-
usb,
via,
Keywords:Seismic fragilityRC precast structures2D and 3D
modellingBeamcolumn connection collapse
nd
cast buildings, to be used in earthquake loss estimation and
seismic risk assessment. An analytical meth-
e likel
interruption.In May 2012, the seismic events in Northern Italy
revealed the
seismic vulnerability of typical Italian precast industrial
buildings.These structures are frequently more exible than
traditional rein-forced concrete frames due to their structural
scheme, which iscomposed of cantilevered columns xed at the base
and a high
e Italian tert of the c
was released only in 2004. As a consequence, a large
numstructures were designed before the enforcement of therecent
seismic regulations, and thus exhibit a number of strdeciencies
(Belleri et al. [1]). The aforementioned decienciesaffect strongly
the response of precast industrial buildings to seis-mic
excitation, as compared to traditional cast-in-place RC
struc-tures, and for this reason this paper investigates whether
theinevitably necessary simplications in the modelling and
method-ologies used to derive fragility curves still allow the
effects of suchdesign deciencies to be captured.
Corresponding author.E-mail address: [email protected]
(C. Casotto).
Engineering Structures 94 (2015) 122136
Contents lists availab
Engineering
lsethe associated direct and indirect consequences in terms of
bothhuman casualties, as well as economic losses due to
business
only in 1987 and a seismic hazard zonation of ththat adequately
considered the hazard in this
pahttp://dx.doi.org/10.1016/j.engstruct.2015.02.0340141-0296/ 2015
Elsevier Ltd. All rights reserved.in Italyrritoryountryber
ofmore
ucturalfering damage for a given severity of ground shaking, and
it can bemathematically formulated by fragility curves, which
describe theprobability of reaching or exceeding a certain damage
limit statefor a given intensity of ground motion. Fragility models
have beendeveloped mostly for residential buildings, and there are
few cap-able of characterising the seismic behaviour of reinforced
concrete(RC) precast structures, notwithstanding the damage
oftenobserved in these structures during moderate earthquakes,
and
structures high exibility, but are often designed only to
transferhorizontal forces by friction or through steel dowels. Fig.
1.1demonstrates how the use of these connections has led to the
lossof support of the structural elements, and consequently to
theircollapse, in the aforementioned recent events.
The poor seismic behaviour of these structures during the
May2012 event in Northern Italy is mainly due to the fact that the
rstseismic design regulation for this typology was introduced1.
Introduction
Seismic fragility is a measure of thodology has been used that
consists of (1) random sampling of one hundred structures for each
buildingtypology, (2) pushover analysis to establish a number of
damage limit states, (3) execution of nonlineardynamic analysis and
comparison of the maximum demand with the limit state capacity to
allocate thestructure in a damage state, and (4) regression
analysis on the cumulative percentage of buildings in eachdamage
state for a set of intensity measure levels to derive the
statistical parameters of the fragility func-tions. The building
population employed in the analysis was generated considering both
material andgeometric variability that was obtained from the eld
surveys of 650 industrial facilities, as well as otherinformation
available in the literature. Several aspects of the fragility
derivation process were furtheranalysed, such as the correlation
between different intensity measure types and damage, the
considera-tion of different collapse mechanisms (e.g. beamcolumn
connection failure) and the differences in theresulting fragility
curves when adopting a 2D or a 3D modelling environment. A good
agreement withpreliminary empirical fragility functions based on
eld data was also observed.
2015 Elsevier Ltd. All rights reserved.
ihood of a building suf-
inter-storey height. The connections between precast beams
andcolumns, and between roof elements and beams should be ableto
sustain the seismic displacement demand associated with theRevised
25 January 2015Accepted 25 February 2015
reinforced concrete (RC) precast industrial buildings suffered
excessive damage, which led to substantialdirect and indirect
losses. The aim of this paper is to present a seismic fragility
model for Italian RC pre-Seismic fragility of Italian RC precast
ind
C. Casotto a,, V. Silva b, H. Crowley b, R. NascimbeneaROSE
Programme, UME School, IUSS Pavia, Italyb European Centre for
Training and Research in Earthquake Engineering (EUCENTRE),
PacDepartment of Civil Engineering and Architecture, University of
Pavia, Italy
a r t i c l e i n f o
Article history:Received 6 April 2014
a b s t r a c t
Despite the moderate grou
journal homepage: www.etrial structures
R. Pinho c
Italy
motions observed during the seismic events in Northern Italy,
May 2012,
le at ScienceDirect
Structures
vier .com/locate /engstruct
-
201
g StrSeveral methodologies have been proposed in the recent
dec-ades for the derivation of damage-ground motion
intensityrelationships, as summarised by Calvi et al. [2]. These
include thestatistical treatment of damage distributions that have
either beenobserved in post-earthquake surveys (empirical
relationships) orsimulated through structural analyses of numerical
models underincreasing earthquake intensity (analytical
relationships). The lat-ter approach allows sensitivity studies to
be carried out to evaluatethe impact of specic aspects, such as
inadequate detailing, on theoverall structural response. In
addition, analytical approaches per-mit the vulnerability
assessment of classes of buildings for whichreliable statistical
damage data might not be available. For this rea-son, an analytical
method was used in the seismic fragility studypresented herein.
One of the main differences between the various
analyticalmethods arises in the procedure used to estimate the
nonlinearresponse of the structure for a given ground motion input.
Thecomputational efciency of static analysis with respect to
dynamicanalysis has triggered the development of many Nonlinear
StaticProcedures, in which the seismic capacity of the structure is
usu-ally represented by a capacity curve and the seismic demand
byan acceleration and/or displacement response spectrum. For
exam-ple, Borzi et al. [3] developed a Simplied
Pushover-basedEarthquake Loss Assessment method (SP-BELA), where
the nonlin-ear behaviour of a random population of buildings is
denedthrough a simplied pushover curve, and the fragility curves
aregenerated through the comparison between the
displacementcapacity limits identied on the pushover curve and the
displace-ment demand from a response spectrum. Bolognini et al. [4]
imple-mented the SP-BELA method for traditional Italian
precastconstructions, adapting the limit states denition and
considering
Fig. 1.1. Failure due to loss of support of the beam during the
May
C. Casotto et al. / Engineerinthe connection failure mechanism
in a simplied way that ignoredthe vertical component of the dynamic
seismic input. Senel andKayhan [5] have also derived fragility
curves for precast industrialbuildings also using simplied pushover
curves for the denitionof the limit states, expressed as a function
of the chord rotationof the columns. However, in this case,
nonlinear dynamic analyseswere employed to obtain the maximum
displacement demands,which were compared with the aforementioned
limit displace-ments. The main drawbacks of this fragility
assessment are theexclusion of the second order effects in the
mechanics-based bilin-ear pushover curves, which in this type of
structures can affectconsiderably the overall behaviour, and the
lack of modelling ofthe connection behaviour.
For what concerns nonlinear dynamic analysis, in general thetwo
most common disadvantages to its use in fragility assessmentare the
increased computational effort and the difculty in
readilyguaranteeing numerical convergence. However, such issues
werenot a main concern within this study as the structures
underinvestigation are relatively simple (single-storey bare
frames),which thus allowed the employment of a large number of
nonlin-ear dynamic analyses and a more accurate representation of
thereal phenomenon. Hundreds of structures were produced
throughMonte Carlo simulation to represent the as built in Italy
and sub-jected to seventy ground motion records using nonlinear
dynamicanalysis. The geometric properties of the structures
generatedwere randomly sampled from probabilistic distributions
obtainedfrom 650 eld surveys, while the material property
distributionswere found in the literature and established using
expert opinion,when such data were not available. The building
stock was classi-ed into a number of typologies according to
geometric cong-uration and the original seismic design, both of
which arecorrelated with the construction age. This methodology was
imple-mented by modelling the structures in both 2D and 3D
frame-works. A pushover analysis was also performed for each
frameand a set of limit states were estimated according both to
strainlevels and maximum top drifts. The capacity of the
connectionswas calculated and connection failure was accounted for
as a col-lapse limit state, estimated with both static and dynamic
methods.
2. Fragility curve methodology
An overview of the analytical methodology for the derivation
ofthe fragility curves is shown in Fig. 2.1. The analytical
methodologycan be summarised in the following steps:
1. Generation of precast RC structures: The characteristics of
thistype of structure were analysed according to building
typolo-gies with homogeneous attributes. For each typology, a
proba-bility density function for each geometric and material
2 Emilia-Romagna earthquake in Northern Italy (Belleri et al.
[1]).
uctures 94 (2015) 122136 123parameter was dened.2. Design,
numerical modelling and damage analyses: The randomly
sampled single structures were designed according to
theadmissible tension method and the provisions of the codein place
at the time of construction (either pre- or post-1996). The
classication of the building stock and the designprocedure outlined
by Bolognini et al. [4] was adopted. Eachgenerated structure was
modelled and subjected to nonlinearstatic and dynamic analyses
using the software OpenSEES[41]. The pushover analysis served the
purpose of dening acapacity curve, and the associated limit states
(LSs) for threelevels of damage. Due to the particular static
scheme and thestructural deciencies affecting the nonlinear
behaviour ofprecast RC buildings, both sectional and global
parameterswere used for the limit state denition. The steel
yieldingstrain characterises the rst limit state and the maximumtop
drift denes the collapse limit state, unless connectionfailure
happens rst. A dynamic analysis was performed using
-
Str124 C. Casotto et al. / Engineeringa suite of selected
accelerograms and the maximum responseof each structure in terms of
maximum top drift wasextracted. These results (displacement demand)
were com-pared with the limit states (displacement capacity), in
orderto allocate each structure into a damage state.
3. Fragility curves derivation: The distribution of buildings in
eachdamage state was stored in a damage probability matrix(DPM),
and related to the corresponding Intensity MeasureLevel (IML) for
each ground motion record (described furtherin Section 2.3). The
DPM was used to derive the statisticalparameters of each fragility
function. This regression analysiswas carried out using the maximum
likelihood method.
Fig. 2.1. Flowchart of the proposed analytuctures 94 (2015)
1221362.1. Generation of the building stock
A Matlab [42] script was developed to incorporate the
differentsteps of the analysis presented in Fig. 2.1 into an
automatedprocess.
2.1.1. Classication of Italian industrial precast buildingsThe
denition of the typologies representative of the as built
in Italy was based on the combination of different factors: the
yearof construction and thus the seismic design code to which
theyshould conform to, and the geometric conguration. A
periodcorresponding to the last 5060 years was considered and
the
ical method to derive fragility curves.
-
building stock subdivided between pre-code and low-code
design,for the structures that date back to before and after 1996,
respec-tively. In fact, the rst (unsatisfactory) attempts to
include provi-sions for the design of reinforced concrete precast
structures inseismic zones were carried out in 1987 and 1996, but
an appropri-ate design code including a specic chapter on precast
structureswas introduced only in 2003 (OPCM 3274 [6]). The very
limitednumber of precast buildings in Italy designed in accordance
withthe latter regulation meant that it was not worth considering
apost-code typology with modern seismic design in the
adoptedclassication. Moreover, the little knowledge of the real
design cri-teria applied in the absence of code provisions in the
decadesbefore the 70s, combined with the relatively scarce design
docu-mentation, results in a large uncertainty in the evaluation of
thecapacity of RC precast structures built in that period.
and from the direct survey of 650 warehouses located in
Tuscany,
material properties indicated by the reference codes (DM
3-03-1975 [10], DM 16-01-1996 [11]) were used to design each
struc-ture. For the design of the low-code typologies a random
choicebetween the steel characteristic yielding value of 380 MPa
and440 MPa was performed, which corresponds to the values
indi-cated by the DM 16-01-1996 [11] regulation for FeB38 andFeB44
ribbed steel bars, respectively. The same approach wasadopted for
the concrete cubic characteristic strength, with ran-domly selected
values of 45, 50 or 55 MPa (each with the sameprobability of
occurrence). For the pre-code typologies, valuesbetween 320 MPa and
380 MPa were randomly chosen for steeltensile strength, according
to the DM 3-03-1975 [10] guidelines,the former referring to FeB32
smooth bars and the latter to theFeB38 ribbed bars. Regarding the
concrete compressive strengthfor this typology, 35, 40, 45 or 50
MPa was randomly chosen froma uniform distribution. Both smooth and
ribbed steel bars were
C. Casotto et al. / Engineering Structures 94 (2015) 122136
125Emilia Romagna and Piedmont regions, built between 1960 and2010.
Part of the survey data were provided by the Seismic RiskPrevention
Area of Tuscany Region [43], which conducted a cam-paign for risk
and hazard assessment of industrial areas, which isfully described
in Ferrini et al. [9]. Additional information was col-lected by eld
teams from the European Centre for Training andResearch in
Earthquake Engineering [44]. The results of theinvestigations were
used to derive the statistical distributions ofthe geometric
properties for each building typology. Some informa-tion required
for this study (e.g. material properties and designloads) could not
be extracted from the surveys, and was insteadobtained from the
literature, or estimated through expert opinion.
The rst typology, more traditional and frequently used,
consistsof a series of one-storeybasic portal frames. Eachportal is
comprisedof twoormorecolumnsxedat thebaseandasaddle
roofbeam,usu-ally simply supported by the columns or with shear
resistant con-nections. The second common typology consists of
one-storeyframes linked by perpendicular straight beams, which
carry themain roof beams or directly support the large span slab
elements.Table 2.1 describes the classication of the building stock
accordingto the structural conguration and the design lateral
load.
2.1.2. Statistical characterisation of the material and
geometricparameters
The concrete and steel characteristic compressive and
tensilestrengths were sampled according to the construction age.
The
Table 2.1Classication of the building typologies used in this
study.
Structural conguration Codelevel
Design lateralloada (%)
Id code
Type 1 Pre-code
2 T1-PC-2
Low-code
4 T1-LC-47 T1-LC-7
10 T1-LC-10
Type 2 Pre-code
2 T2-PC-2
Low-code
4 T2-LC-47 T2-LC-7
10 T2-LC-10Two main categories were selected to represent the
most com-mon geometric congurations of the Italian precast
industrial build-ing stock, as described in Table 2.1. This
classicationwasdevelopedbased on information from the available
Italian literature, from pre-cast elements producers, and designs
reported in Calvi et al. [7,8],a As a percentage of the weight of
the structures.considered in the pre-code classication because of
the progressiveincrease in the use of ribbed bars, passing from 5%
in 1950 to 80%in 1980 (Verderame et al. [12]).
In order to consider the difference between the actual
charac-teristic compressive and tensile strength of the materials
to beused in the modelling and the design values indicated in the
codes,the results obtained by Verderame et al. [12] from an
experimentalcampaign on the actual mechanical properties of
materials wereadopted. Unfortunately, this study provides
information only onsmooth steel bars, hence overstrength coefcients
to the designvalues of those materials for which statistical
studies were notavailable were applied. Therefore, a normal
distribution with amean of 356 MPa and standard deviation of 67.8
MPa was assumedfor the steel yielding strength of smooth bars
(Verderame et al.[12]), while the yielding strength of ribbed bars
and the character-istic strength of concrete were respectively
multiplied by the over-strength coefcients cs (mean value of 1.15
and coefcient ofvariation equal to 7.5%) and cc (mean value of 1.3
and coefcientof variation equal to 15%), following the suggestions
of Bologniniet al. [4]. It is noted that for the modelling, the
overstrength coef-cients were not applied to the same design values
adopted in thedesign, but to new randomly sampled design values. In
fact, thecharacteristic strengths used in the design are generally
unknownwhen trying to assess the capacity of an existing building;
the newsampling thus takes into account the possible mismatch
betweenthe design and the modelling values, which is another source
ofuncertainty.
Table 2.2 summarises concrete and steel characteristicstrengths
(Rck and fsk) used for the design and Table 2.3 providesthe values
used in the modelling. Table 2.4 reports the loadsapplied in the
simulated design: the self-weight of the roof GR
Table 2.2Material properties randomly sampled for the simulated
design of the building stock.
Pre-code (all cases) Low-code (all cases)
Rck (MPa) 35, 40, 45, 50 45, 50, 55fsk (MPa) 320, 380 380,
440
Table 2.3Material properties randomly sampled to model the
building stock.
Pre-code (all cases) Low-code (all cases)
Rck (MPa) 35, 40, 45,50 multipliedby cc
45, 50, 55 multiplied by cc
Smooth Ribbed Ribbed
fsk (MPa) l = 356
r = 67.8380 multiplied by cs 380, 440 multiplied by cs
-
made to use expert opinion to determine an adequate
probabilisticmodel. All the parameters are described in Table 2.5,
noting that
Table 2.4Load cases randomly sampled as a function of the type
of structures and thedimensions of the members. GR is the roof
weight, GLB the lateral beam weight, GB thebeam self-weight, Q1 and
Q2 the accidental and snow weight, respectively.
Load type Type 1 Type 2
GR (kN/m2) Lintercol < 20 m 2.4 2.9Lintercol > 20 m
1.6
GLB (kN/m) 2.4
Table 2.6Summary of the pre-code and low-code design methods and
requirements.
Pre-code Low-code
Seismicaction
Static analysisHorizontal force 2% ofthe total weight
Static analysisHorizontal force for three classesS = 6, 9,
12P-Delta effects considered
Designmethod
Admissible tensionFlexure and
Admissible tensionFlexure and compression for big
126 C. Casotto et al. / Engineering Structures 94 (2015)
122136minimum and maximum truncating values were dened by
expertopinion, with a view to avoid unrealistic parameters.
2.2. Design, numerical modelling and damage analyses
2.2.1. DesignThe structures were designed in compliance with the
pre-code
and low-code classication, as previously noted. The DM 3-03-1975
[10] is the main reference for the pre-code typologies, andthe DM
16-01-1996 [11] for the low-code design. In both casesthe allowable
tension method was employed, which consists inthe comparison of the
maximum values of stresses in the concreteand steel bars with those
of the allowable ones. According to thisand the beam GB are a
function of the length that the roof elementsand the beams need to
cover, Lintercol and Lbeam, respectively.
Several probabilistic distributions (normal, lognormal,
gamma)were considered for the characterisation of the geometric
proper-ties of precast structures. The maximum likelihood approach
wasadopted to select the probabilistic model that provided the
bestt and the chi-square test was employed to evaluate the
good-ness-of-t for a set of signicance levels (1%, 5% and 10%),
asdescribed in Bal et al. [13]. For the cases for which the
probabilitydistributions showed a poor t with the eld data, a
decision was
GB (kN/m) Lbeam < 16 m 3.6 416 < Lbeam < 22 m 5.2 622
< Lbeam < 24 m 6.85 7.524 < Lbeam < 28 m 7.5 8Lbeam
> 28 m 8.55 9.5
Q1 (kN/m2) Normal distribution l = 2; r = 0.4; min = 0.8;max =
3.2
Q2 (kN/m2) Normal distribution l = 2; r = 0.4; min = 0.8;max =
3.2design philosophy, the dimensions of a given member and
theamount of steel reinforcement should increase until the
stressesare lower than the limits of the materials. The seismic
action isapplied as static horizontal loads, corresponding to a
fraction ofthe total weight of the building. This percentage is
very low forthe pre-code design (2%), whilst in the low-code it is
a functionof the seismic region where the structure is located (4%,
7% and10% for seismic zones III, II and I, respectively). Moreover,
in thelow-code designed structures, second order (P-Delta) effects
aretaken into account, as well as the shear demand. These
differences
Table 2.5Geometric dimensions randomly sampled for the
generation of the building stock. h andportals (Lintercol) and
column height (Hcol).
Structural conguration Distribution h
Type 1 Lbeam (m) Lognormal 14.9Lintercol (m) Lognormal 6.8Hcol
(m) Lognormal 6.5
Type 2 Lbeam (m) Normal 8.7Lintercol (m) Normal 16.5Hcol (m)
Normal 6.5between the pre-code and low-code design are summarised
inTable 2.6, while the full design methodology is presented
inCasotto [14].
The type of connection considered in this study consists of
asimple corbel supporting the roof beams. Further details aboutthe
design of the connections can be found in EOTA [15].Connections
relying on friction are allowed in the pre-code design,but not in
the low-code, as stated in the DM 03-12-1987 [16] reg-ulations.
Thus, in pre-code buildings the capacity of the connec-tions was
calculated simply as the friction resistance. The frictioncoefcient
depends on the type of interface that supports the beam(concrete,
rubber pads or steel plates). The denition of thisparameter is a
controversial matter, as in the literature it is foundto vary
between 0.6 and 0.9, whilst in some experimental cam-paigns lower
values between 0.1 and 0.5 have been observed(Magliulo et al.
[17]). Due to this uncertainty, a decision was madeto adopt two xed
values of 0.2 and 0.3, the former close to thelower bound and the
latter the mean of the range found inMagliulo et al. [17], and to
estimate the effect of this parameteron the nal fragility curves.
The load variation due to the verticalacceleration was considered
differently in the 2D and the 3D mod-elling frameworks, as will be
explained in Section 2.2.3. For low-code structures, steel bolts or
bars (so-called dowel connections)can be used to reinforce the
connection. The resistance of thesteelconcrete interaction is
assumed to be the smallest betweenthe shear resistance of the steel
and that of the concrete.
2.2.2. Numerical modellingThe randomly generated structures were
modelled in both a 2D
compression for smalleccentricityStandard shearreinforcement
eccentricity (computation of theneutral axis position)Design of
the shear reinforcementverication of the displacements
Connections Friction connection Connections with standard
steelelementsand 3D environment using the software OpenSEES [41],
con-sidering both the geometric and material nonlinearities. In
the2D framework the structure was represented by the external
framein the direction longitudinal to the main beams, because it is
theframe with less axial load and thus more sensitive to
connectionfailure. The concrete nonlinear behaviour was modelled
using theproposal by Kent-Park and modied by Scott et al. [18],
whilstthe steel was simulated using the Menegotto and Pinto [19]
model.
r are the median and dispersion, describing beam length (Lbeam),
distance between
r min max v2 test Source
0.3 8 30 10% Tuscany database0.28 8 10 Not passed Expert
opinion0.25 4 12 Not passed Tuscany database
2.1 8 10 Not passed Tuscany database3.7 10 25 Not passed Tuscany
database1.3 4 11 10% Tuscany database
-
The numerical model included material inelasticity in a
distributedfashion, using force-based bre nite elements for the
columns,with a mesh of 220 bres and 4 integration points.
Since the beams are pre-stressed precast members designed
toremain elastic under the gravity loads, and the hinge
connectionsdo not allow the additional moments in the columns
producedby the seismic action to be transmitted to the beams, for
the sakeof simplicity it was decided to represent them with elastic
ele-ments. To ensure that no moments are transmitted to the
beams,link elements with no exural stiffness were introduced at
thetop of the columns.
2.2.3. Damage analysesAs mentioned before, two types of analysis
were conducted:
nonlinear static and nonlinear dynamic analysis. The former
wasundertaken to establish a set of limit states (levels of
capacity)and the latter to simulate the seismic event and capture
how thebuilding responds to different levels of ground motion
intensityin terms of internal forces and displacements (which are
then com-pared with the aforementioned limit states). The analyses
were
repeated for the various typologies of precast industrial
buildings,for the three levels of design lateral load (4%, 7% and
10% of thetotal weight) in the low-code design case, and for one
level ofdesign lateral load in the pre-code design case (2% of the
totalweight).
The overall process is summarised in Fig. 2.2: the top
imagesrepresent the pushover analysis of a single 2D frame, with
the def-inition of the two limit states; the middle images present
a singleframe being tested against the suite of accelerograms
throughdynamic analysis, and the resulting maximum response
over-lapped with the pushover curves previously computed. The
bottomimages represent the repetition of the previous two steps for
all theframes that constitute the randomly generated building
stock.
2.2.3.1. Pushover analysis and damage states denition. A
pushovercurve was computed to estimate a set of limit state global
drifts.There are many criteria that can be employed for the limit
statedenition according to the level of complexity of the models
andof the analyses. Crowley et al. [20] considered damage limit
statesbased on the strain levels in the concrete and steel, whilst
other
C. Casotto et al. / Engineering Structures 94 (2015) 122136
127Fig. 2.2. Scheme of the analysis process, pushover analysis of a
single building generatinmultiple records (middle), dynamic
analysis of the building stock for multiple records (g a pushover
curve with limit states (top), dynamic analysis of a single
building forbottom).
-
buildings) a 3D displacement-based pushover was applied,wherein
the increments in each direction were proportional tothe stiffness
in the corresponding direction, in order to
0 2 4 6 8 100.4
0.3
0.2
0.1
0
0.1
0.2
0.3
0.4
Time [s]
Acc
eler
atio
n [g
]
acc>ayacc
ay
0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.040
20
40
60
80
100
120
140
Top Drift [%]
Bas
e Sh
ear [
kN]
pushoverLS1LS2LS connection
Structures 94 (2015) 122136authors (e.g. Erberik [21]; Akkar et
al. [22]) dened these thresh-olds using inter-storey drifts. Three
damage states are applicablein this specic case: none/slight
damage, moderate/extensive dam-age and collapse.
The member exural strength, which characterises the rstlimit
state (LS1), is attained when the reinforcement steel in thecolumns
rst yields. The ultimate strain limits of concreteec = 0.005 and
steel es = 0.015 proposed by Crowley et al. [20] can-not be used to
characterise the collapse limit state in this study, asthey lead to
excessive levels of top displacement. Furthermore,inter-storey
drifts frequently suggested in the literature for dam-age criteria
of RC structures are also inadequate, as traditional RCstructures
with monolithic connections feature a very differentresponse with
respect to RC precast buildings with hinged beamcolumn joints. The
main reason for this difference is the combina-tion of slenderness
and low transverse reinforcement ratio in thelatter. In Deyanova et
al. [23] different methodologies for deningthe ultimate rotation of
precast columns typical of the Italian con-structions have been
compared. These methods include the so-called DDBD method that
follows the recommendations foryielding curvature, ultimate
curvature and plastic hinge lengthby Priestley et al. [24]. Another
approach was based on Cumbia,a momentcurvature software developed
by the same authors,which calculates the displacement at expected
buckling. A bre-element based approach was also adopted and section
analysiswith the nite element software SeismoStruct [45] was
performed.The ultimate drift of the columns was also evaluated
following theapproach by Haselton [25]; Fischinger et al. [26]
found that thismethod best matched the experimental results amongst
all thosethey investigated. The Haselton approach, however,
yieldsunrealistic results for the Italian precast columns due to
thevery low transverse reinforcement ratio (qsh = 0.04%) comparedto
that of the structure tested by Fischinger et al. [26], whereqsh =
0.86%. As far as the ultimate displacement was concerned,all the
methods used by Deyanova et al. [23] gave a wide rangeof results.
It is clear that more investigation is needed in this eldand in the
meantime the exural collapse limit state (LS2) has beenset to 3%
inter-storey drift, as experimentally veried by Brunesiet al.
[27].
Failure due to shear was not considered in the present
studybecause it has not been observed in any of the precast
industrialstructures investigated after Emilia-Romagna events
(Deyanovaet al. [23]). The reasons why exural collapse was
predominantinclude the large column sections, designed for
instability andbuckling, and the slenderness of the columns, due to
the largeinter-storey height.
The collapse limit state is related also with the loss of
support ofthe beam. The connection collapse is evaluated
differently in the2D and 3D framework, and with two different
approaches in the2D framework. The two approaches in the 2D
environment differin the way the friction capacity is calculated
and in the considera-tion of sliding of the beam on the column
support. In the rstapproach, connection collapse is identied when
the shear demandin at least one column exceeds the connection
capacity; thecapacity of the connection is computed assuming a
constant force,proportional to 40% of the axial load (as applied in
Bolognini et al.[4]). In the second method this capacity is
dependent on thevertical component of the ground motion records and
collapse isidentied only when the sliding displacement of the beam
exceedsits support length and unseating occurs. Sliding has
beenaccounted for with Newmark sliding block analysis (Fig.
2.3),adopted from Kramer [28]: the sliding displacement is
computedas the double integration of the acceleration at the
connection
128 C. Casotto et al. / Engineeringnode exceeding the yield
acceleration benchmark (shaded greyarea shown in Fig. 2.3), which
is the acceleration correspondingto the connection resistance
force.The yield acceleration benchmark ay is computed as in the
fol-lowing equation:
ay V cnnmwhere m is the inertial mass at the connection location
and Vcnn isthe shear capacity of the connection, a function of the
friction coef-cient and the axial load N. If N is not considered
constant but vary-ing with the vertical acceleration, the yield
acceleration ay will notbe a horizontal line as in the gure above,
but it will also vary intime. The support length is computed as
half of the corbel length,to consider the worst case scenario where
the columns oscillateout of phase.
Fig. 2.4 shows the limit states evaluated on the pushover
curveincluding connection collapse limit state computed with the
con-stant connection resistance. For this particular case, collapse
dueto connection failure is reached before the other two limit
states.
The 3D modelling framework introduces an additional source
ofcomplexity in the pushover analysis regarding the direction
inwhich the pushover should be performed to dene the limit
states.Given the simplicity of this type of structure (i.e.
single-storey
Fig. 2.3. Newmark sliding block analysis for the evaluation of
sliding displacement.Fig. 2.4. Pushover curve and limit states for
a structure representative of T1-PC-2typology.
-
g Strapproximate the progressive deformation of the structure
sub-jected to a horizontal seismic force in the 3D space. Two
otherpushover analyses were performed loading the structure in
thetwo directions separately, checking whether the x and y
compo-nents of the limit states evaluated on the 3D bi-directional
push-over curve exceed the limit states obtained when loading only
inone direction. In this case, the damage induced by a mainly x-
ory-oriented seismic excitation could be underestimated, and for
thisreason, after the dynamic analysis, the uni-directional limit
statesare used for the comparison with the x and y maximum
displace-ments, whilst the limit states derived with the
bi-directional push-over curve are compared with the modulus of the
displacementvector. The structure is nally allocated to the maximum
damagestate resulting from the three aforementioned comparisons.
Thelimit states were dened on each pushover curve, using the
samecriteria described for the 2D framework. Connection failure,
whichleads to sudden collapse of the structure, was considered to
occurwhen the sliding displacement is exceeded in at least one
direction,considering the two directions separately. The test in
each direc-tion is carried out in the same way as in the 2D
approach with ver-tical acceleration.
2.2.3.2. Dynamic analysis and seismic input. To the
previouslydescribed structural model the following additions were
madefor the dynamic analyses: the masses were lumped at the
jointsand a tangent stiffness proportional damping model was used
witha damping ratio of 2%. Two types of dynamic analyses were
per-formed on the 2D frames; considering only one horizontal
inputor applying both the horizontal and the vertical
accelerations, thusallowing the calculation of the connection
capacity as a function ofthe vertical excitation. The maximum
response of the structure,expressed in terms of maximum top drift,
was compared withthe drift limits dened with the pushover analysis
to allocate eachframe into a damage state. In the 3D environment
the structureswere subjected to accelerograms in the three
directions and themaximum top displacements in x and y and the
modulus of the dis-placement vector were compared with the three
sets of limit statesderived with the uni-directional and the
bi-directional pushovercurves respectively, as previously
described. The contributions interms of damage state per level of
ground motion intensity,obtained from all the samples subjected to
all the records, weresummed up and normalised with respect to the
total number ofbuildings to compute the Damage Probability Matrix
(DPM). Thismatrix contains the percentage of frames in each damage
statefor a set of intensity measure levels representing each
groundmotion record.
The use of real accelerograms for dening the input to
dynamicanalyses was adopted (as opposed to employing synthetic or
arti-cial records, in which the scaling process might lead to
unrealisticproperties in the ground motion records, such as
frequency contentand/or duration). Stewart et al. [29] and Bommer
and Acevedo [30]considered magnitude (M) and distance (R) as
important parame-ters for the earthquake record selection,
complemented by the soilprole (S) at the site of interest, leading
to (M, R, S) record sets. Theregion of interest is Northern Italy,
with particular focus on theregion of Emilia-Romagna, where the
ranges of these parameterscontributing to the 475 years return
period hazard forSa(T = 1.5 s) are Mw from 4 to 6.5 and R from 0 to
20 km, whilstthose contributing to the 2475 years return period are
Mw from4.5 to 6.5 and R from 0 to 30 km (Iervolino et al. [31]).
The soil inthis area is classied by Borzi and Di Capua [32] as
soft, accordingto the EC8 soil classes, or as category C and D,
following the Italiancode classication (NTC2008 [33]). Seventy
accelerograms in the
C. Casotto et al. / Engineerinthree directions (leading to 210
records) were extracted from thePEER database [46]. A low scaling
factor of approximately 1.5was applied to 13 of the ground motion
records in order tosimulate stronger intensity measure levels,
which is an acceptablefactor according to Watson-Lamprey and
Abrahamson [34].Moreover, records with directivity or pulse effects
were avoided.The histograms of PGA and Sa(T = 1.5 s) are presented
in Fig. 2.5.
2.3. Fragility curve derivation
The results from the nonlinear dynamic analyses were assem-bled
in the Damage Probability Matrix, which contained the frac-tions of
sampled structures in each damage state, for a set ofincreasing
intensity measure levels. Then, the cumulative fractionof
structures in each damage state was estimated, by summingthe
percentages of frames belonging to all the subsequent damagestates.
A lognormal cumulative distribution function, expressingthe
probability of exceeding each damage state in a continuousfashion,
was then t to these results. The regression analysis wascarried out
using the maximum likelihood method.
In the 2D approach, that hypothesizes a 40% axial load
reduc-tion to account for vertical acceleration, a simplied
methodologywas employed to include the Probability of Exceedance
(PoE) ofconnection failure. This probability was computed
separately andthen added to the PoE of exural failure to obtain the
total PoEof the ultimate limit state. In fact, the discrete
probabilities forincreasing intensity of the ground motion were
very scatteredand the dispersion was high when trying to t them
with a uniquecontinuous function. The dispersion decreased
considerably con-sidering the two conditional probabilities
separately, because theyare able to describe the two trends visible
in the collapse fragilitycurves (Fig. 2.6): a rst trend when the
demand is not enough toattain exural capacity and collapse is due
only to connection fail-ure, and a second trend when exural failure
starts contributing tocollapse, while connection failure is limited
by the maximum per-centage of frames featuring the connection
collapse mechanism.The total PoE of collapse is the sum of the two
conditional proba-bilities: the probability of attaining connection
collapse,P(CConnection), conditional on the probability of
presenting connec-tion failure mechanism, P(Connection mechanism),
and theprobability of reaching exural failure, P(CFlexure),
conditionalon the probability of having exural failure mechanism,(1
P(Connection mechanism)). The relation to estimate the
totalprobability of exceeding collapse (PoEC) is thus expressed in
thefollowing equation:
PoEC PCConnectionPConnection mechanism PCFlexure1 PConnection
mechanism
The results of this simplied method are analysed in Fig. 2.7,
com-paring the collapse fragility curves that comprise both
failuremechanisms (exure and collapse) with those that consider
onlyexural collapse, and with the yielding fragility curve. The
compar-ison shows that connection collapse plays an important role
in thetotal collapse curve, but also that for the typology in the
plots it ismore likely to occur than yielding, as similarly shown
in Fig. 2.4.This outcome reveals that the criteria used to assess
connection fail-ure (reducing by 40% the axial load and neglecting
the unseatingdisplacement of the beam) were too conservative,
leading to unreli-able results. The method was therefore discarded
in favour of theother two approaches, where the beamcolumn joint
collapse isassessed in a more accurate way. Moreover in the second
approachimplemented within the 2D framework and in the one
appliedwithin the 3D framework, a unique regression analysis was
per-formed with the data comprising both exural and connection
fail-ure, without the need to compute the PoE of connection and
exural
uctures 94 (2015) 122136 129collapse separately.A key point in
the derivation of fragility curves is the selection of
the intensitymeasure (IM) that adequately correlates with
damage.
-
Str40
45
50
130 C. Casotto et al. / EngineeringVarious intensity measures
were considered and compared, usingthe R2 coefcient to quantify the
correlation between the intensitylevels and the cumulative
percentage of frames for each limit state.The peak ground
acceleration (PGA) is a very common measure invulnerability
studies, as Crowley et al. [35] showed when collectingmore than
fourhundred fragility curves. This parameter is also easily
0 0.5 1 1.50
5
10
15
20
25
30
35
PGA [g]
Num
ber o
f rec
ords
Fig. 2.5. Histograms of PGA (left) and Sa(T = 1.5 s) (right
0 100 200 300 400 5000
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
PoE
colla
pse
PoE connection collapsePoE flexural collapsePoE total
Sa (Topt) [cm/s2]
Fig. 2.6. Total probability of exceedance for the collapse limit
state as the sum of the two0.2 (left) and 0.3 (right) friction
coefcient.
0 100 200 300 400 500 6000
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Sa (Topt) [cm/s2]
Prob
abili
ty o
f Exc
eeda
nce
PoE total collapsePoE yieldingPoE flexural collapse
Fig. 2.7. Comparison between the total collapse fragility curve
and the exural collapse a25
30
uctures 94 (2015) 122136extracted fromgroundmotion records;
however, for structureswithlong fundamental periodsof vibration,
this IM leads to very largedis-persion in the results (see Fig.
2.8).
The employment of a spectral quantity, such as spectral
accelera-tion (Sa), introduces the problem of selecting the period
for whichthe spectral ordinate is computed. In fact, the selected
period is of
0 100 200 300 400 500 600 7000
5
10
15
20
Sa (T=1.5 sec) [cm/s2]
Num
ber o
f rec
ords
) of the selected horizontal ground motion records.
0 50 100 150 200 250 300 350 4000
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
PoE
colla
pse
PoE connection collapsePoE flexural collapsePoE total
Sa (Topt) [cm/s2]
conditional probabilities of exural collapse and connection
collapse, T1-PC-2 with
0 50 100 150 200 250 300 350 4000
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Prob
abili
ty o
f Exc
eeda
nce
PoE total collapsePoE yieldingPoE flexural collapse
Sa (Topt) [cm/s2]
nd yielding fragility curves, T1-PC-2 with 0.2 (left) and 0.3
(right) friction coefcient.
-
Absolute Velocity, which considers the total energy stored
duringthe seismic event, but showed to provide a weaker
performance
2
0 0.5 1 1.50
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
PGA [g]
Prob
abili
ty o
f Exc
eeda
nce
LS1LS2yieldingcollapse
2
C. Casotto et al. / Engineering Strgreat importance for the
reduction of the uncertainty in each limitstate curve. The elastic
period is a common choice, but it is not veryrepresentative of the
dynamic properties of a structure, as even forlow intensities the
cracking of concrete elongates the period ofvibration signicantly.
Silva et al. [36] investigated the inuenceof the period of
vibration on the variability of the fragility curves,by computing
the coefcient R2 for a set of elastic periods. The samecorrelation
analysis was carried out for RC precast industrial build-ings, as
shown in Fig. 2.9. Themean R2 curve (themean between therst limit
state and the second limit stateR2 curves) is also presentedand the
optimal period (the periods corresponding to themaximumcorrelation
for each limit state and for themean curves) is indicatedwith a
vertical line. The spectral acceleration at the mean optimalperiod
of vibration Sa(Topt) increases the performance of the secondlimit
state curve (which provides information about the damagestate that
has a larger inuence on the losses) without
substantiallycompromising the rst limit state correlation.
The main drawback of using Sa at the optimal period, as
dis-cussed by Vamvatsikos and Cornell [37], is that it does not
corre-spond to the period of vibration of the structure at a
certaincondition of damage and it would be difcult to select a
priori.The only way to estimate it robustly would be through a
correla-tion analysis similar to that previously described, carried
out for
R LS1 = 0.39 LS2 = 0.38 R
Fig. 2.8. Fragility curves using PGA and correlation coefcients
R2 for typologyT1-PC-2.each typology, since a slight change in
period could penalise thedispersion considerably. As an
alternative, the power-law formwith three spectral values (IMpw)
proposed by Vamvatsikos and
0.5 1 1.5 2 2.5 3 3.5 40.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Period [s]
Corre
latio
n Co
effic
ient
R2
LS1LS2mean
Topt
Fig. 2.9. Correlation coefcient as a function of the period of
vibration of Sa, forT1-PC-2 typology.than the aforementioned IMs.
Moreover, since the purpose of thisstudy is to provide a set of
fragility functions for earthquake lossassessment, Sa(Topt) was
preferred to IMpw. In fact even if IMpwcould be easily estimated
from the Sa values directly provided bymost of the ground motion
prediction equations available in com-mon seismic risk software,
the cross correlation between the spec-tral ordinates combined in
this parameter (see e.g. Baker andJayaram [38]) would need to be
estimated, which would signi-cantly complicate the loss assessment
methodology.
For what concerns the 3D analyses, the structures
evaluatedherein were no longer dominated by a single vibration
mode, butusually by two modes with similar modal contribution in
eachdirection, as well as a similar elastic period. It was decided
to usethe geometric mean between the two horizontal components
andthe period that provides the better correlation coefcient
accord-ing to the correlation analysis previously described. The
geometricmean is now the most widely used horizontal-component
def-inition in ground motion prediction equations (Beyer andBommer
[39]), which is essential for the application of the
derivedfragility curves in loss models. The geometric mean is dened
as:
Sa;GMxyTopt Sa;xTopt Sa;yTopt
q
3. Proposed fragility functions
3.1. Fragility curves
The nal fragility curves derived within the 2D and 3D frame-work
that include vertical acceleration in the dynamic analysesand
unseating of the beam are presented in this section. Resultsfor the
hypothesis of 40% axial load reduction to account for verti-cal
acceleration were discarded, as explained in Section 2.3. Anexample
of the fragility functions obtained within the 2D and
3Denvironments is presented in Fig. 3.1, while the parameters
foryielding and collapse fragility curves are reported in Table
3.1. Itshould be noted that a direct comparison between the
fragilitycurves derived with these two approaches is not reliable;
despitethe same intensity measure type being displayed on the x
axis, theycorrespond to different optimal periods (Topt) and the
geometricmean between the spectral acceleration of the two
horizontal com-ponents is used in the 3D analyses, whilst the
spectral accelerationCornell [37] was tested on the precast
structures. The IMpw com-bines the Sa for different spectral
periods selected a priori in the fol-lowing way:
IMpw Sasa SasbSasa b Sasc
Sasa c
where sa; sb and sc are T1, 150% of T1 and 200% of T1
respectively,and T1 stands for the rst period of vibration. In the
original pro-posal, the period of the rst vibration mode (T1), was
computedfor the elastic period. However, during the various
analyses withinthis study, it was observed that the yielding period
provided a con-siderably better performance, and so it was used
instead of the elas-tic period. The comparison between the IMs
explored so far, shownin Figs. 2.8 and 2.10, reveals the good
performance of spectral quan-tities with respect to PGA and the
similar effect of Sa(Topt) and IMpwon the dispersion reduction.
Other IMs were tested, such as Arias Intensity and
Cumulative
uctures 94 (2015) 122136 131from a single direction is used in
the 2D analyses. These functionswould need to be applied within a
complete loss assessment exer-cise in order to fully appreciate the
difference between them.
-
R2 R2LS1 = 0.89 LS2 38.0= LS1 = 0.88 LS2 = 0.84
0 100 200 300 400 5000
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Sa (Topt) [cm/s2]
Prob
abili
ty o
f Exc
eeda
nce
LS1LS2yieldingcollapse
0 50 100 150 200 250 300 350 4000
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
IMpw [cm/s2]
Prob
abili
ty o
f Exc
eeda
nce
LS1LS2yieldingcollapse
R2 R2
Fig. 2.10. Fragility curves for T1-PC-2 and corresponding
correlation coefcients R2 as a function of IM used: Sa(Topt)
(left), IMpw (right). Only exural collapse fragility curvesare
compared.
0 200 400 600 800 1000 12000
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Sa(Topt) [cm/s2]
Prob
abili
ty o
f Exc
eeda
nce
LS1LS2yieldingcollapse
0 200 400 600 800 1000 12000
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Sa(Topt) [cm/s2]
PoE
Colla
pse
friction = 0.2Data 0.2friction = 0.3Data 0.3
0 100 200 300 400 500 6000
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Sa(Topt) [cm/s2]
Prob
abili
ty o
f Exc
eeda
nce
LS1LS2yieldingcollapse
0 100 200 300 400 500 6000
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Sa(Topt) [cm/s2]
PoE
Colla
pse
friction = 0.2Data 0.2friction = 0.3Data 0.3
Fig. 3.1. Probability of exceedance derived in a 2D framework
(top) and in a 3D framework (bottom) considering the vertical
acceleration component. T1-PC-2 yielding andexural collapse
fragility curves (left), exural and connection collapse curves
(right) for the two friction coefcients.
132 C. Casotto et al. / Engineering Structures 94 (2015)
122136
-
3.2. Discussion connection capacity could be exceeded, but the
beam could stillnot be unseated because of its limited sliding
displacement. The
Table 3.1Results from the 2D and 3D approaches considering the
vertical acceleration. Median (h) and logarithmic standard
deviation (r), and coefcient of correlation (R2) of each
fragilityfunction using friction coefcient of 0.2 and an intensity
measure of Sa(Topt) in cm/s2.
Typology 2D 3D
LS1 LS2 LS1 LS2
Topt h r RLS12 h r RLS22 Topt h r RLS12 h r RLS22
T1-PC-2 0.8 216 0.59 0.84 376 0.55 0.86 2.3 44 0.56 0.94 128
0.26 0.93T1-LC-4 1.6 96 0.48 0.88 306 0.42 0.83 2.3 44 0.53 0.91
133 0.39 0.88T1-LC-7 0.8 276 0.46 0.88 609 0.56 0.81 1.4 112 0.41
0.93 277 0.55 0.66T1-LC-10 0.8 302 0.38 0.93 392 0.53 0.87 0.7 258
0.49 0.84 403 0.52 0.90T2-PC-2 1.7 79 0.51 0.89 166 0.54 0.74 2.2
38 0.52 0.91 125 0.23 0.91T2-LC-4 1.7 80 0.47 0.90 255 0.39 0.86
2.3 43 0.46 0.94 121 0.34 0.88T2-LC-7 0.8 240 0.46 0.88 554 0.45
0.80 1.4 99 0.37 0.96 235 0.47 0.64T2-LC-10 0.8 270 0.41 0.93 379
0.51 0.86 0.7 221 0.48 0.78 422 0.46 0.78
C. Casotto et al. / Engineering Structures 94 (2015) 122136
133It is clear from the comparison between collapse fragility
curveswith and without consideration of connection failure in Fig.
3.1that connection collapse is an important issue that cannot
beneglected and has to be addressed carefully. Connection
failureoccurs only if the shear demand on the top of the column
exceedsthe shear capacity of the connection and the beam unseats
fromthe column support. This is the case only if the column is able
tocarry and transmit a force equal to or larger than the
connectionresistance, according to the hierarchy of the capacities.
This isthe reason why connection collapse is much more frequent
instructures with friction-based connections or in the frames
withstiff columns designed for higher lateral forces. Moreover, the
cho-sen method used to evaluate this particular failure mechanism
caninuence the results considerably.
In the rst methodology, connection failure is estimated basedon
constant column capacity and constant connection
capacity(proportional to the initial axial load reduced by 40%).
The baseshear, when the connection capacity is reached in at least
one col-umn, is found on the pushover curve and dened as the
connectioncollapse limit state, represented in Fig. 3.2 by a
horizontal dottedline. Connection collapse mechanism is thus
evaluated at thebeginning of the pushover analysis as the base
shear at whichthe pushover curve of the structure exceeds the
connection col-lapse limit state (Fig. 3.2 left). This method does
not consider thepossibility that the column capacity could be very
close to the con-nection capacity (Fig. 3.2 right) and it could
easily exceed it duringan acceleration time-history, where both the
capacities vary withthe vertical acceleration. Similarly it does
not consider that the
1400 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.040
20
40
60
80
100
120
Top Drift [%]
Bas
e Sh
ear [
kN]
pushoverLS1LS2LS connection
Fig. 3.2. Connection collapse limit state denition: 2D with
constant connection resistapresenting connection collapse limit
state (right).connection collapse is thus almost independent of the
seismicinput, because the connection limit state is set a priori
with thepushover analysis and it nearly corresponds to the yielding
limitstate, easily attained by weak ground motions. This is why
forthose typologies signicantly affected by connection failure
thecollapse fragility curve can be even more fragile than the
yieldingcurve (see Fig. 2.7). The difference in the response
betweenpresenting and not presenting connection collapse limit
state isdrastic (in the former case failure can occur even before
thebuilding reaches yielding), and therefore it generates a large
scatterin the fragility curves. Furthermore, when following this
methodol-ogy the number of frames with connection collapse
mechanism isvery sensitive to the friction coefcient. Given the
largeuncertainty in the friction coefcient denition, the
consequentimpact on the fragility curves, and especially the
excessive fragilityof collapse curves with respect to yielding
curves, as discussedpreviously, this method was considered
unreliable and it was thusdiscarded.
In the methods where the connection capacity is affected by
thevertical component of the acceleration and the unseating of
thebeam is considered, the aforementioned issue is overcome
byassessing connection collapse when the shear demand time-his-tory
crosses the connection resistance time history and the
slidingdisplacement of the beam exceeds the support length (Fig.
3.3). Inthis case, the friction coefcient seems to have a smaller
impact,because the connection collapse mechanism is now sensitive
tothe vertical component of the ground motion record, and the
tran-sition between collapse fragility curves calculated using
different
1400 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.040
20
40
60
80
100
120
Top Drift [%]
Bas
e Sh
ear [
kN]
pushoverLS1LS2
nce method. Frame presenting connection collapse limit state
(left) and frame not
-
functions. It can be observed in Fig. 3.5 that the value at 50%
of
0.8
ce
Fig. 3.5. Empirical cumulative frequency of occurrence vs Sa(T =
1sec) (Minghiniet al. [40]).
Strlevels of friction coefcient is smoother, as shown previously
inFig. 3.1.
3.3. Comparison with eld data
In order to have an initial consistency check on the reliability
ofthe results obtained herein, a rst comparison with data from aeld
survey of 1133 precast industrial buildings after the 2012Emilia
Romagna earthquakes has been performed. Empirical fragi-lity curves
were derived by Minghini et al. [40] in terms of the lar-gest
between the two horizontal components of Sa at 1 s, for threedamage
states: no damage (D0), slight damage/moderate damage(D1 + D2),
severe damage/heavy damage/collapse (D3 + D4 + D5).In the study by
Minghini et al. [40] the surveyed buildings arenot classied
according to the age of construction or the geometrictypology,
therefore a single fragility function is available for
thecomparison.
Given the features of the empirical curves the following
modi-cations on the analytical method used were needed to
harmonise
0 5 10 15 20 25 30 3530
20
10
0
10
20
30
40
Force [kN]
Tim
e [s
]
Connection Shear CapacityShear Demand
Fig. 3.3. Connection collapse limit state denition: 2D
environment with connec-tion capacity based on the vertical
acceleration component.
134 C. Casotto et al. / Engineeringthe damage scales and the
building typologies:
Collapse limit state (LS2), dened herein as exural or
connec-tion failure, was considered equivalent to the onset ofD3 +
D4 + D5 in Minghini et al. [40] (though it is recognised thatDS5
would have been a better damage state for comparison pur-poses, had
the results for this damage state been available).
A single DPM was assembled summing up the number of build-ings
in each damage state resulting from the dynamic analysisrun for the
typologies considered appropriate for EmiliaRomagna, the Italian
region where the damaged data weretaken from. Considering that the
Emilia Romagna region wasclassied as seismic only in 2003, the
pre-code typology (PC-2) and the low-code typology with the minimum
design lateralload (LC-4) were thought to better represent the
building pop-ulation of the area. Both geometrical congurations
wereincluded with equal weight in the total DPM, given that
thedamage data do not contain this type of information.
A regression analysis was run on the total DPM obtained, usingas
intensity measure the largest value between the two hori-zontal
components of Sa at 1 s.
Fig. 3.4 shows the resulting fragility function for a single
typol-ogy using the 2D modelling environment, whose median is 0.56
gfor LS2, while Fig. 3.3 represents the discrete empirical
fragility0 100 200 300 400 500 600 700 8000
0.1
0.2
0.3
0.4
0.5
0.6
0.7
Sa (1sec) [cm/s2]
Prob
abili
ty o
f Exc
eeda
n
LS1LS2yieldingcollapse
Fig. 3.4. Analytical fragility function for a single typology
using the 3D modellingenvironment.0.9
1
uctures 94 (2015) 122136the cumulative frequency of occurrence
is 0.42 g; in the case ofthe highest damage state this value
corresponds also to the medianof the probability of exceedance. In
order to evaluate this compar-ison it must be considered that the
buildings damaged in theEmilia region were subjected to at least
two strong earthquakes,and thus the nal damage states observed in
some structuresmight have been due to cumulative damage. Hence, the
Minghiniet al. [40] fragility functions might present lower median
valuesthan would be expected for these structures under a single
event.Furthermore, the DS3 + DS4 + DS5 damage state from Minghiniet
al. [40] includes structures that have not collapsed, and so
againthis data is expected to produce lower median values than
wouldbe expected for collapsed buildings alone. Hence, it is
reassuringthat the median fragility functions presented herein
producehigher median values compared to the observed damage
data,but further conclusions cannot be drawn given the large
numberof approximations in the comparison.
4. Conclusions
The aim of this study was to develop a robust methodology
toderive fragility curves for precast RC industrial buildings. A
largeportion of the RC industrial buildings were designed
essentiallyfor static horizontal loads and with simply supported
beam
-
[10] Decreto Ministeriale 3 marzo 1975. Approvazione delle norme
tecniche per le
g Strcolumn joints, and could thus be particularly vulnerable to
thedynamic input from earthquakes. In the current literature
thereseems to be limited experience in the fragility assessment of
suchstructures, and for this reason it is important to investigate
howinevitably necessary simplications in structural modelling
andfragility methodology, commonly applied to regular
cast-in-placebuildings, may or may not inuence the fragility
assessment ofthese precast buildings.
A set of fragility curves has thus been developed,
consideringthe main characteristics of these structures: the weak
beamcolumn connections, which is the principal cause of total
collapseof the building due to loss of support of the beams, even
for mod-erate earthquakes. The variability in the fragility curves
withrespect to the simplications in modelling and type of
analysiswas studied, through the application of a nonlinear
dynamicprocedure in three different manners: in a 2D environment
wherethe frames were tested against horizontal accelerograms only
intheir main direction and the inuence of the vertical
accelerationwas simulated by reducing the axial load by 40%
(Bolognini et al.[4]); in a 2D environment considering the vertical
input of theground motion records; and nally in a 3D environment
where allthe three components of the earthquake records were
considered.Connection failure was explicitly accounted as a
collapse limit state.
The comparison between collapse fragility curves with andwithout
consideration of connection failure demonstrated theimportance of
considering connection collapse mechanism andrepresenting it
robustly. In fact, the outcomes of the 2D analysiswithout vertical
acceleration highlighted some drawbacks regard-ing the connection
failure determination. This approximatemethod rendered the collapse
fragility curves more sensitive tothe friction coefcient used to
compute the connection capacityrather than to the ground motion
intensity. Given the large uncer-tainty in the denition of the
friction coefcient and the drasticchanges in the fragility curves
corresponding to small variationsof this parameter, this method was
discarded. When applying avertical acceleration in the dynamic
analyses both in the 2D and3D framework, the transition between
different levels of frictioncoefcient was much smoother. In order
to be conservative, thenal fragility curves were computed using a
friction coefcient of0.2, but it is underlined that this parameter
requires furtherresearch and calibration.
A direct comparison between the 2D and 3D approaches
withvertical acceleration is not straightforward, due to the
dis-crepancies in the IMs and structural aspects considered
withineach approach. However, the results from this study seem to
indi-cate that a higher fragility is obtained when considering the
threecomponents of the earthquake record. The actual
differencesbetween the 2D and 3D approaches can only be
appreciatedthrough the employment of the respective fragility
functions in acase-study risk assessment application, which will be
carried outas a further development of this work.
A deeper understanding of the structural aspects involved in
thefragility assessment of this specic type of structure has
beenreached herein. Particular attention has been paid to the
connec-tion collapse phenomenon, and the importance of the
selectionof the proper methodology to assess it accurately has
beendemonstrated.
Finally, a preliminary comparison has been performed withdamage
data from eld surveys of the 2012 Emilia Romagna earth-quakes and a
good agreement between the analytical and empiri-cal functions was
observed despite the inevitable approximationsin the harmonisation
of the empirical and analytical data.
It can be concluded that a sound set of fragility functions
for
C. Casotto et al. / EngineerinItalian industrial precast
buildings is now available for earthquakeloss assessment, which
could be employed for the development ofseismic risk mitigation
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The authors would like to thank the Seismic Risk PreventionArea
of Tuscany Region, who kindly shared their database regard-ing the
geometrical properties of the industrial structures. Theauthors are
very grateful for the valuable contribution of DavideBolognini,
whose expert advice on Italian precast structures ismost
appreciatively acknowledged. The authors are also verygrateful to
Anze Babic, Manya Deyanova and Matjaz Dolek for dis-cussions and
input on the seismic behaviour of RC precast indus-trial buildings
which helped improve the collapse limit statemodelling used herein.
The authors would like to express theirgratitude for the comments
and the suggestions of the reviewers,that helped to improve
signicantly the quality of the paper.Finally, the authors would
like to acknowledge the support pro-vided by the European
Commission under FP7 through the nanc-ing of the STREST research
programme, under the framework ofwhich this work has been partially
funded.
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136 C. Casotto et al. / Engineering Structures 94 (2015)
122136
Seismic fragility of Italian RC precast industrial structures1.
Introduction2. Fragility curve methodology3. Proposed fragility
functions4. ConclusionsAcknowledgementsReferencesWeb References
