seismic vulnerability assessment of liquid storage tanks...

Research ArticleSeismic Vulnerability Assessment of Liquid StorageTanks Isolated by Sliding-Based Systems

Alexandros Tsipianitis and Yiannis Tsompanakis

School of Environmental Engineering Technical University of Crete 73100 Chania Greece

Correspondence should be addressed to Yiannis Tsompanakis jtsciencetucgr

Received 28 February 2018 Revised 1 August 2018 Accepted 15 August 2018 Published 3 October 2018

Academic Editor Tadeh Zirakian

Copyright copy 2018 Alexandros Tsipianitis and Yiannis Tsompanakis )is is an open access article distributed under the CreativeCommons Attribution License which permits unrestricted use distribution and reproduction in any medium provided theoriginal work is properly cited

Liquid-filled tanks are effective storage infrastructure for water oil and liquefied natural gas (LNG) Many such large-scale tanksare located in regions with high seismicity )erefore very frequently base isolation technology has to be adopted to reduce thedynamic distress of storage tanks preventing the structure from typical modes of failure such as elephant-foot buckling di-amond-shaped buckling and roof damage caused by liquid sloshing )e cost-effective seismic design of base-isolated liquidstorage tanks can be achieved by adopting performance-based design (PBD) principles In this work the focus is given on sliding-based systems namely single friction pendulum bearings (SFPBs) triple friction pendulum bearings (TFPBs) and mainly on therecently developed quintuple friction pendulum bearings (QFPBs) More specifically the study is focused on the fragility analysisof tanks isolated by sliding-bearings emphasizing on isolatorsrsquo displacements due to near-fault earthquakes In additiona surrogate model has been developed for simulating the dynamic response of the superstructure (tank and liquid content) toachieve an optimal balance between computational efficiency and accuracy

1 Introduction

)e safe functioning of liquid storage tanks is of paramountimportance especially in seismic prone regions since thissevere natural hazard can lead to large-scale technologicaldisasters the so-called NATECH events In general cylin-drical liquid storage tanks are structures that are widely usedto store water petrochemicals and liquefied natural gas(LNG) Many such tanks are located in areas subjected tostrong ground motions and the seismic risk is higher com-pared to conventional structures due to devastating conse-quences Failures of storage tanks due to earthquakes cancause leakages and explosions as shown in many cases in thepast earthquakes (Northridge (1994) Kobe (1995) Chi-Chi(1999)) In any case a robust performance-based seismicdesign is required as significant socioeconomical losses andenvironmental problemsmay result from even aminor failure

Compared to ordinary structures (such as buildings andbridges) liquid storage tanks present different dynamicbehavior due to liquid-tank interaction since they are

subjected to inertial earthquake loads and hydrodynamicpressures )e mechanical model of Housner [1] representsthis behavior in a realistic manner More specifically thehydrodynamic response of the tank-liquid system is di-vided in two uncoupled components the impulsive com-ponent (ie the lower part of the liquid that moveshorizontally and follows the tank wall movements) and theconvective component (ie the upper part of the liquid thatgenerates the sloshing motion) Many studies [2ndash4] haveshown the dominance of impulsive liquid component onthe global tank seismic response In contrast the convectivecomponent can be neglected since it is associated to longperiods (which is gt6 sec for the examined tanks) that aresubstantially higher compared to the fundamental periodof the tank-liquid system (approximately 2 sec for theexamined isolated tanks while it is lt02 sec for fixed-baseconditions) )us typical forms of storage tank failures inpast earthquakes (eg ldquoelephant footrdquo and ldquodiamondshaperdquo buckling types) are mostly related to the impulsivecomponent and less caused by liquid sloshing [5]

HindawiAdvances in Civil EngineeringVolume 2018 Article ID 5304245 14 pageshttpsdoiorg10115520185304245

Base-isolation technology is considered as an efficientapproach to reduce the seismic vulnerability of liquid storagetanks )e fundamental concept of base-isolation is theldquodecouplingrdquo of structure from ground motions by installingisolators ie devices with low horizontal and high verticalstiffness to accommodate the vertical loads of the structure)erefore the stresses and accelerations imposed on thetank are notably reduced even if the displacements are quitehigh due to the increased deformability of the flexiblebearings [6 7] Some large-scale liquid storage tanks isolatedby friction isolators are presented in EPS [8] Firstly twoLNG tanks of Revithoussa Greece each having a capacity of65000m3 are equipped with totally 424 SFPB isolatorsSecondly two large LNG tanks located in Melchorita facilityin Peru [9] are isolated by TFPBs where earthquakes withmagnitude gt8 of Richter scale may occur

Many studies have been devoted to the seismic analysisand vulnerability assessment of liquid storage tanks base-isolated with friction isolators Firstly Wang et al [10]studied the effectiveness of SFPBs installed at the base ofcylindrical tanks using a hybrid structure-hydrodynamicnumerical model Parameters such as tank aspect ratiofriction coefficient of SFPBs and earthquake intensity wereexamined It was concluded that the impulsive pressures canbe significantly reduced due to seismic isolation while theconvective pressures were slightly changed Jadhav andJangid [11] compared the seismic response of liquid storagetanks isolated by elastomeric bearings and sliding systemswhile the continuous liquid mass of the tank was modeled aslumped masses namely sloshing mass impulsive mass andrigid mass Using a similar simplified model of the massesPanchal and Jangid [12] investigated the seismic response ofliquid storage tanks isolated with variable friction pendulumsystem (VFPS) Based on the assumption of the concentratedmasses the kinematic equations for the VFPS and thestorage tank were formed and solved It was concluded thatusing VFPS as base-isolation system for liquid storage tankstheir seismic response could be controlled within desirablelimits

)e work of Abali and Uckan [13] reported the efficiencyof SFPBs in controlling the earthquake response of slendertanks compared to squat tanks More specifically a para-metric analysis was conducted taking into account isolationperiod tank aspect ratio and coefficient of friction It wasderived that base shear was reduced for both squat andslender tanks Conversely sloshing displacements of squattanks were not significantly changed )e double variablefrequency pendulum system (DVFPS) that isolated theliquid storage tank was included in the numerical model ofSoni et al [14] )e examined DVFPS was analyzed fordifferent geometry and friction coefficient values )e mainconclusions derived from this study were that DVFPS withhigher initial stiffness from top sliding surface to bottompresented better behavior for slender tank while the isolatorhaving the same initial stiffness and coefficient of frictionperformed better for the squat tank

Seleemah and El-Sharkawy [15] investigated the dy-namic response of elevated squat and slender liquid storagetanks isolated by elastomeric and sliding bearings (SFPB)

In addition the behavior of the storage tanks was comparedfor the cases where the isolators were placed at the bottomor at the top of the supporting structure It was reportedthat base isolation affected in a beneficial manner theslender tanks and less the corresponding squat tanksFurthermore when an elevated tank was isolated withSFPBs it presented better seismic performance than withelastomeric bearings In addition the examined tankpresented better seismic behavior when isolators wereplaced at the top of the shaft support

Panchal and Jangid [16] examined the seismic behaviorof liquid storage tanks equipped with variable curvaturefriction pendulum system (VCFPS) under near-fault groundmotions )e most important parameters for this in-vestigation were the fundamental period the friction co-efficient and the tank aspect ratio It was found that theVCFPS is a quite effective seismic isolation device in con-trolling base shear sloshing displacement and the impulsivedisplacement of liquid storage tanks

Moeindarbari et al [17] investigated the efficiency ofSFPB and TFPB installed at elevated liquid storage tankssubjected tomultihazard level excitations TFPB is capable ofperforming multiple level analysis at different hazard sce-narios such as Service Level Earthquake (SLE) Design BasisEarthquake (DBE) and Maximum Credible Earthquake(MCE) Hence the results revealed that TFPB outperformedthe SFPB since the adaptive performance of TFPB played animportant role in decreasing the seismic demand on theliquid storage tanks Similarly the effectiveness of twoisolation systems of elevated storage tanks was studied byPaolacci [18] Records from the Kocaeli Earthquake (1999)were used for the dynamic analysis of high damping rubberbearing (HDRB) and SFPB installed at the elevated tankslocated in Habas pharmaceutics plant in Turkey It wasconcluded that elevated tanks isolated both by HDRB andSFPB presented major reductions in base shear as well asstress levels in the tankrsquos wall Due to the limitation ofmaximum bearing displacement and the higher value ofsloshing displacement for the HDRB the SFPB was con-sidered as the superior isolation scheme for this specific casestudy

Bagheri and Farajian [19] investigated the impact of PGAlevel and special characteristics of near-fault impulses on theearthquake performance of liquid storage tanks isolated bySFPBs A mechanical model that accurately estimated theseismic response of the liquid storage tank was adopted )eresults indicated that SFPB is an effective isolation systemcapable of reducing critical parameters such as impulsivedisplacement overturning moment and base shear whilethe sloshing displacement did not present significantchanges Phan et al [20] conducted a seismic fragilityanalysis of elevated liquid storage tanks isolated by concavesliding bearings (CSB) For this purpose a lumped-masssimplified model was used for the examined tank )e cloudmethod was applied for the seismic fragility assessmentwhere nonlinear dynamic analysis through a linear re-gression-based probabilistic model was implemented CSBscheme was found to be an effective isolation system for thereduction of the seismic demand on the tank

2 Advances in Civil Engineering

In the majority of the aforementioned studies theseismic response andor vulnerability assessment of liquidstorage tanks base-isolated by SFPBs or TFPBs was in-vestigated )e influence of many critical parameters (iebase shear aspect ratio isolation period etc) on the resultswas examined and it was proven that single-stage (SFPBs)and multistage (such as TFPBs) friction bearings were ef-fective in reducing the seismic response even when strongnear-fault excitations were imposed On the other hand thenewly appeared QFPB is a state-of-the-art seismic isolationdevice capable of accommodating very large displacementsand performing complex multistage behavior [21] It con-sists of six spherical sliding surfaces with five effectivependula To the best of the authorsrsquo knowledge seismicvulnerability assessment of liquid storage tanks isolated byQFPBs has not been reported in the literature

Accordingly in this study which is an extension ofa recent conference paper of the authors [22] the seismicvulnerability assessment of liquid-filled tanks isolated bydifferent types of friction isolators is examined followingperformance-based design (PBD) principles More specifi-cally the study is focused on the response of single-surfaceisolators SFPBs and the corresponding multiple-surfaceisolators TFPBs and QFPBs Utilizing peak ground accel-eration (PGA) as the intensity measure (IM) and isolatordisplacement as the damage index (DI) for three earthquakehazard levels fragility analysis is performed for each of thesethree sliding bearing configurations Surrogate numericalmodels based on the work of Bakalis et al [23] have beendeveloped for modeling both squat and slender liquid storagetanks Compared to detailed finite element simulations suchmodels combine the minimization of computational cost withadequate accuracy of the dynamic response calculations)eyconsist of a concentrated impulsive mass that is attached toa vertical beam element supported by rigid beam spokesMoreover they can be implemented utilizing any general-purpose structural analysis software and can be used for eitherstatic or dynamic analysis

2 Friction-Based Isolation Devices

21 Single Friction Pendulum Bearings Figure 1(a) depictsa typical SFPB which is a device that uses its special geo-metrical setting to provide seismic isolation [24] )ependulum motion is represented by the spherical bearingsurface while the period of the isolator depends on theradius of curvature of the concave sliding surface Addi-tionally another critical feature of SFPB is that the center ofresistance coincides with the center of mass )us thetorsion response of the superstructure is limited )ereforeparameters such as structural response ductility and energydissipation can be controlled and damage to buildingstructural and nonstructural members and contents can beminimized or even avoided

22 Triple Friction Pendulum Bearings TFPB is an adaptivesliding isolation system that can exhibit different stiffnessand damping properties during its operation [25] and

represents the new generation of friction isolators It utilizesmultiple spherical concave sliding surfaces thus both lowtransmissibility of vibration to the superstructure and zeroresidual displacements at the sliding structure after anearthquake are provided [26] Hence its operation is dif-ferent from the conventional sliding bearings that exhibitconstant stiffness and energy dissipation In TFPBs differentcombinations of curvature and friction of sliding interfacescan be selected Moreover these parameters can be adjusteddepending on the imposed excitation levels )ereforemultiple performance objectives can be achieved which isideal from a PBD perspective

A TFPB consists of three friction pendulum mecha-nisms which are activated at different stages as the seismicdemand is amplified As illustrated in Figure 1(b) thesemechanisms are created via four concave surfaces in a singlebearing According to Constantinou et al [27] the two innersurfaces share the same values for their friction coefficients(μ2 μ3) and radius of curvature (R2 R3) Analogously it isalso common that the outer concave surfaces have the samevalues (μ1 μ4) and (R1 R4) In a typical TFPB functioningsliding occurs in different surfaces as the displacementdemand increases When TFPB approaches its maximumdisplacement capacity the surfaces change again due to thefact that the displacement restraints of the sliders arereached causing incremental hardening behavior [28]

)e calculated values of the force-displacement curve forthe TFPB configuration that has been used in the currentinvestigation are shown in Figure 2(a) As it can be easilynoticed it is divided into several parts depending on theselection of geometrical and frictional parameters )e hor-izontal force of TFPB is a combination of the friction forceand the restoring force due to the curvature of the sphericalsurfaces Normalized horizontal force FW is convenientlyused since the resultant force F is proportional to the verticalforceW Evidently TFPB is ideal for PBD since by selectingappropriate values for friction coefficients and radii of cur-vature for each surface different behavior under service levelearthquake (SLE) where sliding occurs on surfaces 2 and 3design basis earthquake (DBE) where motion stops onsurface 2 and sliding occurs on surfaces 1 and 3 and max-imum considered earthquake (MCE) where sliding occurs onsurfaces 1 and 4 can be achieved [8 17]

23Quintuple FrictionPendulumBearings According to Leeand Constantinou [21] the newly developed QFPB is anextended version of TFPB In particular it consists of sixspherical sliding surfaces five effective pendula and nineoperation regimes (Figure 1(c)) in a single bearing )ecomputed force-displacement curve of the examined QFPB isdepicted in Figure 2(b))e adaptability of isolator behavior isincreased due to the increased number of pendula and slidingpatterns )us although the functioning is similar it is ca-pable of a more complex and multistage performance com-pared to TFPB Additionally QFPB is ideal for highdisplacement demands due to severe earthquake excitations

Similar to TFPBs QFPBs can also be implementedwithin a PBD framework Although the number of sliding

Advances in Civil Engineering 3

surfaces is increased (six for QFPBs vs four in the case ofTFPBs as shown in Figures 2(a) and 2(b) respectively) theperformance levels remain the same in this investigation inparticular service level earthquake (SLE) where slidingoccurs on surfaces 3 and 4 design basis earthquake (DBE)where motion stops on surface 6 and sliding occurs onsurfaces 2 and 5 and maximum considered earthquake(MCE) where sliding occurs on surface 1

231 Model Validation In this section the analytical andexperimental validation of QFPBs utilizing finite elementsoftware SAP2000 [29] is presented following the recom-mendations of Lee and Constantinou [21] )e isolator issimulated in the software as a series model combining onetriple friction pendulum (FP) element with one double FPelement )e double FP isolator is actually a ldquocondensedrdquotriple FP element )is is achieved by specifying arbitraryvalues of the radius of curvature and friction coefficient thatlead to motion initiation of the inner sliding surfaces In thismanner the double FP isolator operation is performedutilizing SAP2000 (Figure 3(a)))e configuration examinedhas friction coefficient values μ3 μ4 lt μ5 le μ2 lt μ6 le μ1

Figures 4 and 5 respectively illustrate the force-dis-placement curves taken from a recent study [21] for theexperimental (tested in the experimental setup at the Uni-versity at Buffalo [30]) and the analytical QFPB modelswhich are compared to the numerical results of the sameconfigurations obtained herein utilizing SAP2000 softwareFirstly the experimental model of one QFPB (Table 1) basedon the multistage experimental setup of the isolator tested atthe University at Buffalo [30] is validated numerically viaSAP2000 software A harmonic excitation with frequencyequal to 0005Hz was imposed to the tested QFPB togetherwith a constant vertical load of W 889644N )e dis-placement amplitude of the imposed harmonic motion wasequal to 127mm since this was the displacement capacity ofthe testing device Figure 4 illustrates the validation of QFPBwith respect to the experimental model As it can be noticedin this plot there is an excellent matching of the force-displacement curves of the experimental model and thecorresponding isolator model developed in SAP2000

)e second validation is performed by comparing theobtained numerical results with the corresponding ones ofthe analytical QFPB model for another case study [21] Inthis example a sinusoidal harmonic excitation is imposed to

1

(a)

43

21

(b)

65

4

32

1

(c)

Figure 1 (a) Section view of SFPBs (b) TFPBs and (c) QFPBs where numbers correspond to different sliding surfaces (adopted from [21])

000

005

010

015

020

025

030

035

040

045

0 200 400 600 800 1000Total displacement (mm)

Nor

mal

ized

hor

izon

tal f

orce

(FW

)

(a)

000

005

010

015

020

025

030

0 200 400 600 800 1000

Nor

mal

ized

hor

izon

tal f

orce

(FW

)

Total displacement (mm)

(b)

Figure 2 (a) Computed force-displacement curves for the examined bearing configurations (a) TFPBs and (b) QFPBs


the isolator having an amplitude of approximately 1m equalto the displacement limit of the analytical model Furtherinformation considering the force-displacement expressionsused for the current validation can be found in the detailedstudy of [21] By observing Figure 5 it can be noticed that thenumerical isolator model developed utilizing SAP2000 cap-tures exactly the behavior of the analytical model Hence theQFPB configuration presented in Figure 5 has been con-sidered suitable for the fragility analysis of the examinedliquid storage tanks Consequently after the successful vali-dation of the present numerical implementation of the ex-amined isolators a detailed parametric study has beenperformed regarding their implementation for the seismicisolation of liquid storage tanks as it will be presented in thesequence

3 Multistep Dynamic Analysis

For such critical infrastructures as liquid storage tanks a widerange of ground motion records should be taken into accountfor the reliable implementation of performance-based design

Consequently a huge number of nonlinear dynamic analysesneed to be executed in an incremental manner Incrementaldynamic analysis (IDA) and multiple-stripe dynamic analysis(MSDA) are the most frequently applied methods [31] Suchmethods are widely used in earthquake engineering forseismic performance assessment of various types of struc-tures )ey are based on the simple concept of scaling eachground motion until it leads to the collapse of the examinedstructure MSDA is ideal for performance-based evaluation ofstructures using a set of ground motion records at multipleperformance levels Many sets of analyses are performed formultiple peak ground acceleration (PGA) levels where at eachanalysis (stripe) a number of structural analyses are per-formed for a group of ground motion records which arescaled every time to a specific PGA value In this way a set ofintensity measure and damage index values is produced

)erefore obtaining the relation between the seismicintensity level and the corresponding maximum responsequantity of the base isolation system is the main objective ofthese multistep procedures A suitable intensity measure(IM) and an engineering demand parameter (EDP) describe

ndash150 ndash100 ndash500

04

03

02

01

ndash02

Experimental model [27]Numerical model

ndash03

ndash04Displacement (mm)

QFPB validation - experimental model

Nor

mal

ized

hor

izon

tal f

orce

(FW

)

0 100 15050

ndash01

Figure 4 Comparison of current numerical QFPB model with experimental results derived from Lee and Constantinou [21]

Rigidconnection

Triple FP element

Double FP element

(a)

Rigid bar (weightless)

Triple FP

W W

Double FP

Displacement-controlling point

(b)

Figure 3 (a) Series model of QFPB with a pair of double and triple FP elements and (b) model equipped with QFPBs as implemented inSAP2000 (adopted from [21])


the seismic intensity level and the friction isolators responserespectively Generally the following steps are implementedfor both MSDA and IDA procedures (a) create an efficientnonlinear finite element model for performing repeatednonlinear dynamic analyses (b) select an appropriate groupof natural or artificial accelerograms (c) choose proper IMand EDP and (d) select scaling factors in order to run theanalyses and obtain the IM-EDP curves

4 Fragility Function Evaluation

Seismic fragility is associated to the probability of exceed-ance of a limit state for a given seismic intensity levelTypically a fragility function is defined by a lognormalcumulative distribution function (CDF) [32]

P(C|IM x) Φln(xθ)

β1113888 1113889 (1)

where P(C|IM x) is the probability that a ground motionwith IM x will lead to structural collapse V denotes thestandard normal CDF θ is the median of the fragilityfunction and β is the standard deviation of lnθ Regarding

the selection of IM the PGA is a valid choice for liquidstorage tanks due to the impulsive load pattern [20 33 34]

In the current study fragility curves related to SFPBsTFPBs and QFPBs displacements are calculated for differentperformance levels namely 50 probability of exceedancein 50 years (ie SLE) 10 probability of exceedance in 50years (ie DBE) and 2 probability of exceedance in 50years (ie MCE) In the present investigation the meth-odology for fragility function fitting proposed by Baker [32]has been adopted in which by performing repeated dynamicanalyses for all ground motions and for each IM levela number of failures (ie in terms of isolatorsrsquo displacement)is determined )e probability of zj failures being observedout of nj groundmotions having IM xj is represented by thefollowing binomial distribution [32]

P zj collapses in nj ground motions1113872 1113873 nj

zj

⎛⎝ ⎞⎠pzj

j

middot 1minuspj1113872 1113873njminuszj

(2)

in which pj is the probability that a ground motion withIM xj will cause failure of the structure

When analysis data are obtained at multiple IM levelsthe product of the binomial probabilities at each levelprovides the likelihood for the entire data set

likelihood 1113945m

j1

nj

zj

⎛⎝ ⎞⎠pzj

j 1minuspj1113872 1113873njminuszj

(3)

where m is the number of IM levels and Π is a product overall levels Substituting Equation (1) for pj the fragility pa-rameters are explicitly included in the likelihood function

Table 1 Parameters of the QFPB model (taken from [21])

Radius (m) Height (m) Coefficient of friction Displacementcapacity (m)

R1 04572 h1 003556 μ1 012 d1 00381R2 02032 h2 003048 μ2 0085 d2 003302R3 00508 h3 002286 μ3 0015 d3 001397R4 00508 h4 002286 μ4 0015 d4 001397R5 02032 h5 003048 μ5 0035 d5 003302R6 04572 h6 003556 μ6 011 d6 00381


03

02

01

ndash01

ndash02

Analytical model [27]Numerical model


QFPB validation - analytical model

Nor

mal

ized

hor

izon

tal f

orce

(FW

)

300 800

Figure 5 Comparison of current numerical QFPB model with analytical results derived from Lee and Constantinou [21]


likelihood 1113945

m

j1

nj

zj

⎛⎜⎝ ⎞⎟⎠Φln xjθ1113872 1113873

β⎛⎝ ⎞⎠

zj

middot 1minusΦln xjθ1113872 1113873

β⎛⎝ ⎞⎠⎛⎝ ⎞⎠

njminuszj

(4)

While the maximization of the likelihood functionproduces the estimates of the fragility function parameters asfollows

θ β1113966 1113967 argθβ max 1113944m

j1

⎧⎨

⎩lnnj

zj

⎛⎜⎝ ⎞⎟⎠ + zj lnΦln xjθ1113872 1113873

β⎛⎝ ⎞⎠

+ nj minus zj1113872 1113873lnΦln xjθ1113872 1113873

β⎛⎝ ⎞⎠

⎫⎬

⎭

(5)

5 Base-Isolated Liquid Storage Tanks

51 General Details )e storage tank models presented byHaroun [35] (Tank B and T types) are used in this workMore specifically Tank B (Figure 6(a)) is a squat cylindricaltank with height to radius ratio HR 067 )e radius of thefirst tank is R 1829m the height of liquid surface isH 12192m the tank wall thickness is t 00254m and thetotal weight of the liquid content is W 12627345 kN )esecond model (Figure 6(b)) is a slender cylindrical tank withheight to radius ratio HR 3 Tank T has radius R 732mheightH 2196m width t 00254m and the liquid weightisW 362454 kN)e fundamental periods of the two tank-liquid systems are Tf-B 0162 sec and Tf-T 0188 sec forTanks B and T respectively

52 SurrogateModels Modeling of liquid storage tanks is notan easy task due to the hydrodynamic response of the tank-liquid system [13 19 23] In general detailed finite-elementmodels are computationally demanding [36] To reduce thecomputational load and model complexity one commonapproach is to develop valid simplified models to effectivelyreplace the complicated three-dimensional (3D) models [37])erefore a simplified representation of the liquid storagetank is adopted herein based on the so-called ldquoJoystickmodelrdquo of fixed-base tanks [23])e developed Joystickmodelconsists of a vertical beam element carrying the impulsivemass that is supported by fully rigid beam-spokes which inturn are supported by the sliding bearings (Figure 6) )e twoexamined models are validated by accurate matching of theimpulsive fundamental period (Ti) provided by Eurocode 8-Part 4 [38] recommendations for liquid storage tanks

As aforementioned the hydrodynamic response ismainly affected by the impulsive liquid component )econvective liquid mass is neglected since several studies[18 39 40] have proven that although the impulsive pressureis reduced due to seismic isolation the convective pressureremains practically unchanged Moreover the effects of the

convective part of liquid content can be separately estimated[23] In the developed surrogate model the weight of thewater is represented as lumped masses at the base beam-spokes of the tank (Figure 6) )erefore the vertical load isdirectly applied to the friction isolation devices )e self-weight of the tank can be omitted as it is only 5 of the totaltank mass [12 16 29 34]

53 Design of Isolation Bearings Generally the design ofstructural isolation systems is an iterative process since thebearing properties are influenced by the structural prop-erties Firstly the maximum bearing displacement has to beevaluated which is mostly affected by the target period of theisolated system the weight of the superstructure and theintensity level of the imposed seismic excitation

In this study the equivalent linear force (ELF) procedureaccording to Eurocode 8 (Soil A ci 14 ag 036 g) isapplied for the preliminary design of tank isolation system[41] )e selected SFPB has friction coefficient μ 008radius of curvature R 188m theoretical period of 275 secand displacement limit of 0305m )e TFPB properties arelisted in Table 2 and the total displacement limit for MCElevel is 0762m which is the sum of all partial displacementlimits Finally a QFPB with the properties is shown inTable 3 while the total displacement limit of 104m (ie thesum of all displacements in Table 3) for MCE level iscomputed following the methodology developed by Lee andConstantinou [21] )e vertical load on the bearings is equalto 29MN for the squat tank and 27MN for the slender tankrespectively

54 Numerical Modeling and Earthquake Selection Aspreviously mentioned each Joystick tank model which issupported either on SFPBs TFPBs or QFPBs is simulatedutilizing the finite element software SAP2000 [29] )issimplified tank model consists of a vertical beam elementcarrying the impulsive mass and is supported by fully rigidbeam-spokes that represent the tank base )e properties ofthe vertical beam were determined using simple structuralanalysis calculations following the recommendations ofEurocode 8-Part 4 [38] In order to test the isolators understrong excitations the near-fault earthquake ground mo-tion set produced within the FEMASAC Project [42] is usedin this investigation (wwwniseeberkeleyeduelibraryfilesdocumentsdatastrong_motionsacsteelmotionsnearfaulthtm) Time-histories derived from natural and simulatedrecords are included in this suite of accelerograms )e useof a sufficient number of properly selected excitations (ieexhibiting certain characteristics to avoid using an excessivenumber of records and maintaining an optimal balanceamong computational cost and accuracy) in conjunctionwith a huge number of MSDAIDA analyses is imperative inorder to achieve reliable fragility analysis results)e specificsuite of acceleration time-histories consists such a case sinceit is a well-established set of impulsive ground motions withepicentral distances less than 10 km and very high PGArecorded values ranging from 045 g to 107 g which isusually used in fragility analysis studies [43]


More specifically for each of the three performancelevels the selected twenty earthquake records are suitablyscaled and then they are imposed at the isolated Joystickmodels until displacement limits are reached Regardingthe numerical analyses the fast nonlinear analysis (FNA) isideal for structural systems in which the nonlinear re-sponse is concentrated at the base isolation system while thesuperstructure remains elastic [29] FNA is a computation-ally efficient approach and is often preferred than direct-integration schemes )e damping for the structural systemis taken equal to 5 and for the impulsive liquid componentequal to 2 [44 45]

6 Numerical Results

61 Fragility Curves As aforementioned maximum dis-placement of the different TFPBs and QFPBs slidingschemes is associated to three hazard levels Accordinglyusing the data listed in Tables 2 and 3 and the isolatorconfigurations previously described the values presented inTable 4 were computed For instance for the TFPB and DBElevel the resulting displacement is derived by adding dlowast2 todlowast6 which gives a displacement limit equal to 0699mFigure 7 illustrates the adopted performance-based ap-proach for the three examined isolator schemes Morespecifically for the examined three hazard levels dotted blue

curves represent SLE continuous red curves denote DBEand dashed black curves correspond to MCE A similarcorrelation of isolatorsrsquo performance with respect to thethree hazard levels has been adopted by Moeindarbari et al[17] for TFPBs

Firstly SLE level with 50 in 50 years probabilityof exceedance (resulting to displacement limits equal to0084 m for TFPBs and 0095 m for QFPBs) is representedby the inner pendulum mechanism of the bearingssecondly DBE level with 10 in 50 years probability ofexceedance which results to displacement limits of0423 m for TFPBs and 0699m for QFPBs and lastlyMCE level with 2 in 50 years probability of exceedanceof the maximum allowable displacement which are equalto 0762 m for TFPBs and 104 m for QFPBs Additionallythe simple SFPB scheme is compared with the twomultistage isolators which is designed only for MCE level(with corresponding displacement limit of 0305m) with2 in 50 years probability of exceedance [8]

Impulsive mass (mi)

Elastic beam elementRigid beam-spokes

Friction isolators

hiXY

(a)

Impulsive mass (mi)

Rigid beam-spokes

Friction isolators

Elastic beam elementhi

XY

(b)

Figure 6 Joystick models for a squat (a) and a slender tank (b)

Table 3 Design parameters for the QFPB isolated squat tank

Sliding surface Effective radius of curvature (m) Coefficient of friction Displacement limit (m)Surface 1 R1eff 584 μ1 01 dlowast1 0344Surface 2 R2eff 112 μ2 006 dlowast2 0134Surface 3 R3eff 0508 μ3 001 dlowast3 0047Surface 4 R4eff 0508 μ4 001 dlowast4 0047Surface 5 R5eff 112 μ5 003 dlowast5 0134Surface 6 R6eff 376 μ6 007 dlowast6 0337

Table 2 Design parameters for the TFPB isolated squat tank

Friction coefficient Radii of curvature (m) Height (m) Effective radii (m) Displacement limit (m)micro1slow μ4slow 009 R1 R4 2235 h1 h4 0102 R1eff R4eff 2133 dlowast1 dlowast4 034micro2slow μ3slow 0071 R2 R3 0406 h2 h3 0076 R2eff R3eff 033 dlowast2 dlowast3 0041

Table 4 PBD levels of friction pendulum isolators

Isolator type SLE DBE MCESFPB - - 0305mTFPB 0084m 0423m 0762mQFPB 0095m 0699m 104m


Accordingly the probability of collapse considering theisolatorsrsquo displacements for TFPBs and QFPBs differentsliding mechanisms (depending on the hazard level) andSFPBs is displayed in the fragility curves presented inFigure 8 Extreme PGA values are used to demonstrate thehigh capabilities of modern multistage isolators while forfixed-base tanks the maximum PGA is much less (ieusually up to 1 g) [20 34] )e embedded plot in Figure 8shows the performance of all isolators within the range ofmore realistic expected PGA values where the differencesamong the ldquotruncatedrdquo fragility curves especially for the

lower PGA levels is more evident It can be seen that for thecase of the minor earthquake hazard scenario of SLE (wheresliding occurs at the inner sliding surfaces) TFPBs presentsbetter results than QFPBs )is is attributed to the values offriction coefficients since TFPBs have higher values(μ2 006 μ3 0071) compared to QFPB (μ3 μ4 001))us it is reasonable that sliding surfaces with lower valuesof friction coefficients will reach the displacement limitearlier than corresponding surfaces with higher values Onthe other hand for the more severe seismic scenarios ofDBE and especially in MCE it is evident that the QFPBs

(a) (b)

(c)

Figure 7 PBD levels in terms of isolator displacements for (a) SFPB (b) TFPB and (c) QFPB isolation schemes

0

01

02

03

04

05

06

07

08

09

1

0 05 1 15 2 25

Prob

abili

ty o

f exc

eeda

nce

PGA (g)

Fragility curves for each PBD level

TFPB MCETFPB DBETFPB SLESFPB MCE

QFPB SLEQFPB DBEQFPB MCE

0010203040506070809

1

0 02 04 06 08 1

Figure 8 PBD fragility curves for SFPB TFPB and QFPB isolation schemes


present significantly better results with respect to the ob-tained fragility estimates

Hence both TFPBs and QFPBs can withstand highdisplacement amplitudes achieving thus lower failureprobabilities even at higher seismic levels It can be noticedthat the multistage bearings of TFPBs and especially QFPBsplay an important role since they assist liquid storage tanksto maintain their structural integrity and functioning It isalso evident that these devices provide much better pro-tection to the superstructure under severe seismic excita-tions compared to simple SFPBs

62 Comparison of Tank Accelerations When a fixed-baseliquid storage tank is considered then its probability of failurepresents high values even for medium intensity levels (asexpressed in terms of PGA values) which is not the case forbase-isolated tanks [20 34] Base-isolation reduces the ac-celeration levels transmitted to the superstructure and it canbe assumed that due to isolation the tank behaves linearlyeven for quite high seismic intensity levels thus damages areavoided in the superstructure for the usually expected range ofPGAs Consequently the emphasis related to failure of thewhole system is given in the present investigation on theisolator displacements thus the probability of failure actuallyrefers to the exceedance of the allowable isolatorsrsquo displace-ment limits for various performance levels

Nonetheless when the imposed PGA reaches extremevalues as examined herein the transmitted acceleration ie the acceleration that is measured at tankrsquos base above theisolators can also reach significant values depending onthe special characteristics of the excitation )is is in-dicatively illustrated in Figure 9 which depicts the maxi-mum accelerations values (ie maximum value of thereduced acceleration transmitted to the superstructure) atthe tank base level above the isolators for each of the twentynear-fault records As it can be easily noticed the storagetank equipped with TFPBs presents the highest values of

base accelerations especially for three records (9 16 and18) )e superstructure isolated with SFPBs presents lowervalues but as shown in the fragility analysis (Figure 8)these isolators exhibit higher collapse probabilities In mostcases the base accelerations of storage tanks isolated withQFPBs are lower compared to those obtained by TFPBs andclose to the ones corresponding to SFPBs )erefore it isderived that overall QFPBs present better results comparedto TFPBs and SFPBs since it is an effective isolator con-figuration that combines lower probabilities of collapse interms of sliding displacements and low values of baseaccelerations transmitted to the superstructure

63 InfluenceofTankSlendernessRatio )eplots in Figure 10illustrate the influence of tank slenderness ratio (HR) in thefragility curves It is reminded that three bearing types wereexamined the single-stage SFPBs and the multistage TFPBsandQFPBs As it can be seen in this plot due to the presence ofthe isolators the fragility curves are not influenced by slen-derness ratio since there is not any significant differenceamong squat and slender tanks In contrast to this findingunanchored slender tanks are more susceptible to upliftingphenomena than the corresponding squat tanks [46] Re-garding TFPBs for DBE and MCE levels squat tanks areslightly less vulnerable compared to slender tanks at low tomedium PGA values For increased seismic intensity andhigher probability of collapse the fragility curves are almostidentical For SLE level there is not any observable differenceIn the case of SFPBs and for MCE scenario squat tanks areslightly less vulnerable than slender tanks for PGA valuesbetween 05 g and 10 g For the case of QFPBs SLE and DBElevels do not present any difference while for the MCE levelthe slender tanks are marginally less vulnerable compared tosquat tanks at low PGA values

64 Influence of λmax Factor A fragility analysis consideringperformance deterioration due to aging contamination etc

000

005

010

015

020

025

030

035

040

1 3 5 7 9 11 13 15 17 19

Acce

lera

tion

(g)

Number of earthquakes

Maximum base accelerations

SFPBTFPBQFPB

Figure 9 Base accelerations of storage tanks equipped with SFPB TFPB and QFPB isolators


of isolators is performed for the squat tank by incorporatingλmax factor in the design of TFPBs friction isolators )isparameter is directly applied to the nominal value of thecoefficient of friction to forecast aging and deteriorationphenomena that will affect the performance of frictionisolation bearings [47] According to the recommendationsof Constantinou et al [27] the value of 11 is selected foraging and 105 for contamination and λmax factor is cal-culated as the product of these two values

As it can be noticed from Figure 11 the incorporation ofλmax in the design of friction isolators for the squat tankaffects the results for the more severe hazard levels Espe-cially for the higher seismicity intensity levels (DBE) theTFPBs designed with the factor λmax present better per-formance while for the low seismicity intensity level (SLE)there are only marginal differences

7 Conclusions

2In this paper the seismic vulnerability of liquid storagetanks isolated with three types of sliding bearings namely

SFPBs and the multistage TFPBs and QFPBs were in-vestigated More specifically the displacement capacity ofSFPBs and of the different pendulum mechanisms of TFPBsand QFPBs were associated to three PBD levels (SLE DBEand MCE) by performing repeated dynamic nonlinear an-alyses A high displacement capacity is a very crucial pa-rameter for the isolators used to protect such criticalinfrastructures especially against severe near-fault earth-quakes Additionally the resulting base accelerationstransmitted at the storage tanks isolated with the afore-mentioned devices were compared In order to achieveoptimal balance between computational efficiency and ac-curacy simplified models were developed for the realisticrepresentation of the hydrodynamic response of liquidstorage tanks

)e following conclusions can be derived from thepresent investigation

(a) Friction isolation bearings with multistage andadaptive behavior (TFPBs and mostly QFPBs)present superior seismic performance compared to

002040608

1

0 05 1 15 2 25

Prob

abili

ty o

fex

ceed

ance

PGA (g)

SFPB (MCE)

Squat tankSlender tank

(a)

Prob

abili

ty o

fex

ceed

ance

PGA (g)


002040608

1

0 05 1 15 2 25

TFPB (SLE)

(b)

Prob

abili

ty o

fex

ceed

ance

PGA (g)


002040608

1

0 05 1 15 2 25

TFPB (DBE)

(c)

Prob

abili

ty o

fex

ceed

ance


002040608

1

0 05 1 15 2 25PGA (g)

TFPB (MCE)

(d)

Prob

abili

ty o

fex

ceed

ance


PGA (g)

002040608

1

0 05 1 15 2 25

QFPB (SLE)

(e)

Prob

abili

ty o

fex

ceed

ance


PGA (g)

002040608

1

0 05 1 15 2 25

QFPB (DBE)

(f )

Prob

abili

ty o

fex

ceed

ance


002040608

1

0 05 1 15 2 25PGA [g]

QFPB (MCE)

(g)

Figure 10 PBD fragility curves of squat and slender tanks using SFPBs TFPBs and QFPBs isolators


single bearings (SFPBs))us they have the ability ofaccommodating much larger displacements (iehigher PGA demand levels)

(b) In general as expected the QFPB is the superiorisolator device due to its ability to withstand higherdisplacements at different PBD levels

(c) Regarding the base accelerations of storage tanksisolated with different friction bearings the bestresults are derived from the superstructure equippedwith QFPBs A QFPB is an efficient base-isolationscheme that can combine the accommodation oflarge displacement amplitudes of near-fault excita-tions with low base acceleration values )us it canprotect the structural integrity of such critical in-frastructure even at high seismic demand levels

(d) )e slenderness ratio of the cylindrical base-isolatedstorage tanks via SFPBs TFPBs and QFPBs do notsignificantly affect the fragility estimations whenmaximum isolator displacements are considered

(e) )e future performance deterioration in the designof sliding bearings represented by the factor λmaxcan influence the fragility analysis results Morespecifically when this factor is incorporated in theanalysis the base-isolated liquid storage tankspresent a slightly less vulnerable performance for thehigher seismic demand levels

Abbreviations

3D )ree-dimensionalCDF Cumulative Distribution FunctionCSB Concave Sliding BearingDBE Design Basis EarthquakeDI Damage IndexDVFPS Double Variable Frequency Pendulum SystemEDP Engineering Demand ParameterELF Equivalent Linear ForceEPS Earthquake Protection SystemsFNA Fast Nonlinear AnalysisFP Friction PendulumHDRB High Damping Rubber BearingIDA Incremental Dynamic AnalysisIM Intensity MeasureLNG Liquefied Natural Gas

MCE Maximum Credible EarthquakeMFPS Multiple Friction Pendulum SystemMSDA Multistripe Dynamic AnalysisNATECH Natural and Technological disastersPBD Performance-Based DesignPGA Peak Ground AccelerationQFPB Quintuple Friction Pendulum SystemSFPB Single Friction Pendulum BearingSLE Service Level EarthquakeTFPB Triple Friction Pendulum BearingVCFPS Variable Curvature Friction Pendulum SystemVFPS Variable Friction Pendulum System

Data Availability

)e data supporting the results reported in the article arequite huge Nevertheless interested readers may access thesedata of the study by directly asking authors to provide them

Disclosure

An earlier version of this work was presented as a poster atthe Second Young Researchers Workshop of Hellenic So-ciety of Earthquake Engineering 3112017 Athens Greece

Conflicts of Interest

)e authors declare that there are no conflicts of interestregarding the publication of this paper

Acknowledgments

)is research has been generously supported by BakopouleioFoundation Greece via a PhD scholarship for the firstauthor which is gratefully acknowledged)e authors wouldalso like to thank Mr Donghun Lee for providing usefulinsight regarding the QFPB analytical model

References

[1] G Housner ldquo)e dynamic behavior of water tanksrdquo Bulletingof the Seismological Society of America vol 53 no 2pp 381ndash387 1963

[2] T Larkin ldquoSeismic response of liquid storage tanks in-corporating soil structure interactionrdquo ASCE Journal of

1

08

06

04

02

00 05 1 15 2 25

PGA (g)

Prob

abili

ty o

f exc

eeda

nce 1

08

06

04

02

00 05 1 15 2 25

PGA (g)

Prob

abili

ty o

f exc

eeda

nce

Without λmaxWith λmax



1

08

06

04

02

00 05 1 15 2 25

PGA (g)

Prob

abili

ty o

f exc

eeda

nce

Figure 11 Comparison of λmax factor influence on TFPBs friction bearingsrsquo performance for the squat tank (a) SLE (b) DBE (c) MCE


Geotechnical and Geoenvironmental Engineering vol 134no 12 pp 1804ndash1814 2008

[3] P K Malhotra ldquoSeismic response of soil-supported un-anchored-liquid storage tanksrdquo ASCE Journal of StructuralEngineering vol 123 no 4 pp 440ndash450 1997

[4] A S Veletsos Y Tang and H T Tang ldquoDynamic response offlexibly supported liquid-storage tanksrdquo ASCE Journal ofStructural Engineering vol 118 no 1 pp 264ndash289 1992

[5] K Bakalis D Vamvatsikos and M Fragiadakis ldquoSeismic riskassessment of liquid storage tanks via a nonlinear surrogatemodelrdquo Earthquake Engineering and Structural Dynamicsvol 46 no 15 pp 2851ndash2868 2017

[6] T Kelly Base Isolation of Structures-Design GuidelinesHolmes Consulting Group Ltd Auckland New Zealand2001

[7] M R Shekari N Khaji and M T Ahmadi ldquoOn the seismicbehavior of cylindrical base-isolated liquid storage tanksexcited by long-period ground motionsrdquo Soil Dynamics andEarthquake Engineering vol 30 no 10 pp 968ndash980 2010

[8] EPS Earthquake Protection Systems 2011 httpwwwearthquakeprotectioncom

[9] V R Panchal and D P Soni ldquoSeismic behavior of isolatedfluid storage tanks a-state-of-the-art reviewrdquoKSCE Journal ofCivil Engineering vol 18 no 4 pp 1097ndash1104 2014

[10] Y P Wang M C Teng and K W Chung ldquoSeismic isolationof rigid cylindrical tanks using friction pendulum bearingsrdquoEarthquake Engineering and Structural Dynamics vol 30no 7 pp 1083ndash1099 2001

[11] M B Jadhav and R S Jangid ldquoResponse of base-isolatedliquid storage tanksrdquo Shock and Vibration vol 11 no 1pp 33ndash45 2004

[12] V R Panchal and R S Jangid ldquoVariable friction pendulumsystem for seismic isolation of liquid storage tanksrdquo NuclearEngineering and Design vol 238 no 6 pp 1304ndash1315 2008

[13] E Abali and E Uckan ldquoParametric analysis of liquid storagetanks base isolated by curved surface sliding bearingsrdquo SoilDynamics and Earthquake Engineering vol 30 pp 21ndash312010

[14] D P Soni P P Mistry R S Jangid and V R PanchalldquoSeismic response of the double variable frequency pendulumisolatorrdquo Structural Control and Health Monitoring vol 18no 4 pp 450ndash470 2011

[15] A A Seleemah and M El-Sharkawy ldquoSeismic analysis andmodeling of isolated elevated liquid storage tanksrdquo Earth-quakes and Structures vol 2 no 4 pp 397ndash412 2011

[16] V R Panchal and R S Jangid ldquoBehaviour of liquid storagetanks with VCFPS under near-fault ground motionsrdquoStructure and Infrastructure Engineering vol 8 no 1pp 71ndash88 2012

[17] H Moeindarbari M Malekzadeh and T TaghkikhanyldquoProbabilistic analysis of seismically isolated elevated liquidstorage tank using multi-phase friction bearingrdquo Earthquakesand Structures vol 6 no 1 pp 111ndash125 2014

[18] F Paolacci ldquoOn the effectiveness of two isolation systems forthe seismic protection of elevated tanksrdquo Journal of PressureVessels Technology vol 137 no 3 article 031801 2015

[19] S Bagheri and M Farajian ldquo)e effects of input earthquakecharacteristics on the nonlinear dynamic behavior of FPSisolated liquid storage tanksrdquo Journal of Vibration andControl vol 24 no 7 pp 1264ndash1282 2016

[20] H N Phan F Paolacci D Corritore B Akbas E Uckan andJ J Shen ldquoSeismic vulnerability mitigation of liquefied gastanks using concave sliding bearingsrdquo Bulleting of EarthquakeEngineering vol 14 no 11 pp 3283ndash3299 2016

[21] D Lee and M C Constantinou ldquoQuintuple friction pen-dulum isolator behavior modeling and validationrdquo Earth-quake Spectra vol 32 no 3 pp 1607ndash1626 2016

[22] A Tsipianitis and Y Tsompanakis ldquoSeismic vulnerabilityassessment of base-isolated liquid fuels tanksrdquo in Proceedingsof 12th International Conference on Structural Safety andReliability (ICOSSAR) Vienna Austria August 2017

[23] K Bakalis M Fragiadakis and D Vamvatsikos ldquoSurrogatemodeling for the seismic performance assessment of liquidstorage tanksrdquo Journal of Structural Engineering vol 143no 4 article 04016199 2016

[24] V A Zayas S S Low and S A Mahin ldquo)e FPS earthquakeresisting system-experimental reportrdquo Report No UCBEERC-8701 Earthquake Engineering Research Center Col-lege of Engineering University of California Berkeley CAUSA 1987

[25] D M Fenz and M C Constantinou ldquoSpherical sliding iso-lation bearings with adaptive behavior theoryrdquo EarthquakeEngineering and Structural Dynamics vol 37 no 2pp 163ndash183 2008

[26] T A Morgan Ee use of innovative base isolation systems toachieve complex seismic performance objectives PhD Dis-sertation Department of Civil and Environmental Engi-neering University of California Berkeley CA USA 2007

[27] M C Constantinou I Kalpakidis A Filiatrault andR A E Lay ldquoLRFD-based analysis and design procedures forbridge bearings and seismic isolatorsrdquo Report No MCEER-11-0004 Multidisciplinary Center for Earthquake Engineer-ing Research University of Buffalo New York NY USA2011

[28] N D Dao K L Ryan E Sato and T Sasaki ldquoPredicting thedisplacement of triple pendulum bearing in a full-scaleshaking experiment using a three-dimensional elementrdquoEarthquake Engineering and Structural Dynamics vol 42no 11 pp 1677ndash1695 2013

[29] CSI SAP 2000 Version 18 Integrated Software for StructuralAnalysis and Design Analysis Reference Manual Computer ampStructures Inc Berkeley CA USA 2016

[30] A Kasalanati andM C Constantinou ldquoExperimental study ofbridge elastomeric and other isolation and energy dissipationsystems with emphasis on uplift prevention and high velocitynear source seismic excitationrdquo Technical Report MCEER-99-0004 Multidisciplinary Center for Earthquake Engineer-ing Research University at Buffalo Buffalo NY USA 1999

[31] D Vamvatsikos and C A Cornell ldquoIncremental dynamicanalysisrdquo Earthquake Engineering and Structural Dynamicsvol 31 no 3 pp 491ndash514 2002

[32] J W Baker ldquoEfficient analytical fragility function fitting usingdynamic structural analysisrdquo Earthquake Spectra vol 31no 1 pp 579ndash599 2015

[33] K Bakalis D Vamvatsikos and M Fragiadakis ldquoSeismicfragility assessment of steel liquid storage tanksrdquo in Pro-ceedings of the ASME 2015 Pressure Vessels and PipingConference Boston Massachusetts USA 2015

[34] S K Saha V A Matsagar and A K Jain ldquoSeismic fragility ofbase-isolated water storage tanks under non-stationaryearthquakesrdquo Bulletin of Earthquake Engineering vol 14no 4 pp 1153ndash1175 2016

[35] M A Haroun ldquoVibration studies and tests of liquid storagetanksrdquo Earthquake Engineering and Structural Dynamicsvol 11 no 2 pp 179ndash206 1983

[36] S Kilic and Z Ozdemir ldquoSimulation of sloshing effects incylindrical containers under seismic loadingrdquo in Proceedings


of the 6th LS-DYNA Anwenderforum DYNAmore DresdenGermany 2007

[37] A Di Carluccio and G Fabbrocino ldquoSome remarks on theseismic demand estimation in the context of vulnerabilityassessment of large steel storage tank facilitiesrdquo ISRN CivilEngineering vol 2012 Article ID 271414 12 pages 2012

[38] CEN Eurocode 8 Design of structures for earthquake re-sistance-Part 4 Silos Tanks and Pipelines European Com-mittee for Standardization Brussels Belgium 2006

[39] I P Christovasilis and A S Whittaker ldquoSeismic analysis ofconventional and isolated LNG tanks using mechanical an-alogsrdquo Earthquake Spectra vol 24 no 3 pp 599ndash616 2008

[40] R A Ibrahim ldquoRecent advances in nonlinear passive vi-bration isolatorsrdquo Journal of Sound and Vibration vol 314no 3ndash5 pp 371ndash452 2008

[41] Y Bouassida E Bouchon P Crespo et al Bridge Design toEurocodes-Worked Examples JRC Scientific and TechnicalReports EUR 25193 EN-2012 2012

[42] P Sommerville N Smith S Punyamurthula and J SunldquoDevelopment of ground motion time histories for phase 2 ofthe FEMASAC Steel Projectrdquo NISEE Report SACBD-97-04SAC Joint Venture Sacramento CA USA 1997

[43] A H M M Billah and M S Alam ldquoSeismic fragility as-sessment of concrete bridge pier reinforced with superelasticshape memory alloyrdquo Earthquake Spectra vol 31 no 3pp 1515ndash1541 2015

[44] M A Haroun and G W Housner ldquoSeismic design of liquidstorage tanksrdquo Journal of the Technical Councils of ASCEvol 107 pp 191ndash207 1981

[45] P K Malhotra T Wenk and M Wieland ldquoSimple procedurefor seismic analysis of liquid-storage tanksrdquo Structural En-gineering International vol 10 no 3 pp 197ndash201 2000

[46] P K Malhotra and A S Veletsos ldquoUplifting response ofunanchored liquid-storage tanksrdquo ASCE Journal of StructuralEngineering vol 120 no 12 pp 3525ndash3547 1994

[47] M C Constantinou A S Whittaker Y KalpakidisD M Fenz and G P Warn Performance of seismic isolationhardware under service and seismic loading Report NoMCEER-07-0012 Multidisciplinary Center for EarthquakeEngineering Research University of Buffalo New York NYUSA 2007


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Submit your manuscripts atwwwhindawicom

Base-isolation technology is considered as an efficientapproach to reduce the seismic vulnerability of liquid storagetanks )e fundamental concept of base-isolation is theldquodecouplingrdquo of structure from ground motions by installingisolators ie devices with low horizontal and high verticalstiffness to accommodate the vertical loads of the structure)erefore the stresses and accelerations imposed on thetank are notably reduced even if the displacements are quitehigh due to the increased deformability of the flexiblebearings [6 7] Some large-scale liquid storage tanks isolatedby friction isolators are presented in EPS [8] Firstly twoLNG tanks of Revithoussa Greece each having a capacity of65000m3 are equipped with totally 424 SFPB isolatorsSecondly two large LNG tanks located in Melchorita facilityin Peru [9] are isolated by TFPBs where earthquakes withmagnitude gt8 of Richter scale may occur

Many studies have been devoted to the seismic analysisand vulnerability assessment of liquid storage tanks base-isolated with friction isolators Firstly Wang et al [10]studied the effectiveness of SFPBs installed at the base ofcylindrical tanks using a hybrid structure-hydrodynamicnumerical model Parameters such as tank aspect ratiofriction coefficient of SFPBs and earthquake intensity wereexamined It was concluded that the impulsive pressures canbe significantly reduced due to seismic isolation while theconvective pressures were slightly changed Jadhav andJangid [11] compared the seismic response of liquid storagetanks isolated by elastomeric bearings and sliding systemswhile the continuous liquid mass of the tank was modeled aslumped masses namely sloshing mass impulsive mass andrigid mass Using a similar simplified model of the massesPanchal and Jangid [12] investigated the seismic response ofliquid storage tanks isolated with variable friction pendulumsystem (VFPS) Based on the assumption of the concentratedmasses the kinematic equations for the VFPS and thestorage tank were formed and solved It was concluded thatusing VFPS as base-isolation system for liquid storage tankstheir seismic response could be controlled within desirablelimits

)e work of Abali and Uckan [13] reported the efficiencyof SFPBs in controlling the earthquake response of slendertanks compared to squat tanks More specifically a para-metric analysis was conducted taking into account isolationperiod tank aspect ratio and coefficient of friction It wasderived that base shear was reduced for both squat andslender tanks Conversely sloshing displacements of squattanks were not significantly changed )e double variablefrequency pendulum system (DVFPS) that isolated theliquid storage tank was included in the numerical model ofSoni et al [14] )e examined DVFPS was analyzed fordifferent geometry and friction coefficient values )e mainconclusions derived from this study were that DVFPS withhigher initial stiffness from top sliding surface to bottompresented better behavior for slender tank while the isolatorhaving the same initial stiffness and coefficient of frictionperformed better for the squat tank

Seleemah and El-Sharkawy [15] investigated the dy-namic response of elevated squat and slender liquid storagetanks isolated by elastomeric and sliding bearings (SFPB)

In addition the behavior of the storage tanks was comparedfor the cases where the isolators were placed at the bottomor at the top of the supporting structure It was reportedthat base isolation affected in a beneficial manner theslender tanks and less the corresponding squat tanksFurthermore when an elevated tank was isolated withSFPBs it presented better seismic performance than withelastomeric bearings In addition the examined tankpresented better seismic behavior when isolators wereplaced at the top of the shaft support

Panchal and Jangid [16] examined the seismic behaviorof liquid storage tanks equipped with variable curvaturefriction pendulum system (VCFPS) under near-fault groundmotions )e most important parameters for this in-vestigation were the fundamental period the friction co-efficient and the tank aspect ratio It was found that theVCFPS is a quite effective seismic isolation device in con-trolling base shear sloshing displacement and the impulsivedisplacement of liquid storage tanks

Moeindarbari et al [17] investigated the efficiency ofSFPB and TFPB installed at elevated liquid storage tankssubjected tomultihazard level excitations TFPB is capable ofperforming multiple level analysis at different hazard sce-narios such as Service Level Earthquake (SLE) Design BasisEarthquake (DBE) and Maximum Credible Earthquake(MCE) Hence the results revealed that TFPB outperformedthe SFPB since the adaptive performance of TFPB played animportant role in decreasing the seismic demand on theliquid storage tanks Similarly the effectiveness of twoisolation systems of elevated storage tanks was studied byPaolacci [18] Records from the Kocaeli Earthquake (1999)were used for the dynamic analysis of high damping rubberbearing (HDRB) and SFPB installed at the elevated tankslocated in Habas pharmaceutics plant in Turkey It wasconcluded that elevated tanks isolated both by HDRB andSFPB presented major reductions in base shear as well asstress levels in the tankrsquos wall Due to the limitation ofmaximum bearing displacement and the higher value ofsloshing displacement for the HDRB the SFPB was con-sidered as the superior isolation scheme for this specific casestudy

Bagheri and Farajian [19] investigated the impact of PGAlevel and special characteristics of near-fault impulses on theearthquake performance of liquid storage tanks isolated bySFPBs A mechanical model that accurately estimated theseismic response of the liquid storage tank was adopted )eresults indicated that SFPB is an effective isolation systemcapable of reducing critical parameters such as impulsivedisplacement overturning moment and base shear whilethe sloshing displacement did not present significantchanges Phan et al [20] conducted a seismic fragilityanalysis of elevated liquid storage tanks isolated by concavesliding bearings (CSB) For this purpose a lumped-masssimplified model was used for the examined tank )e cloudmethod was applied for the seismic fragility assessmentwhere nonlinear dynamic analysis through a linear re-gression-based probabilistic model was implemented CSBscheme was found to be an effective isolation system for thereduction of the seismic demand on the tank

















1

(a)

43

21

(b)

65

4

32

1

(c)


000

005

010

015

020

025

030

035

040

045


Nor

mal

ized

hor

izon

tal f

orce

(FW

)

(a)

000

005

010

015

020

025

030

0 200 400 600 800 1000

Nor

mal

ized

hor

izon

tal f

orce

(FW

)


(b)









04

03

02

01

ndash02


ndash03



Nor

mal

ized

hor

izon

tal f

orce

(FW

)

0 100 15050

ndash01


Rigidconnection

Triple FP element

Double FP element

(a)


Triple FP

W W

Double FP


(b)






P(C|IM x) Φln(xθ)

β1113888 1113889 (1)





zj

⎛⎝ ⎞⎠pzj

j


(2)



likelihood 1113945m

j1

nj

zj

⎛⎝ ⎞⎠pzj


(3)






03

02

01

ndash01

ndash02




Nor

mal

ized

hor

izon

tal f

orce

(FW

)

300 800



likelihood 1113945

m

j1

nj

zj

⎛⎜⎝ ⎞⎟⎠Φln xjθ1113872 1113873

β⎛⎝ ⎞⎠

zj


β⎛⎝ ⎞⎠⎛⎝ ⎞⎠

njminuszj

(4)


θ β1113966 1113967 argθβ max 1113944m

j1

⎧⎨

⎩lnnj

zj

⎛⎜⎝ ⎞⎟⎠ + zj lnΦln xjθ1113872 1113873

β⎛⎝ ⎞⎠


β⎛⎝ ⎞⎠

⎫⎬

⎭

(5)











6 Numerical Results




Impulsive mass (mi)


Friction isolators

hiXY

(a)

Impulsive mass (mi)

Rigid beam-spokes

Friction isolators


XY

(b)











(a) (b)

(c)


0

01

02

03

04

05

06

07

08

09

1

0 05 1 15 2 25

Prob

abili

ty o

f exc

eeda

nce

PGA (g)




0010203040506070809

1

0 02 04 06 08 1










000

005

010

015

020

025

030

035

040

1 3 5 7 9 11 13 15 17 19

Acce

lera

tion

(g)



SFPBTFPBQFPB





7 Conclusions





002040608

1

0 05 1 15 2 25

Prob

abili

ty o

fex

ceed

ance

PGA (g)

SFPB (MCE)


(a)

Prob

abili

ty o

fex

ceed

ance

PGA (g)


002040608

1

0 05 1 15 2 25

TFPB (SLE)

(b)

Prob

abili

ty o

fex

ceed

ance

PGA (g)


002040608

1

0 05 1 15 2 25

TFPB (DBE)

(c)

Prob

abili

ty o

fex

ceed

ance


002040608

1

0 05 1 15 2 25PGA (g)

TFPB (MCE)

(d)

Prob

abili

ty o

fex

ceed

ance


PGA (g)

002040608

1

0 05 1 15 2 25

QFPB (SLE)

(e)

Prob

abili

ty o

fex

ceed

ance


PGA (g)

002040608

1

0 05 1 15 2 25

QFPB (DBE)

(f )

Prob

abili

ty o

fex

ceed

ance


002040608

1

0 05 1 15 2 25PGA [g]

QFPB (MCE)

(g)








Abbreviations



Data Availability


Disclosure




Acknowledgments


References



1

08

06

04

02

00 05 1 15 2 25

PGA (g)

Prob

abili

ty o

f exc

eeda

nce 1

08

06

04

02

00 05 1 15 2 25

PGA (g)

Prob

abili

ty o

f exc

eeda

nce




1

08

06

04

02

00 05 1 15 2 25

PGA (g)

Prob

abili

ty o

f exc

eeda

nce






















































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia

















1

(a)

43

21

(b)

65

4

32

1

(c)


000

005

010

015

020

025

030

035

040

045


Nor

mal

ized

hor

izon

tal f

orce

(FW

)

(a)

000

005

010

015

020

025

030

0 200 400 600 800 1000

Nor

mal

ized

hor

izon

tal f

orce

(FW

)


(b)









04

03

02

01

ndash02


ndash03



Nor

mal

ized

hor

izon

tal f

orce

(FW

)

0 100 15050

ndash01


Rigidconnection

Triple FP element

Double FP element

(a)


Triple FP

W W

Double FP


(b)






P(C|IM x) Φln(xθ)

β1113888 1113889 (1)





zj

⎛⎝ ⎞⎠pzj

j


(2)



likelihood 1113945m

j1

nj

zj

⎛⎝ ⎞⎠pzj


(3)






03

02

01

ndash01

ndash02




Nor

mal

ized

hor

izon

tal f

orce

(FW

)

300 800



likelihood 1113945

m

j1

nj

zj

⎛⎜⎝ ⎞⎟⎠Φln xjθ1113872 1113873

β⎛⎝ ⎞⎠

zj


β⎛⎝ ⎞⎠⎛⎝ ⎞⎠

njminuszj

(4)


θ β1113966 1113967 argθβ max 1113944m

j1

⎧⎨

⎩lnnj

zj

⎛⎜⎝ ⎞⎟⎠ + zj lnΦln xjθ1113872 1113873

β⎛⎝ ⎞⎠


β⎛⎝ ⎞⎠

⎫⎬

⎭

(5)











6 Numerical Results




Impulsive mass (mi)


Friction isolators

hiXY

(a)

Impulsive mass (mi)

Rigid beam-spokes

Friction isolators


XY

(b)











(a) (b)

(c)


0

01

02

03

04

05

06

07

08

09

1

0 05 1 15 2 25

Prob

abili

ty o

f exc

eeda

nce

PGA (g)




0010203040506070809

1

0 02 04 06 08 1










000

005

010

015

020

025

030

035

040

1 3 5 7 9 11 13 15 17 19

Acce

lera

tion

(g)



SFPBTFPBQFPB





7 Conclusions





002040608

1

0 05 1 15 2 25

Prob

abili

ty o

fex

ceed

ance

PGA (g)

SFPB (MCE)


(a)

Prob

abili

ty o

fex

ceed

ance

PGA (g)


002040608

1

0 05 1 15 2 25

TFPB (SLE)

(b)

Prob

abili

ty o

fex

ceed

ance

PGA (g)


002040608

1

0 05 1 15 2 25

TFPB (DBE)

(c)

Prob

abili

ty o

fex

ceed

ance


002040608

1

0 05 1 15 2 25PGA (g)

TFPB (MCE)

(d)

Prob

abili

ty o

fex

ceed

ance


PGA (g)

002040608

1

0 05 1 15 2 25

QFPB (SLE)

(e)

Prob

abili

ty o

fex

ceed

ance


PGA (g)

002040608

1

0 05 1 15 2 25

QFPB (DBE)

(f )

Prob

abili

ty o

fex

ceed

ance


002040608

1

0 05 1 15 2 25PGA [g]

QFPB (MCE)

(g)








Abbreviations



Data Availability


Disclosure




Acknowledgments


References



1

08

06

04

02

00 05 1 15 2 25

PGA (g)

Prob

abili

ty o

f exc

eeda

nce 1

08

06

04

02

00 05 1 15 2 25

PGA (g)

Prob

abili

ty o

f exc

eeda

nce




1

08

06

04

02

00 05 1 15 2 25

PGA (g)

Prob

abili

ty o

f exc

eeda

nce






















































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia








04

03

02

01

ndash02


ndash03



Nor

mal

ized

hor

izon

tal f

orce

(FW

)

0 100 15050

ndash01


Rigidconnection

Triple FP element

Double FP element

(a)


Triple FP

W W

Double FP


(b)






P(C|IM x) Φln(xθ)

β1113888 1113889 (1)





zj

⎛⎝ ⎞⎠pzj

j


(2)



likelihood 1113945m

j1

nj

zj

⎛⎝ ⎞⎠pzj


(3)






03

02

01

ndash01

ndash02




Nor

mal

ized

hor

izon

tal f

orce

(FW

)

300 800



likelihood 1113945

m

j1

nj

zj

⎛⎜⎝ ⎞⎟⎠Φln xjθ1113872 1113873

β⎛⎝ ⎞⎠

zj


β⎛⎝ ⎞⎠⎛⎝ ⎞⎠

njminuszj

(4)


θ β1113966 1113967 argθβ max 1113944m

j1

⎧⎨

⎩lnnj

zj

⎛⎜⎝ ⎞⎟⎠ + zj lnΦln xjθ1113872 1113873

β⎛⎝ ⎞⎠


β⎛⎝ ⎞⎠

⎫⎬

⎭

(5)











6 Numerical Results




Impulsive mass (mi)


Friction isolators

hiXY

(a)

Impulsive mass (mi)

Rigid beam-spokes

Friction isolators


XY

(b)











(a) (b)

(c)


0

01

02

03

04

05

06

07

08

09

1

0 05 1 15 2 25

Prob

abili

ty o

f exc

eeda

nce

PGA (g)




0010203040506070809

1

0 02 04 06 08 1










000

005

010

015

020

025

030

035

040

1 3 5 7 9 11 13 15 17 19

Acce

lera

tion

(g)



SFPBTFPBQFPB





7 Conclusions





002040608

1

0 05 1 15 2 25

Prob

abili

ty o

fex

ceed

ance

PGA (g)

SFPB (MCE)


(a)

Prob

abili

ty o

fex

ceed

ance

PGA (g)


002040608

1

0 05 1 15 2 25

TFPB (SLE)

(b)

Prob

abili

ty o

fex

ceed

ance

PGA (g)


002040608

1

0 05 1 15 2 25

TFPB (DBE)

(c)

Prob

abili

ty o

fex

ceed

ance


002040608

1

0 05 1 15 2 25PGA (g)

TFPB (MCE)

(d)

Prob

abili

ty o

fex

ceed

ance


PGA (g)

002040608

1

0 05 1 15 2 25

QFPB (SLE)

(e)

Prob

abili

ty o

fex

ceed

ance


PGA (g)

002040608

1

0 05 1 15 2 25

QFPB (DBE)

(f )

Prob

abili

ty o

fex

ceed

ance


002040608

1

0 05 1 15 2 25PGA [g]

QFPB (MCE)

(g)








Abbreviations



Data Availability


Disclosure




Acknowledgments


References



1

08

06

04

02

00 05 1 15 2 25

PGA (g)

Prob

abili

ty o

f exc

eeda

nce 1

08

06

04

02

00 05 1 15 2 25

PGA (g)

Prob

abili

ty o

f exc

eeda

nce




1

08

06

04

02

00 05 1 15 2 25

PGA (g)

Prob

abili

ty o

f exc

eeda

nce






















































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia





P(C|IM x) Φln(xθ)

β1113888 1113889 (1)





zj

⎛⎝ ⎞⎠pzj

j


(2)



likelihood 1113945m

j1

nj

zj

⎛⎝ ⎞⎠pzj


(3)






03

02

01

ndash01

ndash02




Nor

mal

ized

hor

izon

tal f

orce

(FW

)

300 800



likelihood 1113945

m

j1

nj

zj

⎛⎜⎝ ⎞⎟⎠Φln xjθ1113872 1113873

β⎛⎝ ⎞⎠

zj


β⎛⎝ ⎞⎠⎛⎝ ⎞⎠

njminuszj

(4)


θ β1113966 1113967 argθβ max 1113944m

j1

⎧⎨

⎩lnnj

zj

⎛⎜⎝ ⎞⎟⎠ + zj lnΦln xjθ1113872 1113873

β⎛⎝ ⎞⎠


β⎛⎝ ⎞⎠

⎫⎬

⎭

(5)











6 Numerical Results




Impulsive mass (mi)


Friction isolators

hiXY

(a)

Impulsive mass (mi)

Rigid beam-spokes

Friction isolators


XY

(b)











(a) (b)

(c)


0

01

02

03

04

05

06

07

08

09

1

0 05 1 15 2 25

Prob

abili

ty o

f exc

eeda

nce

PGA (g)




0010203040506070809

1

0 02 04 06 08 1










000

005

010

015

020

025

030

035

040

1 3 5 7 9 11 13 15 17 19

Acce

lera

tion

(g)



SFPBTFPBQFPB





7 Conclusions





002040608

1

0 05 1 15 2 25

Prob

abili

ty o

fex

ceed

ance

PGA (g)

SFPB (MCE)


(a)

Prob

abili

ty o

fex

ceed

ance

PGA (g)


002040608

1

0 05 1 15 2 25

TFPB (SLE)

(b)

Prob

abili

ty o

fex

ceed

ance

PGA (g)


002040608

1

0 05 1 15 2 25

TFPB (DBE)

(c)

Prob

abili

ty o

fex

ceed

ance


002040608

1

0 05 1 15 2 25PGA (g)

TFPB (MCE)

(d)

Prob

abili

ty o

fex

ceed

ance


PGA (g)

002040608

1

0 05 1 15 2 25

QFPB (SLE)

(e)

Prob

abili

ty o

fex

ceed

ance


PGA (g)

002040608

1

0 05 1 15 2 25

QFPB (DBE)

(f )

Prob

abili

ty o

fex

ceed

ance


002040608

1

0 05 1 15 2 25PGA [g]

QFPB (MCE)

(g)








Abbreviations



Data Availability


Disclosure




Acknowledgments


References



1

08

06

04

02

00 05 1 15 2 25

PGA (g)

Prob

abili

ty o

f exc

eeda

nce 1

08

06

04

02

00 05 1 15 2 25

PGA (g)

Prob

abili

ty o

f exc

eeda

nce




1

08

06

04

02

00 05 1 15 2 25

PGA (g)

Prob

abili

ty o

f exc

eeda

nce






















































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia


likelihood 1113945

m

j1

nj

zj

⎛⎜⎝ ⎞⎟⎠Φln xjθ1113872 1113873

β⎛⎝ ⎞⎠

zj


β⎛⎝ ⎞⎠⎛⎝ ⎞⎠

njminuszj

(4)


θ β1113966 1113967 argθβ max 1113944m

j1

⎧⎨

⎩lnnj

zj

⎛⎜⎝ ⎞⎟⎠ + zj lnΦln xjθ1113872 1113873

β⎛⎝ ⎞⎠


β⎛⎝ ⎞⎠

⎫⎬

⎭

(5)











6 Numerical Results




Impulsive mass (mi)


Friction isolators

hiXY

(a)

Impulsive mass (mi)

Rigid beam-spokes

Friction isolators


XY

(b)











(a) (b)

(c)


0

01

02

03

04

05

06

07

08

09

1

0 05 1 15 2 25

Prob

abili

ty o

f exc

eeda

nce

PGA (g)




0010203040506070809

1

0 02 04 06 08 1










000

005

010

015

020

025

030

035

040

1 3 5 7 9 11 13 15 17 19

Acce

lera

tion

(g)



SFPBTFPBQFPB





7 Conclusions





002040608

1

0 05 1 15 2 25

Prob

abili

ty o

fex

ceed

ance

PGA (g)

SFPB (MCE)


(a)

Prob

abili

ty o

fex

ceed

ance

PGA (g)


002040608

1

0 05 1 15 2 25

TFPB (SLE)

(b)

Prob

abili

ty o

fex

ceed

ance

PGA (g)


002040608

1

0 05 1 15 2 25

TFPB (DBE)

(c)

Prob

abili

ty o

fex

ceed

ance


002040608

1

0 05 1 15 2 25PGA (g)

TFPB (MCE)

(d)

Prob

abili

ty o

fex

ceed

ance


PGA (g)

002040608

1

0 05 1 15 2 25

QFPB (SLE)

(e)

Prob

abili

ty o

fex

ceed

ance


PGA (g)

002040608

1

0 05 1 15 2 25

QFPB (DBE)

(f )

Prob

abili

ty o

fex

ceed

ance


002040608

1

0 05 1 15 2 25PGA [g]

QFPB (MCE)

(g)








Abbreviations



Data Availability


Disclosure




Acknowledgments


References



1

08

06

04

02

00 05 1 15 2 25

PGA (g)

Prob

abili

ty o

f exc

eeda

nce 1

08

06

04

02

00 05 1 15 2 25

PGA (g)

Prob

abili

ty o

f exc

eeda

nce




1

08

06

04

02

00 05 1 15 2 25

PGA (g)

Prob

abili

ty o

f exc

eeda

nce






















































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia



6 Numerical Results




Impulsive mass (mi)


Friction isolators

hiXY

(a)

Impulsive mass (mi)

Rigid beam-spokes

Friction isolators


XY

(b)











(a) (b)

(c)


0

01

02

03

04

05

06

07

08

09

1

0 05 1 15 2 25

Prob

abili

ty o

f exc

eeda

nce

PGA (g)




0010203040506070809

1

0 02 04 06 08 1










000

005

010

015

020

025

030

035

040

1 3 5 7 9 11 13 15 17 19

Acce

lera

tion

(g)



SFPBTFPBQFPB





7 Conclusions





002040608

1

0 05 1 15 2 25

Prob

abili

ty o

fex

ceed

ance

PGA (g)

SFPB (MCE)


(a)

Prob

abili

ty o

fex

ceed

ance

PGA (g)


002040608

1

0 05 1 15 2 25

TFPB (SLE)

(b)

Prob

abili

ty o

fex

ceed

ance

PGA (g)


002040608

1

0 05 1 15 2 25

TFPB (DBE)

(c)

Prob

abili

ty o

fex

ceed

ance


002040608

1

0 05 1 15 2 25PGA (g)

TFPB (MCE)

(d)

Prob

abili

ty o

fex

ceed

ance


PGA (g)

002040608

1

0 05 1 15 2 25

QFPB (SLE)

(e)

Prob

abili

ty o

fex

ceed

ance


PGA (g)

002040608

1

0 05 1 15 2 25

QFPB (DBE)

(f )

Prob

abili

ty o

fex

ceed

ance


002040608

1

0 05 1 15 2 25PGA [g]

QFPB (MCE)

(g)








Abbreviations



Data Availability


Disclosure




Acknowledgments


References



1

08

06

04

02

00 05 1 15 2 25

PGA (g)

Prob

abili

ty o

f exc

eeda

nce 1

08

06

04

02

00 05 1 15 2 25

PGA (g)

Prob

abili

ty o

f exc

eeda

nce




1

08

06

04

02

00 05 1 15 2 25

PGA (g)

Prob

abili

ty o

f exc

eeda

nce






















































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia




(a) (b)

(c)


0

01

02

03

04

05

06

07

08

09

1

0 05 1 15 2 25

Prob

abili

ty o

f exc

eeda

nce

PGA (g)




0010203040506070809

1

0 02 04 06 08 1










000

005

010

015

020

025

030

035

040

1 3 5 7 9 11 13 15 17 19

Acce

lera

tion

(g)



SFPBTFPBQFPB





7 Conclusions





002040608

1

0 05 1 15 2 25

Prob

abili

ty o

fex

ceed

ance

PGA (g)

SFPB (MCE)


(a)

Prob

abili

ty o

fex

ceed

ance

PGA (g)


002040608

1

0 05 1 15 2 25

TFPB (SLE)

(b)

Prob

abili

ty o

fex

ceed

ance

PGA (g)


002040608

1

0 05 1 15 2 25

TFPB (DBE)

(c)

Prob

abili

ty o

fex

ceed

ance


002040608

1

0 05 1 15 2 25PGA (g)

TFPB (MCE)

(d)

Prob

abili

ty o

fex

ceed

ance


PGA (g)

002040608

1

0 05 1 15 2 25

QFPB (SLE)

(e)

Prob

abili

ty o

fex

ceed

ance


PGA (g)

002040608

1

0 05 1 15 2 25

QFPB (DBE)

(f )

Prob

abili

ty o

fex

ceed

ance


002040608

1

0 05 1 15 2 25PGA [g]

QFPB (MCE)

(g)








Abbreviations



Data Availability


Disclosure




Acknowledgments


References



1

08

06

04

02

00 05 1 15 2 25

PGA (g)

Prob

abili

ty o

f exc

eeda

nce 1

08

06

04

02

00 05 1 15 2 25

PGA (g)

Prob

abili

ty o

f exc

eeda

nce




1

08

06

04

02

00 05 1 15 2 25

PGA (g)

Prob

abili

ty o

f exc

eeda

nce






















































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia









000

005

010

015

020

025

030

035

040

1 3 5 7 9 11 13 15 17 19

Acce

lera

tion

(g)



SFPBTFPBQFPB





7 Conclusions





002040608

1

0 05 1 15 2 25

Prob

abili

ty o

fex

ceed

ance

PGA (g)

SFPB (MCE)


(a)

Prob

abili

ty o

fex

ceed

ance

PGA (g)


002040608

1

0 05 1 15 2 25

TFPB (SLE)

(b)

Prob

abili

ty o

fex

ceed

ance

PGA (g)


002040608

1

0 05 1 15 2 25

TFPB (DBE)

(c)

Prob

abili

ty o

fex

ceed

ance


002040608

1

0 05 1 15 2 25PGA (g)

TFPB (MCE)

(d)

Prob

abili

ty o

fex

ceed

ance


PGA (g)

002040608

1

0 05 1 15 2 25

QFPB (SLE)

(e)

Prob

abili

ty o

fex

ceed

ance


PGA (g)

002040608

1

0 05 1 15 2 25

QFPB (DBE)

(f )

Prob

abili

ty o

fex

ceed

ance


002040608

1

0 05 1 15 2 25PGA [g]

QFPB (MCE)

(g)








Abbreviations



Data Availability


Disclosure




Acknowledgments


References



1

08

06

04

02

00 05 1 15 2 25

PGA (g)

Prob

abili

ty o

f exc

eeda

nce 1

08

06

04

02

00 05 1 15 2 25

PGA (g)

Prob

abili

ty o

f exc

eeda

nce




1

08

06

04

02

00 05 1 15 2 25

PGA (g)

Prob

abili

ty o

f exc

eeda

nce






















































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia




7 Conclusions





002040608

1

0 05 1 15 2 25

Prob

abili

ty o

fex

ceed

ance

PGA (g)

SFPB (MCE)


(a)

Prob

abili

ty o

fex

ceed

ance

PGA (g)


002040608

1

0 05 1 15 2 25

TFPB (SLE)

(b)

Prob

abili

ty o

fex

ceed

ance

PGA (g)


002040608

1

0 05 1 15 2 25

TFPB (DBE)

(c)

Prob

abili

ty o

fex

ceed

ance


002040608

1

0 05 1 15 2 25PGA (g)

TFPB (MCE)

(d)

Prob

abili

ty o

fex

ceed

ance


PGA (g)

002040608

1

0 05 1 15 2 25

QFPB (SLE)

(e)

Prob

abili

ty o

fex

ceed

ance


PGA (g)

002040608

1

0 05 1 15 2 25

QFPB (DBE)

(f )

Prob

abili

ty o

fex

ceed

ance


002040608

1

0 05 1 15 2 25PGA [g]

QFPB (MCE)

(g)








Abbreviations



Data Availability


Disclosure




Acknowledgments


References



1

08

06

04

02

00 05 1 15 2 25

PGA (g)

Prob

abili

ty o

f exc

eeda

nce 1

08

06

04

02

00 05 1 15 2 25

PGA (g)

Prob

abili

ty o

f exc

eeda

nce




1

08

06

04

02

00 05 1 15 2 25

PGA (g)

Prob

abili

ty o

f exc

eeda

nce






















































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia







Abbreviations



Data Availability


Disclosure




Acknowledgments


References



1

08

06

04

02

00 05 1 15 2 25

PGA (g)

Prob

abili

ty o

f exc

eeda

nce 1

08

06

04

02

00 05 1 15 2 25

PGA (g)

Prob

abili

ty o

f exc

eeda

nce




1

08

06

04

02

00 05 1 15 2 25

PGA (g)

Prob

abili

ty o

f exc

eeda

nce






















































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia





















































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia


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