2007_Technical Report_Belmouden_Lestuzzi_On the Seismic Vulnerability Assessment of URM Buildings_modeling Okok

On the seismic vulnerability assessment of unreinforced masonry existing buildings in Switzerland

1

ÉCOLE POLYTECHNIQUE FÉDÉRALE DE LAUSANNE

-EPFL-

APPLIED COMPUTING AND MECHANICS LABORATORY

-IMAC-

ON THE SEISMIC VULNERABILITY ASSESSMENT

OF UNREINFORCED MASONRY EXISTING

BUILDINGS IN SWITZERLAND

Authors:

Belmouden Y., Lestuzzi P.

[email protected] , [email protected]

École Polytechnique Fédérale de Lausanne (EPFL)

ENAC-IS-IMAC, EPFL, Station 18, CH-1015, Lausanne, Switzerland

Research Report

Lausanne, 03 December, 2007


2

In theory, there is no difference between theory and practice. But, in practice, there is.

- Jan L.A. Van de Snepscheut


3

Abstract

Earthquakes are considered to be the major cause of structural failure of buildings in Europe. Despite their rarity and

moderate intensity, earthquakes in the interior and particularly in Switzerland have the potential to cause extensive damage

and associated financial losses, due to the vulnerability of the local building stock. The present report summarizes a

contribution for seismic vulnerability assessment of existing unreinforced masonry buildings in Switzerland. The work

presents a methodology for modern fragility curve generation. For this purpose, a classification of typical buildings is

presented. Then, a Swiss-type unreinforced masonry building is selected. An investigation on the non linear behaviour of

unreinforced masonry structures is performed using both simplified and finite element methods. Capacity curves and capacity

spectrum are generated with and without torsion effect. Vulnerability functions are developed based on the EMS98 damage

grade. Moreover, the study shows the need of efficient and reliable simplified methods for seismic analysis of existing

buildings. Thus, a novel approach for capacity curves generation is developed and validated against experimental tests and

numerical results. Finally, the remaining steps that yield to modern fragility curves are defined.

Résumé Les tremblements de terre constituent la principale cause de destruction des bâtiments en Europe. Malgré leur rareté et leur

intensité jugée comme moyenne, les séismes en Europe centrale et en particulier en Suisse ont un grand potentiel destructeur

pouvant engendrer d’importants dommages et des pertes économiques, à cause de la vulnérabilité sismique du stock de

bâtiments local. Le présent rapport résume une contribution pour l’évaluation de la vulnérabilité sismique des bâtiments

existant en maçonnerie en Suisse. Le travail présente une méthodologie pour la génération de courbes de fragilité dites

modernes. Dans ce but, une classification de bâtiments types est présentée. Ensuite, un bâtiment en maçonnerie non armée du

type suisse a été sélectionné. Une investigation portant sur le comportement non linéaire des structures en maçonnerie non

armée est conduite en utilisant une méthode d’analyse simplifiée et la méthode des éléments finis. Des courbes de capacité et

des spectres de capacité sont générées avec et sans considération de l’effet de la torsion. Les fonctions de vulnérabilité sont

développées en fonction de l’échelle de dommage EMS98. En plus, l’étude a démontré le besoin d’une méthode fiable pour

l’analyse sismique des bâtiments existant. Ainsi, une nouvelle approche pour la génération des courbes de capacité a été

développée et validé par rapport à des résultats expérimentaux et numériques. Enfin, les étapes restantes menant aux courbes

de fragilité recherchées sont définies.


4

Contents

1. Introduction………………………………………………………………………….…………...….5

2. Methodology……………………………………………………………………………………..…..6

3. Building classification and typology………………………………………………………………..7

4. Structural analysis and damage assessment………………………………………………….…..11

4.1 Seismic vulnerability assessment using simplified models…………………………….…..11

4.2 Seismic vulnerability assessment using finite element models…….………………..……..14

4.3 A novel analytical model for capacity curves generation………………………………….21

4.3.1 Introduction……………………………………………………………………………....21

4.3.2 Description and hypotheses of the structural model…………………….…………….…22

4.3.3 A Pushover analysis of an URM building………………………………….…………….24

5. Conclusions and futur work……………………………………………………….………….…...31

6. References…………………………………………………………………………………………..31

Annexe I Correspondance entre les classifications de l’EMS-98, Risk_UE

et HAZUS-99………………………………………………………………………………...34

Annexe II Typologie du bâti existant suisse en vue de l'appréciation de sa vulnérabilité

sismique………………………………………………………………………………………42

Annexe III Bâtiments en maçonnerie non armée……...…………………………………..75

Annexe IV Modélisation du bâtiment existant en maçonnerie non armée par la méthode

des éléments finis multifibres……………………………………………………………….99

Annexe V Analyse modale du bâtiment existant en maçonnerie non armée…………...104

Annexe VI Méthode analytique d’analyse statique non linéaire simplifiée des bâtiments

existants en maçonnerie non armée……………………………………...………………..127

Annexe VII Modélisation parasismique…………………………………………………..133


5

1. Introduction

The present work is a contribution to the seismic vulnerability assessment and seismic risk

mitigation in Switzerland as the structural characteristics of Swiss building stock significantly differ

from those included in the existing methodologies. The work aims to provide a building classification

and fragility functions as a first step to develop realistic and modern fragility curves of existing

buildings in Switzerland and in particular for unreinforced masonry (URM) buildings. The present

work is a part of the VFK research project untitled ‘Wirklichkeitsnahe Erdbebenverletzbarkeits und

Verschiebungsfunktionen von Mauerwerksgebäuden’. The part of the EPFL team work concerns the

seismic vulnerability assessment of existing unreinforced masonry buildings in Switzerland. The main

objective is the development of realistic vulnerability functions for a selection of typical Swiss

masonry buildings based first, on the improvement of existing methodologies taking into accounts for

torsion effect and second, on the damage analysis of north Europe earthquake.

In this context, in the few last decades, technical advances have been made in seismic engineering

and particularly in the seismic vulnerability assessment of existing buildings. The vulnerability

assessment focuses on the study of the extent of damage for different earthquake scenarios. There are

two ways to describe the structural damage distribution in a given region: (1) fragility curves and, (2)

damage probability matrix (DPM) [2, 9]. Both of them represent the distribution of damage. The

former is a graphic continuous representation, and the latter uses a tabular discrete representation. One

of the most widely used methodologies is the so-called HAZUS methodology. HAZUS methodology

framework is composed of (1) input databases, (2) analysis modules and, (3) an application software

[1, 2]. HAZUS input data module requires (1) an inventory data from GIS information, (2) earthquake

hazard and geologic data maps and (3) analysis parameters.

In general, the vulnerability assessment of buildings includes (1) hazard analysis, (2) classification

of the critical existing structures with regard to their seismic vulnerability and (3) fragility curves

generation [1]. Fragility curves represent an analytical tool for decision making such as in the decision

process for emergency plans, retrofitting of critical structures as a mean of pre-disaster mitigation,

reinsurance policy and so on [4].

The VFK project started on 01/01/2007. It is organized into four main stages. The first and second

stages finishes on 31/10/2007. These involved the formulation of a methodology for vulnerability

functions and to define a typical Swiss unreinforced masonry existing building. The third phase is

planned to be achieved by 31/03/2008. This deals with capacity and vulnerability curves development.

The fourth phase consists of the application of new vulnerability curves to evaluate the seismic risk of

some examples. This stage is planned to be achieved by the end of 2008.

The report is organized as follows. A simplified description of the methodology is presented.

Then, a typology of existing buildings and a standardized classification of existing buildings are

proposed based on the available data. A summary of seismic analysis of a typical URM building using


6

analytical and finite element methods that include and neglect torsion effect is presented. Moreover, a

novel approach for capacity curves generation and structural damage prediction is developed and

described herein. Finally a preliminary series of fragility functions are developed for the Swiss-type

existing building.

This report is a synthesis of the work done till the end of 2007. More details may be found in the

following references [4, 5, 6, 10, 11, 36].

2. Methodology

By definition, fragility curves provide estimates for the probabilities of reaching or exceeding

different limit states at a given ground shaking intensity for a given building or a stock of buildings. In

general, three methods are provided for fragility curves generation:

(1) the empirical statistical method,

(2) the seismic code method as adopted by HAZUS99 (RMS, 1999),

(3) the analytical method as followed in this study and based on the nonlinear static Pushover

analysis.

Among the above mentioned methods, the third method is the most efficient one in particular

when sufficient and reliable post-earthquake data are unavailable [1]. This approach is used also when

the seismic capacity due to ductility details of structural components can not be implemented with

sufficient accuracy. This is more likely to happen in existing unreinforced masonry buildings. Further

details on the methods can be found in these references [1, 2, 7, and others]. The proposed

methodology for realistic fragility generation is based on the following steps (Fig. 1):

1- A classification of existing buildings based on experts and engineering judgment, structural

criteria (structural wall, frame, slabs, structural regularity, storey height,…), material type

(steel, concrete, masonry, wood, adobe, and others…), and mechanical characteristics

(lateral stiffness indices, seismic resistance indices, elastic period of vibration,…),

2- Nonlinear analysis of the buildings (Pushover analysis, NSP): capacity curves generation,

median capacity curves for typical buildings, reliable and efficient damage grade model;

3- Vulnerability assessment of existing buildings (vulnerability functions, fragility curves in

absence of torsion effect, fragility surfaces if torsion effect is considered),

4- Single and typical multiple degree of freedom systems (Modal spectral analysis (ADRS),

Nonlinear dynamic analysis (IDA), damage models compatibility, seismic records data

base,…),

5- Calibration of existing models such as HAZUS for seismic risk mitigation in Switzerland.


7

InventoryInventory: Class of buildings Structural Structural criteriacriteria: N°storey, storey Heigth,Regularity,…

MechanicalMechanical characteristicscharacteristicscriteriacriteria:: Floor Mass, Inertia, Floor Area, etc….

PushoverPushover analysisanalysis (NSP)(NSP)ModelsModels:

Simplified, FEM

TypicalTypical capacitycapacity curvecurve(bilin. or trilin. Idealization)

DGDG:Damage degree model

DemandDemand SpectrumSpectrum(Scenarios, seismic

microzonation)

TypicalTypical SDOFSDOF(IDA analysis

SeismicSeismicrecords records

(data base)

AnalyticalAnalyticalfragilityfragility curvescurves

(Developpedmethod)

FragilityFragilitycurvescurves

(HAZUS)

HAZUS calibration

TypicalTypical CC (ADRS format)CC (ADRS format)

AnalyticalAnalyticalfragilityfragility curvescurves

Figure 1 Flow chart of the proposed methodology for realistic fragility curves generation

3. Building classification and typology

Classifications and typology of existing buildings is the most challenging task for fragility

analysis. The critical issue is the availability of a building stock and the related database. The

buildings are first categorized into different classes according to their structural system and

characteristics (construction material type) [1]. The model is decomposed into 10 main classes and 7

sub-classes [5] (See Appendix 1). The main criteria followed for the classification is based on the

structural system and material type of the buildings. However, an efficient approach necessitates

including the number of storeys, year of construction (construction age) and class of vulnerability. As

the data of individual buildings is not enough to develop a representative and efficient model for

parameters that affect closely the resulting fragility functions, the curves have to be considered as a

first attempt for seismic vulnerability assessment in Switzerland. This first investigation was

strengthened by a second one performed at the EPFL [6] (voir Annexe 2) in a semester project by

Bieri M., Gentil T., Michaud N (Tabl. 2). This study had focused mainly on the ‘Office Federal des

Douanes’ building stock. Some examples are shown in the figures 3, 4, and 5.


8

Table 1 Proposed classification of existing buildings in Switzerland [5] (voir Annexe 1)


9

Figure 2 An URM typical existing building (Yverdon-les-bains building) [4, 5]

Table 2 Description of the building stock of the ‘Office Federal des Douanes’ [6] (voir Annexe 2)


10

Figure 3 Dörflingen Zollgebäude building [6]

Figure 4 Oberriet building [6]

Figure 5 Vernier building [6]


11

4. Structural analysis and damage assessment of an URM typical existing building

In order to obtain fragility curves, damage states need to be defined. In this study the EMS98-

based damage states are considered. Both HAZUS and Risk_UE damage states are also used and

compared to the EMS98 damage grade. In the EMS98 model, damage states are defined in a

qualitative manner. However, in the HAZUS [2] and Risk_UE [8] models, damage states are defined

in terms of inter-storey drift. A total of five damage grades are provided by all of these models. These

are: none, slight, moderate, extensive, and complete damage. Each damage grade can be defined in

terms of structural damage according to the constructed material type of the building prototype. In this

study, vulnerability functions are developed for typical URM structure using EMS98 damage grade.

Hence, a simplified description of each damage can be found in the references [3, 4, 7]. It is well

known that fragility curves represent a probabilistic measure for the fragility of a prototype of

buildings under various levels of ground motions [1]. Two kinds of fragility curves can be obtained:

empirical fragility curves or analytical fragility curves. The project aims to generate analytical fragility

curves as ultimate goal. For this purpose, a Pushover-based approach is used. In this study,

vulnerability functions are developed only as an intermediate stage before development of fragility

curves. Different methods for structural analysis are tested such as a simplified methods and finite

element method.

4.1 Seismic vulnerability assessment using simplified models

The generated capacity curves are based on the simplified method called ‘Lang’ method [7] (See

Appendix 6). For vulnerability assessment, the Yverdon-les-bains building was selected (Fig. 2, 6).

This building was found to be the representative existing URM building in Switzerland based on

expert judgements and structural criteria. The building is a four storey structure with reinforced

concrete slabs. The building has 35 walls in the longitudinal direction (x-direction) and 15 walls in the

transversal direction (y-direction). All these masonry walls have a same thickness equal to 250mm.

The storey height is equal to 2.5m (Fig. 6). The structural damage criteria followed in the seismic

vulnerability assessment is based on the EMS-98 damage grade [3]. Five damage degrees are

considered: DG1 (Negligible), DG2 (Moderate), DG3 (Substantial to heavy), DG4 (Very heavy), and

DG5 (Destruction). The gravity load (dead+live load) acting on the floor is equal to 7kN/m2. The total

floor mass is equal to 252tons. Additional data and assumptions are given in the following references

[4, 5]. Four cases are investigated for the structural analysis (tabl. 3).

Model Assumptions

M1 Restricted ductility equal to 12 for masonry walls (Lang assumption [7]), Frame effect neglected

M2 Restricted ductility equal to 12 for masonry walls (Lang assumption [7]), Frame effect considered M3 Non restricted ductility for masonry walls, Frame effect neglected

M4 Non restricted ductility for masonry walls, Frame effect considered

Table 3 Case studies of the Yverdon-les-bains building


12

Figure 6 Layout of the ground floor of the Yverdon-les-bains building (X-X : Longitudinal direction, Y-Y : Transversal

direction)

Both capacity curves and capacity spectrum are generated using the simplified model. The

capacity curve represents graphically the seismic behaviour of a building. The graphic ordinate

represents the total base shear of the building while its abscissa represents the roof displacement. The

capacity spectrum represents graphically the seismic behaviour of a building but using spectral

parameters. The graphic ordinate represents the spectral acceleration of the building while its abscissa

represents the spectral top displacement. This transformation is called ‘ADRS’ format. It includes the

dynamic characteristics of the building in comparison to the capacity curves that are restricted only to

static characteristics. The ADRS transformation is detailed in the Applied Technology Council 1996

[4, 16].


13

0

500

1000

1500

2000

2500

3000

3500

0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30

Déplacement au sommet (mm)

Effo

rt tr

anch

ant à

la b

ase

(kN

)M1_xM1_yM2_xM2_yM3_xM3_yM4_xM4_y

Roof Roof DisplacementDisplacement (mm)(mm)

Tota

l Bas

e To

tal B

ase

Shea

rSh

ear ((

kNkN))

Solid lines : Restricted ductilityDotted lines : Infinite ductility

Figure 7 Capacity curves in the principal directions of the Yverdon-les-bains building

0

1

2

3

4

5

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 6.5 7 7.5 8 8.5

Déplacement spectral Sd (mm)

Deg

ré d

e dé

gats

M1_DG_xM1_DG_yM2_DG_xM2_DG_yM3_DG_xM3_DG_yM4_DG_xM4_DG_y

Spectral Spectral DisplacementDisplacement (mm)(mm)

Dam

age

grad

e D

amag

e gr

ade

Figure 8 Vulnerability functions of the Yverdon-les-bains building with regards to the EMS98 damage grade


14

Based on the results from the simplified method, the following remarks are drawn [4]:

1. Ductility of masonry walls: The figure 7 shows the effect of the ductility of

masonry walls on the damage assessment of the building (M1_x and M3_x ; M1_y

and M3_y ; M2_x and M4_x ; M2_y and M4_y ). The structural behaviour shift

from relatively weak behavior (restricted ductility equal to 12 [7]) to a ductile

behaviour (non restricted ductility). This result is considered with caution since the

real behavior is somewhere between these two particular cases.

2. Frame effect: The frame effect substantially increases the global strength or

resistance of the building. The total base shear is increased by 42% in the Y-Y

direction, when it is increased by 69.7% in the X-X direction (Fig. 7).

3. Damage prediction: The results show that all cases are close until the damage grade

2. For the subsequent damage grades, the contribution of the non restricted ductility

characteristic provides additional capacity for the structure to withstand earthquake

with high intensities. Similar results are shown when considering coupling effect

between parallel walls (frame effect). The generated vulnerability functions (Fig. 8)

show the sensitivity of the results from initial assumption of the model. Thus the

vulnerability assessment is influenced by the considered model, particularly for

high damage grades that describe the vulnerability of structures subjected to

relatively strong earthquakes.

Finally, it is evident that the followed simplified method suffers from some limitations such as non

redistribution of forces, plastic hinge and non linearity concentrated only at the first storey, constant

coupling (or frame effect) between walls, no spandrel effect is considered, elastic perfectly plastic law

of behaviour for the walls and so on. Moreover, torsion effect is not considered in the method. Torsion

effect has to be considered in a three-dimensional model of the structure.

4.2 Seismic Vulnerability assessment using finite element models

The structural analysis of the Yverdon-les-bains building was performed with a multifiber smeared

crack model using Drain-3DX software. The material constitutive models for masonry, the mechanical

and geometrical characteristics for the entire structure and the structural modelling assumptions are

given in reference [4]. The building belongs to the ‘M3.4M Pre-Code’ class with regards to the Risk-

UE model [8]. In the ‘XX’ series of models, masonry walls in the ‘ZZ’ direction are omitted.

Similarly, in the ‘ZZ’ series of models, walls in the ‘XX’ direction are not considered. However, for

the ‘XZ’ models, all the walls in both orthogonal directions, ‘XX’ and ‘ZZ’, were considered. The

building is analysed using the simplified method with and without frame effect (100% of the floor out-

of-plane inertia Ipl, and 10% of the floor out-of-plane inertia Ipl) (Tabl. 4).


15

Again, the results obtained from the simplified method are shown and compared to those extracted

from finite element method. The considered models with and without frame effect are named such as

the ‘simplified-1’ and the ‘simplified–2’ model respectively. Both models consider an unrestricted

ductility for masonry walls. Models Lateral load

direction

Frame effect :

Floor out-of-plane stiffness

Structural model without spandrels

M_XX1 X-X Ipl

M_XX2 X-X 10% Ipl

M_ZZ1 Z-Z Ipl

M_ZZ2 Z-Z 10% Ipl

M_XZ1 X-X and Z-Z Ipl

M_XZ2 X-X and Z-Z 10% Ipl

Structural model with spandrels but without rigid offsets

MSZR_XX1 X-X Ipl

MSZR_XX2 X-X 10% Ipl

MSZR_ZZ1 Z-Z Ipl

MSZR_ZZ2 Z-Z 10% Ipl

MSZR_XZ1 X-X and Z-Z Ipl

MSZR_XZ2 X-X and Z-Z 10% Ipl

Table 4 Model assumptions for the Yverdon-les-bains building

0

1000

2000

3000

4000

5000

6000

0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04 0.045 0.05

Déplacement au sommet (m)

Effo

rt tra

ncha

nt to

tal à

la b

ase

(kN

)

M-XX1

M-XX2

MSZR-XX1

MSZR-XX2

Simplifié - 1

Simplifié - 2

Roof displacement (m)

Tota

l bas

e sh

ear(

kN)

Simplified 1

Simplified 2

MSZR-XX1

MSZR-XX2M-XX1

M-XX2

Simplified 1

Simplified 2

Figure 9 Capacity curves generated using finite element method and simplified analysis in the longitudinal direction of the

building without torsion effect


16

0

500

1000

1500

2000

2500

3000

3500

0 0.005 0.01 0.015 0.02 0.025Déplacement au sommet (m)

Effo

rt tra

ncha

nt to

tal à

la b

ase

(kN

)

M-ZZ1

M-ZZ2

MSZR-ZZ1

MSZR-ZZ2

Simplifié ZZ - 1

Simplifié ZZ - 2

Roof displacement (m)

Tota

l bas

e sh

ear(

kN)

Simplified 1

Simplified 2

MSZR-ZZ1M-ZZ1

MSZR-ZZ2M-ZZ2

Simplified 1

Simplified 2

Figure 10 Capacity curves generated using finite element method and simplified analysis in the transversal direction of the


0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04

Déplacement spectral du sommet (m)

Acc

élér

atio

n sp

ectr

ale

(g)

M-XX1

M-XX2

MSZR-XX1

MSZR-XX2

Simplifié XX - 1

Simplifié XX - 2

M3.4M Risk_UE

M3.4L Risk_UE

M3.4L

M3.4M

Simplifié - 2

Simplifié - 1

Roof spectral displacement (m)

Spec

tral a

ccel

erat

ion

(g)

Simplified 1

Simplified 2

Simplified 1

Simplified 2

MSZR-XX1

M-XX1MSZR-XX2

M-XX2

Figure 11 Capacity spectrum generated using finite element method and simplified analysis in the longitudinal direction of

the building without torsion effect


17

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04

Déplacement spectral au sommet (m)

Acc

élér

atio

n sp

ectr

ale

(g)

M-ZZ1

M-ZZ2

MSZR-ZZ1

MSZR-ZZ2

Simplifié ZZ - 1

Simplifié ZZ - 2

M3.4M Risk_UE

M3.4L Risk_UE

M3.4L

M3.4M

Simplifié - 2

Simplifié - 1

Roof spectral displacement (m)

Spec

tral a

ccel

erat

ion

(g)

Simplified 1

Simplified 2Simplified 1

Simplified 2

MSZR-ZZ1M-ZZ1

MSZR-ZZ2M-ZZ2

Figure 12 Capacity spectrum generated using finite element method and simplified analysis in the transversal direction of the


0

1000

2000

3000

4000

5000

6000

7000

8000

0 0.005 0.01 0.015 0.02 0.025 0.03Déplacement au sommet du CM (m)

Effo

rt tra

ncha

nt to

tal à

la b

ase

(kN

)

M-XZ1 Mode 1 Sens XX

M-XZ1 Mode 1 Sens ZZ



Simplifié XX - 1

Simplifié XX - 2

Simplifié ZZ - 1

Simplifié ZZ - 2

Mode 2 Sens XX

Mode 1 Sens XX

Mode 1 Sens ZZ

Mode 2 Sens ZZ

Simplifié XX - 1

Simplifié ZZ - 1

Simplifié ZZ - 2

Simplifié XX - 2

Roof displacement of the center of mass (m)

Tota

l bas

e sh

ear(

kN)

Simplified XX-1

Simplified XX-1

Simplified XX-2

Simplified XX-2

Simplified ZZ-1

Simplified ZZ-2Simplified ZZ-1

Simplified ZZ-2

Mode 2 dirc-XXM-XZ1 Mode 2 dirc-XX

M-XZ1 Mode 1 dirc-XX

M-XZ1 Mode 1 dirc-ZZ


Mode 1 dirc-XX

Mode 1 dirc-ZZ

Mode 2 dirc-ZZ

Figure 13 Capacity curves generated using finite element method in both longitudinal direction (dirc-XX) and transversal

(dirc-ZZ) direction of the building with torsion effect for mode of vibration 1 and 2


18

0

1000

2000

3000

4000

5000

6000

7000

8000


Effo

rt tra

ncha

nt to

tal à

la b

ase

(kN

)





M-XX1

M-XX2

Mode 2 Sens XX

Mode 1 Sens XXMode 1 Sens ZZ

Mode 2 Sens ZZ

M-XX2

M-XX1

Tota

l bas

e sh

ear(

kN)


Mode 2 dirc-XX

Mode 1 dirc-XX Mode 1 dirc-ZZ

Mode 2 dirc-ZZ

M-XX 1

M-XX 2





M-XX 1

M-XX 2

Figure 14 Capacity curves generated using finite element method with and without torsion effect in the longitudinal direction

(dirc-XX) for mode of vibration 1 and 2

0

1000

2000

3000

4000

5000

6000

7000

8000


Effo

rt tra

ncha

nt to

tal à

la b

ase

(kN

)





M-ZZ1

M-ZZ2

Mode 2 Sens XX

Mode 1 Sens XX

Mode 1 Sens ZZ

Mode 2 Sens ZZ

M-ZZ1 M-ZZ2

Tota

l bas

e sh

ear(

kN)


Mode 2 dirc-XX

Mode 1 dirc-XX

Mode 1 dirc-ZZ

Mode 2 dirc-ZZ

M-ZZ2M-ZZ1





M-ZZ 1

M-ZZ 2

Figure 15 Capacity curves generated using finite element method with and without torsion effect in the transversal direction

(dirc-ZZ) for mode of vibration 1 and 2


19

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

0 0.005 0.01 0.015 0.02 0.025 0.03Déplacement spectral du CM (m)

Acc

élér

atio

n sp

ectra

le (g

)





Simplifié XX - 1

Simplifié XX - 2

Simplifié ZZ - 1

Simplifié ZZ - 2Simplifié XX - 1

Simplifié ZZ - 1

Simplifié ZZ - 2

Simplifié XX - 2

Mode 2 Sens XX

Mode 1 Sens XXMode 1 Sens ZZ

Mode 2 Sens ZZ

Spec

tral a

ccel

erat

ion

(g)

Roof spectral displacement of the center of mass (m)

Simplified XX-1

Simplified XX-2

Simplified ZZ-1

Simplified ZZ-2

Mode 2 dirc-XX

Mode 1 dirc-XX

Mode 1 dirc-ZZ

Mode 2 dirc-ZZ

Simplified XX-1

Simplified XX-2

Simplified ZZ-1

Simplified ZZ-2





Figure 16 Capacity spectrum generated using finite element method with torsion effect in the longitudinal direction (dirc-XX)

and transversal direction (dirc-ZZ) for mode of vibration 1 and 2

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04Déplacement spectral du CM (m)

Acc

élér

atio

n sp

ectra

le (g

)





M-XX1

M-XX2

M3.4M Risk_UE

M3.4L Risk_UE

Mode 2 Sens XXMode 1 Sens XX

Mode 1 Sens ZZ

Mode 2 Sens ZZ

M3.4M

M3.4L

M-XX1

M-XX2

Spe

ctra

l acc

eler

atio

n(g

)


Mode 2 dirc-XX

Mode 1 dirc-XXMode 1 dirc-ZZ

Mode 2 dirc-ZZ M-XZ1 Mode 2 dirc-XX




M-XX 1

M-XX 2

Figure 17 Capacity spectrum generated using finite element method with and without torsion effect in the longitudinal

direction (dirc-XX) for mode of vibration 1 and 2


20

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04Déplacement spectral du CM (m)

Acc

élér

atio

n sp

ectra

le (g

)





M-ZZ1

M-ZZ2

M3.4M Risk_UE

M3.4L Risk_UE

Mode 2 Sens XXMode 1 Sens XX

Mode 1 Sens ZZ

Mode 2 Sens ZZ

M3.4M

M3.4LM-ZZ1 M-ZZ2

Spec

tral a

ccel

erat

ion

(g)


Mode 2 dirc-XX

Mode 1 dirc-XXMode 1 dirc-ZZ

Mode 2 dirc-ZZM-XZ1 Mode 2 dirc-XX




Figure 18 Capacity spectrum generated using finite element method with and without torsion effect in the transversal

direction (dirc-ZZ) for mode of vibration 1 and 2

In the following the main results of the vulnerability assessment of the building are given. It

consists of capacity curves and capacity spectrum generated by a simplified method and a finite

element method. However, for a detailed description of the results refer to the reference [4].

1- The results show that both capacity curves (Fig. 9, 10, 13, 14, 15) and capacity spectrum

(Fig. 11, 12, 16, 17, 18) generation are challenging tasks for unreinforced masonry

structures. In particular for deformation capacity prediction for the structure. The failure

criteria was based both on maximum compressive strains in the masonry fibers and on the

global stiffness (significant loss of the stiffness),

2- In general all followed methods (finite element, simplified) give results close to the elastic

stiffness of the building (Fig. 9, 10, 11, 12, 13, 16). However, maximum strengths and

deformations are found to be very different. These performances need to be defined with

sufficient accuracy in order to develop reliable fragility curves that are based on damage

prediction in the structure (strength and deformation criteria). It is found that these

differences are due to various effects such as the spandrel contribution in the structural

behavior, the material constitutive models for masonry structures and the considered failure

modes of behavior. Moreover, it was found that the standardized Risk_UE curves do not

closely match those generated by finite elements and simplified methods. These results

encourage us to develop specific capacity curves and capacity spectra that realistically

represent the behavior of Swiss type buildings.


21

3- In the absence of torsion, the capacity curves (Fig. 9, 10) and the capacity spectra (Fig. 11,

12) are correlated. However, they are not correlated when torsion deformation is

considered (Fig. 13, 14). The capacity curves with or without torsion are substantially

different and then the damage states predictions are different from one curve to another.

The trend is seen for capacity spectra with and without torsion effect (Fig. 17, 18). Another

critical issue is the combination of modes of vibration in the case of multiple significant

modes of vibration: combinations of capacity spectra for different modes of vibration in a

given direction. It should be noted that the capacity curves and the capacity spectra are

plotted with regards to the center of mass. In the presence of torsion, the behavior can

differ from a point to another (center of mass, center of shear, stiff edge, flexible edge and

so on),

4- It has been found that values for structural flexibility, maximum strengths, maximum

deformations, failure mechanisms, and structural collapse extracted when torsion effect is

considered differ substantially from those calculated without torsion. This leads to the

conclusion that the torsion effect has to be considered in the fragility curves.

4.3 A novel analytical model for capacity curves generation

4.3.1 Introduction

In this paragraph, an analytical model for seismic vulnerability assessment of existing

buildings is presented. The need for such models is always motivated by first, the large amount of

structures that should be analyzed in a very short time and second, the search for optimal solutions for

structural retrofitting.

For vulnerability assessment purposes, the analysis of a large number of existing buildings requires

relatively simple approaches that are capable of representing their essential characteristics. The models

should be able to evaluate the ultimate strength, maximum displacements and the failure modes.

Different models are developed based on analytical and finite element approaches [12]. The analytical

models are found to be very simple to use and require lesser amount of data. However they are very

limited, particularly for large building analysis in terms of structural behavior (coupling effect,

distribution of the nonlinearity, force – moment interaction and force redistribution, spandrel effect,

coupling effect between parallel walls, modes of failures prediction and so on). The performed

analyses show that they are conservative and are not able to represent all features of such buildings

[4]. On the other hand, finite element approaches are powerful tools for seismic analysis but they are

time consuming and require large amounts of data. Moreover, refined models based on either discrete

or continuum approaches suffer from strong mesh-dependency and require numerous parameters that

may not be directly extractable from structural analysis. Hence, these models are very sensitive to the

parameter calibration that directly affects the reliability of the results and the analysis stability (lack of

convergence, flip-flop occurrence, sudden load falling, and so on). With such methods it is not


22

possible to treat a stock of buildings. Thus, these methods are cumbersome due to the high analytical

skills required for their numerical implementation and they are restricted only to practitioners with a

high level of knowledge.

A widely used model for structural analysis is the linear (beam-column element) finite element or

the equivalent frame model. Despite some limitations in the equivalent frame model, it is very

attractive in comparison to complex finite element models [12, 13, 14, 15]. Moreover, they have

shown satisfactory results particularly for RC structures. In this context, the proposed model is based

on beam-column element and distributed non-linearity approaches. It is adapted to analytical methods

without use of finite element method.

4.3.2 Description and hypotheses of the structural model

The mathematical model can represent solid walls, frame structural elements (made in beams

and columns), coupled walls and perforated walls [16]. The model can represent different openings.

However, the vertical axis should lies through all vertical piers elements as well as for the horizontal

axes that should lies through all spandrels.

The structural model consists of an assemblage of vertical plane walls with openings that form a

single perforated wall. Each structural wall is made of pier elements with or without rigid offsets and a

portion of spandrels such that there are two kinds of individual walls: exterior walls and interior walls

(Fig. 19). The length of these parts of spandrels is equal to the zero moment length, and can be

updated at each step depending on the bending moments at the spandrel ends.

In the equivalent frame models that are based on finite element method, nonlinear flexural springs

(lumped plasticity) are inserted into the model at the ends of the piers and/or spandrel elements. These

elements are defined in terms of moment-rotation laws. Translational shear springs are added at each

pier and spandrel at mid-points. These springs are expressed in terms of shear force–displacement

laws. However, the occurrence of yielding is unlikely along spandrel spans and piers heights. For this

reason, nonlinearity should be distributed along the clear pier height and clear spandrel length. Thus,

the proposed model is based on the spread nonlinearity approach. Each pier and spandrel can be

discretized into a series of slices [17] and each cross-section is considered as homogeneous. The

structural element behavior is monitored at the center of the slices [17] while bending moments are

evaluated at slice ends.

The mechanical model undergoes flexural as well as shear deformation. In the current formulation,

the model only considers a biaxial interaction between axial forces - bending moments (N-M) and

axial forces - shear forces (N-V). The so-called shifting of the primary curve technique is used [18].

The axial force is evaluated in a simple manner based on initial axial forces plus vertical shear forces

produced in spandrels at joints. A triaxial interaction rule, (N-M-V), is not currently considered. At

present, only interaction curves that represent bending moment or shear force interaction with regards


23

to a compressive axial force are considered. The major features of this model are summarized as

follows:

1- All previous attempts to use simplified models based on static equilibrium method, always consider

a constant zero moment location (Nuray Aydinoğlu [19], Kilar and Fajfar [20], Lang [7], FEMA356

[21], FEMA306 [22], Paquette and Bruneau [23], and others). The wall formulation herein permits the

capture of the coupling effect in elevation due to the nonlinearity distribution in both piers and

spandrels. Thus, the zero moment location in both piers and spandrels can be mitigated during the

nonlinear analysis.

2- In the current development, the variation of the axial vertical loads are considered for piers only and

they are based on an over-simplified approach. The axial loads on piers are updated based on the

initial axial forces at each storey plus the shear forces developed on spandrel ends.

3- The nonlinearity is treated using a smeared plasticity approach [17]. Thus, the piers and spandrels

are discretized into finite homogenized slices [24]. Variable sections can be specified over either

spandrels or piers. In pier elements the axial forces can increase or decrease. In that case, the pier

slices can shift either from elastic-to-plastic or from plastic-to-elastic state depending on the axial

force distribution.

4- The model can take into account both flexural and shear behavior in the inelastic range. The

interaction effect can be defined by using experimental and phenomenological models. These

equations are considered as failure criteria that can be defined by points and linear segments. The non

linear constitutive model for both flexural and shear behavior is considered as a bilinear envelop curve

with a very small post-yield stiffness to avoid numerical problems. The flexural behavior is modelled

as a moment-curvature law that is based on an equilibrium statement in a cross-section.

5- The present formulation deals with a Pushover analysis. It is based on the well-known event-to-

event strategy. A simplified algorithm for systems with interaction effect is presented through an

equilibrium correction at each step of calculation. The analysis is performed by a force-controlled

technique. The change of sign in a structural element is permitted only in the elastic range. In the

inelastic range, this leads to stoppage of the analysis.

6- The structural wall is a planar structure (two-dimensional). However, the sum of all capacity curves,

on the basis of the equal top displacement assumption, permits to analyze an entire building and to

develop capacity curves.


24

F

EdgeEdge wallwall EdgeEdge wallwallIntermediateIntermediate wallwall

Rigid zone

Deformablepart

Opening

F

ih

iL

spl

ph

Figure 19 A schematic representation of equivalent frame model for planar walls with openings

4.3.3. A Pushover analysis of an URM building

The proposed model can be used also for modeling URM structures. The URM piers and spandrels

are subdivided into a series of slices. The slices represent a homogeneous brick and mortar one-phase

material. As known, the masonry material is a weak isotropic material with very limited ductility.

Thus, the softening behavior is very burdensome for computation and causes failure of convergence

problems particularly when the analysis is force-controlled. The post-peak behavior with softening is

beyond the scope of this model. The yield criteria considered are expressed for flexure (Eq. 1) and for

shear behavior (Eq. 2) according to the Magenes model (Ref. [20], [7], and [21]) as follows:

( ) 0, 2 ≤++= NNMMNf βα (1)

( ) ⎜⎜⎝

⎛++

−=N

NNVMINVNf1

211,

γβα ) 01 3322 ≤+−++ NVNV βαβα (2)

Two constants α and β are required for flexure failure criteria, while nine constants αi, βi and γi (for

i=1,3) are required for shear failure criteria (Ref. [30], [31], and [32]). N is the axial compressive load

acting on a pier element. The same failure criteria can be found in many other procedures for masonry

assessment (Ref. [21], [22], [23], [33] and others]. These equations deal with elastic perfectly plastic

models in terms of moment- rotation and shear force – displacement laws. In this study, the behavior

of the spandrel is assumed to be elastic linear in both flexure and shear.

A full-scale two-storey unreinforced masonry tested at the Pavia University was chosen for

model validation (Ref. [30], [31], and [32]). This structure has been extensively studied in literature

with different models:

1- using both a plane-stress nonlinear finite element in a continuum model (F.E.M) and a simplified

finite element point hinge model (SAM: Simplified Analysis of Masonry buildings), [31]


25

2- using a nonlinear eight node solid element (Solid 65, ANSYS Software) with a triaxial yield criteria

initially developed for concrete materials and a simplified phenomenological model [15]

3- using a simplified phenomenological model with a diagonal truss-plasticity approach and upper

bound plasticity theory [7]

4- using a beam element (a macro element) with additional degrees of freedom (TREMURI program)

[35].

A remarkable feature of this structure is that axial loads in piers vary during the experimental

test. The variation of the axial load in the considered structure is exploited to study the sensitivity of

the model to the axial force variation in piers. The structural model is subjected to increasing lateral

forces that are applied at the floor levels, keeping a 1:1 ratio between the force at the first and the

second floor. In this application the door wall D (Fig. 20, 21) was chosen as no flange effect is

considered. The elastic properties of the structure used in the model are summarized as follows:

The maximum compressive strength of a masonry prism orthogonal to the mortar bed, fm, is equal to

7.9MPa [32], and the shear modulus (Geff=90fm) is equal to the effective value. For full data see Ref

[32].

Figure 20 Geometry of the model building


26

145.2

99.2

835.3

07.5

7525.5

235.1 1088.2

365.1

69.1

5314.2

1P 2P 3P

398.3

5069.5

94.094.0

7625.2

5314.2

435.6

Figure 21 Elevation view of the wall D and geometry (in m). Exterior walls length and axial loads on the bottom and top

levels are equal to 1.15m, 56kN, 26.9kN respectively. Interior wall length and axial loads on the bottom and top level are

equal to 1.82m, 133kN, and 64.5kN respectively

In the current application, The (N-M) interaction is shown in the figure 22. However, the (N-V)

interaction was not activated. In fact, it was found that axial forces in the second storey are confined to

the first failure mode domain of validity (Fig. 23) since the variation in axial forces for this storey is

very low. The second and third modes of failures are not activated. However, despite the variation in

axial forces in the first storey, they are confined to the second failure mode domain of occurrence

during the analysis (Fig. 23). Hence, an elastic perfectly plastic model without (N-V) interaction is

used.

0

100

200

300

400

500

600

700

800

900

1000

0 100 200 300 400 500 600Bending moment (kN)

Axi

al fo

rce

(kN

)

Exterior wallsInterior walls

Figure 22 Flexural criteria for rocking mode of failure in piers


27

29

0

50

100

150

200

250

300

350

400

450

500

0 50 100 150 200 250 300Shear force (kN)

Axi

al fo

rce

(kN

)

Vshear mode 1Vshear mode 2Vshear mode 3Minimum Shear

Mode 1Mode 1

Mode 2Mode 2

Mode 3Mode 3

Figure 23 Shear failure criteria for piers only. Mode 1: (cs) shear failure along bed-joints at the end section cracked in

flexure; Mode 2 : (ws) diagonal cracking at the centre of the panel due to mortar joint failure; Mode 3: (b) diagonal cracking

at the centre of the panel due to brick failure

The use of rigid offsets is a crucial issue in equivalent frame modelling. The dimensions of rigid

offsets in piers are calculated based on an empirical approach proposed by Dolce [34]. In this study,

full rigid offsets are considered. The capacity curves (total base shear versus top lateral displacement)

are developed for different cases (Table 5).

In the light of the obtained results, the following recommendations are made:

1- The effect of the axial force - bending moment, (N-M), interaction is showed by the case ‘1’ and

‘2’. As displayed in figure 24, as axial compressive load increases, flexural strength of the piers also

increases with regards to the failure criteria (Fig. 22).

2- The nonlinear effect of shear mechanism is illustrated by cases ‘3’ and ‘4’ in the absence of rigid

offsets, and by cases ‘7’, ‘8’ and ‘9’ in the presence of rigid offsets (Fig. 25). As expected, the

contribution of shear mechanism tends to decrease the capacity of the structure due to the occurrence

of shear damage. This feature is successfully captured by the simplified model.

3- As displayed in figures 24 and 25, the rigid offsets have a significant effect on the global response.

They affect not only the stiffness, but also the strength capacity of the structure (Ref. [15], [24], and

[31]). This is expected as the horizontal element stiffness closely affects the contribution of the frame

mechanism to structural response (cases ‘10’, ‘11’ and ‘12’). The capacity curves obtained from EFM

(case ‘12’) versus PHFE model (case ‘13’) are satisfactory.

4- In cases ‘12’ and ‘13’, the two capacity curves are close to a certain extent in spite of the smeared

approach in the EFM. Both cases ‘5-6’, and ‘12-13’, show the comparison of the modelling

performance, including shear effect and (N-M) interaction rule and using either the EFM and the

PHFE model with or without rigid zones.


28

0

20

40

60

80

100

120

140

160

0 2 4 6 8 10 12 14 16 18

Roof lateral displacement (mm)

Tota

l bas

e sh

ear

(kN

)

ExperimentCase 1Case 2Case 3Case 4Case 5Case 6

Experiment

Case 3

Case 2Case 1, 4 and 6

Case 5

Figure 24 Capacity curves of the wall D with no rigid offsets

0

20

40

60

80

100

120

140

160

180

0 2 4 6 8 10 12 14 16 18

Roof lateral displacement (mm)

Tota

l bas

e sh

ear

(kN

)

ExperimentCase 7Case 8Case 9Case 10Case 11Case 12Case 13

Experiment

Case 8

Case 12

Figure 25 Capacity curves of the wall D with rigid offsets


29

Case Model type

Rigid Zone in Pier

Rigid Zone in Spandrel

(N-M) failure criteria

V Shear effect

Maximum strength ratio (*)

1 PHFE - - - - -20.1% 2 PHFE - - - -15.5% 3 EFM - - - -10.7% 4 PHFE - - - -21.7% 5 PHFE - - -22.4% 6 EFM - - -20.5% 7 EFM (with 2Em) - -9.9% 8 EFM (with 2Em) - - +18% 9 EFM (with 4Em) - -9.9% 10 EFM (with 10Em) - -9.0% 11 EFM (with 2Em) (with 2Em) -8.5% 12 EFM (with 10Em) (with 10Em) -7.1% 13 PHFE (with 10Em) (with 10Em) -9.3%

Legend: PHFE: Point Hinge Finite Element model, EFM: Equivalent Frame Model, (-) Option considered, ( ) Option not considered, (*) The maximum strength ratio=analytical /experimental maximum strengths, Em is the masonry Young Modulus.

Table 5 Case studies for both EFM and PHFE models.

Due to the coupling effect, the resulting crack patterns displayed by the numerical simulation

are different on the left and right sides (Fig. 26, 27). On the other hand, the crack pattern predicted by

the EFM is symmetrical (Fig. 28). The shear cracks on spandrels were not obtained since the spandrels

were modelled as elastic linear. It is clear that the numerical results should be more accurate, in

comparison to the EFM, since both the axial deformation and axial force redistribution were not

considered in the EFM. The axial force and deformation are crucial issues when using failure criteria

for the plastic hinge formation and damage occurrence. Moreover, in comparison to the test crack

pattern, the numerical and analytical results were extracted at 17mm while the tests represent a crack

pattern at 24mm. Also, the shear failure is neglected in the lintels in both models. These are the

reasons for the lack of match between the experimental, the analytical and the numerical crack

patterns.

SSSS

SSSS

FF FF FF

FF

FFFF

FF

SSS:S: Shear

cracks

F:F: Flexuralcracks

Figure 26 Crack patterns from the experimental test of the URM building

(at failure state (top displacement equal to 24mm))


30

FF FF

FF

FF

FFFF

FF

SSSS

Figure 27 Crack patterns from numerical results at 17mm

c c

c

F F F

F

FF

S

FF

Figure 28 Crack patterns from analytical results (on the EFM)

F: flexural crack in one slice, S: shear crack over a pier

Finally, this paragraph presents a simplified formulation of an equivalent frame model. The model

permits to consider many relevant features of structural behavior such as structural wall coupling, zero

moment location shifting, axial force-bending moment interaction, axial force-shear force interaction,

and failure mode prediction. However, in the case of URM buildings, it is well known that smeared

crack approach suffers from a few limitations. The smeared crack model is enable to represent

effectively the rocking and bed joint sliding mode of failures.

For the development of capacity curves, the obtained results from the proposed model show good

agreement with experimental and numerical results (Fig. 24, 25). The model has proven its capability

to satisfactorily predict the maximum strength. The calculated maximum strengths, in particular for

the masonry structure (in the range of 9%), could be judged as good results since the model is based

on simplified approaches in comparison to finite element models. However, the post peak behavior

with softening is not yet obtained since the model is force-controlled. Care should be taken when

modelling dual buildings as frame-wall structures in particular with respect to the initial zero moment

length assumption. In all cases, obtained results should be considered from an engineering point of

view as is generally done for all simplified existing models.

It is evident that the failure mode identification is a challenging task even if finite element models

are used. This feature is sensitive to various analysis parameters such as the modelling of shear

mechanisms, the lateral load pattern and force redistribution capabilities. The proposed model requires


31

further improvements for URM structural modelling (displacement control, variation of axial force in

spandrels, multilinear models with softening).

5. Conclusions and futur work

The report presents a summary of a work dealing with a seismic vulnerability assessment of

unreinforced masonry existing buildings in Switzerland. The work presents a methodology for realistic

fragility curve generation. For this purpose, a classification of typical buildings is presented. Then, an

unreinforced masonry Swiss-type building is selected. An investigation of the non linear behaviour of

unreinforced masonry structures is performed using both simplified and finite element methods.

Capacity curves and capacity spectra are generated with and without torsion effect. Vulnerability

functions are developed based on the EMS98 damage grade. Finally, a novel approach for capacity

curves generation are developed and validated against experimental tests and numerical results.

As the project aims to address seismic risk mitigation in Switzerland, this study represents a

preliminary investigation to accurately and reliably find modern fragility curves. However, the

resulting analytical fragility curves have to be validated by comparison to empirical ones. However,

this is not possible in Switzerland. Hence, attention has to be given to performance limit states and to

the seismic response parameters in the calculation of fragility curves. Both limit states and seismic

response have to be modelled as random variables and as deterministic quantities. All potential

uncertainties in the considered parameters should be considered otherwise the results may be non-

conservative leading to incorrect fragility curves and hence to unreliable economic loss evaluation and

seismic risk mitigation. It is evident that not all uncertainties can be analyzed, hence a certain number

of parameters that affect closely the fragility curves calculation have to be selected and considered.

The next step has to be organized as follows:

• 1- Capacity curves generation for a stock of unreinforced masonry buildings with or without

torsion,

• 2- Fragility curves for a stock of Swiss type URM buildings : statistical + probabilistic model

(a Fragility Curve = integration of probability density function PDF log-normally distributed),

• 3- Proposition of a Swiss-type URM building : typical bilinear capacity curve and a SDOF-

type model,

• 4- Perform a dynamic analysis with a set of records using the SDOF-type model: generate

fragility curves and surfaces with or without torsion,

• 5- HAZUS Calibration for Switzerland-type URM buildings with or without torsion.

6. References

[1] Wen-I L., Chin-Hsiung L., Keh-Chyan T., Study on the fragility of building structures in Taiwan, Natural

Hazards, 37:55-69, 2006.

[2] HAZUS-99, Direct physical damage – general building stock, Chapter 5, HAZUS99 Technical Manual.


32

[3] Grünthal G., Levret A., L’echelle Macrosismique Européenne, European Macroseismic Scale 1998, Cahiers

du Centre Européen de Géodynamique et de Séismologie, Volume 19, Luxembourg 2001.

[4] Belmouden Y., Lestuzzi P., Evaluation de la vulnérabilité sismique des bâtiments existants en Suisse,

Rapport de Recherche. EPFL-ENAC-IS-IMAC, Informatique et Mécanique Appliquées à la Construction.

Publication Nr. 6. Lausanne, Avril, 2006.

[5] Belmouden Y., Lestuzzi P., Eléments de Typologie du Bâti Existant Suisse, Rapport de Recherche. EPFL-

ENAC-IS-IMAC, Informatique et Mécanique Appliquées à la Construction. Publication Nr. 5. Lausanne, Mars,

2005.

[6] Bieri M., Gentil T., Michaud N., Typologie du bâti existant suisse en vue de l’appréciation de sa vulnérabilité

sismique, 2007.

[7] Lang. K., Seismic vulnerability of existing buildings, PhD Thesis, Institute of Structural Engineering, Swiss

Federal Institute of Technology, Zürich, Switzerland, February 2002.

[8] Milutinovic Z. V., Trendafiloski G. S., Vulnerability of current buildings, September report 2003, RISK-UE,

Work Package 4, An advanced approach to earthquake risk scenarios with applications to different European

towns’, Nice, September 2003.

[9] Whitman R. V., Damage probability matrices for prototype buildings, MIT Report R73-57, Massachusetts

Institute of Technology, Department of Civil Engineering Research, Cambridge, Massachusetts, 1996.

[10] Belmouden Y., Lestuzzi P., An equivalent frame model for seismic analysis of masonry and reinforced

concrete buildings, Construction Building and Material Journal, 2007.

[11] Belmouden Y., Lestuzzi P., An Analytical Model for Capacity Curves Generation and Damage Prediction

of Masonry Structures, International Review of Mechanical Engineering, November 2007.

[12] Tzamtzis A. D., Asteris P.G., FE Analysis of complex discontinuous and jointed structural systems: Part 1:

Presentation of the method – A state-of-the-art review, Electronic Journal of Structural Engineering, 1, 2004.

[13] Roca P.; Molins C., Marí A. R., Strength Capacity of Masonry Wall Structures by the Equivalent Frame

Method J. of Struct. Eng., Volume. 131, No. 10, pp. -1601–1610, 2005.

[14] Salonikios T., Karakostas C., Lekidis V., Anthoine A. Comparative inelastic pushover analysis of masonry

frames, Engineering Structures Journal, Volume 25, pp. 1515-1523, 2005.

[15] Kappos A., Penelis G., Drakopoulos C., Evaluation of simplified models for lateral load analysis of

unreinforced masonry buildings, Journal of Structural Engineering, ASCE, Vol. 128, July N°7, pp. 890-897,

2002.

[16] ATC-40, Seismic Evaluation and Retrofit of Concrete Buildings, Vol. 1, Applied Technology Council,

Redwood City, California, 1996.

[17] Belmouden Y., Lestuzzi P., Analytical model for predicting nonlinear reversed cyclic behaviour of

reinforced concrete structural walls, Engineering Structures, Vol. 29/7, pp. 1263-1276, 2007.

[18] ElMandooh K., Ghobarah A., Flexural and shear hysteretic behavior of reinforced concrete columns with

variable axial load, Engineering Structures, Volume 25, pp. 1353-1367, 2003.

[19] Nuray Aydinoğlu M., An incremental response spectrum analysis procedure based on inelastic spectral

displacements for multi-mode seismic performance evaluation, Bulletin of Earthquake Engineering, pp. 3-36,

Volume 1, 2003.


33

[20] Kilar V., Fajfar P., Simple pushover analysis of asymmetric buildings, Earthquake Engineering and

Structural Dynamics, Volume 26, pp. 233-249, 1997.

[21] FEMA 356, Prestandard and commentary for the seismic rehabilitation of buildings, Washington (DC):

Federal Emergency Management Agency, 2000.

[22] FEMA 306, Evaluation of earthquake damaged concrete and masonry wall buildings, basic procedures

manual, Washington (DC): The Partnership for response and recovery, 1999.

[23] Paquette J., Bruneau M., Pseudo-dynamic testing of unreinforced masonry building with flexible diaphragm

and comparison with existing procedures, Construction and Building Materials, Volume 20, pp. 220-228, 2006.

[24] Penelis GR.G., An efficient approach for pushover analysis of unreinforced masonry (URM) structures,

Journal of Earthquake Engineering, Vol. 10, N°3, pp. 359-379, 2006.

[25] Prakash, V., Powell, G.H. and Campbell, S., DRAIN3DX: Base Program Description and User Guide,

UCB/SEMM-1994/07, Berkeley: Department of Civil Engineering, University of California, August 1994.

[26] ETABS, Integrated Building Design Software, Computers and Structures, Inc. Berkeley, California, USA,

Version 9, November 2005.

[27] Bachmann H., Dazio A, A Deformation-Based Seismic Design Procedure for Structural Wall Buildings,

Proceedings of the International Workshop on Seismic Design Methodologies for the Next Generation of Codes,

Bled/Slovenia, A.A. Balkema, Rotterdam 24-27 June 1997.

[28] Dazio A., Entwurf und Bemessung von Tragwandgebäuden unter Erdbebeneinwirkung, (in German),

Institut für Baustatik und Konstruktion, ETH Zürich, Bericht Nr. 254, Birkhäuser Verlag Basel, 2000.

[29] Wilkinson S. M., Hiley R. A., A non-linear response history model for the seismic analysis of high-rise

framed buildings, Computers and Structures Volume 84, pp. 318-329, 2006.

[30] Magenes G., ‘A method for pushover analysis in seismic assessment of masonry buildings’, Paper

186612WCEE, 2000.

[31] Magenes G., Della Fontana A., Simplified non-linear seismic analysis of masonry buildings, Proc. of the

Fifth International Masonry Conference, London, 13th-15th, 1998.

[32] Magenes G., Calvi G. M., In-Plane response of brick masonry walls, Earthquake Engineering and Structural

Dynamics, Volume 26, pp. 1091-1112, 1997.

[33] Tomazevic M., Seismic resistance verification of buildings: Following the new trends, Seismic

Methodologies for the Next Generation of Codes, P. Fajfar and H. Krawinkler (eds.), Balkema, Rotterdam, 1997.

[34] Dolce M., Schematizzazione e modellazione per azioni nel piano delle pareti (Models for in-plane loading

of masonry walls), Corso sul consolidamento degli edifici in muratura in zona sismica, Ordine degli Ingegneri,

Potenza, 1989.

[35] Galasco A., Lagomarsino S., Penna A., On the use of Pushover analysis for existing masonry buildings,

First European Conference on Earthquake Engineering and Seismology, Geneva, Switzerland, 3-8 September,

Paper N°1080, 2006.

[36] Bruchez P, Brussard L., Campana S., Thorens G., Modélisation Parasismique, Projet de semestre, Cycle de

Master, EPFL, Juin 2007.

Documents

2007_Technical Report_Belmouden_Lestuzzi_On the Seismic Vulnerability Assessment of URM Buildings_modeling Okok