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Bulletin of Earthquake Engineering 1: 371–395, 2003.© 2004 Kluwer Academic Publishers. Printed in the Netherlands.

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Seismic Vulnerability Assessment of Gravity LoadDesigned R/C Frames

ANGELO MASIDepartment of Structures, Geotechnics and Geology applied to Engineering, Faculty ofEngineering, University of Basilicata, Potenza, Italy(Tel:+39 0971 205061; Fax +39 0971 205070; E-mail: [email protected])

Received 6 april 2003; accepted 10 October 2003

Abstract. The seismic vulnerability of some frame structures, typical of existing Reinforced Con-crete buildings designed only to vertical loads, has been evaluated. They are representative of buildingtypes widely present in the Italian building stock of the last 30 years. A simulated design of thestructures has been made with reference to the codes in force, the available handbooks and thecurrent practice at the time of construction. The seismic response is calculated through non lineardynamic analyses with artificial and natural accelerograms. Three main types have been examined:bare frames, regularly infilled frames and pilotis frames. The results show a high vulnerability for thepilotis buildings: they can be assigned to the class B of the European Macroseismic Scale of 1998(EMS98). On the contrary, a low vulnerability (class D of EMS98) can be attributed to the regularlyinfilled buildings: in this case collapse can be considered unlikely also with strong earthquakes.An intermediate seismic behavior is shown by buildings without infills, whose vulnerability can beplaced between the classes B and C of EMS98.

Key words: assessment, existing buildings, frames, masonry infills, reinforced concrete, seismicvulnerability, simulated design

1. Introduction

Reinforced Concrete (R/C) buildings make up an increasing proportion of thebuilding stock of many countries all over the world. In Italy and in other earthquake-prone Mediterranean countries they currently represent about 50% of the total.Many of them were built before the advent of seismic codes or with the utilizationof old and inadequate antiseismic design criteria. During past earthquakes (South-ern Italy 1980, USA 1994, Japan 1995, Turkey 1999, Greece 1999, Taiwan 2001)R/C buildings often displayed unsatisfactory seismic behaviour, particularly whentheir design included only vertical loads and ductile detailing was not explicitlyprovided. Thus, the evaluation of seismic vulnerability of R/C building structureshas a key role in the determination and reduction of earthquake impact.

Although the most dangerous consequences of earthquakes in the near future arelikely to come from existing buildings, until now the attention of the community inits various components (researchers, professionals, policy makers, . . . ) has largely

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focused on the seismic design of new buildings (Fardis, 1998). There are a numberof socio-economic reasons for this, including the high costs frequently requestedby the retrofit of R/C buildings and the lack of community concern with safety ingeneral, not only in the seismic field, as experience in other fields corroborates (seefor example safety on job sites).

Along with socio-economic factors, there are also major technical problems.With the exception of some guidelines in Japan (JBDPA, 1977) and USA (FEMA,1992), there is little guidance in the codes for the determination of the seismicresistance of R/C existing buildings. In Europe, the codes are just beginning totackle the problem (see for instance Eurocode 8 - part 3 (CEN, 2002a)).

There is no doubt that the assessment of an existing R/C building is a much moredifficult task than the design of a new one, because it requires work on structures ofwhich only a limited knowledge can be obtained. There are difficulties in determ-ining possible deterioration conditions as well as in obtaining sufficiently accurateknowledge of some structural data (e.g. amount and location of reinforcement)or completeness (e.g. materials strength), as appropriate technical documentationis rarely available. The specificity of the problem calls for the setting up of adhoc methods to assess the seismic vulnerability of R/C buildings in a sufficientlyreliable, as well as inexpensive way.

A crucial aspect of knowledge of the structural characteristics of a building isthe period of its construction. When technical documentation is either not availableor insufficient, most valuable data can be obtained through reference to the codes,the design methods and the typical current practice at the time of construction.Using all the information obtainable from the sources above, a group of structuralcharacteristics typical of the buildings of a certain period and of a certain regioncan be determined. Specifically, through an examination of the codes in force, spe-cifications on the prescribed values of loads and material strengths, the minimumvalues of the dimensions of structural elements and of reinforcement amounts canbe drawn up. More difficulties occur for the evaluation of the values of internalforces actually used in the safety verifications, of the location of reinforcementand of the detailing solutions. For this reason, reference has to be made to thehandbooks commonly adopted in the period and to the technical documentationof real buildings found in the archives of public administrations, building firmsand professional offices. From the handbooks more accurate indications can beobtained regarding the design methods and the arrangement of reinforcement in thestructural elements. Finally, the technical documentation of real buildings enablesverification of the reliability of the data obtained from codes and handbooks, as itshows the design and construction rules actually adopted in practice.

The present study aims at evaluating the seismic vulnerability of some framedstructural types representative of post-1970 R/C existing buildings designed onlyto vertical loads. To obtain a realistic evaluation of their vulnerability, a great dealof work has been carried out to determine the most important structural char-acteristics of these buildings including a thorough examination of the technical

SEISMIC VULNERABILITY ASSESSMENT 373

documentation of the period. It is worth noting the great importance of this matter,for example in using in the European context the above cited approaches (JB-DPA, 1977; FEMA, 1992) or a now available powerful approach based on thesoftware package HAZUS (FEMA-NIBS, 1999) developed in USA. Performanceevaluations reported in these approaches cannot be directly adopted in other coun-tries, as they are relevant to specific R/C style constructions (Kappos, 2001) andare sometimes based on empirical formulas calibrated on observed behaviour anddamage data from local earthquakes.

2. Procedure

The evaluation of the seismic vulnerability of gravity-load designed R/C buildingshas been carried out on the basis of a purposely set up procedure made up of fivemain steps (Masi, 2000; Masi et al., 2001a):(1) some configurations of R/C buildings, typical of the period under examination,

are selected;(2) the structures are designed taking into account only vertical loads, on the basis

of the codes in force, of the available handbooks and of the current practice ofthe period;

(3) the seismic response is calculated through non linear dynamic analyses withartificial and natural accelerograms;

(4) the seismic resistance is evaluated by means of fragility curves relevant to somestructural and non-structural damage parameters (drift, ductility demands, etc.);

(5) the vulnerability class of each type, according to the European MacroseismicScale 1998 (ESC, 1998), is defined taking into account the increasing damagedegrees computed by applying increasing seismic intensities.

2.1. STRUCTURAL TYPE SELECTION

The review of the technical documentation reveals that moment resisting framesare the most widespread structural type. The majority are medium-rise buildingsparticularly in the 3–5 storey range, with internal beams spanning in one directiononly. In the other direction the horizontal stiffness of the vertical resisting elementsis more or less symmetrically distributed.

Based on these observations a reference structure has been defined. It is a fourstorey plane frame, with two bays of 5.0 m span. Interstorey height is equal to3.0 m. Starting from this reference system, three frame types have been defined onthe basis of the position in the building (exterior and interior frames) and of thebeam stiffness (rigid beams, flexible beams and no beams):(1) RB frame: exterior frame with Rigid Beams (0.30 m × 0.50 m);(2) FB frame: exterior frame with Flexible Beams (0.70 m × 0.22 m);(3) NB frame: interior frame with No Beams.

Typically observed dimensions of the beams have been adopted, whereas, incase of NB frames, frequently present as interior frames in vertical load designed

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Figure 1. Layout of frame types.

buildings, a strip of the tile lintel floor diaphragm connecting the columns is con-sidered. The strip width has been computed on the basis of the torsional and flexuralstiffness of structural elements around the columns and is equal to about 1.0 m.

In the exterior frames, the presence and position of infill masonry walls havealso been considered, thus obtaining the types BF (Bare Frame), IF (Infilled Frame)and PF (Pilotis Frame). In conclusion, seven frame types have been defined (Fig-ure 1).

BF-RB and BF-FB types are representative of exterior frames without infills.While infills are generally present, they sometimes have many and/or very largeopenings or they are badly connected to the structure and thus their contributionto the strength and stiffness of the structure can be neglected. On the contrary,IF and PF types are relevant to buildings where infills are well confined by thesurrounding frames and have good mechanical and construction characteristicswithout large openings: IF type is representative of frames with regularly arrangedmasonry infills, while PF type is representative of frames without masonry infillsat the ground floor (soft storey).


2.2. STRUCTURAL DESIGN OF MODELS

A simulated design has been carried out, where internal force values have beencomputed on the basis of the characteristic values of dead and live loads. Live loadshave been assumed equal to 2.0 kN/m2, as prescribed for residential buildings.Safety verifications have been performed according to the allowable stress method,assuming mechanical properties of materials according to post-1970 standards, i.e.,medium quality concrete (Rck 250) with strength close to the C20/25 strength anddeformed steel (FeB 38K) with grade close to S400 type.

The columns have been designed taking into account only axial load and ad-opting the minimum requirements provided in the Italian code of the period (D.M.LL.PP., 1972) regarding reinforcement. The beams have been designed on the basisof the simplified model of continuous beam resting on simple supports. Wherethe dimensions of structural elements and the reinforcement amounts could notbe inferred by code prescriptions or by internal forces values, reference has beenmade to the most prominent handbooks (Santarella, 1968; Pagano, 1968) and to thecurrent practice of the period. In this context an examination of local characteristicsreveals many deficiencies generally due to a lack of attention to detailing: lowamounts of longitudinal and, mainly, of transverse reinforcement with respect tothe correspondent anti-seismic frames, are commonly present.

Beam reinforcement is constant along the height with percentages equal toabout 0.5% in the Rigid Beams and in the range 0.55–0.9% in the Flexible Beams.Shear reinforcement is formed by 45◦ inclined steel bars resulting from the re-inforcement arranged according to the bending moment diagram, and adding thehoops requested by either shear values or minimum code requirements.

In the types relevant to external frames (RB, FB) the columns always havesquare section with 0.30 m dimension. The same occurs in the type relevant tointerior frames (NB), with the exception of the middle column which has 0.30 ×0.40 m and 0.30 × 0.35 m dimensions, respectively at I and II floor level. Allthe columns have four reinforcement bars with diameter equal to 16 mm, 14 mmand 12 mm at I, II and III-IV floor levels, respectively. Percentage values are inthe 0.50–0.68% range. Transverse reinforcement is made up of 6 mm hoops withconstant spacing equal to 0.15 m.

2.3. NON LINEAR RESPONSE EVALUATION

The seismic response has been evaluated by means of inelastic time-history ana-lyses. Models able to represent the selected structural types in a sufficiently reliableway, both in terms of stiffness and resistance, have been implemented by using theDRAIN-2D+ code (Tsai, 1994), in a purposely upgraded version.

As regards the actions, only a limited share of the live loads has been consideredin the evaluation of the seismic response. According to (CEN, 1993, 1994a), the

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following values of the vertical loads for the static situation (Vd) and for the calcu-lation of the seismic effects (Sd) have been, respectively, assumed:

Vd = Gk + 0.3 · Qk

Sd = Gk + 0.3 · 0.85 · Qk

where Gk and Qk are the characteristic values of the dead and live loads.In addition to the energy dissipation due to hysteresis, viscous damping has

also been considered, by assuming the mass-proportional damping and stiffness-proportional damping constants, α and β, function of the frequencies of vibrationand of the equivalent damping ratios of the 1st and 3rd mode. The values of dampingratios, ξ1 and ξ3, are taken equal to 2%, with the exception of the frames withouteffective infills (BF types) where, to take into account the presence of infills noteffective in sustaining seismic loading but able to dissipate some energy, ξ1 and ξ3

have been assumed equal to 5% (Chopra, 2001).

2.3.1. Modeling of R/C members

The hysteretic modeling of R/C members has been carried out by taking intoaccount that the structures being examined are relevant to buildings with medium-good construction characteristics. Moreover, R/C members are rather slender, havelow amounts of longitudinal reinforcement and are reinforced with deformed bars.In all members the shear strength is always larger than the maximum shear force,computed also on the basis of the maximum yield moments at the ends of themember. Anchorage lengths typically available in the members of the examinedbuildings (Santarella, 1968) are able to prevent bond failure (Masi, 2001a). As aconsequence, the most probable failure mechanism will be a flexural one, becauseshear or bond failures, even if possible, appear unlikely (Cosenza et al., 1999).

Thus, a hysteresis model for flexure-dominated members has been considered.Specifically, for both beams and columns, a Takeda-type model has been used,due to its ability to provide simple and numerically stable as well as sufficientlyrealistic hysteretic rules. The degrading stiffness properties are modelled throughthe parameters α1 and α2 (Figure 2), controlling the amount of degradation andenergy dissipation during cyclic loading. Values for R/C members are normally inthe range 0–0.4 and 0–0.6 for α1 and α2, respectively. In the analyses, consideringthe degrading properties of the members under study, α1 = 0.2 and α2 = 0 havebeen assumed.

To account for the effects of cracking due to non-seismic actions, the initialstiffness of R/C members has been taken equal to 70% of the uncracked grosssection.

For material strength, realistic values have to be considered in the evaluationof seismic resistance, therefore the mean rather than the characteristic values havebeen used in the computation of the member strength capacities. A mean strengthfcm = 28 MPa has been assumed for the concrete, according to the expression


Figure 2. Role of α1 and α2 parameters in the shape of the hysteresis cycle.

fcm = (fck + 8) MPa provided in EC2 (CEN, 1991). The mean strength of steelhas been taken equal to fym = 400 MPa. The yield moment has been computedaccording to EC2 and considering, in the columns, the effect of the axial force dueto vertical loads.

2.3.2. Modeling of masonry infills

In R/C existing buildings, infills are usually made of two layers of hollow brickmasonry with a total thickness equal to about 200 mm and scarce mechanicalcharacteristics. Taking into account the modeling capabilities of the program usedin the analyses (DRAIN-2D+), each masonry panel has been modelled by usingplane elements having an elastoplastic force-deformation relation defined by theultimate resistance, Fy , the yield displacement, �y , and the ultimate displacement,�u.

The total resistance and stiffness capacity of each panel has been defined byconsidering an equivalent diagonal strut, whose area has been determined by mul-tiplying the panel thickness tw by an equivalent width bw. The following expressiondue to Mainstone (1974), relevant to rectangular masonry panels, has been used tocompute bw:

bw

dw

= 0.20 · sin(2θ)

(Ew · tw · h3

w · sin(2θ)

Ec · Ip

)(1)

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where hw = panel height, dw = diagonal length, θ = angle of the diagonal withthe horizontal, Ew = modulus of elasticity of masonry, Ec = modulus of elasticityof concrete and Ip = moment of inertia of columns.

The characteristics of the equivalent strut are the area As = bw · tw, the stiffnessKs = (EwAs /dw) and the ultimate resistance Fus = As ·fw. A typical value has beenassumed for the compressive strength of masonry fw, equal to 1.2 N/mm2 (D.M.LL.PP., 1987; Calvi and Recla, 2000). On the basis of the angle of the diagonalwith the horizontal θ , the horizontal components of the stiffness Ks,h = Ks · cos2 θ

and of the ultimate resistance Fus,h = Fus cos θ can be calculated. Finally, thecharacteristics of the equivalent shear panel are as follows:• Area ⇒ Ap = Lw · tw

• Ultimate Resistance ⇒ Fyp = Fus,h

• Equivalent Shear Modulus of elasticity ⇒ Gp,eq = (Ks,hhw)/Ap

• Yield Displacement ⇒ �y = Fyp/Ks,h

• Yield Drift ⇒ �y/hw

where Lw is the panel length equal to the bay width.As already mentioned, given the capabilities of the code at hand, the degrading

behaviour of masonry infills has been taken into account through a purposely setup model (Masi et al., 2001a) which has simple, numerically stable and sufficientlyrealistic hysteretic rules. Each masonry panel is modelled by means of 4 sub-panelsconnected in parallel with a total resistance equal to that of the panel. Each sub-panel has the same yield displacement �y , while the ultimate resistance is 3/10 ofthe total for three of them and 1/10 for the fourth. The progressive deterioration isobtained assuming a suitable value of the ultimate displacement for each sub-panel:all four sub-panels have different displacement ductilities and the weakest sub-panel has the largest ductility. In Figure 3 the monotonic relation force-deformationof a panel is shown.

2.4. SEISMIC INPUT

Two sets of input motions have been used in carrying out the inelastic time-historyanalyses: artificial accelerograms generated from the elastic response spectrum forsite B of EC8 (CEN, 1994b), and natural accelerograms mainly drawn from the1997 Umbria-Marche (Central Italy) seismic sequence.

Artificial accelerograms have a trapezoidal envelope, with a first part with in-creasing intensity t1 secs long, a second part with constant intensity t2 secs longand, finally, a third part with decreasing intensity t3 secs long, where t1, t2 andt3 are dependent on the considered PGA value (CEN, 1994b; Min.LL.PP., 1997).Seven PGA values, in the range 0.05–0.35 g, have been considered for the artificialseismic input (Table I). In Table I also the average values of the effective durationtd (Trifunac, 1975) and of the Arias Intensity AI (Arias, 1970) are reported foreach seismic intensity. The numerical simulations have been carried out by using


Figure 3. Force-deformation relationship of a masonry panel as a combination of 4sub-panels.

Table I. Characteristics of the artificial accelerograms used in theanalyses

PGA[g]

t1[sec]

t2[sec]

t3[sec]

ttot

[sec]td[sec]

AI[cm/sec]

0.05 2.6 10 2 14.6 11.5 5.7

0.1 2.6 10 2 14.6 11.5 22.7

0.15 3.3 12.5 2.5 18.3 14 60.4

0.2 4 15 3 22 18 141.5

0.25 4.6 17.5 3.5 25.6 21 265.3

0.3 5.3 20 4 29.3 24 413.5

0.35 6 22.5 4.5 33 26.5 664.2

8 artificial accelerograms for each intensity. The values of the response parametersare obtained as averages of the results of the 8 step-by-step analyses.

The sample of natural accelerograms used in the analyses (Masi et al., 2001a)is made up of more than 20 recordings with PGA values in the range 0.04–0.58 g.It is worth noting that, in the range PGA = 0.05-0.35 g, the natural accelerogramshave mean values of AI in the range 5–95 cm/s, far lower than the correspondentones of the artificial accelerograms.

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Figure 4a. Normalised base shear NBS vs PGA/g for artificial accelerograms.

3. Non linear dynamic response analyses

The non linear seismic response of models has been analyzed on the basis of thefollowing parameters:• Normalised Base Shear NBS (base shear divided by the total weight);• Interstorey Drift ID (relative storey displacement divided by the storey height);• Curvature ductility demand.The ductility demands have been evaluated in the columns (DC) and in the beams(DB) by considering the maximum values in the frame (DCmax and DBmax). Theaverage values in each storey have also been computed and the maximum valuesamong the storeys (DCs,max and DBs,max) have been considered. In the diagramsof Figures 4–7 the variation of the maximum values of some response parameterswith the seismic intensity in terms of PGA are shown both for artificial and naturalaccelerograms.

The results obtained with the natural accelerograms, given their large scatter,are represented by means of their regression curves referring to the same intervalPGA = 0.05–0.35 g used for the artificial accelerograms. Low values of the correl-ation coefficient R are sometimes obtained (R values in the range 0.3–0.6), due tothe poor ability of PGA to effectively represent the damage potential of a groundmotion. Better correlations (Masi et al., 2001b) are obtained when the results arereported in terms of Arias Intensity (R values in the range 0.5–0.7).

By examining the diagram relevant to the normalised base shear NBS relevant toartificial accelerograms (Figure 4a), three different groups of curves correspondingto the three main structural types under study (BF, IF and PF), can be clearly seen.BF types show the lowest values of base shear: the maximum values of NBS arein the range 0.105–0.135 g, going from the type without beams (BF-NB) to thetype with rigid beams (BF-RB). IF types show the highest values of base shear: the


Figure 4b. Normalised base shear NBS vs PGA/g for natural accelerograms.

maximum values of NBS are in the range 0.36–0.39 g, being the maximum valuerelevant to the frames with rigid beams (IF-RB). Intermediate values are shown bythe PF types: the maximum values are almost the same for frames with rigid andflexible beams and are about equal to 0.18 g. All curves show an increasing trendand a decreasing gradient with seismic intensity, as the structures approach theirmaximum resistances.

The diagram relevant to the natural accelerograms (Figure 4b) shows similartrends from a qualitative point of view, but the results are lower than those obtainedby applying artificial accelerograms. This difference is mainly a consequence ofthe far lower values of Arias Intensity (up to 5–6 times) of natural accelerogramscompared to those of artificial accelerograms. In fact, the curves obtained by ap-plying natural accelerograms are almost coincident with the initial part (PGA up to0.15–0.20 g) of the curves relevant to the artificial accelerograms.

In the diagrams of the maximum interstorey drifts ID relevant to artificial accel-erograms (Figure 5a), the IF type curves and the BF-NB type curve, represent thelower and the upper bounds respectively. Only for the highest values of PGA thecurves of PF types show values larger than those of BF-NB type. The maximumcomputed values of ID for PF types are equal to about 4% (Figure 5a), valuesfor which structural and non-structural elements should be completely collapsed.Also, ID values relevant to moderate-heavy damage states (0.7%–1.5%) are alreadyshown for PGA > 0.1 g. These results clearly highlight how inadequate the seis-mic behaviour of frames with soft storey is: on one hand they have shown NBSvalues up to 40–50% larger than frames without effective infills, on the other handthey undergo disproportionately large effects with increasing seismic intensity. Theresults relevant to IF types corroborates the strong contribution provided by goodquality and regularly arranged infills in reducing seismic effects: ID shows valuesrelevant to damage states ranging from slight (ID = 0.2%) up to moderate (ID <

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Figure 5a. Interstorey drift ID (%) vs PGA/g for artificial accelerograms.

Figure 5b. Interstorey drift ID (%) vs PGA/g for natural accelerograms.

0.5%), for PGA values equal to 0.15 g and 0.20 g, respectively, up to a maximumvalue equal to about 1.5%.

These considerations are also more or less valid, from a qualitative point ofview, for the results relevant to natural accelerograms (Figure 5b) but the valuesare far lower than the artificial ones. As already stated, the difference can be ex-plained by considering the very different values of AI in the two sets of adoptedaccelerograms. Being represented by means of their regression curves, in this casethe results show a more regular trend. Consequently, the peculiar behaviour shownby the pilotis frames under the artificial input motion does not appear: their curvesare always below the curves relevant to BF-NB type.


Figure 6a. Ductility demand on columns DCs,max vs PGA/g for artificial accelerograms.

Figure 6b. Ductility demand on columns DCs,max vs PGA/g for natural accelerograms.

Figures 6a and 6b show the curves of the ductility demands on columns DCs,max.The lowest values are again relevant to the frames with regularly arranged infills.For these structural types, the curves relevant to natural accelerograms (Figure 6b)are almost coincident, with slightly higher values for the IF-RB type. On the con-trary, large differences can be seen in the case of artificial accelerograms (Fig-ure 6a) with high values of PGA: when PGA = 0.35 g, the maximum values ofDCs,max are equal to about 11 and 3, respectively, for IF-RB and IF-FB. Such adifference can be explained by looking at the different global damage pattern. Inboth types, the highest values of DCs,max occur at the ground floor. However, withincreasing PGA the infills on the first floor suffer damage to a greater extent in

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Figure 7a. Ductility demand on beams DBs,max vs PGA/g for artificial accelerograms.

the IF-FB type, making this floor much more deformable than in the IF-RB type.Due to the lower constraint action of the joints between the ground and first floor,lower moment values are detected in the ground floor columns of the IF-FB type.It should be noted that this behaviour does not occur in the bare frames (BF types):in this case the frame with flexible beams shows significantly higher values ofductility demands than the BF-RB type and, furthermore the highest of all types.Pilotis frames show ductility demands on columns, obtained by applying artificialaccelerograms (Figure 6a), which are almost coincident between RB and FB types,and near to the ones of BF-FB type.

The curves of ductility demands on beams DBs,max (Figures 7a and 7b) showvalues far higher than the curves of the ductility demands on columns, in all types.In this case the upper bound is relevant to the bare frame with rigid beams followedby the bare frame with flexible beams. When artificial accelerograms are applied,high values of DBs,max can be observed in BF types for PGA > 0.2 g (Figure 7a),reaching a maximum value equal to 37 in the BF-RB type. This is mainly due totwo reasons:• according to the common practice, in the gravity load dominated design avery small amount of reinforcing steel is placed (usually only two small-mediumdiameter rebars) on the bottom side of beam ends;• for PGA > 0.2 g, moment values due to seismic loads become larger thannegative moment values caused by gravity loads, thus beams yield deeply at theirends for positive moment.

Low values of DBs,max can be observed in PF types, although the lowest valuesare again relevant to IF types, corroborating the favourable contribution of regularlyarranged infills.


Figure 7b. Ductility demand on beams DBs,max vs PGA/g for natural accelerograms.

4. Definition of damage degrees

The evaluation of global damage has been carried out by involving the followingdamage variables, which refer to structural and non structural damage:• DCmax Ductility demand on Columns (max value);• DCs,max Ductility demand on Columns (max among the story average values);• DBmax Ductility demand on Beams (max value);• DBs,max Ductility demand on Beams (max among the story average values);• ID Maximum Interstorey Drift (%).Furthermore, the ductility demands have been compared to the correspondent ulti-mate values of the ductility capacities, thus obtaining the following ratios:• RDCmax = DCmax / DCu (max Ductility Ratio in the Columns);• RDCs,max = DCs,max / DCu (max Ductility Ratio in the Columns among the storyaverage values);• RDBmax = DBmax / DBu (max Ductility Ratio in the Beams);• RDBs,max = DBs,max / DBu (max Ductility Ratio in the Beams among the storyaverage values).There are several expressions for the evaluation of the ductility capacities of R/Celements available in the literature. They are drawn from analytical formulationssupported either by the analysis of experimental results or by expert judgement.Generally, these expressions (e.g., Park and Paulay, 1975; Park and Ang, 1985)are relevant to R/C structures designed according to antiseismic criteria where,for example, high confinement actions due to transverse reinforcement are avail-able. Only a few cases are relevant to members without seismic design. Of these,expressions drawn from statistical elaborations of different experimental investiga-tions (e.g. Fardis, 1998) or obtained from analytical formulations adopting suitable

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values of the ultimate deformations of materials (e.g. Penelis and Kappos, 1997;Calvi and Priestley 1998) are available.

In the present study the latter approach has been used assuming as ultimatevalues, respectively, εcu = 0.005 for the concrete compression strain and εsu =0.02 for the reinforcement tensile strain. Regarding concrete, reference to poorly orunconfined conditions has been made (Mander et al., 1988; Paulay and Priestley,1992), while with regard to reinforcement, the deterioration in presence of highductility demands suggests that only a limited part of the ultimate tensile strain inthe rebars can actually be exploited (Calvi and Priestley, 1998). By applying thisprocedure, ultimate values of the curvature ductility capacities equal to about 30in the rigid beams and 20 in the flexible beams, are obtained. The ultimate valuesof the curvature ductility capacities in the columns are equal to about 10 at thefirst storey (value significant for the PF types) and increase up to about 25 at thethird and fourth storey (value significant for the BF and IF types). The values ofthe ductility ratios in the beams have been computed taking into account that thebeam characteristics remain constant along the frame height. On the contrary, inthe columns the ultimate ductility is strongly influenced by the axial force and thusthe ductility ratios have to be computed in the storey where this ratio is the largerone.

Many damage indices proposed in the literature can be used to evaluate theglobal damage in a R/C structure. A very comprehensive classification, mainlyaimed at clarifying the different approaches that can be used for defining damageindices, is reported in (Kappos, 1997). Generally speaking, a damage index is aquantity ranging from 0 (no damage) to 1 (collapse), whose computation shouldinvolve more than one damage variable. Given the final objective of this study,global damage has been described in terms of damage degrees Ld as defined inthe European Macroseismic Scale (ESC, 1998), ranging from no damage (Ld = 0)to complete destruction (Ld = 5). Following these definitions, the assignment ofdamage degrees has been carried out on the basis of suitable values of the selecteddamage variables (Table II). The relationship assumed between the damage vari-ables and the global damage degrees is mainly based on indications drawn from theliterature (Park and Ang, 1985; Naeim, 1989; Kunnath et al., 1990; FEMA-NIBS,1999; Ghobarah et al., 1999). Due to the good construction characteristics as-sumed for the structural types under examination, the evaluation of damage degreesis essentially ductility-based. However, reduced values of some capacity-demandductility ratios have been assumed, as the fullest exploitation of the monotonicdeformation capacity of structural members might not occur due to a limited contri-bution of the cumulative energy absorption on damage. As regards the drift limits,the peculiar brittle characteristics of masonry infills have been taken into account.


Table II. Evaluation of damage degrees Ld (EMS 98) on the basis of damage variables

Ld Definition DCmax RDCmax RDBmax DCs,max RDCs,max RDBs,max ID [%]

(EMS98) DBmax DBs,max

0 SD = nullNSD = null

<1 – – – – – <0.1

1 SD = nullNSD = slight

≤1 <1 – – 0.1–0.25

2 SD = slightNSD = moderate

– 0.1–0.4 0.2–0.5 – <0.1 <0.2 0.25–0.5

3 SD = moderateNSD = heavy

– 0.4–0.8 0.5–1 – 0.1–0.4 0.2–0.5 0.5–1.0

4 SD = heavyNSD = very heavy

– >0.8 >1 – 0.4–0.8 0.5–1 1.0–1.5

5 Destruction – – – – >0.8 >1 >1.5

(SD = Structural Damage, NSD = Non Structural Damage)

5. Evaluation of damage degrees

The damage degrees resulting from the application of the artificial accelerogramsare reported in Figure 8 for all structural types. High values are generally shown:for PGA = 0.35 g all types are completely collapsed (Ld = 5), with the exceptionof infilled types where a partial collapse is expected (Ld = 4). IF types show noor low damage also in the infills up to PGA values equal to about 0.2 g. The typesrelevant to buildings without infills (BF types) collapse when PGA ≥ 0.2 g. Theworst behaviour is shown by the pilotis frames, which would collapse for PGA ≥0.15 g. A similar high vulnerability is shown by the frames without beams (BF-NBtype). Also for this type, structural damage can be expected already for the lowestintensity (PGA = 0.05 g) and the damage degrees rapidly increase, leading to apossible collapse for PGA ≥ 0.15 g. Significant differences do not appear betweenrigid beam and flexible beam types, particularly in case of infilled frames.

The mean and maximum values of the damage degrees obtained by applyingnatural accelerograms are reported in Figure 9. As already stated, in this case dam-age variable values, given their large scatter, are represented by means of regressioncurves referred to the same PGA interval used for the artificial accelerograms.For this reason, besides the values of damage degrees obtained from the curves,assumed as mean values (Ld values marked with “med” in Figure 9), an estimationof the maximum predictable values has also been made (Ld values marked with“max” in Figure 9) based on the variability of the results.

The exam of the mean values of damage degrees shows much lower valuesthan those obtained from the artificial accelerograms. In fact, also when PGA =0.35 g, all types are not collapsed (Ld ≤ 3), with the exception of PF-FB and BF-NB types, which are near to partial collapse (Ld = 3–4). The maximum values of

388 ANGELO MASI

Figure 8. Damage degrees with EC8-B artificial accelerograms.

damage degrees are closer to those obtained by applying artificial accelerograms,but generally higher in the range PGA = 0.05–0.10 g and lower in the range PGA= 0.25–0.35 g. This alternate trend is partly due to the large scatter of the resultsobtained with the natural seismic input.

The results in Figure 9 show that the highest damage degrees to be expected inthe infilled frame types are moderate or slight, respectively, for the non structuraland for the structural elements. On the other hand, significant damage is to beexpected in the PF-FB and BF-NB types already for PGA = 0.05 g, up to a totalcollapse when PGA > 0.25 g. Intermediate behaviour can be observed for the othertypes. The absence of significant differences between types with rigid or flexiblebeams is corroborated. The role of infills again appears important even if, due toa general tendency to a reduction of effects, the differences among the types aresmaller than those relevant to the artificial accelerograms.

It should be noted that, whereas a comparison of the results based on the samevalues of PGA shows damage degrees computed by applying natural accelero-grams to be remarkably lower than those relevant to artificial accelerograms, theresults are almost coincident when the comparison is based on the Arias Intensity,AI. In fact, artificial accelerograms have generally much higher values of AI, butif similar values of AI are considered in the comparison (e.g. AI ∼= 60), similarvalues of damage degrees are also obtained. This confirms that an energy basedseismic parameter, like the Arias Intensity, can be used in a more effective waythan a peak ground motion parameter (e.g. PGA) to represent the damage potentialof an accelerogram.


Figure 9. Mean and maximum damage degrees with natural accelerograms.

Table III. PGA values and corrispondent EMS98 intensity degrees

PGA [g] 0.05 0.10 0.15 0.20 0.25 0.30 0.35

I_EMS V VI VII VII–VIII VIII VIII VIII–IX

6. Assessment of seismic vulnerability

The seismic vulnerability of buildings can be assessed through the use of differenttechniques. Direct typological and direct mechanical techniques are among thosewidely used in Italy (Dolce, 1996). These techniques have been used in this studyfor the assignment of the vulnerability class of the building types under consid-eration, in line with the classification of the EMS98. In this way, the DamageProbability Matrices provided by Braga et al. (1982), upgraded in (Dolce et al.,2002), can be used to predict the probability of damage, given a seismic intensity.

Seismic vulnerability has been assigned on the basis of a comparison betweenthe damage degrees computed with the numerical simulations and those reportedin the EMS98. For this comparison to be carried out, a correlation between PGAvalues (used in the numerical simulations) and EMS98 intensities is necessary,even if it is well known that these correlations have a large inherent scatter. To thisend, assuming the EMS98 intensity degrees (I_EMS) to be substantially coincidentwith the intensity degrees of MSK scale, as suggested in the manual of EMS98, thefollowing empirical relationship due to Margottini et al. (1985) can be used:

I_EMS = (1/0.258) LOG10[(PGA/g)(981/2.279)] (2)

In Table III the values of I_EMS related to the PGA values considered are reported.

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Figure 10. Vulnerability classes for framed R/C buildings according to EMS98.

By examining the definitions of the seismic intensity degrees in the EMS98,the expected mean and maximum damage degrees can be assigned to each vulner-ability class, when varying the seismic intensity. In the EMS98 six vulnerabilityclasses are considered, arranged in decreasing order from A to F, according tothe structural type and the level of earthquake resistant design (Figure 10). Foreach case, together with the most likely vulnerability class (mean value) a rangeincluding probable cases and less probable or exceptional cases, is provided. Onlythe classes from A to D are herein considered, taking into account that this isthe vulnerability range where the framed R/C buildings designed without seismiccriteria are certainly placed.

In Table IV the mean and maximum values of damage degrees Ld for each vul-nerability class are reported. They have been obtained on the basis of the definitionsof the EMS98 intensity degrees in the range from I_EMS = V (strong) to I_EMS= IX (destructive).

Table IV. Mean and maximum values of damage levels Ld provided by EMS98 for the vulnerabilityclasses A–D

I_EMS Class A Class B Class C Class D

Ld,med Ld,max Ld,med Ld,max Ld,med Ld,max Ld,med Ld,max

V 0 1 0 1 0 0 0 0

VI 1 2 1 2 0 1 0 0

VII 2–3 4 1–2 3 0–1 2 0 1

VIII 3–4 5 2–3 4 1–2 3 0–1 2

IX 4–5 5 3–4 5 2–3 4 1–2 3

In Tables V and VI the damage levels computed through the numerical analysesfor each of the considered structural types, are reported. The values of damage de-


Table V. Damage degrees Ld of the examined structural types computed by applying artificialaccelerograms

Frames with rigid beams Frames with flexible beams Frames with no beams

BF-RB IF-RB PF-RB BF-FB IF-FB PF-FB BF-NB

I_EMS Ld Ld Ld Ld Ld Ld Ld

V 1–2 0 2 2 0 2 2

VI 2–3 1 3 2–3 1–2 3 3

VII 3 1 3–4 3 2 4 4

VIII 4 2–3 5 5 2–3 5 5

VIII–IX 5 4 5 5 4 5 5

Table VI. Mean and maximum values of damage degrees Ld of the examined structural typescomputed by applying natural accelerograms

Frames with Frames with Frames with

rigid beams flexible beams no beams

BF-RB IF-RB PF-RB BF-FB IF-FB PF-FB BF-NB

I_EMS Ld Ld Ld Ld Ld Ld Ld

med max med max med max med max med max med max med max

V 1–2 2 0 1 2 2–3 2 2–3 0 1–2 2 3 2 2–3

VI 2 2–3 1 1–2 2–3 3 2 3 1–2 1–2 2–3 3 3 3

VII 2 2–3 1–2 1–2 2–3 3 2–3 3 1–2 2 3 3–4 3 4

VIII 2–3 3 1–2 2 3 3–4 2–3 3–4 1–2 2 3 4 3 4–5

VIII–IX 3 3–4 2 2 3 4 3 4 2 2 3–4 5 3–4 5

grees are drawn from Figures 8 and 9 making reference to the relationship betweenPGA values and I_EMS reported in Table III.

By comparing the values in Table IV with those in Tables V and VI, some in-teresting observations can be made. Given that, according to EMS98, C is the mostlikely vulnerability class for the structural types under examination, the damagedegrees computed by applying the artificial accelerograms appear clearly over-estimated.

A more realistic evaluation can be made on the basis of the results computed byapplying natural accelerograms. In this case, vulnerability levels matching thoserelevant to framed buildings without or with low earthquake resistant design (L-ERD in Figure 10) can be estimated. Specifically, in accordance with EMS98, theresults of the numerical analyses show that the possible vulnerability classes forthese buildings are placed in the B–D range. Within this range, class C can beconsidered the most likely vulnerability class. As less probable cases, the regularly

392 ANGELO MASI

infilled framed buildings have the lowest vulnerability (class D), whereas the pilotisframes and the frames whose columns are connected only by a strip of the tile lintelfloor diaphragm have the highest vulnerability (class B). It should be noted that,according to EMS98, class D is considered probable for the framed R/C buildingswith moderate earthquake-resistant design (M-ERD) and not very likely for the L-ERD buildings. The results of the present study thus corroborate the thesis that theframes with good quality regularly arranged masonry infills have a good seismicresistance even if designed to carry only vertical loads.

7. Conclusion

A simple and reliable procedure to evaluate the seismic resistance of some struc-tural types of existing R/C buildings has been set up. It is mainly based on anaccurate recognition of the main and widespread structural characteristics of thepost-1970 building stock designed only to gravity loads. To this purpose, the codesin force, the handbook typically in use and, principally, a wide database of originaldesign drawings relevant to real typical buildings of the period under considera-tion have been examined. Consequently, the examined structural models have beenselected and described in such a way as to be representative of real existing R/Cbuildings.

The results confirm the strong role of the seismic input. As regards the selectionof accelerograms, the choice of artificial ones generated according to some codes(e.g., Eurocode 8, CEN, 1994a) appears inadequate for vulnerability assessmentevaluations. They are too onerous when compared to natural accelerograms, as-suming equal PGA values, because of their damage potential and frequency contentas the variations in the preStage 49 draft of Eurocode 8 (CEN, 2002b) implicitlysuggest. Moreover, their conventional characteristics makes them suitable only fordesign purposes. By comparing the results obtained with the two types of seismicinput but assuming equal Arias Intensity values, almost coincident values of theseismic response are obtained, emphasizing that AI is a more effective seismicparameter than PGA to represent the damage potential of an accelerogram.

When using artificial accelerograms unrealistic levels of vulnerability should beassigned, particularly to the BF and PF types. Results close to the behaviour shownby R/C buildings in past earthquakes (i.e. Southern Italy 1980) are obtained byapplying natural accelerograms. Due to the high scatter of the results, in this caseboth mean and maximum values have been taken into account. Maximum valuesexplain the numerous partial or total collapses observed in past strong earthquakes(I_EMS ≥ VIII). Specifically, by comparing the seismic behaviour of the examinedtypes, a high vulnerability is shown by the pilotis frames and by the bare frameswithout beams. On the contrary, a low vulnerability (class D of EMS98) is shownby the frames with regularly arranged good quality masonry infills. In this casethe failure probability can be considered unlikely also after strong earthquakes. An


intermediate behaviour (vulnerability class B–C of EMS98) is shown by the frameswithout infills or with ineffective infills.

Finally, it is worth noting that the evaluations carried out are relevant to planemodels, even if representative of real buildings. Consequently, it is deemed thatwhere the relevant three-dimensional models are analyzed, the assigned vulner-ability classes can change to some extent. Real buildings, made of plane frameshaving different dynamic characteristics, strengths and available ductility, show acomplicated non linear dynamic behaviour. As a result, further studies aimed ata better evaluation of their vulnerability which take into account the interactionsbetween the different plane types are currently in progress.

Acknowledgements

This work was partly supported by Italian National Seismic Service (SSN) withinthe framework of the research Contract “Seismic Vulnerability of R/C Buildings –Part I” carried out by a research group at University of Basilicata formed by thewriter and by Prof. M. Dolce, Dr F. Telesca and Ph. Dr M. Vona. The valuablecontribution of Prof. M. Dolce and some stimulating communications with Prof.A. J. Kappos of University of Thessaloniki are gratefully acknowledged.

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