Gökhan YAZICI 

Members of Examining Committee: 

Assist. Prof Dr. Erdal COŞKUN 

Assist. Prof Dr. Cenk ÜSTÜNDAĞ 

 

 

 

 

January 2022 



i  

ACKNOWLEDGEMENT 

In the name of Allah, the most compassionate and merciful. Alhamdulillah. All praise 

and thanks to Allah for his strength and blessing in allowing me to complete this thesis. 

I am immensely thankful to my supervisor, Assist. Prof. Dr. Gökhan YAZICI, for his 

great guidance and, at times, tremendous patience throughout my studies and thesis at 

Istanbul Kultur University. I am really grateful to him for the knowledge and advice 

he has shared with me. Without his help and guidance, this work would not have been 

completed.  

From the bottom of my heart, I would like to extend my profound thanks to my family, 

without whom my education journey would be impossible to achieve. To my sisters, 

who motivated me to pursue my dreams, I will always be sincerely grateful for their 

everlasting love and support. To my mother, Sado Mohamud Ige, for her unwavering 

hope in me and her prayers. I am extremely thankful to my brother, Abdiaziz Nuh, for 

his hard work, which enabled him to provide me the opportunity to achieve the kind 

of education I aspired to. 

 

  



ii  

University:        İstanbul Kültür University  

Institute:           Institute of Graduate Studies  

Department:     Civil Engineering  

Program:          Structural Engineering  

Supervisor:       Assist. Prof. Dr. Gökhan YAZICI 

ABSTRACT 

The use of base isolation systems is a common and effective method of reducing the 

seismic response of structures. This thesis investigates the seismic response of liquid 

storage tanks in a base isolated structure isolated with Triple Friction Pendulum 

bearings subjected to six unidirectional near-field ground motions. The time history 

analysis of the structure was conducted with the Sap2000 structural analysis program. 

The seismic response of liquid storage tanks with different aspect ratios located in 

different floors was investigated for both the fixed base and the isolated structure using 

the floor accelerations obtained from the time history analysis of the building model.  

Seismic response of the contained liquid has been modelled using a mechanical 

analogue model which considers the flexibility of the tank wall.  The variation of tank 

design parameters namely, the base shear, overturning moment, and liquid sloshing 

displacement were investigated for the fixed base and isolated structure using a 

MATLAB script. The analysis results indicate that base isolation can significantly 

reduce the dynamic response of tanks during earthquake ground motion events, 

especially for the tanks located on the upper floors of the structure.  

 

Keywords: Liquid storage tanks; seismic isolation; triple friction pendulum; 

sloshing. 

 

 

 



iii  

 

 

Üniversite: İstanbul Kültür Üniversitesi  

Enstitüsü: Lisansüstü Eğitim Enstitüsü  

Anabilim Dalı: İnşaat Mühendisliği  

Programı: Yapı (İngilizce)  

Tez Danışmanı: Dr. Öğretim Üyesi Gökhan YAZICI 

ÖZET 

Sismik izolasyon sistemlerinin kullanımı, yapıların sismik tepkisini azaltmak için 

yaygın ve etkili bir yöntemdir. Bu tez, altı tek yönlü yakın alan yer hareketine maruz 

kalan Üçlü Sürtünmeli Sarkaç mesnetleri ile izole edilmiş, sismik izolasyonlu bir 

yapıdaki sıvı depolama tanklarının sismik davranışını araştırmaktadır. Yapının zaman 

tanım alanı analizi Sap2000 yapısal analiz programı ile yapılmıştır. Bina modelinin 

zaman tanım alanı analizinden elde edilen kat ivmeleri kullanılarak, farklı katlarda 

bulunan farklı en boy oranlarına sahip sıvı depolama tanklarının sismik davranışı hem 

sabit taban hem de sismik izolayonlu yapı için incelenmiştir. Depolanan sıvının sismik 

davranışı, tank duvarının esnekliğini dikkate alan mekanik bir analog model 

kullanılarak modellenmiştir. Tank tasarım parametrelerinin değişimi, yani taban 

kesmesi, devrilme momenti ve sıvı çalkantı yer değiştirmesi, bir Matlab betiği 

kullanılarak sabit taban ve sismik izolasyonlu yapı modelleri için araştırılmıştır. Analiz 

sonuçları, sismik izolasyonun, özellikle yapının üst katlarında bulunan tanklar için, 

deprem yer hareketi etkisi altında tanklarda oluşan dinamik etkileri önemli ölçüde 

azaltabileceğini göstermektedir. 

Anahtar Kelimeler: Sıvı depolama tankları; Sismik İzolasyon; Üçlü Sürtünme Sarkaç 

sistemi; Çalkalanma



iv  

TABLE OF CONTENT 

ACKNOWLEDGEMENT ...................................................................................... i 

ABSTRACT ........................................................................................................... ii 

ÖZET..................................................................................................................... iii 

TABLE OF CONTENT ........................................................................................ iv 

LIST OF FIGURES .............................................................................................. vi 

LIST OF TABLES ................................................................................................ ix 

LIST OF ABBREVIATIONS .................................................................................x 

LIST OF SYMBOLS ............................................................................................ xi 

CHAPTER 1............................................................................................................1 

INTRODUCTION ...............................................................................................1 

1.1 Introduction .................................................................................................1 

1.2 The Objectives and Aim of The Thesis .........................................................2 

1.3 Organization of the Thesis ...........................................................................3 

1.4 Literature Review.........................................................................................4 

CHAPTER 2............................................................................................................6 

SEISMIC BASE ISOLATION ............................................................................6 

2.1 Overview .....................................................................................................6 

2.2 Effects of seismic base isolation ...................................................................7 

2.3 Seismic Base Isolation Systems....................................................................8 

2.3.1 Elastomeric Bearings .............................................................................8 

2.3.1.1 Natural Rubber Bearings .................................................................9 

2.3.1.2 Lead Rubber Bearings .....................................................................9 

2.3.1.3 High Damped Rubber Bearings ..................................................... 10 

2.3.2 Sliding Bearings .................................................................................. 10 

2.3.2.1 Single Friction Pendulum Bearings ............................................... 11 

2.3.2.2 Double Friction Pendulum Bearings .............................................. 11 

2.3.2.3 Triple Friction Pendulum Bearings ................................................ 12 

2.4 Geometry of Triple Friction Pendulum Bearings ........................................ 12 

 



v  

CHAPTER 3.......................................................................................................... 14 

MODELING AND ANALYSIS OF THE ISOLATED STRUCTURE............. 14 

3.1 Description of the Isolated Model .............................................................. 14 

3.2 Properties of the Isolators ........................................................................... 15 

3.3 Triple Pendulum Isolator Link Element Properties ..................................... 16 

3.4 Defining Time History Input ...................................................................... 19 

3.5 Defining Load Case ................................................................................... 21 

3.6 Comparison of The Results to Check the Model ......................................... 25 

3.7 Ground Motion Excitation .......................................................................... 28 

3.8 Scaling of the Ground Motion Events ......................................................... 35 

CHAPTER 4.......................................................................................................... 37 

LIQUID STORAGE TANK .............................................................................. 37 

4.1 Liquid Storage Tank Models ...................................................................... 37 

4.2 Mechanical Analogue Model...................................................................... 37 

4.3 Seismic Analysis of Tank and Modeling of Liquid ..................................... 37 

4.4 Model Parameter Properties ....................................................................... 38 

4.5 Seismic Response Parameters .................................................................... 39 

CHAPTER 5.......................................................................................................... 43 

RESULTS AND DISCUSSION ......................................................................... 43 

5.1 Overview ................................................................................................... 43 

5.2 Base Shear ................................................................................................. 44 

5.2 The Liquid Displacement Due to The Sloshing .......................................... 51 

5.3 Overturning Moment .................................................................................. 56 

CHAPTER 6.......................................................................................................... 60 

CONCLUSION AND RECOMENDATION .................................................... 60 

6.1 Conclusion and Recommendation .............................................................. 60 

REFERENCES ..................................................................................................... 62 

APPENDIX A ........................................................................................................ 65 

APPENDIX B ........................................................................................................ 71 

 



vi  

LIST OF FIGURES  

Figure 2.1: The Behavior Of Fixed Base And Isolated Structure [8]. .........................6 

Figure 2.2:  Effect Of The Period Shift In Isolated Structures On Accelerations [10]. 7 

Figure 2.3:  Effect Of The Period Shift In Isolated Structures On Displacement [11]. 8 

Figure 2.4: Natural Rubber Bearing [14] ...................................................................9 

Figure 2.5:  Lead Rubber Bearing [15]. ................................................................... 10 

Figure 2.6: Geometry Of Spherical Friction Pendulum Bearings [22]. ..................... 13 

Figure 3.1: Schematic Of Four-Story Planar Structure (Dimensions In Inches) [23] 15 

Figure 3.2: Link/Support Property Data Of TFP On SAP2000 ................................ 16 

Figure 3.3: U1 Directional Properties On SAP2000................................................. 18 

Figure 3.4: U2 And U3 Directional Properties On SAP2000. .................................. 19 

Figure 3.5: Definition Of Acceleration Time History On SAP2000 ......................... 20 

Figure 3.6: Definition Of Time History Ramp Function On SAP2000. .................... 21 

Figure 3.7: Load Case Model On SAP2000 ............................................................. 22 

Figure 3.8: FNA Vertical Load Case On SAP2000 .................................................. 23 

Figure 3.9: FNA Excitation Load Case On SAP2000 .............................................. 24 

Figure 3.10: Comparison Of Isolator Displacement Histories (Constantino Report) 

[23] ......................................................................................................................... 25 

Figure 3.11: Comparison Of Isolator Displacement Histories (This Report) ............ 25 

Figure 3.12: Comparison Of First Story Drift Ratio Histories (Constantino) [23] .... 26 

Figure 3.13: Comparison Of First Story Drift Ratio Histories (This Report) ............ 26 

Figure 3.14: Comparison Of Roof Acceleration Histories (Conistantio) [23] ........... 27 

Figure 3.15: Comparison Of Roof Acceleration Histories (This Report) .................. 27 

Figure 3.16: Imperial Valley-06 Spectral Acceleration ............................................ 29 

Figure 3.17: Imperial Valley-06 Spectral Displacement .......................................... 29 

Figure 3.18: Imperial Valley-06 Spectral Velocity .................................................. 29 



vii  

Figure 3.19: Coalinga-01 Spectral Acceleration ...................................................... 30 

Figure 3.20: Coalinga-01 Spectral Displacement ..................................................... 30 

Figure 3.21: Coalinga-01 Spectral Velocity ............................................................. 30 

Figure 3.22: Kocaeli Spectral Acceleration ............................................................. 31 

Figure 3.23: Kocaeli Spectral Displacement ............................................................ 31 

Figure 3.24: Kocaeli Spectral Velocity .................................................................... 31 

Figure 3.25: Chi-Chi Spectral Acceleration ............................................................. 32 

Figure 3.26: Chi-Chi Spectral Displacement ........................................................... 32 

Figure 3.27: Chi-Chi Spectral Velocity ................................................................... 32 

Figure 3.28: Iwate Spectral Acceleration ................................................................. 33 

Figure 3.29: Iwate Spectral Displacement ............................................................... 33 

Figure 3.30: Iwate Spectral Velocity ....................................................................... 33 

Figure 3.31: Darfield Spectral Acceleration ............................................................ 34 

Figure 3.32: Darfield Spectral Displacement ........................................................... 34 

Figure 3.33: Darfield Spectral Velocity ................................................................... 34 

Figure 3.34: Collection Of All Matched Accelerograms. ......................................... 35 

Figure 3.35: Target Spectrum To Which The Ground Motions Have Been Scaled ... 36 

Figure 4.1: 5% Damped Spectral Acceleration For Ground Motion (Imperial Valley-

06). ......................................................................................................................... 41 

Figure 5.1: Base Shear Variation Of Three Liquid Storage Tanks On Fixed And 

Isolated Condition Under Imperial Valley-06 .......................................................... 45 

Figure 5.2: Base Shear Variation Of Three Liquid Storage Tanks On Fixed And 

Isolated Condition Under Coalinga ......................................................................... 46 

Figure 5.3: Base Shear Variation Of Three Liquid Storage Tanks On Fixed And 

Isolated Condition Under Kocaeli ........................................................................... 47 

Figure 5.4: Base Shear Variation Of Three Liquid Storage Tanks On Fixed And 

Isolated Condition Under Chi-Chi ........................................................................... 48 



viii  

Figure 5.5: Base Shear Variation Of Three Liquid Storage Tanks On Fixed And 

Isolated Condition Under Iwate ............................................................................... 49 

Figure 5.6: Base Shear Variation Of Three Liquid Storage Tanks On Fixed And 

Isolated Condition Under Darfield .......................................................................... 50 

Figure 5.7: Base Floor Of Liquid Displacement Of Fixed And Base Isolation ......... 52 

Figure 5.8: First Floor Of Liquid Displacement Of Fixed And Base Isolation ......... 53 

Figure 5.9: Second Floor Of Liquid Displacement Of Fixed And Base Isolation ..... 53 

Figure 5.10: Third Floor Of Liquid Displacement Of Fixed And Base Isolation ...... 54 

Figure 5.12: Base Floor Of Overturning Moment Of Fixed And Base Isolation ....... 57 

Figure 5.13: First Floor Of Overturning Moment Of Fixed And Base Isolation ....... 58 

Figure 5.14: Second Floor Of Overturning Moment Of Fixed And Base Isolation ... 58 

Figure 5.15: Third Floor Of Overturning Moment Of Fixed And Base Isolation ...... 59 

Figure 5.16: Fourth Floor Of Overturning Moment Of Fixed And Base Isolation .... 59 

 

 

 

 

 

 

 

 

 

 

 



ix  

LIST OF TABLES  

Table 3.1: Periods of Vibration of Superstructure when Fixed at the Base ............... 15 

Table 3.2: Isolator properties of TFP isolator [23] ................................................... 15 

Table 3.3: Values of Properties of the TFP Isolator Link Element in SAP2000 [23] 17 

Table 3.4: Ground Motion Records ......................................................................... 28 

Table 4.1: Mechanical parameters for the tanks and liquid ...................................... 40 

Table 4.2: Technical specification function of the height-to-radius ratio (H/r) [26]. . 40 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 



x  

LIST OF ABBREVIATIONS 

ERB                : Elastomeric Rubber Bearing 

LRB                 : Lead Rubber Bearing 

PTFE               : Polytetrafluoroethylene   

FP                    : Friction Pendulum 

FPS                  : Friction Pendulum System 

RC                    : Reinforced Concrete 

NRB                 : Natural Rubber Bearing 

LDRB              : Low Damped Rubber Bearing 

HDRB              : High Damped Rubber Bearing 

FNA                 : Fast Nonlinear Analaysis         

LST1                : Liquid Storage Tank 1    

LST2                : Liquid Storage Tank 2   

LST3                : Liquid Storage Tank 3 

 

 

 

 

 

 

 

 

 

 



xi  

LIST OF SYMBOLS 

R1    : R adius of The Outer Bottom Concave Surface of the Triple Friction 

Pendulum  

R2    : Radius of The Inner Bottom Concave Surface of the Triple Friction Pendulum  

R3    : Radius of The Inner Top Concave Surface of the Triple Friction Pendulum  

R4    : Radius of The Outer Top Concave Surface of the Triple Friction Pendulum  

d1     : Displacement Capacity of The Outer Bottom Surface of The Triple Friction 

Pendulum  

d2     : Displacement Capacity of The Inner Bottom Surface of The Triple Friction 

Pendulum  

d3     : Displacement Capacity of The Inner Top Surface of The Triple Friction 

Pendulum  

d4     : Displacement Capacity of The Outer Top Surface of The Triple Friction 

Pendulum  

h1     : Height of The Outer Bottom Surface of The Triple Friction Pendulum  

h2     : Height of The Inner Bottom Surface of The Triple Friction Pendulum  

h3     : Height of The Inner Top Surface of The Triple Friction Pendulum  

h4     : Height of The Outer Top Surface of The Triple Friction Pendulum  

μ1     : Friction Coefficient of The Outer Bottom Surface of The Triple Friction 

Pendulum  

μ2      : Friction Coefficient of The Inner Bottom Surface of The Triple Friction 

Pendulum  

μ3       : Friction Coefficient of The Inner Top Surface of The Triple Friction 

Pendulum  

μ4       : Friction Coefficient of The Outer Top Surface of The Triple Friction 

Pendulum  

h         : uniform thickness of the tank wall 

ρ         :  liquid density (mass) 

 E        : modulus of elasticity.  

Ci        : Impulsive Coefficient  

Cc        : Convective coefficient 

mw        : mass of tank wall 

mr          :  mass of tank roof 



xii  

Se (Timp)        : impulsive spectral acceleration  

Se (Tcon)         : convective spectral acceleration 

hi                    : heights of the centroids of impulsive hydrodynamic pressure wall 

hc                   : heights of the centroids of convective hydrodynamic pressure walls 

hw                  : height center of gravity of the tank wall 

hr                   : height of the center of gravity of the roof 

Q                   :  Total base shear 

M                  : overturning moment 

M’                : overturning moment below base 

d                   : liquid displacement 

g                    : gravity due to acceleration 

Timp               : impulsive period 

Tcon               : compulsive period  

K                  : stiffness  

C                  : damping coefficient  

M                 : mass of the structure  

R(t)              : External Load Vector 

u(t)               : displacement 

u̇(t)               : velocity  

�̈�(t)               : acceleration  

 

 



1  

CHAPTER 1 

INTRODUCTION 

1.1 Introduction 

Conventional seismic-resistant design of structures aims to increase the capacity of the 

structure to withstand the expected lateral inertial forces. However, in terms of cost 

and performance, this method may not be the most efficient. Compared to conventional 

approach, seismic isolation aims to decrease the seismic demand on the superstructure. 

Furthermore, base isolation allows the designer to use a greater variety of architectural 

forms and structural components. 

Base isolation aims to decouple the structure from the damaging effects of earthquake 

ground motions. If the superstructure is isolated from the ground during an earthquake, 

the ground will move, but the structure will only undergo a little movement. The main 

purpose of base isolation is to limit the transfer of earthquake-caused forces to the 

superstructure. Base isolation was first developed in the early 1900s. Base isolation 

works by using isolation bearings with low lateral stiffness, such that in a seismic 

event, when the ground moves strongly, the structure only moves moderately. Base 

isolation reduces the earthquake response of the structure by changing the effective 

fundamental frequency of the system out of the range wherein seismic activity would 

cause the largest inertia forces. In this case, resonance is reduced, and the earthquake 

acceleration response is minimized because the period has been increased well beyond 

the period limit of the seismically induced ground motion [1].  The target fundamental 

period of the isolated structure can be achieved by adjusting the lateral stiffness of the 

isolation system. Base isolation bearings with hysteric force-displacement properties 

have been shown to provide the needed high lateral flexibility and damping while also 

having enough lateral stiffness to resist wind-induced horizontal forces [2]. Over time, 

various base isolation systems have been proposed including, elastomeric rubber 

bearings (ERB), lead rubber bearings (LDB), and PTFE sliding bearings. 

The practice of base isolation has gained prominence in recent decades to provide 

earthquake protection to structures and their components. Today seismic isolation is 

widely used for the seismic protection of structures with motion-sensitive equipment 

(such as computer systems centers), high-risk buildings (such as nuclear power plants),  



2  

and structures of particular significance immediately following earthquakes 

(healthcare centers, disaster management facilities), and storage tanks and vessels.  

This thesis investigates the seismic response of small-scale liquid storage tanks in 

isolated structures. Various types of liquid storage tanks are available, including those 

that are supported on the ground, elevated, and partially buried. The volume, scale, 

and importance of these structures have increased over the years, enabling an 

understanding of their seismic response and the development of appropriate and 

efficient methodologies for their analysis and design to resist seismic ground motion. 

The Friction Pendulum System (FPS) is a remarkably efficient and commonly used 

seismic isolation system of the sliding type. While the volume of filling liquid in a 

storage tank and the weight of the structure are not precisely determined at the time of 

the earthquake, it appears that the FPS performs better since the period of the isolation 

device is not dependent on the mass of the superstructure. 

The seismic behavior of liquid storage tanks is quite complex, especially when 

subjected to near-fault strong ground motions. These seismic events would have an 

effect on the sloshing motion of the liquid [3]. This thesis studies the seismic response 

of liquid storage tanks on isolated structure by FPS subjected to near field ground 

motions. A nonlinear time history analysis is performed on a base-isolated structure, 

and finally, the effect of the base isolation on the response of the liquid tank parameters 

is evaluated and presented. 

1.2 The Objectives and Aim of The Thesis 

The work in this thesis aims to analyze the seismic response of liquid storage tanks 

with different aspect ratios on isolated structures and compare their response with 

liquid storage tanks on fixed base structures. The evaluation of the seismic response 

of the tanks is based on base shear, overturning moment, and sloshing displacement.  

The following tasks will be carried out in order to achieve the objectives: 

 A literature review will be conducted on the seismic response of liquid storage 

tanks on base isolated structures to identify the recent developments and 

research needs in this domain. 



3  

 The theoretical foundations required for modelling and analysis of the isolated 

structure and the liquid storage tanks will be presented.  

 The numerical models to be used in parametric analysis will be prepared and 

calibrated with the models available in the literature review. The isolated 

structure model developed by Sarlis and Constantinou will be used as the 

superstructure model and the model for the liquid storage tanks with 3 different 

aspect ratios will be created using a MATLAB Script.   

 A parametric study will be conducted with a suite of 6 near field earthquake 

ground motions to evaluate the tank design parameters for fixed-base and base 

isolated cases. The storage tanks in the above-mentioned analyses will be 

considered to be totally anchored to the floor in order to experience the floor 

accelerations, and their masses will be considered to have a negligible effect 

on the overall seismic response of the structure.  

 The results and key findings of the parametric study will be presented in the 

conclusions along with topics for further research. 

1.3 Organization of the Thesis 

This thesis is organized into five chapters, which are as follows: 

In chapter one, an introduction to aseismic isolation liquid storage tanks is presented, 

and the aim and objective of the study are shown, as well as the thesis organization is 

described. Also, the literature review findings are presented.  

In chapter two there are three main sections under this chapter. The first section 

presents an overview of seismic base isolation devices and their working principles. In 

the second section, the effects of base isolation systems on the structures are addressed. 

The third section examines the various types of base isolation devices, including their 

categories and subcategories. 

In chapter three, the modeling and analysis of the two-dimensional base-isolated model 

structure with SAP2000 is described. Also, the isolation analysis properties are stated. 

In addition, it presents the seismic ground motion excitations selected for the purpose 

of the analysis of the study.  



4  

In chapter four, a brief description and literature review of seismic analysis of liquid 

storage tanks is addressed. Also, the formulaic and numerical evaluation of a simple 

procedure for analyzing liquid storage tanks is presented. 

In chapter five, the parametric study and its results are presented. Three main 

parameters are the base shear, liquid displacement, and overturning moment of the 

liquid storage tanks.  

Chapter six, which is the last chapter of the thesis, presents the conclusions and 

recommendations.  

1.4 Literature Review 

This section aims to present an assessment of the literature studies on further research 

on the seismic response of liquid storage tanks on isolated structures.  

Harry W. Shenton III and Francis P. Hampton (1999) [4]: In this study, the seismic 

response of an isolated elevated water tank was analyzed using an isolated structure 

model that includes the isolation mechanism, frame structure, and sloshing liquid in a 

separate three-degree of freedom structure. The response spectrum is examined in 

order to determine the natural frequencies and mode shapes. 

A full range of capacity and aspect ratios of the tank and the liquid elevations were 

studied. In comparison to a fixed base tank model, seismic isolation effectively reduces 

overturning moments, base shear, and frame structure drifts. When it came to the 

isolated structure, a single-mode solution was not sufficient since fluid motion had a 

significant impact on the overall structural response. As a result, isolation was more 

successful in the tank with the smallest capacity. Isolation, on the other hand, increased 

the relative convective displacement of fluid in the tank. 

M. K. Shrimali and R. S. Jangid (2003) [5]: performed research on the seismic 

behavior of elevated steel liquid storage tanks. Those tanks are isolated by using linear 

elastomeric bearings under seismic events. The isolation devices are installed at the 

bottom and top of the supported structural steel frame tower in two different tank 

models. The tank models the liquid mass as a lumped mass, often known as sloshing 

mass, and the impulsive mass as a rigid mass. 



5  

Focusing on the tank wall and liquid mass values, the stiffness constant corresponding 

with these lumped masses is being evaluated. In this model, the steel tower structure's 

mass is lumped at the bottom and top. The response of two distinct tank forms, namely 

slender and broad tanks, was evaluated, and a parametric analysis was performed to 

determine the effect of significant system factors on seismic isolation efficacy. Among 

the parameters considered were the tank aspect ratio, tower structure time period, 

damping, and isolation system time period. The seismic response of the isolated tank 

was proven to be significantly reduced in this research.  Furthermore, in terms of 

isolation, a tank with a rigid tower structure is more efficient than a tank with a flexible 

tower structure. 

A. Tokhi and S. Arora (2019) [6]: In this study, intze water tanks, circular water tanks, 

and rectangular water tanks with RCC frame staging in zones of III and V were 

evaluated for seismic analysis and comparison in the empty, half, and fully filled 

conditions using STTAD Pro. According to the three conditions, the intze water tank 

has a higher base shear than the rectangular and circular water tanks in zone III, and 

vice versa in zone IV. When constructing an elevated water tank for full-filled 

situations, the maximum design base shear is critical. 

In Zone III, the circular water tank has the maximum displacement when fully filled, 

while in Zone V, the intze tank had the most displacement. The time period is longer 

for an intze and circular tank in fully filled condition than for a rectangular tank and is 

independent of the other zones. 

 

 

 

 

 

 

 

 



6  

CHAPTER 2 

SEISMIC BASE ISOLATION 

2.1 Overview 

Seismic isolation is a strategy for enhancing a structure's efficiency during earthquakes 

by altering how it reacts. In general, base isolation is an earthquake-prevention 

technique which is used to separate or decouple a structure's motion from ground 

shaking and minimize structural forces [7]. 

The forces transferred to the structure are minimized by isolating it from the ground's 

motion, resulting in a reduction in the demand imposed on the structure's members. 

Separate isolators must always protect the overall superstructure with predetermined 

dynamic properties. Some other isolators are often designed to provide 

significant damping. Displacement and yielding are concentrated at the base isolation 

material position, and the superstructure behaves almost identically to a rigid. 

A conventional or fixed base structure experiences substantial story drifts during 

seismic events, as figure 2.1 shows, which can create long-term damage to the 

structure. On the other hand, isolated structures perform deformation mainly at the 

structure's base [8].  

 

Figure 2.1: The behavior of fixed base and isolated structure [8]. 



7  

2.2 Effects of seismic base isolation 

Seismic base isolation is among the most successful structural control techniques that 

have been developed. It may be used for both new construction and retrofit existing 

buildings and bridges. The base displacements, base accelerations, floor accelerations, 

and relative floor displacements are often used to assess the efficiency of seismically 

isolated structures [9].  

 

Figure 2.2:  Effect of the period shift in isolated structures on accelerations [10]. 

Seismic isolation primarily increases the natural period, which decreases acceleration 

and forces required on the structure [10]; the period shift is shown in figure 2.2.  

As the base isolation increases, the natural time, which improves displacement 

demand, shows in figure 2.3; moreover, the displacement demand is moved from the 

superstructure to the isolation system. 



8  

 

Figure 2.3:  Effect of the period shift in isolated structures on displacement [11]. 

2.3 Seismic Base Isolation Systems 

For the seismic-resistant of structures, several seismic isolation bearings have been 

studied and tested globally. This section provides an overview of each type of bearing's 

fundamental structure and mechanical properties. Isolation devices primarily comprise 

either elastomeric bearings or sliding bearings, though they have been mixed in some 

situations [12]. 

2.3.1 Elastomeric Bearings 

Elastomeric bearings are a vast category of seismic isolation systems. These bearings 

are made up of flexible properties of natural and synthetic elastomeric rubber to obtain 

the suitable properties of an isolation system. The following are some popular 

elastomeric devices: (a) Natural rubber bearing (NRB), (b) Lead rubber bearing 

(LRB), and (c) High-damped rubber bearing (HRB). 

 Every elastomeric isolation bearing comprises multiple layers of rubber pads and 

stiffening plates of steel shims bound along with a strong, semi adhesive. The steel 

shims protect the rubber pads from lateral bulging while providing the device's vertical 

stiffness to support the building weight. The rubber layers are composed of an unfilled 

rubber that provides lateral flexibility [13].  

 



9  

2.3.1.1 Natural Rubber Bearings 

Natural rubber bearings, also referred to as laminated rubber bearings, are made up of 

natural rubber, and a synthetic rubber material used for its hardness and endurance and 

exhibits natural rubber-like properties. Figure 2.4 illustrates a normal, natural rubber-

bearing configuration. Natural rubber bearings are composed of alternate layers of 

rubber and steel shims. To create a laminate bearing, these layers are bonded together 

using a vulcanization process that involves pressure and heat. Steel shims provide 

vertical stiffness to the bearings and prevent the isolated structure from shaking. Steel 

shims also protect the rubber from bursting out when subjected to heavy axial 

compression loads [13]. 

 

Figure 2.4: Natural rubber bearing [14] 

2.3.1.2 Lead Rubber Bearings 

Lead rubber bearings are more capable of providing enough stiffness for wind loads 

and improved damping characteristics than natural rubber bearings. The arrangement 

of a lead rubber bearing is similar to that of a natural rubber bearing, except for the 

presence of one or more circular lead plugs in the center, as illustrated in Figure 2.5. 

In connection with the rubber, the lead plug allows the device to behave bilinearly. 

Under low applied wind loads, the lead plug's high rigidity absorbs most of the load, 

and the configuration exhibits higher stiffness. However, when subjected to strong 

earthquake loads, lead deforms plastically, resulting in the stiffness of the device 

dropping to the stiffness of rubber [13]. 



10  

Furthermore, energy is wasted in a hysteretic way during deformations of the lead 

plug. During strong seismic events, the lead plug deforms similarly to rubber but 

creates heat or releases kinetic energy by turning it into heat. As a result, the hysteretic 

activity of the plug pertains to a reduction in the amount of energy absorbed by the 

structure. Additionally, lead rubber bearings are simple to install, construct, evaluate, 

and design [13]. 

 

Figure 2.5:  Lead rubber bearing [15]. 

2.3.1.3 High Damped Rubber Bearings 

The use of natural rubber bearings with a high damping capacity avoids the need for 

supplemental damping systems. Besides the kind of elastomeric element utilized, their 

construction is identical to that of natural rubber bearings. Increased damping is 

accomplished by using materials such as carbon, oils, and resins. Fillers raised the 

damping to between 20% to 30% of critical damping. When shear strains are less than 

20%, the high damping natural rubber bearings demonstrate a high degree of stiffness 

and damping. This behavior is helpful for reducing deflections caused by wind loads 

in service [13]. 

2.3.2 Sliding Bearings 

Sliding bearing is another kind of seismic base isolation system wherein the sliding 

motion effectively reduces horizontal stiffness. Sliding bearings carry the structure's 

weight on a bearing that is supported by a sliding interface and provided with a low 

coefficient of friction. In most sliding bearings, the sliding interface is made of 

polytetrafluorethylene (PTFE), and the bearing substance is stainless steel. Sliding 

bearings usually use spherical surfaces or smooth flat sliding surfaces. The Friction 



11  

Pendulum System (FPS) bearing is now the most commonly utilized sliding seismic 

isolation bearing globally, and it has a spherical surface. According to pendulum 

mechanisms, FPS bearing, which has more than one mechanism, is multi-spherical 

FPS. The three common types of spherical FPS, as figure 3.6 shows, are (a) single FP 

bearing, (b) double FP bearing, (c) triple FP bearing [16].  

2.3.2.1 Single Friction Pendulum Bearings  

The traditional Friction Pendulum isolator is the Single Friction Pendulum bearing 

system. The single slider sustains the weight support at the structural member's center. 

The single FP bearing isolator also has a low height, which can be helpful in some 

applications. The Single FP isolator provides constant friction, stiffness, and dynamic 

period for all seismic events and displacement stages. An articulated slider on a 

spherical and a spherical surface is used in the bearing system. The slider is coated 

with PTFE (polytetrafluoroethylene), and stainless steel covers the spherical surface. 

Figure 2.6 depicts the geometrical construction of a single FP bearing and identifies 

the described components [17]. 

2.3.2.2 Double Friction Pendulum Bearings  

The double concave FP device was shown to be an effective system for minimizing a 

structure's seismic response during an earthquake. The double concave FP bearing 

comprises two concave stainless-steel surfaces that face one another and are separated 

by an articulated slider. For a proper pressure distribution at the sliding interface, the 

sider's articulation is required to handle various movements over sliding surfaces at 

the top and the bottom [18]. The radii of curvature R1 and R2 on the upper and lower 

concave surfaces may be unequal.  

Therefore, the coefficients of friction are μ1 for one concave sliding surface and μ2 for 

the other surface, which may not always be equal. The height of the sliders h1 and h2 

are the vertical distances from the pivot point to the lower and upper concave surfaces 

consequently. The displacement of the sliders upon the upper concave and the lower 

concave surfaces are d1 and d2 and resulting in the whole bearing displacement 

capacity. Figure 2.6 shows the geometry of double concave friction system [18].  

 



12  

2.3.2.3 Triple Friction Pendulum Bearings 

The triple FP bearing comprises four concave plates divided by an internal discrete 

slider assembly and has three different systems, as shown in figure 2.6. Concave 

surfaces on each side of a spherical inner slider with a low-friction device on both sides 

make up the outer slider [19].  

This creates a first pendulum system that determines the isolation system's properties. 

The outer slider also comprises sliding interfaces between upper and bottom outer 

sliders and the bearing's main spherical surfaces. The second pendulum system is 

created as the bottom sliding surface comes into contact with a curved surface with a 

fixed radius of curvature. Finally, the third pendulum system is created as the upper 

sliding surface comes into contact with another spherical surface with a fixed radius 

of curvature. The features of these three pendulum systems can be designed to 

maximize the seismic isolated structure's efficiency when several degrees of seismic 

hazards are regarded [20].  

2.4 Geometry of Triple Friction Pendulum Bearings 

Triple FP bearings have the following geometrical and frictional properties, which are 

numbered from the bottom to the top of the concave plates. As the outer geometrical 

properties are equal, the inner properties are also identical: R1=R4, R2=R3, μ2=μ3, 

μ1=μ4, h1=h4, h3=h2, d1=d4, d2=d3. The outer concave plates have radii of curvature, 

and it can be inferred that this is the effective radius pendulum, which is the actual 

radius minus the slider height, and that is, Reff1 = R1 − h1, Reff4 = R4 – h4. The inner 

concave plates also have an effective radius pendulum which is the same as the outer 

plates; Reff2 = R2 – h2, Reff3 = R3 – h3.  

The outer surfaces of the slide plates and rigid sliders are coated with a non-metallic 

sliding material characterized by coefficients of friction. The lower main spherical 

surface friction coefficient is smaller than the upper main spherical surface friction 

coefficient. The triple FP bearing is primarily based on the different sliders exceeding 

the maximum horizontal potential of their corresponding slider interfaces during 

motion [21]. 

 



13  

 

Figure 2.6: geometry of spherical friction pendulum bearings [22]. 

 

 

 

 

 

 

 

 

 

 

 

 

 



14  

CHAPTER 3 

MODELING AND ANALYSIS OF THE ISOLATED 

STRUCTURE 

This part presents guidelines on modeling base isolated building. The isolated building 

model that was used in this study was taken from the study of Sarlis and Constantinou 

2015 [23]. In this study, the parameters and modeling procedure will be explained. 

And finally, the model will be used for analyzing the seismic response of elevated 

tank. The type of isolation used is TFP bearing.  

This part, in particular, presents the following: 

 A summary description of the base isolated building. 

 Presentation of the properties of TFP isolator. 

 Defining time history input. 

 Definition of load case. 

 Comparison of the results to check the model. 

3.1 Description of the Isolated Model 

The isolated building model in Figure 3.1 that was used in this study is Sarlis and 

Constantinou's model as mentioned above. The structure is a two-dimensional segment 

of a three-dimensional building with five floors, including the ground level floor, 

which has a plan of 1920in x 768in (19.51m x 48.78m) and a length of 384inches 

(9.75m) between the columns on both the x and y axes and a height of 192inches 

(4.88m). Each floor has a weight of 1080kips (4804 kN) and the total weight of the 

structure including the base floor is 5400kips (24020 kN). Six isolators support the 

two-dimensional building, and each isolator carries 900kips (4003 kN). All floor 

connections are modeled as a rigid diaphragm, with the floor mass given at the joints 

and each joint assigned equal mass. 

Structural damping of 2% of critical for all modes is used when modelling the isolated 

structure. The TCU-065-E component of the 1999 Chi-Chi, Taiwan earthquake is used 

in the analysis [23]. The vibration periods of the first four modes when the model is 

fixed base is presented in Table 3.1. 



15  

Table 3.1: Periods of Vibration of Superstructure when Fixed at the Base 

Mode Period (sec) 

1 0.776 

2 0.253 

3 0.138 

4 0.093 

 

 

Figure 3.1: Schematic of four-story planar structure (dimensions in inches) [23] 

3.2 Properties of the Isolators 

The isolator properties that were used in the analysis are listed in Table 3.2. 

 Table 3.2: Isolator properties of TFP isolator [23] 

Properties Values 

Reff1 = Reff4 (inch), cm (82.5) 210 

Reff2 = Reff3 (inch), cm (7.5) 19.1 

d1 = d4 (inch), cm (17.8) 45.2 

d2 = d3 (inch), cm (0.94) 2.39 

μ1 = μ4 0.108 

μ2 = μ3 0.030 

a1 = a2 = a3= a4 (inch/ sec) cm/sec (2.54) 62.23 

 



16  

3.3 Triple Pendulum Isolator Link Element Properties 

Triple Pendulum Isolator Link Element under the define section properties to the link 

support properties command in SAP2000 was used to model the triple friction 

pendulum bearings. This element has three displacement degrees of freedom, U1, 

which is vertical, U2 and U3, which are horizontal. R!, R2 and R3, represent the 

rotational degrees of freedom. The constraints applied in the model are presented in  

Figure 3.2. 

 

Figure 3.2: Link/support property data of TFP on SAP2000  

 



17  

Table 3.3 shows the numerical values of the parameters used for each of the six 

isolators in the SAP2000 link element, that will be filled in the SAP2000 interface 

window shows in Figure 3.3 and 3.4, Further details of the TFP used in this study may 

be found in Sarlis and Constantinou (2010). 

There are properties of sliding surfaces which are listed below: 

1. Stiffness: is the shear stiffness at the stop just before sliding starts. 

2. Coefficient of friction-slow: Friction Coefficient when the velocity is at zero. 

3. Coefficient of friction-fast: Friction Coefficient when the velocity at a fast rate. 

4. Rate parameter: inverse of the characteristic velocity for friction 

5. Radius: Actual radius of the concave surface. 

6. Stop distance: transversal displacement allowed before reaching a stiff stop 

Table 3.3: Values of Properties of the TFP Isolator Link Element in SAP2000 [23] 

Element Mass (Kip-s2/in) kN-s2/cm (0.003) 0.00525 

Effective Stiffness (Kip/in) kN/cm (9.675) 16.94 

Vertical Stiffness (Kip/in) kN/cm (71176.7) 124649.5 

Rotational/Tortional Stiffness R1=0, R2=Fixed, R3=Fixed 

Rotational Moment of Inertia 1.0 

Properties of Sliding 

Surfaces 

Outer Top Outer  

Bottom 

Inner  

Top 

Inner 

Bottom 

Stiffness (Kip/in) kN/cm (3000) 5254 (3000) 5254 (3000) 5254 (3000) 5254 

Friction of Coefficient-Slow 0.065 0.035 0.015 0.015 

Friction of Coefficient-Fast 0.13 0.07 0.03 0.03 

Rate Parameter (2.54) 1 (2.54) 1 (2.54) 1 (2.54) 1 

Radius (in) cm (82.5) 210 (82.5) 210 (7.5) 19 (7.5) 19 

Stop Distance (in) cm (18) 45.7 (18) 45.7 (2) 5.08 (2) 5.08 

 

 

 

 



18  

Figure 3.3 depicts U1 which is the axial DOF. this DOF is linear, and it is necessary 

to specify the elastic vertical stiffness. 

 

Figure 3.3: U1 directional properties on SAP2000 

Figure 3.4 shows U2 and U3 and they are shear DOF in the two orthogonal directions. 

For elastic analysis, the stiffness associated with these two degrees of freedom should 

be stated as the effective isolator stiffness. And in the nonlinear analysis, the sliding 

surface properties will be determined.  

Also, there will be a torsion degree of freedom that will be designed as R1, and the 

rotational stiffnesses R2 and R3 were fixed in this study. The torsional stiffness (elastic 

DOF) of FP isolators is relatively small, hence a value of zero is appropriate. 

 

 

 

 



19  

 

Figure 3.4: U2 and U3 directional properties on SAP2000. 

3.4 Defining Time History Input 

In this study, defining for the time history input, two function types will be used. First, 

under the time history function, a seismic event excitation will be uploaded by 

choosing a function "from file," as Figure 3.5 shows. The second one will be the ramp 

function, which is under the time history function types for applying the dead load, 

and it will be mentioned a RAMP. As Figure 4.6 shows, the slope of the ramp function 

will be 10 seconds in length.  



20  

 

Figure 3.5: Definition of acceleration time history on SAP2000 

The base isolators used in this study are friction pendulum isolators, which implies 

that their behavior is determined by friction forces, which states that the isolator must 

be loaded with the vertical load before the seismic analyses began. Thus, a time history 

will be used to define the dead load.  

 

 



21  

 

Figure 3.6: Definition of time history ramp function on SAP2000. 

3.5 Defining Load Case 

A load case specifies how load patterns are applied (static or dynamic), how the 

structure responds (linear or nonlinear), and how analysis is carried out (through modal 

analysis, direct integration, etc.) Two default load cases will be defined, the dead and 

the model cases; both of which will be modified.  

The model case: ritz vectors were used as the type of modes. In order to perform fast 

nonlinear analysis, load dependent ritz vectors must be used. The number of Ritz 

vector modes to be used in fast nonlinear analysis must be specified. A total number 

of 200 modes were asked, in this study.  



22  

 

 

Figure 3.7: Load case model on SAP2000 

The dead load case: The load will be applied using the ramp function. For the ramp 

loading, 150-time steps at 0.1 sec intervals were used.  

 



23  

 

Figure 3.8: FNA vertical load case on SAP2000 

Afterward, a new load case for the nonlinear time history will also be added. It will be 

called FNA. For this load case, it will be started from the conclusion of the dead load 

case. The load applied will be an acceleration by using the excitation record event 

function, and it will be scaled from g units. A modal damping constant of 2% was 

used, along with 900, 000-time steps at 0.001sec intervals. 

 



24  

 

Figure 3.9: FNA excitation load case on SAP2000 

 

 

 

 

 

 

 

 

 



25  

3.6 Comparison of The Results to Check the Model 

Figures 3.10 to 3.15 show the results of the analysis re-obtained in the SAP2000 of 

this study by the model, which are then compared to the paper report of Sarlis and 

Constantino [23]. 

 

 

Figure 3.10: Comparison of Isolator Displacement Histories (Constantino report) [23] 

 

Figure 3.11: Comparison of Isolator Displacement Histories (This report) 



26  

 

 

Figure 3.12: Comparison of First Story Drift Ratio Histories (Constantino) [23] 

 

Figure 3.13: Comparison of First Story Drift Ratio Histories (this report) 

 

 

 



27  

 

 

Figure 3.14: Comparison of Roof Acceleration Histories (Conistantio) [23] 

 

Figure 3.15: Comparison of Roof Acceleration Histories (This report) 

 

 

 

 



28  

3.7 Ground Motion Excitation 

Selection of earthquake loading for the purpose of designing and/or analyzing the 

response of a structure is not a straightforward process due to the nature of seismic 

excitation. One possible method for the response of earthquake loading is to assume 

that the structure is subjected to a collection of seismic events that are more likely to 

occur in the area where the structure is located, and then apply that assumption to the 

structure [24]. In this study, a set of six near-field seismic events was applied 

unidirectionally to the seismically isolated structure. The Strong Ground Motion 

database of the Pacific Earthquake Engineering Research (PEER) Center was used. As 

it was mentioned, all the events that have been chosen are near field, meaning that their 

distances are less than 10 km from the fault rupture. These near-field ground motions 

are characterized by large amplitude, high PGV and PGD. And, in particular, the PGA 

is high in this kind of motion since the PGAs of near-fault earthquakes are often high 

and reach the 0.4g PGA recommended by various Building Earthquake Codes. 

Each of the seismic events obtained from the PEER Data Base, for this study, had a 

time history in only one direction, and that direction was H1. All of the events have 

been processed and analyzed with scaling by the SEISMOMATCH program. Some of 

the peak values of the scaled ground motion parameters are mentioned in table 3.4 and 

their acceleration, displacement, and velocity spectrum charts (with 5% damping) are 

shown in Figure 3.16 to 3.33. 

Table 3.4: Ground Motion Records   

No Event RSN Year MW  H1  

     PGA 

(g) 

PGV 

(cm/s) 

PGD 

(cm) 

1 Imperial Valley-06 165 1979 6.53 0.56 48.03 23.37 

2 Coalinga-01 368 1983 6.36 0.58 70.15 82.23 

3 Kocaeli, Turkey 1176 1999 7.51 0.51 55.85 38.53 

4 Chi-Chi, Taiwan 1244 1999 7.62 0.58 50.63 22.60 

5 Iwate, Japan 5619 2008 6.9 0.65 38.87 73.68 

6 Darfield, New Zealand 6897 2010 7 0.65 42.84 20.40 



29  

 

Figure 3.16: Imperial Valley-06 spectral acceleration 

 

Figure 3.17: Imperial Valley-06 spectral displacement 

 

Figure 3.18: Imperial Valley-06 spectral velocity 



30  

 

Figure 3.19: Coalinga-01 spectral acceleration 

 

Figure 3.20: Coalinga-01 spectral displacement  

 

Figure 3.21: Coalinga-01 spectral velocity 



31  

 

Figure 3.22: Kocaeli spectral acceleration 

 

Figure 3.23: Kocaeli spectral displacement 

 

Figure 3.24: Kocaeli spectral velocity 



32  

 

Figure 3.25: Chi-Chi spectral acceleration 

 

Figure 3.26: Chi-Chi spectral displacement 

 

Figure 3.27: Chi-Chi spectral velocity 



33  

 

Figure 3.28: Iwate spectral acceleration 

 

Figure 3.29: Iwate spectral displacement 

 

Figure 3.30: Iwate spectral velocity 



34  

 

Figure 3.31: Darfield spectral acceleration 

 

Figure 3.32: Darfield spectral displacement  

 

Figure 3.33: Darfield spectral velocity 



35  

3.8 Scaling of the Ground Motion Events 

To use seismic records in the design or evaluation of a structural system for earthquake 

hazards, it is suggested that they should be taken from records whose magnitude, 

source-to-site distance, and type of faulting are close to the maximum earthquake 

considered at the site. They are various ground motion scaling procedures. In this 

study, a non-stationary spectral matching procedure was being analyzed. Time domain 

spectral matching is used to create acceleration time histories in non-stationary spectral 

matching techniques. The spectral accelerations of each created acceleration time 

history are fitted almost precisely to the target spectrum using this method. Figure 3.34 

shows the collection of all matched accelerograms, and they are named according to 

their record sequence number (RSN). Although the resulting motions may not be 

realistic in some cases, this is not considered an issue for structural analysis [25].  

Figure 3.35 shows the target earthquake spectrum that was created by using the spectra 

of all of the selected events to generate the target earthquake spectrum and Figure 3.36 

represents a collection of accelerograms showing events that have been unscaled. 

In this study, spectral matching was performed through the use of the SeismoMatch 

software. SeismoMatch is a software that allows earthquake accelerograms to be 

adjusted in order to match a specified target response spectrum.   

 

Figure 3.34: Collection of all matched accelerograms. 



36  

 

Figure 3.35: Target Spectrum to Which the Ground Motions Have Been Scaled 

 

 

 

 

 

 

 

 

 

 

 

 

 

 



37  

CHAPTER 4 

LIQUID STORAGE TANK 

4.1 Liquid Storage Tank Models 

Three steel liquid storage tanks with an isolated and fixed base structure system were 

considered in this study. These liquid storage tanks are placed on the floors of the 

structure, and their elevation heights will vary depending on the floor heights. The 

shapes of the tanks are cylinders, and they are named liquid storage tanks one, two, 

and three (LST1, LST2, and LST3). Their capacities are 7.854, 4.712, and 1.964 cubic 

meters, respectively. Section 4.2 provides a brief explanation of the elevated tanks, 

and Section 3.6 illustrates the frame structure in considerable detail. Table 4.2 provides 

a description of the tank's technical specification function of the height-to-radius ratio 

(H/r). Additionally, Table 4.1 includes mechanical parameters for the tanks and liquid 

that are obtained by the methods described in [26].  

4.2 Mechanical Analogue Model 

Housner, presented a two-mass model for liquid storage tanks that is more suitable and 

is widely used in the majority of international codes [27].  The pressure exerted on the 

liquid as a response to the dynamic motion of the tank can be divided into two 

components – impulsive and convective. When a liquid tank is subjected to a 

horizontal seismic event, both the tank wall and the liquid experience horizontal 

acceleration. The liquid in the tank's lower part acts like a mass rigidly coupled to the 

tank wall. This mass is referred to as "impulsive liquid mass" since it accelerates 

together with the wall, generating hydrodynamic force to be exerted on the tank wall 

and, likewise, on the bottom. Sloshing motion occurs in the upper liquid mass of the 

tank. This mass is referred to as "convective liquid mass," and it generates a convective 

hydrodynamic force on the tank's wall and bottom.  

4.3 Seismic Analysis of Tank and Modeling of Liquid 

The tank was analyzed and detailed as per the simple procedure for tank analysis and 

modelling of liquids proposed by Malhotra that was based on the work of Veletsos and 

co-workers [26]. Malhotra made some adjustments to the procedure that made it easier 



38  

to apply for design. This study will follow the same procedure that was presented with 

the following modifications: 

 Only the first impulsive and first convective modes are used to represent the 

tank-liquid system. 

 Combining the first impulsive mode with the higher impulsive modal mass and 

the first convective mode with the higher convective modal mass. 

 Modifying the impulsive and convective heights to accounting for the 

overturning effect of the higher modes. 

 The impulsive period formula is being generalized so that it may be applied to 

steel and concrete tanks with uniform wall thicknesses. 

As an example, the calculation of the liquid storage tank (LST1) parameters is 

described here, step by step, in order to provide a comprehensive explanation and all 

the other analyzed results are listed in the Appendix A by the help of MATLAB and 

also the MATLAB code scripts for the analysis are in the Appendix B. Before 

analyzing a numerical evaluation, the formulaic parameters are presented and 

discussed in detail in the following section through equations 4.1 to 4.6 by using 

Malhotra’s approach.   

4.4 Model Parameter Properties 

The impulsive (Timp) and convective (Tcon) natural periods are [26] 

𝑇𝑖𝑚𝑝 = 𝐶𝑖
𝐻√ 𝜌 

√𝐻/𝑟 𝑥√ 𝐸 
                           (4.1)    

𝑇𝑐𝑜𝑛= 𝐶𝑐√r                                            (4.2) 

Where: 

h is the uniform thickness of the tank wall, ρ is the liquid density (mass), and E is the 

tank's modulus of elasticity. The Ci and Cc coefficients can be found in Table 1. Ci is 

a dimensionless coefficient, whereas Cc is represented in s/√m. For tanks with non-

uniform wall thickness, h can be computed by taking a weighted average of the tank 

wall's wetted height and assigning the highest weight towards the tank's base, where 

the strain is greatest [26].  



39  

4.5 Seismic Response Parameters 

The formulations of main parameters of the seismic response of liquid storage tank are 

presented here [26].  

1. Base shear: 

Q = (𝑚𝑖 + 𝑚𝑟 + 𝑚𝑤) x 𝑆𝑒(𝑇𝑖𝑚) + 𝑚𝑐𝑆𝑒(𝑇𝑐𝑜𝑛)                 (4.3) 

Where: 

The mi and mc are impulsive and convective masses that are obtained using the data in 

the Table 4.2 and mw is the mass of tank wall, while mr the mass of tank roof. Se(Timp) 

is the impulsive spectral acceleration and Se(Tcon) the convective spectral acceleration 

(obtained from a 0.5% damped response spectrum) [26].  

2. Overturning moment above the base plate 

M = (𝑚𝑖ℎ𝑖 + 𝑚𝑟ℎ𝑟 + 𝑚𝑤ℎ𝑤) x 𝑆𝑒(𝑇𝑖𝑚) + 𝑚𝑐ℎ𝑐𝑆𝑒(𝑇𝑐𝑜𝑛)           (4.4) 

Where: 

The hi and hc are the heights of the centroids of the impulsive and convective 

hydrodynamic pressure walls, respectively, and are obtained from table 4.2. and hw 

and hr are the heights of the tank wall and roof's centers of gravity, respectively [26]. 

3. The overturning moment below the base plate [26]. 

M′ = (𝑚𝑖ℎ′𝑖 + 𝑚𝑟ℎ𝑟 + 𝑚𝑤ℎ𝑤) x 𝑆𝑒(𝑇𝑖𝑚) + 𝑚𝑐ℎ′𝑐𝑆𝑒(𝑇𝑐𝑜𝑛)       (4.5) 

Where: the heights hi’ and hc’ are obtained from Table 4.2.  

4. Liquid displacement due to the sloshing [26]. 

𝑑 = 𝑅
𝑆𝑒(𝑇𝑐𝑜𝑛)

𝑔
                                                                                       (4.6)     

Where: the g is the acceleration due to gravity. 

 

 

 



40  

Table 4.1: Mechanical parameters for the tanks and liquid 

Properties Unit Value of The Three Tanks 

A. General properties  LET1 LET2 LET3 

Height m 2.5 1.5 2.5 

Radius m 1 1 0.5 

Volume m3 7.854 4.712 1.964 

Gravitational Acc. m/s2 9.81 9.81 9.81 

B. Liquid Properties     

Liquid Height m 2 1 1.5 

Liquid Density kg/m3 1000 1000 1000 

Mass of Liquid kg 6.28x103 3.14x103 1.18x103 

C. Wall Properties     

Wall Thickness (Uniform) m 0.005 0.005 0.005 

Modulus of Elasticity N/m2 2*1011 2*1011 2*1011 

 

Table 4.2: Technical specification function of the height-to-radius ratio (H/r) [26]. 

H/r 𝑪𝒊  𝑪𝒄 [s/m] 𝒎𝒊/𝒎𝒍 𝒎𝒄/𝒎𝒍 𝒉𝒊/H 𝒉𝒄/H 𝒉𝒄′/H 𝒉𝒊′/H 

0.3 9.28 2.09 0.176 0.824 0.4 0.521 2.64 3.414 

0.5 7.74 1.74 0.3 0.7 0.4 0.543 1.46 1.517 

0.7 6.97 1.6 0.414 0.586 0.401 0.571 1.009 1.011 

1 6.36 1.52 0.548 0.452 0.419 0.616 0.721 0.785 

1.5 6.06 1.48 0.686 0.314 0.439 0.69 0.555 0.734 

2 6.21 1.48 0.763 0.237 0.448 0.751 0.5 0.764 

2.5 6.56 1.48 0.81 0.19 0.452 0.791 0.48 0.796 

3 7.03 1.48 0.842 0.158 0.453 0.825 0.472 0.825 

 



41  

 

Figure 4.1: 5% damped spectral acceleration for ground motion (Imperial Valley-06). 

Example: Here is the solution analysis for the liquid storage tank 1 (LST1) when the 

tank is on the ground. It is assumed that it is rigid to a concrete mat foundation. The 

radius of the tank is 1 m, and the total height of the tanks is 2.5 m. The ratio of liquid 

height to radius is (H/r = 2). The total mass of water in the tank (ml) is 6283.19 kg. The 

total mass of the tank wall (mw) is 612.61 kg, and the height of its center of gravity is 

1.25 m. The mass of the tank roof (mr) is 122.52 kg and the height of its center of 

gravity (hr) is 2.5 m.  The 5% damped spectral acceleration for ground motion 

(Imperial Valley-06) is shown in figure 4.1. All the other tank material and properties 

are in given in table 4.1. 

Step 1: Model properties 

From Table 4.2: H/r = 2, Ci = 6.21, CC = 1.48 

 

𝑇𝑖𝑚 = 6.21
2√ 1000 

√0.005/1 𝑥√ 2𝑥1011  
=   0.01242𝑠   

 

𝑇𝑐𝑜𝑛=1.48√1 = 1.48𝑠  

 



42  

Step 2: Seismic responses 

From Table 4.2: H/r = 2, mi/ml = 0.763, mc/ml = 0.237 

 

mi = 0.763 × 6.28× 103 = 4.62 × 103 kg 

mc = 0.237 × 6.28× 103 = 1.49 × 103 kg 

From Table 4.2: H/r = 2, hi/H = 0.448, hc/H = 0.751, hi’/H = 0.5 hc’/H = 0.764 

 

From figure 4.1:  Tim =0.01242s, Se (Tim)= 0.604 g, Tcom = 1.48s, Se (Tcon) = 0.33701 

 

Q = (4.62 + 0.6126 + 0.1225)x103 x 0.604 + 1.489𝑥103𝑥0.337 = 3.74 𝑘𝑁 

 

M = (4.62𝑥0.896 +  0.6126𝑥1.25 + 0.1225𝑥2.5) x103x 0.604

+ 1.489𝑥103𝑥1.502𝑥0.337 = 3.9 𝑘𝑁  

 

𝑑 = 1
1.48

9.807
= 0.15 𝑚        

 

 

 

 

 

 

 

 

 

 



43  

CHAPTER 5 

RESULTS AND DISCUSSION 

5.1 Overview 

The seismic response of the three liquid storage tanks (LST1, LST2, and LST3) models 

will be investigated in this section. The results of the analyses for both the isolated and 

fixed base liquid storage tank analyses are described here. We will explore how the 

liquid in the tanks on the floors of the structure, described in Section 3.6, responds to 

two conditions: isolated and non-isolated. 

The entire process of analysing the results can be summarized as follows:  

 Develop a model of a two-dimensional base isolated structure by using 

nonlinear dynamic history analysis as explained in Chapter 3. 

 Again, develop the same previous structure by using the same method of 

analysis (NLDH), but with a fixed base. 

 Analyze three geometrically different liquid storage tanks that have a 

cylindrical shape (see chapter 4). 

 Assume placing the tanks at the center of each floor and apply the floor 

accelerations to them to analyze their response. 

 Finally, evaluate and compare the response results of the tank parameters from 

both frame structures (isolated and non-isolated). 

In this study, six near-fault earthquakes were used. The responses of the liquid storage 

tanks were observed by a parametric analysis, and the following results are presented 

for both isolated and non-isolated conditions:  

1. The total base shear 

2. The liquid displacement due to the sloshing 

3. The overturning moment 

 

 

 



44  

5.2 Base Shear 

Base shear values were computed and presented in Figures 5.1 to 5.6. In general, all 

three liquid storage tanks were analyzed under six near-field seismic events in two 

cases (fixed and isolated) and showed the effectiveness of isolation in reducing the 

base shear demand. In order to make a comparative evaluation, the base shear of the 

tank was divided by its weight. It is clear that the values are reduced in the isolated 

condition. According to the tanks on floor variations, base shear increases as the 

elevation of the tank rise, mostly, however, the top floor has the maximum base shear 

in all tanks.  

The floor variation of base shear forces under Imperial Valley seismic events for liquid 

storage tanks (LST1, LST2, and LST3) in two conditions (isolated and non-isolated) 

are compared and presented in the pictures in Figure 5.1. As expected, the base shear 

is decrease in all of the floors, except the base floor of LST2 and LST3.  

Considering floor elevations (Figure 5.1), the base shear forces in base, first and 

second, third and fourth floor due to LST1 reduce, respectively, by 0.25%, 15%, 22%, 

24%, and 35% assuming isolation model; and the base shear forces in, first and second, 

third and fourth floor due to LST2 reduce respectively, by 31%, 30%, 30% and 45%, 

assuming isolation model, while there is an increase in the base floor. On the other 

hand, due to LST3, the base shear forces in the first and second, third and fourth floor 

reduce respectively by 5%, 19%, 35%, and 44% for the isolation model.  

In general, the foregoing result indicates that base isolation reduces the seismic 

response of the entire system, particularly on the top four floors. Furthermore, the base 

shear force is comparatively larger as the elevation of the tanks increases. 

 



45  

 

 

 

Figure 5.1: Base shear variation of three liquid storage tanks on fixed and isolated 

condition under Imperial Valley-06  

 



46  

 

 

 

Figure 5.2: Base shear variation of three liquid storage tanks on fixed and isolated 

condition under Coalinga 

 



47  

 

 

 

 

Figure 5.3: Base shear variation of three liquid storage tanks on fixed and isolated 

condition under Kocaeli  



48  

 

 

 

Figure 5.4: Base shear variation of three liquid storage tanks on fixed and isolated 

condition under Chi-Chi 

 



49  

 

 

 

Figure 5.5: Base shear variation of three liquid storage tanks on fixed and isolated 

condition under Iwate 



50  

 

 

 

Figure 5.6: Base shear variation of three liquid storage tanks on fixed and isolated 

condition under Darfield 

 



51  

5.2 The Liquid Displacement Due to The Sloshing 

Liquid displacement heights values were analyzed and presented in Figures 5.7 to 5.11. 

In general, all three liquid storage tanks were analyzed under six near-field seismic 

events in two cases (fixed and isolated) and showed the effectiveness of isolation in 

decreasing liquid displacement due to the sloshing in the majority of the case, but the 

base floor is not decreasing. In order to make a comparative evaluation, the 

displacement sloshing heights of the tanks, each figure presents when all the tanks are 

on same floor. 

When the tanks are placed on the base floor, the liquid displacement heights due to the 

sloshing under six near-field seismic events for liquid storage tanks (LST1, LST2, and 

LST3) in two conditions (isolated and non-isolated) are compared and presented in the 

pictures in Figure 5.7. The first two liquid storage tanks (LST1 and LST2) are obtained 

close values while the LST3 is lower in all the events.  

Considering to base floor (Figure 5.7), the liquid displacement heights in Imperial 

Valley-06, Coalinga-01, Kocaeli, Chi-Chi, Iwate, and Darfield due to LST1 increase, 

respectively, by 170%, 54%, 397%, 13%, 24% and 99% assuming isolation model; 

also, the liquid displacement heights in Imperial Valley-06, Coalinga-01, Kocaeli, Chi-

Chi, Iwate and Darfield due to LST2 increase, respectively, by 171%, 47%, 386%, 

11%, 23% and 96% assuming isolation model. 

On the other hand, due to LST3, the liquid displacement heights in Imperial Valley-

06, Coalinga-01, Kocaeli, Chi-Chi, Iwate, and Darfield due to LST2 increase, 

respectively, by 222%, 64%, 528%, 13%, 87% and 127% assuming isolation model. 

The abovementioned result on the base floor indicates that base isolation increases the 

displacement liquid heights, considerably. But in general, according to the compared 

results between non-isolated and isolated tanks, the maximum displacements are 

significantly decreased due to base isolation in the majority of cases. 

 



52  

 

 

Figure 5.7: Base floor of liquid displacement of fixed and base isolation  

 

 



53  

 

Figure 5.8: First floor of liquid displacement of fixed and base isolation  

 

 

Figure 5.9: Second floor of liquid displacement of fixed and base isolation  

 



54  

 

 

 

Figure 5.10: Third floor of liquid displacement of fixed and base isolation  

 



55  

 

Figure 5.11: Fourth floor of liquid displacement of fixed and base isolation  

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 



56  

5.3 Overturning Moment 

The overturning moment values were analyzed and presented in Figures 5.12 to 5.16; 

all of those values are normalized by dividing the isolated values over its 

corresponding fixed base values. In general, all three liquid storage tanks were 

analyzed under six near-field seismic events in two cases (fixed and isolated) and 

showed the effectiveness of isolation in decreasing the overturning moments, but there 

are few findings at the base, first and second floor which are not decreasing. According 

the second and the first floor, under the Coalinga-01 excitation values is not decreasing 

in all the three storage tanks, but the base floor, due to the LST1, LST2 and LST3, the 

overturning moments in Imperial Valley, Kocaeli, and Darfield are not decreasing.  

The findings of the overturning moments that are compared here appear in 

APPENDIX A. 

Considering to top floor (the fourth floor), the overturning moment in Imperial Valley-

06, Coalinga-01, Kocaeli, Chi-Chi, Iwate, and Darfield due to LST1 decrease, 

respectively, by 39%, 20%, 54%, 49%, 42% and 50% assuming isolation model; also, 

the overturning moments in Imperial Valley-06, Coalinga-01, Kocaeli, Chi-Chi, Iwate, 

and Darfield due to LST2 decrease, respectively, by 45%, 26%, 57%, 54%, 44% and 

55% assuming isolation model. On the other hand, due to LST3, the overturning 

moments in Imperial Valley-06, Coalinga-01, Kocaeli, Chi-Chi, Iwate, and Darfield 

due to LST2 decrease, respectively, by 46%, 12%, 64%, 59%, 40% and 54% assuming 

isolation model. 

Considering to the third floor, the overturning moment in Imperial Valley-06, 

Coalinga-01, Kocaeli, Chi-Chi, Iwate, and Darfield due to LST1 decrease, 

respectively, by 27%, 8%, 44%, 31%, 42% and 52% assuming isolation model; also, 

the overturning moments in Imperial Valley-06, Coalinga-01, Kocaeli, Chi-Chi, Iwate, 

and Darfield due to LST2 decrease, respectively, by 32%, 18%, 45%, 38%, 48% and 

58% assuming isolation model. On the other hand, due to LST3, the overturning 

moments in Imperial Valley-06, Coalinga-01, Kocaeli, Chi-Chi, Iwate, and Darfield 

due to LST2 decrease, respectively, by 38%, 5%, 58%, 55%, 38% and 54% assuming 

isolation model.  



57  

Corresponding to the second floor, there will be an increase the overturning moment 

in Coalinga-01, in all the storage tanks, LST1, LST2, and LST3, respectively, by 13%, 

12% and 14% assuming isolation model. But all the other excitations at this floor will 

be decreasing as follows: the Imperial Valley-06, Kocaeli, Chi-Chi, Iwate, and 

Darfield due to LST1 decrease, respectively, by 25%, 38%, 32%, 17%, and 35% 

assuming isolation model; also, the overturning moments in Imperial Valley-06, 

Kocaeli, Chi-Chi, Iwate, and Darfield due to LST2 decrease, respectively, by 31%, 

45%, 33%, 21%, and 38% assuming isolation model. On the other hand, due to LST3, 

the overturning moments in Imperial Valley-06, Coalinga-01, Kocaeli, Chi-Chi, Iwate, 

and Darfield due to LST2 decrease, respectively, by 21%, 43%, 49%, 24% and 38% 

assuming isolation model.  

According to the compared results between non-isolated and isolated tanks, the 

overturning moments are significantly decreased due to base isolation in the majority 

of cases. As the height of the tank elevation decreases, the percentage reduction also 

decreases, and the top floor has the maximum value on all of the tanks. 

 

Figure 5.12: Base floor of overturning moment of fixed and base isolation  



58  

 

Figure 5.13: First floor of overturning moment of fixed and base isolation  

 

 

Figure 5.14: Second floor of overturning moment of fixed and base isolation  



59  

 

Figure 5.15: Third floor of overturning moment of fixed and base isolation  

 

 

Figure 5.16: Fourth floor of overturning moment of fixed and base isolation  

 

 

 

 



60  

CHAPTER 6 

CONCLUSION AND RECOMENDATION 

6.1 Conclusion and Recommendation 

The seismic response of liquid storage tanks supported by a base-isolated structure was 

analyzed using six near-field horizontal earthquake ground motions. Then, the seismic 

response of the isolated tanks was compared to the response of tanks on fixed base 

structure in order to determine the effectiveness of seismic isolation. The liquid storage 

tanks that were investigated in this thesis had three aspect ratios, namely LST1, LST2, 

and LST3. In this study, nonlinear time history analysis was used to determine the 

seismic demands of the liquid storage tanks. Afterwards, parametric analyses were 

carried out in order to determine the impacts of various essential structural parameters 

on seismic base shear forces, liquid displacement, and overturning moments of base 

isolated liquid storage tank structures. Overall, the use seismic isolation devices 

considerably decrease the amount of base shear, overturning moment, and liquid 

displacement. The following conclusions may be made from the results acquired from 

the evaluations of the six near-field selected earthquake records when the typical 

assumed parameters for the isolation system and the tank are taken into consideration: 

1. For the practical range of tank aspect ratios, seismic isolation is efficient in 

decreasing overturning moments, base shear, and liquid displacement. The 

relative decreases are highest for smaller aspect ratio tanks as compared to the 

similar fixed-base design. In low-capacity tanks with a high aspect ratio, 

isolation showed the lowest improvements for the range of parameters 

evaluated. 

2. During seismic excitations, liquid displacement, base shear, and overturning 

moments can be controlled more efficiently by isolated structures than fixed 

base structures. In general, the percentage reduction of the overturning moment 

and base shear increases on the tanks located on the upper floors of the isolated 

structure in comparison with the tanks on the fixed base structure. The 

maximum percentage reduction is found on the top floor. There is one 

exception among the floors: the base floor with the base-isolator, which was 

not decreased. 



61  

This study investigated the influence of seismic isolation on the base shear, 

overturning moment and liquid sloshing displacement for small scale tanks on 

structures. Due to limited size of the tanks considered in the study, the influence of the 

sloshing action on the overall response of the structure was neglected and this 

influence can be considered as a topic for further research. 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 



62  

REFERENCES  

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[6] A. Tokhi and S. Arora, “Seismic Analysis and Comparison of Overhead INTZE 

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[10] E. Blandford et al., “Advanced seismic base isolaton methods for modular 

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[11] F. Naeim, “Seismic design handbook,” p. 450, 1997. 

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Complex Seismic Performance Objectives Tokyo Institute of Technology,” Pacific 

Earthq. Eng. Res. Cent., no. July, 2011. 



63  

[13] J. M. K. and Farzad Naeim, “Design of Seismic Isolated Structures: From Theory 

to Practice,” Earthq. Spectra, 2000. 

[14] http://www.kawakinct.co.jp/english/buildings/a_s01.html 

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on Background Base Isolation for Earthquake Resistance,” City, pp. 1–9, 1906. 

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2004. 

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Environ. Sci., vol. 143, no. 1, pp. 1–12, 2018. 

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Pacific Conf. Earthq. Eng., no. 056, pp. 1403–1424, 2007. 

[19] H. Moeindarbari and T. Taghikhany, “Seismic optimum design of triple friction 

pendulum bearing subjected to near-fault pulse-like ground motions,” Struct. 

Multidiscip. Optim., vol. 50, no. 4, pp. 701–716, 2014. 

[20] T. Morgan and S. Mahin, “The optimization of multi-stage friction pendulum 

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[22] I. E. Kavvadias, et al, “Finite element modeling of single and multi-spherical 

friction pendulum bearings,” Compdyn 2017 - Proc. 6th Int. Conf. Comput. Methods 

Struct. Dyn. Earthq. Eng., vol. 2, no. June, pp. 4408–4416, 2017. 

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64  

[25] Abrahamson, N. A. “Non-stationary spectral matching. Seismological research 

letters,” Vol. 63, 1992. pp. 30. 

[26] P. K. Malhotra, et al. “Simple procedure for seismic analysis of liquid-storage 

tanks,” Struct. Eng. Int. J. Int. Assoc. Bridg. Struct. Eng., vol. 10, no. 3, pp. 197–201, 

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[27] Housner, G. W., and M. A. Haroun. "Dynamic analysis of liquid storage tanks I 

II.” (1980). 

[28] Rostampour, M.A. (2022). Elastic Response Spectra, ElasticSpec.m 

(https://www.mathworks.com/matlabcentral/fileexchange/78029-elastic-response-

spectra), MATLAB Central File Exchange. Retrieved February 10, 2022. 

 

 

 

 

 

 

 

 

 



65  

APPENDIX A 

Results for different important parameters of the tank analysis of different geometric 

elevated tanks (LST1, LST2, and LST3) that are supported on a fixed and isolated base 

structure by the help of MATLAB coding are recorded in tabular form in Tables I and 

VI, which are composed of base shear, overturning moment, and displacement. 

Table I: Base Shear, Overturning Moment and Sloshing Displacement of LST1 

(Isolated) 

 

 

Case Elevation Time History 

Base Shear 

(kN) 

 

Overturning 

Moment 

(kNm) 

Sloshing 

Displacement 

(m) 

 

B
as

e 
Is

o
la

tt
ed

 M
o
d
el

 

 

B
as

e 
F

lo
o

r 

 

Imperial Valley 06 2.5994 3.2590 0.0999 

Coalinga-01 4.3967 5.5061 0.1682 

Kocaeli, Turkey 2.0053 2.6987 0.0994 

Chi-Chi, Taiwan 2.9862 3.5833 0.0953 

Iwate, Japan 2.3748 2.8568 0.0767 

Darfield 2.3725 3.0864 0.1047 

F
ir

st
 F

lo
o
r 

 

Imperial Valley 06 2.5974 3.2565 0.0998 

Coalinga-01 3.2851 4.4596 0.1367 

Kocaeli, Turkey 1.8605 2.4817 0.0896 

Chi-Chi, Taiwan 3.0496 3.6806 0.1000 

Iwate, Japan 2.5262 3.0839 0.0870 

Darfield 2.1148 2.7305 0.0909 

S
ec

o
n
d
 F

lo
o
r 

 

Imperial Valley 06 2.6426 3.3242 0.1029 

Coalinga-01 3.4964 5.0295 0.1446 

Kocaeli, Turkey 1.907 2.5513 0.0927 

Chi-Chi, Taiwan 3.1234 3.7901 0.1048 

Iwate, Japan 2.5272 3.0836 0.0869 

Darfield 2.0748 2.6703 0.0881 

T
h

ir
d

 F
lo

o
r 

 

Imperial Valley 06 2.8063 3.5701 0.1141 

Coalinga-01 4.0953 5.2284 0.1446 

Kocaeli, Turkey 1.9159 2.5644 0.0933 

Chi-Chi, Taiwan 3.2283 3.9490 0.1122 

Iwate, Japan 2.4508 2.9692 0.0817 

Darfield 2.2247 2.8942 0.0982 

F
o

u
rt

h
 F

lo
o

r 

 

Imperial Valley 06 2.8351 3.6133 0.1161 

Coalinga-01 4.3214 5.3667 0.1599 

Kocaeli, Turkey 2.0053 2.6988 0.0994 

Chi-Chi, Taiwan 2.8351 3.6133 0.1161 

Iwate, Japan 2.6352 3.2470 0.0944 

Darfield 2.3582 3.0961 0.1075 



66  

Table II: Base Shear, Overturning Moment and Sloshing Displacement of LST1 

(Fixed) 

Case Elevation Time History 
Base Shear 

(kN) 

Overturning 

Moment 

(kNm) 

Displacement 

(m) 

 

F
ix

ed
 B

as
e 

M
o
d
el

 

B
as

e 
F

lo
o
r 

Imperial 06 2.6060 2.7444 0.0369 

Coalinga-01 5.5042 6.0547 0.1092 

Kocaeli, Turkey 1.2698 1.3542 0.0200 

Chi-Chi, Taiwan 4.7315 5.1206 0.0837 

Iwate, Japan 3.7804 4.0496 0.0618 

Darfield 2.7383 2.9975 0.0526 

F
ir

st
 F

lo
o
r 

 

Imperial Valley 06 3.0511 4.9449 0.1318 

Coalinga-01 3.3290 3.8775 0.0921 

Kocaeli, Turkey 2.1155 2.8723 0.1079 

Chi-Chi, Taiwan 3.0225 3.6685 0.1016 

Iwate, Japan 2.6976 3.5953 0.0651 

Darfield 2.1711 2.8173 0.0950 

S
ec

o
n
d
 F

lo
o
r 

 

Imperial Valley 06 3.3864 4.4412 0.1538 

Coalinga-01 3.7106 4.4476 0.1179 

Kocaeli, Turkey 2.9562 4.1258 0.1644 

Chi-Chi, Taiwan 4.2217 5.5370 0.1660 

Iwate, Japan 2.9473 3.7140 0.1156 

Darfield 3.0247 4.0869 0.1519 

T
h
ir

d
 F

lo
o
r 

 

Imperial Valley 06 3.6750 4.8743 0.1736 

Coalinga-01 4.5423 5.6999 0.1752 

Kocaeli, Turkey 3.2715 4.6005 0.1861 

Chi-Chi, Taiwan 4.3950 5.7033 0.1923 

Iwate, Japan 3.8980 5.1430 0.1808 

Darfield 4.3682 6.1114 0.2447 

F
o
u
rt

h
 F

lo
o
r 

 

Imperial Valley 06 4.3607 5.9051 0.2206 

Coalinga-01 5.1890 6.6701 0.2193 

Kocaeli, Turkey 4.0870 5.8258 0.2420 

Chi-Chi, Taiwan 5.2862 7.0367 0.2527 

Iwate, Japan 4.2271 5.6380 0.2034 

Darfield 4.3837 6.1362 0.2460 

 

 

 

 



67  

Table III: Base Shear, Overturning Moment and Sloshing Displacement of LST2 

(Isolated) 

Case Elevation Time History 

Base Shear 

(kN) 

 

Overturning 

Moment 

(kNm) 

Displacement 

(m) 

 

IS
O

L
A

T
E

D
 B

A
S

E
 

B
as

e 
F

lo
o
r 

Imperial 06 1.5704 0.9456 0.1003 

Coalinga-01 1.6387 1.3750 0.1606 

Kocaeli, Turkey 1.4703 0.8911 0.0972 

Chi-Chi, Taiwan 1.6658 0.8801 0.0932 

Iwate, Japan 1.3579 0.7998 0.0764 

Darfield 1.5817 0.9563 0.1032 

F
ir

st
 F

lo
o
r 

 

Imperial Valley 06 1.5755 0.9488 0.1007 

Coalinga-01 2.1795 1.1944 0.1289 

Kocaeli, Turkey 1.3274 0.8031 0.0869 

Chi-Chi, Taiwan 1.7333 1.0218 0.0981 

Iwate, Japan 1.5064 0.8911 0.0870 

Darfield 1.3958 0.8408 0.0894 

S
ec

o
n
d
 F

lo
o
r 

 

Imperial Valley 06 1.5820 0.9528 0.1011 

Coalinga-01 2.0502 1.3379 0.1339 

Kocaeli, Turkey 1.3137 0.7946 0.0860 

Chi-Chi, Taiwan 1.8166 1.0731 0.1041 

Iwate, Japan 1.4845 0.8776 0.0855 

Darfield 1.3888 0.8366 0.0889 

T
h
ir

d
 F

lo
o
r 

 

Imperial Valley 06 1.7399 1.0501 0.1125 

Coalinga-01 2.3056 1.3720 0.1379 

Kocaeli, Turkey 1.4654 0.8881 0.0968 

Chi-Chi, Taiwan 1.8832 1.1141 0.1089 

Iwate, Japan 1.4119 0.8329 0.0803 

Darfield 1.4808 0.8932 0.0955 

F
o
u
rt

h
 F

lo
o
r 

 

Imperial Valley 06 1.7682 1.0675 0.1145 

Coalinga-01 2.5482 1.5214 0.1553 

Kocaeli, Turkey 1.4703 0.8911 0.0972 

Chi-Chi, Taiwan 1.7682 1.0675 0.1145 

Iwate, Japan 1.6897 1.0040 0.1002 

Darfield 1.6088 0.9721 0.1047 

 

 

 

 



68  

Table IV: Base Shear, Overturning Moment and Sloshing Displacement of LST2 

(Fixed) 

Case Elevation Time History 

Base Shear 

(kN) 

 

Overturning 

Moment 

(kNm) 

Displacement 

(m) 

 

F
IX

E
D

 B
A

S
E

 

B
as

e 
F

lo
o
r 

Imperial 06 0.7511 0.4330 0.0369 

Coalinga-01 1.9656 1.3552 0.1092 

Kocaeli, Turkey 0.4213 0.2417 0.0200 

Chi-Chi, Taiwan 1.8156 0.9389 0.0837 

Iwate, Japan 1.5395 0.8162 0.0618 

Darfield 0.9263 0.5463 0.0526 

F
ir

st
 F

lo
o
r 

 

Imperial Valley 06 2.2913 1.2049 0.1305 

Coalinga-01 1.6653 0.9773 0.0918 

Kocaeli, Turkey 1.6232 0.9853 0.1082 

Chi-Chi, Taiwan 1.9737 1.3569 0.1011 

Iwate, Japan 1.5936 0.7982 0.0644 

Darfield 1.4695 0.8863 0.0946 

S
ec

o
n
d
 F

lo
o
r 

 

Imperial Valley 06 2.2813 1.3836 0.1514 

Coalinga-01 2.3243 1.1988 0.1178 

Kocaeli, Turkey 2.3675 1.4438 0.1616 

Chi-Chi, Taiwan 2.6752 1.6019 0.1657 

Iwate, Japan 1.8618 1.1101 0.1126 

Darfield 2.2310 1.3554 0.1494 

T
h
ir

d
 F

lo
o
r 

 

Imperial Valley 06 2.5335 1.5389 0.1695 

Coalinga-01 2.8004 1.6768 0.1734 

Kocaeli, Turkey 2.6348 1.6085 0.1808 

Chi-Chi, Taiwan 2.9913 1.7967 0.1884 

Iwate, Japan 2.7060 1.6301 0.1732 

Darfield 3.5057 2.1406 0.2409 

F
o
u
rt

h
 F

lo
o
r 

 

Imperial Valley 06 3.1861 1.9409 0.2163 

Coalinga-01 3.4077 2.0509 0.2170 

Kocaeli, Turkey 3.4232 2.0941 0.2374 

Chi-Chi, Taiwan 3.8551 2.3226 0.2497 

Iwate, Japan 3.0002 1.8113 0.1943 

Darfield 3.5145 2.1460 0.2415 

 

 

 

 

 



69  

Table V: Base Shear, Overturning Moment and Sloshing Displacement of LST3 

(Isolated) 

Case Elevation Time History 
Base Shear 

(kN) 

Overturning 

Moment 

(kNm) 

 

Displacement 

(m) 

 

IS
O

L
A

T
E

D
 B

A
S

E
 

B
as

e 
F

lo
o
r 

Imperial 06 0.3582 0.3816 0.06 

Coalinga-01 0.5499 0.3687 0.0898 

Kocaeli, Turkey 0.2997 0.3355 0.0628 

Chi-Chi, Taiwan 0.4018 0.3820 0.0474 

Iwate, Japan 0.3577 0.3912 0.0580 

Darfield 0.3182 0.3437 0.0599 

F
ir

st
 F

lo
o
r 

 

Imperial Valley 06 0.3722 0.3990 0.0684 

Coalinga-01 0.5406 0.5609 0.0892 

Kocaeli, Turkey 0.3166 0.3565 0.0675 

Chi-Chi, Taiwan 0.4030 0.3836 0.0477 

Iwate, Japan 0.4140 0.4235 0.0650 

Darfield 0.3092 0.3319 0.0571 

S
ec

o
n
d
 F

lo
o
r 

 

Imperial Valley 06 0.4052 0.4398 0.0774 

Coalinga-01 0.6455 0.6521 0.1094 

Kocaeli, Turkey 0.3066 0.3440 0.0647 

Chi-Chi, Taiwan 0.4122 0.3949 0.0502 

Iwate, Japan 0.4500 0.4679 0.0749 

Darfield 0.3135 0.3373 0.0583 

T
h
ir

d
 F

lo
o
r 

 

Imperial Valley 06 0.4123 0.4487 0.0794 

Coalinga-01 0.6844 0.7386 0.1286 

Kocaeli, Turkey 0.2857 0.3182 0.0590 

Chi-Chi, Taiwan 0.4253 0.4112 0.0538 

Iwate, Japan 0.4915 0.5193 0.0863 

Darfield 0.3480 0.3780 0.0677 

F
o
u
rt

h
 F

lo
o
r 

 

Imperial Valley 06 0.4225 0.4612 0.0822 

Coalinga-01 0.7552 0.8263 0.1479 

Kocaeli, Turkey 0.2997 0.3355 0.0628 

Chi-Chi, Taiwan 0.4225 0.4612 0.0822 

Iwate, Japan 0.5442 0.5845 0.1007 

Darfield 0.3680 0.4049 0.0733 

 

 

 

 



70  

 

Table VI: Base Shear, Overturning Moment and Sloshing Displacement of LST3 

(Fixed) 

Case Elevation Time History 

Base Shear 

(kN) 

 

Overturning 

Moment 

(kNm) 

Displacement 

(m) 

 

F
IX

E
D

 B
A

S
E

 

B
as

e 
F

lo
o
r 

Imperial 06 0.2415 0.2114 0.0186 

Coalinga-01 0.5802 0.4529 0.0546 

Kocaeli, Turkey 0.1239 0.1094 0.0100 

Chi-Chi, Taiwan 0.4400 0.4000 0.0419 

Iwate, Japan 0.3901 0.4287 0.0310 

Darfield 0.2394 0.2240 0.0263 

F
ir

st
 F

lo
o
r 

 

Imperial Valley 06 0.3927 0.4242 0.0740 

Coalinga-01 0.5076 0.3955 0.0524 

Kocaeli, Turkey 0.3375 0.3825 0.0733 

Chi-Chi, Taiwan 0.5028 0.7080 0.0756 

Iwate, Japan 0.4612 0.4581 0.0506 

Darfield 0.2947 0.3143 0.0533 

S
ec

o
n
d
 F

lo
o
r 

 

Imperial Valley 06 0.5009 0.5581 0.1036 

Coalinga-01 0.5486 0.5709 0.0915 

Kocaeli, Turkey 0.5197 0.6078 0.1231 

Chi-Chi, Taiwan 0.7036 0.7680 0.1328 

Iwate, Japan 0.5691 0.6152 0.1074 

Darfield 0.4800 0.5431 0.1038 

T
h
ir

d
 F

lo
o
r 

 

Imperial Valley 06 0.6312 0.7196 0.1394 

Coalinga-01 0.7181 0.7804 0.1378 

Kocaeli, Turkey 0.6400 0.7564 0.1560 

Chi-Chi, Taiwan 0.8376 0.9213 0.1668 

Iwate, Japan 0.7463 0.8349 0.1562 

Darfield 0.7007 0.8166 0.1644 

F
o
u
rt

h
 F

lo
o
r 

 

Imperial Valley 06 0.7519 0.8688 0.1724 

Coalinga-01 0.8426 0.9344 0.1719 

Kocaeli, Turkey 0.7744 0.9230 0.1929 

Chi-Chi, Taiwan 1.007 1.131 0.2131 

Iwate, Japan 0.8661 0.9830 0.1889 

Darfield 0.7522 0.8801 0.1785 

 

 

 



71  

 

APPENDIX B 

MATLAB code used for the tank analysis. 

% Simple Procedure for Seismic Analysis of Liquid-Storage Tanks Script 

clear 

close 

% Tank Parameters 

htank= 2.5; %Height of the tank (m) 

H=2; % Height of the liquid (m) 

r=1; % Radius of the tank (m) 

rho=1000; % Rho Liquid (kg/m3) 

rhosteel= 7800; %(kg/m^3) 

Esteel= 2*10^11; % Modulus of elasticity (N/m^2) 

h=0.005; %tank wall thickness (m) 

ml=pi*r^2*H*rho; %mass of the liquid (kg) 

mroof=pi*r^2*h*rhosteel; %mass of the roof (kg) 

mwall=2*pi*r*htank*h; %mass of the wall (kg) 

% Earthquake Input 

acc=load('eqa.txt'); %Read Story Acceleration from the file eqa.txt 

dt=0.01; %Time interval 

[Spai,Spvi,Sai,Svi,Sdi,T]=ElasticSpec(acc,dt,20,9.807,0.02,2); %Response Spectra 

for impulsive component [28] 

[Spac,Spvc,Sac,Svc,Sdc,T]=ElasticSpec(acc,dt,20,9.807,0.005,2); %Response 

Spectra for convective component [28] 

 

 

 



72  

% Calculation of the mechanical analogue system parameters 

HrTable=[0.30 9.28 2.09 0.176 0.824 0.400 0.521 2.640 3.414; 0.500 7.74 1.74 0.3 0.7 

0.4 0.543 1.460 1.517; 0.7 6.97 1.60 0.414 0.586 0.401 0.571 1.009 1.011; 1.0 6.36 

1.52 0.548 0.452 0.419 0.616 0.721 0.785;1.5 6.06 1.48 0.686 0.314 0.439 0.690 0.555 

0.734; 2.0 6.21 1.48 0.763 0.237 0.448 0.751 0.500 0.764; 2.5 6.56 1.48 0.810 0.190 

0.452 0.794 0.480 0.796; 3.0 7.03 1.48 0.842 0.158 0.453 0.825 0.472 0.825]; 

HrRat= H/r; %H/r Ratio 

miml=interp1(HrTable(:,1),HrTable(:,4),HrRat,"linear"); 

mcml=interp1(HrTable(:,1),HrTable(:,5),HrRat,"linear"); 

mi=miml*ml; %impulsive mass (kg) 

mc=mcml*ml; %convective mass (kg) 

hiH=interp1(HrTable(:,1),HrTable(:,6),HrRat,"linear"); 

hcH=interp1(HrTable(:,1),HrTable(:,7),HrRat,"linear"); 

hi=hiH*H; %Height of the impulsive mass (m) 

hc=hcH*H; %Height of the convective mass (m) 

Ci=interp1(HrTable(:,1),HrTable(:,2),HrRat,"linear"); 

Cc=interp1(HrTable(:,1),HrTable(:,3),HrRat,"linear"); 

Timp=Ci*(H*rho^0.5)/((h/r)^0.5*Esteel^0.5); % Period of the impulsive component 

(s) 

Tcon=Cc*r^0.5; % Period of the convective component (s) 

%Seismic Response 

STimp=interp1(T,Sai,Timp); %Spectral Accelation for the impulsive component 

STcon=interp1(T,Sac,Tcon); %Spectral Accelation for the impulsive component 

Q=(mi+mwall+mroof)*STimp+mc*STcon; %Total Base Shear 

M=(mi*hi+mwall*htank/2+mroof*htank)*STimp+mc*hc*STcon; %%Total 

Overturning Moment 

d=r*STcon/9.807; %Sloshing Displacement 

 

  


	ACKNOWLEDGEMENT
	ABSTRACT
	ÖZET
	TABLE OF CONTENT
	LIST OF FIGURES
	LIST OF TABLES
	LIST OF ABBREVIATIONS
	LIST OF SYMBOLS
	CHAPTER 1
	INTRODUCTION
	1.1 Introduction
	1.2 The Objectives and Aim of The Thesis
	1.3 Organization of the Thesis
	1.4 Literature Review


	CHAPTER 2
	SEISMIC BASE ISOLATION
	2.1 Overview
	2.2 Effects of seismic base isolation
	2.3 Seismic Base Isolation Systems
	2.3.1 Elastomeric Bearings
	2.3.1.1 Natural Rubber Bearings
	2.3.1.2 Lead Rubber Bearings
	2.3.1.3 High Damped Rubber Bearings

	2.3.2 Sliding Bearings
	2.3.2.1 Single Friction Pendulum Bearings
	2.3.2.2 Double Friction Pendulum Bearings
	2.3.2.3 Triple Friction Pendulum Bearings


	2.4 Geometry of Triple Friction Pendulum Bearings


	CHAPTER 3
	MODELING AND ANALYSIS OF THE ISOLATED STRUCTURE
	3.1 Description of the Isolated Model
	3.2 Properties of the Isolators
	3.3 Triple Pendulum Isolator Link Element Properties
	3.4 Defining Time History Input
	3.5 Defining Load Case
	3.6 Comparison of The Results to Check the Model
	3.7 Ground Motion Excitation
	3.8 Scaling of the Ground Motion Events


	CHAPTER 4
	LIQUID STORAGE TANK
	4.1 Liquid Storage Tank Models
	4.2 Mechanical Analogue Model
	4.3 Seismic Analysis of Tank and Modeling of Liquid
	4.4 Model Parameter Properties
	4.5 Seismic Response Parameters


	CHAPTER 5
	RESULTS AND DISCUSSION
	5.1 Overview
	5.2 Base Shear
	5.2 The Liquid Displacement Due to The Sloshing
	5.3 Overturning Moment


	CHAPTER 6
	CONCLUSION AND RECOMENDATION
	6.1 Conclusion and Recommendation


	REFERENCES
	APPENDIX A
	APPENDIX B