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
13: Comparison of norm of residuals from linear and power regres
sion analyses for the relationship of probability of bar buckling
with S s a l .............................................................................................. 92
14: Comparison of norm of residuals from linear and power regres
sion analyses for the relationship of probability of bar buckling
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
Table 17: Estimated Probabilities of Cover Spalling and Bar Buckling
based on Effective Span over Pier Height R a t io s ........................ 101
Table 18: Estimated Probabilities of Cover Spalling and Bar Buckling
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 9: Site response spectra for various ground conditions a t 10% in
50 year hazard level for O ttaw a ................................................... 26
Figure 10: Site response spectra for various ground conditions a t 40% in
50 year hazard level for O ttaw a ................................................... 27
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
gression, (a) and (b): Cover Spalling and Bar Buckling for
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
gression, (a) and (b): Cover Spalling and Bar Buckling for
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
regression, Bar Buckling for Different Site Conditions a t 40%
in 50 year Hazard L e v e l ................................................................... 87
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
regression, (a) and (b): Cover Spalling and Bar Buckling for
Different Site Conditions at 10% in 50 year Hazard Level . . 90
Generalized Fragility Relationships Based on Sp^n * by linear
regression, (a) and (b): Cover Spalling and Bar Buckling for
Different Site Conditions at 40% in 50 year Hazard Level . . 90
Generalized Fragility Relationships Based on - pa™ * by power
regression, Bar Buckling for Different Site Conditions a t 2% in
50 year Hazard Level ....................................................................... 91
Generalized Fragility Relationships Based on Spa™ * by power
regression, Bar Buckling for Different Site Conditions a t 10%
in 50 year Hazard L e v e l ................................................................... 91
xv
Figure 81: Generalized Fragility Relationships Based on Spa™* by power
regression, Bar Buckling for Different Site Conditions a t 40%
in 50 year Hazard L e v e l ................................................................... 92
Figure 82: Generalized Fragility Relationships Based on p s * by linear re
gression, (a) and (b): Cover Spalling and Bar Buckling for
Different Site Conditions at 2% in 50 year Hazard Level . . . 94
Figure 83: Generalized Fragility Relationships Based on p s * by linear re
gression, (a) and (b): Cover Spalling and Bar Buckling for
Different Site Conditions at 10% in 50 year Hazard Level . . 95
Figure 84: Generalized Fragility Relationships Based on p s * by linear re
gression, (a) and (b): Cover Spalling and Bar Buckling for
Different Site Conditions at 40% in 50 year Hazard Level . . 95
Figure 85: Generalized Fragility Relationships Based on p s * by power
regression, Bar Buckling for Different Site Conditions a t 2% in
50 year Hazard L e v e l .............................................................. 96
Figure 86: Generalized Fragility Relationships Based on p s * by power
regression, Bar Buckling for Different Site Conditions a t 10%
in 50 year Hazard L e v e l ........................................................... 96
Figure 87: Generalized Fragility Relationships Based on p s * by power
regression, Bar Buckling for Different Site Conditions a t 40%
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
Section B-B (Units in mm)
(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
Section B-B (Units in mm)
(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%
Site Class A Site Class B Site Class C Site Class D Site Class E
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
Site Class A Site Class B Site Class C Site Class D Site Class E
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
A - Site Class A B - Site Class B C - Site Class C D - Site Class D E - Site Class E
0.4 0.6 0.8EDP, Drift Ratio (%)
40% in 50 years
1.2
MJ. 0.4
A - Site Class A B - Site Class B C - Site Class C D - Site Class D E - Site Class E
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
Site Class A Site Class B Site Class C Site Class D Site Class E
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
Site Class A Site Class B Site Class C Site Class D Site Class E
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
Effective Transverse Reinforcement Ratio (%)
(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
Effective Transverse Reinforcement Ratio (%)
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
Effective Transverse Reinforcement Ratio (%)
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
Effective Transverse Reinforcement Ratio (%)
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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