Citation
Analysis of bridge health index for the city and county of Denver, Colorado

Material Information

Title:
Analysis of bridge health index for the city and county of Denver, Colorado
Creator:
Jiang, Xin
Place of Publication:
Denver, Colo.
Publisher:
University of Colorado Denver
Publication Date:
Language:
English
Physical Description:
1 electronic file : ;

Thesis/Dissertation Information

Degree:
Doctorate ( Doctor of Philosophy)
Degree Grantor:
University of Colorado Denver
Degree Divisions:
Department of Structural Engineering, CU Denver
Degree Disciplines:
Structural Engineering
Committee Chair:
Rens, Kevin L.
Committee Members:
Li, Chengyu
Rutz, Frederick
Xi, Yunping
Corotis, Ross B.

Subjects

Subjects / Keywords:
Bridges -- Colorado -- Denver ( lcsh )
Bridges -- Evaluation -- Colorado ( lcsh )
Bridges ( fast )
Bridges -- Evaluation ( fast )
Colorado ( fast )
Colorado -- Denver ( fast )
Genre:
bibliography ( marcgt )
theses ( marcgt )
non-fiction ( marcgt )

Notes

Review:
The current Bridge Health Index (BHI) in the Pontis Bridge Management System applied to assess the health conditions for bridges located in the City and County of Denver (CCD) does not provide an accurate analysis of the health condition of its relatively small bridge network. The first stage of this study explores both the calculation results and the computing methodology of the current BHI. It was concluded that the current BHI is subjective to a municipality's often imprecise cost data. The first stage of this study developed an alternate diagnostic tool, the Denver Bridge Health Index (DBHI). It has already been adopted in the Pontis BMS of the CCD Public Works Department. In order to utilize the DBHI to provide the CCD engineers valuable references in maintenance, repair, and rehabilitation (MR & R) decision making, the second stage of this study examines both the calculation results and the computing methodology of the DBHI. It was concluded that the current health index coefficients (ks and ksN) do not reflect actual deterioration levels of the condition states. The second stage of this study was to develop a historical inspection data based-methodology to determine the actual ks (ksJ & R) coefficients for the current Pontis Bridge Management System.
Bibliography:
Includes bibliographical references.
General Note:
Department of Civil Engineering

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Source Institution:
University of Colorado Denver
Holding Location:
Auraria Library
Rights Management:
All applicable rights reserved by the source institution and holding location.
Resource Identifier:
857905140 ( OCLC )
ocn857905140

Full Text
ANALYSIS OF BRIDGE HEALTH INDEX FOR
THE CITY AND COUNTY OF DENVER,
COLORADO
by
Xin Jiang
M.S., College of Engineering and Applied Science, 2009
M.S., College of Engineering at Northeast Forestry University,
B.S., College of Engineering at Northeast Forestry University,
2006
2003
A thesis submitted to the
Faculty of the Graduate School of the
University of Colorado in partial fulfillment
of the requirements for the degree of
Doctor of Philosophy
Structure Engineering
2012


UMI Number: 3505846
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This thesis for the Doctor of Philosophy degree by
Xin Jiang
has been approved for the
Structure Engineering
by
Kevin L. Rens, Chair
Kevin L. Rens, Advisor
Chengyu Li
Frederick Rutz
Yunping Xi
Ross B. Corotis
Date: 4-
13-2012
ii


Jiang, Xin (Ph.D., Structure Engineering)
Analysis of Bridge Health Index for the City and County of Denver, Colorado
Thesis directed by Professor Kevin L. Rens.
ABSTRACT
The current Bridge Health Index (BHI) in the Pontis Bridge Management System applied
to assess the health conditions for bridges located in the City and County of Denver
(CCD) does not provide an accurate analysis of the health condition of its relatively small
bridge network. The first stage of this study explores both the calculation results and the
computing methodology of the current BHI. It was concluded that the current BHI is
subjective to a municipalitys often imprecise cost data. The first stage of this study
developed an alternate diagnostic tool, the Denver Bridge Health Index (DBHI). It has
already been adopted in the Pontis BMS of the CCD Public Works Department. In order
to utilize the DBHI to provide the CCD engineers valuable references in maintenance,
repair, and rehabilitation (MR&R) decision making, the second stage of this study
examines both the calculation results and the computing methodology of the DBHI. It
was concluded that the current health index coefficients (ks and ksN) do not reflect actual
deterioration levels of the condition states. The second stage of this study was to develop
a historical inspection data based-methodology to determine the actual ks (ksJ&R)
coefficients for the current Pontis Bridge Management System.
The form and content of this abstract are approved. I recommend its publication.
m
Approved: Kevin L. Rens


DEDICATION
I dedicate this work to my wife, Ming Ma, for her love, support,
friendship, and for her continuously encouraging me to achieve my success. To my two
years old boy, he will be a joy and a blessing in my whole life.
IV


ACKNOWLEDGMENTS
I would like to thank Dr. Kevin L. Rens, chair of my thesis committee, for his
knowledgeable guidance and support. Dr. Rens gave me the excellent guidance
throughout this thesis.
I also would like to thank Dr. Chengyu Li, Dr. Frederick Rutz, Dr. Yunping Xi,
and Dr. Ross B. Corotis for being committee members of my thesis.
The CCD bridge management group led by James Barwick is acknowledged for
several years of research support. Personnel from the CCD including James Hamblin,
Bret Banwart, and William Melton provided valuable input on maintenance management
of CCD infrastructure throughout the years and are acknowledged.
v


TABLE OF CONTENTS
CHAPTER
I. INTRODUCTION........................................................1
Bridge Management History.........................................1
Current CCD Pontis BMS............................................4
II. BRIDGE HEALTH INDEX................................................9
Commonly Recognized (CoRe) Elements...............................9
Condition States..................................................9
Bridge Health Index..............................................11
Pontis Bridge Health Index Methodology...........................12
Failure Cost-based BHI........................................14
Repair Cost-based BHI.........................................18
III. PROBLEMS..........................................................22
Problems with Computational Results..............................22
Problems in Computing Methodology................................26
Element Value in Pontis BHI Computation.......................26
Effects of Element Value on Pontis BHI........................29
Conclusion.......................................................30
IV. ANALYSIS...........................................................31
Weighting Point and Simplified BHI...............................31
Using Weighting Point Methodology in the Pontis BMS..............32
Conclusion.......................................................36
V. DENVER BRIDGE HEALTH INDEX.........................................38
Condition Index (Cl) Zones.......................................38
vi


Nonlinear Health Index Coefficient ksN...............................40
Weight Coefficient Adjustment Method.................................45
Denver Bridge Health Index...........................................48
Comparison between Pontis BHI and DBHI...............................55
VI. ISSUE..................................................................58
Background Knowledge.................................................59
Element Classification............................................59
Dynamic Calculation Report (DCR)..................................60
Issue................................................................62
Sample Bridges....................................................62
CCD Major and Minor Bridge Networks...............................68
Summary...........................................................70
Analysis.............................................................71
Mathematic Derivation.............................................71
Reason of Trend...................................................74
Reason of Issue...................................................76
Conclusion...........................................................80
VII. METHODOLOGY TO DETERMINE ACTUAL ks VALUE ..............................81
Background Knowledge.................................................81
Element Inspection Data...........................................82
Element Transition Model..........................................85
Methodology..........................................................86
Development of the Element Transition Model.......................86
Ideal Element Transiton Model.....................................91
Methodology.......................................................95
vii


Conclusion
101
VIII. METHODOLOGY IMPLEMENTATION AND ksJ&R.............................103
Background Knowledge.............................................103
Methodology Implementation.......................................104
Data Preparation.............................................105
Data Processing..............................................109
Determination of the Average Initial Ages (Ts) for Every Element under
Each Element Category.....................................112
Computation of the KSJ&R for Every Element under Each Element
Category..................................................114
Computation of the ksJ&R for Each Element Category........115
Actual Health Index Coefficient ksJ&R............................116
Generation of ksJ&R..........................................116
Application of ksJ&R.........................................118
Comparison of ks, ksN, and ksJ&R.............................120
IX. SUMMARY, CONCLUSION, AND RECOMMENDATIONS FOR FURTHER
STUDIES................................................................124
Summary..........................................................124
The First Stage..............................................124
The Second Stage.............................................127
Conclusion.......................................................129
Recommendations For Further Studies..............................129
APPENDIX A. The 144 CoRe Elements in Pontis Bridge Inspection Coding Guide ..131
APPENDIX B. Pontis BHI for 162 Major Bridges in CCD from 2000 to 2006. 137
APPENDIX C. DBHI for 162 Major Bridges in CCD from 2000 to 2006 ..... 142
viii


APPENDIX D. The 350 Lowest-EHI Elements under Each Element Category in CCD
Major Bridge Network...................................................147
APPENDIX E. The 50 Lowest-EHI Elements under Each Element Category in CCD
Minor Bridge Network...............................................169
APPENDIX F. Methodology to Determine ksJ&R for Elements with 3 CSs.173
APPENDIX G. Methodology to Determine ksJ&R for Elements with 5 CSs.176
REFERENCES.........................................................179
IX


LIST OF TABLES
Table
II. 1 Levels of deterioration of each CoRe element................................10
11.2 CSs of steel open girder-painted (element key: 107)..........................11
11.3 Health index coefficients ks of the CSs......................................13
11.4 Failure cost-based BHI for 10 major sample bridges...........................15
11.5 Repair cost-based BHI for 10 major sample bridges............................19
III. 1 Distribution of Bridge Age for the Entire 615 CCD Bridges..................22
111.2 Element Distribution for 8th Avenue Viaduct Bridge (D-03-V-150).............27
111.3 Total Element Value (TEV) for 8th Avenue Viaduct Bridge (D-03-V-150)........28
111.4 Current Element Value (CEV) for 8th Avenue Viaduct Bridge (D-03-V-150)......29
IV. 1 Failure Cost-based and Repair Cost-based Element Weighting Point for 8th Avenue
Viaduct Bridge (D-03-V-150)........................................................33
IV. 2 Weight Coefficient-based Element Weighting Point for 8th Avenue Viaduct Bridge
(D-03-V-150).......................................................................36
V. 1 Condition Index (Cl) Scale..................................................39
V.2 Condition Index (Cl) Zones.....................................................39
V.3 Linear Health Index Coefficients ks............................................40
V.4 EHI based on Linear ks for 8th Avenue Viaduct Bridge (D-03-V-150).............42
V.5 Nonlinear Health Index Coefficients ksN........................................44
V.6 EHI based on Nonlinear ksN for 8th Avenue Viaduct Bridge (D-03-V-150).........44
V.7 Unadjusted Weight Coefficients for 8th Avenue Viaduct Bridge (D-03-V-150).....46
V.8 Weight Coefficient Adjustment Method for 8th Avenue Viaduct Bridge (D-03-V-
150)...............................................................................48
V.9 Element Distribution for 8th Avenue Viaduct Bridge (D-03-V-150)...............50
V.10 Adjusted Weight Coefficients for 8th Avenue Viaduct Bridge (D-03-V-150)......51
x


V. 11 Calculation of DBHI for 8th Avenue Viaduct Bridge (D-03-V-150).................51
V. 12 DBHI for 10 Major Sample Bridges...............................................52
VI. 1 Classification of 144 CoRe elements............................................59
VI.2 The 2008 element inspection data for the sample bridge D-20-MB-785 (Location:
56th Ave. & W. Havana)................................................................63
VI.3 The numerical calculation result for the sample bridge D-20-MB-785..............63
VIA The 2008 element inspection data for the sample bridge D-03-V-180 (Location:
Evans over Santa Fe)..................................................................64
VI.5 The numerical calculation result for the sample bridge D-03-V-180...............64
VI.6 The 2006 element inspection data for the sample bridge F-16-DW (Location: 125
ML SBND)..............................................................................66
VI.7 The numerical calculation result for the sample bridge F-16-DW .................66
VI.8 Paired-samples T test result from SPSS program..................................67
VI.9 Element condition for bridge networks............................................68
VI. 10 The numerical calculation results for the major bridge network................69
VI. 11 The numerical calculation results for the minor bridge network................69
VI. 12 Influencing factors of Adbhi based on ksN for sample bridges...................75
VI. 13 Influencing factors of Adbhi based on ksN for CCD major and minor bridge
networks..............................................................................75
VI. 14 Average quantities in CS1 and all other CSs of total elements included in each
element category for major and minor bridge networks..................................77
VI. 15 Average quantities in CS1 and all other CSs of damaged elements included in each
element category for major and minor bridge networks..................................78
VI. 16 Linear and nonlinear health index coefficients ks (ksN)........................79
VI. 17 Averages of intermediate ks and ksN............................................79
VI. 18 Difference between intermediate ks and ksN....................................79
VII. 1 Element inspection data in the 2010 CCD Pontis BMS database...................84
VII.2 Sample of element inspection data for the bridge railing........................88
xi


VII.3 Condition states of P/S concrete open girder (element key: 109).............96
VII. 4 CDOT suggested CS scales for cracks and percent loss of bearing area in P/S
concrete girder.....................................................................97
VIII. 1 Element inspection data in the 2010 CCD bridge network...................106
VIII.2 Data inaccuracies for sample bridges.......................................107
VIII.3 Determination of the first ages for sample bridge..........................112
VII1.4 Computation of the KSJ&R for every element with 4 CSs......................115
V11I.5 Computation of the ksJ&R...................................................115
VIII.6 Data processing for elements with 5 CSs....................................116
VIII.7 Data processing for elements with 4 CSs....................................117
VIII.8 Data processing for elements with 3 CSs....................................117
VIII.9 Improved health index coefficients ks......................................118
VIII. 10 Influencing factors of Adbhi based on ksJ&R for sample bridges...........118
VIII. 11 Influencing factors of Adbhi based on ksJ&R for CCD major and minor bridge
networks...........................................................................119
VIII.12 Linear health index coefficients ks.......................................121
VIII.13 Nonlinear health index coefficients ksN....................................121
VIII. 14 Actual health index coefficients ksJ&R....................................121
xii


LIST OF FIGURES
Figure
I. 1 Flowchart of the BHI Analysis Procedure..........................................8
II. 1 Distribution of the Entire 615 CCD Bridges in 2006 based on Failure Cost-based
BHI..................................................................................16
11.2 Distribution of 308 Major CCD Bridges in 2006 based on Failure Cost-based BHI. 17
11.3 Distribution of 307 Minor CCD Bridges in 2006 based on Failure Cost-based BHI.
17
11.4 Distribution of the Entire 615 CCD Bridges in 2006 based on Repair Cost-based
BHI..................................................................................19
11.5 Distribution of 308 Major CCD Bridges in 2006 based on Repair Cost-based BHI. 20
11.6 Distribution of 307 Minor CCD Bridges in 2006 based on Repair Cost-based BHI. 21
III. 1 Photograph of the 8th Avenue Viaduct Bridge (D-03-V-150).....................23
111.2 Flexure Cracks at the Pier Cap.................................................24
111.3 Buckle of the Web..............................................................24
111.4 Broken Bearing Guides and Corrosion at the Pot Bearings.......................24
V. 1 Trend of Health Index Coefficient of Condition States.........................41
V.2 Comparison of Trends of Linear and Nonlinear Health Index Coefficient of
Condition States.....................................................................43
V.3 A Linear Step Curve for Calaulating the Adjustment Factor in Weight Coefficient
Adjustment Method....................................................................47
V.4 Distribution of the Entire 615 CCD Bridges in 2006 based on DBHI...............53
V.5 Distribution of 308 Major CCD Bridges in 2006 based on DBHI....................54
V.6 Distribution of 307 Minor CCD Bridges in 2006 based on DBHI....................54
V.7 Distribution of the Entire 615 CCD Bridges in 2006 based on Failure Cost-based
BHI, Repair Cost-based BHI, and DBHI.................................................55
V.8 Trend of BHI Related to the Age of Bridge........................................56
xiii


VI. 1 Dynamic Calculation Report.................................................61
VII. 1 2010 CCD Pontis BMS database schematic diagram............................83
VII.2 Age range of element inspection data........................................89
VII.3 Distributions of historical bridge/element inspections in 2011 CCD Pontis BMS
based on the age..................................................................91
VII.4 The ideal transition model of element with 4 CSs............................92
VII.5 Element conditions at ti (0), t2, t3, and t4................................97
VII. 6 The RSLC and SLC in the ideal transition model of element with 4 CSs...... 100
VIII. 1 Flow chart of methodology implementation..................................105
VII 1.2 Determination of elements repaired after 2000 by utilizing EHI variation trends
.................................................................................109
VIII.3 Element Inspection System................................................111
VIII.4 A flow chart of a database program of determining the initial ages (ts)..114
VIII.5 Distribution of the entire 862 CCD bridges in 2010 based on Pontis BHI, DBHI
with ksN and DBHI with ksJ&R.....................................................120
VII 1.6 Comparison of trends of ksN, ks, and ksJ&R for n=5.......................122
VIII. 7 Comparison of trends of k,N, ks, and ksJ&R for n=4.......................122
VIII.8 Comparison of trends of ksN, ks, and ksJ&R for n=3.......................123
xiv


CHAPTER
I. INTRODUCTION
Bridge Management History
For modem civilization, a countrys infrastructure is essential to a countrys
success. The United States transportation system has expanded to become the largest and
most modem highway system in the world since the 1950s (Roberts and Shepard, 2000).
The majority of the around 600,000 bridges in the U.S. highway system were built during
two periods of time. The first period of bridge construction occurred in the 1930s during
the depression years and the second period of bridge construction happened in the 1950s
and 1960s (Hadavi, 1998). As a consequence, the bridges built in these two periods have
grown old and may shortly need replacement or major repairs. These facts illustrate the
necessity of a rational procedure to determine which actions, and the costs associated
with them, are to be taken in order to provide safety and a satisfactory level of bridge
service (Rens et al., 2005).
On December 15, 1967, the collapse of the 2,235-ft long Point Pleasant Bridge,
also known as the Silver Bridge, over the Ohio River between West Virginia and Ohio,
illustrated the need for programs of inspection and maintenance of bridges (Hartle et ah,
1991). The Point Pleasant Bridge was built in 1928 and its failure occurred without
warning resulting in 46 fatalities. The collapse of the Point Pleasant Bridge was
precipitated by the stress corrosion failure of an eyebar link. Because of its deadly
consequences, the collapse exposed the necessity of a rational program to conduct
periodic inspections of the nations bridges (Rens et ah, 2005). Some reasons for bridge
failure are corrosion, fatigue, inappropriate design, wind, scour, earthquake, floods, and
1


fire (Harik et al., 1990). In most cases, failures can be prevented by periodic
maintenance inspections. Shortly sfter the collapse of the Point Pleasant Bridge, it led to
a national concern about the safety of each bridge in the United States and as a
consequence, congress was urged to create a national bridge inspection program (Hartle
et al., 1991). Since that time, bridge infrastructure management has become increasingly
important in public agencies.
The National Bridge Inventory Program (NBIP) was formed as a result of the
Federal Highway Act of 1968 (Czepiel, 1995). The Federal Highway Administration
(FHWA) requires each state to provide information about each bridge in their inventory
as described in the National Bridge Inspection Standard (NBIS), issued in April 1971.
This information is used to generate a National Bridge Inventory (NBI). Before the
NBIS was developed, there was no clearly defined maintenance program in place to
evaluate bridges; in fact, before 1968 the exact number of bridges was not even known
(Hadavi, 1998). Due to the Federal Highway Act of 1970, the Special Bridge
Replacement Program (SBRP) was formed. SBRP takes the NBI data and provides
funding to states to either help rehabilitate or replace an agencys bridge. The bridge is
analyzed based upon its sufficiency rating and its inadequacy (Czepiel, 1995).
The FHWA uses a set of guidelines for allocating funds based on the conditions
of bridges determined by the NBI. A study on the guidelines for determining bridge
needs to evaluate the accuracy of funding allocation was conducted by the United States
General Accounting Office (U.S. GAO). The study determined that the sufficiency
ratings used by FHWA from the NBI to determine which bridges are eligible for federal
funding are inadequate and indicate more bridges as being deficient than are actually in
2


critical need for rehabilitation (U.S. GAO, 1991). The NBIS data for a given bridge are
limited and do not supply the detailed information that can be used to predict a bridges
future condition or provide an estimate on future maintenance and repair needs of an
agency bridge inventory (WSDOT, 2010).
Recognizing that a different strategy towards future bridge preservation was
needed, the National Cooperative Highway Research Program (NCHRP) published a
report in December 1987 to provide the framework for a Bridge Management System
(BMS). The overall objective of this report was to develop a model bridge management
system that could be implemented by a state or local transportation agency (WSDOT,
2010). Due to dwindling budgets for DOTs, an increasing pressure to minimize the cost
of maintenance has created the necessity of BMS (Wolfgram, 2005). In 1993, it became
required for all state agencies to have an operating BMS according to the federal
mandates for bridge management outlined in the American Association of State Highway
and Transportation Officials (AASHTO) Guidelines for Bridge Management (AASHTO,
1993). These guidelines suggest that a BMS should contain four basic components: data
storage, cost and deterioration models, optimization models for analysis, and updating
functions (Attoh-Okine, 2003).
Darbani and Hammad (2007) state Governmental agencies in many countries
started developing Bridge Management Systems after a number of bridge collapses
during the 70s". BRIDGIT, developed under an AASHTO-sponsored NCHRP,
determines project-level maintenance, repair, and rehabilitation (MR&R) for each bridge
and is ideal for smaller bridge populations (Hawk, 1999). LIFECON LMS, Life Cycle
Maintenance and Management Planning System, a European BMS, organizes planning,
3


construction, maintaining, repairing, rehabilitation, and replacing structures while
considering safety, serviceability, economy, ecology, and other aspects of life-cycle
planning (Vesikari and Soderqvist, 2003). Ontario Bridge Management System (OBMS),
a Canadian BMS, makes use of photos, documents and commentary in addition to a new
element-level manual (Thompson et al., 2003).
Pontis Bridge Management System (Pontis BMS) is comprehensive software
tool initially developed by FHWA and now available from AASHTO as an
AASHTOWare product (FHWA, 2011). Pontis BMS is now being used by forty-one
States and five municipalities. Pontis BMS supports the complete bridge management
cycle, including bridge inspection and inventory data collection and analysis,
recommending an optimal preservation policy, predicting need and performance
measures for bridges, and developing projects to include in an agency's capital plan
(Robert et al., 2003). Most notably, Pontis BMS provides a systematic procedure for the
allocation of resources to the preservation and improvement of the bridges in a network
by considering both the costs and benefits of maintenance policies versus investments in
improvements or replacement (FHWA, 2011). The latest version of the Pontis software,
Pontis 4.4, is available from AASHTO. A new Web-based version of the software,
Pontis 5.0, is currently under development.
Current CCD Pontis BMS
The definition of bridge management is a process of combining management,
inspection, engineering, and economic information in order to help determine the best
actions to take on bridges in a network over a given period of time (AASHTO, 1993). A
BMS is a tool for managing bridges and to help agencies meet their objectives. One main
4


objective was to evaluate the health conditions of existing bridges and subsequently to
make maintenance, repair, and rehabilitation strategies. The Pontis BMS, a product of
AASHTO, is being used by 41 DOTs in the United States (Thompson and Shepard,
2000). Countless other smaller city agencies presumable use the system as well. The
CCD Public Works Department has been involved since 2000 in the development and
implementation of the Pontis BMS. Pontis relies on the biennial visual inspection of
major CCD bridges and triennial visual inspection of minor CCD bridges. Major
structures are identified as those structures whose span length exceeds 20 feet (6.1
meters) while minor structures are less. The implementation of Pontis as an active tool
for bridge management has been evolving for the past 10 years in the CCD.
Limited financial resources relative to the demand for overcoming existing
deficiencies in bridges make it difficult for transportation agencies to carry out
maintenance activities on bridge structures as frequently as necessary (Al-Wazeer et al.,
2008). The 2009 Report Card for Americas Infrastructure reported that more than 26%,
or one in four, of the nations bridges are either structurally deficient or functionally
obsolete. While some progress has been made in recent years to reduce the number of
deficient and obsolete bridges in rural areas, the number in urban areas is rising. A S17
billion annual investment is needed to substantially improve current bridge conditions.
Currently, only SI0.5 billion is spent annually on the construction and maintenance of
bridges (ASCE, 2009). It is significant to identify the bridges most in need of
maintenance and apply efficient rehabilitation strategies to best utilize available financial
resources.
5


In the Pontis BMS, the Bridge Health Index (BHI) is a diagnostic tool used to
assess bridge health condition. The BHI can be calculated directly from element level
inspection data. The BHI ranges from 0 to 100, which indicates from the worst condition
to the best condition of a bridge. It can be developed for a single bridge or a network of
bridges. Thus, the condition at any point in time can be obtained from the health index
trends for a single bridge. The list of bridges in the worst condition can be identified
from a bridge distribution network. The BHI is an excellent diagnostic tool in bridge
health assessment.
Although the BHI is being used by most states to track bridge health condition
and support decision making, CCD engineers consider that the current BHI does not meet
its needs. Jensen (2007) states The current BHI is not in line with all of the defects on a
bridge. This is because the computation of this performance measure neglects Smart
Flags elements in the bridge, which are deterioration processes, such as scour, fatigue,
and settlement. Engineers at the CCD are of the opinion that the current BHI neglects
the effect of element damage on bridge health, function, and safety (Jiang and Rens,
2010).
The first stage of this study is from 2007 to 2009 and is introduced in Chapters I
through V in this dissertation. It is based on the 2007 Denver bridge network, which has
308 major bridges and 307 minor bridges. There are three goals in the first stage of this
study:
(1) Review the current calculating method of the Pontis BHI and demonstrate the
influencing factors including cost.
6


(2) Modify Pontis BHI which was termed the Denver Bridge Health Index
(DBHI). The DBHI and its corresponding formula consider the effect of element damage
on bridge health and function.
(3) Analyze the CCD network of bridges and compare the original and modified
BHI methodologies.
To achieve these three goals, a specific Denver major bridge (D-03-V-150)
located at 8th Avenue between Mariposa St. and Vallejo St. was used as an example to
illustrate the current calculation procedure of the BHI and to demonstrate the deficiency
of the calculation results. This example was also used to calculate the DBHI, a more
rational BHI, with the application of the nonlinear health index coefficient and using the
weight coefficient adjustment factor.
Figure 1.1 is the research flowchart presenting the BHI analysis procedure in this
thesis.
7


Figure 1.1 Flowchart of the BHI analysis procedure
8


CHAPTER
II. BRIDGE HEALTH INDEX
Commonly-Recognized (CoRe) Elements
The AASHTO Guide for Commonly Recognized Structural Elements, often
called the AASHTO CoRe Element Manual, introduces the definition of each element
and the unit of measurement for as many as 108 elements (Thompson and Shepard,
2000). Most states have successfully used the AASHTO CoRe elements as the basis for
data collection, performance measurement, resource allocation, and management decision
support. State agencies may supplement the AASHTO CoRe Element Manual with their
own element definitions. The Pontis Bridge Inspection Coding Guide was developed by
the Colorado Department of Transportation (CDOT) in 1997. It is intended to
supplement the AASHTO CoRe Element Manual with clarifying information and
additional elements unique to Colorado bridges and structures (CDOT, 1998). Colorado
adds 36 elements such as precast panel concrete deck, prestress (P/S) concrete floor
beam, and bridge wingwalls. The 144 CoRe elements in the Pontis Bridge Inspection
Coding Guide are included in Appendix A. The CCD Public Works Department has
collected element level inspection data based on the Pontis Bridge Inspection Coding
Guide for 615 total structures. The total structures include 308 major structures and 307
minor structures. The CCD, like many other public works entities, uses the AASHTO
CoRe elements as the basis for its Pontis BMS.
Condition States
The AASHTO CoRe Element Manual defines each structural and nonstructural
element and the descriptions for associated condition states (CSs). The definitions and
9


descriptions reflect the most common processes of deterioration and the effect of
deterioration on serviceability. AASHTO CoRe element manual generally defines the
levels of deterioration of each CoRe element as follows (Thompson and Shepard, 2000):
Table II.1 Levels of deterioration of each CoRe element
Deterioration
level
Description
1. Protected
2. Exposed
3. Attacked
4. Damaged
The elements protective materials or systems are sound and functioning as intended to
prevent deterioration of the element.
The elements protective materials or systems have partially or completely failed, leaving
the element vulnerable to deterioration.
The element is experiencing active attack by physical or chemical processes, but is not
yet damaged.
The element has lost important amounts of material, such that its serviceability is suspect.
5. Failed The element no longer serves its intended function.
The above levels in Table II.1 are denoted Condition State 1 (CS1) through
Condition State 5 (CS5) respectively and each CoRe element has a set of 3-5 CSs. The
element level inspection supplies the total quantity of each element and the quantity of
the element in each respective CS. With this information, the severity of the deterioration
and the quantity of the deterioration can be determined for an individual element. Table
II.2 is an example of CSs for a structural element: Steel-Open girder-Paintcd.
10


Table II.2 CSs of steel open girder-painted (element key: 107)
CS Condition term
1 There is no evidence of active corrosion and the paint system is sound
and functioning as intended to protect the metal surface.
2 There is little or no active corrosion. Surface or freckled rust has formed
or is forming. The paint system may be chalking, peeling, curling or
showing other early evidence of paint system distress but there is no
exposure of metal.
3 Surface or freckled rust is prevalent. The paint system is no longer
effective. There may be exposed metal but there is no active corrosion
which is causing loss of section.
4 The paint system has failed. Surface pitting may bepresent but any
section loss due to active corrosion does not yet warrant structural analysis
of either the element or the bridge.
5 Corrosion has caused section loss and is sufficient to warrant structural
analysis to ascertain the impact on the ultimate strength and/or serviceability
of either the element or the bridge.
Bridge Health Index
Cheng and Melhem (2005) report that the BHI is a single number indicator of the
structural health of a bridge. They go on to say that it is an integral measure which meets
bridge management engineers need for measuring bridge health condition. This
indicator is expressed as a percentage ranging from 0% (worst condition) to 100% (best
condition).
The premise of the BHI is that each bridge element has an initial asset value
representing the best condition state when the bridge is new. When the bridge
deteriorates with age, the asset value of each bridge element reduces and represents a
lower condition state. After repair, maintenance, or rehabilitation, the asset value of each
bridge element increases and represents an improved condition state (Shepard and
Johnson, 2001).
11


In the Pontis BMS, the BHI is calculated by a series of formulas in two steps.
Step one calculates the element health index (EHI) according to the condition rating
distribution from the element-level inspection information. Step two computes the entire
BHI based on the weighted EHI. The Pontis system uses two weighting methods: the
failure cost-based weighting method and the repair cost-based weighting method. Each
weighting method is dependent on cost.
The following two items are next addressed: (1) Presenting the two BHI
methodologies used in the Pontis BMS: failure cost-based BHI methodology and repair
cost-based BHI methodology, (2) Presenting the BHI results and the bridge distributions
for the entire 615 CCD bridges using two cost-based BHI methodologies.
Pontis Bridge Health Index Methodology
According to AASHTO (2003), the health index of an individual element (He) is
the ratio of the summation of the quantities in each condition state multiplied by a
corresponding coefficient to the total quantity of the element. It can be calculated by the
following formula:
Zm,
He =^=------x 100%
LQs
s
Equation II.1
Where
He is the health index of an individual element (EHI),
5 is the index of the condition state,
qs is the quantity of the element in the sth condition state,
ks is health index coefficient corresponding to the sth condition state.
12


The health index coefficients of the CSs ks are fractional values calculated as
follows:
k
s
n-s
n -1
Equation II.2
Where
ks is the health index coefficient for the sth condition state,
n is the number of applicable condition states ( n=3, 4, and 5),
5 is the index of the condition state (s =1, 2,ri).
The health index coefficients ks take the following values shown in Table 11.3.
Table II.3 Health index coefficients ks of the CSs
Number of CSs CS1 CS2 CS3 CS4 CS5
3 1.00 0.50 0.00
4 1.00 0.67 0.33 0.00
5 1.00 0.75 0.50 0.25 0.00
The health index (H) of the entire bridge can be evaluated as a weighted average
of the health indexes of bridge elements based on element total quantity and relative
importance. According to AASHTO (2003), it can be calculated by the following
formula:
Y.HeQeWe
H = -------x 100%
Z Q'We
e
Euation 11.3
Where
H is the health index of the entire bridge (BHI),
13


e is the index of an element,
Qe is the total quantity of element e,
We is the weighting factor of that element, and determined by either the elements
failure cost or an empirically assigned value as relative importance (AASHTO,
2003).
Failure Cost-based BHI
In the Pontis system, one of the element weighting options that adopts element
failure cost as weighting factor is the failure cost-based weighting method. According to
AASHTO (2003), the corresponding failure cost-based BHI is calculated by following
formula:
H =
XVeQeFCe
e_______
Y.QeFCe
- x 100%
Euqation II.4
Where
FCe is total element failure cost calculated as a sum of its agency and user failure
cost components (AASHTO, 2003).
Equation II.4 was applied to the 162 major CCD bridges which have complete
inspection data from 2000 to 2006. The results are shown in Appendix B. Among these
results, 10 bridges were selected to be shown in Table II.4. This is because their BHIs
during 2000 to 2006 are all between 90% and 100% and have extremely minimal
decrease with age. In fact, with the exception of three inspections, all inspection
conditions are above 97%. This is despite the fact that they all have severe element
14


damage. In addition, these 10 major bridges will be also used for repair cost-based BHI
and DBHI.
Table II.4 Failure cost-based BHI for 10 major sample bridges
Failure cost-based BHI (%)
Bridge key 2000 2002 2004 2006
D-01-CC-014 99.984 98.972 98.972 98.086
D-01-CC-017 100.000 100.000 99.094 99.094
D-01-CC-019 100.000 99.398 98.382 98.382
D-03-V-046 99.774 99.769 99.426 99.074
D-03-V-090 99.782 99.475 98.332 98.252
D-03-V-150 99.810 96.886 90.844 90.424
D-04-BOST-51 99.982 99.447 99.407 99.320
D-31-PB-410 99.442 99.114 97.681 97.336
D-31-PB-650 99.404 99.159 97.541 97.541
D-31-PB-690 99.908 99.908 99.816 99.816
The 2006 data in Table II.4 can be expanded to include the entire 615 CCD bridge
network as illustrated in Figure II. 1.
15


Bridge Distribution
i1 i 1
90-100 80-89 70-79 60-69 50-59 40-49 30-39 20-29 10-19 0-9
Bridge Health Index
Figure II.1 Distribution of the entire 615 CCD bridges in 2006 based on failure cost-
based BHI
As shown in Figure II. 1, almost 90% of 615 bridges are in the highest BHI level.
This result indicated the majority of the bridges were in a good health condition.
However, 61% of bridges in the 90-100% range have served the CCD for over 20 years.
Figures II.2 and II.3 show the distributions for 308 major CCD bridges and 307
minor CCD bridges in 2006 based on failure cost-based BHI.
16


100
Bridge Distribution
I 1 I I 1 I 1 I 1 I 1iii
90-100 80-89 70-79 60-69 50-59 4049 3039 2029 1019 09
Bridge Health Index
Figure II.2 Distribution of 308 major CCD bridges in 2006 based on failure cost-
based BHI
Bridge Distribution
280
90100 8089 7079 6069 5059 4049 3039 2029 1019 09
Bridge Health Index
Figure 11.3 Distribution of 307 minor CCD bridges in 2006 based on failure cost-
based BHI
17


Repair Cost-based BHI
Another option is called the repair cost-based weighting method. The weighting
factor is the product of a weight coefficient and the cost of the most expensive element
repair action. According to AASHTO (2003), the corresponding repair cost-based BHI is
calculated by Equation 11.5:
Y.HeQeRCe
H =
TQeRCe
x 100%
Equation II.5
Where
RCe is the most expensive element repair action cost defined for each element,
we is the weight coefficient assigned to each element according to elements
importance (AASHTO, 2003).
Equation II.5 was applied to 162 major CCD bridges which have complete
inspection data from 2000 to 2006. The results are located in Appendix B. Table II.5
shows the repair cost-based BHI for previous 10 major sample bridges from 2000 to
2006, using Equation II.5.
18


Table II.5 Repair cost-based BHI for 10 major sample bridges
Repair cost-based BHI (%)
Bridge key 2000 2002 2004 2006
D-01-CC-014 99.886 97.886 97.881 96.801
D-01-CC-017 100.000 100.000 97.837 97.837
D-01-CC-019 100.000 99.814 97.429 97.428
D-03-V-046 99.994 99.994 99.452 99.009
D-03-V-090 99.996 99.605 98.921 98.908
D-03-V-150 99.886 99.492 98.451 97.762
D-04-BOST-151 99.990 99.814 99.810 98.820
D-31-PB-410 99.967 99.801 99.098 98.933
D-31-PB-650 99.983 99.811 97.954 97.954
D-31-PB-690 99.772 99.771 99.544 99.544
The 2006 data in Table 11.5 can be expanded to the entire 615 CCD bridges as
shown in Figure II.4.
100
Bridge Distribution
Figure II.4 Distribution of the entire 615 CCD bridges in 2006 based on repair cost-
based BHI
19


As shown in Figure II.4, 81.46% of 615 bridges are in the highest BHI level. This
result is similar to the failure cost-base BHI result in Figure II. 1. However, among 501
bridges, 56% of them have served the CCD for over 20 years.
Figures II.5 and II.6 show the distributions for 308 major CCD bridges and 307
minor CCD bridges in 2006 based on repair cost-based BHI.
100-,
Bridge Distribution
c
Q
s
S
&
1
a>
o
s.
90-
80-
234
............... ..............I 1i'i
90-100 80-89 70-79 60-69 50-59 40-49 30-39 20-29 10-19
0
0^9
Bridge Health Index
Figure II.5 Distribution of 308 major CCD bridges in 2006 based on repair cost-
based BHI
20


100-1
Bridge Distribution
I--------------------1*1 I
90-100 80-89 70-79 60-69 50-59 40-49 30-39 20-29 10-19 0-9
Bridge Health Index
Figure II.6 Distribution of 307 minor CCD bridges in 2006 based on repair cost-
based BHI
21


CHAPTER
III. PROBLEMS
Although bridge management engineers use the Pontis BHI to prioritize
maintenance and rehabilitation, it is felt that the current methodology does not give an
accurate portrayal of the condition of the network (Jiang and Rens, 2010). To point out
the deficiencies of the current BHI, the problems with the computational results and the
computing methodology will be presented in this chapter. In order to illustrate the
problems, Tables II.4 and II.5 and Figures II. 1 and II.4 from Chapter II are discussed
based on CCD expertise and actual inspection data.
Problems with Computational Results
The Pontis BHI does not accurately represent the CCD bridge network. The
accuracy of BHI calculation is suspect. According to the current results, almost 90% of
the CCD bridges lie in the highest BHI level between 90% and 100% as was shown in
Figure II. 1. This is despite the fact that the majority of the CCD network has served the
community for many years as shown in Table III. 1.
Table III.l Distribution of bridge age for the entire 615 CCD bridges
Age of bridge (years) Over 20 20-15 15-10 10-5 Under 5 Unknown Total
Number of bridges 368 28 86 39 63 31 615
In addition, several known bridges that arc due significant repair show up in the
highest rated area (90%-100%). For example, 8th Avenue Viaduct bridge
(D-03-V-150) is located on the west 8th Avenue over the railroad tracks between
Mariposa St. on the east and Vallejo St. on the west and is shown in Figure III. 1. Using
the Pontis BHI, 2006 BHI results of this bridge are 90.4% for the failure cost-based BHI
22


and 97.8% for the repair cost-based BHI (shown in Tables II.4 and II.5). Actually, this
bridge has served 26 years and repair is probably warranted due to the numerous cracks
in the pier cap supports, buckles of the webs, broken bearing guides, and the corrosion at
the pot bearings. Figures III.2 through III.4 show the crack in the cap, buckles of the
webs, broken bearing guides, and the corrosion at the pot bearing, respectively.
Figure III.l Photograph of the 8th Avenue Viaduct bridge (D-03-V-150).
This bridge is located in metro Denver on the west 8th Avenue over the railroad tracks
between Mariposa St. on the east and Vallejo St. on the west.
23


Figure 111.2 Flexure cracks at the pier cap.
Several tension cracks extend in the cap section.
Figure 111.3 Buckle of the web.
Visible buckle existed on the box girder exterior web.
Figure 111.4 Broken bearing guides and corrosion at the pot bearings
24


Another deficiency of the current overall BHI is its sensitivity. Even when a
bridge suffers large amounts of element damage between inspections, the BHI only
decreases an extremely minimal amount as was shown in Tables II.4 and II.5. For
example, 8th Avenue Viaduct bridge (D-03-V-150) listed in Tables II.4 and II.5 had many
new cracks in the pier cap supports which had been an ongoing distress since the year
2000. Cracks had been propagating in width and length at every biennial inspection as
shown in Figure III.2. In addition buckled webs (Figure III.3), and broken bearing guides
and the corrosion at the pot bearings (Figure III.4) were identified in recent inspections.
However, as shown in Table II.5, the trend of the repair cost-based BHI of this bridge is
99.886% in 2000, 99.492% in 2002, then 98.451% in 2004, and finally 97.762% in 2006.
The overall BHI decrease is merely 2.124% between 2000 and 2006. This minimal
decrease in numerical results can hardly tell bridge management engineers any extent of
element damage which had happened. It does not raise a flag that any local element
deterioration issue may be developing.
Finally, another feature of the BHI is that the rationality of bridge distribution in
BHI is suspect. Figure II. 1 shows the bridge distribution plotted by BHI. Figure II. 1
indicates that almost 90% of total bridges ranked in the top 10% level (90%-100%).
However, only 5.5% were in 80% 89%; 2.0% in 70% 79% and less than 4% ranked
in other interval levels below 70%. The significant disparity in bridge condition
distribution between the top 10% level and other levels misleads bridge management
engineers between the limits of good and poor conditions. In other words, is it credible
25


that an overwhelmingly majority of the bridge network is still in outstanding condition
even though many are in the 20-30 year old range?
Problems in Computing Methodology
Element Value in Pontis BHI Computation
The key idea of the current Pontis BHI is that elements are assigned weights
according to the economic consequences of element failure when the element-level health
indexes are converted to the bridge-level health index. The BHI presented in Chapter II
can also be presented in an equivalent alternate matter. According to Shepard and
Johnson (2001), Pontis BHI is the ratio of the current element value to the initial element
value of all elements on the bridge. Equations III. 1 through III.3 are equivalent but more
intuitive forms compared to Equations II. 1 through II.3. Although both Equations III. 1
through III.3 and Equations II. 1 through II.3 determine the same BHI results, element
value defined in the former helps analyze the problems in the current Pontis BHI
methodology. Therefore, presenting Pontis BHI computation (Equations III. 1 through
III.3) utilizing element value is necessary.
hi = !£cev iYjEv)*m%
Equation III.l
Where
HI is the Bridge Health Index,
CEV is the current element value,
TEV is the total element value.
TEV = TEQ FC
Equation III.2
26


Where
TEQ is the total element quantity,
FC is the failure cost of element.
CEV = '£{QCSi *ki)*FC
Equation III.3
Where
QCSj is the quantity in the condition state i,
kj is the health index coefficient for the condition state i.
Tables III.2 through III.4 present an application of Equations III. 1 through III.3 to
the 8th Avenue viaduct bridge (D-03-V-150). Using Equation III. 1 and Tables III.3 and
III.4, the final BHI calculation is:
HI = i^CEV /^TEV )* 100% = (S7566901/S8368242)* 100% = 90.424%
Table III.2 Element distribution for 8th Avenue Viaduct bridge (D-03-V-150)
Element Element inspection data
No. key description Unit TEQ QCS, qcs2 qcs3 qcs4 qcs5 EHI (%)
e(l) 14 P Cone Deck/AC Ovly inches 8895.28 8895.28 0.00 0.00 0.00 0.00 100
e(2) 101 Unpnt Stl Box Girder inches 1444.76 1300.28 144.48 0.00 0.00 97
e(3) 106 Unpnt Stl Opn Girder inches 176.48 176.48 0.00 0.00 0.00 100
e(4) 210 R/Conc Pier Wall Feet 164.59 164.59 0.00 0.00 0.00 100
e(5) 215 R/Conc Abutment Feet 27.43 27.43 0.00 0.00 0.00 100
e(6) 234 R/Conc Cap inches 175.26 0.00 175.26 0.00 0.00 67
e(7) 305 Elastomeric Flex Jt inches 27.43 27.43 0.00 0.00 100
e(8) 314 Pot Bearing Each 86.00 27.00 4.00 55.00 34
e(9) 326 Bridge Wingwalls Each 4.00 4.00 0.00 0.00 100
e( 10) 331 Cone Bridge Railing Each 874.78 874.78 0.00 0.00 0.00 100
e(ll) 333 Other Bridge Railing Each 569.98 569.98 0.00 0.00 100
e(12) 334 Metal Rail Coated Each 722.38 633.38 0.00 89.00 0.00 0.00 94
e( 13) 338 Cone Curbs/SW Each 722.38 722.38 0.00 0.00 0.00 100
QCS| through QCS5 are element quantities in CSI through CS5.
27


Table III.3 Total element value (TEV) for 8th Avenue Viaduct bridge (D-03-V-
150)
No. Element Unit failure cost (FC) Calculation Resulting TEV TEV (%)
key description TEQ FC
e( 1) 14 P Cone Deck/AC Ovly $78 8895.28*78 $693832 8.29
e(2) 101 Unpnt Stl Box Girder $740 1444.76*740 $1069122 12.78
e(3) 106 Unpnt Stl Opn Girder $2344 176.48*2344 $413669 4.94
e(4) 210 R/Conc Pier Wall $14573 164.59*14573 $2398570 28.66
e(5) 215 R/Conc Abutment $31573 27.43*31573 $866047 10.35
e(6) 234 R/Conc Cap $8740 175.26*8740 $1531772 18.30
e(7) 305 Elastomeric Flex Jt $2319 27.43*2319 $63610 0.76
e(8) 314 Pot Bearing $4349 86*4349 $374014 4.47
e(9) 326 Bridge Wingwalls $1205 4*1205 $4820 0.06
e( 10) 331 Cone Bridge Railing $456 874.78*456 $398900 4.77
e(l 1) 333 Other Bridge Railing $442 569.98*442 $251931 3.01
e(12) 334 Metal Rail Coated $285 722.38*285 $205878 2.46
ef 13) 338 Cone Curbs/SW $133 722.38*133 S96077 1.15
Total(XTEV) $8368242 100
28


Table III.4 Current element value (CEV) for 8th Avenue Viaduct bridge (D-03-V-
150)
No. key Element description Calculation KQCSi kj) FC Resulting CEV
e(l) 14 P Cone Deck/AC Ovly 8895.28*1.0*78 S693832
e(2) 101 Unpnt Stl Box Girder [1300.28*1.0+144.48*0.67]*740 $1033840
e(3) 106 Unpnt Stl Opn Girder 176.48*1.0*2344 $413669
e(4) 210 R/Conc Pier Wall 164.59*1.0*14573 $2398570
e(5) 215 R/Conc Abutment 27.43*1.0*31573 $866047
e(6) 234 R/Conc Cap 175.26*0.67*8740 $1026288
e(7) 305 Elastomeric Flex Jt 27.43*1.0*2319 $63610
e(8) 314 Pot Bearing [(27*1.0)+(4*0.5)+(55*0)]*4349 $126121
e(9) 326 Bridge Wingwalls 4*1.0*1205 $4820
e(10) 331 Cone Bridge Railing 874.78*1.0*456 $398900
e(l 1) 333 Other Bridge Railing 569.98*1.0*442 $251931
e(12) 334 Metal Rail Coated [(633.38* 1.0)+(89*0.5)]*285 $193196
e( 13) 338 Cone Curbs/SW 722.38*1.0*133 $96077
Total(XCEV) $7566901
Effect of Element Value on Ponds BHI
The product of the weight taken as an economic cost and the element quantity is
defined as an element value. The problem with the current Pontis BHI methodology is
ascribed to an element value. The potential effects of an element value on the BHI are as
follows:
(1) The EHI multiplied by a higher element value will play a decisive role in
determining the BHI. Oppositely, the EHI multiplied by a lower element value
will play an extremely minimal role even though the EHI is zero due to the
element failure. This was demonstrated in Table III.3.
(2) The element value only indicates its percentage in the total element value
(TEV) of a bridge in terms of economic cost but not the effect of element damage
29


on the bridge health and function. This effect should be applied as a weight to
convert the clement-level health indexes to the bridge-level health index. The
actual meaning of the element value multiplied by the EHI is the residual element
value (same as CEV in Equation III.3). It is therefore objective to say the Pontis
BHI is the percentage for residual element value CEV out of total element value
TEV of a bridge in terms of economic cost. This results in misleading results
as were demonstrated in Tables II.4 and II.5 and Figures II. 1 and II.4.
Conclusion
The study presented in the first 2 sections of this chapter helps conclude that the
current BHI measure will not help bridge agencies gain a reasonable BHI from the results
and will not support decision-making. The reliability of the BHI is a serious problem
which concerns CCD bridge management engineers. Therefore, a modification for the
BHI calculation was necessary and is presented in the following chapters.
30


CHAPTER
IV. ANALYSIS
In the Pontis BMS, the EHI are combined into to the BHI according to the product
of element quantity and the weighting factor assigned to each element based on the
elements importance as was demonstrated in Equation II.3. If the weighting factor
represents importance for each element, this product reflects importance for each EHI.
The weighting point, a newly constructed concept, is used to describe the relative
importance of the EHI. As a result, a simplified formula for computing the BHI is
obtained (Jiang and Rens, 2010).
Weighting Point and Simplified BHI
It is complicated to simultaneously analyze all the factors that affect the BHI in
the final computational formula. Therefore, a final simplified weighting point was
developed for the bridge management engineer as an analysis tool to observe the
integrated effect of all original factors in the computational formula with respect to the
BHI. After determining the EHI, the weighting points for each element, f¥Pe, which
represent the relative importance of the EHI, will be used to combine the EHI to a final
overall BHI. Equation IV. 1 is a simplified formula using the weighting point idea to
compute the BHI. This simplified formula yields the exact same result as current Pontis
BHI as presented in Equation II.3 and Equation III. 1.
" = 1 HeWPe
Equation IV.l
Where
H is Bridge Health Index,
31


He is element health index,
WPe is element weighting point, Y,wpe =100%,
e is the index of an element.
Using Weighting Point Methodology in the Pontis BMS
There are two options for utilizing the weighting point in the current Pontis BMS.
Following are the equations for the two cost-based weighting points. Equation IV.2 is the
failure cost-based weighting point and is designated as Option 1. Equation IV.3 is the
repair cost-based weighting point as is termed Option 2.
Q FC
WP = ^---e x 100%

Equation IV.2
WP = jfVC,M* X100%
HQ.KC.W.
Equation IV.3
A question to be answered includes How will the element weighting point affect
the BHI? Another question to be answered is Will options 1 and 2 be the most reliable
methodologies to obtain reasonable results of the BHI?" In order to answer these
questions, an experimental calculation of the BHI for 8th Avenue Viaduct bridge (D-03-
V-150) using Equations IV.2 and IV.3 was completed as shown in Table IV.1. Note that
Equations IV.2 and IV.3 produce the same results as Equations II.4 and II.5.
32


Table IV.l Failure cost-based and repair cost-based element weighting point for 8th
Avenue Viaduct bridge (D-03-V-150)
No. Element Weighting point (%) EH I (%)
key description Option 1 Option 2
e(l) 14 P Cone Deck/AC Ovly 8.29 63.27 100
e(2) 101 Unpnt Stl Box Girder 12.78 20.94 97
e(3) 106 Unpnt Stl Opn Girder 4.94 2.53 100
e(4) 210 R/Conc Pier Wall 28.66 2.94 100
e(5) 215 R/Conc Abutment 10.35 0.39 100
e(6) 234 R/Conc Cap 18.30 3.13 67
e(7) 305 Elastomeric Flex Jt 0.76 0.22 100
e(8) 314 Pot Bearing 4.47 0.61 34
e(9) 326 Bridge Wingwalls 0.06 0.02 100
e( 10) 331 Cone Bridge Railing 4.77 2.07 100
e(H) 333 Other Bridge Railing 3.01 1.34 100
e( 12) 334 Metal Rail Coated 2.46 1.67 94
e(13) 338 Cone Curbs/SW 1.15 0.86 100
BHI: IWPexHc 90.4 97.8
The weighting point was computed for each element based on Equation IV.2 for
option 1 and Equation IV.3 for option 2. For a comparison, observe that:
(1) The ratio of 28.66% to 0.06%, which reflects the difference between the
maximum weighting point and the minimum weighting point, is 478 for option 1.
The ratio of 63.27% to 0.02% for option 2 is 3164. In other words, these ratios
are on the order of 100 to 1000.
(2) Using option 2, the summation of weighting points for e(l) and e(2) is
84.21%, while the summation of weighting points from e(3) through e(13) is
15.79%. In other words, 2 of the elements end up accounting for 84% of the final
BHI. In contrast, 10 of the remaining elements account for less than 16% of the
final BHI.
(3) The weighting point is proportional to the element quantity and the element
33


cost. For example, a repair with a large cost will assign too much importance to
the weighting point, while it should be focused on safety.
(4) Using either option 1 or option 2, the weighting point is a numerical value
which is always a constant factor in any BHI calculation. What should happen is
that when an element condition becomes distressed and hence poorly functioning,
the weighting point should increase. In other words, its relative importance and
overall contribution to the BHI should be more pronounced.
(5) In this experimental calculation for Table IV. 1, the element health indexes
were calculated based on real 2006 inspection data. This calculation shows that
the EHI of e(6): R/Conc Cap is 67% and that of e(8): Pot Bearing is 34%. But the
BHIs calculated by the simplified formula of Equation IV. 1 are 90.4% using
option 1 and 97.8% using option 2. In other words, the overall high BHI number
hides the fact that low elements conditions exist.
The results of the BHI indicate that the 8th Avenue Viaduct bridge (D-03-V-150)
is in good health with ratings of 90.4% and 97.8%. The cause of the high rating is
entirely attributed to points (1) through (5) above. The potential effect of element value
on the BHI was already introduced in the second section of Chapter Ill-Problems in
Computing Methodology. The failure cost of option 1 and repair cost of option 2
multiplied by element quantity are both defined as element value. Therefore, using
Equations IV.2 and IV.3, the clement weighting point is the percentage for its element
value out of the total element value TEV of a bridge. It does not indicate the relative
importance of the EHI according to the effect of element damage on bridge health and
function.
34


Another option is to use a weight coefficient as the weighting factor and to
remove element quantity and hence remove cost from the computing formula of the
weighting point. The weight coefficient, termed option 3, represents the importance of
elements to bridge health and function. To develop the weight coefficients, many
meetings were held between University of Colorado Denver experts and CCD experts.
Each element was discussed based on all participants opinions. Eventually, the final
values of weight coefficients were determined as shown in Appendix A.
Equation IV.4 is termed the weight coefficient-based weighting point.
WPe ==^xl00%
LWe
e
Equation IV.4
Where
WPe is element weighting point, Yjwpe =100%,
we is element weight coefficient,
Equation IV.4 (Option 3) was applied to the 8th Avenue Viaduct bridge (D-03-V-
150) which is shown in Table IV.2.
35


Table IV.2 Weight coefficient-based element weighting point for 8th Avenue Viaduct
bridge (D-03-V-150)
Element Weighting point (%)
No. key description weight coefficient Option 3 EHI (%)
e(l) 14 P Cone Deck/AC Ovly 6 6.25 100
e(2) 101 Unpnt Stl Box Girder 12 12.50 97
e(3) 106 Unpnt Stl Opn Girder 12 12.50 100
e(4) 210 R/Conc Pier Wall 15 15.63 100
e(5) 215 R/Conc Abutment 12 12.50 100
e(6) 234 R/Conc Cap 15 15.63 67
e(7) 305 Elastomeric Flex Jt 7 7.29 100
e(8) 314 Pot Bearing 6 6.25 34
e(9) 326 Bridge Wingwalls 4 4.17 100
e(10) 331 Cone Bridge Railing 2 2.08 100
e(ll) 333 Other Bridge Railing 2 2.08 100
e( 12) 334 Metal Rail Coated 2 2.08 94
e( 13) 338 Cone Curbs/SW 1 1.04 100
BHI (%): XWPeXH, 90
Using this method, the element weighting point was calculated using the element
weight coefficient and was therefore independent of cost. But if the EHI in Table IV.2
are assigned to elements, the BHI result is still at 90%. This is misleading because the
individual EHI of reinforced concrete cap is 67% and that of pot bearing is 34% which is
severe impact to bridge health and function. The cost is removed but the overall BHI is
still arguably too high.
Conclusion
This section explored currently used Pontis calculation methods using the element
weighting point to calculate the BHI. The result of this analysis finds 3 main points:
1. In the Pontis BMS, the element weighting points using Equations IV.2 and IV.3
are based on element values (repair cost and failure cost).
2. The element weighting point using Equation IV.4 is based on the elements
36


importance to bridge health and function. Although an improvement, the concept
still misleads with a high BHI and low rated elements.
3. A further revised method must be developed using the theory that the element
weighting point should stress the effect of element damage on bridge health and
function.
The further revised method in this study is called the Denver Bridge Health Index
(DBHI) which will be introduced in Chapter V.
37


CHAPTER
V. DENVER BRIDGE HEALTH INDEX
As analyzed in Chapter IV, the Pontis element weighting point has deficiencies
and should stress the effect of element damage on bridge health and function. It was
demonstrated that a modification of the BHI was necessary. The key idea included in the
modification, from heretofore called the DBHI were emphasizing the effect of element:
(1) damage on EHI; (2) health index on BHI. Three important modifications are
proposed to the original Pontis formula (Jiang and Rens, 2010):
(1) In reference to option 3 discussed in chapter IV (Equation IV.4), element
quantity and cost were removed from the formula.
(2) The introduction of the nonlinear health index coefficient ksN.
(3) The introduction of the weight coefficient adjustment method.
In order to present the rationality of modifications, and to determine the
adjustment factor value, Condition Index (Cl) zones are introduced below.
Condition Index (Cl) Zones
A Condition index (Cl) is a numerical measure of the current state of a structure
from a low of 0% to a high of 100%. It uniformly and consistently describes and ranks
the condition of structure or structure components. The condition index is meant to focus
management attention on those structures most likely to warrant immediate repair or
further evaluation (Greimann et al., 1991). The condition index scale has been adopted
since 1989 and is listed in Table V.l.
38


Table V.l Condition index (Cl) scale
Value Condition description
85-100 Excellent-No noticeable defects, some aging or wear visible
70-84 Very good-Only minor deterioration or defects evident
55-69 Good-Some deterioration or defects evident, function not impaired
40-54 Fair-Moderate deterioration, function not seriously impaired.
^ Poor-Serious deterioration in at least some portion of structure,
function seriously impaired
10-24 Very poor-Extensive deterioration, barely functional
0-9 Failed-General failure or failure of a major component no longer functional
In addition, for management purposes, the Cl scale is calibrated in order to group
structures into 3 basic zones as listed in Table V.2.
Table V.2 Condition index (Cl) zones
Zone Cl Range (%) Action
1 71-100 Immediate action not required
2 41-70 Economic analysis of repair alternatives recommended to determine appropriate maintenance action
3 0-40 Detailed evaluation required to determine the need for Repair, rehabilitation or reconstruction, safety evaluation recommended.
As the Cl zones in Table V.2 indicated, the purpose of the Cl zones is to draw
attention to a particular problem that may require further investigation. Therefore, in the
study of following sections, Cl zones are used to group element conditions, based on
element health index. They are also used to group overall bridge conditions, based on
DBHI.
39


Nonlinear Health Index Coefficient ksN
According to Pontis theory (AASHTO, 2003), the EHI is the ratio of the sum of
the current quantities in each CS multiplied by corresponding coefficients, over the initial
total quantity of the element. It was presented in Chapter II by Equation 11.2 in which ks
is the health index coefficient corresponding to the sth CS. The health index coefficients
for the CSs ks are fractional values calculated by Equation V. 1:
k. =
n-s
n -1
Equation V.l
Where
ks is the health index coefficient for the sth condition state,
n is the number of applicable condition states ( n=3, 4, and 5),
s is the index of the condition state (s =1, 2,..., n).
Table V.3 gives the health index coefficients which are according to EquationV.l.
Table V.3 Linear health index coefficients ks
Number of CSs CS1 CS2 CS3 CS4 CS5
3 1.00 0.50 0.00
4 1.00 0.67 0.33 0.00
5 1.00 0.75 0.50 0.25 0.00
Table V.3 can be illustrated with Figure V.l.
40


Sth condition State
Figure V.l Trend of health index coefficient of CSs.
Shown is the linear health index coefficient for n=5, n=4, and n=3 (n represents the number of CSs).
As shown in Figure V.l, the health index coefficients are linear values when n is
equal to 3,4, or 5 depending upon the type of the CoRe element.
Based on linear ks, the EHI from 2000 to 2006 were computed for the 8th Avenue
viaduct bridge (D-03-V-150) as shown in Table V.4.
41


Table V.4 EHI based on linear ks for 8th Avenue Viaduct bridge (D-03-V-150)
No. Element key Element description 2000 EHI (%) 2002 2004 2006
e(l) 14 P Cone Deck/AC Ovly 100 100 100 100
e(2) 101 Unpnt Stl Box Girder 100 100 100 97
e(3) 106 Unpnt Stl Opn Girder 100 100 100 100
e(4) 210 R/Conc Pier Wall 100 100 100 100
e(5) 215 R/Conc Abutment 100 100 100 100
e(6) 234 R/Conc Cap 100 100 67 67
e(7) 305 Elastomeric Flex Jt 95 100 100 100
e(8) 314 Pot Bearing 100 34 34 34
e(9) 326 Bridge Wingwalls 100 100 100 100
e(10) 331 Cone Bridge Railing 100 100 100 100
e(l 1) 333 Other Bridge Railing 100 100 100 100
e(12) 334 Metal Rail Coated 94 94 94 94
e( 13) 338 Cone Curbs/SW 100 100 100 100
As shown in Table V.4, the EHI of e(6): R/Conc Cap changes from 100% in 2000
to 67% in 2006 based on linear ks. Acorrding to Table V.2, 67% is ranked in Cl zone 2.
Element condition in Cl zone 2 should accords with the action Economic analysis of
repair alternatives recommended to determine appropriate maintenance action".
However, the actual element damage of e(6): R/Conc Cap was severe. As described in
Chapter III, 8th Avenue Viaduct bridge has served 26 years and repair is probably
warranted due to the numerous cracks in the pier cap supports as shown in Figure III.2.
Therefore, the element condition of e(6): R/Conc Cap should be ranked in Cl zone 3
corresponding to the action "Detailed evaluation required".
As analyzed above, the EHI based on linear ks is not rational. In other words, in
order to make the EHI more conservative, nonlinear health index coefficient (ksN) lines
are presented in Figure V.2.
42


1
2 3 4
Sth condition State
Figure V.2 Comparison of trends of linear and nonlinear health index coefficient of
CSs.
represents linear ks; represents nonlinear ksN. (n represents number of CSs).
Figure V.2 shows the comparison between 3 linear ks lines and 3 nonlinear k,N
lines. In either linear coefficient lines or nonlinear coefficient lines, the trends of the
health index coefficients descend with the increasing CSs. These descending trends
result in gradually reducing of the EH I, and finally result in gradually reducing of BHI
with the increasing element deterioration. However, compared to the linear ks lines, the
nonlinear ksN lines are located at the lower positions. In other words, except for the first
point and the last points in each line, each point in the nonlinear ksN lines is lower than its
corresponding point in the linear ks lines. For example (n=5), k2, k3, and Iq are 0.75, 0.5,
and 0.25 respectively, by contrast, k2N, k3N, and k/1 are 0.6, 0.3, and 0.1 respectively.
Compared to the linear descending trend, these nonlinear descending trends result in
more greatly reducing of EHI and finally result in more greatly reducing of BHI with the
43


increasing element deterioration. In another words, using nonlinear ksN, the BHI
calculation result will be more conservative.
Table V.5 gives the nonlinear ksN value corresponding to the Figure V.2.
Table V.5 Nonlinear health index coefficients ksN
Number ofCSs CS1 CS2 CS3 CS4 CS5
3 1.00 0.20 0.00
4 1.00 0.40 0.10 0.00
5 1.00 0.60 0.30 0.10 0.00
Based on nonlinear ksN, the EH I from 2000 to 2006 were computed for the 8th Avenue
viaduct bridge (D-03-V-150) as shown in Table V.6.
Table V.6 EHI based on nonlinear ksN for 8th Avenue Viaduct bridge (D-03-V-150)
No. Element key Element description 2000 EHI (%) 2002 2004 2006
e(l) 14 P Cone Deck/AC Ovly 100 100 100 100
e(2) 101 Unpnt Stl Box Girder 100 100 100 94
e(3) 106 Unpnt Stl Opn Girder 100 100 100 100
e(4) 210 R/Conc Pier Wall 100 100 100 100
e(5) 215 R/Conc Abutment 100 100 100 100
e(6) 234 R/Conc Cap 100 100 40 40
e(7) 305 Elastomeric Flex Jt 92 100 100 100
e(8) 314 Pot Bearing 100 32 32 32
e(9) 326 Bridge Wingwalls 100 100 100 100
e( 10) 331 Cone Bridge Railing 100 100 100 100
e(l 1) 333 Other Bridge Railing 100 100 100 100
e( 12) 334 Metal Rail Coated 91 91 91 91
e(13) 338 Cone Curbs/SW 100 100 100 100
Compared to Table V.4, Table V.6 shows the EHI arc reduced when the nonlinear
ksN is used. The EHI of e(6): R/Conc Cap changes from 100% in 2000 to 67% in 2006
based on linear ks. However, based on nonlinear ksN, this decrease trend changes from
100% in 2000 to 40% in 2006. As analysis for Table V.4, the actual element damage of
e(6): R/Conc Cap was severe, therefore this element condition should be ranked in Cl
44


zone 3. The EHI 40% based on nonlinear ksN is right ranked in Cl zone 3 according to Cl
zones category. The e(6): R/Conc Cap accords with the action Detailed evaluation
required to determine the needfor Repair, rehabilitation or reconstruction, safety
evaluation Recommended. Therefore, the EHI based on nonlinear ksN is much more
conservative than that based on linear ks.
Weight Coefficient Adjustment Method
The weight coefficient was introduced to further define the effect of the individual
element on the overall bridge structure. It also reflected the relative importance of
various elements. For example, railings and curbs had less impact on the overall bridge
condition when compared to the effect of primary structural elements such as beams.
Therefore, the proposed weight coefficients assign more value to more significant
structure elements. Relative initial weight coefficients of the 8th Avenue Viaduct bridge
elements (D-03-V-150) are listed in Table V.7. The table shows that the reinforced
concrete pier wall and the cap are the most important, and that the concrete curbs and
sidewalks are the least important. The normalized weight coefficients are defined by
Equation V.2 and are listed in Table V.7.
we(%) = =^xl00%
e
Equation V.2
Where
we is element weight coefficient.
45


Table V.7 Unadjusted weight coefficients for 8th Avenue Viaduct bridge (D-03-V-
150)
No. Element key Element description EHI (%) We we (%)
e(l) 14 P Cone Deck/AC Ovly 100 6 6
e(2) 101 Unpnt Stl Box Girder 94 12 13
e(3) 106 Unpnt Stl Opn Girder 100 12 13
e(4) 210 R/Conc Pier Wall 100 15 16
e(5) 215 R/Conc Abutment 100 12 13
e(6) 234 R/Conc Cap 40 15 16
e(7) 305 Elastomeric Flex Jt 100 7 7
e(8) 314 Pot Bearing 32 6 6
e(9) 326 Bridge Wingwalls 100 4 4
e( 10) 331 Cone Bridge Railing 100 2 2
c(ll) 333 Other Bridge Railing 100 2 2
e( 12) 334 Metal Rail Coated 91 2 2
e( 13) 338 Cone Curbs/SW 100 1 1
I 100
Deterioration correlates with a decrease in EH I, and finally results in a decrease in
the overall BHI. Distresses of various elements at a specific level now take different
effects on the overall BHI because of the individual element weight coefficients.
Furthermore, distresses of a specific element at various levels also have different effects
on the overall BHI. Greimann et al. (1991) developed condition assessment procedures
for various components making up lock and dam structures as part of the Repair,
Evaluation, Maintenance, and Rehabilitation Program for the United States Army Corps
of Engineers. As part of this work, it became clear that, as the distress of an individual
element became more severe, its relative importance to the overall condition of the
structure became larger (Greimann et al., 1991). To account for this, the weight
coefficients were adjusted or amplified with variable adjustment factors. Similarly, this
variable adjustment factor was introduced to the DBHI to increase the weight coefficient
as its EHI decreases. Figure V.3 illustrates adjustment factor versus EH1 relationship.
46


The adjustment factor has a maximum value of eight, that is if an element has an EHI less
than 40%, its importance increases eight times. Adjusted element weight coefficients of
the 8th Avenue Viaduct bridge (D-03-V-150) and its normalized form are listed in Table
V.8. Table V.8 shows that the weight coefficients of element e(6) and e(8) which have
low EHI (40% and 32%) are increased eight times. This illustrates that as these
individual elements conditions decrease, the relative importance of element e(6) and e(8)
and their effect on the overall structure condition are increased.
10
9
u
IQ
c
V
E
4->
in
3
<
0 10 20 30 40 50 60 70 80 90 100
Element Health Index(%)
Figure V.3 A linear step curve for calculating adjustment factor in weight coefficient
adjustment method.
47


Table V.8 Weight coefficient adjustment method for 8,h Avenue Viaduct bridge (D-
03-V-150)
No. Element key Element description EHI (%) AF we WcaJ We" (%)
e(D 14 P Cone Deck/AC Ovly 100 1 6 6 2
e(2) 101 Unpnt Stl Box Girder 94 1 12 12 5
e(3) 106 Unpnt Stl Opn Girder 100 1 12 12 5
e(4) 210 R/Conc Pier Wall 100 1 15 15 6
e(5) 215 R/Conc Abutment 100 1 12 12 5
e(6) 234 R/Conc Cap 40 8 15 120 49
e(7) 305 Elastomeric Flex Jt 100 1 7 7 3
e(8) 314 Pot Bearing 32 8 6 48 20
e(9) 326 Bridge Wingwalls 100 1 4 4 2
e( 10) 331 Cone Bridge Railing 100 1 2 2 1
e(l 1) 333 Other Bridge Railing 100 1 2 2 1
e( 12) 334 Metal Rail Coated 91 1 2 2 1
c( 13) 338 Cone Curbs/SW 100 1 1 1 0
I ________100
Denver Bridge Health Index
The DBHI is the accumulation of weighted individual EHI and is given by
Equations V.3 through V.5.
//,=-*=------x 100%
S
Equation V.3
Where
He is the element health index,
5 is the index of the condition state,
qs is the quantity of the element in the s,h condition state,
ksN is the nonlinear health index coefficient corresponding to the sh condition
state.
48


< = we A F
Equation V.4
Where
w/7 is the adjusted weight coefficient,
we is the weight coefficient,
AFe is the adjustment factor.
y h waj
DBHl = -4= x 100%
Equation V.5
Where
DBHI is the Denver Bridge Health Index.
Tables V.9 through V.l 1 present the application of the DBHI
Avenue Viaduct bridge (D-03-V-150). Using Equation V.5, the final
y Hwa>
^ 137 46
DBHI = x 100% =---------x 100% 56.6%

243
formulas to the 8th
BHI calculation is:
Compared to 90.4% of the failure cost-based BHI and 97.8% of the repair cost-
based BHI, the DBHI 56.6% is much more in line with the known element defects of 8th
Avenue Viaduct bridge (D-03-V-150). It is unreasonable that the Pontis BHI for this
bridge is in the highest BHI level 90%-100%. That is because according to the Cl zones
category, 90.4% and 97.8% are ranked in Cl zone 1 corresponding to the action
Immediate action not required'. However, as described in Chapter III, this bridge has
served 26 years. Repair is probably warranted due to the numerous cracks in the pier cap
49


supports, buckles of the webs, broken bearing guides, and the corrosion at the pot
bearings as were shown in Figures III.2 through III.4. Therefore, the condition state of
this bridge should not be ranked in Cl zone 1. Pontis BHIs, 90.4% and 97.8%, cannot
give engineers any warning of individual element defect. Oppositely, the DBHI for this
bridge, 56.6%, is ranked in Cl zone 2 corresponding to the action Economic analysis of
repair alternatives recommended to determine appropriate maintenance action, So, the
DBHI of 56.6% causes a flag to be raised so that the engineer can look into the reason of
low number.
Table V.9 Element distribution for the 8lh Avenue Viaduct bridge (D-03-V-150)
Element Element inspection data (%)
No. key description unit quantity 9i 92 93 94 9s EH1 (%)
e(l) 14 P Cone Deck/AC Ovly SF 95749 100 0 0 0 0 100
e(2) 101 Unpnt Stl Box Girder LF 4739.99 90 10 0 0 94
e(3) 106 Unpnt Stl Opn Girder LF 579 100 0 0 0 100
e(4) 210 R/Conc Pier Wall LF 540 100 0 0 0 100
e(5) 215 R/Conc Abutment LF 90 100 0 0 0 100
e(6) 234 R/Conc Cap LF 575 0 100 0 0 40
e(7) 305 Elastomeric Flex Jt LF 90 100 0 0 100
e(8) 314 Pot Bearing EA 86 31 5 64 32
e(9) 326 Bridge Wingwalls EA 4 100 0 0 100
e(10) 331 Cone Bridge Railing LF 2870 100 0 0 0 100
e(l 1) 333 Other Bridge Railing LF 1870 100 0 0 100
e(12) 334 Metal Rail Coated LF 2370 88 0 12 0 0 91
e( 13) 338 Cone Curbs/SW LF 2370 100 0 0 0 100
qi through q5 are element quantities in CS1 through CS5.
50


Table V.10 Adjusted weight coefficients for 8th Avenue Viaduct bridge (D-03-V-150)
No. Element key Element description EH1 (%) AF we weaj
e(l) 14 P Cone Deck/AC Ovly 100 1 6 6
e(2) 101 Unpnt Stl Box Girder 94 1 12 12
e(3) 106 Unpnt Stl Opn Girder 100 1 12 12
e(4) 210 R/Conc Pier Wall 100 1 15 15
e(5) 215 R/Conc Abutment 100 1 12 12
e(6) 234 R/Conc Cap 40 8 15 120
e(7) 305 Elastomeric Flex Jt 100 1 7 7
e(8) 314 Pot Bearing 32 8 6 48
e(9) 326 Bridge Wingwalls 100 1 4 4
e( 10) 331 Cone Bridge Railing 100 1 2 2
e(ll) 333 Other Bridge Railing 100 1 2 2
e( 12) 334 Metal Rail Coated 91 1 2 2
e(13) 338 Cone Curbs/SW 100 1 1 1
Table V.ll Calculation of DBHI for the 8th Avenue Vi
No. Element key Element description EH I (%) Calculation Ht wcaj
e(l) 14 P Cone Deck/AC Ovly 100 6 6
e(2) 101 Unpnt Stl Box Girder 94 12 11.28
e(3) 106 Unpnt Stl Opn Girder 100 12 12
e(4) 210 R/Conc Pier Wall 100 15 15
e(5) 215 R/Conc Abutment 100 12 12
e(6) 234 R/Conc Cap 40 120 48
e(7) 305 Elastomeric Flex Jt 100 7 7
e(8) 314 Pot Bearing 32 48 15.36
e(9) 326 Bridge Wingwalls 100 4 4
e( 10) 331 Cone Bridge Railing 100 2 2
e(l 1) 333 Other Bridge Railing 100 2 2
e(12) 334 Metal Rail Coated 91 2 1.82
e(13) 338 Cone Curbs/SW 100 1 1
I 243 137.46
Equation V.5 was applied to 162 major CCD bridges which have complete
inspection data from 2000 to 2006. The results are shown in Appendix C. Table V.12
shows the DBHI for previous 10 major sample bridges from 2000 to 2006, using
Equation V.5.
51


Table V.12 DBHI for 10 major sample bridges
Bridge key DBHI (%)
2000 2002 2004 2006
D-01-CC-014 99.635 71.745 71.745 65.528
D-01-CC-017 100.000 100.000 52.020 52.020
D-01-CC-019 100.000 98.406 51.661 51.658
D-03-V-046 91.429 90.103 62.221 61.982
D-03-V-090 90.400 84.710 56.697 56.589
D-03-V-150 99.237 76.336 56.930 56.636
D-04-BOST-151 99.864 99.175 98.428 62.632
D-31-PB-410 84.262 84.352 65.817 59.160
D-31-PB-650 86.849 86.700 55.035 55.035
D-31-PB-690 95.000 95.000 78.947 78.947
As introduced in Chapter II, 10 bridges were selected to be shown in Table II.4.
This is because their BHIs from 2000 to 2006 are all between 90% and 100% and have
extremely minimal decrease with age despite the fact that they all had severe element
damage. Therefore, the condition states of these 10 bridges should not be consistently
ranked in Cl zone 1. Compared to Table 11.4, Table V.12 shows that the BHIs of these 10
bridges have obvious descending with increasing age. In addition, the bridge conditions
in 2006 are mostly ranked in Cl zone 2.
The 2006 data in Table V.12 can be expanded to include the entire 615 CCD
bridges network as illustrated in Figure V.4.
52


100
Bridge Distribution
90-
l-
90-100 80-89 70-79 60-69 50-59 40-49 30-39 20-29 10-19 0-9
Bridge Health Index
Figure V.4 Distribution of the entire 615 CCD bridges in 2006 based on DBHI
As shown in Figure V.4, a new bridge network distribution is presented.
Compared to the bridge distributions shown in Figure II. 1, DBHI reasonably distributes
182 bridges previously ranged in the 90%-100% interval to the levels under 90%.
Similarly, compared to Figure II.4, 138 bridges were redistributed to the level under 90%.
These redistributed bridges actually have various extents of element damage according to
real element inspection data.
Figures V.5 and V.6 show the distributions for 308 major CCD bridges and 307
minor CCD bridges in 2006 based on DBHI.
53


100
Bridge Distribution
90-
C? 80-
1I1
90-100 80-89 70-79 60-69 50-59 4049 3039 2029 1019 09
Bridge Health Index
Figure V.5 Distribution of 308 major CCD bridges in 2006 based on DBHI
100-,
Bridge Distribution
90-
$>
*C
A
1
8
&
S
c
§
£
80-
90100 8089 7079 6069 5059 4049 3039 2029 1019 09
Bridge Health Index
Figure V.6 Distribution of 307 minor CCD bridges in 2006 based on DBHI
54


Comparison between Pontis BHI and DBHI
To illustrate the advantages of the DBHI, the comparison of the entire 615 CCD
bridges distributions utilizing failure cost-based BHI, repair cost-based BHI, and DBHI is
shown in Figure V.7.
100-1
Bridge Distribution
4>
O)
o
re
O
0
v
CD
re
c
U
L.
Q>
0.
Failure cost-baesd BHI
Repair cost-based BHI
EOT DBHI
2 3
ffl r
ft
90-100 80-89 70-79 60-69 50-59 40-49 30-39 20-29 10-19
Bridge Health Index
11 t
1 'T~
0-9
Figure V.7 Distribution of the entire 615 CCD bridges in 2006 based on failure cost-
based BHI, repair cost-based BHI, and DBHI.
Figure V.7 displays bridge distributions in each BHI interval level. In the BHI
level 90%-100%, comparing 545 bridges (88.6%) for the failure cost-based BHI to 363
bridges (59%) for DBHI, the difference is 182 bridges (29.6%). Similarly, comparing
501 bridges (81.4%) for the repair cost-based BHI to 363 bridges (59%) for DBHI, the
difference is 138 bridges (22.4%). Obviously, either 182 bridges or 138 bridges have
various extents of element damage and are ranged in the actual BHI levels below 90% by
DBHI.
55


Another comparison of the BHI trends related to the age of bridge using failure
cost-based BHI, repair cost-based BHI, and DBHI is shown in Figure V.8.
Figure V.8 Trend of BHI related to the age of bridge.
Three lines in this figure respectively represent the trends of BHI using three BHI methods. For each BHI
method, each point in the line represents the average of BHIs for those bridges whose ages are ranged to
relevant 10 years interval.
Generally speaking, bridge health and function deteriorate with bridge age.
Referring to Figure V.8, three lines representing the BHI related to the bridge age
correctly present this deterioration trend. However, compared to the upper two lines
representing failure cost-based BHI and repair cost-based BHI, the line representing the
DBHI is more steep. In other words, the deterioration rate of the DBHI decreases faster
than the failure cost-based BHI and the repair cost-based BHI. Heam (1996) stated the
bridge deterioration process accelerates rapidly with increasing age, and in a short
period of time the deterioration growth correlates with a rapid decrease in bridge health
56


condition The steep slope of the DBHI greatly accords with this fact. The DBHI can
alert engineers of potential bridge health and function problems at an earlier deterioration
stage.
57


CHAPTER
VI. ISSUE
An increasing number of agencies are utilizing the BHI based on element level
inspection data. The Pontis user group was surveyed to determine the current use of the
BHI for bridge management decision making. The survey results revealed that the BHI
or a modified BHI is being used to predict the condition of a specific structure and for
prioritizing projects at the network level (Kang and Adams, 2010). The CCD has
successfully developed the DBHI to track bridge health condition as presented in
Chapters I through V. As a result, it is being used as a basis for resource allocation and
maintenance, repair, and replacement (MR&R) decision support.
Kang and Adams (2010) state that There are no standards or guidelines for
decision making based on the BHI. Since the BHI is relatively new, andfamiliarity with
it is still growing, there is limited experience among agencies for using it. Although the
DBHI is providing valuable analysis and timely alert notices of bridge health condition
for CCD engineers, it was still in the process of improvements in its MR&R decision
support. CCD engineers are of the opinion that DBHI may have a potential sensitivity
issue due to uncertainties and variabilities inherent in element weight coefficients.
However, this author is of the opinion that some deviations exist between the estimated
nonlinear ksand the theoretical actual health index coefficients and this consequently is
causing the sensitivity issue.
The second stage of this study is introduced in Chapters VI through VIII in this
dissertation. It is based on the 2010 CCD bridge network, which has 490 major bridges
and 372 minor bridges. There are three goals in the second stage of this study:
58


(1) Present the sensitivity issue in the DBHI based-MR&R decision support and
analyze the reason of the sensitivity issue of ksN.
(2) Develop a methodology of determining the improved ks.
(3) Implement methodology and determine the improved ks, which is named
ksJ&R
Finally, the CCD bridge condition distribution will be presented based on the DBHI and
using the improved ks.
Background Knowledge
Element Classification
When the DBHI of a bridge is low, this raises a safety flag for engineers, and
warns them to pay attention to specific elements of the bridge needing maintenance. As a
result, it is necessary to first again review the bridge elements.
As shown in Table VI. 1, all 144 CoRe elements in Appendix A can be divided
into three element categories based on the number of CSs. All elements under each
category are grouped into different parts of a bridge structure. The average we of all
elements under each element category is also listed in Table VI. 1. In this dissertation,
MR&R activities will be restricted within these defined categories which will be further
explained later.
Table VI.1 Classification of 144 CoRe elements
Element category CS count Number of elements Elements grouped by parts Average we
1 5 40 Deck(23), superstructure! 10), substructure^), miscellaneous^), smartflags(2), general remarks! 1) 9.6
11 4 68 Deck(4), superstructure^), substructure! 19), culverts(4), miscellaneous! 13), smartflags(3) 10.68
III 3 36 Miscellaneous(22), smartflags(8), channel/roadway alignment(6) 3.44
59


An analysis of Table VI. 1 reveals the following trends:
1. From a structural component point of view, all deck, superstructure, and
substructure elements are included in Category I with 5 CSs and in Category II
with 4 CSs.
2. Looking at the element categories, all elements included in Category III with 3
CSs are miscellaneous elements (such as wingwall, railing, etc.), smart flag
elements (like scour, settlement, etc.), and channel/roadway alignment elements.
3. From the perspective of element importance, the average we of elements
included in category 1 with 5 CSs and category II with 4 CSs are respectively 9.6
and 10.68. The average we of elements included in category III with 3 CSs is
3.44.
Therefore, one can conclude that elements with 4 or 5 CSs are associated with structural
related condition states, and consequently elements with 3 CSs are associated with non-
structural condition states.
Dynamic Calculation Report (DCR)
In order to utilize the DBHI to help aid with element MR&R decision making, the
DCR was developed as shown in Figure VI. 1. The DCR utilizes DBHI methodology.
The user can modify or change the element quantity distribution to simulate element
MR&R activities, thus it is dynamic. Two output functions of the DCR include the
current DBHI and the DBHI under element MR&R activities (DBHIMR&R) for single or
multiple elements. DCR implementation includes the following steps:
(1) The user can choose the Bridge Key and select the bridge.
(2) All element information and element inspection data of the chosen bridge are
60


displayed in the report. The EHI and DBHI are automatically calculated.
(3) After completing steps 1 and 2, the user can input the new element quantity
distribution in the CS area. The EHI under the element MR&R (EHIMR&R)
activities and the resulting DBHIMR&R are automatically calculated.
Figure VI. 1 shows the DCR for bridge D-02-PR-057 as an example. The
information on the 10 elements associated with this bridge and the element inspection
data are displayed in the report.
Minor CCD Bridee: D-02 -PR-057

ID Element Key Description Quantity (%) EHI EHI*0***
CS! CS2 CS3 CS4 CS5
*0) 30 Conug Orthotpc Deck 100 0 0 0 0 100*/.
C) 121 PStl Thru TrussBot 96 4 0 0 0 .1 98%
*3) 126 PStl Thru TrussTop 0 100 100 60*/. 100%
e(4) 132 Paint Stl Floor Beam 96 4 000 98/.
*5) 215 R Cone Abutment 100 100"/.
e(6) 304 Open Expansion Joint 100 0 0 100%
e(7) 311 Moveable Bearing 100 0 0 100*/.
<8) 321 RConc Approach Slab too 0 0 0 100%
*9) 326 Bridge Wmgwalls 100 0 0 100%
*10) 334 Metal Rail Coated 100 TOafiK 0 000 100/.
- - -
- - -
- - AT -
- - -
- - -
DBHI 81.8V. DBHI^ 99.4%
Figure VI.1 Dynamic Calculation Report
The 10 individual EHI and the DBHI of 81.8% are automatically calculated. The MR&R
activity is chosen for e(3) (elementMR&R) which is 100% in CS2. The repair activity,
61


shown in the grey area, is such that 100% of element quantity improves to CS1. This
means that e(3) is assumed to be repaired, and consequently the individual EHIMR&R
becomes 100%. As a result, the DBHIMR&R improves to 99.4%.
The DCR enables engineers to observe the consequence of element MR&R
activity and its improvement to the DBHI. One can also observe which element MR&R
activity most effectively improves the DBHI. This numerical calculation result is one of
the tools for element MR&R decision making.
Issue
After the DCR was applied to many individual CCD bridges and to the CCD
major and minor bridge networks, an issue arose. The DBHIMR&R was more sensitive to
the elements with 3 CSs which are arguably relatively less important (ie: non-structural).
This will be demonstrated in the next section where the DCR numerical calculation
results for the three sample bridges and major and minor bridge networks are presented
and discussed to demonstrate the sensitivity.
Sample Bridges
Table VI.2 shows the element information and inspection data of bridge D-20-
MB-785. In Table VI.3, the EHI are calculated based on 2010 element inspection data.
In this example, e(5) bridge railing, is the only element with MR&R issues. The EHI
and EHImr&r of e(5) are 15.20% and 100% respectively, and consequently the DBHI is
76% and the DBHIMR&R is 100%. The DBHI of 76% is entirely the result from the
single element damage of e(5): bridge railing. A concern is whether the EHI is too
sensitive to non-structural elements such as bridge railing. This will be explored with
sample bridges with multiple MR&R scenarios next.
62


Table VI.2 The 2008 element inspection data for the sample bridge D-20-MB-785
(Location: 56th Ave. & W. Havana)
Element inspection data (%)
No. Element key Element description CS count Unit Total quantity 4i 42 43 44 45
e(l) 40 P Cone Slab/AC Ovly 5 SF 362.32 100 0 0 0 0
e(2) 338 Cone Curbs/SW 4 LF 31.70 100 0 0 0
e(3) 321 R/Conc Approach Slab 4 EA 2.00 100 0 0 0
e(4) 215 R/Conc Abutment 4 LF 45.72 100 0 0 0
e(5) 333 Other Bridge Railing 3 LF 31.70 0 76 24
e(6) 326 Bridge Wingwalls 3 EA 4.00 100 0 0
e(7) 300 Strip Seal Exp Joint 3 LF 45.72 100 0 0
qi through q5 are element quantities in CS1 through CS5.
Table VI.3 The numerical calculation result for the sample bridge D-20-MB-785
No. Element key Element description CS count we EHI (%) EHIMRiR (%) Option 1
e(l) 40 P Cone Slab/AC Ovly 5 14 100.00 100.00
e(2) 338 Cone Curbs/SW 4 1 100.00 100.00
e(3) 321 R/Conc Approach Slab 4 2 100.00 100.00
e(4) 215 R/Conc Abutment 4 12 100.00 100.00
e(5) 333 Other Bridge Railing 3 2 15.20 100.00
e(6) 326 Bridge Wingwalls 3 4 100.00 100.00
e(7) 300 Strip Seal Exp Joint 3 7 100.00 100.00
DBHI / DBHImr&r: 76% 100%
The first sample bridge (D-20-MB-785) had only one element MR&R option
because only one element was damaged. A comparison is now made for a bridge with
two possible element MR&R options as shown in Table VI.4 and VI.5. The element
MR&R option scenarios are limited to categories in this dissertation in order to compare
the sensitivity level of each element category to the DBHI. Element categories were
previously defined and discussed in Table VI. 1. The element information and inspection
data of the second sample bridge D-03-V-180 is shown in Table VI.4. The EHI are
calculated based on element inspection data. The resulting DBHI is 69%. Two element
MR&R options are considered: option 1 is to repair e(l): concrete deck and e(2): steel
open girder, which have 5 CSs with an average we of 9.5; Option 2 is to repair e(9):
63


bridge wingwalls which has 3 CSs and an average we of 4. The DBHIMR&R of option 1
and option 2 are 74% and 86%, respectively. The results indicate that the DBHI is more
sensitive again to the elementMR&R with 3 CSs which are not as important from the
structural perspective.
Table VI.4 The 2008 element inspection data for the sample bridge D-03-V-180
(Location: Evans over Santa Fe)
Element inspection data (%)
No. Element key Element description CS count Unit Total quantity qi q: Or q- qs
e(l) 13 Unp Cone Deck/AC Ovl 5 SF 5622.59 0 100 0 0 0
e(2) 107 Paint Stl Opn Girder 5 LF 2812.69 82 1 15 2 0
e(3) 338 Cone Curbs/SW 4 LF 592.53 100 0 0 0
e(4) 321 R/Conc Approach Slab 4 EA 2.00 100 0 0 0
e(5) 215 R/Conc Abutment 4 LF 48.77 93 7 0 0
e(6) 234 R/Conc Cap 4 LF 195.07 94 4 2 0
e(7) 205 R/Conc Column 4 EA 40.00 97 3 0 0
e(8) 333 Other Bridge Railing 3 LF 385.27 99 0 1
e(9) 326 Bridge Wingwalls 3 EA 4.00 0 100 0
e(10) 310 Elastomeric Bearing 3 EA 144.00 67 33 0
e(l 1) 300 Strip Seal Exp Joint 3 LF 97.54 97 3 0
q, through q5 are element quantities in CS1 through CS5.
Table VI.5 The numerical calculation result for the sample bridge D-03-V-180
We EH1 (%) EHIMRiR (%)
No. Element key Element description CS count x, Xt y> yi Option 1 Option 2
e(l) 13 Unp Cone Deck/AC Ovl 5 ,> :!I 100.00 60.00
e(2) 107 Paint Stl Opn Girder 5 100.00 87.60
e(3) 338 Cone Curbs/SW 4 1 100.00 100.00 100.00
e(4) 321 R/Conc Approach Slab 4 2 100.00 100.00 100.00
e(5) 215 R/Conc Abutment 4 12 95.87 95.87 95.87
e(6) 234 R/Conc Cap 4 15 96.02 96.02 96.02
e(7) 205 R/Conc Column 4 16 98.50 98.50 98.50
e(8) 333 Other Bridge Railing 3 2 99.45 99.45 99.45
e(9) 326 Bridge Wingwalls 3 4 4 20.00 20.00 20.00 100.00
e( 10) 310 Elastomeric Bearing 3 6 73.33 73.33 73.33
e(l 1) 300 Strip Seal Exp Joint 3 7 97.19 97.19 97.19
DBHI/DBHIMR&R: 69% 74% 86%
64


For the second example, engineers may erroneously conclude that the damage
condition of elementsMR&R with 5 CSs of option 1 is less serious than that of the
elementMR&R with 3 CSs of option 2.
The third sample bridge (F-16-DW) provides three element MR&R scenarios, of
which the elementsMR&R are all under the condition of serious damage. Again, the
element MR&R option scenarios are limited to categories in order to compare the
sensitivity level of each element category to the DBHI. Table VI.6 presents the element
information and inspection data of sample bridge F-16-DW. The EHI are calculated in
Table VI.7 based on element inspection data. The DBHI is 38%. Consider three element
MR&R options: option 1 is to repair e(4): steel cap and e(5): steel pin/hanger, which each
has 5 CSs and an average we of 17.5; Option 2 is to repair e(9): reinforced abutment and
e( 10): reinforced column, which each have 4 CSs and an average we of 14; Option 3 is to
repair the two elements with 3 CSs and an average we of 6.5, which are e(12): bearing
and e( 13): expansion joint. The DBHIMR&R of option 1, option 2, and option 3 are 42%,
42%, and 43%, respectively. In other words, the sensitivity level of DBHIMR&R for the
non structural elementsMR&R with 3 CSs of option 3 is approximately equivalent to that
for the structural elementsMR&R with 4CSs of option 2 and 5CSs of option 1. Again, this
implies that the non-structural elements have equal or greater effect to MR&R activities.
65


Table VI.6 The 2006 element inspection data for the sample bridge F-16-DW
(Location: 125 ML SBND)
Element inspection data (%)
No. Element key Element description CS count Unit Total quantity 9i 92 93 94 9s
e(l) 334 Metal Rail Coated 5 LF 147.52 0 0 0 98 2
e(2) 13 Unp Cone Deck/AC Ovl 5 SF 1324.87 0 100 0 0 0
e(3) 107 Paint Stl Opn Girder 5 LF 429.77 0 66 33 1 0
e(4) 231 Paint Stl Cap 5 LF 69.49 0 11 67 22 0
e(5) 161 Paint Stl Pin/Hanger 5 EA 35.00 0 97 0 3 0
e(6) 338 Cone Curbs/SW 4 LF 147.52 100 0 0 0
e(7) 331 Cone Bridge Railing 4 LF 147.52 100 0 0 0
e(8) 321 R/Conc Approach Slab 4 EA 2.00 100 0 0 0
e(9) 215 R/Conc Abutment 4 LF 41.45 0 60 40 0
e( 10) 205 R/Conc Column 4 EA 3.00 67 0 0 33
e(l 1) 326 Bridge Wingwalls 3 EA 4.00 75 25 0
e( 12) 311 Moveable Bearing 3 EA 14.00 0 100 0
e(13) 304 Open Expansion Joint 3 LF 39.62 31 50 19
e( 14) 308 Constr Non Exp Jt 3 LF 56.69 0 100 0
q, through q5 are element quantities in CS1 through CS5.
Table VI.7 The numerical calculation result for the sample bridge F-16-DW
wc EH I (%) EH]mr&r (%)
No. Element key Element description CS count Xi X, y> yt Option 1 Option 2 Option 3
e(l) 334 Metal Rail Coated 5 2 9.79 9.79 9.79 9.79
e(2) 13 Unp Cone Deck/AC Ovl 5 7 60.00 60.00 60.00 60.00
e(3) 107 Paint Stl Opn Girder 5 12 49.46 49.46 49.46 49.46
e(4) 231 Paint Stl Cap 5 > 100.00 28.92 28.92
e(5) 161 Paint Stl Pin/Hanger 5 100.00 58.55 58.55
e(6) 338 Cone Curbs/SW 4 1 100.00 100.00 100.00 100.00
e(7) 331 Cone Bridge Railing 4 2 100.00 100.00 100.00 100.00
e(8) 321 R/Conc Approach Slab 4 2 100.00 100.00 100.00 100.00
e(9) 215 R/Conc Abutment 4 :: - 27.88 100.00 27.88
e( 10) 205 R/Conc Column 4 66.67 100.00 66.67
e(l 1) 326 Bridge Wingwalls 3 4 80.00 80.00 80.00 80.00
e( 12) 311 Moveable Bearing 3 7 6'5 20-00 20.00 20.00 20.00 20.00 100.00
e( 13) 308 Constr Non Exp Jt 3 20.00 20.00 100.00
e(14) 304 Open Expansion Joint 3 7 40.77 40.77 40.77 40.77
DBHI / DBHIMR&R: 38% 42% 42% 43%
A statistical analysis can be used to support the statement that elements with 3
CSs are more sensitive to the DBHI compared to elements with 4 and 5 CSs. Twenty
bridges were randomly selected from the 862 CCD bridge database. For each individual
66


bridge, element MR&R were completed for elements with 3 CSs and elements with 4 or
5 CSs and the respective DBHIMR&R were calculated. Paired-sample T test was
completed to compare the DBHIMR&R associated with two MR&R strategies. A
confidence interval of 95% with a significance level of 0.05 was utilized. The parameter
p is interpreted as the average difference between DBHIMR&R for 3 CSs elementsMR&R
and DBHImr&r for 4 or 5 CSs elementsMR&R. The null hypothesis is H0: p=0 and the
alternative hypothesis is Ha: p^O. The general results are shown in Table VI.8. The
statistical analysis reveals that it is not plausible that p=0, and positive value of p
indicates that DBHIMR&R for 3 CSs elementsMR&R tend to be larger than DBHIMR&R for 4
or 5 CSs elementsMR&R. Therefore, the null hypothesis (Ho: p=0) is rejected, and the
alternative hypothesis (Ha: p^O) is accepted. The statistical results conclude that we are
95% confident that the DBHIMR&R for elements with 3 CSs is 0.33% to 13.4% higher
than DBHImr&r for elements with 4 or 5 CSs (p=0.02). The statement that elements with
3 CSs are more sensitive to the DBHI is confirmed.
Table VI.8 Paired-samples T test result from SPSS program.
Paired Differences
Pair 1 Mean (P) Std. Deviation Std. Error Mean 95% Confidence Interval of the Difference Lower Upper t df Sig. (2- tailed)
DBHImr&r for 3 CSs elementsMR&R .0686400 .1395664 .0312080 .0033209 .1339591 2.199 19 .040
DBHImr&r for 4 or 5 CSs elementsMR&R
67


CCD Major and Minor Bridge Networks
The total CCD bridge network consists of 862 bridge structures, 474 major
bridges and 336 minor bridges, for which the DBHI can be computed. Table VI.9
separately introduces the element condition for the major bridge network and the minor
bridge network. For each category of elements with 3, 4, and 5 CSs, Table VI.9
illustrates a count of the number of total and damaged elements and presents the average
we and average EHI of damaged elements. The Denver Bridge Network Health Index
(DBNHI) is the average of all DBHI. The DBNHI is equal to 77% for the major bridge
network and 86% for the minor bridge network. Three element MR&R options for the
major and minor bridge networks are shown in Tables VI. 10 and VI. 11, respectively.
Similarly, the element MR&R option scenarios are limited to categories in order to
compare the sensitivity level of each element category to the DBHI.
Table VI.9 Element condition for bridge networks
Major bridge network Minor bridge network
Element Damaged! 1) / Average we Average EHI Damaged! 1) / Average wc Average EHI
categories total(2) of(l) of(l)(%) total(2) of(l) of (t) (%)
Elements with 5 CSs 376/837 8.01 62.13 107/390 8.50 63.85
Elements with 4 CSs 815/1879 8.71 79.51 125/864 8.53 54.79
Elements with 3 CSs 447/1328 5.50 56.06 65/615 3.86 37.41
Total / DBNHI: 1638/4044 77% 297/1869 86%
68


Table VI.10 The numerical calculation results for the major bridge network
ElementMR&R
description
Average EHIMR&R (%)
Average Average
we EH I (%)
Option 1 Option 2 Option 3
350 damaged elements w/ 5 CSs 8.05 59.35 100.00 59.35 59.35
350 damaged elements w/ 4 CSs 7.28 56.10 56.10 100.00 56.10
350 damaged elements w/ 3 CSs 5.69 44.95 44.95 44.95 100.00
DBNHI / DBNHImr&r: 77% 82% 81% 85%
Table VI.11 The numerical calculation results for the minor bridge network
ElementMR&R
description
Average EHIMR&R (%)
Average Average
wc EHI (%)
Option 1 Option 2 Option 3
50 damaged elements w/ 5 CSs 12.34 49.18 100.00 49.18 49.18
50 damaged elements w/ 4 CSs 11.44 33.06 33.06 100.00 33.06
50 damaged elements w/ 3 CSs 3.82 23.38 23.38 23.38 100.00
DBNHI / DBNH1mr&r: 86% 88% 89% 91%
For the major bridge network in Table VI.9, the number of damaged elements is
376, 815, and 447 for element with 5,4, and 3 CSs respectively. The EHI of damaged
elements included in each element category are calculated and ranked in a sorted EHI list.
The 350 lowest-EHI elements with 3 CSs, 4 CSs and 5 CSs were chosen from the EHI
list of each element category and assigned MR&R option 3, option 2 and option 1,
respectively, as shown in Table VI. 10. These elements are shown in Appendix D. The
average we and EHI of the 350 damaged elementsMR&R were determined for each option.
The major DBNHI is 77%. The major DBNHIMR&R of option 1, option 2, and option 3
are 82%, 81 %, and 85%, respectively. The sensitivity level of major DBNHIMR&R for the
69


non-structural elementsMR&R with 3 CSs of option 3 is slightly greater than that for the
structural elementsMR&R with 4CSs of option 2 and 5CSs of option 1.
For the minor bridge network in Table VI.9, similar results were obtained. The
number of damaged elements is 107, 125, and 65 for element with 5,4, and 3 CSs,
respectively. The EHI of damaged elements included in each element category are
calculated and ranked in a sorted EHI list. The 50 lowest-EHI elements with 3 CSs, 4
CSs and 5 CSs were chosen from the EHI list of each element category and assigned
MR&R option 3, option 2 and option 1, respectively, as shown in Table VI. 11. These
elements are shown in Appendix E. The average we and EHI of the 50 damaged
elementsMR&R were calculated for each option. The minor DBNHI is 86%. The minor
DBNHImr&r of option 1, option 2, and option 3 are 88%, 89%, and 91%. The sensitivity
level of minor DBNHIMR&R for the non-structural elementsMR&R with 3 CSs of option 3 is
approximately equivalent to that for the structural elementsMR&R with 4CSs of option 2
and 5CSs of option 1. This is similar with the previous result for the major bridge
network, the three individual sample bridges, and the statistical analysis.
Summary
In summary, when focusing on the consequence of repair of the difference (Adbhi)
between DBHI and DBHIMR&R or the Adbnhi between DBNHI and DBNHIMR&R, the
benefit of element MR&R activities for non-structural elementsMR&R with 3 CSs is
always approximately equal or slightly greater than that for structural elementsMR&R with
4 and 5 CSs. Since the DBNHI is the average of all DBHI, a trend existing in the above
sample bridges and bridge networks is that the DBHI is more sensitive to the
70


elementsMR&R with 3 CSs, even though they are weighted smaller. The sensitivity should
be with the elements with 4 and 5 CSs which are weighted higher.
Analysis
The DBHI was observed to be more sensitive to the elementsMR&R with 3 CSs.
The goal is to analyze the reason for this trend through a mathematic derivation, and,
consequently to find an analytical reason for the sensitivity issue.
Mathematic Derivation
As mentioned previously, the benefit or consequence of repair is the difference
(Adbhi) between the repaired and unrepaired states. Actually Adbnhi is the average of all
Adbhi- Therefore, the purpose of this section is to provide an equation for Adbhi, and to
develop the factors that influence the Adbhi and the variation trends that result in the
increasing Adbhi- In other words, the analysis can help engineers to understand which
elementsMR&R result in more benefit (Adbhi)- The mathematical derivation is as follows:
(1) DBHI:
H]Wf +H2wj' +- + H,w? + + HjWf + + //<
WJ + Hf + + Wf +- + Wf +- + W*
e=l
Where
He is the EHI of e(e),
weaJ is the adjusted weight coefficient of e(e).
y hxj
e e
DBHI = -£!--

71


(2) DBHIV1R&R:
//* =100%, AF** = 1, wf = AFf
wf,
//
m&R
100%, AFf
1, wf =AF;'a**wJ=wj,
DBHI
MR&R
f Hwf
/ e e
w:
//, wf + IF W? +- + //,MV + + // *** wf
+ + //.W?
+ + W"J + + MJ
//, W,0-' + H2w2 + + Wf H-h H-----1- Hnwf
W| ^ W2 + + H(. + + Hy + + VV^j
H,wf +H2wf + --- + Hiwf + H jWj + --- + Hwf +wi-Hiwf + +w. -//(vv";
nf + ny7 + + w/ + + w ^ + 4- wf 4- wf + + w; w
, ,aJ
aJ

a/


Where
through Hjm&R are the EHIMR&R of e(i) through e(j),
ApMR&R trough AFjMR&R are the adjustment factor under element MR&R
activity of e(i) through e(j),
wf through wf are the adjusted weight coefficient under element
MR&R activity of e(i) through e(j),
w, through Wj are the weight coefficient of e(i) through e(j).
72


(3) Simplification:
Let
Get
I = H,wf + H2 wf + + //,. wf + + H, wf + + // wf,
II = wf + wf + + wf + + wf + + wf,
a = wi Ht wf H--1-Wj Hj wf,
b = w, wf H-----h w.
; ]
wf.
DBH1 =p (l>0, 11*0, II >l)
DBHr
I + a
II + b
, (lI + 6>0)
(4) Adbhp
adbhi = dbhimr&r -dbhi
I + a I
~II + 6 II
(l + q)H-l(lI + 6)
(ll + />)ll
_ Ha lb
~ (II + 6)II
(5) Properties of ADBhm
II > 0, II + b > 0
v Denominator (il + /?)ll > 0
a-b = (w(. Hiwf -i-1-wj Hwf)-(wi wf h--1- wy. wf)
= wf (l -//,)+ + wf (l H t) > 0
then, a> b
and II > I, I > 0
v Ila > Ib, then numerator(Ua -\b)>0
_ \\a-\b
Dfl"/_(II + 6)II
>0
73


(6) Factors and variation trends affecting ADBhi:
Ha t -Ib i
DBH/ ~ (ii + z>4)ii
DBHl
v simulate variation trend utilizing (a b)
8,
He < 40%
40% 1,
H > 70%
Two observations are obtained from the above mathematic derivation.
1. The influencing factors of Adbhi are Hi and w;.
2. Increasing wj (wif) and decreasing Hi (Hi|) are two variation trends that result
in increasing ADBhi (Adbhi!)-
In other words, if an elementMR&R consists of higher Wi and lower Hi, then it is possible to
receive more benefit. In the next section, this theory is applied to previous sample
bridges and CCD major and minor network in order to analyze the reason of trend.
Reason of Trend
Table VI. 12 and Table VI. 13 present Adbhi and influencing factors of element
MR&R scenarios for previous sample bridges and CCD bridge network, respectively.
74


Table VI.12 Influencing factors of Adbhi based on ksN for sample bridges
Influencing factors
Element we EHI (%)
Sample bridges MR&R options key x, x; A yt Adbhi <%)
Option 1 for 13 7 9 5 60.00 73.80 5
D-03-V-180 element w/ 5 CSs 107 12 87.60

Option 2 for element w/ 3 CSs 326 4 4 20.00 20.00 17
Option 1 for 231 15 17 5 28.92 43.74 4
element w/ 5 CSs 161 20 58.55
F-16-DW Option 2 for element w/ 4 CSs 215 205 12 14 16 27.88 66.67 47.28 4
Option 3 for element w/ 3 CSs 311 308 6 6.5 7 20.00 20.00 20.00 5
Table VI.13 Influencing factors of ADbhi based on ksN for CCD major and minor
bridge networks
Influencing factors
Bridge network Element MR&R options Average we Average EHI (%) Adbhi (%)
Option lfor 350 elements w/ 5 CSs 8.05 59.35 5
CCD major bridge network Option 2 for 350 elements w/ 4 CSs 7.28 56.10 4
Option 3 for 350 elements w/ 3 CSs 5.69 44.95 8
Option lfor 50 elements w/ 5 CSs 12.34 49.18 2
CCD minor bridge network Option 2 for 50 elements w/ 4 CSs 11.44 33.06 3
Option 3 for 50 elements w/ 3 CSs 3.82 23.38 5
As shown in Table VI.12, for sample bridge (D-03-V-180), option 2 for elements
with 3 CSs corresponded to a lower we of 4 and a lower EHI of 20% and produced a
75


higher Adbhi of 17%. Similar results were obtained for bridge F-16-DW: a lower we of
6.5 and a lower EHI of 20% corresponding to option 3 for elements with 3 CSs generated
the highest Adbhi of 5%.
In Table VI. 13, for the major bridge network, option 3 for elements with 3 CSs
with a lower we of 5.69 and a lower EHI of 44.95% resulted in the highest Adbhi of 8%.
Similar results were obtained for the minor bridge network: a lower we of 3.82 and a
lower EHI of 23.38% corresponding to option 3 for elements with 3 CSs generated the
highest Adbhi of 5%.
In summary, the experimental results of the sample bridges, including the
networks, do not support the theory that higher Wj and lower H; result in higher Adbhi-
The relatively lower Hj of elementsMR&R with 3 CSs is the reason of trend. To be
consistent between experimental data from bridge network and the theory, further
analysis to find the reason for sensitivity issue is necessary.
Reason of Issue
Based on the above analysis, it is necessary to review EHI calculating
methodology in order to determine why the EHI is more sensitive to 3 CSs elements as
supposed to 4 and 5 CSs elements. The EHI is calculated by following Equation VI. 1.
X k?q,
He =^=-------x 100%
Z ^
5
Equation VI. 1
Where
s is the index of the condition state.
qs is the quantity of the element in slh condition state.
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ksN is the nonlinear health index coefficient corresponding to the sth condition
state.
As shown in Equation VI. 1, qs and ksN are two influencing factors of He. Both qs and ksN
are discussed next to determine the reason of sensitivity issue.
Consider qs first. Table VI. 14 presents the average quantities in CS1 (the CS
without element damage) and all other CSs of total elements included in each element
category. Comparing 82% of elements with 3 CSs to 86% and 68% of elements with 4
and 5 CSs in CS1 for major bridge network and similar comparison for minor bridge
network, it is concluded that the damage distribution of total elements with 3 CSs is not
much broader than that of total elements with 4 or 5 CSs. Table VI. 15 shows the average
quantities in CS1 (the CS without element damage) and all other CSs of damaged
elements included in each element category. Again, comparing 47% of elements with 3
CSs to 69% and 28% of elements with 4 and 5 CSs in CS1 for major bridge network and
similar comparison for minor bridge network, it is concluded that the damage extent of
damaged elements with 3 CSs is not much greater than that of damaged elements with 4
or 5 CSs. Therefore, qs does not account for the reason of sensitivity issue.
Table VI. 14 Average quantities in CS1 and ail other CSs of total elements included
in each element category for major and minor bridge networks
Major bridge network Minor bridge network
Average quantity (%) in Average quantity (%) in
Element description CS1 (w/o damage) all other CSs (w/ damage) Total (%) CS1 (w/o damage) all other CSs (w/ damage) Total (%)
Total elements w/ 5 CSs 68 32 100 80 20 100
Total elements w/ 4 CSs 86 14 100 90 10 100
Total elements w/ 3 CSs 82 18 100 92 8 100
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Table VI.15 Average quantities in CS1 and all other CSs of damaged elements
included in each element category for major and minor bridge networks
Major bridge network Minor bridge network
Average quantity (%) in Average quantity (%) in
Element description CS1 (w/o damage) all other CSs (w/ damage) Total (%) CS1 (w/o damage) all other CSs (w/ damage) Total (%)
Damaged elements w/ 5 CSs 28 72 100 27 73 100
Damaged elements w/ 4 CSs 69 31 100 30 70 100
Damaged elements w/ 3 CSs 47 53 100 27 73 100
Consider ksN next. Table VI.16 presents the linear and nonlinear health index
coefficients ks and ksN. According to Table VI. 16, two similarities between ks and ksN are
observed:
(1) The health index coefficient of the first CS is 1 for each element category of
ks or ksN.
(2) The health index coefficient of the last CS is 0 for each element category of
ks or ksN.
AASHTO defines the first CS as a good condition, while the last CS is the failed
condition. The intermediate CSs have different extents of element damages. According
to Tables VI. 17 and VI. 18 which introduce intermediate CSs, two differences between ks
and ksN are as follows:
(1) In Table VI. 17, the average of intermediate ks is 0.5 for each element
category, and the averages of intermediate ksN have a descending trend from
element category I to III.
(2) The intermediate ks are not equal to the intermediate ksN for each element
category in Table VI. 17. The differences between intermediate ks and ksN arc
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shown in Table VI. 18.
Table VI.16 Linear and nonlinear health index coefficients ks (ksN)
Element ks (ksN)
category description CS1 CS2 CS3 CS4 CS5
I Elements with 5 CSs 1.00(1.00) 0.75 (0.60) 0.50(0.30) 0.25 (0.10) 0.00 (0.00)
II Elements with 4 CSs 1.00(1.00) 0.67 (0.40) 0.33 (0.10) 0.00 (0.00)
III Elements with 3 CSs 1.00(1.00) 0.50(0.20) 0.00(0.00)
Table VI.17 Averages of intermediate ks and ksN
Element ks (ksN)
category description CS2 CS3 CS4 Average
I Elements with 5 CSs 0.75 (0.60) 0.50(0.30) 0.25 (0.10) 0.50(0.33)
II Elements with 4 CSs 0.67 (0.40) 0.33 (0.10) 0.50 (0.25)
III Elements with 3 CSs 0.50 (0.20) 0.50(0.20)
Table VI.18 Difference between intermediate ks and ksN
Element ks ksN
category description CS2 CS3 CS4
I Elements with 5 CSs 0.15 0.20 0.15
II Elements with 4 CSs 0.27 0.23
III Elements with 3 CSs 0.30
Referring to the above two differences between ks and ksN, two main conclusions
are obtained:
(1) In Table VI.17, the average of intermediate ksN of category III with 3 CSs
(0.2) is less than that of category II with 4 CSs (0.25) and category I with 5 CSs
(0.33).
(2) Based on Figure V.2, the ksN is the reduced ks. As shown in Table VI. 18, the
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decrease (ks ksN) of category III with 3 CSs is 0.3, which is more than any value
of both category II with 4 CSs and category I with 5 CSs.
The above two points result in relatively lower ksN of the element with 3 CSs and, finally,
result in relatively lower EHI of elements with 3 CSs. In other words, the reason for the
sensitivity issue is the relatively lower ksN of the element with 3 CS.
Conclusion
The analysis presented in the last section helps conclude that the most essential
cause of the sensitivity issue is ksN. The ksN was determined subjectively by engineering
experience. Therefore, a non-subjective health index coefficient was necessary and is
presented in the following chapters.
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CHAPTER
VII. METHODOLOGY TO DETERMINE ACTUAL k, VALUE
Background Knowledge
The AASHTO CoRe Element Manual defines each element and the associated 3-
5 condition states. The health index coefficient is an indicator that reflects the
deterioration level of the condition state. This indicator may change from 0 (worst
condition) to 1 (best condition). Presently, there are no analytical or experimental
methods or techniques to determine health index coefficients.
The Pontis BHI methodology has the following two characteristics: (1) both
failure and repair BHIs are based on cost; (2) the health index coefficients were assigned
a series of linear subjective ks values. The problems associated with Pontis BHI
methodology and analysis results demonstrated that a modification of the BHI was
necessary. The key idea included in the modification, called the DBHI, was emphasizing
the effect of element damage on EHI and EHI on BHI. One of the important
modifications proposed to the original Pontis formula is to change health index
coefficients from the linear ks values to the nonlinear ksN values based on engineering
experience. As a result, the DBHI can address all element damages and is more
conservative. Also, the bridge distribution based on DBHI for the entire CCD bridge
network is more rational than that based on Pontis BHI as presented in Chapter V.
However, some deviations still exist in between the nonlinear ksN values and the
actual health index coefficients. Although nonlinear ksN are better, they were still
determined subjectively. This is evident when low w; and low Hi result in the highest
Adbhi as demonstrated in the examples of Chapter VI. There are two possible reasons for
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the deviations. One possibility could be that the ksN of the element with 3 CSs are less
than actual values, or another that the ksN of the element with 4 or 5 CSs are greater than
actual values. Both possibilities result in over-sensitivity of DBHI to the elements with 3
CSs. Therefore, the deviation between the nonlinear ksN values and the actual empirical
health index coefficients is the reason causing the sensitivity issue when utilizing the
DBHI with element MR&R decision making. To minimize the deviations and to obtain
the actual health index coefficients is a solution to develop by which the sensitivity issue
can be eliminated.
In conclusion, any improved health index coefficients (improved ks) should: (1)
reflect actual deterioration level of the condition state; (2) help provide an objective
reference for the element MR&R decision making; and (3) be determined by a reliable
non-subjective methodology.
Element Inspection Data
Thompson and Shepard (2000) state One of the most immediate applications of
CoRe elements is the collection and analysis of performance data. The data collected
through the biennial bridge inspection process would be stored in a database, with
subsequent users, generally in the office and sometimes many years later, unable to apply
any sort of subjective interpretation to the data. Although some degree of analysis or
interpretation may be applied by an inspector or engineer at the time of inspection, it is
essential that the raw, objective data be stored so that the analysis may be updated or
improved at a later time." Thompson and Shepard (2000) also go on to say that after an
increasing number of agencies developed bridge management system databases using the
CoRe elements, these same agencies started using element inspection data for many types
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of agency decisions. The CCD, like many other public works entities, has successfully
used the raw and objective element inspection data as a basis for performance
measurement, resource allocation, and management decision support. Since the
improved ks is an actual health index coefficient determined from empirical data, any sort
of subjective interpretation would be avoided. Therefore, by a survey of the entire actual
CCD Pontis BMS data, the raw and objective element inspection data is a source to
improve ks. Figure VII. 1 is the 2010 CCD Pontis BMS database schematic diagram.
Figure VII.1 2010 CCD Pontis BMS database schematic diagram
There are 490 major bridges, 1627 major bridge inspections, and a total of 24275 element
inspection data points contained in the 2010 CCD Pontis BMS. Similarly, the database
contains 372 minor bridges, 875 minor bridge inspections, and 5981 total element
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inspection data points. All the element inspection data of every bridge inspection of each
bridge are respectively listed in Table VII. 1.
Table VII.1 Element inspection data in the 2010 CCD Pontis BMS database
Element
Bridge . inspection data (%)
p_______________inspection ______________
No. key year built No. year No. key description T q. q< q?
1 31 Timber deck 100 0 0 0
1 2004 11 600 Genl remarks 100 0 0 0 0
1 D-01-CC-010 1977 : : : J :
1 31 Timber deck 100 0 0 0
3 2010 11 600 Genl remarks 100 0 0 0 0
1 23 Cone deck 100 0 0 0 0
696 D-31-PB-902 2007 1 2009 : : : : : : : :
10 338 Cone curbs/SW 100 0 0 0
1 60 Railroad deck 100 0 0 0 0
862 F-17-QH 2005 1 2005 ; ; ; ; ; i i ;
10 341 Substr cone coating 100 0 0
Total: 862 Total: 2502 Total: 30256
q! through q5 are element quantities in CS1 through CS5.
Table VII. 1 lists 862 bridges, 2502 bridge inspections, for a total of 30256 sets of element
inspection records in the CCD Pontis BMS database. These are the same total numbers
as shown in Figure VII. 1. As shown in Table VII. 1, these inspection data records all
refer to different bridges, or elements, or inspection years, and therefore, they have
distinct disarray and no regularity. As a result, they cannot be used directly. It is
necessary to present the correlation and regularity within the element inspection data by a
tool, which is an element transition model.
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Element Transition Model
After the CS was defined, transition began immediately. When a bridge element
deteriorates, a transition is made from one condition state to a poorer one. When an
element MR&R action is subjected to a specific bridge element, a transition is caused to
improve the condition state.
In the Pontis BMS, the transition concept appears in the Pontis Bridge
Management Release 4 Technical Manual (AASHTO, 2003). In chapter 4: modeling
system, one can find the following quote Deterioration of bridges is a probabilistic
phenomenon it is not possible to predict with certainty how each element of each bridge
will deteriorate over time. Since bridges consist of different quantities of elements that
deteriorate differently from each other, there is no meaningful way to quantify or even to
speak about, deterioration of entire bridges. Pontis BMS addresses this dilemma
through the element transition probabilities model (Scherer and Glagola, 1994). The
probabilities model is actually a Markovian decision model. It predicts the probability
that a given unit of an element will transfer from one CS to another in one year due to
element deterioration or element MR&R action. The initial transition probability for
each element is provided through expert opinions. All of these data are assembled into
element transition probability matrices. Pontis updates the element transition
probabilities model using expert advice and historical inspection data. However, in the
Pontis Bridge Management Release 4 Technical Manual (AASHTO, 2003), one can also
find the following quote Most element transition probabilities cannot be updated from
the historic data in the current version of the system (Pontis Release 4 and higher) due to
the change of the format in which MR&R work history is stored in Pontis.
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