Sensitivity of Analytical Fragility Functions toCapacity-related Parameters

DRAFT FOR COMMENTS

Dina DAyala1, Abdelghani Meslem11University College London

Sensitivity of Analytical Fragility Functions toCapacity-related Parameters

Dina DAyala, Abdelghani MeslemVersion: 1.0April, 2013

GEM Foundation 2010. All rights reserved

The views and interpretations in this document are those of the individual author(s) and should not be attributed to GEMFoundation. This report may be freely reproduced, provided that it is presented in its original form and thatacknowledgement of the source is included. GEM Foundation does not guarantee that the information in this report iscompletely accurate, hence you should not solely rely on this information for any decision-making.

Citation: DAyala D., Meslem A. Sensitivity of analytical fragility functions to capacity-related parameters, GEM TechnicalReport 2013-X, GEM Foundation, Pavia, Italy.www.globalquakemodel.org

ii

ABSTRACT

Recent extensive literature review, which has been conducted within the framework of the development of the GEM Guidefor Selecting of Existing Analytical Fragility Curves and Compilation of the Database, has shown that often fragilityfunctions are generated using simplified assumptions to reduce the calculation efforts. Some of the most widelyimplemented simplifications are: the use of default values to model structural characteristics-related parameters; the use of2-D models, and ignoring, for the case of infilled RC buildings, the contribution of infill panels in the seismic response bymodelling them as bare frame structures. However, these assumptions may highly decrease the reliability and accuracy ofthe obtained results introducing important epistemic uncertainty in the fragility function construction process. The presentdocument is devoted to provide, for GEM guidelines users, details on the effect that the choice of building capacity-relatedparameters and their expected uncertainty, might have on the results of vulnerability and fragility functions derivation and,hence, steer users towards a better quantification of such uncertainties. The document presents the result of investigationon the sensitivity of structure response to variation in structural characteristics-related parameters values (i.e. in terms ofmechanical properties, geometric configuration and dimension, structural details) and in mathematical modelling (i.e.completeness of models). The classes of structures considered are low-ductility RC buildings designed according to earlierseismic codes, and which are in general characterized by poor quality of materials, workmanship and detailing. Thisbuilding class constitutes one of the largest portions of existing residential building stock in earthquake prone countries.

Keywords: sensitivity analysis, uncertainty capacity, analytical fragility functions

iii

TABLE OF CONTENTS

PageABSTRACT..............................................................................................................................................................................iiTABLE OF CONTENTS.......................................................................................................................................................... iiiLIST OF FIGURES ................................................................................................................................................................. vLIST OF TABLES....................................................................................................................................................................vi1 Introduction ....................................................................................................................................................................... 7

1.1 Purpose.................................................................................................................................................................... 71.2 Scope..................................................................................................................................................................... 101.3 Organization and Contents .................................................................................................................................... 12

2 Adopted procedure of analysis........................................................................................................................................ 122.1 Selected structural characteristics-related parameters and range of expected values .......................................... 122.2 Selected analysis type ........................................................................................................................................... 132.3 Choice of mathematical modelling ......................................................................................................................... 14

2.3.1 Modelling RC members .............................................................................................................................. 14Modelling element-related parameters................................................................................................................... 14Performance criteria............................................................................................................................................... 162.3.2 Modelling unreinforced masonry infill panels.............................................................................................. 16Modelling element-related parameters................................................................................................................... 16Performance criteria............................................................................................................................................... 172.3.3 Definition of global threshold damage states.............................................................................................. 18

2.4 Index building......................................................................................................................................................... 213 Effect of structural characteristics-related parameters .................................................................................................... 234 Effect of mathematical modelling .................................................................................................................................... 28

4.1 The use of bare frames model to represent masonry infilled RC building.............................................................. 284.2 The use of two-dimensional (planar) model ........................................................................................................... 30

5 Derivation of fragility curves ............................................................................................................................................ 31

5.1 Median valuesids,d

S and dispersionids

.......................................................................................................... 31

Procedure 1: Distribution parameters computed from sensitivity analysis ............................................................ 32Procedure 2: First-Order Second-Moment (FOSM) ............................................................................................... 33

5.2 Effect of structural characteristics parameters and mathematical modeling-based dispersion.............................. 356 Basic elements and parameters for modeling and analysis requirement........................................................................ 377 Final Comment................................................................................................................................................................ 38REFERENCES ..................................................................................................................................................................... 39ANNEX A Quality classification for index building analysis ............................................................................................ 44

iv

Parameters for quality classification/index building................................................................................................ 44Number of subclass for index building ................................................................................................................... 44Quality classification for index building .................................................................................................................. 44

ANNEX B Modelling of masonry infill panels .................................................................................................................. 48

vLIST OF FIGURES

PageFigure 1.1 Calculations effort and uncertainty at different steps in analytical vulnerability assessment ................................8Figure 2.1 Idealisation into fibers of reinforced concrete members......................................................................................14Figure 2.2 Comparison of load-displacement curves obtained from fiber-based and plastic hinges structural models with

result from experimental test (Colangelo 2005) for RC Bare Frame intended to represent the ground floor of a four-storey building and is representative of older structures designed using Italian RC non-seismic code provisions.....15

Figure 2.3 Diagonal strut model for masonry infill panel modelling. (a) Equivalent diagonal strut representation of an infillpanel; (b) Variation of the equivalent strut width as function of the axial strain; (c) Envelope curve in compression. 16

Figure 2.4 Parametric analysis for the reduction strut width (ared) parameter. .....................................................................17Figure 2.5 Effect of envelop curve on the simulation of the capacity functions. (a) Effect of strain at maximum stress, m;

(b) Effect of ultimate strain, ult. ...................................................................................................................................18Figure 2.6 Force-displacement curve for infilled RC building and definition damage conditions at global level. (a) Force-

displacement relationships at global level; (b) Force-displacement relationships for the infill panels.........................21Figure 2.7 Typical four-storey masonry infilled RC building of 1970s located in a high-seismically region of Turkey.........22Figure 3.1 Influence of concrete compressive strength on the deformation capacity of the building. ..................................23Figure 3.2 Sensitivity of the structure response to the variation in compressive strength of concrete.................................25Figure 3.3 Sensitivity of the structure response to the variation in tensile strength of steel.................................................25Figure 3.4 Sensitivity of the structure response to the variation in transverse reinforcement spacing.................................25Figure 3.5 Sensitivity of the structure response to the variation in storey height. ................................................................26Figure 3.6 Sensitivity of the structure response to the variation in thickness of infill panels ................................................26Figure 3.7 Sensitivity of the structure response to the variation in compressive strength of infill panel...............................26Figure 4.1 Comparison of the resulted adaptive pushover curves from infilled frame and bare frame models, considering

concrete compressive strength as variable parameter ...............................................................................................28Figure 4.2 Comparison between the use of infilled frame and bare frame models for different structural characteristics

configuration ...............................................................................................................................................................29Figure 4.3 Comparison of capacity curves obtained by 3-D model with those obtained by superposition of 2-D models. ..30Figure 5.1 Comparisons of fragility curves of the structures with and without considering the contribution of masonry infill

walls............................................................................................................................................................................33Figure 5.2 Comparisons of fragility curves of the structures using distribution parameters and FOSM method. (a) Resulted

fragility curves from set of infilled frame models; (b) Resulted fragility curves from set of bare frame models...........35Figure 5.3 Comparisons of structural capacity (structural characteristics and mathematical modelling) uncertainty-based

fragility curves with total uncertainty-based fragility curves. (a) Considering set of infilled frame models; (b)Considering set of bare frame models. .......................................................................................................................36

Figure B- 1 Comparison of capacity functions obtained using different formulae for the effective width of equivalent strut.The RC frame is one-storey, single bay, intended to represent the ground floor of a four--storey masonry infilled

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concrete building and are representative of older structures designed using Italian reinforced concrete non-seismiccode provisions. Experimental data was collected from Colangelo (2005).................................................................48

Figure B- 2 Variation of reduction factor for different equations for the effective width of equivalent strut. .........................50

LIST OF TABLES

Table 1.1 Parameters characterizing building capacity and seismic response ......................................................................9Table 1.2 Uncertainties in capacity parameters considered in the literature for the derivation of fragility curves of RC

buildings......................................................................................................................................................................11Table 2.1 Range of expected values for the structural characteristics-related parameters associated to the building class

represented by the index building ...............................................................................................................................13Table 2.2 Definition of limit states at structure level as per several guidelines.....................................................................20Table 2.3 Definition of different damage conditions at global level proposed in GEM AVM(see also Figure 2.6) ...............21Table 2.4 Classification of 4-storey RC building according to the GEM Basic Building Taxonomy......................................22Table 3.1 Implemented models for sensitivity analysis to structural characteristics-related parameters..............................24Table 3.2 Effect of the variation in the structural characteristics-related parameters values on the structure response .....27Table 4.1 Sensitivity of structural response to the contribution of masonry infill panels.......................................................29Table 5.1 Median value and dispersion calculated for each threshold of damage state, and used in Figure 5.1................33Table 5.2 Comparison of median value and dispersion calculated using distribution parameters and FOSM procedure....34Table 5.3 Comparison of structural characteristics and mathematical modelling dispersion with record-to-record

dispersion, and average value of total dispersion (as per literature)...........................................................................36Table 6.1 Basic attributes (elements) for modelling and analysis requirement for reinforced concrete buildings ................37Table 6.2 Basic attributes (parameters) for modelling and analysis requirement for reinforced concrete buildings.............37

Table A- 1 Expected value range and average value associated to structural characteristics-related parameters qualityclassification and index buildings analysis..................................................................................................................46

Table B- 1 Formulae of equivalent masonry strut's effective width as per literature ............................................................49Table B- 2 Range of values of equivalent strut width computed from different relationships for the infill panels. ................49

.

71 Introduction

1.1 Purpose

The process of analytical fragility assessment is essentially based on two components, namely (see Figure 1.1): theground motion intensity-to-structural response functions, P(IM|SR), and the structural response-to-damage state functions,P(SR|DS). These functions are the products of two independent procedures; namely, the Structural Analysis and theDamage Analysis. At each of these steps, a certain level of uncertainty should be expected and has to be taken intoaccount by users in the estimation of seismic risk. The level of the uncertainty will depend upon the simplification andassumption which researchers and engineers do implement in aim to reduce data gathering and calculation efforts.

With regard to the structural analysis, there are a number of uncertainties involved in the estimation of the performance ofthe building for given levels of intensity. These uncertainties concerned both the capacity modeling of the examinedbuilding and the demand modelling. The uncertainty in capacity modeling is directly affected by the choice of structuralcharacteristics-related parameters and mathematical model to compute and estimate the response of a structure. Theuncertainty in the demand is introduced by the record-to-record variability, which captured the variability in the complexityof the mechanism of the seismic source, path attenuation and site effects of the seismic event (FEMA 2003; NIBE-FEMA2003; ATC 2011).

With regard to the damage analysis, damage thresholds modelling is in general affected by the conservative character indefining the different global limit states, the choice of the implemented damage model and its consistency with the type ofanalysis, the used damage indicator to represent a structures damage states and the correlation with the chosen intensitymeasure (FEMA 1999; FEMA 1999; NIBE-FEMA 2003).

Regarding the fragility analysis, this is in general related to the choice of fitting procedure and sampling methods for theconstruction of fragility curves, taking into account the identified and quantified uncertainties from structural analysis anddamage analysis (FEMA 1999; Wen et al. 2004; Pagnini et al. 2008; ATC 2011).

This present document is devoted to examine the parameters that are associated to the building capacity modeling, only(Figure 1.1). The purpose is to fill the gap regarding the availability of details on the effect and the choice of these buildingcapacity-related parameters with regard to the expected uncertainties that might have on the results of vulnerability andfragility functions derivation and, hence, help GEM end-user to decide with more efficient way for a better quantification ofthe uncertainties. Table 1.1 shows the different parameters characterizing building capacity and seismic response. Thisclassification has been made based on the recent extensive literature review that has been conducted within theframework of the development of the GEM Guide for Selecting of Existing Analytical Fragility Curves and Compilation ofthe Database (DAyala and Meslem 2012).In the definition of structure capacity, structural characteristics and mathematical modeling constitute fundamentalattributes in assigning a particular building to a specific class, in determining the representativeness of a particular index

8building or class of buildings for a given exposed building stock, and ultimately in estimating their seismic performance interms of fragility and vulnerability functions.

Figure 1.1 Calculations effort and uncertainty at different steps in analytical vulnerability assessment

With reference to the structural characteristics attributes, which is introduced in terms of mechanical properties, structuraldetails, geometric configuration and dimensions, it has been widely observed that default values, provided in existingguidelines/codes (e.g. ATC 1996; FEMA 1999; ASCE 2000) and implemented in commonly used structural programs (e.g.CSI 2009), are assigned to represent the associated parameters, e.g. a default value of concrete strength, or steelstrength, or an estimate of transverse reinforcement spacing, or hinges capacities...etc. (e.g. Inel and Ozmen 2006,Salvador et al. 2008, Khan & Naqvi 2012). Usually, this is due either to lack of information, especially, for the case of older

Uncertainty in structural characteristics modellingCapacity

modelling

DemandModelling Uncertainty in mathematical modelling

Uncertainty in definition of damage thresholds

Record-to-record variability

Sampling and fragility curve fitting model

Monte CarloSampling

FullPartitioning

ReducedPartitioning

Structural AnalysisP(SR|IM)

Damage AnalysisP(DS|SR)

DamageThresholdsModelling

Fragility AnalysisP(DS|IM)FragilityCurves

Generation

9structures, where design documents are generally not available, or to expedience. Moreover, it has been also observedthat fragility curves of buildings located anywhere in the world have been generated using, for instance, HAZUS capacitycurves (FEMA 1999) derived for buildings in the US (Lourdes et al. 2007; Vacareanu et al. 2007). This is particularlycommon when studies are conducted for large portions of the building stock and resources for direct survey and dataacquisition are modest. Typically, differences in construction techniques and detailing between different countries aresignificant, even when buildings are nominally designed to the same code clauses.Regarding the mathematical modeling, it has been found from many studies (Kircil and Polat 2006, Howary and Mehanny2011) that for the case of masonry infilled reinforced concrete (RC) buildings, fragility functions were generated fromanalysis of bare frames models, ignoring the contribution of infill panels in the seismic response; hence, reducing theability of these models to capture the real behaviour of the structures. The literature review has also shown that authorsattempt to simulate buildings as two-dimensional modeling instead of three-dimensional modeling; omit shear failure incolumns or beams...etc.

Table 1.1 Parameters characterizing building capacity and seismic responseStructural Characteristics

Mechanical Characteristics Compressive strength of concrete (fc)Tensile strength of steel reinforcement bar (fy)Compressive strength of masonry infill (fw)

Dimension Characteristics Total height (Lz) / Storey height (az)Number of storeys (nz)Plan dimensions (Lx, Ly) - Bay length

Structural Detailing Tie spacing at the column (Sc)Reinforcement ratio at the column ()Hardening ratio of steel (bh)

Geometric Configuration Perimeter Frame Building - Space Frame Building (PFB/SFB)Rigid Roof / Deformable Roof (RR/DR)Column orientation (OR)

Mathematical ModellingNumerical Modelling Bare frame/infilled frame for masonry infilled RC buildings.

3-D / 2-D element-by-element2-D storey-by-storey1-D global model

Performance Criteria Yield and ultimate capacitiesOut-of-plane failure mechanisms in masonry buildingsShear failure mechanisms

As a consequence, these different choices of assumptions and simplifications may highly decrease the reliability andaccuracy of the obtained results introducing important aleatoric and epistemic uncertainties in the fragility functionconstruction process (Dolsek 2012). Although these uncertainties have been accounted in some previous seismicvulnerability studies (see Table 1.2), apart from Liel and Deierlein (2008), very few of these studies have consistentlyanalyzed or examined the effect of the variability of several structural characteristics or of the simplified modellingassumptions on the generated fragility curves, with the scope of estimating the level of uncertainties that should be takeninto account. Moreover, the uncertainties were accounted for in different ways based on the nature of consideredparameters and the needs of each study. Table 1.2 summarizes some examples on how these different capacity-relateduncertainties have been accounted for as per several references from literature. In most of these previous studies, theuncertainty has not been fully accounted for by considering all the attributes (i.e. structural characteristics-related

10

parameters, and mathematical modeling) in accordance to what has been recommended in the existing guidelines, suchas NIBE-FEMA (2003), HAZUS-MH (FEMA 2003), ATC-58 (ATC 2011).

In most of the references from literature, the aleatoric uncertainties associated to the structural characteristics-relatedparameters are accounted for by considering the probabilistic variability in their values (Rossetto, and Elnashai 2004;Bakhshi and Karimi 2006; Iervolino et al. 2007; Ay and Erberik 2008; Polese 2008; Rajeev and Tesfamariam 2011; Uma etal. 2011; Jiang et al. 2012; Dolsek 2012). In some others vulnerability studies the effect of dispersion in structuralcharacteristics-related parameters are accounted for by survey of a large number of existing buildings and definition of amedian and standard deviation of the sample of buildings, after calculation of the capacity and damage threshold for eachbuilding in the sample (DAyala et al. 1997; Lang and Bachmann 2004; DAyala 2005; DAyala, and Paganoni 2010). Withregard to the mathematical modeling, the associated epistemic uncertainties are in general underlined with regards to theparameters of the hysteric models, modeling shear failure mechanisms in concrete elements and the consideration ofmasonry infill walls contribution in RC buildings; modeling out-of-plane failure mechanisms in masonry buildings. Withrespect to the contribution of masonry infill panels to the response of RC structures, some studies have highlighted thedifferent performance of the building due to the irregularities and distribution of infill panels (e.g. Dymiotis et al. 1999; Ellul2006, Dolsek and Fajfar 2008, DAyala et al 2009, Mulgund and Kulkarni 2011), however, only few studies have showntheir direct effect on fragility curves (e.g. Sattar and Liel 2010, Haldar et al. 2012).

1.2 Scope

the main scope of this present document is to analyze the effect of the variation in structural characteristics-relatedparameters values, and of the mathematical modelling choices, with particular reference to inclusion of infill and modeldimension, on the structure response and generated fragility curves. The objective is to provide guidance for the GEMend-user in estimating the level of uncertainties that should be taken into account, with respect to the different choices ofsimplifications and assumptions modelling that can be made in evaluating seismic performance and generating fragilitycurves.

Accordingly, the sensitivity study presented in this document has been conducted for the class of structures that aredefined as low-ductility RC buildings designed according to earlier seismic codes, and which are in general characterizedby poor quality of materials, workmanship and detailing. The main reason for the choice of this class of buildings is that itconstitutes one of the largest portions of existing residential building stock in earthquake prone countries.

To best identify the expected mean and range for the various parameter analysed a real frame in Turkey, is the referenceprototype, however the methodology and results obtained are applicable to other typologies and locations, once the basicdata is available. The sensitivity study is based on nonlinear static adaptive pushover analysis selecting forty-two (42) 3Dmodels. Indeed, when using this type of analysis the variation in the structural stiffness at different deformation levels, andconsequently the system degradation can be better accounted for. The observations of the influence of variability of theselected parameters are conducted in terms of deformation capacity, considering different damage thresholds. The effectof mathematical model is investigated by performing a comparative analysis of fragility curves derived with and withoutconsidering the contribution of masonry infill panels, and between 3-dimension and 2-dimension models.

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Table 1.2 Uncertainties in capacity parameters considered in the literature for the derivation of fragility curves of RC buildings

Reference

Uncertainty in Capacity (C)

Uncertainty in Structural Characteristics Uncertainty in Mathematical Modelling

Dispersion inMechanical

Characteristics(ME)

Dispersion in DimensionCharacteristics (DM)

Dispersion inStructural Detailing

(ST)

Dispersion inGeometric

Configuration (GE)Dispersion in Numerical

Modelling (NM)Dispersion in Performance

Criteria (PC)

Comp

ress

ivestr

ength

ofco

ncre

te(fc

)

Tens

ilestr

ength

ofre

infor

ceme

nt(fy

)

Comp

ress

ivestr

ength

ofma

sonr

yinfi

ll(fw

)

Plan

dimen

sions

(Lx,

Ly)

Total

heigh

t(Lz

)

Stor

eyhe

ight(

a z)

Numb

erof

store

ys(n

z)

Tiesp

acing

atthe

colum

n(Sc

)

Rei

nfor

cem

ent r

atio

at t

he c

olum

n (

)

Hard

ening

ratio

ofste

el(b

h)

Colum

norie

ntatio

n(OR

)

Rigid

Roof

/Defo

rmab

leRo

of(R

R/DR

)

Perim

eterF

rame

Build

ing-S

pace

Fram

eBu

ilding

(PFB

/SFB

)

Infille

dfra

me/B

aref

rame

syste

m

3D/2D

eleme

nt-by

-elem

ent

2-D

store

y-by-s

torey

1-D

globa

lmod

el

Yield

ing/U

ltimate

capa

cities

Shea

rfail

urem

echa

nisms

Jiang et al. (2012) Rajeev & Tesfamariam (2011) Howary and Mehanny (2011) Verbicaro et al. (2009) Ozer and Erberik (2008) Kappos et al. (2006) uncertainty in capacity ()Rossetto and Elnashai (2005) Inel and Ozmen (2006) Polese et al. (2008) Iervolino et al. (2007) Liel and Deierlein (2008) NIBE-FEMA (2003) Uncertainty associated with the capacity curve ()

ATC-58 (ATC 2011) Uncertainty of the in situ constructed building with the construction documents, material properties () Uncertainty in modelling

degradation, mechanisms andsystem interactions ()

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1.3 Organization and Contents

The present documented is divided in five chapters besides the present. The second one explains the procedure that hasbeen adopted to conduct the sensitivity analysis, regarding the selected structural characteristics-related parameters to beexamined, choice of analysis type, choice of mathematical modelling, and choice of index building and quality. Chapter 3present and discuss results of different sensitivity of structure responses to the structural characteristics-relatedparameters. These results are presented in terms of deformation capacities for different damage conditions. Chapter 4present and discuss results of sensitivity of structure response to the numerical modelling completeness related to theconsideration or non-consideration of masonry infill panels contribution, and the use of planer model (i.e. 2-D models).Chapter 5 discuss the influence of capacity-related parameters uncertainty on the derived analytical fragility curves andcompares the different options in considering the dispersion as per several references from literature. Chapter 6 providesthe basic attributes (in terms of elements parameters) for modelling and analysis requirement, And, Chapter 7 providesgeneral comments regarding the outcomes of this present document.

In addition, the document provides ANNEXES. ANNEX A with regards to the quality classification for index buildinganalysis, and which provide: (a) the procedure that has been followed to identify the basic parameters for the qualityclassification of building, and hence, which will be considered for the sensitivity analysis; (b) the choice of the mostexpected values range and their means. ANNEX B with regards to the modelling of masonry infill panel, and whichprovide: (a) result of comparative analysis of several existing formula from literature for the modelling of infill panels, and tojustify the choice of the selected one to be implemented in the rest of study within framework of this document; (b) thebasic parameters in modelling of infill panels, and which have identified based on their result of sensitivity on the structureresponse.

2 Adopted procedure of analysis

In the followings, details are provided regarding the different steps, and assumed assumption that have been adopted inthe implementation of sensitivity analysis; in terms of the parameters that were considered to examine their effects on thestructure response performance and choice of range of expected values; the choice of analysis type that has beenselected; the choice of mathematical modeling adopted in the different analyses (the adopted modeling techniques andtheir differences, and definition of global damage states); and the selected index building.

2.1 Selected structural characteristics-related parameters and range of expected values

In the present document, the investigated structural characteristics-related parameters are those associated to mechanicalproperties, geometric configuration, and structural details; and which are in general affected by the quality of workmanship;i.e. compressive strength of concrete, yield strength of reinforcement, strength and stiffness of infill walls (in terms ofcompressive strength and thickness), story height, and transverse reinforcement spacing. The choice of range of expectedvalues for each parameter (see Table 2.1) is based on the results of structural characteristics assessment available fromdifferent literature sources such as direct studies(Ay 2006, Bal et al. 2008), post-earthquakes surveys (EERI 2000, EEFIT2003, Ellul 2006), the requirement from different versions of earlier seismic codes, e.g. TS500 (TSE 1985), and valuesadopted in previous similar studies on seismic vulnerability (Gulkan et al. 2002, Erol et al. 2004, Kappos 2006).

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The values shown in Table 2.1 have been selected as a result of a process that was followed in defining the differentranges, and which has been reported with details in ANNEX A. Such value ranges represent the most feasible range ofexpected values characterizing the low-ductility RC buildings class, typically designed according to earlier seismic codesand, in general, characterized by poor quality of materials, workmanship and detailing.

Table 2.1 Range of expected values for the structural characteristics-related parameters associated to the building class representedby the index building

Parameters Range of most expected values for Poor Quality Class of Buildings Central valueLower Bound Upper BoundCompressive strength of concrete (fc) 14 MPa 20 MPa 17 MPaTensile strength of steel (fy) 200 MPa 320 MPa 260 MPaTransverse reinforcement spacing (S) 150 mm 250 mm 200 mmfloor-to-floor Story height (h) 2.5 m 3.2 m 2.8 mThickness of infill walls (tw) 13 cm 19 cm 16 cmCompressive strength of infill walls (fw) 1.0 MPa 1.5 MPa 1.25 MPa

2.2 Selected analysis type

The accuracy of any selected procedure for structural response analysis might depend on the type of the selected analysisapproach, and the adopted mathematical model that must be consistent with the type of analysis implemented. In presentwork, the sensitivity analyses have been based on the implementation of Static Adaptive Pushover Analysis (SAPA), whichis an extension and advanced from conventional pushover analysis. In fact, when using SAPA method the lateral loaddistribution is not kept constant but rather continuously updated during the analysis, according to the modal shapes andparticipation factors derived by eigenvalue analysis carried out at each analysis step. Due to its ability to update the lateralload patterns according to the constantly changing modal properties of the system, it overcomes the intrinsic weaknessesof fixed-pattern displacement pushover and provides a more accurate performance-oriented tool for structural assessment,providing better response estimates than existing conventional methods, especially in cases where strength or stiffnessirregularities exist in the structure (Papanikolaou and Elnashai 2005; Bento et al. 2008).

Nevertheless, adaptive pushover analysis may not be exempt from limitations which can be summarized as follows:excessive force concentration at the locations of the structure where the damage first develops; the combination of themodal contributions; the updating procedure of the lateral load vector. This being directly related to the frequency andmodal shapes computed at each step, the procedure defeats its purpose in presence of extensive nonlinear deformationor brittle failure as the modal shapes include imaginary components and hence the vector is not updated. (Papanikolaou etal. 2006).

It is worth to mention that in literature one can find other more sophisticated methods which in general are based onnonlinear dynamic analysis, such as Incremental Dynamic Analysis (IDA) which has been recommended in recentguidelines, e.g. ATC-58 (ATC 2011). These types of analysis are more complex and time consuming, requiring more inputdata. However, for the purpose of the present study, i.e. sensitivity analysis, the use of adaptive pushover analysis is quitesufficient to ensure the accuracy and reliability of the outcomes of this document. It is useful to recall that adaptivepushover analysis has been widely used recently in many nonlinear studies, for masonry buildings (e.g. Lourenco et al.2011), steel buildings (e.g. Shakeri et al. 2012), and RC buildings (e.g. Chaulagain et al. 2013). Recent work by Abbasniaet al. 2013, has shown that the adaptive pushover analysis method can capture the results of IDA analysis with a

14

reasonable accuracy (e.g. high ability to reproduce the capacity curve obtained with IDA and reproduce IDA envelops,accuracy in estimation of interstorey drift).

2.3 Choice of mathematical modelling

The reliability of mathematical models relies on the rigorous and logical representation of all part of the structures withcomparable level of complexity so that their influence on the behavior and seismic vulnerability is adequately accountedfor. An account of the choices made in each step of the mathematical modelling is provided in the following.

2.3.1 Modelling RC members

Modelling element-related parametersA reinforced concrete member is composed of three types of materials: unconfined concrete (corresponding to the cover),confined concrete (corresponding to the core concrete) and reinforcing steel. All reinforced concrete components aredetailed with transverse steel which provide both shear resistance and confining action for the core concrete. Theresponse of RC components and consequently the frame system is a function of the behavior of the confined core and thelongitudinal steel. In the case of non-ductile sections, the response of the core will be only marginally different from theresponse of the cover concrete.

In the framework of this present study, fiber-based structural modeling was adopted to model reinforced concretemembers (see Figure 2.1). Indeed, this numerical technique of modeling allows characterizing in higher detail, thenonlinearity distribution in RC elements by modelling separately the different behaviour of the materials constituting the RCcross-section (.i.e. cover and core concrete and steel) and, hence, to capture more accurately response effects on suchelements. Fibre-based modelling models a structural element by dividing it into a number of two-end frame elements, andby linking each boundary to a discrete cross-section with a grid of fibres. The material stress-strain response in each fibreis integrated to get stress-resultant forces and rigidity terms, and from these, forces and rigidities over the length areobtained through finite element interpolation functions which must satisfy equilibrium and compatibility conditions. Figure2.1 shows an example of idealization into fibers of reinforced concrete members using SeismoStruct (SeismoSoft 2013).The cover concrete is modelled using unconfined properties while the core concrete is modelled with properties dependingon confinement models.

Figure 2.1 Idealisation into fibers of reinforced concrete members

15

In fact, there are several advantages which justify the use of fiber-based structural modelling:- Fiber-based modelling may easily take into account the case of complex cross-sections. Indeed, a fiber cross-

section can have any general geometric configuration formed by sub-regions of simpler shapes; geometricproperties are calculated through the numerical integration.

- Since each fiber is associated to a given uniaxial stress-strain material response, higher accuracy and morerealistic behavior effects can be captured in a fiber-based model.

- This technique has also the ability to take into account the case of complex stress-strain behaviour. Since eachfiber can have any stress-strain response, this technique allows modelling nonlinear behavior in steel members,reinforced concrete members (unconfined and confined concrete), and composite members as shown in Figure2.1.

- Since the length of the fiber is not constrained, the cross-section defined at each of the two ends can be different,and therefore, the response can be roughly estimated. Precision can be increased with more integration points.

Figure 2.2 Comparison of load-displacement curves obtained from fiber-based and plastic hinges structural models with result fromexperimental test (Colangelo 2005) for RC Bare Frame intended to represent the ground floor of a four-storey building and is

representative of older structures designed using Italian RC non-seismic code provisions.

It is worth to mention that users might employ, as an alternative strategy to model reinforced concrete members, the well-known lumped plastic-hinge structural modeling of which many application to derivation of fragility curves can be found inliterature. The characterization of these lumped plastic hinges requires a moment-curvature diagram to be defined, whichcan be obtained from the monotonic loading of the cross-section, and an assumed plastic hinge length. The simplificationsand hence limitations of applicability of this method is recognised by sevral authors (e.g. Charney and Bertero 1982,Bertero et al. 1984, Monteiro et al. 2008)

By way of example, considering as reference a simple experimental portal frame with well-defined hinge formation andfailure mechanism tested by Colangelo (2005) as shown in Figure 2.2, the rresults obtained with the fiber-based modelshows a good agreement with experimental data, regarding the ability to predict the gradual transition from initiation of theplasticity (at 0.3% drift) to the complete formationof the hinge (estimated at 1% drift) whereas for the lumped-plastic hingemodel the transition from linear to plastic occurs over a much narrower range of drift and for higher lateral capacity(estimated at 0.5% drift). Hence, use of such model would introduce epistemic uncertainty in the computation of fragilitycurves for states of damage prior to collapse. The accuracy would be further reduced in the case of elements with complexcross-sections and/or with complex strength, or specific geometry, such as captive columns.

16

Performance criteriaWithin the context of a fibre-based modelling approach for the reinforced concrete frames, the different performancechecks are carried out for each integration section of the selected member. Material strains do usually constitute the bestparameter for identification of the performance state of a given structure, especially for the case of structures with differentconfigurations and ductility levels. Two limit states are identified at element level:

Yielding of element (limit state of serviceability) corresponding to the yielding of the steel in tension. Crushing of element corresponding to the ultimate concrete compressive strain, given by (Priestley et al. 1996):

cc

suyhscu f

f

4.1004.0 (2.1)

It is worth to mention that, alternatively, the limit of chord rotation corresponding to the condition of yield rotation andultimate rotation, may also be used to model the performance criteria at element level (ASCE 2000, CEN 2004).

2.3.2 Modelling unreinforced masonry infill panelsIn general practice, the infill walls are commonly made of masonry bricks or blocks, varying in specific weight, strength andbrittleness depending on age and quality of construction. In the literature, many models of infill panel have been proposedin an attempt to improve the simulation of the real behavior of infilled frames. Although there is a robust body of work ondeveloping mezo-modelling for the numerical simulation of infill panels by 2-dimensional finite element (see Ellul 2006,DAyala et al 2009, Ellul and DAyala 2012 for thorough literature reference and alternative modeling strategies), currentlythe diagonal strut model (see Figure 2.3) is still the most frequently used by researchers as a simplified modelingapproach for bulk analysis, and has been adopted in many documents and new guidelines, such as, CSA-S304.1 (CSA2004), ASCE/SEI 41-06 (ASCE 2006), NZSEE (2006), MSJC (2010)etc.

Figure 2.3 Diagonal strut model for masonry infill panel modelling. (a) Equivalent diagonal strut representation of an infill panel; (b)Variation of the equivalent strut width as function of the axial strain; (c) Envelope curve in compression.

Modelling element-related parametersThe equivalent strut width (see Error! Reference source not found.a) is the most investigated parameter to assess thestiffness and strength of an infill panel. As per literature, different formulae have been proposed by several researchers(Holmes 1963; Liauw and Kwan 1984, Paulay and Priestley 1992). A comparative analysis to show variance associatedwith this models is provided in ANNEX B. For the GEM study the model adopted is the one based on the early work ofMainstone and Weeks (1970) and Mainstone (1971), following the recommendation given by ASCE/SEI 41-06 (ASCE2006) and by several other provisions and guidelines such as, FEMA-356 (ASCE 2000):

(a) (b) (c)

17

infr

.

colhI.a40

1750

, where,

41

inf4

2sininf

hcolIcE

tmE

I

(2.1)

I is coefficient used to determine equivalent width of infill strut; colh is column height between centrelines of beam; infh is

height of infill panel; cE is expected modulus of elasticity of frame material; mE is expected modulus of elasticity of frame

material (taken as mm fE 550 ; where mf is compressive strength of infill material); colI is moment of inertia of column;

infr is diagonal length of infill panel; inft is thickness of infill panel and equivalent strut; and is angle whose tangent is the infillheight-to-length aspect ratio.

Performance criteriaThe implementation of diagonal strut model requires the definition of the followings: the reduced strut width ared (Figure2.3.b); and the envelope curve in compression in terms of strain at maximum stress and ultimate strain (Figure 2.3.c).Within the framework of developing this present document, a parametric analysis was conducted for these parameters,which show very complex inter-relationship and in general are best calibrated directly from experiment (see Figure 2.4 andFigure 2.5). The parametric analysis was conducted for the case of one-storey, single bay, RC frame intended torepresent the ground floor of a four--storey masonry infilled concrete building and are representative of older structuresdesigned using Italian reinforced concrete non-seismic code provisions. Experimental data was collected from Colangelo(2005).

Estimation of reduced strut width ared

When the elastic limit of the infill panel is exceeded due to the cracking, the contact length between the frame and the infilldecreases as the lateral and consequently the axial displacement increases, affecting thus the area of equivalent strut. Totake into account this fact the width of the equivalent strut must be reduced. In this work, the strut area is assumed to varylinearly as function of the axial strain as shown in Figure 2.3.b. This variation takes place between two strains: strut areareduction strain (1) and residual strut area strain (2).According to Al-Chaar (2002), a reduction factor for infill panel damage can takes values of 0.7 and 0.4 for moderate andsevere damage, respectively. From the result of parametric analysis, it has been observed that the strut width reductionparameter has a significant influence on the peak load leading to differences of up to 38% from the minimum value.However, this factor does not seem to have a significant effect on the ultimate drift at failure of the infill panel (see Figure2.4).

Figure 2.4 Parametric analysis for the reduction strut width (ared) parameter.

18

Estimation of envelop curve in compression

With regards to the envelop curve, it is well known that in general failure of infill panel occurs at small lateral displacementbefore the frame reaches its strength. However, the system frame-infill panel is able to resist increasing lateral loads, byacting as confinement to the cracked panel. This effect leads to a less brittle behavior of the infill and smootherredistribution between the two components and loss of capacity of the system. According to Crisafulli (1997), thedescending branch of the strength envelope can be described by a parabolic curve as it is shown in Figure 2.3.c. Crisafulli(1997) also assumed that the expression of strain-stress proposed by Sargin et al. (1971) originally for concrete canapproximately represent the envelope curve for masonry.

The parametric analysis was conducted for the two parameters defining an envelope cuve, i.e. Strain at Maximum Stress(m) and Ultimate Strain (ult) considering several ratios ult/m as shown in Figure 2.5. In addition, m which should becalibrated through the consideration of experimental data, may vary from 0.001 to 0.005, as reported in SeismoStruct(2013). The result of parametric analysis has shown that both parameters, m and ult, do not seem to have an effect on thepeak load capacity, while it significantly influences the post-peak branch of the capacity curve, hence, influencing theuncertainty in evaluation of post peak performance points.

For the present study, the assumption that has been considered is that a complete collapse occurs just after appearanceof cracking as it has been widely observed from experiment. The envelope curve model used is ult = 5.5m (m = 0.0012).

Figure 2.5 Effect of envelop curve on the simulation of the capacity functions. (a) Effect of strain at maximum stress, m; (b) Effect ofultimate strain, ult.

2.3.3 Definition of global threshold damage statesRegarding the evaluation of different limit states at the level of the structure, there is a lack of clear guidance in theliterature, beyond some qualitative description of observed damage. The existing relations and expressions for thecalculation of capacities (i.e. performance criteria) are in general mostly defined at the element (ass described in theprevious subsection) rather than at the global level. At the global level, the damage thresholds are defined conservativelyon the basis of a minimum number of elements having reached or past a specific damage threshold.

19

Several definitions have been implemented in guidelines and codes for the estimation of the global damage states,through the observation of the progression of local damage at elements level (Table 2.2). As per most of documents, thedamage are described by three main levels, as shown in Table 2.2.

For instance, ASCE 41-06 (ASCE 2007) describes damage levels by:- Immediate Occupancy (IO): level for which the building is expected to sustain minimal or no damage to their

structural elements and only minor damage to their non-structural components;- Life Safety (LS): level for which the building may experience extensive damage to structural and nonstructural

components; and- Collapse Prevention (CP): level for which the building is may experience a significant hazard to life safety

resulting from failure of non-structural components.Similarly, the damage level in a building is defined in Eurocode-8 (CEN 2005) by three limit states:

- Damage Limitation (DL): Building meeting this level is considered as slightly damaged;- Significant Damage (SD): Building meeting this level is considered as significantly damaged; and- Near Collapse (NC): Building meeting this level is considered as heavily damage.

From an analytical point of view the challenge is to correlate the qualitative description of damage provided in the abovedefinitions with specific performance to be identified numerically in terms of strain, drift or attainment of strength thresholdson a given number of elements, as per indication of the numerical models. For instance, Dolsek and Fajfar (2008) proposethe following correlation: Damage Limitation (DL), Significant Damage (SD), and Near Collapse (NC), as per theEurocode-8 (CEN 2005) definitions, where DL is attained for the value of lateral drift causing the last infill in a storeystarting to degrade. For the case of bare frames this threshold is attained at the yield displacement of the idealizedpushover curve; SD limit state is attained when the rotation at one hinge of any column exceeds 75% of the ultimaterotation; NC limit state is attained when the rotation at one hinge of any column exceeds 100% of the ultimate rotation.This implies that the structure will become unstable if one of the columns at one storey fails.

As mentioned earlier, the global damage definition provided in literature (Table 2.2) are very conservative and wouldproduce significant bias in the fragility curve derivation in relation to empirical fragility curves, derived for instance on thebasis of the EMS 98 damage state description (Grunthal 1998), for which 5 grades of damage are used: Grade 1:negligible to slight damage (no structural damage, slight non-structural damage); Grade 2: moderate damage (slightstructural damage, moderate non-structural damage); Grade 3: substantial to heavy damage (moderate structural damage,heavy non-structural damage); Grade 4: very heavy damage (heavy structural damage, very heavy non-structuraldamage); and Grade 5: destruction (very heavy structural damage)

For this reason in the framework of GEM Analytical Vulnerability Method (GEM-AVM), while four global limit states havebeen considered in a manner similar to the previous study, Slight Damage, Moderate Damage, Near Collapse, andCollapse, these have been associated with a more distributed progression of local damage through several structural andnon-structural elements. The choice has been made based on the existing definitions presented above as per differentexisting guidelines, and also on field observation and earthquake reconnaissance data that have been reported in manydocuments, such EERI report (2000), EEFIT report (2003). For the purpose of the present study of sensitivity, only SlightDamage, Moderate Damage and Near Collapse are considered, as presented in Table 2.3 (see also Figure 2.6).

20

The choice of relating a global damage thresholds or state to a higher proportion of damaged elements within a structure isparticularly significant for low engineered structures which might present RC columns of variable dimensions and orientedaccording to architectural rather than structural criteria, hence showing diverse interstorey drift related performance

Table 2.2 Definition of limit states at structure level as per several guidelines.

ASCE

/SEI

41-0

6(AS

CE20

07);

ATC-

58-2

(ATC

2003

),FE

MA-3

56(A

SCE

2000

)

Performance Level Immediate Occupancy (IO) Life Safety (LS) Collapse Prevention (CP)

Conc

rete

Fram

es

PrimaryMinor hairline cracking; limitedyielding possible at a fewlocations; no crushing (strainsbelow 0.003)

Extensive damage to beams;spalling of cover and shearcracking (

21

Table 2.3 Definition of different damage conditions at global level proposed in GEM AVM(see also Figure 2.6)

Damage State Description

Slight Damage RC members: first yielding at column, no crushing.Masonry infills: appearance of cracking in masonry infills

Moderate Damage RC members: cover spalling at several locations for columns and beamsMasonry infills: crushing/failing of infills at first story; extensive cracking at other stories

Near Collapse RC members: extensive crushing in some columns/beamsMasonry infills: extensive crushing/failing of infills

Figure 2.6 Force-displacement curve for infilled RC building and definition damage conditions at global level. (a) Force-displacementrelationships at global level; (b) Force-displacement relationships for the infill panels.

2.4 Index building

Low ductility reinforced concrete frame structures constitute one of the largest portions of existing residential building stockin several earthquake prone countries and in the rest of the world. For the sensitivity analysis, the class of structureconsidered is a typical four-storey RC building, built according to the first generation of seismic codes, in the 1970s andlocated in a high-seismically region of Turkey; see Figure 2.7 and Table 2.4. The building is representative of residentialbuildings stock designed according to the earlier seismic codes, and which are in general characterized by low strengthconcrete, mild steel smooth rebars, relatively high strength infill, and general poor construction details and quality. Thebuilding has four bays with the raster of 4m in the X direction, and four bays with the raster of 3m in the Y direction. Theslab has the thickness of 15 cm. The amount and arrangement of longitudinal reinforcement in columns and beams areshown in Figure 2.7. In addition of the self-weight of the structure the 2 kN/m2 of permanent load was assumed in order torepresent floor finishing and partitions, and 30% of participating live load (live load = 2 kN/m2) was also adopted.

The analyses were performed by SeismoStruct (Seismosoft 2013), which is a fiber-based finite elements softwareframework for simulation applications in earthquake engineering using finite element method. The infill panel isrepresented by means of two diagonal struts placed between the beam-column joints able to resist load in compression. Ingeneral, 40% to 60% of masonry infill panels present in the infilled RC building are structurally effective as the remaining

22

portion of the masonry infills are meant for functional purpose such as doors and windows openings (Pauley and Priestley,1992). In this present document, the buildings were modeled using 50 % masonry infills (external panels), as shown inFigure 2.7.

3D view of the building Plan view of the building

Reinforcement of columns in storey-1 and 2 Reinforcement of columns in storey-3 and 4

Figure 2.7 Typical four-storey masonry infilled RC building of 1970s located in a high-seismically region of Turkey.

Table 2.4 Classification of 4-storey RC building according to the GEM Basic Building Taxonomy

# GEM Taxonomy 4-Storey RC BuildingAttribute Attribute Levels Level 1 Level 21 Material of the Lateral Load-Resisting System Material type (Level 1) CR CIP

Material technology (Level 2)Material properties (Level 3)

2 Lateral Load-Resisting System Type of lateral load-resisting system (Level 1) LFINF DUSystem ductility (Level 2)

3 Roof Roof material (Level 1) RC RC1Roof type (Level 2)

4 Floor Floor material (Level 1) FC FC1Floor type (Level 2)

5 Height Number of stories H:46 Date of Construction Date of construction YEP:19757 Structural Irregularity Type of irregularity (Level 1) IRN

Irregularity description (Level 2) IRH IROHIROH IROV

8 Occupancy Building occupancy class - general (Level 1) RES RES2Building occupancy class - detail (Level 2)

23

3 Effect of structural characteristics-related parameters

In many situations when there is lack of information, especially, for the case of older structures, where design documentsare generally not available, researchers and engineers attempt to adopt estimated or default values to be assigned forstructural characteristics-related parameters. This section of the present document, aim to provide details for engineers onthe consequences of their different choices, and hence, take into account the expected uncertainty with respect to theaccuracy in predicting the response of the structure.

Considering what has been discussed in Section 2.1 with regard to the selected most probable values range and mean,associated to each structural characteristics-related parameter, several models have been implemented to evaluate theeffect on the structure response, as shown in Table 3.1. The values chosen within each range for each parameter in Table3.1 (see also Table 2.1), are considered the most expected values that might be possibility assigned by the assessor, incase of lack of information (e.g. design documents are not available), to represent the class of low-ductility RC buildingsconstructed with earlier seismic codes.

Figure 3.1 shows example of resulted force-displacement capacities, from adaptive pushover analysis, with respect to thevariation in concrete compressive strengths values. The result clearly shows the effect of this parameter on thedeformation capacity of the structure; however, in terms of load capacity, almost no significant influence has beenobserved.

As result of sensitivity analyses, Figure 3.2 to Figure 3.7 show the influence of the variation in values for all structuralcharacteristics-related parameters, that have been considered in this study, on the structural response, for differentdamage condition in terms of roof drift. Table 3.2 summarizes the level of sensitivity of the response to the change foreach parameter in terms of Coefficient of Variation (CV), defined as ratio of standard deviation to mean value, and thepercentage difference (Diff) in deformation capacity for different damage condition.

The result of sensitivity analysis has shown that structural characteristics-related parameters are found to have asignificant effect on the structural response, for different damage condition. Indeed, at the highest level of damage aremarkable variation (CV reaches a value up to 38%) in terms of deformation capacity (roof drift) has been observed evenfor a modest variation in compressive strength of concrete (CV = 12.7%), as shown in Figure 3.2 and Table 3.2; however,no significant difference in structural response has been found at the lowest level of damage, i.e. Slight Damage.

Figure 3.1 Influence of concrete compressive strength on the deformation capacity of the building.

24

Table 3.1 Implemented models for sensitivity analysis to structural characteristics-related parameters

Variability Concrete CompressiveStrength [MPa]Steel Yield

Strength [MPa]Transverse Reinforcement

Spacing [mm]Story

height [m]Thickness of Infill

Panel [cm]Compressive Strength

of Infill [MPa]Number of

StoryesNumber of Bays Dimension

X Direction Y Direction

Conc

rete

Comp

ress

iveSt

reng

th

14 260 200 2.8 16 1.25 4 4x4m 4x3m 3-D15 260 200 2.8 16 1.25 4 4x4m 4x3m 3-D16 260 200 2.8 16 1.25 4 4x4m 4x3m 3-D17 260 200 2.8 16 1.25 4 4x4m 4x3m 3-D18 260 200 2.8 16 1.25 4 4x4m 4x3m 3-D19 260 200 2.8 16 1.25 4 4x4m 4x3m 3-D20 260 200 2.8 16 1.25 4 4x4m 4x3m 3-D

Stee

lYiel

dSt

reng

th

17 200 200 2.8 16 1.25 4 4x4m 4x3m 3-D17 220 200 2.8 16 1.25 4 4x4m 4x3m 3-D17 240 200 2.8 16 1.25 4 4x4m 4x3m 3-D17 260 200 2.8 16 1.25 4 4x4m 4x3m 3-D17 280 200 2.8 16 1.25 4 4x4m 4x3m 3-D17 300 200 2.8 16 1.25 4 4x4m 4x3m 3-D17 320 200 2.8 16 1.25 4 4x4m 4x3m 3-D

Tran

sver

seRe

infor

ceme

ntSp

acing

17 260 150 2.8 16 1.25 4 4x4m 4x3m 3-D17 260 175 2.8 16 1.25 4 4x4m 4x3m 3-D17 260 200 2.8 16 1.25 4 4x4m 4x3m 3-D17 260 225 2.8 16 1.25 4 4x4m 4x3m 3-D17 260 250 2.8 16 1.25 4 4x4m 4x3m 3-D

Stor

yheig

ht 17 260 200 2.5 16 1.25 4 4x4m 4x3m 3-D17 260 200 2.8 16 1.25 4 4x4m 4x3m 3-D17 260 200 3.2 16 1.25 4 4x4m 4x3m 3-D

Thick

ness

ofInf

illPa

nel 17 260 200 2.8 13 1.25 4 4x4m 4x3m 3-D

17 260 200 2.8 16 1.25 4 4x4m 4x3m 3-D17 260 200 2.8 19 1.25 4 4x4m 4x3m 3-D

Comp

ress

iveSt

reng

thof

Infill 17 260 200 2.8 16 1.00 4 4x4m 4x3m 3-D17 260 200 2.8 16 1.25 4 4x4m 4x3m 3-D17 260 200 2.8 16 1.50 4 4x4m 4x3m 3-D

25

Figure 3.2 Sensitivity of the structure response to the variation in compressive strength of concrete

Figure 3.3 Sensitivity of the structure response to the variation in tensile strength of steel

Figure 3.4 Sensitivity of the structure response to the variation in transverse reinforcement spacing

26

Figure 3.5 Sensitivity of the structure response to the variation in storey height.

Figure 3.6 Sensitivity of the structure response to the variation in thickness of infill panels

Figure 3.7 Sensitivity of the structure response to the variation in compressive strength of infill panel

27

Table 3.2 Effect of the variation in the structural characteristics-related parameters values on the structure responseParameters Parameters values Slight Damage Moderate Damage Near Collapse

Range CV [%] CV [%] Diff. [%] CV [%] Diff. [%] CV [%] Diff. [%]Compressive strength of concrete (fc) 14MPa ~ 20MPa 12.71 4.13 11.11 37.47 197.56 32.28 139.08Tensile strength of steel (fy) 200MPa ~ 320MPa 16.62 6.24 12.50 9.22 30.80 7.12 22.27Transverse reinforcement spacing (S) 150mm ~ 250mm 19.76 0.00 0.00 17.01 48.39 13.24 39.50floor-to-floor Story height (h) 2.5m ~ 3.2m 12.39 19.16 45.09 17.96 42.32 10.59 22.93Thickness of infill walls (tw) 13cm ~ 19cm 18.75 31.49 66.67 19.85 49.23 16.65 39.68Compressive strength of infill walls (fw) 1.0MPa ~ 1.5MPa 20.00 44.30 128.57 33.17 102.08 14.90 34.35

For the tensile strength of steel, as shown in Figure 3.3, the effect has been found to be pretty different comparing to thecompressive strength. The effect is almost insignificant. For a CV= 16.1% of tensile strength, the CV in deformationcapacity increases very slightly from Slight Damage to Moderate Dam-age and attains a value of only 9.2%, and then de-creases to 7% at Near Collapse.

Increased ductility is accounted for by transverse reinforcement spacing, adopting a range of values obtained fromliterature on structural characteristics assessment in existing buildings (EERI 2000, Inel & Ozmen 2006). According to theresults, the structural response has been found to be moderately affected by the full range of variation in transversalreinforcement spacing (s=150 to 250mm), as shown in Figure 3.4. For a variation of spacing CV = 19.76%, the CV instructural response attained a value of 18% and 10.6% for Moderate Damage and Near Collapse, respectively. At SlightDamage level, no difference was observed in the structural response, as this parameter, although improves the concreteconfinement has no effect on the onset of yielding in the concrete elements or cracking of the infills.

Floor-to-floor story height also shows a moderate effect on the seismic performance of the structure (see Figure 3.5). Thefull range of variation CV = 12.4% leads to comparable difference in roof drift at different damage condition (CV indeformation capacity reaches value from 10.6 to 19.2%).

The effect of strength and stiffness of infill walls was examined in terms of compressive strength and the thickness of infillwalls. The sensitivity analysis was conducted for values from 13cm to 19cm for thickness and 1.0MPa to 1.5MPa forcompressive strength of masonry infill walls, as shown in Figure 3.6 and Figure 3.7, respectively. According to the resultof analyses, the two parameters have shown significant effect on the structural performance, at Slight to ModerateDamage condition. For a total variation of the thickness of infill walls, 18.75%, the structural response has been found tobe CV=31.5% at Slight Damage and decrease to 19.85% at Moderate Dam-age. For CV=20% in compressive strength ofinfill walls, the variation in structural response has been found to be CV=44.3% at Slight Damage and de-crease to 33.2%at Moderate Damage. Both parameters show a significantly reduced effect on the structural response at Near Collapse,CV=16.65% due to variation of compressive strength and 14.9% due to variation of thickness of infills, as the contributionof infill past the peak capacity is significantly reduced. This can be explained by the fact that the damage in infills ingeneral occurs at an early stage comparing to the RC members (see Figure 3.1, softening branch of the curve); hence,the infills will start to have less effect with increasing damage.

It is evident from the results shown above that for low-ductility buildings characterized by poor quality of materials,workmanship and detailing, structural characteristics-related parameters variation might have a significant effect onestimating realistic structural response. Most importantly it should be noted that the relationship between parameters and

28

response is non-linear, non-monotonic and non-correlated for the three damage thresholds, indicating that values forepistemic uncertainty cannot be interpolated or extrapolated linearly from one state to the next.

4 Effect of mathematical modelling

The effect of model completeness is investigated by performing: (1) a comparative analysis of structure response andperformance generated with and without considering the contribution of masonry infill panels (comparing the extractedresults from infilled frames system with those exacted from bare frames system); (2) a comparative analysis betweenusing two-dimensional (2-D) modeling and three-dimensional (3-D) modeling in the evaluation of building response.

4.1 The use of bare frames model to represent masonry infilled RC building

Extensive literature review (see DAyala and Meslem 2012) has shown that often, researchers and engineers attempt toconduct vulnerability assessment of infilled RC buildings using bare frame models without considering infills, in order toreduce the calculation efforts. Depending on the level of stiffness and structural capacity of the infills and their connectionto the main structural system , such simplifying assumption may render the capacity curve and fragility curves obtainedwherein totally unrepresentative of the assumed building class.

To clearly demonstrate this, a comparative analysis is performed between two modelling hypotheses, i.e. modeling withoutinclusion of infills (bare frames system) and modeling with inclusion of infills as described in Section 3 (infilled framessystem). Figure 4.1 shows an example of comparison of resulted adaptive pushover curves using bare frame model withthe resulted from infilled frame model, with respect to variation in concrete compressive strength.

Figure 4.1 Comparison of the resulted adaptive pushover curves from infilled frame and bare frame models, considering concretecompressive strength as variable parameter

On comparing the behaviour of two modelling hypotheses, and for the same structural characteristics configuration, aremarkable difference in estimating the response of the building is observed as it can be seen from Figure 4.1. This

29

important difference, shows how much the uncertainty can be significant in evaluation of seismic performance if infills arenot considered in modelling. Indeed, the stiffness of structures increased with the presence of infills. However, at smallvalue of displacement (value of top drift 0.25%) a first crush of infill was observed for the infilled structures. This first crushoccurred for the infill panels located at ground floor and then second floor, as shown in Figure 2.6.b. On the other hand,the presence of infill panels have caused the occurrence of first crush of concrete members (Moderate Damage level), andthen the ultimate capacity at the global level (Near Collapse level), at earlier stage (at top drift of 0.36~1.09% and0.77~1.85%, respectively, for the considered values range of concrete compressive strength). However, bare framestructures show more flexibility regarding the occurrence of the first crush of concrete member and then the ultimatecapacity (at top drift of 1.25~1.62% and 1.34~2.88%, respectively, for the considered values range of concretecompressive strength).

In addition to concrete compression strength parameter, the comparison between the two modeling hypotheses has beenalso conducted considering values ranges for tensile strength of steel, transverse reinforcement spacing, and floor-to-floorstory height. In total nineteen infilled frame models, and nineteen bare frame models are considered, as shown in Figure4.2. As shown in Table 4.1, the computed mean value of deformation capacity at Slight Damage level for the whole rangeof variation of all parameters has been found to be 6 times greater for bare frame models than the one calculated forinfilled frame models. At Moderate Damage level, the difference in the structural response between infilled frame and bareframe structures is 2.2 times greater for bare frame models than the value for infilled frame models. For Near Collapse,this factor, in terms of mean value, is estimated to have a value of 1.8.

Figure 4.2 Comparison between the use of infilled frame and bare frame models for different structural characteristics configuration

Table 4.1 Sensitivity of structural response to the contribution of masonry infill panels.

Roof DriftSlight Damage Moderate Damage Near Collapse

Mean [%] CV [%] Mean [%] CV [%] Mean [%] CV [%]Infilled Frame 0.08 8.71 0.69 24.88 1.30 20.35Bare Frame 0.48 7.54 1.53 5.96 2.29 18.10Factor 6 2.2 1.8

30

On comparing the ability of capturing the sensitivity, the bare frame models seem to be no sensitive to change in structuralcharacteristics-related parameters, comparing to the case of infilled frame models (see Figure 4.2). Indeed, at themoderate damage bare frame models have shown less sensitivity, with respect to the variation in structural characteristicsparameters values. At Near Collapse damage, the non-sensitivity of bare frame models is mostly remarkable with respectto the change in the value of steel tensile strength.

In the literature, some authors (e.g. Pasticier et al. 2008) have argued that uncertainty and variations in structuralcharacteristics-related parameters might be considered not as critical as the uncertainty in the seismic record, for instance.However, it is important to mention that this statement could be based on a specific result of sensitivity that was conductedusing bare frame models. It is worth to recall that in the work by Liel and Deierlein (2008), the sensitivity study, wasconducted using bare frame structures as numerical models; however, the parameters considered as variable are numberof storey and framing system.

4.2 The use of two-dimensional (planar) model

The employment of two-dimensional (planar) model for the derivation of either vulnerability functions/fragility curves orcapacity curves have been widely employed in literature, for instance, Erberik & Elnashai (2003, 2004) for 5-storey RCbuilding, UTCB (2006) for 13-storey RC building in Bucharest, Barbat et al. (2006), for a range of 2-8 stories for RC andmasonry buildings in Barcelona, Howary and Mehanny (2011) for 8-storey RC buildings in Cairo. The aim is to reduce thecomputational effort, especially when using nonlinear dynamic analysis. However it should be kept in mind that theepistemic uncertainty associated with this modelling strategy can be significant, especially for buildings with irregulargeometries or with buildings with non-uniform distribution of infills.

Figure 4.3 shows a comparison of capacity curves obtained by 3-D with those obtained by superposition of 2-D models. Itis clearly seen that there is a remarkable difference between the two procedures. By using 2-D models, the displacementcorresponding to first crush of concrete member seems to be overestimated. The first crush is estimated to be at top driftof 1.28%. However, for 3-D model the first crush of concrete is estimated to be at top drift of 0.45%. In addition to that, thepeak loading capacity is underestimated by using 2-D models.

Figure 4.3 Comparison of capacity curves obtained by 3-D model with those obtained by superposition of 2-D models.

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5 Derivation of fragility curves

Fragility functions express the probability of a damage state, ids , sustained by an examined building class, being reachedor exceeded given a level of ground motion intensity measure, IM . The fragility functions correspond to n number ofdiscrete descriptive damage states, which are typically correlated with a threshold of a selected response variable (e.g.roof drift, interstorey drift, ultimate capacity), estimated from the structural analysis of the simulated building class. Thisthreshold represents the capacity of the building class, i.e. the ability of their structures to withstand a given level ofdamage or to be in a state of damage given a measure of ground motion intensity IM . Therefore, the fragility functionsare constructed by estimating the probability of the generic structural response, D , reaching or exceeding a specifiedthreshold id , conditioned to a range of ground motion intensity measure IM . As commonly done in most of seismicfragility studies, the functions are assumed to take the form of lognormal cumulative distribution functions having a medianvalue and logarithmic standard deviation, or dispersion. The mathematical form for such a fragility functions is:

ids

IM|DIMIM|idDFIM|idsDSF

ln(5.1)

Where is the standard normal cumulative distribution function; IMD| is the lognormal mean of Dconditioned on the

ground motion intensity, IM ; andids

is the lognormal standard deviation of IMD | .

In literature a variety of intensity measures have been used to define fragility curves. The result of investigation has shown

that Spectral Acceleration ( TSa ), Spectral Displacement ( TSd ), and Peak Ground Acceleration (PGA) are the mostwidely used as intensity measures for analytical fragility curves, for different building typologies (DAyala and Meslem

2012). It is worth to mention that TSa and TSd are most easily correlated with the structural response and henceare considered as the most suitable variable for damage functions, especially for nonlinear static or dynamic-basedmethodologies. Methods based on limit state analysis and simplified methods tend to use PGA, also for ease of correlation

with empirical vulnerability analyses. For instance, considering the case of developing dS -based fragility curves, theEquation 5.1 becomes:

ids,dS

TdSln

ids

1dS|idsDSF

(5.2)

whereids,d

S is the median value of spectral displacement at which the building reaches the threshold of damage state,

ids .

5.1 Median valuesids,d

S and dispersionids

For nonlinear static-based fragility curves,ids,d

S is obtained by the transformation of adaptive pushovers curves, definedin terms of base shear vs. top displacement, into the equivalent Single Degree of Freedom (SDoF) capacity curves,

defined in terms of pseudo spectral acceleration ( aS ) vs. spectral displacement ( dS ), and which can be carried out using

32

the standard approach documented in many codes of practice, e.g. ATC-40 (ATC 1996); HAZUS-MH MR3 (FEMA-NIBS2003).

In the following, fragility curves are derived for the two modelling hypotheses: infilled frame and bare frame models,considering the expected range and central values of each structural characteristics-related parameter, as shown in Table2.1. Nineteen infilled frame models and nineteen bare frame models are selected. See Figure 4.2 and Table 3.1 for theconsidered parameters and variation of values, which are considered the most expected values that might be possibilityassigned, in case of lack of information, to represent the class of low-ductility RC buildings constructed with earlier seismiccodes (see Section 3).

Procedure 1: Distribution parameters computed from sensitivity analysis

The medianids,d

S is obtained as the central values (or the expected mean values) of the full range of variations of the

structural characteristics-related parameters considered in this study, as described in Section 2.3.3. The variabilityids

associated to each damage state threshold, is obtained by calculating, for the full range of variations, the lognormal ofeach structure response and the variance.

Figure 5.1 shows the fragility curves derived for each set of modelling choices, i.e., infilled frame and bare frame models.The corresponding values of spectral displacement and dispersion for each damage state threshold are presented inTable 5.1. It is evident form Figure 5.1 the role played by the inclusion or exclusion of the masonry infill in the modelling.The exclusion of infills contribution leads to a significant bias in fragility curves. The median displacement capacity variesfrom infilled frame models to bare frame models by a factor of 6.2, 2.2, and 1.8 for Slight Damage, Moderate Damage, andNear Collapse, respectively, as shown in Table 5.1. Indeed, when masonry infilled RC building are modelled as bareframe structure, the resulted fragility curves show greater lateral displacement capacity for all damage levels; whereas, thebuilding is found to be more vulnerable when the infilled frame model is used. In fact, the result of adaptive pushoveranalysis has shown that the first-storey mechanism is the most recurring, and modelling the infills leads to the occurrenceof this mechanism for smaller drifts compared to the case of bare frame assumption. It should be noted that difficultieshave been encountered to predict shear failure in columns. It is to recall that shear column failure might have a significanteffect on the structure performance, especially for structures designed without considering horizontal actions, or buildingwith low concrete strength.

With regards to the level of dispersion, this latter has found to be almost less different at Slight Damage (by factor of 0.7)and Near Collapse Damage (by a factor of 0.9), and remarkable at Moderate Damage (by a factor of 0.3), between the twomodelling hypotheses. On the other hand, the results have clearly showed that the value of dispersion varies from onestate of damage to the next, and this variation is neither linear nor monotonic, for the two modelling hypotheses. The valueof dispersion is found to be 0.32, 0.54, and 0.44 at Slight Damage, Moderate Damage, and Near Collapse, respectively,for set of infilled frame model; while for set of bare frame models the value is found to be 0.24, 0.17, and 0.40 at SlightDamage, Moderate Damage, and Near Collapse.

In the literature, the uncertainty in the structural capacity is accounted for by assuming an average values, constant for alldamage states. For instance, Kappos et al. (2006) constructed fragility curves by assuming an average value of 0.3 and0.25 for the uncertainty in the capacity for low and high code buildings, respectively, for all building types and constant alldamage states. These values have been suggested by FEMA-NIBS (2003) and HAZUS-MH (FEMA 2003). Throughout thestudy by Shahzada et al. (2011) a same default value of 0.3 was assigned for the uncertainty associated with the capacitycurve of buildings for all damage states, as it is proposed in Wen et al. (2004). Satter and Liel (2010) and Raghunandan et

33

al. (2012) have used a default value of 0.5, which has been suggested based on previous research work by Liel et al.(2009), to account for uncertainty due to the structural modelling, for Collapse level only.

The different values ofids

associated to damage state thresholds that have been obtained from numerical analysis are

found to be within the range of values used from various sources in literature.

Table 5.1 Median value and dispersion calculated for each threshold of damage state, and used in Figure 5.1

SystemSlight Damage (SD) Moderate Damage (MD) Near Collapse (NC)

Median [mm] Median [mm] Median [mm] Set of infilled frame models 7 0.32 61 0.54 114 0.44Set of bare frame models 43 0.24 132 0.17 206 0.40Ratio 6.2 0.7 2.2 0.3 1.8 0.9

Figure 5.1 Comparisons of fragility curves of the structures with and without considering the contribution of masonry infill walls.

Procedure 2: First-Order Second-Moment (FOSM)Recently, the First-Order Second-Moment (FOSM) method has been suggested by Vamvatsikos and Fragiadakis (2010)

for the estimation of the median valueids,d

S and the dispersionids

for every limit state. Actually, this method has been

already implemented in some previous studies, such as by Lee and Mosalam (2005) and Baker and Cornell (2008,), toestimate uncertainty associated with structural response. For the implementation of this method, the number of simulationsrequired is 12 K , where K is number of random variables. For a given limit state, the log of the median spectraldisplacement threshold is considered as a function of the random parameters. As four random parameters have beenused, this can be written as follows:

h,s,fy,fcfXfSln d (5.2)

where X ( h,s,fy,fcX ) is the vector of random modelling parameters with mean:

hSfyfc ,,,X (5.3)

34

The random parameters are set equal to their meankX

(where, k = 1,..., 4) to evaluate 0dSln . The remain K2simulations are obtained by considering in turn the parameter values (

kXkX ) while all other variables remain equal

to their meanjX

(with, kj ), obtainingmax

ln XdS andmin

ln XdS .

Using the second derivative of f with respect to kX , the median- is estimated as:

K

kX

Xk

Xdd

Xd

dX

K

k kdS k

k

kk

k

kX

d X

SSSSX

fSm1

22max

002

12

20

ln

minmax

lnln2ln21ln

21ln

(5.4)

and by assuming lognormality, the median displacement threshold can be computed simply as:

dSlnd

mexpS (5.5)

The standard deviation of the logs (dispersion) is estimated using a first-order derivative of f with respect to kX :

2

2

1minmax

2

1

22

minmax

lnlnk

kk

k

kX

X

K

k kk

Xd

Xd

X

K

k k XXSS

Xf

(5.6)

In Equations 5.4. and 5.6, the standard deviationskX is determined simply on the basis of the sensitivity analysis range,

having assumed a uniform distribution for each parameter (see Section 3), cons