-
Seismic Vulnerability Assessmentof Reinforced Concrete
Buildings
Using Hierarchical Fuzzy RuleBase Modeling
Solomon Tesfamariam,a) M.EERI, and Murat Saatcioglu,b)
M.EERI
A reliable building vulnerability assessment is required for
developing arisk-based assessment and retrofit prioritization.
Tesfamariam and Saatcioglu(2008) proposed a simple building
vulnerability module where the buildingperformance modifiers are in
congruence with FEMA 154. This paper is anextension of the building
vulnerability assessment that include detailedperformance modifier
in congruence with FEMA 310 that is represented in aheuristic based
hierarchical structure. Some of the input parameters areobtained
through a walk down survey and are subject to vagueness
uncertaintythat is modelled through fuzzy set theory. A knowledge
base fuzzy rule basemodeling is developed and illustrated for
reinforced concrete buildingsdamaged in the 1 May 2003 Bingl,
Turkey earthquake.DOI: 10.1193/1.3280115
INTRODUCTION
Seismic risk analysis of reinforced concrete (RC) buildings can
be undertaken byintegrating site seismic hazard, building
vulnerability, and importance/exposure factor.Tesfamariam and
Saatcioglu (2008) have proposed a simple hierarchical risk
assessmenttool that incorporates building performance modifiers in
congruence with FEMA 154(2002). This paper is an extension of the
building vulnerability module by incorporatingelaborate structural
deficiencies as specified in FEMA 310 (1998; Table 1).
Discussionand implementation of the overall risk assessment, by
considering site seismic hazardand building importance/exposure are
outside the scope of this paper, and are providedin Tesfamariam and
Saatcioglu (2008).
The interactions between the structural deficiencies provided in
Table 1 are complex,and often full-fledged nonlinear structural
analysis is performed. However, the complex-ity of building
vulnerability assessment can be handled through a system based
ap-proach. A system is defined as an assemblage of components
acting as a whole(Meirovitch 1967). Building structures are
essentially an assemblage of different com-ponents, e.g., beams,
columns, slabs, and hence they can be described as a system.
Each
a) Assistant Professor, School of Engineering, The University of
British Columbia | Okanagan, 3333 Universityway, Kelowna, BC,
Canada, V1 V 1V7, Tel: (250)-807-8185, E-mail:
[email protected]
b) Professor and University Research Chair, University of
Ottawa, Ottawa, Ontario Canada K1A 0R6, Tel:(613)-562-5800 ext
6129; Fax: (613)-562-5173, E-mail: [email protected]
235
Earthquake Spectra, Volume 26, No. 1, pages 235256, February
2010; 2010, Earthquake Engineering Research Institute
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236 S.TESFAMARIAM AND M. SAATCIOGLUsystem in turn encapsulates
different subcomponents and be described as a subsystem.In this
paper, a heuristic based building vulnerability assessment
hierarchical structure isproposed and illustrated in Figure 1.
Seismic risk assessment and decision making is subject to
uncertainty (Wen et al.2003). Klir and Yuan (1995) have broadly
categorized uncertainty into vagueness andambiguity. The vagueness
(imprecision) refers to lack of definite or sharp
distinction,whereas ambiguity is due to unclear distinction of
various alternatives, which is furtherdivided into discord
(conflict) and non-specificity. In a walk down survey, for
example,
Table 1. Summary of building performance modifiers of FEMA 310
(1998)
C1: Concrete Moment Frames Basic structural checklist
Supplementary structural checklist
Building system Load pathAdjacent buildingsMezzaninesWeak
storySoft storyGeometryVertical
discontinuityMassTorsionDeterioration of concretePost-tensioning
anchors
Lateral force resisting system Redundancy Flat slab
framesInterfering walls Prestressed frame elementsShear stress
check Short captive columnsAxial stress check No shear failures
Strong column/weak beamBeam barsColumn-bar splicesBeam-bar
splicesColumn-tie spacingStirrup spacingJoint reinforcingJoint
eccentricityStirrup and hooksDeflection compatibilityFlat slabs
Connections diaphragms Concrete columns Lateral load at pile
capsDiaphragm continuityPlan irregularityDiaphragm reinforcement
atopeningsthe evaluation is performed by an expert and the
information is readily provided in lin-
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SEISMIC VULNERABILITY ASSESSMENT OF REINFORCED CONCRETE
BUILDINGS 237guistic terms (e.g., compliant, noncompliant). As a
result, this type of assessment isprone to subjective judgments
(Hadipriono and Ross 1991) and vagueness uncertaintydominates the
evaluation process. The uncertainty resulted from imprecision and
vague-ness can be handled through the fuzzy set theory (Zadeh
1965).
FUZZY RULE BASE MODELING
The basic theory of fuzzy sets was first introduced by Zadeh
(1965) to deal with thedifficulties in quantifying the uncertainty
where human intervention was significant. Afuzzy set describes the
relationship between an uncertain quantity x and a
membershipfunction x, which ranges between 0 and 1. A fuzzy set is
an extension of the traditionalset theory (in which x is either a
member of set A or not) in that an x can be a memberof set A with a
certain degree of membership x. Fuzzy logic maps qualitative
judgementinto numerical reasoning. The strength of fuzzy logic is
that it can integrate descriptive(linguistic) judgement and
numerical data and use approximate reasoning algorithms topropagate
the uncertainties.
Details of the fuzzy rules and aggregation process are provided
in Tesfamariam andSaatcioglu (2008). However, sufficient details
required for the subsequent discussion areprovided below.
MEMBERSHIP FUNCTIONS-FUZZIFICATION
The basic input parameters have a range of values that is knows
as a universe ofdiscourse; say for vertical irregularity values may
range between 0 to 100%. These val-ues can be grouped into a
linguistic quantifiers; e.g., low (L), medium (M), and high(H). The
process of assigning these linguistic values can be viewed as a
form of datacompression, which is known as granulation (Zadeh
1994). The fuzzification processconverts the input values into a
homogeneous scale by assigning corresponding mem-berships x with
respect to their specified granularities (e.g., L, M, H).
Membershipfunction essentially embodies knowledge base in the fuzzy
system, and is a crucial partof the fuzzy base modelling. At each
level of the hierarchy (Figure 1), three-tuple mem-
Level3
Level4
Building vulnerability
Weakstory
Increase in demand Decrease in resistance
Structural degradation/weakening
Planirregularity
Shortcolumn
Year ofconstruction
CorrosionDamaged fromprevious EQ.
Codeenforcement
Year ofconstruction
Designquality
Problems ofadjacency
Floorelevation
Spacing b/nadjacent buildings
Verticalirregularity
Softstory
Relative strengthat joints
Walls
Structuralwalls
Masonrywalls
Re-entrantcorners
Diaphragmcontinuity
Redundancy Constructionquality
Diaphragms JointsColumnsTorsionalirregularity
Level 1
Level 2
Figure 1. Detailed RC buildings vulnerability assessment.
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238 S.TESFAMARIAM AND M. SAATCIOGLUbership values are used.
Different methods of assigning membership values or functionsto a
fuzzy variable are available (Ross 2004), and herein a heuristic
based method isused.
FUZZY RULE BASEAND INFERENCING
For linguistic consequent parameters, Mamdani-type inferencing
can be used (Mam-dani 1977). Mamdanis inference mechanism consists
of three connectives: the aggrega-tion of antecedents in each rule
(AND connectives), implication (i.e., IF-THEN connec-tives), and
aggregation of the rules (ALSO connectives). The IF-THEN rules can
beestablished as
Ri: IF x1 is Ai1 AND x2 is Ai2 THEN y is Bi, i = 1, . . . ,n
1Thus, for each level of the hierarchy, a fuzzy rule base (FRB) has
to be established.
Given the rule base and corresponding fuzzification, fuzzy
inferencing is performed us-ing Equation 1.
DEFUZZIFICATION
At each level of the hierarchy, the fuzzy output is converted
into a crisp numberthrough a process of defuzzification. Several
techniques are available for defuzzification,e.g., Center of Area,
Center of Maxima and Mean of Maxima (Klir and Yuan 1995). Inthis
paper, the weighted average method is used (Ross 2004):
z* =
i=1
N
ix x
i=1
N
ix
2
where z* is the defuzzified value, x the universe of discourse
for the specified input pa-rameter, and ix are the three-tuple
fuzzy numbers.
HIERARCHICAL FUZZY RULE BASE MODELING
In a fuzzy based modeling, increase in number of input
parameters results in an ex-ponential increase in the number of
rules. This is described as a curse of dimensionality,and causes
problems in computational efforts, real time performance, and
system defi-nition (Torra 2002). Several alternatives have been
presented to deal with the curse ofdimensionality. These include;
i) identification of functional relationships, ii) sensory fu-sion,
iii) rule hierarchy, and iv) interpolation (Torra 2002). The rule
hierarchy decom-poses at the level of rules, whereas Magdalena
(2002) showed decomposition at the levelof variables. For example,
from Figure 1, it can be shown that increase in demand (Level2)
have five inputs; walls, relative strength at joints, vertical
irregularity, redundancy, andplan irregularity (Level 3). Using a
three-tuples fuzzy number, the required numbers ofrules are 35=243.
However, a rule hierarchy shown in Figure 2 can be developed by
con-
sidering the functional relation of each performance modifier,
consequently the required
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SEISMIC VULNERABILITY ASSESSMENT OF REINFORCED CONCRETE
BUILDINGS 239number of rules is reduced to 832=72. The rule bases
shown in Figure 2 are, R1 to R3, andfive intermediate rules, TR1 to
TR5 (T is used to denote temporary rule). For example,
thestructural weakness in the vertical elements, weak story and
soft story are aggregatedthrough TR1. Output of TR1 is aggregated
with short column effects through R1 to obtainvertical
irregularity.
With the hierarchical rule base structure, the concept of
fuzzification and defuzzifi-cation becomes important. The
three-tuple fuzzy set output can be defuzzified to obtaina crisp
singleton value. In turn, this singleton value is fuzzified into
the next level. Witheach defuzzification step, there is a potential
for loss of information. Alternatively, thethree-tuple fuzzy sets
can be used as input to the next FRB. However, this may generatea
potential for fuzziness explosion. In general the inclusion or
exclusion of defuzzifica-tion step is the problem of finding a
trade-off between loss and explosion of fuzziness,respectively
(Torra 2002). A defuzzification step is introduced at each level of
the ag-gregation.
BUILDINGVULNERABILITY
The hierarchical structure of Figure 1 shows different
performance modifiers forbuilding vulnerability quantification.
Building vulnerability to ground shaking and asso-ciated damage can
be grouped into two categories (Saatcioglu et al. 2001); factors
con-tributing to increased seismic demand (e.g., soft story frame,
weak column-strong beam,vertical irregularities); and factors
contributing to reduced ductility and energy absorp-tion capacity
(e.g., construction quality, year of construction, structural
degradation).
Weak story
Increase in demand
Planirregularity
Short column
Verticalirregularity
Soft story
Relative strengthat jointsWalls
Re-entrantcorners
DiaphragmcontinuityRedundancy
Torsionalirregularity
TR3
R1
R2TR4
R3
TR2
TR1
TR5
Figure 2. Hierarchical fuzzy rule base decomposition for
increase in demand.The increase in demand and decrease in
resistance are inherent system properties andcan be described as
endogenous parameters. The building vulnerability can also be
af-
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240 S.TESFAMARIAM AND M. SAATCIOGLUfected through an exogenous
parameter, such as problem of adjacency. The problem ofadjacency
can simultaneously contribute to an increase in demand and decrease
in re-sistance of the affected building.
INCREASE IN DEMAND
Vertical Irregularity (VI)
The vertical irregularity parameter reflects the presence of
discontinuity and/orabrupt change in strength and stiffness along
the building height. The vertical irregulari-ties considered in
this paper are soft story (SS), weak story (WS), and short column
ef-fect (SCE). Granulation of the SS, WS, and SCE are shown in
Figure 3a3c, respec-tively. Derivation of these granulations is
discussed within each subsection.
Soft Story (SS)
Soft story (SS) is defined by stiffness of the lateral force
resisting system in anystory being less than 70% of the stiffness
in an adjacent story (above or below) or lessthan 80% of the
average stiffness of the three stories (above or below) (FEMA 310
1998;FEMA 450-1 2004). Further, FEMA 450-1 (2004) specifies that
extreme soft story issaid to exist when lateral force resisting
system in any story is less than 60%. Reported
0
0.5
1
0 20 40 60 80 100
Soft story, SSI
mem
bers
hip
, SS
LH M
0
0.5
1
0 20 40 60 80 100
Height ratio, SCE
mem
bers
hip
, SC
E LH M
0
0.5
1
0 20 40 60 80 100
Strength irregularity factor, ci
mem
bers
hip
,
ci
LH M
a) b)
c)
Figure 3. Granulation of the basic risk items for vertical
irregularity, a) soft story, b) strengthirregularity factor (weak
story), and c) height ratio (short column effect).parametric
analyses, Chintanapakdee and Chopra (2004), Das and Nau (2003),
Magliuloet al. (2002) and Al-Ali and Krawinkler (1998), for
example, have quantified the impact
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SEISMIC VULNERABILITY ASSESSMENT OF REINFORCED CONCRETE
BUILDINGS 241of SS on drift demand of the ground floor (Figure 4).
From Figure 4, it can be shownthat the soft story limits fairly
encapsulate the uniform building code (UBC) drift limitof 0.004
(0.4%). The percentage of soft story shown in Figure 4 is used for
the granu-lation of the SS (Figure 3a).
Weak Story (WS)
Weak story (WS) is defined by lateral force resisting system
strength of any story isless than 80% of the adjacent story
strength (above or below). A weak story structurewith story
strength less than 65% of the story above is prohibited (Al-Ali and
Krawin-kler 1998), and these limits are assigned based on judgment.
The weak story is far moredamaging than soft story (Al-Ali and
Krawinkler 1998). The potential for weak storycan be computed
through strength irregularity factor ci (Ministry of Public
Worksand Settlement 1998):
ci = Aei Aei+1 0.80 3where Ae=effective shear area of any
storey, and the indices i and i+1 show two adjacentfloors.
Valmundsson and Nau (1997) and Al-Ali and Krawinkler (1998),
among others,have undertaken a parametric analysis on the impact of
strength irregularity factor onductility demand, which are
summarized in Figure 5. Figure 5 shows the relative com-parison of
ductility demands of weak first story building over regular
building. FromFigure 5, it can be highlighted that for a small
strength reduction, the ductility demandis significant. Figure 5
also shows that the FEMA 310 (1998) 80% limit is not conser-vative.
The strength irregularity factor shown in Figure 5 is used for the
fuzzification ofweak story (Figure 3b).
Short Column Effect/Captive Columns (SCE)
FEMA 310 (1998) specifies that there shall be no columns at a
level with height/depth ratios less than 50% of the nominal
height/depth ratio of the typical columns at
0
1
2
3
4
5
0 0.25 0.5 0.75 1 1.25 1.5
Dri
ft(%
)Soft story
Das and Nau 2003
Magliulo et al. 2002
Al-Ali and Krawinkler 1998
Chintanapakdee and Chopra2004
Softsto
ry
ExtremeSoftsto
ry
UBC Limit
Figure 4. Soft story and corresponding drift limits.
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242 S.TESFAMARIAM AND M. SAATCIOGLUthat level for life safety
and 75% for immediate occupancy. Das and Nau (2003) haveperformed
parametric analysis on the impact of short column effect on the
sheardemand/capacity ratio, and the results are illustrated in
Figure 6. The Das and Nau(2003) results corroborate the FEMA 310
(1998) Life safety and Immediate Occupancyperformance limits. The
nominal height/captivated open space ratio is used in the
fuzzi-fication of short column effect (Figure 3c).
Relative Strength at Joints Weak Column-Strong Beam (RSJ)
The current capacity design practice dictates the strong column
and weak beam de-sign. This design practice ensures that a plastic
hinge is formed at the beam, which willenable the system to absorb
the demand, and minimize the load transferred to the col-umns. From
a field visual observation, the impact of relative strength at
joints can lin-guistically be assessed and corresponding
fuzzification is provided in Table 2.
0.0
1.0
2.0
3.0
4.0
5.0
6.0
0 0.25 0.5 0.75 1
Ductility
dem
and
ratio
strength irregularity factor (ci)
Valmundsson andNau1997
Al-Ali and Krawinkler 1998
Weaksto
ry
Figure 5. Weak story and corresponding ductility demand
ratio.Figure 6. Impact of short column effects on the maximum shear
demand/capacity.
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SEISMIC VULNERABILITY ASSESSMENT OF REINFORCED CONCRETE
BUILDINGS 243Redundancy
Structural redundancy of a building can be defined as the number
plastic hinges ofthe structural system that must yield or fail to
produce collapse (Bertero and Bertero1999). zcebe et al. (2003)
have quantified measure of redundancy through a normal-ized
redundancy ratio nrr:
nrr =Atrfx 1fy 1
Agf4
where fx, fy=number of continuous frame lines in the critical
story in x and y directions,respectively; Atr=the tributary area
for a typical column; Atr is taken as 25 m
2 if fx and fy areboth greater than or equal to 3. In all other
cases, Atr is taken as 12.5 m
2.
The nrr values computed from the Dzce Database 1 and plotted in
Figure 7a. Figure7a show that with increase in observed damage, the
nrr values decrease. The nrr valuesare used for the fuzzification
of redundancy (Figure 7b).
Table 2. Fuzzification of relative strength at jointsand
re-entrant corners
Relative Strength at Joints L M H
Negligible 0.9 0.1 0Low 0.7 0.3 0Moderate 0 0.5 0.5High 0 0.3
0.7Significantly high 0 0.1 0.9
0
0.2
0.4
0.6
0.8
1
1.2
0 2 4 6
Damage
nrr
0
0.5
1
0 0.5 1 1.5 2
Normalized redundancy ratio, nrr
mem
bers
hip
,
nrr
LH M
a) b)
Figure 7. Quantification of redundancy a) normalized redundancy
ratio, b) granulation of nor-malized redundancy ratio.1 SERU,
Middle East Technical University, Ankara, Turkey; Archival Material
from Dzce Database located atwebsite
http://www.seru.metu.edu.tr.
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244 S.TESFAMARIAM AND M. SAATCIOGLUPlan Irregularity (PI)
Three basic parameters are used to quantify plan irregularity
(PI): torsional irregu-larity, diaphragm continuity, and plan
building shape.
Torsional Irregularity (TI)
Torsional irregularity is introduced due to the lack of symmetry
in plan, e.g., varia-tion in perimeter strength-stiffness, false
symmetry and mass eccentricities, which willinduce torsional
induced force. FEMA 450-1 (2004) indicates that torsional
irregularityand extreme torsional irregularity exist when the
computed maximum story drift (in-cluding accidental torsion) at one
end of the structure is more than 1.2 and 1.4 times,respectively,
of the average of the story drift. These threshold values are used
in thefuzzification of torsional irregularity (Figure 8a).
Diaphragm Continuity (DC)
FEMA 450-1 (BSSC 2004) indicated that diaphragm discontinuity is
said to existwhen diaphragms have abrupt discontinuities or
variations in stiffness. Abrupt disconti-nuity is said to exist
with the presence of a cut-out or open areas that is 50% of
thegross enclosed diaphragm area and variation in stiffness is said
to exist when there is achanges in effective diaphragm stiffness of
more than 50% from one story to the next. Thisproblem is more
severe with flexible diaphragms (Masi et al. 1997). Thus, in this
paper, forrigid diaphragms, diaphragm action is neglected. For the
flexible diaphragms, the cut-out oropen areas are used in the
fuzzification of diaphragm continuity (Figure 8b).
Re-Entrant Corners (REC)
The shape of the building has an effect on the vulnerability of
plan layout to seismicloads. Different symmetrical shapes (both in
x and y direction) of buildings can be used(, ). However,
re-entrant corner buildings having irregular shapes (L, T, U, H,
+),may be prone to torsion and stress concentration. FEMA 450-1
(BSSC 2004) indicates
0
0.5
1
0 0.5 1 1.5 2
Torsional irregularity, TI
mem
bers
hip
, TI
L HM
0
0.5
1
0 20 40 60 80 100
Diaphragm continuity, DC
mem
bers
hip
, D
C
LH M
a) b)
Figure 8. Granulation of the basic risk items used in a plan
irregularity, a) torsional irregularity,and b) diaphragm
continuity.that irregularity due to re-entrant corners is said to
exist when projection of the structure
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SEISMIC VULNERABILITY ASSESSMENT OF REINFORCED CONCRETE
BUILDINGS 245beyond a re-entrant corner is greater than 15% of the
plan dimension of the structure inthe given direction. Linguistic
assessment and fuzzification of re-entrant corners are pro-vided in
Table 2.
Walls
The moment-resistant frames resist lateral forces by bending and
shearing of col-umns and beams, which are connected by moment
connections. The columns are respon-sible for overall strength and
stability and hence are critical elements. Performance ofbare frame
RC buildings is often modified through the use of structural walls.
Thesestructural walls can be categorized under structural (or
shear) walls and masonry walls.
Shear walls resist seismic forces almost entirely when used in
buildings. They typi-cally act as vertical cantilevers and provide
lateral bracing to the system, while receivinglateral forces from
diaphragms and transmitting them to the foundation. Shear
wallstructures have been reported to behave well under moderate to
strong earthquake exci-tations (Saatcioglu et al. 2001).
Many older frame buildings include masonry infill panels. Though
unreinforced ma-sonry behaves in a brittle manner and is regarded
as undesirable construction materialfor seismically active regions,
they may act as shear walls in controlling deformations,and may
save non-ductile concrete frames until their elastic limit is
exceeded. Therehave been many cases of non-ductile frames that have
survived strong earthquakes dueto the participation of masonry
infill walls, especially when the wall-to-floor area ratio
ishigh.
From the walk down survey, the structural wall is linguistically
evaluated and thecorresponding fuzzification is shown in Table
3.
DECREASE IN RESISTANCE (DR)
Construction Quality (CQ)
Quality of construction and material used is detrimental to
ensuring the intended de-sign protection is in place. Examples of
poor construction quality are: construction er-ror; improper
construction procedures; lack of anchorage of beam and column
reinforce-ment; poor concrete quality. Dimova and Negro (2005) have
performed experimental
Table 3. Fuzzification of structural walls
Structural walls L M H
Bare frame 0 0.1 0.9Lightly reinforced masonry walls 0 0.3
0.7Heavily reinforced masonry walls 0.7 0.3 0Lightly reinforced
shear walls 0.5 0.5 0Heavily reinforced shear walls 0.9 0.1 0work
to quantify the influence of construction deficiencies on the
seismic response ofstructures. They constructed two identical
buildings where one was built with proper
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246 S.TESFAMARIAM AND M. SAATCIOGLUconstruction design and
detailing, and other building with construction deficiencies. Asa
result of these deficiencies, the yield displacement and
corresponding base shear forcehas decreased by 27% and 12%,
respectively. Similarly, ultimate story displacement andmaximum
base shear force are reduced by 34% and 22%, respectively.
The construction quality is qualitatively determined and the
corresponding fuzzifi-cation is shown in Table 4.
Design Quality (DQ)
Design quality is introduced to encapsulate the level of
detailing considered in seis-mic design. Irrespective of the year
of construction and in situ construction practice, thelevel of
design quality may be detrimental to the building survivability
under earth-quake. Proper design quality of the columns and/or
shear walls, joints, and diaphragmsensures better resistance to
seismic loads.
The design quality is qualitatively determined linguistically
and the correspondingfuzzification is shown in Table 4.
Year of Construction (YC) and Code Enforcement (CE)
During the initial site investigation, the original design
drawings may not be readilyavailable. The YC can be used to infer
important information about the seismic designcode provision and
consequently information about ductility, strength and detailing.
Thetransformation and fuzzification of YC is discussed in
Tesfamariam and Saatcioglu(2008). However, as it was observed from
different reconnaissance reports (e.g., Turkey,China), lack of code
enforcement (CE) is prevalent. This necessitates consideration
ofboth the YC and CE. The linguistic descriptors and corresponding
fuzzification for CEare shown in Table 5.
Table 4. Fuzzification of construction quality and de-sign
quality
Construction quality L M H
Poor 0 0.1 0.9Moderate 0 0.5 0.5Good 0.9 0.1 0
Table 5. Fuzzification of Code enforcement
Code enforcement L M H
Lenient 0 0.1 0.9Moderate 0.3 0.5 0.2
Stringent 0.9 0.1 0
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SEISMIC VULNERABILITY ASSESSMENT OF REINFORCED CONCRETE
BUILDINGS 247Structural Degradation andWeakening
Damage from Previous Earthquake (DPE)
Buildings damaged and repaired from previous earthquakes are
prone to the sametype of damage (Penelis and Kappos 1997), due to
substandard repair. Thus, in the walkdown survey and previously
logged information, one of the information collected is thelevel of
damage incurred from previous earthquakes and the corresponding
repair andupgrade performed. The linguistic parameters used to
quantify the severity of damageand corresponding fuzzification are
summarized in Table 6.
Deterioration (Corrosion)
Seismic evaluation is often carried out under the assumption
that the structural com-ponents are sound and attention is given to
detailing and other structural deficiencies.Nevertheless,
structures exposed to deleterious environmental conditions, e.g.,
parkinggarages, are prone to deterioration with time. Consequently,
capacity of structural ele-ments may be compromised and the
building can be severely damaged under moderateseismic load. For
seismic resistance, the criticality of each element may be ranked
asbeams/girders, columns and joints, in an increasing order. The
linguistic descriptors andcorresponding fuzzification are shown in
Table 7.
Problem ofAdjacency
Problem of adjacency is said to exist when two adjacent
buildings with differentfloor levels and small separation distances
are subject to seismic loads. When the floor
Table 6. Damage from previous earthquake
Damage fromprevious earthquake Description L M H
Severe Severely damaged and standard repair 0 0.3 0.7Moderate
Moderate damage and standard repair 0.3 0.5 0.2Negligible Any type
damage and high standard repair, or no
damage0.9 0.1 0
Table 7. Damage due to deterioration
Deterioration (corrosion) L M H
Extremely severe 0 0.1 0.9Severe 0 0.3 0.7Moderate 0.3 0.5
0.2Good 0.7 0.3 0
Extremely good 0.9 0.1 0
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248 S.TESFAMARIAM AND M. SAATCIOGLUheights of the two adjacent
buildings do not coincide, differences in dynamic responsegenerate
impact loads on the adjacent building columns that can introduce
discontinui-ties of the lateral force resisting system. FEMA 310
(1998) specifies that buildings ofsame height, with matching floor
levels are exempt from this analysis. Thus, the poten-tial for
pounding between two adjacent buildings is determined by
considering floor el-evation level and spacing between adjacent
buildings. A 4% spacing limit threshold isspecified for Life Safety
and Immediate Occupancy (FEMA 310 1998), which is used inthe
fuzzification of problem adjacency (Figure 9) and linguistic
constants are used forthe fuzzification of floor elevation is
provided in Table 8.
CASE STUDY
On 1 May 2003, the city of Bingl, Turkey, was struck with an
earthquake momentof magnitude Mw=6.4, with a consequent 168
casualties, 520 injury and several buildingdamages. The total
economic loss to the Turkish national economy was estimated to be
over400 million U.S. dollars (Dogangn 2004). The observed damage
level is classified into five
Figure 9. Granulation for spacing between two adjacent
buildings.
Table 8. Fuzzification of relative height of slabs
Spacing between twocorresponding slabs Description L M H
Same level Slabs of two adjacent buildings are at thesame
level
0.9 0.1 0
Slightly different Slabs are slightly off the same level, and
notat mid height
0.2 0.3 0.5
Mid height Slab of one building is at mid height of theadjacent
building
0 0.1 0.9
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SEISMIC VULNERABILITY ASSESSMENT OF REINFORCED CONCRETE
BUILDINGS 249discrete states: none ND, light LD, moderate MD,
severe SD, and collapse CD. Defi-nition of each damage state is
summarized in Table 9. Summary of the Bingl Database 2 isgiven in
Table 10.
The performance indicators shown in Figure 1 are collated from
the Bingl Databaseand other reported studies (Yakut 2004). The
performance indicators are synthesized andsummaries are plotted in
Figures 10 and 11. The field reconnaissance reports for the
per-formance indicators shown in Figures 10a and 10d are provided
at five discrete scales,{1, 2, 3, 4, 5}, where 1 and 5 correspond
to ND and CD, respectively.
Figures 10a10c show the building performance modifiers for NRR,
WCSB, and thepresence of corrosion, respectively. As expected, with
increasing level of observed dam-age the three modifiers show a
decreasing trend. Figure 10d shows the potential forpounding,
however, the observed damage shows no discernible correlation.
Figures 11a and 11b show the relation between torsional
irregularity and short col-umn effect on prevalent damage,
respectively. Figure 11c shows negligible impact ofdiaphragm
continuity. Of all performance modification factors, the lack of
constructionquality shows the highest impact on the prevalent
damage states (Figure 11d).
Initial screening of the data shows that the year of
construction has a counter intui-tive result such that the newer
structures are showing more damages. One possible ex-planation is
that newer buildings are designed for higher ductility, however,
due to poorconstruction practice and lenient code enforcement, the
expected ductility capacity isundermined. Whereas, the older
buildings lack ductility, nevertheless, the stronger infillmaterial
aid in resisting seismic induced load and prevent severe damages.
Thus, the ba-sic risk item identified under year of
constructioncode enforcementis specified aslenient.
Inputs to the basic risk items obtained from the Bingl Database
are furnished inlinguistic and numeric values (Table 10). These
inputs values are not as defined in the
Table 9. Damage state definitions employed
Damage state Column Beam Shear wall Infill wall
Light/none Visible flexural andinclined hairlinecracks
Visible flexuraland inclinedhairline cracks
Visible flexuralhairline cracks
Surface crack alongthe boundaries
Moderate Clear flexural andshear cracks
Wide flexural andinclined cracks,spalling of concrete
Visible inclinedhairline cracks andclear flexuralcracks
Diagonal crosscracks, separationfrom the frame
Severe/collapse
Slab of one buildingis at mid heightof the adjacentbuilding
Large cracks, plastichinge formation, crushingof concrete
Complete diagonalcracks, spalling ofconcrete, exposure
ofreinforcement
Through cross cracks,rupture of bricks2 SERU, Middle East
Technical University, Ankara, Turkey; Archival Material from Bingl
Database located atwebsite http://www.seru.metu.edu.tr.
-
Ta
Bu C Corrosion Pounding potential R/C
BN 0 5 M
B 75 4 5 M
B 98 5 0 M
B 76 5 0 L
B 88 5 0 L
B 02 3 0 N
B 90 0 5 M
BN 88 5 3 L
B 90 5 5 L
B 5 5 M
B 99 5 3 S
B 89 5 5 S
B 00 5 5 M
B 97 5 5 L
B 98 5 5 L
B 96 5 5 N
B 5 5 N
B 90 5 3 L
B 92 5 5 S
B 91 5 0 M
B 95 5 5 N
B 5 5 N
B 5 0 L
B 03 5 5 L
B 01 0 3 S
B 03 5 5 C
B 96 5 5 N
B 96 5 5 S
Da
250S.TESFA
MARIAMANDM.SAATCIOGLUble 10. Summary of Bingl database for Tier
2 evaluation
ilding ID Walls BC-joint Redundancy SC WS SS TI DC REC CQ Y
G-10-3-10 RCF 2 0.536 No Yes Yes Yes No Yes Poor
NG-10-3-3 RCF 5 0.408 No No No No No No Poor 19
NG-10-4-4 RCF 2 0.167 No Yes Yes Yes No No Average 19
NG-10-4-6 RCF 2 0.291 Yes No No Yes No No Average 19
NG-10-4-7 RCF 2 0.136 No Yes Yes Yes No No Average 19
NG-10-4-9 RCSW 5 0.227 No Yes Yes Yes Yes No Good 20
NG-10-5-1 RCSW 5 0.171 No No Yes Yes No No Average 19
G-10-5-11 RCF 2 0.326 No No Yes No No No Average 19
NG-10-5-2 RCSW 5 0.134 No No No Yes No Yes Good 19
NG-11-2-3 RCF 2 0.770 No Yes Yes No No Yes Poor
NG-11-4-1 RCSW 2 0.024 No No Yes Yes No Yes Poor 19
NG-11-4-2 RCF 0 0.172 No Yes Yes Yes No Yes Poor 19
NG-11-4-4 RCF 2 0.026 No Yes Yes Yes No Yes Poor 20
NG-11-4-5 RCF 5 0.343 No Yes No Yes No Yes Average 19
NG-3-4-1 RCF 2 0.154 No Yes No No No No Poor 19
NG-3-4-2 RCF 5 0.161 No No No No No No Average 19
NG-3-4-4 RCF 2 0.196 No Yes No No No No Average
NG-5-5-1 RCF 2 0.101 No Yes Yes Yes No Yes Average 19
NG-6-2-8 RCF 5 0.214 No No No Yes No Yes Poor 19
NG-6-3-1 RCF 5 0.183 Yes No Yes No No Yes Average 19
NG-6-3-10 RCF 2 0.615 No Yes Yes Yes No Yes Good 19
NG-6-3-11 RCF 2 0.319 No Yes Yes Yes No Yes Average
NG-6-3-12 RCF 0 0.225 No Yes Yes Yes No Yes Average
NG-6-3-4 RCF 5 0.436 No No No No No Yes Average 20
NG-6-4-2 RCF 0 0.025 Yes Yes Yes Yes Yes Yes Poor 20
NG-6-4-3 RCF 0 0.057 No No Yes Yes No Yes Poor 20
NG-6-4-5 RCF 5 0.377 No No No Yes No Yes Good 19
NG-6-4-7 RCSW 5 0.026 No No No No No Yes Poor 19
mage: N=None, L=Light, M=Moderate, S=Severe, C=Collapse
-
SEISMIC VULNERABILITY ASSESSMENT OF REINFORCED CONCRETE
BUILDINGS 251previous section. As a result, initial transformations
into commensurable units are made.Observation for WS, SS, SC, TI,
REC, and DC are linguistically provided as yes forpresent and no
for not present. The transformation values selected are in
congruencewith the prevalent universe of discourse. The
transformation values for WCSB and cor-rosion are shown in Figure
12a and Figure 12b, respectively. Also, in Figure 12c
thetransformation for potential for pounding is provided.
A step by step FRB aggregation through a hierarchical structure
is provided in Tesfa-mariam and Saatcioglu (2008), and for brevity
is not repeated here. For the Bingl da-tabase (Table 10 and
hierarchical structure provided in Figure 1, the building
vulnerabil-ity index IBV is computed and plotted in Figures 13 and
14, without and with theconsideration of the problem of adjacency,
respectively. Both figures show that with increas-ing observed
damage states, the IBV value increases.
CONCLUSIONS
Risk-based seismic assessment approach is proposed for
prioritizing buildings forretrofit and repair. Risk-base
prioritization incorporates engineering decision making as-
Normalized Redundancy Ratio
0.0
0.2
0.4
0.6
0.8
1.0
0 1 2 3 4 5 6
Damage
nrr
Beam Column Joints
0
1
2
3
4
5
0 1 2 3 4 5 6
Damage
Beam
-colu
mn
join
t
Pounding
0
1
2
3
4
5
0 1 2 3 4 5 6
Damage
Pote
ntialfo
rpoundin
g
Corrosion
0
1
2
3
4
5
0 1 2 3 4 5 6
Damage
Severity
ofcorr
osio
na) b)
c) d)
Figure 10. Building performance modifiers a) normalized
redundancy ratio, b) beam columnjoints quality, c) prevalent
corrosion, and d) potential for pounding.pects, such as damage
estimation, and societal value, tolerance to the consequence of
-
810s
No YesTorsional Irregularity
88
10
s
No YesShort columnsa) b)
252 S.TESFAMARIAM AND M. SAATCIOGLU3
1
0 0 0
3
7
3
0 00
1
4
5
1
0
2
4
6
8
10
None Light Medium Severe Collapse
Damage states
No.ofB
uildin
gs
Good Average PoorConstruction quality
2
3 3
1
0
4
6
4 4
1
0
2
4
6
None Light Medium Severe Collapse
Damage states
No.ofB
uildin
g
5
9
7
4
11
0 0
1
00
2
4
6
8
10
12
None Light Medium Severe Collapse
Damage states
No.ofB
uildin
gs
No YesDiaphragms continuity
6 6
4
1
0
1 1 1
00
2
4
6
None Light Medium Severe Collapse
Damage states
No.ofB
uildin
g
1
3
2 2
1
3
5
3
2
0
2
1
2
0 00
2
4
6
8
10
None Light Medium Severe Collapse
Damage states
No.ofB
uildin
gs
High code
Moderate code
Pre code
Year of construction
c) d)
e)
Figure 11. Building performance modifiers a) torsional
irregularity, b) short columns effects, c)diaphragm continuity, d)
construction quality, and e) year of construction.
-
SEISMIC VULNERABILITY ASSESSMENT OF REINFORCED CONCRETE
BUILDINGS 253failure. The risk-based prioritization is undertaken
by integrating site seismic hazard(SSH), building vulnerability,
and importance/exposure factors. The complexity ofbuilding
vulnerability assessment is handled through a systems theory, where
the com-plex problem is managed by a simple hierarchical structure.
The vagueness uncertainty
0 1 2 3 4 5 6
Condition score
Negligible
Low
Signif icantly high
High
Moderate
0 1 2 3 4 5 6
Condition score
Extremely good
Good
Extremely severe
Severe
Moderate
0 1 2 3 4 5 6
Potential for pounding
Extremely good
Good
Extremely severe
Severe
Moderate
a) b)
c)
Figure 12. Transformation values a) relative strength at the
joint, b) corrosion, and c) potentialfor pounding.
0.0
0.2
0.4
0.6
0.8
1.0
1 2 3 4 5
Damage State
Buildin
gVuln
era
bility
IBVFigure 13. Building vulnerability for 1 May 2003 Bingl
Earthquake (without problem ofadjacency).
-
254 S.TESFAMARIAM AND M. SAATCIOGLUencountered as a result of
subjective walk down survey are handled through a fuzzy settheory,
and fuzzy rule based modeling is used to incorporate decision
makers attitudeand intuitive knowledge in the aggregation process
using FRB modeling.
The proposed method is illustrated using the 1 May 2003 Bingl
earthquake damageobservations. Results of the building
vulnerability index show a correlation with ob-served damage,
albeit extracted from limited data sets. The proposed method needs
fur-ther calibration and refinement with existing data, and can
also be augmented with ana-lytical work. Furthermore, lateral
strength index and other unique vulnerabilityindicators (e.g.,
overhang ratio) need to be considered. Furthermore, the parameters
in-dicated in Figure 1 are subject to different types of
uncertainties, consequently, the FRBneed to be extended to
incorporate different uncertainties and consider also different
un-certainty propagation techniques.
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(Received 11 November 2008; accepted 10 July 2009