probabilistic performance-based seismic risk assessment …

PROBABILISTIC PERFORMANCE-BASED SEISMIC RISK

ASSESSMENT OF BRIDGE INVENTORIES WITH LOSS AND

IMPACT ESTIMATES

A thesis submitted to the Faculty of Graduate and Postdoctoral Affairs

in Partial Fulfillment of the requirements for the degree

Masters of Applied Science

by

Kandasamy Vishnukanthan

Department of Civil and Environmental Engineering Carleton University

Ottawa-Carleton Institute o f Civil and Environmental Engineering

January 2013

©2013 Kandasamy Vishnukanthan

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Canada

A bstract

Among the evolving challenges in earthquake engineering practices, accurate seis

mic risk assessment of bridges in developed countries, like Canada, has significant

impact on public safety and maintaining socioeconomic development of the society.

There are various approaches developed for seismic vulnerability and risk assessment

of bridges in recent years. However, these existing seismic risk assessment m ethod

ologies cannot be easily applied to all the bridges in large transportation networks

because th a t would require exceedingly vast amount of resources and time. This the

sis presents a new approach for seismic risk assessment of large bridge inventories in/

a city or region or national bridge network based on the framework of probabilistic

performance based seismic risk assessment. Sample concrete bridges from the City

of Ottawa transportation network are used in a pilot study to dem onstrate the va

lidity of the approach. Prom the concrete bridge samples, five bridges are selected as

representatives of the inventory group in the O ttaw a region for detailed investigation

and calibration of the damage fragility relationships. Three dimensional nonlinear

time history analysis of the representative bridges have been carried out. To account

for the influences of local site effects, microzonation information are used to generate

site-specific seismic hazard curves for the representative bridges. Simulated ground

motions compatible with the site specific seismic hazard and scaled recorded ground

motions near Ottawa are used as input excitations in nonlinear tim e history analysis

of the representative bridges. From responses predicted by the nonlinear tim e history

analysis, seismic demand models are developed. Damage fragility relationships are

derived for the damage states of concrete cover spalling, longitudinal bar buckling

and unseating or loss of span failure modes. The probability of bridge damage cor

responding to the calculated bridge responses is estimated. Using d a ta from HAZUS

models, loss models and decision fragility curves are developed for downtime and

repair cost. A normalizing procedure to obtain generalized fragility relationships in

terms of structural characteristic parameters related to bridge span and size and lon

gitudinal and transverse reinforcement ratios is presented. The overriding advantage

of the proposed probabilistic seismic risk assessment methodology is th a t quantitative

information on the probability of failure of all the bridges in the entire inventory can

be easily evaluated by using the developed normalized fragility relationships w ithout

the need for carrying out detailed nonlinear tim e history analysis of each bridge. From

the quantitative assessment results, priority lists of the bridge inventory for seismic

decision making on safety and risk mitigation can be established.

A cknow ledgm ents

I thank my supervisors Dr. David T. Lau and Dr. Siva Sivathayalan, for their

invaluable guidance and support throughout this research. I would also like to thank

the financial support provided by the Canadian Seismic Research Network by NSERC

SNG program. I would also like to acknowledge Ms. C. Duclos, Dr. J. Zhao and

Mr. A. Nouraryan of the City of O ttaw a for providing sample bridge information,

and Dr. John Adams for providing the seismic hazard information of O ttaw a from

the Natural Resources Canada (GSC). I would like to show my gratitude towards my

family and loved ones for their support and encouragement during my research.

Table of C ontents

A bstract ii

A cknow ledgm ents iv

Table o f C ontents v

List o f Tables v iii

List o f Figures x

List o f A cronym s xv ii

List o f Sym bols x ix

1 Introduction 1

1.1 Background and M o tiv a tio n .......................................................................... 1

1.2 O b jec tiv es................................................................................................................ 4

2 D evelopm ent o f U niform H azard Spectra for Perform ance-B ased

Seism ic V ulnerability A n alysis 5

2.1 In tro d u ctio n ........................................................................................................ 5

2.2 Uniform hazard sp e c tra .................................................................................... 7

2.3 National Building Code of Canada (NBCC) ............................................ 8

2.3.1 Seismic hazard maps in the N B C C ............................................... 8

v

2.3.2 2475-year UHS for different Site Classes ...................................... 9

2.3.3 UHS for different hazard levels and Site C la s s e s ........................... 11

2.4 Simulated ground m o tio n s ............................................................................ 12

2.4.1 Bedrock s p e c tra ...................................................................................... 13

2.4.2 The program S IM Q K E ........................................................................ 14

2.4.3 The CUQuake P ro g ram /In te rface .................................................... 15

2.4.4 Generation of simulated motions: input and outputs ............... 17

2.5 Ground response analysis................................................................................ 21

2.5.1 Soil-modeling ap p ro ach ........................................................................ 21

2.5.2 Soil-properties used in analysis .................. 22

2.6 Derivation of UHS curves for 10%/50 year and 40%/50 year hazard levels 27

3 Seism ic R isk A ssessm ent M eth od ology for Bridge Inventory 33

3.1 In tro d u ctio n ....................................................................................................... 33

3.2 Structural models .......................................................................................... 38

3.2.1 Superstructure ...................................................................................... 39

3.2.2 Substructure ......................................................................................... 40

3.2.3 Fundamental vibration p e r io d ........................................................... 44

3.3 Hazard a n a ly s is ................................................................................................. 46

3.3.1 Selection of ground m o t io n s .............................................................. 47

3.3.2 Probabilistic seismic hazard c u r v e s ................................................. 49

3.4 Demand a n a ly s is ............................................................................................. 53

3.5 Damage analysis ............................................................................................. 60

3.6 Loss analysis .................................................................................................... 70

4 G eneralized Fragilty R elationsh ips 81

4.1 In tro d u ctio n ....................................................................................................... 81

4.2 Effective longitudinal reinforcement ratio *) 82

vi

4.3 Effective span over pier height ratio ( Spa£ ) 88

4.4 Effective transverse reinforcement ratio (p s *) 93

4.5 Fragility evaluation of sample bridge in v en to ry ......................................... 98

5 C onclusions and R ecom m endations 104

5.1 C o n c lu sio n s ......................................................................................................... 104

5.2 Recomm endations............................................................................................... 105

List o f R eferences 111

vii

List o f Tables

Table

Table

Table

Table

Table

Table

Table

Table

Table

Table

Table

Table

3: Site Classification for Seismic Site Response, NBCC 2010 . . 7

4: Values of Fa as a Function of Site Class and So(0.2), NBCC 2010 10

5: Values of F„ as a Function of Site Class and Sa(1.0), NBCC 2010 10

6: Reference Ground Condition factors, GSC open file 4459 . . . 14

7: Input parameters of the soil response model for various ground

co n d itio n s .............................................................................................. 25

8: Unit weights of bridge components according to CHBDC . . . 42

9: Probability of cover spalling and bar buckling of representative

bridges a t different hazard levels for all Site C la s se s ................. 69

10: Repair cost ratios for Highway B r id g e s ......................................... 71

11: Restoration time for Highway b r id g e s ............................................. 72

12: Comparison of norm of residuals from linear and power regres

sion analyses for the relationship of probability of bar buckling

with p l * ................................................................................... 87



with S s a l .............................................................................................. 92



with p s * ................................................................................................. 97

viii

Table 15: Effective Structural Characteristics Parameters of Bridges in

the Sample Bridge In v en to ry ............................................................. 100

Table 16: Estimated Probabilities of Cover Spalling and Bar Buckling

based on Effective Longitudinal Reinforcement R a t io s .............. 101


based on Effective Span over Pier Height R a t io s ........................ 101


based on Effective Transverse Reinforcement R a t io s ................. 102

Table 19: Summary of Estim ated Performance Probabilities for Sample

In v e n to ry .............................................................................................. 102

Table 20: Priority List of Bridge Inventory to Improve Life Safety . . . . 103

Table 21: Priority List of Bridge Inventory to Minimize Repair Costs . . 103

ix

List o f Figures

Figure 1: UHS curves for different site conditions a t 2% in 50 year hazard

level for Ottawa, C a n a d a ................................................................ 11

Figure 2: Comparison of Bedrock response spectrum with Site Classes

A and C at 2%/50 year hazard le v e l ............................................ 14

Figure 3: Screen snapshots of the CUquake p r o g r a m ............................... 17

Figure 4: Compound intensity function used for ground motion genera

tion ........................................................................................................ 18

Figure 5: Matched Response Spectra for Bedrock a t different hazard lev

els ........................................................................................................ 19

Figure 6: Artificial ground motions of matched response spectra for

bedrock at different hazard levels ............................................... 20

Figure 7: Typical ground profile used for site response analysis of various

ground conditions for Ottawa ...................................................... 25

Figure 8: Site response spectra for various ground conditions a t 2% in

50 year hazard level for O ttaw a ................................................... 26





Figure 11: Spectral ratios between 10%/50 year and 2%/50 year site re

sponse spectra for various ground c o n d i t io n s ........................... 29

x

Figure 12: Spectral ratios between 40% and 2%/50 year site response

spectra for various ground conditions ......................................... 29

Figure 13: (a) and (b) F itted curves for derivation of the 10%/50 year

UHS curves using two scenarios ................................................... 29

Figure 14: (a) and (b) F itted curves for derivation of the 40% in 50 year

UHS curves using two scenarios ................................................... 30

Figure 15: UHS curves for different site conditions a t 10%/50 year hazard

level for Ottawa, C a n a d a ................................................................ 30

Figure 16: UHS curves for different site conditions a t 40% in 50 year haz

ard level for Ottawa, C a n a d a ......................................................... 31

Figure 17: (a) Comparison of UHS derived from site response analysis

with proposed UHS by GSC for Site Class C a t 10%/50 year

probability level; and (b) Comparison of UHS derived from site

response analysis with proposed UHS by GSC for Site Class C

at 40%/50 year probability l e v e l ................................................... 32

Figure 18: (a) Blair Road Bridge Profile; (b) Cross section of Blair Road

Bridge superstructure; (c) Cross section of Blair Road Bridge

c o lu m n ................................................................................................. 35

Figure 19: (a) Terminal Avenue Bridge Profile; (b) Cross section of Ter

minal Avenue Bridge superstructure; (c) Cross section of Ter

minal Avenue Bridge c o lu m n ......................................................... 36

Figure 20: (a) Hunt Club Road Bridge Profile; (b) Cross section of Hunt

Club Road Bridge superstructure; (c) Cross section of Hunt

Club Road Bridge co lu m n ................................................................ 37

Figure 21: (a) Walkley Road Bridge Profile; (b) Cross section of Walkley

Road Bridge superstructure; (c) Cross section of Walkley Road

Bridge c o lu m n .................................................................................... 38

xi

Figure 22: Spine model for Blair Road Bridge ............................................. 42

Figure 23: Spine model for Terminal Avenue Bridge ................................... 43

Figure 24: Spine model for Hunt Club Road Bridge ................................... 43

Figure 25: Spine model for Walkley Road B r id g e .................................... 43

Figure 26: (a) and (b): First modal shape for Blair Road Bridge free

expansion bearing case (Ti = 2.39s) and fixed bearing case

(Ti = 1.35s) ....................................................................................... 45

Figure 27: First modal shape for Terminal Avenue Bridge (Xi = 1.28s) 45

Figure 28: First modal shape for Hunt Club Road Bridge (Ti = 0.82s) . 46

Figure 29: First modal shape for Walkley Road Bridge {T\ = 1.14s) . . 46

Figure 30: Matched Response Spectra for Site Class C at different hazard

le v e l s .......................... 48

Figure 31: Scaled Response Spectra for Site Class C at different hazard

l e v e l s ..................................................................................................... 49

Figure 32: Hazard curves for Blair Road Bridge w ith free expansion bear-

Figure 33:

mg case ..............................................................................................

Hazard curves for Blair Road Bridge w ith fixed bearing case

50

51

Figure 34: Hazard curves for Terminal Avenue B r i d g e .............................. 51

Figure 35: Hazard curves for Hunt Club Road Bridge .............................. 52

Figure 36: Hazard curves for Walkley Road B r id g e ..................................... 52

Figure 37: Demand curves for Blair Road Bridge with free expansion

bearing c a s e ....................................................................................... 55

Figure 38: Demand curves for Blair Road Bridge with fixed bearing case 55

Figure 39: Demand curves for Terminal Avenue Bridge ........................... 56

Figure 40: Demand curves for Hunt Club Road B r id g e .............................. 56

Figure 41: Demand curves for Walkley Road Bridge ................................. 57

xii

Figure 42: Probability of exceedance of drift ratio for Blair Road Bridge

with free expansion bearing c a s e ................................................... 57

Figure 43: Probability of exceedance of drift ratio for Blair Road Bridge

with fixed bearing c a s e ................................................................... 58

Figure 44: Probability of exceedance of drift ratio for Terminal Avenue

Bridge ................................................................................................. 58

Figure 45: Probability of exceedance of drift ratio for Hunt Club Road

Bridge ................................................................................................. 59

Figure 46: Probability of exceedance of drift ratio for Walkley Road

Bridge ......................... 59

Figure 47: Column damage model for Blair Road Bridge modeled scenar

ios ........................................................................................................ 62

Figure 48: Column damage model for Terminal Avenue Bridge ............... 63

Figure 49: Column damage model for Hunt Club Road Bridge ............... 63

Figure 50: Column damage model for Walkley Road B r id g e ...................... 64

Figure 51: Damage fragility curves for Blair Road Bridge w ith free ex

pansion bearing case ....................................................................... 66

Figure 52: Damage fragility curves for Blair Road Bridge w ith fixed bear

ing case .............................................................................................. 66

Figure 53: Damage fragility curves for Terminal Avenue B r id g e ............... 67

Figure 54: Damage fragility curves for Hunt Club Road B r i d g e ............... 67

Figure 55: Damage fragility curves for Walkley Road Bridge ................... 68

Figure 56: Interim loss models for Blair Road Bridge modeled scenarios 72

Figure 57: Interim loss models for Terminal Avenue Bridge ...................... 73

Figure 58: Interim loss models for Hunt Club Road Bridge ...................... 73

Figure 59: Interim loss models for Walkley Road B r id g e ............................. 74

xiii

75

75

76

76

77

78

78

79

79

80

84

85

Seismic decision fragility curves based on repair cost for Blair

Road Bridge with free expansion bearing c a se ...........................

Seismic decision fragility curves based on repair cost for Blair

Road Bridge with fixed bearing c a s e ............................................

Seismic decision fragility curves based on repair cost for Ter

minal Avenue Bridge .......................................................................

Seismic decision fragility curves based on repair cost for Hunt

Club Road B r id g e .............................................................................

Seismic decision fragility curves based on repair cost for Walk

ley Road B r id g e .................................................................................

Seismic decision fragility curves based on downtime for Blair

Road Bridge with free expansion bearing c a se .........................../

Seismic decision fragility curves based on downtime for Blair

Road Bridge with fixed bearing c a s e ............................................

Seismic decision fragility curves based on downtime for Termi

nal Avenue B r id g e ........................................ ....................................

Seismic decision fragility curves based on downtime for Hunt

Club Road B r id g e .............................................................................

Seismic decision fragility curves based on downtime for Walk

ley Road B r id g e .................................................................................

Generalized Fragility Relationships Based on * by linear re

gression, (a) and (b): Cover Spalling and Bar Buckling for

Different Site Conditions at 2% in 50 year Hazard Level . . .

Generalized Fragility Relationships Based on p ^ * by linear re


Different Site Conditions at 10% in 50 year Hazard Level . .

xiv

Figure 72:

Figure 73:

Figure 74:

Figure 75:

Figure 76:

Figure 77:

Figure 78:

Figure 79:

Figure 80:

Generalized Fragility Relationships Based on pL * by linear re


Different Site Conditions at 40% in 50 year Hazard Level . . 85

Generalized Fragility Relationships Based on p i * by power

regression, Bar Buckling for Different Site Conditions a t 2% in

50 year Hazard Level ....................................................................... 86

Generalized Fragility Relationships Based on p L * by power

regression, Bar Buckling for Different Site Conditions a t 10%

in 50 year Hazard L e v e l ................................................................... 86

Generalized Fragility Relationships Based on p t * by power



Generalized Fragility Relationships Based on by linear

regression, (a) and (b): Cover Spalling and Bar Buckling for

Different Site Conditions at 2% in 50 year Hazard Level . . . 89

Generalized Fragility Relationships Based on 5p°n * by linear



Generalized Fragility Relationships Based on Sp^n * by linear



Generalized Fragility Relationships Based on - pa™ * by power


50 year Hazard Level ....................................................................... 91

Generalized Fragility Relationships Based on Spa™ * by power



xv

Figure 81: Generalized Fragility Relationships Based on Spa™* by power



Figure 82: Generalized Fragility Relationships Based on p s * by linear re


Different Site Conditions at 2% in 50 year Hazard Level . . . 94







Figure 85: Generalized Fragility Relationships Based on p s * by power


50 year Hazard L e v e l .............................................................. 96



in 50 year Hazard L e v e l ........................................................... 96



in 50 year Hazard L e v e l ........................................................... 97

xvi

List o f Acronym s

A cronym s D efin itio n

CHBDC Canadian Highway Bridge Design Code

DM damage measure

DTR downtime ratio

DV decision variable

EDP engineering demand param eter

GSC Geological Survey of Canada

IM intensity measure

NBC National Building Code of Canada

NBCC National Building Code of Canada

NEHRP National Earthquake Hazard Reduction Program

PBEE performance-based earthquake engineering

PEER Pacific Earthquake Engineering Research Center

PGA Peak Ground Acceleration

xvii

PGV Peak Ground Velocity

PSHA probabilistic seismic hazard analysis

RCR repair cost ratio

RGC Reference ground condition

SPD structural performance database

UHS Uniform Hazard Spectra

xviii

List of Sym bols

Sym bols D efin ition

A-n amplitude

A, gross section area

dft diameter of the Longitudinal reinforcement

D column diameter

D M median DM

D V ) median DV

E D P the median EDP

f'c concrete compressive strength

Fa Soil modification factor for high frequency (5 Hz)

Fv Soil modification factor for low frequency (1 Hz)

Fy specified minimum yield stress

Fye expected yield stress

Fu specified minimum tensile strength

expected tensile strength

yield strength of transverse reinforcement

power spectral density function

intensity envelope function

regression parameters

distance from the point of fixity to the point of inflection

plastic hinge length

mean annual frequency of occurrence

axial load

standard normal distribution function

random phase angle

factor applied to estim ate the expected tensile strength

factor applied to estim ate the expected yield stress

volumetric transverse reinforcement ratio

Pier longitudinal reinforcement ratio

Effective longitudinal reinforcement ratio

Pier transverse reinforcement ratio

Effective transverse reinforcement ratio

first mode spectral acceleration

Span over pier height ratio

SP-™ - Effective span over pier height ratio

Ti fundamental period

Vs_3o Average shear wave velocity

Vs ,30 Mid-range of average shear wave velocity

xxi

C hapter 1

Introduction

1.1 Background and M otivation

Recent observations of the damage caused to bridges in major earthquakes have raised

questions about the safety of existing bridge structures constructed using previous old

design standards. Additionally, from investigation and analysis of the behavior and

performance of structures in past earthquake events, various deficiencies have been

identified in structures constructed during different time periods in the past. The

extensive damage and huge economic loss due to earthquake damage to structures

during 1994 Northridge and 1995 Kobe earthquakes as well as the more recent 2009

i/A quila and 2010 Chile earthquakes give plenty of evidence to these observations

[1]. To enhance the resistance behavior as well as performance of bridge structures,

there is an urgent need to improve the reliability of existing seismic risk evaluation

methodologies and practices.

There are at least 50,000 bridges in Canada [2]. Many existing highway bridges in

the province of Ontario are constructed decades ago using obsolete design standards.

Based on available statistics, Ontario is ranked third among provinces in Canada

in terms of having oldest bridge infrastructure after Quebec and Nova Scotia. It

is estimated th a t bridges in Ontario have passed 56% of their useful life based on

1

2

the observation th a t bridges in Ontario have a mean useful life of 43.3 years. In

comparison, this ratio for Nova Scotia and Quebec provinces are 66% and 72%, re

spectively [3]. From experiences of past earthquakes as well as from complete studies

and experimental research, it is recognized th a t bridges constructed using obsolete

design standards particularly in the 60s and 70s are vulnerable to suffer significant

damage during major earthquakes.

There are several drawbacks and limitations in the current seismic risk assessment

practice. In current practice, typically only a few high priority structures are selected

for detailed investigation, which is based on check-list assessment and physical on-site

inspection. However, there are too many bridges in a large transportation network.

To quantify the vulnerability and risk of the bridges in a city or a provincial region or a

national transportation network, the current approach is time consuming and requires

vast amount of resources. Therefore, it is not realistic to carryout the seismic risk

assessment of bridges in a large bridge inventory. In addition, although the existing

approach can give detailed information on the seismic performance and vulnerability

of individual bridges, such as strength and ductility demands, degradation behavior

and failure mechanism, it does not give high level assessment information on the risk

and vulnerability of the entire bridge infrastructure from a system perspective [4].

Recognizing these limitations of the existing approach, engineers and researchers have

developed the concept of seismic risk assessment methodologies by means of fragility

relationships.

Numerous studies have applied fragility relationships for quick evaluation of

the vulnerability and risk of structures and identifying the likelihood of failure of

structures. The fragility curves are typically generated based on consideration of

performance-based earthquake engineering (PBEE) design principles. In probabilis

tic performance-based seismic risk evaluation, the probability of reaching a given

specified damage state under specific seismic hazard is estimated [5].

3

Probabilistic performance-based methodologies in earthquake engineering have

been developed by several research groups. The early implementation of the PBEE

methodology (FEMA-356) was developed as improvement to the conventional seismic

design practice for building in the United States by introducing the performance ob

jectives defined in terms of displacement, drift, ductility, and material behavior under

specified design earthquake events [1]. Recently, researchers at the Pacific Earthquake

Engineering Research Center (PEER) have developed a second generation of PBEE

methodology for seismic design and assessment of buildings and bridges by improving

the procedure developed in FEMA-356 [1]. The improved PBEE methodology can

be used to measure the performance of structures in a rigorous probabilistic manner.

The PEER PBEE methodology involves four phases [6]: hazard analysis, demand

analysis, damage analysis and loss analysis. The first phase is seismic hazard analysis

that aims to develop site-specific hazard curves by quantifying the ground motions at

a particular site. The second phase is demand analysis, which is a structural analysis

of the design structure to determine its responses to a range of seismic loading th a t

is representative of the seismic hazard for the site. The third phase is damage analy

sis that relates the actual damage to the capacity of the structure using conditional

probability. The final phase, loss analysis, is to review the potential economic losses

as a result of the expected damage levels.

Recognizing the importance of bridges as a vital link in public infrastructure, the

focus of the study herein is the seismic risk and vulnerability assessment of bridge

infrastructure. Most bridges in a large bridge inventory can be separated in to groups

based on shared structural characteristic parameters such as spans, pier reinforcement

ratios, material strengths, curve and skew. Seismic performance of bridges can be

linked to structural characteristic parameters as well as local site conditions. I t can be

expected th a t bridges with similar structural characteristics designed and constructed

in same time period using similar design standard will perform in a similar manner

under particular earthquake loading [4]. Theoretically, performing performance-based

assessments on a representative group of bridges in a bridge inventory would provide

the necessary information needed to develop generalized fragility relationships th a t

can be used to assess the performance of other bridges in the bridge inventory. The

aim of the research is to develop a probabilistic performance-based seismic risk assess

ment methodology that can be applied to obtain a quantitative measure of the risk

information of all the bridges in the entire inventory. W ith such information avail

able, the overall risk and performance of all the bridges from a system perspective

can be quantified, which can be used to assist decision making on safe operation and

risk mitigation of the bridge network system.

1.2 O bjectives

The main objectives of this study are:

i To develop a new seismic risk assessment methodology for bridge inventories in a

city or region or national bridge network based on the framework of probabilistic

performance-based seismic risk assessment.

ii To validate the proposed methodology by applying the developed performance-

based seismic risk assessment methodology in a pilot study of Canadian bridges

considering influence of local site conditions.

iii To estimate the economic loss and im pact on functionality of the evaluated

bridges.

C hapter 2

D evelopm ent o f U niform Hazard S p ectra

for Perform ance-B ased Seism ic

V ulnerability A nalysis

2.1 Introduction

Performance-based seismic risk assessment is a relatively new concept in earthquake

engineering. Many studies have shown th a t seismic risk in highly populated ar

eas can be mitigated effectively through performance-based seismic risk assessment

of structures [1,7,8]. Most of the existing highway bridges in Canada were con

structed several years ago using obsolete design standards. Past seismic events have

demonstrated th a t bridges constructed using traditional, outdated earthquake design

approaches tend to be vulnerable during earthquakes. Therefore, seismic risk assess

ment of bridges can be an effective tool to improve life safety and direct emergency

management resources. This can be accomplished through performance-based earth

quake engineering methodology (PBEE) incorporating seismic hazard analysis [9].

Ottawa is ranked third in Canada in terms of highest seismic risk. The term

seismic risk encompasses both the seismic hazard and the potential for damage given a

5

seismic event. This populated city is located in the Western Quebec seismic zone th a t

extends from Montreal, Quebec to Ottawa, Ontario [10]. The first step in evaluating

the seismic risk in O ttaw a is an assessment of the seismic hazard of the region. The

seismic hazard of a given site can be well represented by a Uniform Hazard Spectrum

(UHS) [9], and therefore, Uniform Hazard Spectra of Ottawa are used for seismic

hazard analysis to provide the essential probabilistic hazard information required for

the seismic vulnerability analysis [11].

The 1985 Mexico-city earthquake, a subduction zone event a t 350km from the

city, clearly highlights th a t soil amplification due to subsoil conditions strongly influ

ences the potential vulnerability of structures. Subsoil conditions of a region can be

classified based on the knowledge of the response expected at a site due to earthquake

loading. One such classification system, identified as the National Earthquake Haz

ard Reduction Program (NEHRP) soil site classification, is based on the measured

travel-time weighted average shear wave velocity (V s ,3 0 ) in the upperm ost 30 m of the

ground (or the average standard penetration resistance or undrained shear strength

of the soil to a depth of 30 m [12] if (V s ,3 0 ) values are not available). Based on the

perceived competence of the top 30m of the soil profile, sites are classified into six

classes, from Site Class A to Site Class F. Generally, sites are classified based on the

(Vs,3 0) values as presented in Table 3 [13]. Additionally, any site th a t consists of

problematic soils (liquefiable soils, sensitive clays etc.) is defined as Site Class F. Site

specific geotechnical evaluation and dynamic response analysis are required for Site

Class F. The Site Classes are intended to reflect the level of local soil amplification

for a given seismic load intensity at different structural periods. The seismic load

intensity for a given hazard level is presented by a Uniform Hazard Spectrum in the

NEHRP approach.

7

Table 3: Site Classification for Seismic Site Response, NBCC 2010

Site ClassG round Profile

N am e

A verage Shear W ave

Velocity, Vs (m /s )

A Hard rock Vs >1500

B Rock 760< V s <1500

Very dense soil andC

soft rock360< <760

D Stiff soil 180< Vs <360

E Soft soil Vs <180

2.2 Uniform hazard spectra

The uniform hazard spectrum can be simply described as a composite of the types of

earthquakes th a t contribute to the hazard at a certain probability level [14]. The UHS

curves are currently being considered as the standard means for specifying the seismic

hazard for performance-based design of structures in Canada. The UHS curves can be

generated by using many different methods. Generally, they are derived from conven

tional probabilistic seismic hazard analysis (PSHA). Basic Steps of the PSHA are: (1)

Identifying the all the seismic sources zones to evaluate their seismic potential based

on the recent seismic activities. (2) Characterizing the distribution of earthquake

magnitudes and source-to-site distances from each source (3) predicting the resulting

distribution of ground motion intensity. (4) Integrating over all earthquake magni

tudes and distances to compute the annual rate of exceeding a given ground motion

intensity [14,15]. Repeating this process for a number of vibration periods defines

the uniform hazard spectrum, which is a response spectrum with equal probability of

exceedance of a certain hazard a t all structural periods.

In some cases, UHS are used to simulate artificial ground motion tim e histories

by spectrum matching [16] to perform nonlinear time history analysis. These ground

motion records are referred to as UHS compatible time histories. The spectra of the

simulated time histories should closely match the target UHS response spectrum when

taken as a suite. Therefore, more than one type of ground motions are required to

match the target spectrum over the entire period range of interest [16]. Additionally,

UHS can be used as target spectrum for scaling the ground motions tim e histories at

a specified period or over the range of periods of interest.

2.3 N ational Building C ode of Canada (N B C C )

This site classification system proposed by NEHRP has been adopted in the 2005

National Building Code of Canada (NBCC 2005) [17] for the first time, and its use

continues in the current version of the National Building Code of Canada (NBCC

2010) [18]. Unlike NEHRP which uses Site Class B as the reference ground condition,

the Canadian code uses Site Class C as the reference. The NBCC prescribes the

seismic hazard corresponding to the 2475-year event (2% chance of exceedance in 50

years) in the form of UHS for firm ground (Site Class C) condition across the country.

The data prescribed by NBCC 2010 for the 2475-year event has been obtained from

the work reported by the Geological Survey of Canada (GSC) [19].

2.3.1 Seism ic hazard m aps in th e N B C C

The first National Building Code of Canada (NBC), which included seismic design

provisions, was published in 1941 [20]. However, seismic hazard maps were adopted

in the National building code of Canada for the first tim e in 1953. Periodically since

1953, four generations of seismic hazard maps (1953, 1970, 1985, and 2005) have been

produced for national building code applications [21,22]. The new hazard maps (2005)

present 5% damped UHS for sites on firm ground conditions (Site Class C) a t prob

ability level of 2% in 50 year in contrast to those produced in 1985 for NBCC 1995.

The reason for this change is th a t even though the structures were designed for higher

probability-hazard level, the actual level of performance of the structures reached at

lower probability-hazard level. The current maps are developed using the Cornell-

McGuire approach using GSCFRISK (customized version of the FRISK88) [21]. In

this approach, the spatial distribution of earthquakes is represented by seismic source

zones that are areas or faults. Additionally, the exponential relation of Gutenberg

and Richter is used to describe the magnitude-recurrence relationship [23]. The new

hazard model also incorporates the recent earthquakes in Canada and around world

wide.

2.3.2 2475-year U H S for different S ite Classes

In order to investigate the local site effects on seismic performance and behavior

of bridges, UHS curves of O ttaw a for different site conditions are necessary. This

is easily achieved for the 2475-year hazard level, because NBCC 2010 provides the

base UHS data specific to firm ground (Site Class C) conditions as the reference

UHS across Canada, and in addition specifies two scaling factors F a and F v . The F a

factor represents the effects of relatively higher frequency content, and is dependent

on both the Site Class and the spectral acceleration a t 0.2 seconds, Sa(0.2). F v factor

representing the long period response on the other hand is related to the Site Class

and Sa(1.0). Tables 4 and 5 [18] present the F a and F v provided in NBCC2010.

Site specific F a and Fv values are generally obtained by linear interpolation given

the Site Class and seismic hazard. The range of UHS obtained by modifying the

reference ground condition using F a and Fv factors is shown in Figure 1 for various

Site Classes in Ottawa. As discussed earlier, such characterization is possible only for

the probability level of 2% in 50 years because soil modification factors (F a and F v)

are not presented for other hazard levels in NBCC 2010 nor is available in any other

sources.

T ab le 4: Values of F a as a Function of Site Class and Sa(0.2), NBCC 2010

Site

Class

Sa(0.2)

< 0.25

Sa(0.2)

= 0.50

Sa(0.2)

= 0.75

Sa(0.2)

= 1.00

Sa(0.2)

> 1.25

A 0.7 0.7 0.8 0.8 0.8

B 0.8 0.8 0.9 1.0 1.0

C 1.0 1.0 1.0 1.0 1.0

D 1.3 1.2 1.1 1.1 1.0

E 2.1 1.4 1.1 0.9 0.9

T able 5: Values of F„ as a Function of Site Class and Sa(1.0), NBCC 2010

Site

Class

Sa(1.0)

< 0.1

Sa(1.0)

= 0.2

Sa(l.O)

= 0.3

Sa(l.O)

= 0.4

Sa (1.0)

> 0.5

A 0.5 0.5 0.5 0.6 0.6

B 0.6 0.7 0.7 0.8 0.8

C 1.0 1.0 1.0 1.0 1.0

D 1.4 1.3 1.2 1.1 1.1

E 2.1 2.0 1.9 1.7 1.7

11

0.8■Q— Site Class A ■«— Site Class B -*— Site Class C -fc— Site Class D

— Site Class E

0.7

~ 0.6 O)

» 0.5

B 0.3Q .

0.2

0.5 2.5 3.5Period (s)

F ig u re 1: UHS curves for different site conditions a t 2% in 50 year hazard level for Ottawa, Canada

2.3.3 UH S for different hazard levels and Site C lasses

In the present study, earthquake events of 2475-year, 475-year, and 100-year return

periods, which correspond to an exceedance probability level of 2% /50 year, 10%/50

year, and 40%/50 year respectively are considered. The UHS of O ttaw a for firm

ground condition (Site Class C) a t these three hazard levels are available from the

GSC [19]. While this data is similar to the 2475-year data provided in NBCC, the

UHS for the other Site Classes at these hazard levels (10%/50 year and 40%/50 year)

cannot be developed through a procedure similar to th a t noted in the previous section

since site scaling factors F a and F v for these hazard levels are not available in the

literature. In other words, current literature provides d a ta for (1) all Site Classes at

2475-year hazard level, or (2) different hazard levels bu t on reference ground. The

UHS data required for performance-based analysis at different Site Classes and hazard

12

levels will have to be developed.

Therefore, the objective of this chapter is to develop UHS curves for city of O ttaw a

for various ground conditions at 10%/50 year and 40%/50 year using soil amplification

analysis. This is required to generate the probabilistic hazard model of the bridges.

Appropriate Fa and F v factors in the context of site amplification are developed from

soil amplification analysis. This requires a suite of input bed-rock tim e histories with

specific characteristics to match the expected motions at a given hazard level, and

the ground response analysis is used to develop the UHS curves. Simulated bedrock

ground motions are used as input motions for an equivalent linear 1-D site response

analysis, commonly known as the SHAKE analysis [24], Typical ground profile of

Ottawa for a depth of 30 m for each Site Class is assumed based on the mean value

of average shear wave velocity w ithin the specified range. Ground surface (output)

motion for each Site Class at different hazard levels is predicted. The UHS curves for

10%/50 year and 40%/50 year are derived from response spectra of predicted surface

ground motions by incorporating a scaling procedure. This procedure is explained in

depth in following sections.

2.4 Simulated ground m otions

For the purpose of derivation of UHS at different probability levels, the response

spectra, of surface ground motions are required. In order to obtain the ground mo

tions at the surface, a ground motion analysis is conducted by specifying the soil

profile and the input motion a t base level such as at bedrock in SHAKE analysis [24].

Appropriate input motion (time histories) compatible with the hazard level and the

bedrock type are required as input to the SHAKE analysis. While actual recorded

motions matching the hazard characteristics are the preferred input, such d a ta is gen

erally not available and input tim e histories for SHAKE analysis are obtained either

13

by scaling measured records, or by creating simulated records w ith specific charac

teristics. Artificial ground motions compatible to the bedrock hazard spectrum at

different hazard levels are generated using the ground motion simulation program

SIMQKE [25]. The simulated records provide a realistic representation of ground

motion for the earthquake magnitudes and distances th a t contribute most strongly

to hazard at the selected cities and probability level [16].

2.4.1 Bedrock spectra

The hazard spectra for bedrock a t 2%/50 year, 10%/50 year and 40%/50 year hazard

levels are obtained from firm ground condition spectral acceleration values by dividing

by reference ground condition (RGC) factors in Table 6 [10]. Since the same RGC

factors are used to derive the hard rock response spectra by GSC for 10%/50 year

and 2%/50 year hazard levels [19,21], it can be interpreted that these RGC factors

remained unchanged over the hazard levels. However, it is not realistically correct

because RGC factors can vary due to inelastic behavior of the soil a t different hazard

levels. Since there is no other way to obtain the bedrock response spectra, this

procedure is adopted in the present study. In addition, this methodology is consistent

with the approach used by GSC, and hence the NBCC. For the verification of these

results, the resulting bedrock response spectrum using RGC factors is compared to the

UHS obtained for Site Class A using the NBCC site factors at 2%/50 year probability

level are compared in Figure 2. This Figure shows th a t there is a significant deviation

of spectral acceleration between these curves at the period of 0.2 sec. To be consistent

with NBCC 2010 UHS, the spectral acceleration in the period range of 0.1 to 0.2 sec

for bedrock response spectra is assumed to be constant and taken as the spectral

acceleration value at 0.1 sec. Since the same values of RGC factors are used for other

hazard levels, the same assumption is made to adjust the bedrock response spectra

at other hazard levels as well.

14

T able 6: Reference Ground Condition factors, GSC open file 4459

P e r io d (s) 0.1 0.15 0.2 0.3 0.4 0.5 1 2 PGA

R G C F ac to r 1.39 1.73 1.94 2.17 2.3 2.38 2.58 2.86 1.39

0.7— *— Site Class C - + - Bedrock (RGC) — •— Site Class A

Input to SIMQKE

0.6

— 0.5

0.4 Site C lassR G C

0.3

o. 0.2

0.1

020.8 1 1.2 1.4 1.6 1.80.2 0.4 0.60

Period (s)

F ig u re 2: Comparison of Bedrock response spectrum with Site Classes A and C at 2%/50 year hazard level

2.4.2 T he program SIM Q KE

The basic theoretical background for SIMQKE is the relationship between the re

sponse spectrum for arbitrary damping and the expected Fourier am plitudes of the

ground motion [26]. The SIMQKE program generates the simulated ground motions

th a t closely correlate with the user defined intensity envelope and target response

spectrum parameters. SIMQKE generates artificial ground motions by following pro

cedure: (1) the spectral density function is derived from the given response spectrum,

(2) the generated peak acceleration is adjusted to match the target value, and (3) the

15

ordinates of the spectral density function are adjusted to smoothen the m atch [26].

First, the SIMQKE program computes a power spectral density function from

user defined input parameters such as parameters of intensity envelope, damping

and spectral ordinates as a function of period. It then generates statistically inde

pendent artificial acceleration tim e histories through th e superposition of sinusoids

(Equation (1)) having amplitudes (A n), frequencies (u>n ), and random phase angles

(</?n). Characteristics of the sinusoidal waves such as amplitudes ( A n ) and frequen

cies (u n) can be derived from the stationary power spectral density function ( G ( oj))

and the target response spectrum, whereas random phase angles (<pn ) can be gener

ated by seeds of random number. To simulate the transient characteristics of real

earthquakes, z(t) are usually multiplied by an intensity envelope function (I(t)). The

intensity function I(t) can be a trapezoidal, or exponential, or compound intensity

envelope [25].

z{ t ) = I ( t ) ^ , + (pn ) (1)n

2.4.3 The CUQuake P rogram /Interface

While the SimQke program is quite versatile in simulating time history to m atch the

input response spectra, it is somewhat difficult to use. T he generation of the input file

and post-processing of the output file to extract the tim e history d a ta are fairly time

consuming, and might introduce inadvertent errors. Further, the response spectral

values specific to the site have to be input when generating site specific simulated time

histories. For analysis compatible with NBCC, site specific response spectral values

are retrieved from the Geological survey of Canada, and converted to the required

site conditions by using appropriate RGC factors as discussed in the previous section.

A program, herein called CUQuake, was developed to simplify the simulation of

site specific time histories for any Canadian location. Given an address (or a selected

point in a map) and the desired hazard level and bedrock class this program will use

the algorithms specified in SimQke to generate the required number of tim e histories,

and converts them to a format compatible to th a t required for the subsequent ground

response analysis. The graphical user interface is less error prone when entering input

options, and the graphical view of the generated spectra compared to the target facil

itates a quick evaluation of the match. The use of this program can reduce the time

spent in preparing the required input of tim e histories for SHAKE analysis as well as

nonlinear time history analysis. The SIMQKE program can be used w ith three differ

ent input options, but option 1 th a t uses the target response spectrum as the prim ary

input is appropriate given the NEHRP characterization, and the CUQuake program

only incorporates this option. CUQuake program determines the latitude and Longi

tude of the given site using google-maps api, and then retrieves site specific uniform

seismic hazard spectra at reference ground conditions from GSC. This inform ation is

used to generate the target spectrum input to SimQke. The generated tim e history

data is output both as a text file suitable to be input for SHAKE analysis (discussed

later), and in a graphical form for evaluation and comparison of its characteristics

with the input target spectra. Figures 3(a) and 3(b) show the snapshots of the user

interface of the CUquake program.

17

CUQuake * Artificial Motion Generator for Canadian

File Edit Tools

' S 3 Select (peaSon.. ^ 3 Sn&ofce Options.- J 6 ? generate Motions... - j X

location [Carteton Urvversty, U25Colonel By Or, Ottawa, ON K1S5B6

R eam Period [Hazard]

[2475 Years ^1 s As Vs > 1500

Cazlason Dnlvarsity, 1125 Colonel By Dr, Ottawa, OH K1S SBC Cached data.Coordinate*: 45.386 *H 7S.69S4*!Latitude: 45.386longitude: -75.695H3CC spectral acceleration valuesTal(?x) PGA(g) Sa<0.2) SaiO.S) Sa(l.O) Sa(2.0)247S 0.324 0.635 0.309 0.137 0.046975 0.201 0.386 0.186 0.087 0.02847S 0.122 0.249 0.122 0.056 0.018100 0.039 0.089 0.043 0.017 0.006

SimQuake Data R e O ptions^

of Motions Spectral Period Range

h to To M sec .

NixitoofSinooiHngCydesinSenQualce 4

dT (seconds) tntendty Envelope0-01 M |Trape« ^ & iw elo p e ’

Trape a idal/Sangomd Envelope Parameters

Rise Tine (%) toM lQ-000 £%jIle v d f tn e (K) 20 (g ) Power |o (jgjj

Exponen tial ParametersAmpiiude, Ao Alpha Beta

1° M l°«” E?] I0.000 gg

X

(a) (b)

F ig u re 3: Screen snapshots of the CUquake program

2.4.4 G eneration o f sim ulated m otions: input and ou tp u ts

The input data to SimQke contains desired response spectrum param eters, Intensity

envelope parameters, peak ground acceleration in g, number of cycles to smooth the

response spectrum, damping coefficients, and target response spectrum specified as

spectral velocity ordinates in (in/s) as a function of period. When using the CUQuake

program, location (address or postal code) information is input instead of the target

response spectrum, and in addition the desired hazard level and bedrock class are

specified to generate motion compatible with the required hazard level. The bedrock

underling the soils in Ottawa has a shear Vs ps2500 m /s, and thus all motions were

generated on Class A bedrock.

To define desired response spectrum parameters, the smallest and largest period

of desired spectrum are taken as 0.01 and 2 sec respectively. To specify the inten

sity envelope, according to the characteristics of Val-des-Bois earthquake records, a

compound intensity envelope function is assumed as shown in the Figure 4. Peak

ground acceleration is retrieved by the CUQuake program from the GSC for each of

18

the target response spectrum. The study conducted by Nguyen [27] suggests th a t

simulated motions generated using 1 to 7 smoothing cycles in SimQke produce ac

ceptable smooth response spectra. Thus, 7 smoothing cycles were used in generating

the motion.

0.8.l(t)=e-°150-3)

= - 0.6

0.4

0.2

0 5 10 15 20 25 30Time (sec)

F ig u re 4: Compound intensity function used for ground motion generation

For the purpose of input motions for site response analysis, SIMQKE was used

to generate ten ground motions th a t are compatible with the compound intensity

function and corresponding target response spectra a t three specific hazard levels.

The acceleration response spectra of tim e histories for three ground motions (one

ground motion per each hazard level) generated by SIMQKE are shown in Figure 5

along with the corresponding uniform hazard spectra for Ottawa. The corresponding

three generated ground motion records are also shown in Figure 6.

Spec

tral

Acc

eler

atio

n (g

)

19

0.5•Q— 2%/50 year bedrock -#— 10%/50 year bedrock

— 40%/50 year bedrock 2%/50 year matched 10%/50 year matched 40%/50 year matched

0.45

0.4

0.35

0.3

0.25

0.2

0.15

0.1

0.05

0.6 0.80.2 0.4Period (s)

F ig u re 5: Matched Response Spectra for Bedrock at different hazard levels

Acc

eler

atio

n (g)

A

ccel

erat

ion

(g)

Acc

eler

atio

n (g

)

20

0.22%/50 year matched!

0.1

- 0.1

- 0.2

-0 330

Time (s)

0.210%/50 year matched |

0.1

- 0.1

- 0.2

-0.3

Time (s)

- 40%/50 year matched |

1______ _____.... ....... .............

Time (s)

F ig u re 6: Artificial ground motions of matched response spectra for bedrock at different hazard levels

21

2.5 Ground response analysis

Local site conditions play a vital role in contrplling earthquake damage due to incom

ing seismic waves from earthquakes. Soil modification factors or Site factors F a and

F v have been used in seismic design codes to take into account for the amplification

effects of local soil conditions on ground motion [28]. These Fa and Fv factors are de

fined as amplification factors at a period of 0.2 and 1 sec, respectively. These factors

for a particular site can be developed through ground response analysis. As discussed

earlier, site factors are not available for the 10%/50 year and 40%/50 year hazard

levels in NBCC 2010. Therefore, this section presents a methodology to develop UHS

curves at above hazard levels for different Site Classes in Ottawa th a t will perm it

analysis within the same framework as the 2%/50 year UHS using response spectra

of amplified ground motions.

2.5.1 Soil-m odeling approach

The computer program ProShake [24] is utilized to perform ground response analysis.

ProShake is an equivalent linear analysis program th a t analyzes vertically propagat

ing shear waves through a linear viscoelastic soil profile [29]. It is a user-friendly

implementation of the original SHAKE program [30] and has been th a t calibrated

against SHAKE91 [31]. SHAKE analysis is formulated in terms of to ta l stresses,

and thus it is not capable of predicting the excess pore pressures th a t developed in

saturated soils during seismic shaking. Hence, the ground water table depth is not

considered for the ground response analysis. The analysis procedure used in this pro

gram adopts an equivalent linear approach to model the actual nonlinear, inelastic

response of soils. The characteristics of the non-linear stress-strain response are input

in the form of strain dependent shear modulus and damping. In the equivalent linear

approach, an iterative procedure is used to find an effective shear strain th a t yields

22

strain compatible secant shear modulus and linear damping ratio th a t approximately

equal the actual non-linear hysteretic behavior of cyclically loaded soils [32]. The pro

gram also simply assumes th a t the shear modulus and damping ratio remain constant

throughout the shaking duration. It also considers th a t all damping as viscous rather

than differentiate the forms of damping such as plastic hysteretic damping or viscous

damping. In spite of the various approximations adopted in the SHAKE analysis,

this soil-modeling approach has been shown to provide reasonable estimates of soil

response for engineering practices [29].

For the present study, simulated ground motions obtained from the methods dis

cussed in the previous section are used as input bedrock motions. These input motions

are propagated through the soils at the site using SHAKE analysis to determ ine the

surface motions, and thus to estim ate the amount of amplification of ground motions

between bedrock and the ground surface.

2.5.2 Soil-properties used in analysis

Paleoseismic studies indicate th a t two-thirds of city of Ottawa is located on loose

post-glacial sediments th a t overly firm bedrock. Therefore, the main geological units

of concern consist of a very loose post-glacial soil w ith low shear-wave velocities

(Vs<150 m/sec) and very firm bedrock with high shear-wave velocities (Vs>2300

m/sec) [28]. Such high shear wave velocity contrast is expected to cause increased

site amplifications compared to sites in Western Canada or California. As previously

discussed, Site Classes are categorized based on the average shear wave velocity in

the top 30 m of soil (Table 3). Seismic soil modeling for each Site Class is carried

out for one soil profile. For this task, typical ground profile for each Site Class in the

Ottawa region is assumed to consist of upper 30 m of soil that representative to each

Site Class (using the range of V s ,30 in Table 3) and the bedrock (Vs=2500 m /s and

p=24 kN /m 3). For consistency of procedures, the profile for each Site Class in the top

23

30 m of soil is divided into 30 equal layers. The soil profile shown in Figure 7 is used

to develop a one-dimensional model of typical profile for each Site Class in SHAKE

analysis. Appropriate modulus reduction and damping curves th a t are representative

of the different soil layers are used to characterize the non-linear soil behaviour.

NBCC 2010 terms Site Class A as hard rock, and this is base layer for SHAKE

analysis for all soil profiles. For soil modeling of profile of Site Class A, built-in

modulus reduction and damping curves in the ProSHAKE program for rock is used

to characterize the behaviour of the site. The unit weight of the hard rock is estim ated

to be 24 kN /m 3 and shear wave velocity is assumed to be constant throughout the

thirty layers and taken as 2500 m /s.

The Site Class B ground profile is defined as rock. As the soils become softer,

the shear modulus decreases and damping increases with shear strain. Therefore, the

rock (Idriss) [31] modulus reduction and damping curves are used in soil modeling

of Site Class B, since these curves represent softer rock (lower modulus and higher

damping values than that of curves used for hard rock). Unit weight of this material

is taken as 22 kN /m 3. Mid-range of average shear wave velocity (Vs,3o) of Site Class

B is used to define the shear wave velocity of each layer in the top 30 m.

The Site Class C consists of very dense soil and soft rock. Two different profiles

are modeled by changing the average shear wave velocity profile in this case, given its

importance as the reference ground. The first case is representative of very dense soil,

and second one the soft rock. For both models, the Seed & Idriss sand curves [33]

for modulus reduction and damping are used to represent the non-linear behaviour of

the material. The unit weight of Site Class C material is considered as 19 kN /m 3. In

the first case, the shear wave velocity of each layer is assumed to be equal to th a t of

Us,30 for Site Class C. In the second case, where the material is considered soft rock,

a value closer to the upper bound of the Vs ,30 range of Site Class C is assumed for

all layers.

The Site Class D is identified as stiff soil from NBCC 2010. Sites th a t fall within

classification in the Ottawa region may include clayey soils. To model a soil profile

representative of this Site Class, the modulus reduction and damping curves for this

profile are defined through the curves proposed by Vucetic-Dobry [34] using plasticity

index (PI). The plasticity index for stiff soil in O ttaw a varies from 55 to 20 [35].

Therefore, the PI range is divided into equal intervals of five values to define same

value for each five-layer of thirty-layer from top to bottom to account for its natural

variation with depth. The unit weight of stiff soil is assumed to be 18 kN /m 3. The

shear wave velocity of top to bottom layers is defined in equal intervals varying from

(Ps ,30 — e) to (Vs,30 + e)- where e is semi-range of uncertainty.

The Site Class E is defined the site consist of the soft soil. The soil profile was

defined by following a procedure similar to th a t in Site Class D but w ith different

plasticity indices. The P I range of 40 to 10 was used for defining the modulus re

duction and damping curves in this case. The unit weight of the soft soil is taken

as 17 kN /m 3. Motazedian et al. [12] have conducted seismic surveys across the city,

and report that average shear wave velocity of soft soils in Ottawa is about 140 m /s.

Same procedure discussed in Site Class D is used to define shear wave velocity of each

layer but 1/5,30 taken as actual measured Vs ,30 (140 m /s). All the input param eters

of soil model for each Site Class are Shown in Table 7.

25

Output su rface ground motion

(1) Hard Rock(2) Rock(3) Soft R ock & Very D ense Soil(4) Stiff Soil(5) Soft Soil

Bedrock y = 24 KN/m3 Vs = 2500 m/s

Input bedrock ground motion

Figure 7: Typical ground profile used for site response analysis of various ground conditions for Ottawa

Table 7: Input parameters of the soil response model for various ground conditions

P ro p ertiesS ite Class

A B C D E

Material nameHard

RockRock

Soft

Rock

Dence

Soil

Stiff

Soil

Soft

Soil

Thickness of the ground (m) 30 30 30 30 30 30

No. of layers 31 31 31 31 31 31

Layer thickness (Top 30m) (m) 1 1 1 1 1 1

Material shear wave velocity (m/s) 2500 1130 710 560 255+Z 125+Z

Material unit weight (kN/m3) 24 22 19 19 18 17

Bedrock shear wave velocity (m/s) 2500 2500 2500 2500 2500 2500

Bedrock unit weight (kN/m3) 24 24 24 24 24 24

Modulus reduction & Damping

curvesRock

Rock

(Idriss)

Sand (Seed

Sz Idriss)

Vucetic-

Dobry

Vueetic-

Dobry

26

In order to estimate the response a t the ground surface, each of the ten simulated

time histories for each hazard level (2%/50 year, 10%/50 year and 40%/50 year) is

input into the three soil profiles for each Site Class in SHAKE analysis. Figures 8-10

show the response spectra for different site conditions obtained from surface ground

motions by these analyses. Results of these analyses are used to develop the UHS

curves for 10%/50 year and 40%/50 year probability levels as discussed in the following

section.

—0 — Site Class A —»■■■■ Site Class B - * - Site Class C (Soft Rock) —*— Site Class C (Dense Soil)

Site Class D — Site Class E ____

Period (s)

F ig u re 8: Site response spectra for various ground conditions at 2% in 50 year hazard level for Ottawa

—0 — Site Class A —■— Site Class B- * - Site Class C (Soft Rock)- * - Site Class C (Dense Soil) — — Site Class D— Site Class E

8 10-

Period (s)

F ig u re 9: Site response spectra for various ground conditions a t 10% in 50 year hazard level for Ottawa

27

o Site Class A Site Class B

- ♦ - Site Class C (Soft Rock) —*— Site Class C (Oense Soil) — Site Class D Site Class E

CDCog©

§<

Period (s)

F ig u re 10: Site response spectra for various ground conditions a t 40% in 50 year hazard level for Ottawa

2.6 Derivation of U H S curves for 10% /50 year and

40% /50 year hazard levels

The resulting site response spectra at each of the three hazard levels follows the sim

ilar patterns over the period ranges considered. Therefore, a scaling procedure based

on the spectral ratios of site response spectra is adopted in this study to develop

the UHS curves for the specified hazard levels that is of a similar p a tte rn as 2%/50

year UHS developed from NBCC 2010. First, for the entire period range, spectral

ratios between 10%/50 year and 2%/50 year site response spectra, and 40%/50 year

and 2%/50 year site response spectra are estimated to establish spectral relation

ships. The resulting spectral relationships curves are illustrated in Figures 11 and 12.

These results shows that the spectral ratios varies over the period range rather than

remain a constant. Then these spectral relationship curves are used to obtain the

UHS curves at specified hazard levels by scaling down the 2% 50 year UHS obtained

(Figure 1) using site factors F a and F v (NBCC 2010). The procedure explained above

is expressed in Equations (2) and (3). Due to different ratios applied for scaling the

28

spectral acceleration values a t each period, the resulting UHS were not smooth. How

ever a smoother spectra is derived for performance based study, and two approaches

are considered for the derivation of smooth response spectra from these scaled UHS

curves.

In the first approach, the spectral acceleration value in the period range of 0.04

to 0.2 sec is assumed to be constant and the spectral acceleration value a t 0.04 sec

from the soil amplification analysis results is assigned as this constant. In the second

approach, the constant spectral acceleration value over the same period range is taken

as the average spectral acceleration value calculated from the maximum and minimum

values obtained in the soil amplification analysis. The spectral acceleration value at

other periods (0.5, 1.0, 2.0, and 4.0 sec) are taken as the same value obtained from

scaling. Figures 13 and 14 present the UHS curves obtained by scaling down the

2%/50 year UHS with the smoothed curves using the procedure explained above.

The maximum envelope from two approaches is used in the construction of the final

UHS curves for other hazard levels in the present study. Figures 15 and 16 show the

two resulting UHS curves for 10%/50 year and 40%/50 year obtained from the two

approaches.

( 5 ,a ( T 1)) io % /5 o year(Sa(Tl))lQ%/5Qyear

( 5 ,a (T 1) ) 2%/50 year J[ (> S a (T l) )2 % /5 0 yea r] N Q C C 2010

Site response(2)

, Q f T " \ \ — \ ( ‘S'a (2ni) )4 0 % /5 0 year~\ [ f Q ( T \"\ 1W a l- t 1 ) j40% /50 year ~ / q /np \ \ X l / /2 % /5 0 year} / /B C C 2010

„ l / /2 % /5 0 year J Site response

(3)

29

0.75— Site Class A— Site Class B— Site Class C (Soft Rock)— Site Class C (Dense Soil) ~ Site Class D— Site Class E

0.7

« 0.65

0.6

0.55

g 0.451

0.4

CO 0.35

2.5 3 3.50 0.5 1 1.5 2Period (s)

4

F ig u re 11: Spectral ratios between 10%/50 year and 2%/50 year site response spectra for various ground conditions

0.45—o - Site Class A —■— Site Class B - ♦ - Site Class C (Soft Rock) — Site Class C (Dense Soil) —&— Site Class D

— Site Class E

0.4

w 0.35

0.3

© 0.25

0.2

0.10.5 2.5 3.5

Period (s)

F ig u re 12: Spectral ratios between 40% and 2%/50 year site response spectra for various ground conditions

Srte Class A Site Class 8

- Site Class C1 Site Class C2 Site Class O Site Class E

-S a«D.04)S Sa(0.04)

S#(0.04)

O— Sa<0.04) S. (0.04)

Site Class A Site Class 8 Site Class C1 Site Class C2 Site Class O Site Class E

<S.(T))

( M A M

B------ (Sa(T))(Sa(7))

D------ (Sa(T))

E------ (S.fT))

0.05 -

(a) (b)

F ig u re 13: (a) and (b) Fitted curves for derivation of the 10%/50 year UHS curves using two scenarios

30

Site Class A

Site0.2

Siteatco

0.15eSiat8<

Ito

Period (s)

C2

e010.15

oIe1

0.05,

Period (s)

(a) (b)

F ig u re 14: (a) and (b) F itted curves for derivation of the 40% in 50 year UHS curves using two scenarios

0.5« — Site Class A -■— Site Class B -*— Site Class C -E»— Site Class D ■*— Site Class E

0.45

0.4

0.35

o 0.25

a. 0.15:

0.05

0.5 2.5 3.5Period (s)

F ig u re 15: UHS curves for different site conditions a t 10%/50 year hazard level for Ottawa, Canada

31

0.25^ — Site Class A ■■— Site Class B -*— Site Class C

— Site Class D— Site Class E

0.2O)co'ro 0.15 Jf- 0)<DOo< Iro O.bo ,dj I LQ- r73 1

2.5 3.50.5Period (s)

F ig u re 16: UHS curves for different site conditions at 40% in 50 year hazard level for Ottawa, Canada

The developed 10%/50 year and 40%/50 year UHS curves for different site con

ditions from soil amplification analysis follow the same trend as the 2% in 50 years

UHS curves derived based on the site factors F a and F v presented in NBCC. To

check the validity of these results, the derived UHS for Site Class C a t 10%/50 year

and 40%/50 year probability levels are compared with the UHS proposed by GSC

as shown in Figure 17. This Figure highlights th a t there is a significant increase in

spectral acceleration values a t high frequencies of the derived response spectra com

pared to the UHS proposed by GSC. However, the portion of the derived response

spectra in low frequencies matches with the proposed UHS by GSC. The reason for

the higher spectral acceleration values in high frequencies is possibly the resonance

effects. Since large part of the derived UHS for Site Class C matches w ith proposed

UHS by GSC in Figure 17, it can be concluded th a t the derived UHS curves for other

site conditions are also consistent with Site Class C. Therefore, they can be used

32

for performance based seismic risk evaluation in the next chapter. These results are

based on the site response analysis of one soil profile th a t is representative of each

Site Class. The final results can be improved by considering multiple ground profiles

per Site Class and by using site specific soil properties for site response analysis.

0.35 Site Class C (GSC)— Site Class C (Site Res. Ana.)

0.3

0.25

0.2

5 0.15

0.05

0.5 2.5 3.5Period (s)

0.16 Site Class C (GSC)— Site Class C (Site Res. Ana.)0.14

0.12

S 0.06

0.04

0.02

0.5 1.5 2.5 3.5Period (s)

(a) (b)

F ig u re 17: (a) Comparison of UHS derived from site response analysis with proposed UHS by GSC for Site Class C at 10%/50 year probability level; and (b) Comparison of UHS derived from site response analysis w ith proposed UHS by GSC for Site Class C at 40%/50 year probability level

C hapter 3

Seism ic R isk A ssessm ent M ethodology for

Bridge Inventory

3.1 Introduction

Recent studies on performance based seismic risk assessment of bridges by Waller [4]

and Lau et al. [36,37] have shown th a t bridges with similar characteristics and struc

tural properties, such as degree of skew, span length, continuity, reinforcement ratio,

and other structural configurations and design details, can be expected to respond

similarly during seismic events and have similar vulnerability to earthquake damage.

Bridges constructed during a particular period of time typically have similar design

details and thus similar structural properties because their design and construction

are based on similar design codes and standards.

In collaboration with the City of Ottawa, ten concrete bridges w ith column piers

are selected as the sample bridge inventory in the present study. This sample in

ventory includes bridges constructed between 1966 and 2005 of different geomet

ric layouts. Five bridges are selected as representative of the bridge inventory for

the derivation of the fragility relationships between structural responses and damage

states in the new probabilistic performance-based seismic evaluation methodology by

33

34

nonlinear time history analysis.

The first selected bridge on Blair Road, as shown in Figure 18, is a continuous

four span concrete bridge with a prestressed hollow core deck. It crosses Highway

417 in Ottawa. The Blair Road Bridge is straight in alignment and has four columns

in each bent. The deck is supported on fixed bearings a t the middle bent and on

expansion bearings at the other bents and abutments. To account for the influence of

the field operational conditions of the bridge on its seismic behavior, two boundary

condition scenarios are considered for the Blair Road Bridge. The first model scenar

ios assumes the expansion bearings are free to move, whereas in the second case the

expansion bearings are assumed fixed due to constraints by friction and road debris.

The other selected representative bridges shown in Figures 19-21, are located on Ter

minal Avenue crossing Alta Vista Drive, Hunt Club Road crossing A irport Parkway,

and Walkley Road crossing Airport Parkway, respectively. Similar to the Blair Road

Bridge, each of these bridges has a prestressed hollow core deck. For these bridges,

the deck is supported on fixed bearings a t the bents and on expansion bearings a t the

abutments. The Terminal Avenue bridge is a continuous two span concrete bridge

and supported by a two-column bent. The Hunt Club Road bridge and Walkley

Road bridge are continuous three span bridges and supported by two-column bents

and five-column bents, respectively.

35

-22403.0- -20136.0- -20136.0- -22402.0-826.0

EXP EXP FIX EXP EXP i

914.4-

m a2438.4-

PROFILE(units in m m )

(a)-23928.0

000000-^-0 OOQOOOOOOO0508.0-

6738.0-914.4

r 1067.0

-19964.4-

Section A-A (units in mm)

(b)

-12-#9

Spiral @ 82.55

Section B-B (Units in mm)

(c)

F ig u re 18: (a) Blair Road Bridge Profile; (b) Cross section of Blair Road Bridge superstructure; (c) Cross section of Blair Road Bridge column

36

A

| 1 9 .U I .*.i

_.T838.0EXP

762.0—

FIX j EXP i

! j 1 2286.0—-j—

PROFILE (Units in mm)

(a)

-15544.0-

y O O O O O

762.0—

0 - ^ - 0 OOO OOOOO/0457.2-*

BiL

—' 2286.0

-914.5

Section A-A (Units in mm)

BI

J 5153.0

20


(b) (c)

-#11

-#5 Spiral @ 63.5

F ig u re 19: (a) Terminal Avenue Bridge Profile; (b) Cross section of Terminal Avenue Bridge superstructure; (c) Cross section of Terminal Avenue Bridge column

37

A

-15671.8- -34188.4- -15748.1-

1066.9EXP FIX FIX EXP

1066.8-

PROFILE(Units in mm)

-3200.4-

(a)

-13716.0

1524.0

9144.0Section A-A(Units in mm)

(b)

#5 Spiral @ 101.6


(C)

F ig u re 20: (a) Hunt Club Road Bridge Profile; (b) Cross section of Hunt Club Road Bridge superstructure; (c) Cross section of Hunt Club Road Bridge column

38

-12192.0- -22250.4 -12192.1-r660.3

J■jpr

EXP FIX

762.0—

1828.8 — —PROFILE(Units in mm)

FIX EXP

(a)

OOOOOOOOOOO OOOQOOOOOOOOQOQOO

r 914.7

762.0—

J

J

Section A-A (Units in mm)

’14-#14

•#5 Spiral @ 63.5

Section B-B(Units in mm)

(b) (c)

F ig u re 21: (a) Walkley Road Bridge Profile; (b) Cross section of Walkley Road Bridge superstructure; (c) Cross section of Walkley Road Bridge column

3.2 Structural m odels

The representative bridges are modeled by three dimensional spine models using the

SAP2000 program. Line elements are used for modeling the bridge components ac

cording to the guidelines specified by Aviram et al [38]. Considering the geometry,

the Blair road bridge has no skew angle, but the other representative bridges have a

small skew. However, for purpose of the study here to demonstrate the proposed new

approach, the effect of the small skew angle is ignored herein. On m aterial modeling,

the core concrete materials in the bridge piers are modeled by the confined m aterial

model by Mander [39]. For the other parts of the bridges, the concrete m aterials are

modeled as unconfined material model by Mander [39]. In order to more accurately

39

determine the behavior and capacity of the bridge components, the expected m aterial

properties of reinforcing steel are used in nonlinear tim e history analysis of the repre

sentative bridges. The expected yield strength and tensile strength of the reinforcing

steel are calculated by Equations (4) and (5) as specified in ANSI/AISC 341 [40] and

considering Canadian seismic design requirements [41].

F ye = R y * F y (4)

F ue = R t * F u (5)

where Fye is the expected yield stress, R y is factor applied to estim ate the expected

yield stress, F y is specified minimum yield stress, F ue is the expected tensile strength,

R t is factor applied to estimate the expected tensile strength, and F u is specified

minimum tensile strength.

3.2.1 Superstructure

The bridge deck of the representative bridge is modeled by linear elastic equivalent

beam elements as the deck and girders are assumed to remain elastic during dynamic

responses. The bridge decks and girder spans are discretized into ten equivalent

elements for each span according to the minimum requirements specified in ATC-

32 [42]. Based on the element length, the rotational mass of the bridge deck is

computed and assigned to each element according to the procedure explained by

Aviram et al [38]. As recommended in ATC-32 [42], it is expected th a t prestressed

concrete bridges do not experience cracking during responses. Therefore, there is

no property modifier applied to the moment of inertia of prestressed bridge deck

section. In addition to the self-weight of the bridge structural components, additional

dead load due to weights of sidewalks, asphalt cover, barrier walls, railings and posts

40

are estimated using the data reported in Canadian Highway Bridge Design Code

(CHBDC) [43] and applied to the deck elements.

3.2.2 Substructure

Bridge columns are modeled by linear elastic column elements w ith consideration

of the cracking properties of concrete. They are discretized into 5 to 6 elements as

recommended [42]. To more accurately determine seismic demands, effective or crack

section properties are used in the modeling of the bridge columns by modifying the

shear area, torsional resistance and moment of inertia with property modifiers. The

property modifiers used for the shear area and torsional resistance are 0.8 and 0.2

respectively [38]. The moment of inertia for the columns of representative bridges

under cracked deformation states is determined by moment curvature analysis using

the X tract program [44], The estim ated property modifier for moment of inertia

for Blair road bridge, Terminal Avenue bridge, Hunt Club road bridge, and Walkley

road bridge are 0.34, 0.62, 0.58 and 0.55, respectively. Rigid link elements are used to

model the connection offsets between the bridge columns and the centroid locations

of the bridge deck cross-sections. Bridge bearings are modeled using multi-linear

elastic link elements in SAP2000. The expansion bearings are allowed to translate in

longitudinal and transverse directions and ro ta te about transverse axis to represent

boundary conditions of the bridge. For fixed bearings, both translation and rotation

in all directions are restricted.

For simplicity, the soil structure interaction effect is not considered in this study.

The foundations are assumed as rigid and the boundary conditions at the bottom of

the columns are assumed as fixed in all directions. To accurately capture the force-

displacements behaviors of the structure, potential plastic hinges are modelled at the

two ends of bridge columns [45]. Columns with expansion bearings are modelled as

ideal cantilevers which deform in single curvature, and plastic hinges can only form

41

at the bottom of the columns [45]. The columns without bearing has fixed boundary

conditions at top and bottom of the columns and are modeled to deform in double

curvature with potential plastic hinges forming at the top and bottom . The plastic

hinge length is computed from column properties and expected m aterial properties

using Equation (6) proposed by Priestly [45]. The plastic hinge zone of the column

is modelled by fiber hinge model, which has been calibrated through iteration using

a property modifier applied to gross area, shear area and moment of inertia to m atch

the fundamental period of the structure with fiber hinges with the elastic fundam ental

period of the original structure [38].

L p = 0.08L + 0.022f yed b > 0 .0 U f yedb (6)

where L is the distance from the point of fixity to the point of inflection in m, d&

is the diameter of the Longitudinal reinforcement in m, and iye is the effective yield

stress in Mpa.

The modelling of bridge abutm ent can have significant influences on the bridge

responses. There are three common types of abutm ent models for seismic response

analyses, such as roller abutment, simplified abutm ent and spring abutm ent models.

The spring abutm ent model is typically adopted to model soil structure interaction

effect. However, for the study here, the roller abutm ent model is adopted in or

der to obtain lower-bound estimates of the longitudinal and transverse resistance of

the bridge [38]. The abutm ents are modeled by as roller abutment allowing transla

tional and rotational displacements in the longitudinal direction of the bridge. As

suming stoppers or shear keys at the abutm ents prevent any transverse movement,

fixed boundary condition is assigned in the transverse direction of the representative

bridges.

The Table 8 shows the unit weights obtained from CHBDC for the structural

42

components and the members fixed to the structure.

Table 8: Unit weights of bridge components according to CHBDC

Bridge Component Unit weight, kN /m 3

Prestressed deck 24.5

Side walks 23.5

Asphalt 23.5

Column 24

Foundation 24

The spine models of the representative bridges are shown in Figures 22-25, respec

tively.

! ]X.

\

Figure 22: Spine model for Blair Road Bridge

F ig u re 23: Spine model for Terminal Avenue Bridge

F ig u re 24: Spine model for Hunt Club Road Bridge

Vi

•v.J

\v

F ig u re 25: Spine model for Walkley Road Bridge

44

3.2.3 Fundam ental v ibration period

The first vibration modal periods and mode shapes of the representative bridges

are determined by modal analysis. These fundamental periods are used for scaling

recorded ground motions to obtain uniform hazard spectra compatible ground mo

tions at different hazard levels a t the bridge sites. These scaled UHS compatible

ground motions are then used as input excitations in nonlinear tim e history analysis

of the representative bridges. Additionally, following the probabilistic seismic risk as

sessment methodology, the first mode spectral acceleration values a t different hazard

levels are used to develop the seismic demand curves. Figures 26-29 show the first

modal shapes of the Blair Road bridge, Terminal Avenue bridge, H unt Club Road

bridge, and Walkley Road bridge, respectively.

(a)

45

(b)

F ig u re 26: (a) and (b): First modal shape for Blair Road Bridge free expansion bearing case (T \ = 2.39s) and fixed bearing case (Ti = 1.35s)

Figure 27: First modal shape for Terminal Avenue Bridge (Ti = 1.28s)

46

\ <v

F ig u re 28: First modal shape for Hunt Club Road Bridge (Ti = 0.82s)

'•* WK \i

F ig u re 29: First modal shape for Walkley Road Bridge (T \ = 1.14s)

3.3 Hazard analysis

In seismic hazard analysis of performance-based risk assessment methodology, a site

specific hazard model is developed to determine the annual probability of exccedance

of seismic events of varying intensity at the specific site of the bridge. To perform this

work, it is necessary to select a representative intensity measure (IM) for the site’s

seismic hazard th a t minimizes uncertainty in the probability analysis. For bridge

structures, the IM can be defined in terms of the first mode 5% damped elastic spectral

47

acceleration of the structure (Sa (Ti)), the Peak Ground Acceleration (PGA) and the

Peak Ground Velocity (PGV) for probabilistic performance-based evaluations [6]. In

the present study, the 5% damped elastic spectral acceleration is adopted as intensity

measure in developing the framework of performance-based seismic risk assessment

of bridge inventory.

3.3.1 Selection o f ground m otions

Selection of suitable ground motion time histories for nonlinear tim e history analysis

is important. Typically, the time series are selected from recorded ground motions

by considering factors such as similar magnitudes, similar distances and similar site

conditions. But to perform this task, there is not enough strong ground motion

data existing in regions of eastern Canada around the Ottawa area except the recent

5.5 magnitude earthquake(Val-des-bois,2010) [46]. Therefore, artificially simulated

ground motion records are used as input excitation for nonlinear tim e history analysis

of the selected representative bridges. Numerous studies have shown th a t simulated

records and actual earthquake records are functionally equivalent, from both linear

and nonlinear perspectives [16]. For this study, assuming compound intensity func

tion, the artificial time histories are generated to match the uniform hazard spectrum

(UHS) curves by using SIMQKE program [25]. Ten acceleration tim e histories are

generated for each hazard level per Site Class, for a to tal of 150 ground motions for

the Ottawa region considering the different combinations of hazard levels and Site

Classes. The comparison of the response spectra from simulated UHS compatible

ground motions for Site Class C a t different hazard levels is shown in Figure 30.

Additionally, scaled Val-des-bois earthquake [46] is also used to supplement the

simulated ground motions for structural analysis in the investigation. The actual Val-

des-bois ground motions are scaled by a factor to minimize the difference in spectral

acceleration ordinates in the period range with the UHS curves by the least-square

48

method [47]. Following the ASCE/SEI 7 Scaling procedure, the period range consid

ered for scaling is 0.2T to 1.5T, where T is the fundamental period [48]. However,

since the objective of this study is to develop generalized fragility curves th a t can

be used for the assessment of all the bridges in the network inventory, therefore, the

entire period range of the target UHS curves is considered for scaling process. The

Figure 31 shows the scaled response spectra for Site Class C at different hazard levels.

0.7e — 2%/50 year UHS ■*— 10%/50 year UHS ■*— 40%/50 year UHS 2%/50 year matched 10%/50 year matched 40%/50 year matched

0.6

3 0.5

0.4

0.3

\

3.52.50.5Period (s)

F ig u re 30: Matched Response Spectra for Site Class C at different hazard levels

49

■ e — 2 % 1 5 0 years UHS -*— 10%/50 years UHS ■*— 40%/50 years UHS Originall Val-de-Bois Scaled to 2% /50 years Scaled to 10%/50 years Scaled to 40%/50 years

O)

0.8

0.6

0.4

0.2

2.5 3.50.5Period (s)

F ig u re 31: Scaled Response Spectra for Site Class C a t different hazard levels

3.3.2 Probabilistic seism ic hazard curves

As presented earlier, the primary goal of the seismic hazard analysis is to develop a

site-specific seismic hazard curve th a t relates the mean annual frequency of occurrence

(A/m ) to intensity measure [9]. The mean annual frequency of exceedance at different

hazard levels is determined by using conventional probabilistic seismic hazard analysis

as with the values provided by GSC [19]. From past studies [49-51], seismic hazard

of a site can be approximated as a linear function on a log space. Thus the median

hazard curve is commonly assumed to have a power-law form in linear space with two

regression parameters (k and k0) in the range of the ground motions investigated as

shown in Equation (7).

A = k 0 [ I M ] ~ k (7)

50

To establish this relationship, intensity measures, the first mode spectral accel

eration values ( S a(Ti ) ) of the representative bridges are obtained from UHS curves

(Chapter2 : Figures 1, 15 and 16) using the fundamental period (Xi) of the repre

sentative bridges. Using the mean annual frequency of exceedance values of hazard

levels and corresponding intensity measures determined using first mode period of the

representative bridges, seismic hazard curves are developed in the form of Equation

(7) for all site classes. Figures 32-36 show the hazard curves obtained for the Blair

Road Bridge for both free expansion bearing case and fixed bearing case, Terminal

Avenue Bridge, Hunt Club Road Bridge, and Walkley Road Bridge respectively.

O Site ClassSite Class

* Site Classt> Site Class* Site Class

y=2E y=5E-y=1E—

y=2E—06*x~1 85 y=6E-06*x~1'75

10Sa(T 1) (g)

Figure 32: Hazard curves for Blair Road Bridge with free expansion bearing case

Site Class A ■ Site Class B* Site Class C> Site Class D★ Site Class E

y=2E-06*x'167 y=5E-06*x"1 68 y=9E-06*x~1 72

Sa(T1) (g)

F ig u re 33: Hazard curves for Blair Road Bridge with fixed bearing case

y=2E-05*x 1 67 y=5E-05*x~1 66

Sa(T1) (g)

F ig u re 34: Hazard curves for Terminal Avenue Bridge

52

10

10-2

10

1010

o■*>*

Site Class A Site Class B Site Class C Site Class D Site Class E

• y=8E-06*x"

' y=1E-05*x"

■ y=3E-05*x"

•y=5E-05*x

y=1E-04*x"1 712

1.639

1.694

-1.649

Sa(T1) (g)

F ig u re 35: Hazard curves for Hunt Club Road Bridge

Site Class ASite Class BS te Class CSite Class D

-1 .659

Sa(T1) (g)

Figure 36: Hazard curves for Walkley Road Bridge

3.4 Dem and analysis

53

The objective of the demand analysis is to predict the response of the structure

subjected to the earthquake loading of the site specific ground motions suite. In

performance based methodology, the probable effect of site-specific ground motions

on a structure is determined in terms of engineering demand param eters (EDPs).

There are different choices of response measures or ED Ps such as plastic rotation,

drift ratio,and displacement ductility. In the present study, drift ratio is selected as

EDP. Some studies [6,9,52] have shown th a t the most efficient and practical demand

model is the relationship between first mode spectral acceleration (S a( T i)) and drift

ratio. Assuming th a t the demand follows a lognormal probability distribution for

a given IM, the distribution of EDPs for given IMs is defined in liner-form w ith

two regression parameters, as shown in Equation (8 ) in logarithmic space [6 ]. The

parameters of the above linear function can be obtained by linear regression using

the least square method in the logarithmic space.

I n ( E D P ) = A + B l n ( I M ) (8 )

where E D P is the median EDP.

Seismic demands of the representative bridges are predicted using nonlinear tim e

history analysis subjected to simulated and scaled Val-des-Bois ground motions in

horizontal bi-directions such as longitudinal and transverse directions to predict the

seismic demand. Newmark direct integration method ( 7 = 0.5 and = 0.25) was

employed in time step integration in the nonlinear analysis. The damping behavior

of the bridges are assumed as 5% mass proportional and stiffness proportional dam p

ing. The maximum horizontal displacement along the longitudinal direction at the

top of the critical pier of each representative bridge is obtained and used to compute

54

the seismic demand of the bridge in terms of drift ratio. Using the estim ated drift

ratios and corresponding first mode spectral accelerations, linear regression is per

formed in log space to establish the relationship given by Equation (8 ) of the interim

demand model. Figures 37-41 show the interim demand models developed for the

representative bridges for the different Site Classes. Regression coefficients A and B

are determined from the resulting interim demand model logarithmic linear functions.

The results from regression analyses show th a t the ground condition has little effect

on the EDP-IM relationship. Using the relationship of the interim demand model,

probability of exceedance of the representative EDP of the evaluated bridge can also

be evaluated using Equation (9) [9].

P ( E D P / I M ) = 1 — (f>I n ( E D P ) — A — B l n ( I M )

& l n ( E D P / I M )

where </>() is the standard normal distribution function.

(9)

To develop the probability distribution relationships expressed in Equation (9),

dispersion of maximum drift ratios are computed separately at each hazard level for

all Site Classes. The plot of probable drift ratio for the Blair Road Bridge cases,

Terminal Avenue Bridge, Hunt Club Road Bridge, and Walkley Road Bridge are

shown in Figures 42-46.

55

10%

o ra a: <e

0 .01%


1.013y=0.2095 x

y=0.2004 x0.983y=0.1794 x0.963y=0.1642 x0.917y=0.1371*x

0 .1%

Sa(T1) (g)

F ig u re 37: Demand curves for Blair Road Bridge with free expansion bearing case

10%

1%

<0CHIC

0 . 1%

0 .01%

: Class A i Class B i Class C i Class D : Class E 1.0614 *x0-994

l.0574*x09750.9430510*X0.9170471*x0.8690413*X

Sa(T1)(g)

F ig u re 38: Demand curves for Blair Road Bridge with fixed bearing case

Drift

Rati

o (%

)

56

10% r

os£*

0 .01%

Site Class A Site Class B Site Class C Site Class D Site Class E y=0.0633*x°"° y=0.0611*x° 980 y=0.0577*x° 963 y=0.0546*x° 946 y=0.0483*x° 900

0 . 1% -

Sa(T1) (g)

F ig u re 39: Demand curves for Terminal Avenue Bridge

10 r :

0.1

0.0110 '

Site C lass A Site C lass B Site C lass C Site C lass D Site C lass E

• y=0.0240*x°"59

■ y=0.0226*x° 9674

■ y=0.0222*x°'9614

•y=0.0218*x°'9544

y=0.0213*x°9405

Sa(T1) (g)

Figure 40: Demand curves for Hunt Club Road Bridge

57

0101* i—o


0.9737y=0.0444 x0.9494y=0.0421 x0.933y=0.0392 x

y=0.0369 x0.8712y=0.0348*x

0.01

Sa(T1) (g)

F ig u re 41: Demand curves for Walkley Road Bridge

10% in 50 Years

2% in 50 Years

A - Site Glass A B - Site Glass B C - Site Class C D. -. Site Class D E - Site Glass E

1% 2% 3% 4%EDP, Drift Ratio

1

0.75

£ 0.5LU

0.25

ImVA - Site Class A . B. - Site Class B ..

\ \ \ E

C - Site Class C D - Site Class D E - Site Class E

vvS0% 1% 2%

EDP, Drift Ratio 40% in 50 Years

3%

0 .2%

EDP0.4%

Drift Ratio0 .6%

F ig u re 42: Probability of exceedance of drift ratio for Blair Road Bridge with free expansion bearing case

58

10% in 50 years

2% in 50 years

A - Site Class A B - Site Class 8 C - Site Class C D - Site Class DE - Site Class E

1% 2% EDP, Drift Ratio

A - Site Class A .B .-S ite Class B. C ~ Site Class C D - Site Class D E - Site Class E

0.5% 1% 1.5%EDP, Drift Ratio 40% in 50 years

A - Site Class A B - Site Class B C - iSite Class C D - Site Class D E - Site Class E

0.2% 0.4%EDP, Drift Ratio

0 .6%

F ig u re 43: Probability of exceedance of drift ratio for Blair Road Bridge with fixed bearing case

10% in 50 years

1

0.75

0.5

0.25

2% in 50 years

00%

I-A - Site Class A B - Site Class B

I \ \ A C - Site Class C\ \ \ : \ D - Site Class D

i m C D : E E - Site Class E-

V V N-1% 2% EDP, Drift Ratio

A - Site Class A B - S i te Class B C - Site Class C D - Site Class D E - Site Class E

0.5% 1% 1.5%EDP, Drift Ratio 40% in 50 years

A - Site Class A B - Site Class B C - Site Class C D - Site Class D E - Site Class E

„ 0.75

0.2% 0.4%EDP, Drift Ratio

0 .6%

Figure 44: Probability of exceedance of drift ratio for Terminal Avenue Bridge

[|AII/dQ3]d .SP

(l/\ll/dQ3)d

59

10% in 50 years

1

0.8

0.6

0.4

0.2

0

2% in 50 years' \ \ A - Site Class A

B - Site Class B\ C - Site Class C D.T.Site Class D.

) k I1 c b E E - Site Class E

L... V ;V V0.5 1 1.5EDP, Drift Ratio (%)

w. 0.4


0.4 0.6 0.8EDP, Drift Ratio (%)

40% in 50 years

1.2

MJ. 0.4


0.2 0.3EDP, Drift Ratio (%)

u re 45: Probability of exceedance of drift ratio for Hunt Club Road Bridge

10% in 50 Years

2% in 50 Years

- Site Class A -S ite Class B- Site Class C- Site Class. D.- Site Class E

0.5 1 1.5EDP, Drift Ratio (%)

0.8

€ 0.6 a. a tn a. 0.4

0.2

1

0.8

1 0.6 CLaw o.4 o.

0.2

Site Class A Site Class B Site Class C site Class d Site Class E

0.5 1 1.5EDP, Drift Ratio (%)

40% in 50 Years

- Site Class A- Site Glass B- Site Class C- Site Class D- Site Class E

0.1 0.2 0.3 0.4EDP, Drift Ratio (%)

0.5

Figure 46: Probability of exceedance of drift ratio for Walkley Road Bridge

3.5 Dam age analysis

60

Damage experienced by the structure in terms of damage measures [DM] can be

linked to structural response described in terms of EDP. The relationships for quan

tification of bridge damage can be accomplished through observed damage states

from experiments in laboratories or earthquake events. Several damage states or

failure mechanisms, such as concrete crushing, cover spalling, longitudinal bar buck

ling, longitudinal reinforcement fracture, transverse reinforcement fracture, and loss

of axial load capacity [52] can be considered as damage states of reinforced concrete

columns. However, in the present study, concrete cover spalling, longitudinal bar

buckling and unseating or loss of span support damage states th a t can be identified

during post-event bridge inspections, are considered for the formulation of the pro

posed assessment methodology. The damage state of cover spalling represents the

initiation of failure, longitudinal bar buckling is considered to represent the s ta rt of

more substantial damage with serious consequent effect on the seismic load resistant

capacity of the bridge, and unseating represents the complete collapse failure of the

bridge.

In performance based methodology, an interim damage model is derived to relate

damage states with EDPs. It can be developed through experimental testing or

infield observations or analytical estimates of behavior of reinforced concrete columns

[5,53,54]. There are existing general damage models developed from databases of

collected experimental results on reinforced concrete columns th a t can be used to

develop specific damage models for the representative bridges. The damage model

developed by Berry and Eberhard [5] on cover spalling and bar buckling damage states

is adopted in this study based on the analysis of a worldwide structural performance

database (SPD) of cyclic lateral load tests of 253 rectangular reinforced and 163

spiral-reinforced concrete columns of different m aterial and structural properties [55].

61

Berry and Eberhard [5] have derived performance models for reinforced concrete

column tha t relate median column damage to median EDPs by parameterized regres

sion analysis of the experimental results in the SPD database. Equations (10) and

(11) show the performance models developed by Berry and Eberhard [5] for cover

spalling and bar buckling damage states of spiral reinforced concrete columns given

by the column properties. They have compared the estimated performance values

obtained from Equations (10) and (11) at which damage is expected to occur to the

damage observation from the experimental tests in the SPD database. Based on the

comparison study, they have developed general damage model (cumulative probabil

ity of cover spalling and bar buckling damage states as a function of A^ damage; ) th a t

can be easily converted to damage model for specific columns.

A,bb calc

L = L 6 ( 1 _ A ^ f J V + 1 0 B ) <10>

L ^ =3-25( 1 + ^6bPe//-^) ( 1 _ ^ ^ ) ( 1+ 10d)

where P is the axial load, A g is the gross section area, f'c is the concrete compres

sive strength, L is the distance from point of fixity to point of inflection, D is the

column diameter, k e bb is taken as a constant value 150 for spiral reinforced concrete

column, ef f = p3! r is the volumetric transverse reinforcement ratio, ps is the trans-J c

verse reinforcement ratio, f ys is the yield strength of transverse reinforcement, and db

is the longitudinal bar diameter.

The specific damage models for cover spalling and bar buckling damage states of

the representative bridges are developed by adapting the column performance models

by Berry and Eberhard [5]. First, the drift ratio at the onset of cover spalling and on

set of bar buckling are estim ated using Equations (10) and (11). The general damage

model is adjusted by multiplying with the estimated drift ratios. For unseating, the

62

damage model is assumed to be a step function, which is obtained from the measured

seat width of the representative bridges. The drift ratio at unseating is estim ated

from the allowable seat width of the representative bridges. The damage model for

the selected damage states for the Blair Road Bridge, Terminal Avenue Bridge, Hunt

Club Road Bridge, and Walkley Road Bridge Columns are shown in Figures 47-50.

0.9

0.8

§> 0.7COEO 0.6

Cover SpallingUniseating

0.5

1 0.4a. o

i 0.3Bar Buckling

0.2

0.1

A d ftmand (0 \L \ / 0 >

F ig u re 47: Column damage model for Blair Road Bridge modeled scenarios

Prob

abili

ty

of Pi

er D

amag

e Pr

obab

ility

of

Pier

Dam

age

63

0.9

0.8

0.7UnseatingCover Spalling

0.6

0.5

0.4

0.3Bar Buckling

0.2

0.1

20 25

F ig u re 48: Column damage model for Terminal Avenue Bridge

0.9

0.8Cover Spalling

Unseating0.7

0.6

0.5

0.4

0.3 Bar Buckli

0 .2

2 0(%)■ d e m a n d

Figure 49: Column damage model for Hunt Club Road Bridge

0.9

0 .8

S> 0.7 UnseatingC over Spalling

0 .6

0.5

s 0.4COJQOA- 0.3

0 .2

Bar Buckling0.1

2 0 25&df>m.avi.d (%))

F ig u re 50: Column damage model for Walkley Road Bridge

Depending on the nature of the damage sates, they can be grouped into two

categories of discrete or continuous damage states. For continuous dam age states, the

relation between EDP and median DMs can be defined by Equation (12). However,

in some cases of damage analysis, the damage states may be considered as discrete

quantities and th a t can be simplified to act as continuous damage states when the

coefficients of variation for each of the discrete damage states are approximately

equal [6 ]. Then in this case, the regression parameters in Equation (12) are assumed

to be C=0, D = l, and <Jin ( E D P / i M ) = coefficient of variation [6 ]. The coefficient of

variation of cover spalling and bar buckling damage states are obtained from Berry

and Eberhard’s experimental studies, whereas for the case of unseating, the coefficient

of variation is taken as zero because the drift ratio at which unseating occurs is

constant (seat width is constant).

65

l n ( D M ) = C + D l n ( E D P ) ( 1 2 )

where D M represents the median DM

By combining the demand model developed in the preceding step w ith the devel

oped damage model using Equation (13), it is possible to derive the column damage

fragility curves, which gives the probability of exceedance of the damage sta te a t a

selected representative bridges for different site conditions are shown in Figures 51-55.

The estimated probability of cover spalling and bar buckling at first mode spectral

acceleration (S a( T i )) of the representative bridges are presented in Table 9. The re

sults for the unseating failure mode are not presented in Table 9 as the probability is

zero at the first mode spectral accelerations. The results highlights th a t probability

of failure at different hazard levels increases from Site Class A through Site Class

E. Since the soil become softer from Site Class A through Site Class E, it can be

interpreted from these results is the significant impact th a t local soil conditions have

on increased vulnerability of bridges on soft soil sites.

given level of seismic hazard [6 ]. The resulting column damage fragility curves for the

l n ( D M ) - (C + D A + D B l n ( I M ) ) '(13)

l n ( E D P /I M ) ln (D M /E DP )

66

Bar Buckling°> 100%

80%

60%

Cover Spalling 40%c 100%

X> 2 0%80%

0%0.1 0.2 0.3

Sa(T1) (g) Unseating

0.4 0.560%

40%100%

CD3 2 0% (G nI 0% 80%

0.1 0.2 0.3 Sa(T1)(g)

0.4 60%

40%

0 %0.1 0.2 0.3 0.4 0.5

—— Site C lass A- — Site C lass B 1 • * Site C lass C— • Site Class D

Site Class E

— Site Class A - — Site Class B • • ■ Site Class C — • Site Class D

Site Class E

Site Class A- — Site Class B * 11 Site Class C — ■ Site Class D

Site Class E

Sa(T1) (g)

F ig u re 51: Damage fragility curves for Blair Road Bridge with free expansion bearing case

°> 2 0 %Bar Buckling

0.4 0.5

Site Class A Site Class B Site Class C Site Class D Site Class E^ 1 0%

Cover Spalling


0.2 0.3Sa(T1) (g) Unseating

O 40%

= 2 0%

Site Class A0.2 0.3Sa(T1) (g)

— Site Class B Site Class C Site Class D Site Class E

0.2 0.3Sa(T1) (g)

0.4 0.5

Figure 52: Damage fragility curves for Blair Road Bridge with fixed bearing case

67

Bar Buckling? 10%

7.5%, . y<?//5%

Cover Spalling80%

5%JD60%

0 %0.1 0.2 0.3

Sa(T1) (g)Unseating

0.4 0.540%

o> 4%20%

3%0%0.1 0.2 0.3

Sa(T1)(g)0.4 0.5

2 %

0 %0.1 0.2 0.3 0.4 0.5

—— Site Class A • — Site Class B • 1 • Site Class C — • Site Class D

Site Class E— Site Class A- — Site Class B • • • Site Class C — * Site Class D

Site Class E

—- Site Class A — Site Class B ■ • Site Class C - • Site Class D

Site Class E

Sa(T1) (g)

F ig u re 53: Damage fragility curves for Terminal Avenue Bridge

Bar Buckling

roQ.cok_0)>oO

<+->o>* 4—»

15to_ao

Cover Spalling

— Site Class A — Site Class B ■ - Site Class C

— * Site Class DSite Class E

0.2 0.3Sa(T1)(g)

O)cZo3mCO

CO

oI?15tojQo

1.5

0.5

o 0

0.3o>cCD0)</>cD

■4—o>?15CQAo

0 .2

0.1

Site Class A — Site Class B

Site Class C — — Site Class D

Site Class E

0.1 0.2 0.3Sa(T1) (g) Unseating

--------- Site Class A ............: / / .— — — Site Class B / / t. . . . . . . . site Class C / ' ■ ' * '• — • — • Site Class D

Site Class E/ ' y > :

0.1 0.2 0.3Sa(T1) (g)

0.4 0.5

Figure 54: Damage fragility curves for Hunt Club Road Bridge

Prob

abilit

y of

Cove

r Sp

alling

(%

)

68

Bar Buckling

50

40

30

20

10

0

Cover Spalling

----------- Site C lass A— — — Site C lass B . . . . . . . . site C lass C

— — Site C lass DSite C lass E

. . . . . „•4..»-

0.1 0.2 0.3Sa(T1) (g)

0.4 0.5

Site Class A— — — Site Class B

Site Class C Site Class D Site Class E

1.5o>c15CD(J)cZ>H—o£1510no

0.5

0.2 0.3Sa(T1)(g) Unseating

Site C lass A— - — Site C lass B

Site C lass C ■ — ■ — • Site C lass D

Site C lass E

0.1 0.2 0.3Sa(T 1) (g)

0.4 0.5

F ig u re 55: Damage fragility curves for Walkley Road Bridge

-69

T able 9: Probability of cover spalling and bar buckling of representative bridges at different hazard levels for all Site Classes

S ite

C lass

R e p r e se n ta t iv e

B r id g e s

C over S p a llin g B a r B u c k lin g

2% in

5 0 y r

10% in

50yr

40% in

50yr

2% in

50yr

10% in

5 0 y r

40% in

5 0 y r

A

Blair Road (Exp) 0.557% 0.010% 0.000% 0.002% 0.000% 0.000%

Blair Road (Fix) 0.597% 0.016% 0.000% 0.004% 0.000% 0.000%

Terminal Avenue 0.571% 0.016% 0.000% 0.001% 0.000% 0.000%

Hunt Club Road 0.197% 0.004% 0.000% 0.001% 0.000% 0.000%

Walkley Road 0.217% 0.005% 0.000% 0.000% 0.000% 0.000%

B

Blair Road (Exp) 4.807% 0.321% 0.008% 0.107% 0.001% 0.000%

Blair Road (Fix) 3.228% 0.229% 0.003% 0.065% 0.001% 0.000%

Terminal Avenue 3.148% 0.222% 0.003% 0.017% 0.000% 0.000%

Hunt Club Road 1.105% 0.051% 0.000% 0.012% 0.000% 0.000%

Walkley Road 1.253% 0.072% 0.001% 0.004% 0.000% 0.000%

C

Blair Road (Exp) 12.689% 1.465% 0.083% 0.626% 0.017% 0.000%

Blair Road (Fix) 7.444% 0.769% 0.019% 0.226% 0.006% 0.000%

Terminal Avenue 7.938% 0.827% 0.020% 0.208% 0.001% 0.000%

Hunt Club Road 3.104% 0.207% 0.003% 0.053% 0.001% 0.000%

Walkley Road 3.050% 0.224% 0.003% 0.013% 0.000% 0.000%

D

Blair Road (Exp) 20.984% 3.588% 0.295% 1.646% 0.076% 0.002%

Blair Road (Fix) 12.905% 1.895% 0.064% 0.612% 0.024% 0.000%

Terminal Avenue 14.017% 2.090% 0.067% 0.269% 0.008% 0.000%

Hunt Club Road 6.440% 0.738% 0.011% 0.186% 0.006% 0.000%

Walkley Road 6.107% 0.652% 0.013% 0.052% 0.001% 0.000%

E

Blair Road (Exp) 33.741% 8.684% 0.894% 3.681% 0.351% 0.009%

Blair Road (Fix) 21.926% 8.102% 0.284% 1.406% 0.217% 0.001%

Terminal Avenue 24.007% 9.298% 0.330% 0.696% 0.095% 0.000%

Hunt Club Road 12.628% 2.572% 0.053% 0.463% 0.028% 0.000%

Walkley Road 12.413% 4.033% 0.081% 0.149% 0.016% 0.000%

3.6 Loss analysis

Accurate loss estimate based on da ta based risk assessment results is im portant for

decision making on mitigating the im pact of potential earthquake damage, which

are of immediate concerns to emergency managers, recovery planners, and structural

engineers and owners before or after earthquakes. The objective of the loss analysis

in this study is to formulate the decision fragility curves that relate the probability of

exceedance of certain decision limit sates as a function of IMs. This can be performed

through integration of the interim loss models w ith the damage fragility curves derived

in damage analysis. The interim loss models are formulated as relationships between

damage measures and corresponding decision variables (DVs) [6 ].

Decision variables for bridges can be grouped into two categories [6 ]: functional

DVs and repair DVs. Functional DVs describe post-earthquake operational states of

the bridge, such as required lane closures, reduction in traffic volume, or complete

bridge closure. Repair DVs include downtime or restoration time and repair cost. In

the present study, the two most common DVs such as downtime and repair cost are

selected for decision making consideration of the impact of the bridge performance

on the transportation network. Similar to the relationships defined in the previous

phases, an interim loss model, relating DV to DM, can be developed in the continuous

form as shown in Equation (14).

l n ( D V ) = E + F l n ( D M ) (14)

where ( D V ) represents the median DV.

For the development of the interim loss models for repair cost and downtime deci

sion variables, the repair cost ratio (RCR), which is defined as repair cost normalized

by replacement cost, and restoration tim e values as suggested by HAZUS [56] are

adopted. Here, the damage states of cover spalling, bar buckling and unseating are

assumed to be equivalent to the HAZUS damage levels of slight, extensive and com

plete [52]. Tables 10 and 11 show the RCRs and restoration time values for highway

bridges corresponding to the considered damage states in the present study. The mean

RCR values given in Table 10 for each damage state is directly applied to derive the

loss models based on repair cost. However, for downtime, similar to the definition

of RCR, downtime ratio (DTR) is estimated by normalizing the mean restoration

time value given in Table 11 for each damage state by the replacement tim e in the

derivation of the loss models. To accomplish this task, the restoration tim e for the

complete damage state (unseating) is taken as the replacement time. Considering the

damage measure as the median drift ratio for each damage state, the loss models are

developed according to Equation (14) by performing least square regression in linear

space [6 ]. The variations of repair cost ratio and ratio of downtime to replacement

time with median drift ratio for the representative bridges are shown in Figures 56-59.

T ab le 10: Repair cost ratios for Highway Bridges

M odified R epair C ost Ratio

(R C R ) for All Bridges

Dam age

S tate

HAZUS

D am age S ta teM ean Range

Spalling Slight 0.03 0.01 to 0.03

Moderate 0.08 0.02 to 0.15

Bar buckling Extensive 0.25 0.10 to 0.40

Unseating Complete 2 /n 0.30 to 1.0

where n is number of spans

DV

=Rep

air

Cost

Rat

io

72

T ab le 11: Restoration tim e for Highway bridges

C o n tin u o u s R esto ra tio n

F u n c tio n s for H ig h w a y B rid ges

(a fte r A T C -1 3 , 1985)

D a m a g e

S ta te

H A Z U S

D a m a g e S ta te

M e a n

(d a y s)a (d a y s)

Spalling Slight 0.6 0.6

Moderate 2.5 2.7

Bax buckling Extensive 75 42

Unseating Complete 230 n o

Repair C ost Downtime0.5

0.45 0.9

0.80.4

S 0.70.35

0.3

0.50.25

B 0.40.2

0.15 o 0.3

Q 0.20.1

0.05 0.1

12DM, Median drift ratio (%) DM, Median drift ratio (%)

Figure 56: Interim loss models for Blair Road Bridge modeled scenarios

DV=R

epair

Cos

t Ra

tio

DV=R

epair

Cos

t Ra

tio

73

Repair Cost Downtime

0.9 0.9

.§ 0.80.8

0.7 5! 0.7y=461.4x3059

0.6 M 0.6a .a)a. 0.50.5

0.4 E 0.4

0.3 0.3

0.2 > 0.2

0.1

(%)DM, Median drift ratio DM, Median drift ratio (%)

F ig u re 57: Interim loss models for Terminal Avenue Bridge

Repair Cost Downtime0.7

0.6

0.5

0.4

0.3

0.2

0.1

DM, Median drift ratio (%)

0.9o>■I 0.8

| 0.7 <o8 0.6 Q.<Doe 0.5uI 0.4 cI 0.3 OII> 0.2

DM, Median drift ratio (%)

Figure 58: Interim loss models for Hunt Club Road Bridge

74

Repair Cost Downtime0.7

0.90.6

.§ 0.8

o 0.5 j) 0.7

0.60.4a: 0.5

8- 0.3 E 0.4

0.3Q 0.2

> 0.2

14DM, Median drift ratio (%)DM, Median drift ratio (%)

F ig u re 59: Interim loss models for Walkley Road Bridge

Using the loss models developed above, decision fragility curves can be obtained

by incorporating the demand and damage models into Equation (15) [6 ]. They can

be identified as probability of exceedance of certain DV limit sta te as a function of

IM. Figures 60-64 show the decision fragility curves at different levels of repair cost

ratio for the representative bridges. Similarly, for different level of downtime, these

relationships are shown in Figures 65-69.

P(DV/ IM) = 1 -(f)l n ( D V LS) - ( E + F C + F D A + F D B l n j l M ))

’ \ J D F 2(7ln { E D P / I M ) + F 2(Jl n ( D M / E D P ) + ® ln{DV/ D M )

(15)

75

g 0.75 orII■g 0.5>£ 0.25

RCR=25% RCR=50%

=- 0.25

------------- Site Class A— — — Site Class B . . . . . . . site Class C• — — • Site Class 0

Site Class E

1 1.5Sa(T1) (g) RCR=75%

.................................. • yyA

A / s y*

• 4 j i rror

/ > > .■* — — — site Class Bi i « ■ i i . Site Class C

/ : / ySite Class E

0.5Sa(T1) (g)

g 0.75 0CII■g 0.5A

£■ 0-25

1.5

g 0.7501ii-g 0.5A

I 0.25

/ / / 'Site Class A Site Class B Site Class C

Site Class E

0.5 1.5Sa(T1) (g)

RCR=100%T :

......... ../ V y

/ v y 's

-A.« ........

A . .

AV / s y ' — — — Site Class B> . . . . . . . s ite Class C

A ? / y '■ — • — • Site Class D

Site Class E

0.5 1Sa(T1) (g)

1.5

F ig u re 60: Seismic decision fragility curves based on repair cost for Blair Road Bridge with free expansion bearing case

RCR=25% RCR=50%

o roc rii>•oA>o

0.75

0.25

0.8

c roo rii>

T3A>o

0.6

0.4

0.2

Site Class ASite C a ss BSite C a ss CSite Class DSite Class E

0.5 1Sa(T1) (g) RCR=75%

-------------Site Class A— — — Site Class B . . . . . . . s ite Class C• — ■ — ■ Site Class D

Site Class E

0.5 1Sa(T1)(g)

Site Class A— — — Site Class B

Site Class C — — • Site Class D

Site Class E

0.5 1Sa(T1) (g)

RCR=100%0.4

o roo rii>

T 3A>o

0.3

0 .2

0.1

------------Site Class A— — — Site Class B. . . . . . . s ite Class C

— ■ — ■ Site Class D

Site Class E

/ / : / /

/ /: / /

0.5 1Sa(T1) (g)

F ig u re 61: Seismic decision fragility curves based on repair cost for Blair Road Bridge with fixed bearing case

76

RCR=25% RCR=50%0.8

0.6

0.4

0.2

0

— ------- S ite C la ss B g 0.3 — — — s i te Class B

■ S ite C la ss C

— • — ■ S ite C la ss 0

S ite C la ss E

.................

q:ii•S 0.2A

% „ .

. . . . . . . s i te Class C

- — • — ■ S ite Class D S ite Class E

0.5 1Sa(T 1) (g)

RCR=75%

0.5 1Sa(T1)(g)

RCR=100%

Site C la ss A Site Class A Site Class B Site Class C Site Class D Site Class E

Site C la ss B

Site C la ss C

Site C la ss D

Site C la ss E

0.5 1Sa(T 1) (g)

0.5 1Sa(T 1) (g)

F ig u re 62: Seismic decision fragility curves based on repair cost for Terminal Avenue Bridge

RCR=25% RCR=50%0.1

0.08

0.06

0.04

0.02

0

---------Site Class A---------Site Class B• Site Class C---------Site Class D

Site Class E

/ c /;/ # '

0.5 1

x 10Sa(T1) (g) RCR=75%

a:occii>•oA>QCL

— Site Class A— Site Class B • ■ ■ ■ Site Class C— Site Class D

Site Class E

0.5 1

0.02

0.015

0.01

s1 0.005

1.5

1.5

Site Class A Site Class B Site Class C Site Class D

Site Class E

x 10

0.5 1Sa(T1) (g)

RCR=100%

an o a: n > T3 A > Q CL

Site Class A Site Class B• Site Class C •-------- Site Class D

Site Class E

Sa(T 1) (g)0.5 1

Sa(T1) (g)1.5

Figure 63: Seismic decision fragility curves based on repair cost for Hunt Club RoadBridge

P[D

V>dv

=RC

R]

P[D

V>dv

=RC

R]

77

RCR=25% RCR=50%0.15

0.1

0.05

/ 7---------Site Class A---------Site Class B

Site Class C---------Site Class D

Site Class E

/ 7 / 7

/ 7 v'' -.. y r / . /. :S s ' •*

/ s y s .

i0.5 1

Sa(T1) (g) RCR=75%

1.5

0.05

0.04

0.03

0.02

0.01

0

Site Class A Site Class B■ " ■ • " Site Class C Site Class D

Site Class E

0.5 1Sa(T1) (g)

0.08

g 0.06a:n■g 0.04A

ST 0.02

0

0.04

g 0.03

---------Site Class BSite Class C

------- Site Class DSite Class E

I / / /

/ 7 7/ 7 ' 7" S 's y

onii>■oA>o

0.02

0.01

0

0.5 1Sa(T1)(g)

RCR=100%

1.5

Site Class A Site Class B Site Class C Site Class D

Site Class E

0.5 1Sa(T1) (g)

F ig u re 64: Seismic decision fragility curves based on repair cost for Walkley Road Bridge

78

DTR=0.435%=1 day DTR=3%=1 week

£ 0.75aii

■a 0.5A

| 0.25

Site Class A — Site Class B

Site Class C— — ■ Site Class D

Site Class E

0.5 1Sa(T1) (g)

DTR=13%=1 month

0.25

Site Class A— Site Class B

Site Class C Site Class D Site Class E

0.5 1Sa(T1) (g)

cr

1

0.75

0.5Q II > x>A >9 0.25 a.

1.5

1.5

.....p } /

---------Site Class A-----— Site Class B........... Site Class C------- - Site Class D

Site Class E

0.5 1Sa(T1) (g)

DTR=39%=3 months

1.5

Site Class A— Site Class B

site Class C ■ — ■ — Site Class D

Site Class E

0.5 1Sa(T1) (g)

1.5

F ig u re 65: Seismic decision fragility curves based on downtime for Blair Road Bridge with free expansion bearing case

DTR=0.435%=1 day DTR=3%=1 week

ori— Q II >•oA>o

j.lll

/ ( \ v .

I f / / ? — Site Class A

f a ? ■ — — — Site Class B

f a : .............. Site Class C

P ?Site Class E

0.5 1Sa(T1) (g)

DTR=13%=1 month

1.5

craii

-g 0.5A>QQ.

----------- Site Class A— — — Site Class B

Site Class C y ^ ^ «•* **

• —• • — * Site Class DSite Class E

• /V

0.5 1Sa(T1)(g)

1.5

cri-Qll-S 0.5A>QCL

/ V

/ ' / s / > > .

y ^ > - v* ' V ‘ ........'/ > vkr > *

— — Site Class A — — — Site Class B• Site Class C• — • — • Site Class D

Site Class E

0.5 1Sa(T1) (g)

DTR=39%=3 months

1.5

Site Class ASite Class B

Site Class CSite Class DSite Class E

0.5 1Sa(T1) (g)

F ig u re 6 6 : Seismic decision fragility curves based on downtime for Blair Road Bridge with fixed bearing case

79

DTR=0.435%=1 day

P- 0.75

ad(-Qll>T3A>QCL

--------- Site Class A— — — Site Class B........... Site Class C• — • — ■ Site Class D

Site Class E

0.5 1Sa(T1) (g)

DTR=13%=1 month

1.5

£ 0.75

0.5

0.25

0

DTR=3%=1 week

.......... Site Class A— — — Site Class B

• site Class C • — Site Class D

Site Class Ef a

f a y ,*//>

: y

0.5 1Sa(T1) (g)

DTR=39%=3 months

1.5

F 0.6 Site Class ASite Class BSite Class CSite Class DSite Class E

---- Site Class A---- - — Site Class B

> • • Site Class C

Site Class E

0.5 1Sa(T1) (g)

0.5 1Sa(T1) (g)

F ig u re 67: Seismic decision fragility curves based on downtime for Terminal Avenue Bridge

DTR=0.435%=1 day

sss5”DTR=3%=1 week

Site C ass A

0.8

0.6

- — Site Class B ■ Site Class C Site Class D

Site Class E

Qii

---------- Site Class A— — — Site Class B

Site Class C — — ■ Site Class D

Site Class E

0.5 1Sa(T1)(g)

DTR=13%=1 month

0.5 1Sa(T1) (g)

DTR=39%=3 months

Site Class ASite Class A Site Class B Site Class C Site Class D Site Class E

Site Class BSite Class C

— — Site Class D Site Class E

O 0.04

> 0.02

0.5 1Sa(T 1) (g)

0.5 1Sa(T1) (g)

Figure 68: Seismic decision fragility curves based on downtime for Hunt Club RoadBridge

P[D

V>dv

=DTR

] P[

DV>

dv=D

TR]

80

0.4

0.3

0.2

0.1

00

DTR=0.435%=1 day

- Site Class A ' Site Class B

Site Class C 1 Site Class D

Site Class E

DTR=3%=1 w eek

0.5 1Sa(T1) (g)

DTR=13%=1 month

Site C lass A— — Site C lass B

■ - ■ ■ ■ Site C lass C - — ■ Site C lass D

Site C lass E

0.5 1Sa(T1) (g)

0.8

* 0.6 Site Class A Site Class B Site Class C Site Class D Site Class E

0.2

S’ 0.15Qii-g 0.1A>§■ 0.05

1.5

0.5 1Sa(T1)(g)

DTR=39%=3 months

-----------Site C lass A------ — Site C lass B' ■ ■. ■1 ■ Site C lass C ■ — ■ — ■ Site C lass D

Site C lass E/ /

/ / v'

-----

0.5 1Sa(T1) (g)

1.5

F ig u re 69: Seismic decision fragility curves based on downtime for Walkley Road Bridge

C hapter 4

Generalized Fragilty R elationships

4.1 Introduction

Prom past seismic events, it is identified th a t bridges constructed using obsolete stan

dards have seismic deficiencies in their performance and behavior. Carrying out

seismic vulnerability and risk assessment of bridges and taking m itigating measure

ments based on the assessment results can significantly reduce the damage and loss

of future earthquakes. Due to increasing impact of seismic activities in Canada and

around the world, it is im portant to evaluate the seismic vulnerability and risk of

existing bridges constructed using obsolete design standards to enhance public safety

and maintain economic well being of society. However, it is not realistic to carry

out detailed investigation for all the bridges in a large bridge transportation network

inventory because of time consuming and the requirement of vast am ount of engineer

ing efforts on modeling and analysis. Thus, this chapter presents a new seismic risk

assessment approach for bridge inventory based on generalized fragility relationships

derived and calibrated from the analysis of representative bridges from the inventory.

In this new methodology, probability of failure of representative bridges are re

lated to structural characteristics incorporating a normalization procedure to generate

81

82

generalized fragility relationships th a t can be used for evaluating the seismic vulnera

bility and risk of other bridges with similar structural characteristics. The advantage

of this new assessment methodology is th a t evaluation of the seismic vulnerability and

risk of large number of bridges with similar characteristics does not require detailed

structural modeling and nonlinear tim e history analysis of all the bridges.

The basic premise of the assessment methodology developed in the present work

is that structural performance of bridges is related to structural characteristic pa

rameters [4, 36, 37]. For this work, three structural characteristic param eters are

considered: (1) Pier longitudinal reinforcement ratio (pl ), (2) Span over pier height

ratio (^ jp ) , and (3) Pier transverse reinforcement ratio (ps). In this study, the repre

sentative bridge inventory includes a variety of bridges of different geometric layout.

Therefore, to compare the seismic load experienced by each pier, structural character

istics parameter need to be normalized. The derivation of the normalized or effective

structural characteristic parameters is presented in the following sections.

4.2 Effective longitudinal reinforcem ent ratio

( P L * )

Since the amount of longitudinal reinforcement is directly related to bending strength

of the column, p L * should be a valid performance parameter to relate w ith structural

damage. In order to develop a relationship between damage probability w ith struc

tural characteristic of bridge column, it is essential to account for the differences in

size and configuration of different bridge structures. Effective longitudinal reinforce

ment ratio is defined by modification using the tributary lateral load resisted by a

bridge column. For the work here, first param eter of effective number of spans for a

bridge is obtained by Equation (16), which is based on the consideration of lateral

83

load resisted by the column. Effective tribu tary span area for the bridge column

is then determined from Equation (17). Finally, taking the reference span area as

the tributary span area of one of the representative bridges, a modified longitudinal

reinforcement ratio is obtained by Equation (18).

To calibrate the new methodology based on effective longitudinal reinforcement

ratio, a relationship is developed between the estim ated probabilities of cover spalling

and bar buckling (presented in Table 9) and effective longitudinal reinforcement ratios

of representative bridges by linear regression. The developed generalized fragility

curves for different site conditions a t 2%, 10%, and 40% in 50 year probability level

are shown in Figures 70-72, respectively. These results highlights th a t the correlation

of probability of failure with p l * for bar buckling damage state is not good as th a t

of cover spalling damage state. Thus, to further explore the optim um regression

behavior of the structural characteristic param eter pL * for bar buckling damage state,

the data show for bar buckling in Figures 70(b)-72(b) are analysed again using a

power regression. Based on the norm of residuals obtained from regression analyses

presented in Table 12, it is observed th a t the generalized fragility relationship for bar

buckling follows more closely as a power-law relationship as shown in Figures 73-75.

These analysis results show the probability of occurrence of the damage states such

as cover spalling and bar buckling decreases with increasing effective longitudinal

reinforcement ratio for all Site Classes a t a specific hazard level. Also, it can be

observed th a t there is a significant drop in damage probability from low (2%/50

year) to other probability of hazard levels such as moderate (10%/50 year) and high

(40%/50 year). W ith larger longitudinal reinforcement ratio, the column is stronger,

thus the probability of failure decreases. Additionally, the displacement capacity for

the column with small longitudinal reinforcement ratio is smaller th an those of the

column with lager reinforcement ratio [57]. Therefore, these results shows a consistent

relationship for all Site Classes by the correlation.

84

E f f e c t i v e S p a n s = A c tu a l S p a n s —P i e r s w i t h E x p . B r g s -

(16)

„ „ , , _ . _ , B r id g e L e n g th x B r i d g e W i d t hE f f e c t i v e T r i b u ta r y S p a n A r e a p e r C o l . =

E f f e c t i v e S p a n s x iVo. o / Co/, per P i e r(17)

r , , ±. / *N R e f e r e n c e S p a n A r e a p e r Col.f f e c w e pL (pL ) - E ^ e c t iv e T r i b u t a r y S p a n A r e a p e r C o l . X pL ^

4.5• Site Class A■ Site Class B♦ Site Class C± Site Class D* Site Class E

• Site Class A■ Site Class B♦ Site Class C* Site Class D* Site Class E

4

5- 3.5p> 25 O)

3

m 2.5

2

1.52 10 o £ 1

0.5

020 0 5Effective Longitudinal Reinforcement Ratio (%)

10Reinforcement

15 20Effective Longitudinal Reinforcement Ratio (%) Ratio

(a) (b)

F ig u re 70: Generalized Fragility Relationships Based on p i * by linear regression, (a) and (b): Cover Spalling and Bar Buckling for Different Site Conditions at 2% in 50 year Hazard Level

Prob

abili

ty

of Co

ver

Spall

ing

(%)

trj

Prob

abili

ty

of Co

ver

Spal

ling

(%)

85

12 0.4Site C lass A Site C lass B Site C lass C Site C lass D Site C lass E

Site C la ss A Site C la ss B S ite C la ss C Site C lass D Site C lass E

0.3510

□>c

0.25

6 0.2

_ 0.15 la to _a 2 0.1

Cl

20.05

0200 5 10

Effective Longitudinal Reinforcement Ratio (%)15RatioReinforcement Effective Longitudinal R einforcem ent Ratio (%)

(a) (b)

ig u re 71: Generalized Fragility Relationships Based on p i * by linear regression, (a) and (b): Cover Spalling and Bar Buckling for Different Site Conditions at 10% in 50 year Hazard Level


0.9

0.7

0.6

0.5

0.4

0.3

0.2

0.1

Effective Longitudinal Reinforcement Ratio (%)

0.01

0.009

~ 0.008 5**0.007

"! 0.006 m| 0.005

J . 0.004

| 0.003 o£ 0.002

0.001

0

• Site Class A ■ Site Class B♦ Site Class C A Site Class D* Site Class E

A\ .............

X------- A----

(a)

5 10 15Effective Longitudinal Reinforcement Ratio (%)

(b)

20

F ig u re 72: Generalized Fragility Relationships Based on pL * by linear regression, (a) and (b): Cover Spalling and Bar Buckling for Different Site Conditions at 40% in 50 year Hazard Level

86

4.5• Site C lass A■ Site C lass B♦ Site C lass C* Site C lass D* Site C lass E

* 3.5

“ 2.5

0.5

Effective Longitudinal Reinforcem ent Ratio {%)

F ig u re 73: Generalized Fragility Relationships Based on pL * by power regression, Bar Buckling for Different Site Conditions at 2% in 50 year Hazard Level

0.4• Site C lass A■ Site C lass B♦ Site C lass C* Site C lass D* Site C lass E

0.35

0.3

o 0.25=jm

Jj 0.2

:§■ 0.15

0.05

Effective Longitudinal Reinforcem ent Ratio (%)

F ig u re 74: Generalized Fragility Relationships Based on p i * by power regression, Bar Buckling for Different Site Conditions at 10% in 50 year Hazard Level

87

0.009

0.008

0.007

0.006

0.005

0.004

0.003

0.002

0.001

• Site C lass A■ Site C lass B♦ Site C lass C* Site C lass D* Site C lass E

Effective Longitudinal Reinforcement Ratio (%)

F ig u re 75: Generalized Fragility Relationships Based on p l * by power regression, Bar Buckling for Different Site Conditions at 40% in 50 year Hazard Level

T able 12: Comparison of norm of residuals from linear and power regression analyses for the relationship of probability of bar buckling with p l *

H azard level S ite ClassN orm o f Residuals

L inear Regression Power R egression

2% in 50 year

A 0.003% 0 .0 0 2 %B 0.048% 0.025%C 0.318% 0.047%D 0.799% 0.077%E 2 .2 0 2 % 0.113%

10% in 50 year

A 0 .0 0 0 % 0 .0 0 0 %B 0 .0 0 1 % 0 .0 0 1 %C 0 .0 1 0 % 0 .0 0 2 %D 0.041% 0.005%E 0.141% 0.084%

40% in 50 year

A 0 .0 0 0 % 0 .0 0 0 %B 0 .0 0 0 % 0 .0 0 0 %C 0 .0 0 0 % 0 .0 0 0 %D 0 .0 0 1 % 0 .0 0 0 %E 0.006% 0 .0 0 1 %

88

4.3 Effective span over pier height ratio ( ^ n*)

In order to relate damage probability with geometry of the structure, a structural

characteristic parameter, effective span over pier height ratio is considered in this

investigation. The effective span over pier height ratio is obtained by normalizing

with the laterally supported tributary span resisted by the column. This structural

characteristic parameter can be readily computed for each bridge in the inventory.

First, effective span length is determined by dividing the total span length by effective

number of spans, which is calculated from Equation (16). Afterwards, effective span

length over height is determined by dividing the effective tributary span length by

the pier height. The process of calculating this ratio is shown in Equation (19).

For the new calibration methodology based on effective span over pier height ra

tio, a linear regression is performed to develop a relationship between the estim ated

probability of failure of the representative bridges and effective span over pier height

ratio. The resulting generalized fragility curves for different ground conditions at

2 %, 10%, and 40% in 50 year hazard level are presented in Figures 76-78, respec

tively. The correlation of probability of failure with effective span over pier height

ratio show a very good correlation for all Site Classes at different hazard levels con

sidered for the concrete cover spalling failure mechanism while the correlation with

the structural characteristic param eter of longitudinal bar buckling is not as good.

Therefore, similar to longitudinal reinforcement ratio, a power regression analysis is

performed for the data show for bar buckling damage state in Figures 76(b)-78(b).

From norm of residuals presented in Table 13, relationship obtained from the power

regression analysis show a more consistent relationship for bar buckling as shown in

Figures 79-81, compare to th a t of the linear regression analysis.

These results show th a t the variation of the probability of cover spalling and bar

buckling with effective span over pier height ratio follows an opposite trend, compared

89

to the normalized fragility relationships of effective longitudinal reinforcement ratio.

However, the distribution of the results for effective span over pier height ratio is

not good as longitudinal reinforcement ratio. This can be explained due to the fact

th a t span over pier height is an indirect param eter for strength and ductility of bridge

column structural member, whereas longitudinal reinforcement ratio is directly related

to the strength and ductility capacities of the column. The results for the three hazard

levels are similar.

_ , „ , S p a n . , S p a n * N T o ta l S p a n L e n g thE f f e c t i v e (— z— ) = ..----------- T~d----------- F (19)v L ' v L 1 E f f e c t i v e no . o f S p a n s x L

35 4.5

• Site Class A■ Site Class B4 Site Class C4 Site Class D* Site Class E

• Site C lass A■ Site C lass B4 Site C lass C4 Site C lass D* Site C lass E

c 25

o3CD

COCDO.■&

* 20

5 10Q_

0.5

14Effective [5^ n ] Effective [ ^ ]

(a) (b)

F ig u re 76: Generalized Fragility Relationships Based on by linear regression, (a) and (b): Cover Spalling and Bar Buckling for Different Site Conditions at 2% in 50 year Hazard Level

90

0.4

• Site C lass A■ Site C lass B♦ Site C lass Ca Site C lass D* Site C lass E

• Site Class A■ Site C lass B♦ Site C lass CA Site C lass D* Site C lass E

0.35

0.3O)c(0Cl

COq5>oOo

o 0.25

0.2

il* 0.15

10-Qo0.

0.05£*

Effective [ ^ p ] Effective(a) (b)

F ig u re 77: Generalized Fragility Relationships Based on Spa™* by linear regression, (a) and (b): Cover Spalling and Bar Buckling for Different Site Conditions at 10% in 50 year Hazard Level

Site Class A Site Class B

♦ Site Site

* Site

>8 0.8 0.008

.s 0.7 P 0.007

W 0.6 0.006

o 0.5 £ 0.005

& 0.004

S 0.3 g 0.003 o£ 0.002£ 0.2

6 8 10Effective [ £ p ]

(a)

• Site Class A ■ Site Class B♦ Site Class C* Site Class D* Site Class E

• it

-----------4

i t J r

4 = t —6 8 10

Effective [ S p ](b)

12 14

F ig u re 78: Generalized Fragility Relationships Based on - ?jn - by linear regression, (a) and (b): Cover Spalling and Bar Buckling for Different Site Conditions at 40% in 50 year Hazard Level

91

• Site C lass A■ Site C lass B♦ Site C lass C* Site C lass D* Site C lass E

4.5

S? 3.5o3

CD

| 2.5 ‘o * 2.a(0X5gCL

0.5

Effective

F ig u re 79: Generalized Fragility Relationships Based on Sp°n* by power regression, Bar Buckling for Different Site Conditions at 2% in 50 year Hazard Level

0.4• Site C lass A■ Site C lass B♦ Site C lass CA Site C lass D* Site C lass E

0.35

0.3

o 0.25

0.2

0.05

Effective [ ^ ]

F ig u re 80: Generalized Fragility Relationships Based on Sp™ by power regression, Bar Buckling for Different Site Conditions at 10% in 50 year Hazard Level

92

0.009• Site Class A■ Site Class B♦ Site Class C* Site Class D* Site Class E

0.008

£ 0.007O)| 0.006 O“ 0.005nm

0.004‘o£•

0.003

£ 0.002

0.001

Effective [ ^ ]

F ig u re 81: Generalized Fragility Relationships Based on by power regression, Bar Buckling for Different Site Conditions at 40% in 50 year Hazard Level

T able 13: Comparison of norm of residuals from linear and power regression analyses for the relationship of probability of bar buckling with Sp°n*

H azard level Site ClassN orm of Residuals

L inear Regression Power R egression

2% in 50 year

A 0.003% 0.003%B 0.057% 0.059%C 0.229% 0.189%D 0.564% 0.499%E 1.334% 1.173%

10% in 50 year

A 0 .0 0 0 % 0 .0 0 0 %B 0 .0 0 1 % 0 .0 0 1 %C 0.007% 0.009%D 0.026% 0.024%E 0.182% 0.182%

40% in 50 year

A 0 .0 0 0 % 0 .0 0 0 %B 0 .0 0 0 % 0 .0 0 0 %C 0 .0 0 0 % 0 .0 0 0 %D 0 .0 0 1 % 0 .0 0 0 %E 0.003% 0.003%

93

4.4 Effective transverse reinforcem ent ratio (p s *)

Similar to effective longitudinal reinforcement ratio, a structural characteristic param

eter of effective transverse reinforcement ratio is defined to investigate the probability

of failure of column in a bridge. Transverse reinforcement ratio is indirectly related to

the strength of the column. It provides confinement to the longitudinal reinforcement

to prevent longitudinal bar buckling and to provide sufficient deformability (ductil

ity) of the column. Therefore, this param eter concerns the confinement effect of the

bridge column on its probability of failure. This normalized structural characteristic

parameter is also obtained by adopting the same concept and mechanisms used in the

definition of effective longitudinal reinforcement ratio. The normalization process is

given in Equation (20).

In order to create a calibration model based on p s * for new methodology, the

generalized fragility relationship is derived by linear regression by relating the damage

probability with effective transverse reinforcement ratio. Figures 82-84 show the

generalized fragility relationships for different Site Classes at the hazard level of 2 %,

10%, and 40% in 50 year. Similar to the results based on linear regression analysis

for other structural characteristic parameters, the relationship for bar buckling is

not as good. Hence, to optimize the relationship behavior for the d a ta show for bar

buckling in Figures 82(b)-84(b), a power regression analysis is performed. The norm

of residuals reported in Table 14 highlight th a t the relationship from power regression

analysis shows a good fit as shown in Figures 85-87.

The results for the cover spalling and bar buckling show th a t the generalized

fragility curves of ps * follow the same trend as effective longitudinal reinforcement

ratio. Observed and experimental Studies by Saatcioglu and Razvi indicates th a t

lateral deformation capacity increases with increasing amount of transverse reinforce

ment [58]. Thus, with increasing transverse reinforcement ratio to reinforced concrete

94

column, the probability of failure decreases. Therefore, these results have consistent

relationships for all Site Classes a t different hazard levels.

Although the effective transverse reinforcement ratio p$* is an im portant pa

rameter th a t effect the ultim ate inelastic behavior of bridge pier columns, it is not

directly related to strength of the structural components. The results of p s * show

th a t they are not as consistent as the result obtained from the effective longitudinal

reinforcement ratio Pl *• Therefore, based on this preliminary analysis the effective

longitudinal reinforcement ratio p ^ * is a better more consistent structural charac

teristic parameter for seismic risk evaluations of bridge inventory by the proposed

method.

. / *\ R e f e ren c e E f f e c t i v e T r ib u ta r y S p a n A r e a p e r C o l.E f f e A v e Ps (ps ) = B / f e c t i v e T r ib u ta r y S p a n A re a p e r C o l. X P s

(20)

• Site Class A■ Site Class B♦ Site Class C* Site Class D* Site Class E

30

? 25

a 10

Effective Transverse Reinforcement Ratio (%)

4.5• Site Class A■ Site Class B♦ Site Class Ca Site Class D* Site Class E

# 3.5o>

I 3o“ 2.5TOCDo>*.aTO£32a_

0.5


(a) (b)

F ig u re 82: Generalized Fragility Relationships Baaed on ps * by linear regression, (a) and (b): Cover Spalling and Bar Buckling for Different Site Conditions at 2% in 50 year Hazard Level

95

12 0.4Site Class A Site Class B Site Class C Site Class D Site C lass E

Site C lass A Site C lass B Site C lass C Site C lass D Site C lass E

0.3510

0.3

8o 0.25

6 0.2

0.154

0.1

20.05

03 4 5

Effective Transverse Reinforcement Ratio (%)61 2

Effective Effective Transverse Reinforcement Ratio (%)(a) (b)

F ig u re 83: Generalized Fragility Relationships Based on p s* by linear regression, (a) and (b): Cover Spalling and Bar Buckling for Different Site Conditions at 10% in 50 year Hazard Level

1

0.9

0.8

0.7

0.6

0.5

0.4

0.3

0.2

0.1

0

VX .

XT

Site Class A Site Class B Site Class C Site Class 0 Site Class E

2 3 4 5Effective Transverse Reinforcement Ratio (%)

(a)

Site C lass A Site C lass B Site C lass C Site C lass O Site Class E

0.009

0.008

? 0.007

5 0.006 00s 0.005

>. 0.004

5 0.003

0.002

0.001

2 3 4 5Effective Transverse Reinforcement Ratio (%)

(b)

F ig u re 84: Generalized Fragility Relationships Based on ps * by linear regression,(a) and (b): Cover Spalling and Bar Buckling for Different Site Conditions at 40% in 50 year Hazard Level

96

4.5• Site C lass A■ Site C lass B♦ Site C lass C4 Site C lass D* Site C lass E

# 3.5O)I 3“ 2.5 (0

CD

o 2 •2*n<0no0.

0.5


F ig u re 85: Generalized Fragility Relationships Based on ps* by power regression, Bar Buckling for Different Site Conditions a t 2% in 50 year Hazard Level

0.4* Site C lass A■ Site C lass B* Site C lass C4 Site C lass D* Site C lass E

0.35

0.3

o 0.25

0.2

CL

0.05


F ig u re 8 6 : Generalized Fragility Relationships Based on p$* by power regression, Bar Buckling for Different Site Conditions at 10% in 50 year Hazard Level

97

0.009* Site C lass A ■ Site C lass B* Site C lass C 4 s ite C lass D* Site C lass E

0.008

S? 0.007

= 0.006

“ 0.005 (0 mo 0.004

B 0.003

£ 0.002

0.001


F ig u re 87: Generalized Fragility Relationships Based on ps* by power regression, Bar Buckling for Different Site Conditions at 40% in 50 year Hazard Level

T able 14: Comparison of norm of residuals from linear and power regression analyses for the relationship of probability of bar buckling with p s *

H a za rd leve l S ite C la ssN o r m o f R esid u a ls

L in ear R e g r e ss io n Pow er R e g r e s s io n

2% in 50 year

A 0.003% 0.003%B 0.077% 0.063%C 0.409% 0.262%D 0.965% 0.719%E 2.710% 1.773%

10% in 50 year

A 0.000% 0.000%B 0.001% 0.001%C 0.013% 0.007%D 0.047% 0.029%E 0.237% 0.221%

40% in 50 year

A 0.000% 0.000%B 0.000% 0.000%C 0.000% 0.000%D 0.001% 0.000%E 0.006% 0.001%

98

4.5 Fragility evaluation of sam ple bridge inventory

As discussed earlier, the sample inventory includes a variety of bridges of different

geometric layout. For application of the new seismic risk assessment approach to

the sample inventory, the structural characteristics parameters of all the bridges in

the inventory are determined based on information on the structural drawings of

the bridges. Using the normalization procedure described in preceding sections, the

effective structural characteristics param eters of p l *, Sp(£ l* and p s * are computed.

The actual and evaluated effective characteristic parameters of the sample bridge

inventory are presented in Table 15.

The probability of failure of the bridges in the inventory including the representa

tive bridges based on the actual site conditions of the individual bridges are estim ated

by utilizing seismic microzonation information of the City of O ttaw a [12]. The es

timated probability of failure of the damage states of concrete cover spalling and

longitudinal bar buckling for low (2% in 50 year), moderate (10% in 50 year), and

high (40% in 50 year) probability seismic events are tabulated in Tables 16-18. These

results highlight that damage probability based on Spa * parameter, which is also

referred to as a geometric parameter, are relatively high for cover spalling and bar

buckling failure modes at all hazard level. However, the damage probability based

on p i * and p s * parameters are im portant to evaluate the risk of bridges in term s of

strength and capacity.

Even though the study from previous sections highlights that pL * is a better pa

rameter for seismic risk evaluations of bridge inventory, for demonstration purposes

here, the maximum envelope value of damage probability from the three structural

characteristic parameters are summarized in Table 19. From the results, a priority

list of vulnerable bridges for consideration of improving life safety and for minimizing

repair cost can be established to support decision making in retrofit planning and

resource allocation. The probable performance under high hazard intensity level (2%

in 50 year) are investigated to produce the results to improve life safety. As Op

posed to improving life safety, damage probabilities under moderate and low hazard

intensity levels are reviewed to prepare the priority list to minimize repair cost and

improve service by minimizing disruptions after an earthquake. For improvement to

life safety, the damage probabilities of bar buckling damage state for the seismic haz

ard level of 2% in 50 year (extreme earthquake events) are considered and prioritized

from maximum to minimum. For the case of minimizing the repair cost after small

earthquakes, the probability of failure of the damage state of cover spalling for the

seismic hazard of small earthquake of potentially 40% in 50 year are considered and

prioritized from maximum to minimum. The results for the above two investigations

are presented in Tables 20 and 21.

T able 15: Effective Structural Characteristics Parameters of Bridges in the Sample Bridge Inventory

Stru.No

YearBuilt

TotalSpanM

DeckW idth

(m)

No.of

Spans

Col.Height

(m)

Piersw ithExp.Brgs

Abut.w ithExp.Brgs

Effec.No.of

Spans

No.of.

Col./B en t

Trib.SpanA rea/C ol.

P l P S P L * PS* S p a n * SiteConditionL

1 1966 39.0 15.5 2 5.2 0 2 1 2 303.1 4.44% 1.94% 7.45% 3.26% 7.57 Site Class B

2 a 1968 85.1 23.9 4 6.7 2 2 1 4 508.5 1.19% 1 .2 1 % 1.19% 1 .2 1 % 12.70 Site Class A

2 b 1968 85.1 23.9 4 6.7 0 2 3 4 169.5 1.19% 1 .2 1 % 3.56% 3.63% 4.23 Site Class A

3 1969 57.2 19.7 3 9.2 0 2 2 3 187.4 1.84% 1.32% 4.99% 3.58% 3.11 Site Class B

4 1972 65.6 13.7 3 5.8 0 2 2 2 225.0 4.62% 0.83% 10.44% 1.87% 5.66 Site Class C

5 1972 46.6 26.2 3 5.9 0 2 2 5 1 2 2 .2 4.46% 1.25% 18.56% 5.20% 3.99 Site Class C

6 1982 61.0 2 0 .0 2 5.0 0 2 1 3 405.7 2 .2 2 % 1.46% 2.78% 1.83% 12.13 Site Class E

7 1982 74.0 8.7 3 5.9 0 2 2 l 320.1 5.15% 0.42% 8.18% 0.67% 6.27 Site Class C

8 1991 44.0 6.3 3 7.8 1 2 1 2 137.5 1.77% 1.64% 6.55% 6.07% 5.64 Site Class C

9 1993 1 1 2 .0 10.3 4 4.7 2 2 1 1 1154.7 1.13% 1 .2 1 % 0.50% 0.53% 23.83 Site Class C

1 0 1995 83.0 13.0 3 9.3 0 2 2 2 268.9 2.05% 0.67% 3.88% 1.27% 4.48 Site Class C

101

T able 16: Estimated Probabilities of Cover Spalling and Bar Buckling based on Effective Longitudinal Reinforcement Ratios

Bridge

NoP L *

Site

Condition

Cover Spalling B ar B uckling

2 % in

50yr

1 0 % in

50yr

40% in

50yr

2 % in

50yr

1 0 % in

50yr

40% in

50yr

1 7.45% Site Class B 2.874% 0.193% 0.004% 0 .0 2 1 % 0 .0 0 0 % 0 .0 0 0 %2 a 1.19% Site Class A 0.601% 0.009% 0 .0 0 0 % 0 .0 0 2 % 0 .0 0 0 % 0 .0 0 0 %2 b 3.56% Site Class A 0.543% 0.008% 0 .0 0 0 % 0 .0 0 2 % 0 .0 0 0 % 0 .0 0 0 %3 4.99% Site Class B 3.354% 0.228% 0.005% 0.031% 0 .0 0 0 % 0 .0 0 0 %4 10.44% Site Class C 5.766% 0.563% 0.013% 0.053% 0 .0 0 1 % 0 .0 0 0 %5 18.56% Site Class C 1.713% 0.044% 0 .0 0 0 % 0.028% 0 .0 0 0 % 0 .0 0 0 %6 2.78% Site Class E 27.000% 9.250% 0.536% 1.810% 0.182% 0 .0 0 2 %7 8.18% Site Class C 6.894% 0.707% 0 .0 2 1 % 0.071% 0 .0 0 1 % 0 .0 0 0 %8 6.55% Site Class C 7.711% 0.812% 0.027% 0.091% 0 .0 0 2 % 0 .0 0 0 %9 0.50% Site Class C 10.731% 1.198% 0.048% 1.718% 0.055% 0 .0 0 2 %

1 0 3.88% Site Class C 9.044% 0.982% 0.036% 0.165% 0.003% 0 .0 0 0 %

Table 17: Estimated Probabilities of Cover Spalling and Bar Buckling based on Effective Span over Pier Height Ratios

Bridge

NoS p a n *

L

Site

C ondition

Cover Spalling B ar Buckling

2 % in

50yr

1 0 % in

50yr

40% in

50yr

2 % in

50yr

1 0 % in

50yr

40% in

50yr

1 7.57 Site Class B 2.985% 0.171% 0.004% 0.026% 0 .0 0 0 % 0 .0 0 0 %2 a 12.70 Site Class A 0.641% 0 .0 1 0 % 0 .0 0 0 % 0 .0 0 2 % 0 .0 0 0 % 0 .0 0 0 %2 b 4.23 Site Class A 0.387% 0.009% 0 .0 0 0 % 0 .0 0 0 % 0 .0 0 0 % 0 .0 0 0 %3 3.11 Site Class B 1.467% 0.082% 0 .0 0 0 % 0 .0 0 2 % 0 .0 0 0 % 0 .0 0 0 %4 5.66 Site Class C 5.762% 0.540% 0 .0 2 1 % 0.066% 0 .0 0 1 % 0 .0 0 0 %5 3.99 Site Class C 4.166% 0.338% 0.006% 0.024% 0 .0 0 0 % 0 .0 0 0 %6 12.13 Site Class E 32.210% 10.531% 0.831% 4.099% 0.314% 0.006%7 6.27 Site Class C 6.338% 0.613% 0.026% 0.088% 0 .0 0 1 % 0 .0 0 0 %8 5.64 Site Class C 5.739% 0.537% 0 .0 2 1 % 0.065% 0 .0 0 1 % 0 .0 0 0 %9 13.76 Site Class C 23.018% 2.720% 0.184% 3.745% 0.227% 0.008%

1 0 4.48 Site Class C 4.638% 0.398% 0 .0 1 0 % 0.034% 0 .0 0 0 % 0 .0 0 0 %

102

T able 18: Estimated Probabilities of Cover Spalling and Bar Buckling based on Effective Transverse Reinforcement Ratios

Bridge

NoP S*

Site

Condition

Cover Spalling B ar Buckling

2 % in

50yr

1 0 % in

50yr

40% in

50yr

2 % in

50yr

1 0 % in

50yr

40% in

50yr

1 3.26% Site Class B 2.703% 0.184% 0.003% 0 .0 2 0 % 0 .0 0 0 % 0 .0 0 0 %2 a 1 .2 1 % Site Class A 0.569% 0.009% 0 .0 0 0 % 0 .0 0 2 % 0 .0 0 0 % 0 .0 0 0 %2 b 3.63% Site Class A 0.408% 0.008% 0 .0 0 0 % 0 .0 0 1 % 0 .0 0 0 % 0 .0 0 0 %3 3.58% Site Class B 2.452% 0.167% 0.003% 0.017% 0 .0 0 0 % 0 .0 0 0 %4 1.87% Site Class C 9.894% 1.088% 0.054% 0.255% 0.006% 0 .0 0 0 %5 5.20% Site Class C 2.579% 0.146% 0 .0 0 0 % 0.030% 0 .0 0 0 % 0 .0 0 0 %6 1.83% Site Class E 27.933% 9.223% 0.608% 2.126% 0.185% 0 .0 0 2 %7 0.67% Site Class C 12.552% 1.431% 0.077% 2.199% 0.075% 0 .0 0 1 %8 6.07% Site Class C 0.678% 0 .0 0 0 % 0 .0 0 0 % 0 .0 2 2 % 0 .0 0 0 % 0 .0 0 0 %9 0.53% Site Class C 12.848% 1.469% 0.080% 3.515% 0.131% 0 .0 0 2 %

1 0 1.27% Site Class C 11.227% 1.260% 0.066% 0.575% 0.015% 0 .0 0 0 %

Table 19: Summary of Estimated Performance Probabilities for Sample Inventory

Cover Spalling B ar BucklingBridge Site

2 % in 1 0 % in 40% in 2 % in 1 0 % in 40% inNo Condition

50yr 50yr 50yr 50yr 50yr 50yr

1 Site Class B 2.985% 0.193% 0.004% 0.026% 0 .0 0 0 % 0 .0 0 0 %2 a Site Class A 0.641% 0 .0 1 0 % 0 .0 0 0 % 0 .0 0 2 % 0 .0 0 0 % 0 .0 0 0 %2 b Site Class A 0.543% 0.009% 0 .0 0 0 % 0 .0 0 2 % 0 .0 0 0 % 0 .0 0 0 %3 Site Class B 3.354% 0.228% 0.005% 0.031% 0 .0 0 0 % 0 .0 0 0 %4 Site Class C 9.894% 1.088% 0.054% 0.255% 0.006% 0 .0 0 0 %5 Site Class C 4.166% 0.338% 0.006% 0.030% 0 .0 0 0 % 0 .0 0 0 %6 Site Class E 32.210% 10.531% 0.831% 4.099% 0.314% 0.006%7 Site Class C 12.552% 1.431% 0.077% 2.199% 0.075% 0 .0 0 1 %8 Site Class C 7.711% 0.812% 0.027% 0.091% 0 .0 0 2 % 0 .0 0 0 %9 Site Class C 23.018% 2.720% 0.184% 3.745% 0.227% 0.008%

1 0 Site Class C 11.227% 1.260% 0.066% 0.575% 0.015% 0 .0 0 0 %

103

T ab le 20: Priority List of Bridge Inventory to Improve Life Safety

Bridge

No

Site

Condition

Cover Spalling B ar B uckling

2 % in

50yr

1 0 % in

50yr

40% in

50yr

2 % in

50yr

1 0 % in

50yr

40% in

50yr

6 Site Class E 32.210% 10.531% 0.831% 4.099% 0.314% 0.006%9 Site Class C 23.018% 2.720% 0.184% 3.745% 0.227% 0.008%7 Site Class C 12.552% 1.431% 0.077% 2.199% 0.075% 0 .0 0 1 %

1 0 Site Class C 11.227% 1.260% 0.066% 0.575% 0.015% 0 .0 0 0 %4 Site Class C 9.894% 1.088% 0.054% 0.255% 0.006% 0 .0 0 0 %8 Site Class C 7.711% 0.812% 0.027% 0.091% 0 .0 0 2 % 0 .0 0 0 %3 Site Class B 3.354% 0.228% 0.005% 0.031% 0 .0 0 0 % 0 .0 0 0 %5 Site Class C 4.166% 0.338% 0.006% 0.030% 0 .0 0 0 % 0 .0 0 0 %1 Site Class B 2.985% 0.193% 0.004% 0.026% 0 .0 0 0 % 0 .0 0 0 %

2 a Site Class A 0.641% 0 .0 1 0 % 0 .0 0 0 % 0 .0 0 2 % 0 .0 0 0 % 0 .0 0 0 %2 b Site Class A 0.543% 0.009% 0 .0 0 0 % 0 .0 0 2 % 0 .0 0 0 % 0 .0 0 0 %

T able 21: Priority List of Bridge Inventory to Minimize Repair Costs

Cover Spalling B ar B ucklingBridge Site

2 % in 1 0 % in 40% in 2 % in 1 0 % in 40% inNo C ondition

50yr 50yr 50yr 50yr 50yr 50yr

6 Site Class E 32.210% 10.531% 0.831% 4.099% 0.314% 0.006%9 Site Class C 23.018% 2.720% 0.184% 3.745% 0.227% 0.008%7 Site Class C 12.552% 1.431% 0.077% 2.199% 0.075% 0 .0 0 1 %

1 0 Site Class C 11.227% 1.260% 0.066% 0.575% 0.015% 0 .0 0 0 %4 Site Class C 9.894% 1.088% 0.054% 0.255% 0.006% 0 .0 0 0 %8 Site Class C 7.711% 0.812% 0.027% 0.091% 0 .0 0 2 % 0 .0 0 0 %5 Site Class C 4.166% 0.338% 0.006% 0.030% 0 .0 0 0 % 0 .0 0 0 %3 Site Class B 3.354% 0.228% 0.005% 0.031% 0 .0 0 0 % 0 .0 0 0 %1 Site Class B 2.985% 0.193% 0.004% 0.026% 0 .0 0 0 % 0 .0 0 0 %

2 a Site Class A 0.641% 0 .0 1 0 % 0 .0 0 0 % 0 .0 0 2 % 0 .0 0 0 % 0 .0 0 0 %2 b Site Class A 0.543% 0.009% 0 .0 0 0 % 0 .0 0 2 % 0 .0 0 0 % 0 .0 0 0 %

C hapter 5

C onclusions and R ecom m endations

5.1 Conclusions

This thesis presents the formulation of a new probabilistic performance-based seismic

risk assessment methodology suitable for quick and reliable assessment of large bridge

inventories in a city, regional or national bridge network. The new methodology

based on the use of generalized fragility relationships of concrete bridges requires only

minimal engineering effort in determining simple structural characteristics param eters

of the evaluated structures without the need of detailed nonlinear time history analysis

of all the bridges, thus allowing relatively simple and fast evaluation of large bridge

inventories. The generalized fragility relationships are derived and calibrated from

detailed structural modeling and nonlinear time history analysis of only a few selected

representative bridges in the inventory. The new approach is efficient and yet can

provide accurate detailed assessment information for large number of bridges in a

network inventory th a t is more reliable than typical quick assessment check-list type

of approach. Using this new approach, high level assessment information on the

vulnerability and risk of the entire bridge infrastructure can be developed from a

limited amount of structural details. Based on th is methodology bridges most a t risk

are identified and prioritized for detailed engineering evaluations. The assessment

104

105

results obtained using the proposed new evaluation approach for bridge inventory can

provide critically needed information for better decision making on resource allocation

by bridge engineers, owners, and bridge authorities for more efficient and effective

seismic risk mitigation and management of bridge infrastructure.

5.2 R ecom m endations

In this study, generalized fragility relationships have been developed by relating the

structural characteristic parameters to the probability of failure obtained from de

tailed nonlinear time history analysis of representative bridges through a normaliza

tion process. The proposed methodology can be directly applicable to any system

in the same category with similar structural characteristics to obtain quantitative

system performance information for better seismic decision making and resource al

location. However, to improve the relevance and robustness of the quick assessment

methodology developed here, it is necessary to develop additional calibration models

for other structural type and category of bridges, such as steel, emergency and critical

bridges. Separating bridges in the inventory into different structural types and cate

gories based on structural characteristics such as pier type, horizontal curves, skew,

span numbers, etc, would improve the accuracy of the generalized fragility relation

ships. Additionally, the accuracy of the developed generalized fragility relationships

can be further enhanced by considering soil structure interaction effect for realistic

evaluation of quantitative system performance information of bridge inventory. In

addition, for a complete evaluation of probability of failure of bridges, the proposed

methodology may be improved by considering other failure mechanisms such as loss

of confinement, lap-splice failure and loss of axial load carrying capacity.

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