Tanks

Dynamic buckling and seismic fragility of anchored steel tanks bythe added mass method

N. Buratti*, and M. Tavano

DICAM Department of Civil, Chemical, Environmental and Materials Engineering, University of Bologna, Italy

SUMMARY

Buckling plays a fundamental role in the design of steel tanks because of the small thicknesses of the wallsof this class of structures. The rst part of the paper presents a review of this phenomenon forliquid-containing circular cylindrical steel tanks that are fully anchored at the base, considering the differentbuckling modes and especially the secondary buckling occurring in the top part of the tank.

A case study based on a cylindrical tank is then introduced in order to investigate various aspects ofdynamic buckling. The nite element model of the case study tank is set-up using the added mass methodfor uid modelling. The inuence of pre-stress states caused by hydrostatic pressure and self-weight on thenatural periods of the structure is rst studied and it is found that this inuence is very small as far as theglobal behaviour of the tanks is considered, while it is important for local, shell-type, vibration modes.

In the following, the efciency and sufciency of different ground motion intensity measures is analysedby means of cloud analysis with a set of 40 recorded accelerograms. In particular, the peak ground displace-ment has been found being the most efcient and sufcient intensity measure so far as the maximum relativedisplacement of the tank walls is concerned.

Finally, incremental nonlinear time-history analyses are performed considering the case study structureunder recorded earthquake ground motions in order to identify the critical buckling loads and to derivefragility curves for the buckling limit state. Copyright 2013 John Wiley & Sons, Ltd.

Received 28 December 2012; Revised 30 April 2013; Accepted 9 May 2013

KEY WORDS: steel tanks; earthquake response; nite elements; added mass; buckling; ground-motionintensity measures; fragility curves

1. INTRODUCTION

Buckling plays a fundamental role in the design of steel tanks because of the small thicknesses ofthe walls of this class of structures. Many researchers have studied the seismic behaviour ofanchored liquid-storage tanks, investigating the effect of hydrodynamic uidstructureinteraction on structural response. Past studies have concluded that circular cylindrical anchoredtanks containing a homogeneous liquid develop a cantilever-type behaviour under horizontalaccelerations [110]. The hydrodynamic response of the tank-liquid system is characterised bythe superposition of two different contributions, named impulsive component and convectivecomponent, respectively. If the tank walls are rigid, the impulsive component represents theportion of liquid that moves in unison with the tank walls. The liquid that moves with a long-period sloshing motion in the upper portion of the tank is represented by the convectivecomponent. These two components can be considered uncoupled, because there are signicantdifferences in their natural periods [2]. Furthermore, because the sloshing motion of theconvective component is typically associated to long periods, this latter component gives only

*Correspondence to: N. Buratti, DICAM Department of Civil, Chemical, Environmental and Materials Engineering,University of Bologna, Italy.E-mail: [email protected]

Copyright 2013 John Wiley & Sons, Ltd.

EARTHQUAKE ENGINEERING & STRUCTURAL DYNAMICSEarthquake Engng Struct. Dyn. 2014; 43:121Published online 4 July 2013 in Wiley Online Library (wileyonlinelibrary.com). DOI: 10.1002/eqe.2326

a small contribution to the total hydrodynamic pressure on the tank walls and therefore, the globaltank response is mainly inuenced by the impulsive component.

The complicated deformed congurations of liquid storage tanks and the interaction betweenuid and structure result in a wide variety of possible failure mechanisms during earthquakes.Brown et al. [11] and Haroun [12] reported the damage on steel tanks due to the 1994Northridge earthquake and to the 1979 Imperial Valley earthquake. Damage on steel tanks wasalso observed by the authors of the present paper after the 2012 Emilia earthquake, in NorthernItaly, and is documented in Section 2. Shell buckling, damage and collapses of tank roofs,base-anchorage failures, tank support-system failures, differential settlements, partial upliftingand pipe failures are the most observed failure modes. Among all these failure modes, shellbuckling is what this paper focuses on.

In past studies, the buckling problem for on-grade steel tanks was investigated by means ofnumerical models in which the different buckling modes (elephant0s foot, diamond shape andsecondary buckling) are highlighted and discussed separately. However, there is lack of studiesin which the buckling phenomenon is considered in its entirety. In order to study the seismicvulnerability of liquid storage tanks with respect to buckling, there is the need to set up aunique criterion able to identify the buckling load for the structure, including all types ofpossible buckling modes and to use such criterion to build fragility curves. This is what isperformed in the present work. Fragility curves for steel tanks can also be found in ORourke[13] and Salzano [14], even if they are not specic for buckling. In fact, they refer to moregeneral damage states, dened by the HAZUS damage classication [15]. In the present work,fragility curves for buckling are obtained by means of incremental time-history analysesperformed on a three-dimensional model of an anchored steel tank with a height-to-diameterratio typical of petroleum tank farms (H/D = 0.4).

When setting up a tank model, the problem of how to model the liquid immediately arises.Various approaches have been proposed in the literature, for example, analytical approaches[16], FEM-based models adopting either added-mass approximations or uid-specic niteelements [1720], BEMFEM coupled models [21], and smoothed particle hydrodynamics [22, 23].In the present paper, the added mass method was chosen for liquid modelling because it representsa good compromise between accuracy and computational cost [24].

Non-linear dynamic analyses using a set of 40 recorded accelerograms were performed usingthe nite element software ABAQUS (Rhode Island, USA) [25, 26] in order to investigate theefciency and sufciency of different ground-motion intensity measures (IMs). Then,incremental dynamic analyses were carried out, and their results were processed using theBudianskyRoth buckling criterion [27, 28] and pseudo-equilibrium paths [24], in order toprovide an estimate of the dynamic buckling load and to understand which was the dominantbuckling mode. Finally, the dynamic buckling loads were used to make some considerationsabout the seismic fragility of the tank with respect to buckling.

2. BUCKLING OF STEEL TANKS UNDER SEISMIC ACTIONS

The buckling behaviour of steel tanks under seismic excitation has been analysed by means ofexperimental and computational studies, and two main buckling types have been dened:elasticplastic buckling and elastic buckling. These two buckling types are explicitly mentionedin actual codes as Eurocode 8 [29] and New Zealand guidelines [30] and implicitly accountedfor in the API formulation [31].

The elasticplastic behaviour is associated with the so called elephants foot buckling, whichis characterised by an outward bulge just above the base of the tank. This kind of buckling isclearly visible in the picture in Figure 1 that was taken by the authors during a eld surveyafter the Emilia earthquake that struck Northern Italy in May 2012. The bottom of the shell isnormally in a biaxial stress state consisting of hoop tension and axial compression. The bulgeformation results from the large circumferential tensile stresses due to the internal pressures(hydrostatic and hydrodynamic due to vertical excitation), in combination with the axial

2 N. BURATTI AND M. TAVANO

Copyright 2013 John Wiley & Sons, Ltd. Earthquake Engng Struct. Dyn. 2014; 43:121DOI: 10.1002/eqe

compression stresses due to the overturning moment caused by horizontal earthquake excitation.In fact, when the hoop stress reaches the yield limit, the annular strips of the tank cannotsustain any load increment and therefore, the structural scheme resisting to a further verticalload increment is represented by a tall plate a few millimetres thick. It is immediate tounderstand how this element can reach quickly a buckling failure. Eurocode 8 and NewZealand guidelines suggest the Rotter [32] formula to compute the buckling capacity withrespect to elasticplastic buckling,

f pb sc1 1pRtwf y

!22435 1 1

1:12 r1:5

r f y=250r 1

; (1)

where sc1 0:605EwtwR is the Eulers critical axial compressive stress, R is the tank radius, p is thetotal internal pressure, Ew and tw are the elastic modulus and the thickness of the tank walls, fy isthe steel yielding stress, and r is a coefcient dened as r =R/(400 t).

The elastic buckling is associated with the so-called diamond-shape buckling, characterisedby shell crippling at the base of the tank (Figure 2). This type of buckling is due to the axialcompression forces developed at the general meridian line that are due to the self-weight of thetank walls and roof and to the increment given by the seismic action. The diamond shapebuckling is much less common than the elephants foot because it occurs at small values ofhoop stress. The axial membrane stress that needs to induce elastic buckling in a shell dependson the internal pressure and the amplitude of imperfections in the shell. In particular, the lattertend to decrease the buckling stress to a fraction of the classical (Eulers) buckling stress. Theinternal pressure reduces the effective imperfection amplitude and therefore increases the

Figure 1. Elephants foot buckling, emilia earthquake, Italy, 20 and 29 May 2012.

Figure 2. Diamond shape buckling, emilia earthquake, Italy, 20 and 29 May 2012.

DYNAMIC BUCKLING AND SEISMIC FRAGILITY OF ANCHORED STEEL TANKS 3


buckling stress. Because of these reasons, the buckling capacity with respect to elastic bucklingcan be computed by applying a proper knockdown factor, a^ , to the critical Eulers axialcompressive stress for an axially loaded, linear-elastic cylinder,

f mb a^0:605EwtwR

(2)

The knockdown factor takes into account imperfections sensitivity of the bent cylindrical shelland proper values of it were given by the European Convention for Constructional Steelwork in[33]. Eurocode 8 and NZSEE propose a different formula for the elastic critical buckling stresswith regard to the elastic buckling limit state, which represents a further development ofequation 2 [34].

In addition to the well-known elephants foot and diamond shape buckling modes, a third kindof buckling, due to external pressure and cavitation, is mentioned by Rammerstofer et al. [3] andconrmed also by observations on real tanks after earthquakes (Figure 3). However, this bucklingmode is not covered by current codes, and until now, no empirical formula associated to it existsin literature. In the present work, this third buckling mode is named secondary buckling, inorder to distinguish it from the rst type of elastic buckling (diamond shape). Computationalstudies on secondary buckling are mainly by Virella et al. [24]. From a mechanical point ofview, it is caused by the pressure at the top of the shell, where the resultant pressure(superposition of the hydrodynamic and hydrostatic pressures) acts in the inward direction, thuscausing axial compression forces in the annular strips, as illustrated in Figure 4. Thesecompression forces in addition to the small thickness of the tanks walls at the top, may lead toan elastic buckling problem, which appears in the form of cavitation.

3. FLUID MODELLING WITH THE ADDED MASS METHOD

The added mass method was rst developed by Westergaard [19] in a seminal study concerning thedynamic interaction between dams and reservoir systems. According to Westergaard, thehydrodynamic pressures that the water exerts on the dam during an earthquake are the same as if afraction of the volume of water moved together with the dam. Westergaard considered the dam asrigid. Later Lee and Tsai studied the dynamic interaction between the retained water and a exibledam using modal analysis [35, 36]. They considered the dam as a EulerBernoulli beam andshowed that the added mass, which vibrates together with the structure during the imposedexcitation, results from the hydrodynamic effect due to the current deection of the structure and thecurrent response of the entire system. Therefore, the added mass is a function of the mode shapes ofboth the structure and the reservoir.

Figure 3. Secondary buckling, emilia earthquake, Italy, 20 and 29 May 2012.



As far as liquid-containing tanks are concerned, two main categories of added mass models canbe found in the literature, those aimed at simulating the global behaviour of tanks (e.g. theoverturning moment and the total base shear), which use a few lumped masses, one for eachpressure component [3739], and those aimed at analysing the local behaviour of tank walls.Examples of this latter category of added mass models, which will be used in the present studyand discussed in the following, can be found in Virella et al. [20, 24, 40].

The inertia of the portion of the uid that acts impulsively is lumped in with the inertia of thetank walls, and the added masses are calculated from pressure distributions of rigid tanks.Proceeding in this way, the added mass values are constant during the dynamic simulation. Butthis approach is not strictly correct; in fact, after what Lee and Tsai have shown for exiblestructures the added mass depends on the deection of the structure and therefore is notconstant over time [35, 36]. However, in case of tank liquid systems, the studies by Veletsosand Yang [6] and Haroun and Housner [7] have shown that the pressure distribution due to theliquid impulsive component in rigid and exible tanks are similar, in particular for broad tanks(H/R< 1) as indicated by the diagrams in Figure 5. Therefore, an added mass method thatemploys constant over time masses can be applied with reference to broad tanks.

It is worth noticing that the added mass model is easily implemented in any FEMsoftware because it does not require any special purpose nite element. Furthermore, DeAngelis, Giannini [37] favourably compared the results obtained by using this model withexperimental tests [37].

impp impp

hydp hydp

Buc

klin

g zo

ne

imp hydp p

Figure 4. Compression force developed in an annular strip located in the zone of buckling, after [24].

00

0.2

0.3

0.5 0.5

1 1

2

H/R = 5

0.4

0.6

0.8

1

0

0.2

0.4

0.6

0.8

1

0.5 1 0 0.5 1

H/R = 3

ci() ci1()

Figure 5. Pressure distribution along the tank height (a) for rigid and (b) for the rst mode of exibletanks, after [2].



4. CASE STUDY: A STEEL TANK UNDER SEISMIC ACTIONS

According to the previous considerations, a broad tank was considered in the present study,whose geometric characteristics are taken from Virella [24] and are shown in Figure 6. A 90%lling level was considered. The tank is assumed without a roof structure. Because full baseanchorage is considered and the primary interest of the paper is on the buckling of the cylindershell, the model has clamped conditions at the base. The tank walls material is steel S275 withelastic-hardening constitutive behaviour, dened the following mechanical properties: yieldstrength fy = 275.0MPa, ultimate strength fu = 430.0MPa, elastic modulus E = 210000.0MPa andstrain hardening modulus Eh = 3888.0MPa.

4.1. Finite element model

The nite element analysis package ABAQUS [25, 26] was used to carry out all the analyses. Anite element mesh of 7080 elements was used to assure convergence of the solution. Themesh size was dened performing a convergence study in which a set of nonlinear staticanalyses was performed on meshes with decreasing size until the results did not show anysignicant mesh dependency [41]. Further, details can be found in [34]. Four-node,doubly curved shell elements with reduced integration and nite membrane strain formulationwere employed.

From a practical point of view, the added mass approach essentially consists in deriving liquidmasses from pressure distributions and to attach them to the shell nodes of a nite element modelby means of one-direction elements, as shown in Figure 7. Because the added masses aredetermined from the hydrodynamic pressure that is normal to the shell surface, they must bedened in such a way that they only add inertia in that direction. Therefore, the one-directionelements (MPC type LINKS in ABAQUS) have supports oriented in their local axes thatconstrain the motion of the nodal masses to the normal direction of the shell. The motion of

30480 mm

2425 mm

2416 mm

2416 mm

2416 mm

2416 mm

1088

0 m

m12

089

mm

12.7 mmwt =9.5 mmwt =7.9 mmwt =7.9 mmwt =7.9 mmwt =liquid level

Figure 6. Geometric characteristics of the tank considered (in mm).

Pinned rigid linkSupportsAdded masses

Figure 7. Schematic representation of the added-mass model, after [20].



each support is restricted in the global tangential and vertical directions, whereas it is free in theradial direction. The added mass model is obtained from a pressure distribution for the impulsivemode of the tank-liquid system and the convective component is neglected [20, 24]. Theimpulsive pressure distribution is obtained from the horizontal rigid body motion of a rigidtank-liquid system and can be expressed in a cylindrical reference system as

pi z; y; t ci z xg t rR cos y ; (3)where z indicates the coordinate along the axis of the cylinder, y is the circumferential position, tis the general time, xg t is the ground acceleration time history, r is the water density and thefunction ci(z) describes the pressure distribution along the tanks height and can be determinedafter Veletsos and Shivakumar [2]. The lumped mass at each node of the mesh is computed bymultiplying the pressure acting on the tank walls (equation (2)) by the tributary area of thenode and dividing by the reference ground acceleration an xg t cos y . Therefore, for thegeneral interior node, the expression of the lumped mass is given by equation (4),

mi piE2size

an ci z rRE2size; (4)

where Esize is the edge length of the rectangular nite elements used that was set in the presentwork equal to 500mm.

5. MODAL ANALYSIS

Prior to the dynamic buckling analysis, the modal properties of the tank were investigated. Inparticular, the rst 30 natural periods and mode shapes of the tank-liquid system were evaluatedunder two different assumptions, that is, by either neglecting or considering the pre-stress stateproduced by the hydrostatic pressure and the self-weight of the tank. Table I reports the naturalperiods obtained. Only the odd natural periods are listed because, due to the symmetry of thestructure, duplicated natural modes were obtained. The pre-stress state strongly affects the naturalperiods of the tank-uid system, by reducing the natural periods. However, if the natural periods areplotted versus the number of circumferential waves, n, as performed in Figure 8, it is possible tonotice that the effect of the pre-stress state is smaller for the modes characterised by low

Table I. Effect of the pre-stress on the periods, T, of the rst 30 natural modes :n and m indicate the numberof circumferential and axial waves, respectively.

Pre-stress considered Pre-stress neglected

Mode T [s] m n T [s] m n

1 0.96 1 8 2.74 1 143 0.96 1 9 2.70 1 155 0.93 1 10 2.69 1 137 0.92 1 7 2.60 1 169 0.89 1 11 2.54 1 1211 0.84 1 12 2.46 1 1713 0.83 1 6 2.32 1 1815 0.79 1 13 2.31 1 1117 0.75 1 14 2.19 1 1919 0.71 1 15 2.07 1 2021 0.69 1 5 2.02 1 1023 0.67 1 16 1.96 1 2125 0.64 1 17 1.85 1 2227 0.61 1 18 1.75 1 2329 0.58 1 19 1.72 1 9



circumferential wave numbers (e.g. n< 10). The results found here and collected in Table II are inagreement with the results of Virella et al. [40].

It must be noted that Figure 8 refers to the rst 30 modes extracted byABAQUS, which extractsmodes in decreasing order of natural period, but the participating mass in the x-direction of thesemodes is very small, and therefore, these modes are not the most signicant in describing theglobal response of the structure; however, they may be important for the local behaviour of thetanks walls.

For this reason, a second analysis was performed, considering only the natural modes with thelargest participating mass ratio, ax, and in particular, a number of modes that sufces in order toobtain a total participating mass greater than the 85% of the total mass of the system; sevenmodes were required for the tank-uid system considered. All the details about these modesare reported in Table II, from which it is possible to note that they are all cantilever-typemodes (n = 1). In the light of what is shown in Figure 8, for these modes, the effect of pre-stress states is negligible. Therefore, pre-stress states can be neglected when investigating theglobal behaviour (i.e. the total shear force or the overturning bending moment at the base) ofthe structure under earthquake accelerations.

6. DYNAMIC BUCKLING ANALYSIS

6.1. Overview of the analysis procedure

Once the added mass model has been validated through modal analysis, dynamic time-history analysesare performed including both material and geometric nonlinearities. The nonlinear equations of motionare solved using an implicit time-integration technique available in ABAQUS/Standard [26]. Only

5 10 15 20 250.5

1

1.5

2

2.5

3

3.5

4

Circumferential wave number nT

[s]

Prestress state consideredPrestress state neglected

Figure 8. Dependency of the natural period of the rst 30 modes of the tank on the circumferentialwave number, n.

Table II. Effect of the pre-stress on periods, T, of the cantilever-type vibration modes with the largesteffective modal masses, ax: n and m indicate the number of circumferential and axial waves, respectively.

Pre-stress considered Pre-stress neglected

Mode T ax m n T ax m n[s] [] [] [] [s] [] [] []

1 0.22 0.44 1 1 0.22 0.43 1 12 0.22 0.14 >1 1 0.22 0.15 >1 13 0.18 0.09 >1 1 0.18 0.10 >1 14 0.22 0.08 >1 1 0.22 0.08 >1 15 0.18 0.05 >1 1 0.18 0.05 >1 16 0.20 0.04 >1 1 0.20 0.03 >1 17 0.23 0.03 >1 1 0.21 0.02 >1 1



unidirectional ground-motions were considered here, therefore, the model was accelerated only inthe x-direction. The main objective of the analysis performed herein is to estimate the dynamicbuckling load, which in this case is represented by the peak ground acceleration (PGA) thatproduces buckling, PGAcr. To this aim, the dynamic simulation is not performed using theoriginal ground motion record, but the base accelerogram, xg t , is scaled according toincreasing values of PGA. In particular, several analyses are performed for increasing values ofPGA, from 0.02 g to 0.75 g.

It is worth noticing that the PGA is the most widely used ground motion IM used in theliterature related to tanks [11, 13, 14, 24, 4244], therefore, it will be adopted in this sectionof the present paper. Alternative IMs will be investigated and discussed in Section 7.1.

6.2. Evaluation of the critical buckling load

To identify the dynamic buckling load of the tank, the BudianskyRoth criterion [2, 4, 24, 27, 28, 45],which has been used extensively in the literature to determine the dynamic buckling load ofstructures, was employed in the present study. According to the aforementioned criterion,different analyses of the structure for several load levels (PGA values in this case) need to becarried out, and the load value for which there is a signicant jump in the response for a smallincrease in the load indicates that the structure moves from a stable state to a critical state.The rst step required by the BudianskyRoth criterion is to monitor the transient response ofselected points of the structure. Criteria used to select the most representative node of thestructure are discussed at the end of this Section. For now, with the sole purpose of illustratingthe criterion, the attention is focused on the transient response of one node. From Figure 9, itis evident how a signicant jump in the displacement eld can be observed only for PGAsabove 0.70 g.

The dynamic buckling load can be more clearly identied by plotting the maximum radialdisplacement of the control node recorded during the different analyses versus the correspondingPGA values, as performed in Figure 10. The so obtained points can be used to t a bilinearregression model, thus producing a so called pseudo-equilibrium path, as proposed by Virella et al.[24]. The intersection of the two lines constituting the path provides an estimate of the critical PGA,PGAcr, that is, the ground-motion intensity at the transition from the stable to the unstable path.

In order to dene the control node, two grids of points were xed in those parts of the structurewhere the maximum deformations and plasticization were expected (see Figure 11). The pseudo-equilibrium paths were then built for each node belonging to the two grids, and the actual controlnode was assumed to be the one that developed the smallest critical PGA value. This criterion isparticularly important because the position of the control node may change in the different analyses.

6.2.1. Buckling models observed during the analyses. Figure 12 shows the deformed shape of thetank walls at a general step of the dynamic analyses performed, and it is particularly illustrative

0 1 2 3 4 5 6 7 8 9 1050

0

50

time [s]

ur [m

m]

PGA=0.10gPGA=0.30gPGA=0.40gPGA=0.50gPGA=0.60gPGA=0.65gPGA=0.70gPGA=0.75g

Figure 9. Time histories of the radial displacement of one node of the FE model for increasing PGA valuesof the base accelerogram.



Secondary buckling

Elephant footbuckling

Figure 12. Deformed shape of the tank at the onset of buckling.

0 10 20 30 40 500

0.2

0.4

0.6

0.8

Critical PGA=0.645g

max|ur| [mm]

PGA

[g]

Figure 10. Pseudo-equilibrium path for one node of the FE model.

Ground

motion

Figure 11. Grid points among which the control node is searched.



because two buckling phenomena can be observed. The rst one is the presence of secondarybuckling at the upper-middle part of the shell. The second one is the formation of anelephants foot bulge at the bottom of the tank, in the yielded region (see Figure 13). In thiscase, secondary buckling occurred for PGA values larger than 0.40 g, a few seconds after thepeak base acceleration. The elephants foot bulge at the base developed for PGA values largerthan 0.55 g. Because the elephants foot buckling has been widely discussed in the literatureand it is fully covered by the current regulations, our attention is mainly focused on the localbuckling at the upper-middle part of the shell. In particular, it is not yet clear if it is a pureelastic buckling or if material yielding plays a direct role as for the elephants foot buckling. Arst step in understanding this issue is to perform analyses assuming a linear elastic behaviourfor the material. The results of such analyses showed that the secondary buckling phenomenonoccurred even when considering linear elastic materials; therefore, it can be dened as a purelyelastic buckling.

6.2.2. Effect of plasticity. In order to understand the inuence of material yielding on the criticalPGA, the pseudo-equilibrium paths resulting from elastic and elasticplastic analyses werecompared, as illustrated in Figure 14. As expected, the elasticplastic critical PGA is lowerthan the elastic one. In particular, a reduction of about 40% is observed. Therefore, thepseudo-equilibrium paths are strongly inuenced by material yielding. Furthermore, it isinteresting to notice that the control node to which the elasticplastic curve is referred to isstill located in an elastic region; this means that the failure mode is still characterised by pure

+0.00e+00+8.60e05+1.72e04+2.58e04+3.44e04+4.30e04+5.16e04+6.02e04+6.88e04+7.74e04+8.60e04+9.46e04+1.03e03

Figure 13. Equivalent plastic strain and elephants foot bulge at the base of the tank.

0 20 40 60 800

0.2

0.4

0.6

0.8

0.645gElastic path

0.371g

Elasticplastic path

max|ur| [mm]

PGA

[g]

Figure 14. Elastic and elasticplastic pseudo-equilibrium paths.



elastic buckling, but the value of PGA at which this buckling occurs is strongly reduced byplastic strains in other parts of the structure. We can conclude that material yielding leads toimportant changes in global behaviour of the structure.

7. SEISMIC VULNERABILITY

7.1. Efciency and sufciency of ground-motion intensity measures

The seismic vulnerability of structures is often characterised by a fragility curve that gives theprobability of occurrence for a general limit state as a function of a ground-motion IM. Thislatter is a parameter describing the intensity of ground motions and in particular, their severityon structures. Examples of commonly used IMs are the PGA, the peak ground velocity (PGV),the peak ground displacement (PGD), the pseudo spectral accelerations (PSA) at differentperiods, etc. Past studies dealing with seismic risk analysis and fragility curves for liquid-containing tanks may be found in Iervolino et al. [46], ORourke et al. [13], Salzano et al.[14] and Talaslidis et al. [47], in all these studies, the PGA is used as IM.

The limit state considered in the present paper is the dynamic buckling, and the probability of failureis intended as the probability of having buckling for a given value of a certain ground motion intensitymeasure im, as expressed by equation (5)

Pf P IMcr im ; (5)

where IMcr is the random variable, which represent those particular values of the IM producingbuckling. The probability of failure in equation (5) can be rewritten in terms of conditionalprobability as

Pf P buckling IM im:j (6)

The correct choice of the IM is of crucial importance in describing the structural response.Because for liquid-storage tanks, there is lack of studies in the literature about this topic, acontribution on the efciency and sufciency of four different ground-motion IMs is given here.

7.1.1. Efciency. According to Tothong [48], an IM is dened efcient if its adoption results inrelatively small variability of structural response for a given IM level, that is, if the IM is a goodpredictor of structural response (e.g. maximum displacement). Different approaches may be usedto evaluate efciency, the most common being stripe/multi-stripe analysis, IDA capacity-basedanalysis and cloud analysis. An extensive discussion of those different analysis methods isavailable in Baker [49].

All the aforementioned methods listed require to scaling ground motions to specic target IMvalues with the exception of cloud analysis. With this latter method, the structure is subjected to aset of ground motions that, in general, are either left unmodied, or all records are scaled by aconstant factor if the unmodied records are not strong enough to induce the structuralresponse level of interest. The set of IM levels of the accelerograms and their associatedstructural-response values resulting from nonlinear dynamic analysis are sometimes referred toas a cloud, because they form a rough ellipse when plotted. Regression analysis can be usedon this cloud of data to compute the conditional mean and standard deviation of differentstructural-response values given IM. A linear relationship between the logarithms of the twovariables often provides a reasonable estimate [49].

In the present work, cloud analysis was adopted to avoid ground-motion scaling because theeffects of such procedure have not been yet fully investigated as far as liquid containing tanksare concerned. Forty nonlinear time-history analyses are performed using 40 differentaccelerograms from the Next Generation of Ground-Motion Attenuation Models (NGA) projectdatabase [50], chosen according to the following criteria [51]: (i) moment magnitude, Mw,



spanning from 6.0 to 8.0; (ii) JoynerBoore distance. RJB, spanning from 0.0 to 30.0 km; (iii) nopulse-like records, according to the classication by [52]; (iv) maximum usable period greaterthan 3.0 s [53]; (v) only one horizontal component per record. In addition to the aforementionedcriteria, in order to increase the goodness of the efciency analysis, accelerograms were selectedin order to obtain a set PGA values as logarithmically spaced as possible. The magnitude - distancedistribution of the accelerograms used is depicted in Figure 15.

In Figure 16, for each analysis, the maximum radial displacement, max |ur|, occurring in the tank isplotted in double-logarithmic scale versus the four different IMs taken into consideration. For eachcase, the linear regression model

ln max urj j b0 b1 ln im e (7)

was tted. In Equation (6), im indicates the general intensity measure, b0, e, b1 areunknown regression coefcients, and e is a standard error term. In cloud analysis, theefciency may be quantied by the standard deviation of the error term, se. This latter parameter isreported in Figure 16 together with the slope of the regression line and the coefcient ofdetermination R2.

From the results reported in Figure 16, it is possible to notice that the structural responseseems to be scarcely correlated with PGA and PSA, whereas it has a very strong correlationwith PGD (se= 0.29, R

2 = 0.86), which can be dened the most efcient ground-motion IM. Inthe literature, the PGD is considered an efcient IM for exible structures with long periods[54]. In the uid-tank system investigated in the present paper, two groups of modes can beidentied: short-period cantilever-type modes controlling the global behaviour (e.g. overturningbending moment, base shear, etc.) and long-period shell-type model, characterised by a numberof circumferential waves greater than 1. The maximum radial displacement, max |ur|, isprobably connected to the latter group of modes, in fact, from Figure 17, it is possible tonotice that the deformed shape of the tank assumes a wave form, typical of shell modal forms,in the upper-middle part, where the maximum radial displacements occurs.

7.1.2. Sufciency. An IM is considered sufcient if the distribution of structural response values fora given IM value is independent of other parameters involved in the calculation of seismic hazard,mainly, magnitude, source to site distance and e (this latter parameter describes how manystandard deviations the spectral acceleration at a given period is distant from the mean spectralacceleration predicted by a given attenuation relationship [48]). Sufciency is particularlyimportant for dening sound ground motion selection criteria for nonlinear analyses [48].

In cloud analyses, sufciency is analysed by evaluating the correlation between the residuals ofthe linear regression described in Section 6.1.1 with the aforementioned parameters involved in

0 5 10 15 20 256

6.5

7

7.5

8

RJB [km]

Mw

Figure 15. Magnitude-distance distribution of the 40 accelerograms used for efciency and sufciency analysis.



101 100 101

101 100 101

102 101 100

102 101 100

101

101

102

103

PGA [g]

Slope: 0.62 R2: 0.25 : 0.67

PSA(T1) [g]

Slope: 0.54 R2: 0.16 : 0.71

PGV [m/s]

Slope: 0.94 R2: 0.68 : 0.44

PGD [m]

Slope: 0.75 R2: 0.86 : 0.29

max

|u r| [m

m]m

ax|u r|

[mm]

max

|u r| [m

m]m

ax|u r|

[mm]

101

102

103

101

102

103

101

102

103

a

b

c

d

Figure 16. Efciency of ground-motion intensity measures: peak ground acceleration (PGA) (a), Spectralacceleration at the rst natural period, Sa(T1) (b), peak ground velocity (PGV) (c), peak ground

displacement (PGD) (d).



hazard calculation. In the present study, the sufciency was evaluated with respect to Mw and RJBby tting the following linear regression models:

ln rim b0 b1Mw eln rim b0 b1RJB e

(8)

where rim indicates the residuals of the regression performed using Equation (6) considering theintensity measure, im.

As an example, Figures 18 and 19 show the dependency onMw (a) and RJB (b) of residuals obtainedby tting the model in Eq. (6) considering either IM=PGD or IM=PGA. It is clearly evident that PGAis less sufcient than PGD especially in terms of Mw. Figures 17 and 18 also give the slopecoefcient of the regression line depicted and the p-value for the F-statistics corresponding tothe null hypothesis b1 = 0. A summary of the results is provided in Table III from which it ispossible to conclude that the most efcient measure is PGD, which shows sufciency also ingeneral terms.

7.2. Fragility analysis

7.2.1. Denition of the ground-motion set for fragility analysis. The fragility with respect to dynamicbuckling is evaluated for a case study atmospheric tank located in the industrial plant in Milazzo, Italy.

In order to derive site-specic fragility curves, the accelerograms used for incremental dynamicanalysis were selected on the basis of information on the response spectrum at Milazzo. Inparticular, the 5% damped elastic spectrum with 475 years return period is calculated using theItalian Seismic Code prescriptions [55]. A type A soil is assumed and therefore, according tothe Italian code, a reference PGA of 1.89m/s2 is considered.

Accelerograms were selected from the NGA ground-motion database, identifying a group of 14records with an average acceleration response spectrum compatible (according to EC8 criteria) withthe previously dened site spectrum. Spectral compatibility was dened in the period range[Tmin = 0.178 s, 2 Tmax = 0.456 s] to account the main for cantilever-type modes (n = 1). This periodrange was dened according to the general criteria suggested by EC8. Furthermore, given the resultsin terms of efciency long-period spectral accelerations are well-correlated with PGD [54] andin order to take into account the effect of long-period local modes, spectral compatibility wasrequired also in the long period range T> 1.0 s.

Dening the range of signicant periods for spectral compatibility, it is possible to select those 14accelerograms whose average spectrum best ts the site-specic elastic spectrum in that range. Inparticular, an automatic procedure has been implemented allowing to analyse all the possible

Figure 17. Deformed shape of the tank when the maximum radial displacement was attained in one of theanalyses performed.



combinations of the required number of accelerograms in order to identify the group with the best t.The accelerograms selected are listed in Table IV and their PSA response spectra are depicted inFigure 20 together with their average spectrum.

To investigate the fragility with respect to dynamic buckling, the incremental dynamic analysisprocedure presented in Section 6.2 is repeated for the tank subjected to the 14 response spectrum-compatible accelerograms. Applying the BudianskyRoth criterion to the results of each of them,14 pseudo-equilibrium paths are built and therefore, 14 values of PGAcr are obtained. At the sametime, it is possible to dene also the critical values for all the other IMs considered in the presentpaper. All these critical values are collected in Table V. However, the results of accelerograms 1,2 and 7 are considered to be unreliable, because the scale factor associated with them is too high[56]. Because of this reason, these three accelerograms are excluded from the calculations ofSection 6.3 to obtain the fragility curves.

6 6.5 7 7.5 81.5

1

0.5

0

0.5

1

1.5

resid

uals

Slope: 0.03 pvalue: 7.64e1

0 5 10 15 20 251.5

1

0.5

0

0.5

1

1.5

resid

uals


Mw

RJB [km]

a

b

Figure 18. Sufciency of peak ground displacement (PGD) in terms of moment magnitude (a) andJoynerBoore distance (b).

Table III. Results of the sufciency analysis.

Mw RJB

IM Slope p-value Slope p-valuePGA 0.930 9.06 107 0.0076 0.597PSA(T1) 0.988 9.52 107 0.0178 0.241PGV 0.482 3.15 104 0.0130 0.167PGD 0.029 0.764 0.0030 0.626IM, intensity measure; PGA, peak ground acceleration; PGV, peak ground velocity; PGD, peak grounddisplacement.



It is interesting to notice that the control nodes to which the 14 pseudo-equilibrium paths are referredto may change from one path to the other. By looking at the position of the control nodes, we foundthat for 12 out of 14 paths, the control node is located in the upper-middle part of the tank, wherethe material is elastic; in these cases, the failure mode is characterised by secondary buckling. Forthe remaining two cases, it is associated to elephants foot buckling, in fact, the control node islocated in the middle-low part, where the material is yielded, and an outward bulge has formed.

6 6.5 7 7.5 81.5

1

0.5

0

0.5

1

1.5

Mw

resid

uals


0 5 10 15 20 251.5

1

0.5

0

0.5

1

1.5

RJB [km]

resid

uals


a

b

Figure 19. Sufciency of peak ground acceleration (PGA) in terms of moment magnitude (a) andJoynerBoore distance (b).

Table IV. The 14 spectrum-matching accelerograms used for fragility analygis: earthquake and stationname, year, component, moment magnitude, Mw and JoinerBoore distance, RJB. Earthquake and station

names are as dened by the NGA project [50].

Earthquake name Station name Year Component MW RJB [km]

Irpinia, Italy Auletta 1980 N-S 6.90 9.52Northridge, CA, USA Pacoima Dam (downstr) 1994 E-W 6.69 4.92Irpinia, Italy Auletta 1980 E-W 6.90 9.52Northridge, CA, USA LittlerockBrainard Can 1994 N-S 6.69 46.31Denali, Alaska R109 2002 E-W 7.90 42.99Whittier Narrows, CA, USA Pasadena-CIT Kresge Lab. 1987 N-S 5.99 6.77Irpinia, Italy Bagnoli Irpinio 1980 E-W 6.22 17.79Loma Prieta,CA, USA Gilroy Array #1 1989 E-W 6.93 8.84San Fernando,CA, USA Old Seismo Lab 1971 N-S 6.61 21.5Whittier Narrows,CA, USA Pasadena-CIT Kresge Lab. 1987 E-W 5.99 6.77Northridge, CA, USA LA-Wonderland AVE 1994 E-W 6.69 15.11Irpinia, Italy Sturnio 1980 N-S 6.22 20.38Northridge, CA, USA Pacoima Dam (downstr) 1994 N-S 6.69 4.92Northridge, CA, USA LA-Grifth Park Observatory 1994 N-S 6.69 21.2



Furthermore, the average value of PGAcr is 0.348 g, so that we can conclude that secondary bucklingshould be of great concern to designers because it seems to be the dominant failure mode and it occursat relatively low levels of PGA.

7.2.2. Fragility curves. The probability of failure in equation (5) is essentially the denition of thecumulative density function (CDF) for the random variable IMcr, that is, the critical values of theground-motion IM under consideration. Therefore, it can be expressed as

Pf P IMcr im FIMcr im (9)

Using the data in Table V, the empirical CDF can be computed for each IM. The four empiricalCDFs obtained are plotted in Figure 20. From this gure, it is immediate to notice that lessuncertainty is associated to the buckling phenomenon if described in terms of PGD, that is, the CDFin terms of PGD is the steepest one. On the contrary, high uncertainty is associated to the dynamicbuckling when described in terms of PSA.

Assuming a lognormal distribution for the random variables IM, as commonly performed in theliterature [47, 57, 58], the cumulative probability functions can be characterised by the rst two

Table V. Critical scale factors, SFcr, and Buckling loads in terms of PGA, PSA(T1), PSV and PGD, for thetank subjected to 14 response-spectrum compatible accelerograms.

Accelerogram SFcr

PGAcr PSAcr PSVcr PGDcr

[g] [g] [m/s] [mm]

1 8.68 0.54 1.41 0.53 3202 8.26 0.43 0.78 0.53 7493 1.86 0.11 0.27 0.10 594 4.72 0.28 0.74 0.30 615 2.21 0.13 0.46 0.14 776 3.22 0.29 0.71 0.12 97 11.25 0.55 0.88 0.51 588 0.75 0.31 0.89 0.24 489 2.04 0.41 0.95 0.22 4910 5.26 0.59 1.03 0.42 5211 3.50 0.39 0.81 0.30 5012 2.80 0.22 0.77 0.12 2113 1.02 0.44 0.74 0.31 4614 1.13 0.18 0.34 0.15 27

PGA, peak ground acceleration.

PGA 0.1 1.00

0.2

0.4

0.6

0.8

T [s]PS

A [g

]

Target spectrumEC8 lower boundActual spectraMean spectrum[0.2 T1, 2T1]

Figure 20. Response spectra of the 14 selected accelerograms and compatibility with the target spectrum inthe selected range of periods.



moments. Once the mean and the standard deviation are known, it is possible to compute the lognormalCDF. The so computed curves are plotted in Figure 21 together with the empirical CDF, and also, thecoefcient of variation is highlighted. From the gure, we can notice that the analytical curves have agood t; this implies that the lognormal distribution model is well-suited to the buckling problem ofliquid-storage tanks.

8. CONCLUSIONS AND FUTURE WORK

In the present work, the seismic behaviour of liquid containing cylindrical tanks was investigated usingthe added mass method in order to simulate the uidstructure interaction. The added mass wascomputed from the impulsive pressure distribution for rigid tanks, and therefore, the added masswas constant during the simulation. This approach is correct for broad tanks, where the pressuredoes not change much depending on whether the tank is assumed to be rigid or exible. The mainndings of the present paper are listed in the succeeding text.

The pre-stress state due to the hydrostatic and hydrodynamic pressures on the tank walls has alarge effect on shell-type modes, and in particular, it reduces their periods, but it does not haveimportant effects on the cantilever-type vibration modes (i.e. modes characterised by a numberof circumferential waves n= 1) that control the global response of the liquid-tank system.

Nonlinear dynamic analyses have shown that the added-mass model allows to simulate two typesof buckling modes: elephants foot buckling and secondary buckling. However, the dominantfailure mode is the secondary buckling at the upper-middle part of the shell.

Contrary to the elephants foot buckling, the secondary buckling is an elastic buckling mode, butit is strongly inuenced by the occurrence of plasticity in other parts of the structure.

The nite element model developed was used in order to investigate the efciency and sufciency offour different ground-motion IMs, that is, the PGA, peak ground velocity, PGD and spectral accelera-tion at the natural period of the rst cantilever-type natural mode. PGD has been found being the mostefcient and sufcient IM as far as the maximum radial displacement of the tank walls is concerned.

The average dynamic buckling load resulting from 14 analyses using spectrum-compatibleaccelerograms corresponds to PGAcr = 0.35 g, so that the secondary buckling should be of greatconcern to the designer, although not yet explicitly covered by current standards.

Fragility curves, in terms of the attainment of a buckling limit state, have been obtained, consid-ering the four aforementioned IMs.

ACKNOWLEDGEMENTS

The authors acknowledge the nanical support of the Italian Department of Civil Protection, ReLUIS20102013 project Task 2.2.3: Industrial Plants, Nuclear Plants, and Lifelines.

0 0.5 1 1.5 20

0.2

0.4

0.6

0.8

1

P (IM

cr

im)

[ ])( [ ], [ ], [ ],im PGA g PSA g PGD m PGV m s

PGA, COV =0.35, COV =0.90

PGD, COV =0.20PGV, COV =0.26

( )11PSA mT =

Figure 21. Empirical and analytical (lognormal) fragility curves for buckling in terms of the various intensitymeasures considered in the present paper.



REFERENCES

1. Hamdan FH. Seismic behaviour of cylindrical steel liquid storage tanks. Journal of Constructional Steel Research2000; 53(3):307333.

2. Veletsos AS, Shivakumar P. Dynamic response of tanks containing liquids or solids, in Computer Analysis andDesign of Earthquake Resistant Structures DE Beskos and SA Anagnostopoulos, Editors, Computational Mechanics,Inc. 1997.

3. Rammerstorfer FG, Scharf K, Fisher FD. Storage Tanks Under Earthquake Loading. Applied Mechanics Reviews1990; 43(11):261282.

4. Veletsos, AS. Seismic response and design of liquid storage tanks in Guidelines for the Seismic Design of Oil andGas Pipeline Systems. Committee on Gas and Liquid Fuel Lifelines of the ASCE Technical Council on LifelineEarthquake Engineering, Editor, ASCE: New York, 1984

5. Hunt B, Priestley MJN. Seismic water waves in a storage tank. Bulletin of the Seismological Society of America1978; 68(2):487499.

6. Veletsos, AS, Yang JY. Earthquake response of liquid storage tanks, in Advances in Civil Engineering throughEngineering Mechanics - Second Annual Engineering Mechanics Division Specialty Conference, ASCE: NorthCarolina State University, Raleigh, North Carolina, U.S.A. 1977; 124.

7. Haroun MA, Housner GW. Earthquake response of deformable liquid storage tanks. Journal of Applied Mechanics1981; 48(2):411417.

8. Housner GW. The dynamic behaviour of water tanks. Bulletin of the Seismological Society of America, 1963; 53(1):381387.

9. Jacobsen LS. Impulsive hydrodynamics of uid inside a cylindrical tank and of uid surrounding a cylindrical pier.Bulletin of the Seismological Society of America 1949; 39(3):189204.

10. Graham EW, Rodriguez AM. The characteristics of fuel motion which affect airplane dynamics. Journal of AppliedMechanics 1952; 19(3):381388.

11. Brown KJ, et al., Seismic performance of los angeles water tanks, in Fourth U.S. Conference on Lifeline EarthquakeEngineering, MJ ORourke, Editor : San Francisco. 1995, 668675.

12. Haroun MA. Behaviour of unanchored oil storage tanks: imperial valley earhquake. Journal of Technical Topics inCivil Engineering 1983; 109(1):2340.

13. ORourke MJ, So P. Seismic fragility curves for on-grade steel tanks. Earthquake Spectra 2000;16(4):801815.14. Salzano E, Iervolino I, Fabbrocino E. Seismic risk of atmospheric storage tanks in the framework of quantitative risk

analysis. Journal of Loss Prevention in the Process Industries 2003; 16(5):403409.15. HAZUS. Earthquake loss estimation methodology, National Institute of Building Sciences, prepared by Risk

Management Solutions: Menlo Park, CA, USA, 1997.16. Fischer FD, Rammerstorfer FG. A rened analysis of sloshing effects in seismically excited tanks. International

Journal of Pressure Vessels and Piping 1999; 76(10):693709.17. Zienkiewicz OC, Taylor RL, Nithiarasu P. The nite element method for uid dynamics. 6th ed ed2005, Amsterdam ;

London: Elsevier Butterworth-Heinemann. xii, 435 p., [6] p. of plates.18. Zienkiewicz OC, Taylor RL. The nite element method for solid and structural mechanics. 6th ed2005, Oxford ;

Burlington, MA: Elsevier Butterworth-Heinemann. xv, 631 p., [4] p. of plates.19. Westergaard HM. Water pressures on dams during earthquakes. Transactions of the American Society of Civil

Engineers 1933; 98:418433.20. Virella JC, LE Suarez, Godoy LA. Effect of pre-stress states on the impulsive modes of vibration of cylindrical tank-

liquid systems under horizontal motions. Journal of Vibration and Control 2005; 11(9):11951220.21. Kim MK, et al. Seismic analysis of base-isolated liquid storage tanks using the BEFEBE coupling technique. Soil

Dynamics and Earthquake Engineering 2002; 22(912):11511158.22. Gingold RA, Monaghan JJ. Kernel estimates as a basis for general particle methods in hydrodynamics. Journal of

Computational Physics 1982; 46(3):429453.23. Gingold RA, Monaghan JJ. Smoothed particle hydrodynamics - theory and application to non-spherical stars.

Monthly Notices of the Royal Astronomical Society 1977; 181:375389.24. Virella JC, Godoy LA, Surez LE. Dynamic buckling of anchored steel tanks subjected to horizontal earthquake

excitation. Journal of Constructional Steel Research 2006; 62:521531.25. Hibbit HD, Karlsson BI, Soresen P. ABAQUS Standard Users Manual, 2002.26. Hibbit HD, Karlsson BI, Soresen P. ABAQUS Theory Users Manual, 2002.27. Budiansky B, Roth RS. Axisymmetric dynamic buckling of clamped shallow spherical shells, in Collected Papers on

Instability of Shell Structures (TN-D-1510), NASA, 1962 597606.28. Budiansky B. Dynamic Buckling of Elastic Structures: Criteria and Estimates, G Herrmann, Editor, Pergamon Press:

Oxford, 1967, 83106.29. European Committee for Standardization - CEN. Eurocode 8: design of structures for earthquake resistance - Part 4:

silos, tanks and pipelines, 2006.30. Priestley MJN, et al. Seismic design of storage tanks. Recommendations of a Study Group of the New Zealan

National Society for Earthquake Engineering, 1986.31. API. Welded Tanks for Oil Storage, 2008.32. Rotter MJ. Local collapse of axially compressed pressurized thin shell cylinders. Journal of Structural Engineering

1990; 116(7): 19551970.



33. European Convention for Constructional Steelwork (ECCS). Buckling of Steel Shells - European Recommendations(4th Edition), ECCS: Brussels, Belgium, 1988.

34. Tavano M. Seismic response of tank-uid systems: state of the art review and dynamic buckling analysis of a steeltank with the addedd mass method, in Department of Civil, Environmental and Materials Engineering, University ofBologna, 2012.

35. Lee GC, Tsai CS. Time-domain analyses of dam-reservoir system. I exact solution. Journal of EngineeringMechanics 1991; 117(9):19902006.

36. Tsai CS, Lee GC. Time-domain analyses of dam-reservoir system. II substructure method. Journal of EngineeringMechanics 1991; 117(9):20072026.

37. De Angelis M, Giannini R, Paolacci F. Experimental investigation on the seismic response of a steel liquidstorage tank equipped with oating roof by shaking table tests. Earthquake Engineering and Structural Dynamics2010; 39(4):377396.

38. Shrimali MK, Jangid RS. Seismic response of base-isolated liquid storage tanks. JVC/Journal of Vibration andControl 2003; 9(10):12011218.

39. Shrimali MK, Jangid RS. Seismic response of liquid storage tanks isolated by sliding bearings. EngineeringStructures 2002; 24(7):909921.

40. Virella JC, Godoy LA, Surez LE. Fundamental modes of tank-liquid systems under horizontal motions. EngineeringStructures 2006; 28: 14501461.

41. Malhotra PK. Practical nonlinear seismic analysis of tanks. Earthquake Spectra 2000; 16(2):473492.42. Virella JC, Surez LE, Godoy LA A static nonlinear procedure for the evaluation of the elastic buckling of anchored

steel tanks due to earthquakes. Journal of Earthquake Engineering 2008; 12(6):9991022.43. Sun J, Zhang R, Zhang L. Investigation on seismic vulnerability of vertical storage tanks based on probability

estimate method. World Information on Earthquake Engineering 2009; 25(1):3742.44. Krausmann, E, AM Cruz, Affeltranger B, The impact of the 12 May 2008 Wenchuan earthquake on industrial

facilities. Journal of Loss Prevention in the Process Industries 2010; 23(2):242248.45. Tanov R, Tabiei A, Simitses GJ. Effect of static preloading on the dynamic buckling of laminated cylinders under

sudden pressure. Mechanics of Composite Materials and Structures 1999; 6(3):195206.46. Iervolino I, Fabbrocino G, Manfredi G, Fragility of standard insutrial structures by a response surface based method.

Journal of Earthquake Engineering 2004. 8(6):927945.47. Talaslidis DG, et al., Risk analysis of industrial structures under extreme transient loads. Soil Dynamics and

Earthquake Engineering 2004. 24(6):435448.48. Tothong P Luco N, Probabilistic seismic demand analysis using advanced ground motion intensity measures.

Earthquake Engineering and Structural Dynamics 2007; 36(13):18371860.49. Baker JW Vector-valued ground motion intensity measures for probabilistic seismic demand analysis, in Department

of Civil and Environmental Engineering, University of Stanford: Sanford, CA, U.S, 2005.50. Power M, et al. An overview of the NGA project. Earthquake Spectra 2008. 24(1):321.51. Buratti N, Stafford PJ Bommer JJ. Earthquake accelerogram selection and scaling procedures for estimating the

distribution of drift response. Journal of Structural Engineering 2011; 137(3):345357.52. Baker JW. Quantitative classication of near-fault ground motions. Bulletin of the Seismological Society of America

2007; 97(5):14861501.53. Boore DM, Bommer JJ. Processing of strong-motion accelerograms: needs, options and consequences. Soil

Dynamics and Earthquake Engineering 2005; 25(2):93115.54. Buratti, N. A comparison of the performances of various groundmotion intensity measures, in 15th World

Conference on Earthquake Engineering, Lisbon, Portugal, 2012.55. Italian Ministry of Infrastructures. Norme Tecniche per le Costruzioni (Building Code), 2008.56. Bommer JJ, Acevedo AB. The use of real earthquake accelerograms as input to dynamic analysis. Journal of

Earthquake Engineering, 2004. 8(Special Issue 1):4391.57. Cornell CA, et al. Probabilistic basis for 2000 SAC federal emergency management agency steel moment frame

guidelines. Journal of Structural Engineering 2002; 128(4):526533.58. Buratti N, Ferracuti B, Savoia M. Response surface with random factors for seismic fragility of reinforced concrete

frames. Structural Safety 2010; 32(1):4251.



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