buratti-savoia_recorded and simulated gm for fragility analysis of rc structures

8/3/2019 Buratti-Savoia_recorded and Simulated GM for Fragility Analysis of RC Structures

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Recorded and Simulated Ground Motion Time Histories for SeismicFragility Analysis of RC Structures

N. Buratti, B. Ferracuti, M. SavoiaDISTART-Tecnica delle Costruzioni. Universit degli Studi di Bologna. Viale del Risorgimento 2, Bologna.

Keywords: seismic fragility, incremental dynamic analysis, recorded/simulated accelerograms.

ABSTRACT:In seismic reliability assessment, nonlinear analysis procedures are mandatory. Therefore, selection of ac-

celerograms is a central step in characterization of seismic demand on structures. In the present paper both re-corded and artificial accelerograms have been adopted to evaluate seismic fragility curves of a RC framestructure: three criteria for selection of real accelerograms, and two methods for generation of artificial timehistories have been considered and results have been compared.

1 INTRODUCTIONSelection of ground motion time histories for

nonlinear dynamic analysis of RC frames is a centralstep in characterization of seismic demand on struc-

tures: time histories must provide a good representa-tion of uncertainties of ground motion possibly oc-curring in the site considered. This aspect is evenmore important when accelerograms are selected toevaluate seismic fragility (Pinto, 2001; Pinto et al.,2004; Buratti et al., 2007). In this case, not onlymean value of structural demand, but also variabilityof possible ground motions must be considered inorder to evaluate structural failure in a probabilisticframework. Current practice consists in selecting re-cords according to a specific magnitude-distance

scenario (McGuire, 1995), where the latter is definedperforming probabilistic seismic hazard analyses, oraccording to a reference response spectrum.

In the present work, both recorded and artificialaccelerograms have been used to evaluate seismicfragility of a RC frame structure; three different cri-teria to select recorded ground motion time historiesand two methods to obtain simulated accelerogramshave been investigated. As for recorded ground mo-tions, two selection criteria (according to M-R sce-nario (McGuire, 1995) and PGA-PGV scenario)

based on seismic hazard analysis and one method

based on compatibility with code spectrum have been considered. On the opposite side, simulatedtime histories have been generated as response spec-trum compatible and by the method proposed bySabetta and Pugliese (1996), depending on seismic

hazard scenario of the site considered.Seismic fragility curves for the ultimate limit

state condition (in terms of interstorey drift) havebeen calculated for a case study RC frame structure,using incremental dynamic analysis (IDA) with theabove-mentioned ground motion time histories.

2 CRITERIA FOR ACCELEROGRAMSELECTION

Usually, for design of new structures, effects in-duced by earthquakes are evaluated using a responsespectrum of acceleration or displacements. However,in some cases these simplified approaches are notappropriate and fully dynamic analysis is required,(i.e. highly irregular structures, base isolated struc-tures, structures dominated by higher modes, etc.).

In these cases a suitable set of accelerograms must be selected to represent the seismic excitation, andnonlinear dynamic analysis is required. Furthermore,when assessing safety of existing structures, espe-cially if reliability analysis (Pinto, 2001; Pinto et al.,2004) is required, non linear analysis procedures aremandatory and variability of structural response be-comes as important as its mean values. Therefore se-lection criterion of acceleration time histories be-comes even more delicate. In fact, in order toevaluate seismic reliability of structures adoptedtime histories need to provide for a correct represen-

tation of variability of possible ground motion at thesite considered.

Three basic options are available to obtain accel-eration time histories: 1) real accelerograms re-corded during earthquakes (Figure 1a), 2) artificial


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accelerograms, that can be generated according to aresponse spectrum (Figure 1b) or according to a sce-nario expressed in terms of magnitude and site-epicentre distance (Figure 1c), 3) synthetic accelero-grams generated from seismological source modelsand accounting for source-site path and site effects.

In the present work both recorded and artificialaccelerograms have been used. In particular threedifferent criteria for the selection of recorded accel-erograms, and two different methods for generation

of artificial time histories have been considered.

2.1 Recorded acceleration time historiesReal strong-motion records are now easily acces-

sible in large numbers and their retrieval and ma-nipulation is relatively straightforward. Selectioncriteria for the records can be different (Bommer andAcevedo, 2004), depending if information about theseismic hazard at the site of interest is available.

In the first case, selection criterion of real recordsis based on compatibility with the response spec-

trum, because information on seismic sources andactivity rates is not given and Uniform Hazard Spec-trum (UHS) only can be used.

In the second case, i.e. if a site-specific seismichazard assessment is available, criteria for selectingsuitable records can be quite different. Current stateof best practice in selecting accelerograms for as-sessing the nonlinear demand of structures is basedon the definition of an hazard representative scenarioin terms of magnitude (M) and site-fault distance(R). Other authors (Trombetti et al., 2005) proposeto define the seismic scenario in terms of PeekGround Acceleration (PGA) and Peek Ground Ve-locity (PGV) with desired return periods.

In the present work, the following sets of re-corded acceleration time histories have been used: 1)

three sets of spectrum compatible acceleration timehistories, proposed by Iervolino et al. (2006); 2) oneset, selected according to magnitude-distance (M-R)scenario; 3) one set, defined in terms of PGA-PGVscenario as proposed by Trombetti et al. (2005).These criteria are described with more details in thefollowing.

2.1.1

Time histories compatible with code spectraSeismic design codes define rules to select re-corded accelerograms for nonlinear dynamic analy-sis, according to design response spectra. Italianguidelines in Ordinanza del Presidente del Consig-lio dei Ministri n. 3431 (OPCM 3431) prescribethat mean response spectrum of the selected set ofaccelerograms must match elastic response spec-trum, at 5% damping, defined by the code, i.e. dif-ference between these two spectra must be less than10% in two ranges 0.15 s 2.0 s and 0.15 s 2 T,where Tis the natural period of the structure. Euro-

code 8 (CEN, 2002) adopts the same rules with anadditional constraint for the peek ground accelera-tion: mean PGA of the selected accelerograms must

be greater than or equal to the response spectrumvalue at T= 0.

As for the number of time histories to be used innonlinear dynamic analyses, both codes prescribe atleast 3 registrations. In this case, maxima of their ef-fects on structures (displacements, deformations,forces, etc.) must be considered. Otherwise, if 7 ormore time histories are used, mean values of their

effects can be considered.With reference to different seismic zones for It-aly, Iervolino et al. (2006) adopted the EuropeanStrong Motion Database (Ambraseys et al., 2004) toselect combinations of records complying withOPCM 3431 and EC8 prescriptions. Accelerogramsets selected in Iervolino et al. (2006) are availableat RELUIS internet web site (http://www.reluis.it)and have been adopted in the present work. Two setsmatching OPCM 3431 response spectrum for highseismicity zones (reference PGA = 0.35g) are used:the first one (indicated in the following as R-OPCM(US)) contains seven recorded accelerogramsthat do not need to be scaled to be compatible withcode spectrum, while the second set (R-OPCM(S))contains seven accelerograms that need to be lightlyscaled in order to achieve compatibility with the ref-erence spectrum. In addition, a third set (R-EC8)containing seven time histories matching EC8 re-sponse spectrum for high seismicity zones (referencePGA = 0.35g) has also been given in Iervolino et al.(2006) and adopted in the present study.

2.1.2 Time histories consistent with the hazardscenarioTwo possible approaches are available to obtain

hazard information with reference to a specific site(Reiter, 1990): Deterministic Seismic Hazard Analy-

0 2 4 6 8 10 12 14 16 18 20 22 240.5

0

0.5Recorded acceleration time history

t[s]

a[g]

0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 300.2

0

0.2

t[s]

a[g]

Artificial Sabetta & Pugliese

0 2 4 6 8 10 12 140.5

0

0.5Artificial SIMQKE

t[s]

a[g]

(a)

(b)

(c) Figure 1. Examples of acceleration time histories: a) recorded;b) artificial generated according to Sabetta and Pugliese(1996); c) artificial generated by Simqke.


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sis (DSHA) or Probabilistic Seismic Hazard Analy-sis (PSHA).

The basis of the first approach (Reiter, 1990;Kramer, 1996) is to develop earthquake scenarios,defined by location (distanceR) and magnitude (M),which could affect the site under consideration.Then a controlling earthquake is selected, i.e. theearthquake, among all those considered, giving the

greater ground motion in the site under investigation(or alternatively, the maximum credible earthquake(Reiter, 1990; Kramer, 1996)). The resulting groundmotions at the site are then calculated using attenua-tion relations (e.g. PGA, PGV, Sa(T), etc.).

The second approach, introduced by Cornell in1968 (Cornell, 1968; Reiter, 1990), is the mostwidely used and has been adopted in the presentwork. The essence of PSHA is to identify all possi-

ble earthquakes that could affect the site under con-sideration, by all feasible combinations of magnitudeMand distanceR, and to characterize the frequencyof occurrence of different earthquakes through a re-currence relation (e.g. the Gutenberg-Richter law).Attenuation relations are then employed to calculatethe ground motion at the site due to each of theseearthquakes. Finally, the recurrence rate at whichdifferent levels of ground motion may occur at thesite is calculated. Different ground motion measures(called intensity measures IM) can be used such asPGA, PGV, spectral acceleration Sa(T)etc. With thisapproach the controlling earthquake scenarios needto be obtained by disaggregation of the site hazard at

a specified probability. This can be done using oneof existing techniques (Chapman, 1995; McGuire,1995; Harmsen et al., 1999; Bazzurro and Cornell,1999).

Both DSHA and PSHA yield dominant scenarioscontributing to the hazard for the different parts ofthe response spectrum (i.e. for different periods), de-fined by a magnitude M, distance R and number oflogarithmic standard deviations above or belowthe logarithmic mean from the ground motion pre-diction equation used in the analysis. Once the con-trolling earthquake scenarios have been identified,the final step is to select a number of recorded timehistories accordingly. Generally, only M and R areconsidered, although recently Backer and Cornell(2006) proposed to use also . If PSHA is per-formed, the current state of best practice (McGuire,1995) is based on first disaggregating, with respectto magnitude Mand distanceR, the site probabilisticseismic hazard, evaluated using spectral accelerationSa(T1) as IM, at a period close to the natural periodof the structure, at a specified probability. Typically10% probability of exceedence in 50 years (return

period of 475 years) is adopted if ultimate limit stateis considered. Formally, this disaggregation repre-sents the conditional probability mass function(PMF) ofM, R, given the event that Sa(T1) exceedsthe value associated to the considered return period

(Bazzurro and Cornell, 1999). Records are then cho-sen to match within tolerable limits the mean or mo-dal value of the MandR PMF.

In the present work, PSHA has been performedfor the site of Scalea (Cosenza), adopting seismoge-netic zones and earthquakes recurrence relations de-fined by INGV (2004) and attenuation law proposed

by Ambraseys et al. (1996) with the corrections pro-

posed by INGV (2004). The intensity measure IMused is the spectral acceleration Sa(T1) at the naturalperiod of the structure. Disaggregation of the hazardis depicted in Figure 2. According to McGuire(1995) modal value of the PMF has been used to de-fine the controlling event ( 4.6=M , km18=R ).Clearly, a search carried out in terms of an exactmatch with the design scenario cannot be performed.Therefore, interval are defined for each parameter(MorR). Recorded time histories have been chosenfrom European Strong Motion Database accordingto the earthquake scenario defined by the controllingevent, considering a difference of 1 point of magni-tude equal to a difference of 40 km in epicentral dis-tance. Seven acceleration time histories have beenselected from the Database, theirMandR values be-longing to the intervals: 6.60.6 =M and

km3014 R = . Adopted time histories have beenrecorded in free field at sites with very stiff or rocksoils. This set of acceleration time histories will beindicated in the following as R-MR (Recorded-Magnitude Distance).

Another approach to select hazard consistent time

histories has been proposed by Trombetti et al.(2005). The basis of this method is to use naturaltime histories with values of peek ground accelera-tion PGA and peek ground velocity PGV compatiblewith those corresponding to a given return period asassigned by the Code, obtained performing a PSHAof the site considered. Trombetti et al. (2005) pro-

posed different sets, with regard to different limitstates and different seismicity levels. Also in thiscase an exact match between records PGA-PGVvalues and reference ones cannot be obtained andsome degree of approximation must be accepted. In

particular, in that study higher importance to the

Figure 2. M-R disaggregation of probabilistic seismic hazard ofSa(T1) with a return period of 475 years.


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match of PGA than of PGV is given. All the abovementioned sets are available at RELUIS internet website. The set of records proposed by Trombetti et al.(2005) for ultimate limit state, in high seismicityzones contains 8 time histories obtained from PEERstrong motion database, and has been adopted in the

present work. All the records derive from events oc-curred in USA or Canada. This set will be indicated

in the following as R-PGAPGV.2.2 Artificial time histories

Many methods have been proposed for simulatingthe ground motion. A first category of models simu-late accelerograms by filtering and windowing aGaussian noise, or by using autoregressive movingaverage models. Another possible approach providesaccelerograms whose response spectra match a tar-get response spectrum. In addition a third categoryof models has been developed: stochastic methods

that combine seismological models of the spectralamplitude with results of random vibration theory.High-frequency ground motion is modeled as band-limited Gaussian noise in which energy is distributedover a specified duration.

In the present work, two different techniques areadopted to generate artificial accelerograms. Thefirst one generates acceleration time histories com-

patible with reference response spectrum, the secondone according to a given magnitude-distance sce-nario.

2.2.1 Spectrum-compatible artificial time historiesArtificial spectrum-compatible accelerogramshave been generated using SIMQKE software (Gas-

parini and Vanmarcke, 1976). This program gener-ates a power spectral density function from the re-sponse spectrum, and then derives sinusoidal signalshaving random phase angles and amplitudes. The si-nusoidal signals are then superposed. An iterative

procedure can be used to improve the match of theaccelerogram response spectrum with the target re-sponse spectrum, by calculating the ratio between

the target and actual response values at selected fre-quencies; power spectral density function is then ad-justed by the square of this ratio, and a new groundmotion is generated. The main advantage of this ap-

proach is that acceleration time-series almost completely compatible with the elastic design spectrumcan be generated.

However, it is now widely accepted that the useof such artificial records is problematic, especiallyfor nonlinear analyses. The basic problem with spec-trum-compatible artificial records is that they gener-ally have an excessive number of cycles of strongmotion and consequently they possess unreasonablyhigh energy content. This issue can be partially re-duced adopting amplitude envelope functions.

In addition these artificial records are obtainedmatching the acceleration time series to the entire

elastic design spectrum. The latter will generally bea uniform hazard spectrum, enveloping the groundmotions from several seismic sources. Therefore isnot realistic that a single accelerogram matches theentire spectrum.

In numerical simulations presented in the follow-ing, 20 time histories compatible with OPCM re-sponse spectrum have been generated adopting a

trapezoidal amplitude envelope function and settingthe duration of the stationary part of the time histo-ries equal to 10s. This set will be indicated as A-SQ.

2.2.2 Nonstationary artificial time histories(Sabetta and Pugliese, 1996)

Sabetta and Pugliese model (Sabetta and Pugli-ese, 1996) allows for the generation of artificial ac-celerograms starting from magnitude Mof the eventconsidered, epicentral distanceR and soil type of thesite considered. This model adopts four strong mo-tion indicators to generate artificial time histories.

These indicators are strong-motion duration, Ariasintensity, central frequency (Fc) and frequency

bandwidth (Fb) of the signal. Their values are ob-tained through the use of ground motion predictionequations (attenuation laws).

The simulation of a nonstationary strong groundmotion is achieved through an empirical model,where time dependence and frequency content of thesignal are represented through the signal spectro-gram. The spectrogramPS(t, f) is a frequency-timedecomposition of the expected energy of a process, a

natural extension of the power spectrum to the nonstationary case. Sabetta and Pugliese assumed thatthe spectrogram can be factorized by a series of

power spectral densities, calculated at differenttimes, and fitted with a lognormal function. The lat-ter is defined by physical parameters such as the in-stantaneous average powerPa(t), the central fre-quency Fc(t), and the frequency bandwidth Fb(t).With the above defined parameters a lognormalfunction approximatingPS(t,f) can be derived:

[ ]2

2

2

)(lnln

2

)(),(

tf

aapprox ef

tPftPS

= (1)

where )( t and are derived from Fc(t) and Fb(t).Moreover,Fc(t) andFb(t) are approximated by func-tions derived from regression analyses, and dependon magnitude M and soil type. Pa(t) describes theamplitude variation of ground motion in time. Its in-tegral in time domain corresponds to the Arias inten-sity. Sabetta and Pugliese adopted a lognormalfunction with parameters that can be expressed as afunctions of Arias intensity and strong motion dura-

tion, to approximate Pa(t). Predictions of these pa-rameters values are obtained from attenuation laws,depending by magnitude M, distanceR and soil type.Therefore, once magnitude, distance and soil typeare defined, an approximate ),( ftPSapprox function


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tain fragility curves are available in literature (Vam-vatsikos and Cornell, 2002; Pinto et al., 2004;Backer and Cornell, 2006; Buratti et al., 2007); oneof the most widely used approaches is to performmulti-record IDAs. Two different methods can beused. They are described in the following.

4.1 Fragility by probabilistic quantification of DMIn the first case a probabilistic quantification of

DM at different levels of IM is calculated. It iscommon to use (Stoica et al., 2007) a two-parameterlognormal function to describe the probability distri-

bution of the response variable of interest, e.g.,maximum interstorey drifts over the height max (DM) for a given ground motion intensity levelSa(T1) (IM). The two-parameter lognormal distribu-tion is convenient because its parameters can be eas-ily fitted using the method of moments or maximumlikelihood estimates. Figure 4 shows an example of

this method: coloured lines represent results of in-cremental dynamic analyses, and black thin solidlines are lognormal distributions of maximum in-terstorey drift max fitted at (three) different levels ofSa(T1).

Once probability distributions of max at differentlevels of Sa(T1) are known, fragility value for

( ) )( 11 TSTS aa = can be easily evaluated as:

( )( ) ( )( )[ ]CTSPTSP amaxaf >= 11 . (2)where C denotes structural capacity (e.g.

03.0 =max ). If a lognormal distribution is used,Equation 2 becomes:

( )( ) ( )

=

ln1

CTSP af (3)

where is standard normal cumulative distributionfunction, with and being mean value and stan-dard deviation of the logarithm of max for

)()( 11 TSTS aa = .Blue line (first method) in Figure 5 shows fragil-

ity curve obtained by this method: as reported in this

example, for high values ofSa(T1), a non monotonic

variation of fragility values could be obtained. Infact, this first method may present some drawbacks.

First of all, according to Stoica et al. (2007)when response parameters are distributed far fromthe origin (e.g., for relatively large ground motionintensity levels), the spread of a two-parameter log-normal distribution would be distorted because ofthe lower bound constraint to the origin. This distor-tion may have a significant influence in both in-terstorey drift values and computed probabilities. InFigure 4, the distorted shape of pdf for the highestconsidered value ofSa(T1) is evident.

Secondly, if the response parameter of interest isthe maximum interstorey drift, its values cannot al-ways be obtained for large values of Sa(T1) due to

convergence numerical problems. Using availabledrift values only (converged analyses) to character-ize the distribution of max would distort probabilitycomputations.

Furthermore, in order to obtain response parame-ters for high values of the Sa(T1), accelerograms mayneed to be highly scaled, and so results could be notvery realistic (Shome et al., 1998)

4.2 Fragility by probabilistic quantification offailure capacity

In the second method (Backer and Cornell, 2006;Buratti et al., 2007), failure capacity is found scalingthe considered ground motion up to the attainmentof structural failure. According this method, eachground motion has a single Sa,C(T1) (IM) value asso-ciated with its collapse. By repeating this process fora set of ground motions, a set ofSa,C(T1) values as-sociated with the onset of collapse can be obtained.Probability of collapse at a given Sa(T1) = )( 1TSa level can then be estimated as the fraction of recordsfor which collapse occurs at a level lower than

)( 1TSa . Distribution of Sa,C(T1) levels causing thestructure to collapse is often fitted by a lognormaldistribution. Figure 6 shows an example of thismethod: coloured crosses represent Sa,C(T1) values

bringing structure to the considered limit state asso-

Figure 4. Probabilistic quantifications of max at different lev-els ofSa(T1), obtained through lognormal distributions (set R-EC8, see Section 5).

0 1 2 3 4 50

0.2

0.4

0.6

0.8

1

Sa(T

1) [g]

Pf

First method

Second method

Figure 5. Fragility curves (set R-EC8, see Section 5) calcu-lated: 1) by probabilistic quantification of max at differentlevels ofSa(T1); 2) by probabilistic quantification ofSa(T1) val-ues causing structural failure.


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ciated to different ground motions and thin blackline indicates the fitted lognormal distribution.Figure 7 shows the corresponding empirical cumula-tive distribution and the fitted cdf.

This second method is computationally more ex-pensive, because Sa,C(T1) values must be found foreach curve with the required precision To this pur-

pose a bisection algorithm can be adopted. Never-theless, drawbacks of the first method are avoided.For this reason, the second method is used in the fol-lowing.

5 THE CASE STUDYIn the present study, fragility curves obtained us-

ing time histories selected according to different cri-teria have been compared. The case study is a 3-floor RC frame structure, described below.

5.1 The RC frame structureGeometry of the RC frame structure, cross sec-

tions dimension and reinforcements are reported inFigure 8 and Table 1. Dead (qD =33kN/m) and live(qL= 4.3kN/m) loads are prescribed on beams. Liveload of first floor is 1.5 times greater than of uppertwo floors.

5.2 Acceleration time historiesSets of accelerograms adopted to perform IDAs

are summarized in Table 2. Figure 9 depicts accel-eration response spectra of the adopted accelero-grams, in order to allow a better comparison of spec-tral shapes. All spectra have been scaled at acommon value in correspondence of the first natural

period of the structure (i.e. T1 = 0.6s). Identification

codes of adopted accelerograms, are those adopted by European Strong Motion Database for R-OPCM(US), R-OPCM(S), R-EC8, and PEER data-

base for R-PGAPGV, and are listed in Figure 9.By comparing acceleration response spectra cor-

responding to various sets of accelerograms, the fol-lowing remarks can be done: 1) except for the caseof R-MR set, mean response spectra are quite simi-lar, with maximum values around 0.8-1.0gfor peri-ods in the interval 0.1-0.4 s, and similar decayinglaws for higher periods; 2) mean response spectrum

corresponding to R-MR set is quite different, withmaximum value up to 1.5 g, and almost constantvalues for periods greater than 1 second (see Figure9d); 3) as for artificial sets, dispersion of responsespectra around mean value is very small as far as A-SQ set is considered; 4) on the contrary, variabilityaround mean value of acceleration time histories ob-tained from Sabetta and Pugliese method is very

Figure 6. Probabilistic quantification of Sa(T1) levels causingstructural failure Sa,C(T1), by lognormal distribution (set R-EC8, see Section 5).

0 1 2 3 4 50

0.2

0.4

0.6

0.8

1

Sa(T

1) [g]

Pf

Empirical CDF

Fitted Lognormal CDF

Figure 7. Fragility curve obtained by probabilistic quantifica-tion of Sa,C(T1) levels causing structural failure: empirical cu-mulative distribution vs. fitted lognormal distribution (set R-EC8, see Section 5).

Figure 8. Case study RC frame structure.

Table 1. Cross sections of RC frame structure.Section Width____

cm

Height____cm

As As Stirrups

A 30 30 220 220 10@20B 30 30 320 320 10@20C, D, E, F 40 40 218 218 10@20G, M 30 60 418 218 10@20H 30 60 218+

120218+420

10@20

I 30 60 218+220

218 10@20

L 30 50 218 318 10@20 N 30 50 218+

320218+420

10@20

O 30 50 518 218 10@20P 30 50 218+

320218 10@20


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similar with respect to those of sets containing realaccelerograms (compare Figure 9g-h with Figure 9a-e).

5.3 Incremental dynamic analyses5.3.1 Numerical model

Nonlinear dynamic analyses required by IDA

have been performed using the software Opensees

(Mazzoni et al., 2005). Beams and columns aremodelled as finite elements with distributed inelas-ticity, based on flexibility formulation. Fiber discre-tization is adopted for beam and column sections.

Nonlinear constitutive laws are defined for concreteand steel. Concrete section is subdivided in uncon-fined and confined zones and Saenzs (Ceb-Fip1993) and Manders (Mander et al., 1988) models

are adopted, respectively. Mechanical behaviour of

0 1 2 3 4

0

0.5

1

1.5

2

T[s]

Sa

(T1

)[g]

ROPCM(US)

000055XA

000055YA

000182XA

000182YA

000290XA

000290YA

001231YA

Mean

0 1 2 3 4

0

0.5

1

1.5

2

T[s]

Sa

(T

1

)

[g]

APGAPGV

0141270

G06090

G06230

GIL067

HEC000

LA0000

S2330

SJTE225

Mean

0 1 2 3 40

0.5

1

1.5

2

T[s]

Sa

(T1

)[g]

ROPCM(S)

000182XA

000201YA

000290XA

001255YA

001707YA

005819YA

005820YA

Mean

0 1 2 3 4 5

0

0.5

1

1.5

2

T[s]

Sa

(T

1

)

[g]

ASQ

0 1 2 3 40

0.5

1

1.5

2

T[s]

Sa

(T1

)[g]

REC8

000055YA

000182YA

000287YA

000290XA

000290YA

000594YA

006500XA

Mean

0 1 2 3 4

0

0.5

1

1.5

2

T[s]

Sa

(T1

)[g]

ASP(50)

0 1 2 3 40

0.5

1

1.5

2

T[s]

Sa

(T1

)[g]

RMR

000126YA

000134XA

000171XA

000229YA

000665YA

001313YA

006115XA

Mean

0 1 2 3 4

0

0.5

1

1.5

2

T[s]

Sa

(T

1

)

[g]

ASP(8)

Figure 9 Acceleration response spectra of time histories adopted in the present study: a) R-OPCM(US); b) R-OPCM(S); c) R-EC8; d)R-MR; e) R-PGAPGV;f) A-SQ;g) A-SP(50); h)A-SP(8).

(a) (e)

(b) (f)

(c) (g)

(d) (h)


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reinforcing steel is described with a bilinear model.Geometric second order effects are taken into ac-count by P-delta method. Equations of motion aresolved by Newmark algorithm. Convergence checkis defined by the energy criterion, which usually al-lows for a better accuracy than displacement or forcecriterion. Opensees software offers more than onesolution algorithm for non linear equations involvedin the problem. Then, in order to increase chances ofconvergence, if one method fails, other algorithmscan be adopted in sequence starting from the last so-

lution point. If no convergence is still achieved, in-tegration time step is reduced. If still no convergenceis attained, the analysis is discarded and a newanalysis is performed by slightly varying the currentvalue ofSa(T1).

5.3.2 Results from different sets of accelerogramsResults of incremental dynamic analyses are de-

picted in Figure 10. Solid coloured thin lines repre-sent IDAs performed using different time historiesof each set. Dots represent results of the dynamic

analyses. Structural capacity is fixed at max = 0.03and thick line represents mean IDA curve. The latterhas been plotted only for Sa(T1) values where allanalyses converged. All the curves are quite regular,i.e. max values are monotonically increasing withSa(T1); this behaviour can be explained by the factthat the damage measure used is the maximum in-terstorey drift between all floors, therefore is intrin-sically more stable than other DM (e.g. floor dis-

placements) could be. It is worth noting that spreadof results obtained employing A-SQ set is muchsmaller than in other cases. Moreover results ob-

tained adopting R-MR and A-SP(8) sets have lowervalues of dispersion with respect to those obtained

by R-OPCM(US), R-OPCM(S) and R-EC8 sets.Comparison of mean IDA curves obtained from dif-ferent sets of time histories is depicted in Figure 11.

All mean curves at low levels ofSa(T1) (Sa(T1)< 1g)are in good agreement, but in this range nonlinearstructural behaviour is limited. At higher values ofSa(T1), mean curves are considerably speeded:curves obtained from R-MR, A-SQ and A-SP(50)sets produce the lowest mean interstorey drift;whereas OPCM(US) and R-EC8 sets produce thehighest mean interstorey drift values. It is worth not-

ing that both R-OPCM(US) and R-EC8 sets containthe record 000290YA which presents a an anoma-lous (high) response spectrum forT> 2s. This re-cord is then particularly demanding for the structure,undergoing very high seismic loading even when its

period elongates due to nonlinear material behav-iour. Of course since the number of time histories ofR-OPCM(US) and R-EC8 sets is low (7 time histo-ries), even a single anomalous accelerogram canhighly influence results.

5.4 Fragility curvesFragility curves (Figure 12) have been obtained

by a probabilistic characterization (see Section 4.2)of the levels of Sa(T1) causing structural failureSa,C(T1). Values of Sa,C(T1) obtained from differentsets are depicted in Figure 13. Crosses representSa,C(T1) values obtained by different accelerograms.Fitted lognormal distributions are represented bythin black lines. Estimates of parameters of log-normal distributions (mean value and standard de-viation of the corresponding normal distribution)used to characterize the distributions of Sa,C(T1) are

reported in Table 3. A-EC8 produces the highestfailure probabilities, i.e. is the most demanding setfor the structure, this is clear even from IDA curves(see Figure 10). In addition this set contains 2 timehistories with high spectral values for T > 2 s. A-OPCM(US) and R-PGAPGV produce slightly lowerfailure probabilities.

Estimates of lognormal distribution parametersobtained from these three sets are very similar, onlya small difference in mean value can be observed. R-OPCM(S) and A-SP(50) give even lower failure

probabilities: these curves are defined by higher val-ues of and lower dispersions than in the previouscases. The set of recorded accelerograms giving thelower failure probabilities is R-MR: in this case thehighest estimate of is obtained. This is the moresite specific set of recorded time histories. Thereforeis less demanding for the structure than the sets de-fined with spectrum compatibility criterion. In factthe spectra used for these latter sets are valid for all

possible sites in high seismicity zones (referencePGA = 0.35 g), thus they must be representative ofground motions that are not possible at the consid-ered site.

Finally, A-SQ set produces a completely differentfragility curve, in fact this set gives an estimate ofcomparable with those of other sets, but a com-

Table 2. Adopted sets of acceleration time histories.Set name Accelerograms NRealR-OPCM(US) compatible with OPCM spectrum 7R-OPCM(S) compatible with OPCM spectrum af-

ter scaling7

R-EC8 compatible with EC8 spectrum 7R-MR obtained by PSHA disaggregation

(M, R).7

R-PGAPGV compatible with PGA-PGV PSHAhazard scenario.

8

ArtificialA-SQ by SIMQKE and OPCM response

spectrum.20

A-SP(50) by Sabetta and Pugliese method (M,R).

50

A-SP(8)i by Sabetta and Pugliese method (M,R), reduced set obtained randomlychoosing sets of 8 accelerograms formA-SP(50) set.

8

A-SP(8) by Sabetta and Pugliese method (M,R), reduced set obtained adopting aUniform Design.

8


10/12

pletely different (lower) estimate of its variability.This set is not able to give a good representation ofvariability of seismic events.

All the sets composed by recorded time historiesgive Sa,C(T1) values with an high scatter. For thisreason, recorded time histories are usually consid-ered able to give an adequate representation of thevariability of possible earthquakes at the site consid-

ered. It is worth noting that if recorded accelero-

grams are adopted, the estimate of the ground mo-tion variability is obtained by the implicitassumption that past events (included in strong mo-tion databases) can give an adequate prediction of

possible future events. Of course with this approachthe completeness of databases is a crucial point. Fur-thermore record selection procedure can be notstraightforward and should be performed by an ex-

pert operator.

0 0.03 0.05 0.1 0.150

1

2

3

4

Sa

(T

1)

[g]

max interstorey drift, max

ROPCM(US)

0 0.03 0.05 0.1 0.150

1

2

3

4

Sa

(T

1)

[g]


RPGAPGV

0 0.03 0.05 0.1 0.150

1

2

3

4

Sa

(T1

)[g]


ROPCM(S)

0 0.03 0.05 0.1 0.150

1

2

3

4

Sa

(T1

)[g]


ASQ

0 0.03 0.05 0.1 0.150

1

2

3

4

Sa

(T1

)[g]


R

EC8

0 0.03 0.05 0.1 0.150

1

2

3

4

Sa

(T1

)[g]


A

SP(50)

0 0.03 0.05 0.1 0.150

1

2

3

4

Sa

(T1

)[g]


RMR

0 0.03 0.05 0.1 0.150

1

2

3

4

Sa

(T1

)[g]


ASP(8)

Figure 10. Results of incremental dynamic analyses performed with different sets of time histories: a) R-OPCM(US); b) R-OPCM(S);c) R-EC8; d) R-MR; e) R-PGAPGV;f) A-SQ;g) A-SP(50); h)A-SP(8).

(a) (e)

(b) (f)

(c) (g)

(d) (h)


11/12

The set A-SP(50), containing artificial time histo-ries generated with Sabetta and Pugliese method, iscapable of giving a good representation of variabilityof ground motions. This happens mainly becauseuncertainty (represented by epsilon) of ground mo-

tions predictions ( i.e. central frequency, frequencybandwidth, Arias intensity and strong motion dura-tion) by attenuation laws (see Section 2.2.2), has

been explicitly included in the procedure to generatetime histories. Of course attenuation laws parametersand uncertainties are estimated using available datafrom recorded time histories, but in this case an in-terpretative model is introduced, making the proce-dure more consistent.

Furthermore Mand R values used as input in at-

tenuation laws approximating physical characteris-tics of strong motion, have been chosen in agree-ment with those of acceleration time histories of theR-MR set ( , R ).

Considering 50 time histories gives a good de-scription of uncertainty on expected earthquakes butis computationally too expensive for practical appli-cations. Therefore criteria to define reduced sets of

artificial accelerograms must be defined. To thispurpose sets containing 8 time histories generated bySabetta and Pugliese method have been consideredin order to check if even with a limited number ofacceleration time histories, Sabetta and Pugliesemethod could produce results representative of thevariability of seismic action.

Fragility curves obtained by A-SP(50), A-SP(8)and three different A-SP(8)i sets (A-SP(8)1, A-SP(8)2, and A-SP(8)3) are compared in Figure 14. Itis evident from fragility curves that adopting 8 ac-celerograms randomly generated by Sabetta and

Pugliese method cannot give a stable representationof the variability of ground motion at the consideredsite. On the other hand if 8 acceleration time histo-ries are generated adopting, as here proposed, a uni-form design (see Section 2.2.2) a fragility curve, A-SP(8) in good agreement with the reference one (A-SP(50)) is obtained.

6 CONCLUSIONSFragility analysis of a RC frame structure, adopt-

ing different sets of acceleration time histories have been performed. Both artificial and real accelero-

0 0.03 0.05 0.10

1

2

3

4


Sa

(T

1)

[g]

ROPCM(US)

ROPCM(S)

REC8

RMR

RPGAPGV

ASQ

ASP(50)

A

SP(8)

Figure 11. Mean IDA curves obtained using different sets ofaccelerograms.

Table 3. Estimates of lognormal distributions parameters usedto characterize distributions ofSa,C(T1).

Set [ln(g)] [ln(g)]R-OPCM(US) 0.49412 0.44418R-OPCM(S) 0.63983 0.35546R-EC8 0.42437 0.46107R-MR 0.74613 0.34345R-PGAPGV 0.50384 0.44125A-SQ 0.59911 0.08100

A-SP(50) 0.62171 0.32947A-SP(8) 0.67769 0.30246

0 1 2 3 4 50

0.2

0.4

0.6

0.8

1

Sa(T

1) [g]

Pf

ROPCM(US)

ROPCM(S)

REC8

RMR

RPGAPGV

ASQ

ASP(50)

ASP(8)

Figure 12. Fragility curves obtained using all the different sets

of time histories.0 2 4 6 8

0

0.5

11.5

2

2.5

3

3.5

4

ROPCM(US)

ROPCM(S)

REC8

RMR

RPGAPGV

ASQ

ASP(50)

ASP(8)

Sa,C

(T1

)[g]

Figure 13. Sa(T1) levels that causing structural failure Sa,C(T1),obtained from different sets of accelerograms.

0 1 2 3 4 50

0.2

0.4

0.6

0.8

1

Sa(T

1) [g]

Pf

ASP(50)

ASP(8)1

ASP(8)2

ASP(8)3

A

SP(8)

Figure 14. Fragility curves obtained from different sets gener-ated by Sabetta and Pugliese method.


12/12

grams have been investigated. The objective was toverify if artificial accelerograms may represent notonly the mean structural response, but also its vari-ability if compared with sets of recorded accelero-grams.

As for recorded accelerograms, they are usuallypreferred for nonlinear analysis but, especially if se-lected according to a spectrum compatibility crite-

rion, it is difficult to obtain sets representative of theuncertainty on possible ground motions. Accelera-tion time histories chosen with reference to site spe-cific hazard scenario can give better results. Withthis approach the completeness of the strong motiondatabase adopted is a crucial point and record selec-tion should be performed by an expert operator.

Artificial accelerograms, generated in order tomatch a response spectrum, are not a good alterna-tive, due to many issues they may present: firstlythey generally have an excessive number of cyclesof strong motion (unreasonable high energy content)and secondly they have an high frequency content

because are generated matching the entire spectrum.Results obtained in the present work, seem to con-firm this behaviour.

Artificial accelerograms generated according tothe method proposed by Sabetta and Pugliese (1996)are shown to posses the required variability to be agood alternative to recorded ones, especially for re-liability analysis, because they can be generated ex-

plicitly counting for uncertainty on possible groundmotions. Furthermore if generated with the proce-

dure adopted in this work, a good estimate of disper-sion of structural response may be obtained evenwith a limited number of accelerograms.

Such preliminary conclusions still requires furtherinvestigation: more complex structures shall be in-vestigated.

7 ACKNOWLEDGEMENTSFinancial support of (Italian) Department of Civil

Protection (Reluis 2005 Grant Task 7: Innovative

techniques for seismic protection) is gratefully ac-knowledged.

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buratti-savoia_recorded and simulated gm for fragility analysis of rc structures

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