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Application of nondestructive evaluation techniques in bridge inspections as a tool for bridge management systems

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Title:
Application of nondestructive evaluation techniques in bridge inspections as a tool for bridge management systems
Creator:
Nogueira, Carnot L
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English
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xi, 138 leaves : illustrations ; 28 cm

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Subjects / Keywords:
Bridges -- Maintenance and repair ( lcsh )
Bridges -- Testing ( lcsh )
Bridges -- Inspection ( lcsh )
Bridges -- Inspection ( fast )
Bridges -- Maintenance and repair ( fast )
Bridges -- Testing ( fast )
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bibliography ( marcgt )
theses ( marcgt )
non-fiction ( marcgt )

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Bibliography:
Includes bibliographical references (leaves 130-138).
General Note:
Department of Civil Engineering
Statement of Responsibility:
by Carnot L. Nogueira.

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Auraria Library
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41470681 ( OCLC )
ocm41470681
Classification:
LD1190.E53 1998m .N64 ( lcc )

Full Text
APPLICATION OF NONDESTRUCTIVE EVALUATION
TECHNIQUES IN BRIDGE INSPECTIONS AS A TOOL
FOR BRIDGE MANAGEMENT SYSTEMS
by
Carnot L. Nogueira
B.S., Federal University of Pernambuco, 1994
A thesis submitted to the
University of Colorado at Denver
in partial fulfillment
of the requirements for the degree of
Master of Science
Civil Engineering
1998


1998 by Carnot L. Nogueira
All rights reserved.


This thesis for the Master of Science
degree by
Carnot L. Nogueira
has been approved
by
Kevin L. Rens
Judith J. Stalnaker
John R. Mays
1 z.z.33
Date


Nogueira, Carnot L. (M.S., Civil Engineering)
Application of Nondestructive Evaluation Techniques in Bridge Inspections as a
Tool for Bridge Management Systems
Thesis directed by Assistant Professor Kevin L. Rens, P.E.
ABSTRACT
The importance of maintenance of existing structures has been addressed in
several works and federal programs in the past few decades. Several long-term
projects related to inspection and evaluation of structures have been conducted by
federal agencies. The first example of this emphasis on the maintenance of the
infrastructure system is the bridge inventory system established in the 1970s.
The second example is the Repair, Evaluation, Maintenance, and Rehabilitation
(REMR) program conducted by the United States Army Corps of Engineers for
the analysis of the deterioration of hydraulic and navigation structures in the
1980s. One of the main concerns of the REMR program is the inspection and
rating of deteriorating navigation structures. The use of new nondestructive
evaluation technologies in the inspection of structures and the application of
IV


probabilistic deterioration models constitute powerful tools in the maintenance
and management of infrastructure systems. In this work, the use of a Markovian
deterioration model for bridge management systems and the application of
nondestructive evaluation technologies in bridge inspections were reviewed for
the possible implementation in the bridge management system of the City and
County of Denver (CCD). As a result, a computational program was developed to
help administrate financial resources for the maintenance of the CCD bridge
network. The program is integrated into a Geographic Information System (GIS)
application developed for the CCD bridge management system (BMS). In
addition, a methodology for a systematic application of nondestructive evaluation
(NDE) methods in the bridge inspection is proposed. The proposed method for
applying NDE technology in the inspections is explained and an example for
concrete bridges presented.
This abstract accurately represents the content of the candidates thesis. I
recommend its publication.
Signed.
Kevin L. Kens
v


ACKNOWLEDGMENTS
I would like to express my deepest feelings of sincere gratitude to:
My father, my mother, my son, and Deborah.
Bernardo Horowitz, for encouraging my scholarly inclinations.
Kevin Lee Rens, for giving me guidance as my advisor.
Dave Transue, Michael Schuller, and Dave Woodham, for their assistance and
support.
Terry Gruber, from the City and County of Denver, for the support and
confidence.
Ed Maez, Jim Geist, and Bill Melton, from the City and County of Denver, for
sharing their experience and for their help in understanding the Lonco reports.
Judith J. Stalnaker and John R. Mays, for being committee members of my thesis.
I also would like to thank the financial support of the Accounting Court of
Pernambuco, Brazil, and express my thankfulness to the Counselor Ruy Lins de
Albuquerque as well as the other Counselors, and also Gustavo Pimentel da Costa
Pereira, and Analucia Mota Vianna Cabral. I have an unconditional faith on the
importance of this Court for the development of Pernambuco.
Finally, I would like to thank the CAPES Foundation for the support.
Praise is more obtrusive than a reproach.
(Nietzsche)
But the goddess of vengeance, from whom nothing is hidden, looked forth from
her secret dwelling with angry eyes and beheld the terrible deed committed here.
(Gods and Heroes Gustav Schwab)
There is an ancient story that King Midas hunted in the forest a long time for wise
Silenus, the companion of Dionysus, without capturing him. When Silenus at last
fell into his hands, the king asked what was the best and most desirable of all
things for man. Fixed and immovable, the demigod said not a word, till at last,
urged by the king, he gave a shrill laugh and broke out into these words: Oh,
wretched ephemeral race, children of chance and misery, why do you compel me
to tell you what it would be most expedient for you not to hear? What is the best
of all is utterly beyond your reach: not to be born, not to be, to be nothing. But the
second best for you is to die soon.
(Oedipus at Colonus Sophocles)


CONTENTS
Figures................................................................x
Tables.................................................................xi
Chapter
1. Introduction......................................................1
2. Bridge Management Systems.........................................4
2.1 Introduction......................................................4
2.2 Characteristics of BMSs..........................................7
2.3 GIS and BMSs....................................................11
3. Bridge Inspection................................................13
3.1 Overview.........................................................13
3.2 Condition Rating.................................................17
3.3 Sufficiency Rating...............................................21
4. Deterioration Model..............................................23
4.1 Markovian Model..................................................23
4.1.1 Deck.............................................................27
4.1.2 Superstructure...................................................29
4.1.3 Substructure.....................................................30
vii


4.2 Transition Matrices...............................................31
4.2.1 Classification Schemes............................................31
4.2.2 Transition Probability Matrices...................................37
4.3 Deterioration Curves..............................................40
5. Nondestructive Evaluation and Bridge Management Systems.46
5.1 Overview..........................................................46
5.2 Deterioration Models and NDE Methods..............................52
5.3 Types of Deterioration and NDE Methods............................53
5.4 Integration of NDE and BMSs......................................54
6. Nondestructive Evaluation Applied to Concrete Bridge Inspection...57
6.1 Overview..........................................................57
6.2 General Guidelines on the Use of NDE Techniques...................60
6.3 Development of the BENT Method....................................61
7. Summary, Conclusions, and Recommendations for further work.74
7.1 Summary...........................................................74
7.2 Conclusions.......................................................74
7.3 Recommendations for further work..................................75
Appendix
A. Structure Inventory and Appraisal Sheet.............................78
B. Database............................................................81
viii


C. Data and Transition Matrices.......................................84
D. Deterioration Curves..............................................102
E. Users Manual of the Program......................................108
F. Photographs (Deterioration Processes).............................118
Bibliography............................................................130
IX


FIGURES
Figure
4.1 Decrease of condition rating with the age of the component..............24
4.2 Transitions of condition ratings for all bridges........................35
4.3 Generic transition probability matrix...................................37
4.4 Transition probability matrix...........................................39
4.5 Transition probability matrix...........................................42
4.6 Deterioration curve for substructure....................................44
C.l to C.l 1 Transitions of condition ratings...............................86
C. 12 to C. 16 Deterioration matrices.........................................97
x


TABLES
Table
3.1 Condition rating guidelines...................................19
4.1 Markovian property............................................27
4.2 Markovian property............................................28
4.3 Markovian property............................................29
4.4 Markovian property............................................30
4.5 Markovian property............................................30
4.6 Markovian property............................................30
4.7 Markovian property............................................30
4.8 Condition rating vectors and condition ratings................43
6.1 Information required in evaluation of concrete structures.....58
6.2 Problematic concrete members..................................59
6.3 Further development needs general...........................60
6.4 Further development needs reinforced and prestressed concrete....60
6.5 Critical structures in the CCD................................62
6.6 Adequacy of NDE methods for deterioration in the bridges......66
xi


1. Introduction
In a Bridge Management System (BMS) one of the main questions that
needs to be answered about each structure is whether or not the bridge will continue
to satisfactorily function in a determined period of time. The administration of a
group of bridge structures in a network requires the development of methods for
predicting the general state of the components of the system. This global behavior
can be analyzed by the application of probabilistic methods.
In recent years two factors have determined the necessity of a new approach
in the administration of bridge systems. The first factor is the natural aging of the
structures the bridges in the United States are reaching their service life limit,
becoming structurally deficient and functionally obsolete [Hudson et al., 1987;
Scherer and Glagola, 1994] and the accurate assessment of the condition of their
components is a critical task. The second factor is related to the development of
nondestructive evaluation (NDE) techniques. The advantages of these techniques -
in contrast to destructive techniques wherein sacrifice of specimens is required -
include early detection of flaws that can eventually provoke costly repairs or even
fatal accidents.
The main objective of this thesis is the establishment of a methodology for
the application of NDE techniques to the components of a bridge network.
1


Specifically the use of NDE techniques for the inspection of concrete elements of
bridges is analyzed and presented in this work.
This thesis is organized as follows:
Chapter Two brings an introduction to BMSs is and the description of
its characteristics. Emphasis is given to the reasons that determine the
necessity of the introduction of NDE techniques.
Chapter Three presents the current practice of biennial bridge inspections
in the United States. The condition ratings used to express the state of
the bridges and its components, which are adopted in the deterioration
model, are explained.
Chapter Four presents the development of the deterioration model
algorithm used in this thesis. The deterioration curves for the main
components of the bridges are obtained by the application of the
Markovian method are presented. The application of the deterioration
curves in the administration of the bridge network is also presented.
Chapter Five contains information about recent applications of NDE
techniques in bridge inspections. A review of recently proposed
methods is given. The advantages and obstacles for the application of
NDE are explained. Finally, a systematic methodology, Bridge
Evaluation using Nondestructive Testing BENT, for the use of NDE
techniques in BMS is presented.
2


In Chapter Six an example of the application of BENT methodology is
presented for concrete bridges. Different deterioration processes are
analyzed and their implications emphasized. A review of recent
developments in NDE testing is also presented.
In Chapter Seven conclusions and recommendations for further work is
presented.
3


2. Bridge Management System
2.1 Introduction
The majority of the nearly 580,000 bridges in the U.S. highway system were
built during two periods of time. The first period of bridge construction in the U.S.
occurred in the 1930s during the Great Depression years and the second period of
bridge construction happened in the 1950s and 1960s [Hadavi, 1998]. About 75%
of these bridges were constructed before 1935 [Hudson et al., 1987]. As a
consequence, the bridges built in these two periods are growing old and will demand
replacement or major repairs in relatively short periods. These statistics illustrate
the importance 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 service.
On December 15, 1967, the collapse of the 2,235-foot 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 al., 1990], The Point Pleasant Bridge was built in 1928 and its
failure occurred without warning killing 46 people. The reason for the collapse of
the Point Pleasant Bridge was the fracture of an eyebar. Because of its deadly
4


consequences the collapse exposed the necessity of a rational program to conduct
periodic inspections of the nations bridges.
Bridges can fail for several reasons: scour, wind, fatigue, earthquake, floods,
corrosion, failure of a member, inappropriate design, and fire [Taly, 1998; Harik et
al., 1990], Maintenance inspections and actions need to be periodically undertaken
to detect and prevent failures.
The collapse of the Point Pleasant Bridge 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 standard. Therefore, in 1971, the National
Bridge Inspection Standard (NBIS) was created to institute federal parameters for
bridge inspections, report formats, inspector qualifications, and inspection
procedures. Manuals for bridge inspection were created and adopted. The Federal
Highway Administration (FHWA) Bridge Inspectors Training Manual 70 was first
published in 1970 and was used in training programs for bridge inspectors for
several years. Another important manual, the FHWA Recording and Coding Guide
for the Structure Inventory and Appraisal of the Nations Bridges, was released in
1972. During the 1970s it became clear that the fund availability did not meet the
maintenance costs required for the bridge inventory. In 1978, the Surface
Transportation Assistance Act created guidelines for funding maintenance and
5


replacement of all public bridges over 20 feet in length. The NBIS program,
formerly restricted to the bridges in the main federal highways, was extended to
include these bridges. The Bridge Inspectors Training Manual (BITM) 90 [Hartle
etal., 1990] revised, upgraded, and replaced the Bridge Inspectors Training
Manual 70. This new Manual is divided in 21 chapters and brings detailed and
comprehensive information about the inspection and evaluation of bridge
components and bridge inspection reporting systems. The BITM 90 also presents a
chapter about the application of nondestructive testing, referred as advanced
inspection techniques, in the inspection of bridges. In addition, the FHWA initiated
the Intermodal Surface Transportation Efficiency Act of 1991 (ISTEA). ISTEA
mandated the creation of systems to manage bridges in each state Department of
Transportation and Metropolitan Planning Organization. It also funded long-term
research projects that address problems of the next century. In the later part of the
1990s new Federally Funded Programs have been established, such as NEXTEA,
BESTEA, and ISTEA II. In addition to the activities referred in the ISTEA of 1991,
these new programs will address specific topics such as a timber bridge program,
scour counter measures, research of innovative materials, load and resistance factor
design specifications, and application of NDE in bridge assessment (Densmore,
1998).
6


2.2 Characteristics of BMSs
To adequately manage an infrastructure system implies obtaining maximum
performance from available resources. Therefore, management implies
optimization. The difficulty arises in the quantification of the parameters involved
in the mathematical model to be applied. The determination of the more appropriate
action to be executed (repair, rehabilitation, or replacement) can be done by the
comparison of the costs and benefits for each action. Maintenance actions taken at
appropriate time intervals increase the service life of the bridge and are more cost
effective than replacement of the structure. By forecasting future needs one can
contrast several scenarios to better utilize available resources. The future condition
of the bridges can be determined by the analysis of historical data and the
application of probabilistic models.
BMSs can be defined as a proactive and rational approach to conduct the
actions needed for the administration of a bridge network. This is performed in
order to achieve maximum performance with the application of minimum
expenditures. Several tasks related to the management of a bridge system need to
be accomplished. These tasks can be divided into two groups:
(1) Database module:
Maintenance of historical and present data;
7


Definition of bridge conditions;
Definition of bridge importance and other characteristics;
Definition of the maintenance activities;
Identification of bridges for posting;
Characterization of the commonly occurring damages, and
Characterization of the used resources for the maintenance actions.
(2) Management module:
Analysis of historical data;
Determination of the future bridge conditions;
Construction of deterioration curves for main bridge components;
Comparison of benefits obtained by the application of the different actions at
different periods of time;
Determination of future costs of the actions;
Definition of inspection schedule of the bridges in the system.
It can be inferred by the actions of the management module that BMSs strongly
depend upon an efficient deterioration prediction model. For instance, a prediction
model based on historical data can only be used to make accurate forecasting if the
data utilized in the model correspond to the real state of the bridge. In other words,
the accuracy of the model, as well as the tasks in the management module, depend
8


upon the quality of the data collected in the field during the inspections and used in
the model.
The probability of failure of a bridge component must be always taken into
account in the administration of a bridge network. The failure of a bridge member
can be catastrophic and usually provokes traffic interruption requiring high cost
emergency repairs. Failures can also cause accidents and unsafe conditions for the
public. Another important factor to be considered is that the maintenance costs tend
to rapidly increase when a deterioration process begins.
The recent collapse of a Denver metropolitan pedestrian bridge caught the
attention of the personnel of the Department of Public Works of the City and
County of Denver (CCD) for the necessity of more accurate inspections. The
collapse occurred without warning and although it did not cause any injuries it
urged the application of NDE techniques in the inspection of bridges. Since there is
a similar structure in the same area of the collapsed one and considering that both
structures had been inspected and found to be safe for the public a demand for a
more precise inspection of the second bridge was established.
A BMS database must contain information about every bridge in the system
and must be able to perform an individual analysis of a specific structure as well as
9


to perform a network level analysis. In order to maintain a certain degree of
simplicity, one of the main concerns in developing a BMS is its modularity [Smith
et al., 1997], Another very important feature is its flexibility to import and export
information, its ability to interact with other computer programs and database
software, and its capability to automatically update the probabilistic model
whenever new data is included. The complexity and extension of a database can be
adjusted to the needs of the users. A very simple database containing only historical
data used for the deterioration prediction model can be the basis of a BMS. On the
other hand a database can include detailed inspection reports, extensive lists of
repair and maintenance expenses, information about the personnel involved in the
maintenance operations, and even store drawings, surveying records, sketches, and
photographs [Lindbladh, 1990; Wei and Sing, 1997], A list of common defects
containing definitions of deficiencies encountered in the structure can also be
included as part of the BMS [Barrett et al. 1997]. Geographic Information System
(GIS) technology can be used to associate spatial information with the bridge
system and can be used to show the relationship of the bridge network with other
infrastructure systems such as the highway system. GIS technology has also been
applied to bridge planning [Hammad et al., 1993].
10


2.3 GIS and BMSs
A GIS can be described as a computational program capable of holding,
analyzing, and displaying spatial data. A GIS contains two types of information:
attribute data and spatial data. The attribute values entered are recorded and added
to data files and one can perform operations and analysis of the data and also create
graphical output (reports) using available data. The spatial data uses a coordinate
system and three different graphic objects: points, lines, and polygons. The main
distinction between a GIS and a traditional database is the ability of the GIS to
associate spatial data and its attributes using mathematical topology rules
[Simkowitz, 1990]. By associating and displaying spatial (geographic position) and
attribute data (object attributes) a GIS can perform much more consistent and
convenient views of the objects and of the systems to which they belong [Petzold
and Freund, 1990].
The GIS objects are displayed in maps that are organized in layers.
Different layers can contain information about geographic objects of the same
system. Placing one layer over the other (the layers are transparent) one can
observe the interaction of the systems shown on each layer. It is important to
emphasize the main benefit one can obtain when using a GIS for the management of
systems: the geographic information about the system and its components (roads,
bridges) are precisely shown on the GIS maps and their attributes can be retrieved
11


and analyzed while the map is exhibited. Data collection for a precise location of
the bridges can be easily performed with electronic equipment. In most cases the
bridge positions are determined by other geographic data such as intersections of
two or more street centerlines or by the intersection of street center lines and
streams or canals.
A pilot study for the creation of a BMS based on a GIS platform was
developed in a project recently undertaken by the University of Colorado at Denver
and the Public Works Department of the CCD [Neiman, 1998; Rens et ai, 1998].
One of the benefits of the program is the storage of drawings, surveying records,
sketches, photographs and other information in magnetic media and CD-ROMs.
This will prevent records from aging and further deterioration. Furthermore, digital
storage will also allow easier access to all the information in the documents.
Frequent use of old maps and documents contribute to their degeneration, this factor
will be minimized with the use of the system. Because of its importance and
because it is used by each state to report the bridge data to the FHWA, as required
by the NBIS, the Structure Inventory and Appraisal list also needs to be included in
the database. The project is now being expanded to the entire 750 bridge network of
the CCD. The deterioration model presented in this thesis, as well as the procedure
for the application of NDE methods, constitute part of the GIS-based BMS under
development.
12


3. Bridge Inspection
3.1 Overview
Bridges and other structures deteriorate with time and use. The deterioration
process is affected by several characteristics: traffic, rain, freeze and thaw cycles,
climate, pollution, temperature variation [Hearn, 1996], This process can lead to
failure of a bridge member. After a certain period of time has elapsed the
deterioration process accelerates and in a relatively short time interval the
components lose the capacity to carry the loads they were designed to support.
Periodical bridge inspections are therefore necessary to assess the extension,
implications, and current state of the deterioration process. Inspections not only
help to prevent failure but also deliver information necessary for effective
administration of the bridge network. During the inspections the needs for urgent
repairs, maintenance actions, and replacements of bridges are detected and reported.
Based on these reports the administrator can define priorities and establish programs
to apply the available resources to the most critical bridges.
The requirement, periodicity, and procedures for bridge inspections in the
United States are addressed in several Acts and references. The Surface
Transportation Assistance Act of 1978 determined that all the public bridges over 20
13


feet in length should be inspected and inventoried in accordance with the National
Bridge Inventory System. The National Bridge Inspection Standards regulate the
inspection procedures, frequency of inspections, qualification of personnel,
inspection report format, and inventory [Hartle et al., 1990]. The inspections need
to be performed at regular time intervals not longer than 2 years. Some of the
manuals used as references for bridge inspection methodology are listed below:
Federal Highway Administration (FHWA) Bridge Inspectors Training
Manual 1990;
Manual for Maintenance Inspection of Bridges (American Association of State
Highway Officials AASHTO Manual);
Bridge Inspectors Manual for Movable Bridges (FHWA);
Culvert Inspection Manual (FHWA), and
Inspection of Fracture Critical Bridge Members (FHWA).
One of the most important aspects of a bridge inspection is related to the
qualification of the personnel involved in the inspection work. Minimum
qualifications for the individual responsible for the inspections can be found in the
NBIS [Hartle et al., 1990]. These qualifications include registration as a
professional engineer, qualification for registration, or a minimum experience of ten
years in bridge inspections. The reports of the inspections need to meet the
requirements of the NBIS, therefore, some uniformity in the structure of the
14


inspection reports is required. The Structure Inventory and Appraisal (SI&A) sheet
constitutes a set of fields to be filled with information about each individual
structure in accordance with the manuals mentioned above. Appendix A illustrates
a sample SI&A sheet. Information needed to build the historical database to be used
in the deterioration model can be obtained from the SI&A sheet. The sufficiency
rating (field 137), condition ratings (fields 58, 59, and 60), structure identification
(field 8), year built (field 27), average daily traffic (field 29), and average daily
truck traffic (field 109) are some of the information that can be obtained from the
Structure Inventory and Appraisal Sheet.
The identification of the common defects found during the inspections and
their precise characterization can be very useful. A description of the most common
deficiencies that occur in concrete, timber, and steel bridges can be found in the
Bridge Inspectors Training Manual [Hartle et al., 1990], During the inspection,
information other than the integer values of condition ratings must be acquired.
Sketches and notes taken during the inspection improve the inspection quality and
serve as important reference to accurately determine the causes and consequences of
the deterioration. In fact, the numbers that express the ratings are a very low
precision reference and cannot possibly convey the complex information associated
with the state of the deteriorating bridge. Since the input information for the
deterioration model and as for the BMS database are taken directly from the
15


inspection reports it is important to emphasize the importance of collecting accurate
data during the inspections. As a consequence, the inspections are the link between
the real bridge condition and the forecasted deterioration curves obtained by the
application of the deterioration model. Therefore the basis of the BMS is the
condition ratings obtained during the inspections. The BMS analysis is only as
good as the available data [Hudson et ai, 1993].
The bridge inspection programs adopted by some European countries have
some similarities to the program currently adopted in the United States [NHCRP,
1996]. Germany adopts four levels of inspection: visual inspections every 3
months, a more accurate inspection every 3 years, detailed inspections on a 6 year
basis, and special inspections for the assessment of damage. In France, two kinds of
inspections are performed: regular inspections during intervals less than 5 years, and
special detailed inspections: just after the construction of the bridge, before the
warranty expiration, and whenever a problem in the bridge is detected. In the
United Kingdom, three levels of inspections are adopted: biennial general
inspections, principal inspections on a 6 to 10 year basis, and special damage
assessment inspections.
16


3.2 Condition Rating
Condition ratings, also called condition indexes, are quantitative descriptors
of the state of a structure. Condition indexes and condition rating processes are
widely used in assessment for maintenance of structures [Hartle et al., 1990],
Procedures for rating hydraulic structures have been developed for the U. S. Corps
of Engineers [REMR, 1996; Greiman et al. 1994; Stecker et al. 1993; Greiman et al.
1993; Greiman et al. 1992; Greiman et al. 1990], By associating a deteriorated state
to a number, instead of using qualitative description of the state, much more
flexibility and uniformity can be achieved in monitoring a set of similar structures.
Because of its numerical format, the condition ratings can be used in mathematical
models in order to determine future condition states of the structures. Therefore
condition ratings are very appropriate to be used in computerized management
systems. The adoption of condition ratings in the evaluation of a group of structures
with similar characteristics will allow consistency and uniformity. This will permit
comparisons between the structures and the establishment of priorities on a relative
basis. Furthermore, by associating a condition rating to a condition description an
automated association with the appropriate action can also be performed.
The Bridge Inspectors Training Manual [Hartle et al., 1990] brings detailed
information about condition ratings to be applied to the inspection of bridges which
17


are reported in the SI&A sheet. Five items in the SI&A Sheet (Appendix A) receive
overall condition ratings [Hartle et al., 1990]:
Item No. 58
Item No. 59
Item No. 60
Item No. 61
Item No. 62
Deck
Superstructure
Substructure
Channel and Channel Protection
Culverts
The items 58, 59, and 60 are considered major primary components of a
bridge and for this reason their condition ratings are often used in deterioration
models. Some authors also emphasize the importance of the wearing surface
[DeStefano et al., 1997]. The condition ratings used for the evaluation of the deck,
superstructure, or substructure must be assigned according to the description given
in Table 3.1.
Although the main primary components of a bridge work together and the
behavior of each component can affect the function of the others, the analysis of the
bridge cannot be based on the analysis of only one main component. Some authors
suggest that the analysis of the condition of the bridge can be based upon the
18


TABLE 3.1 Condition rating guidelines [Hartle et al 1990]
Code Description
N NOT APPLICABLE.
9 EXCELLENT CONDITION.
8 VERY GOOD CONDITION no problems noted.
7 GOOD CONDITION some minor problems.
6 SATISFACTORY CONDITION structural elements show some
minor problems.
5 FAIR CONDITION all primary structural elements are sound but may
have some minor section loss, cracking, spalling, or scour.
4 POOR CONDITION advanced section loss, deterioration, spalling, or
scour.
3 SERIOUS CONDITION loss of section, deterioration, spalling, or
scour have seriously affected primary structural components. Local
failures are possible. Fatigue cracks in steel or shear cracks in concrete
may be present.
2 CRITICAL CONDITION advanced deterioration of primary structural
elements. Fatigue cracks in steel or shear cracks in concrete may be
present or scour may have removed substructure support. Unless
closely monitored it may be necessary to close the bridge until
corrective action is taken.
1 IMMINENT FAILURE CONDITION major deterioration or
section loss present in critical structural components, or obvious vertical
or horizontal movement affecting structure stability. Bridge is closed to
traffic but corrective action may put bridge back in light service.
0 FAILED CONDITION out of service; beyond corrective action.
19


condition of the deck alone [Glagola, 1992], Even though the deck protects the
superstructure and the substructure a realistic analysis needs to consider the other
components as well. For example, if one assumes that the bridge deteriorates
depending upon the deck alone, one could imagine a situation where the deck and
the superstructure are in perfect condition but the substructure is in need of urgent
repair. For this reason the study of the deterioration rates of the three main
components (i.e., deck, superstructure, and substructure) will be independently
considered. Since a problem in any of the main components of the bridge can lead
to an unsafe situation to the whole structure it will be assumed that the component
in the worst condition will determine the need of repairs in the bridge. The
deteriorated component then creates a weak link between the other components.
Accordingly, instead of assuming a priori that the deck will determine the
deterioration of the superstructure and substructure (or that the superstructure or the
substructure will determine the condition of the deck) an independent analysis of the
three components will permit a more realistic and precise description of the bridge
condition.
While condition ratings may constitute the only way to make a probabilistic
analysis of the deterioration of the bridge, they are in fact very limited descriptors of
the bridge condition. Integer numbers from 0 to 9 cannot convey possibly the
complex situation of deteriorating structures. No accuracy can be guaranteed in the
20


association of the condition number to the description of the state. The lack of a
more precise description of the states creates a gray zone in the intermediate ratings.
For example, several different scenarios can be associated with a condition rating of
7. Choosing the corrective action based only upon a condition number may lead to
a wrong decision.
Factors related to the personnel involved with the inspection also affect the
rating of the bridges. Since the condition ratings are based upon a subjective
judgment of the inspectors opinion, the ratings are found not to be the same if
different people are involved in the inspections. Many bridges span a long time,
about 20 years, without any decrease in the condition ratings. This usually happens
with a condition rating of 7. It may be a consequence of a tendency (bias) to assign
the same rating of the previous inspection.
3.3 Sufficiency Rating
The sufficiency rating for each bridge is determined by a 0-100 scale and
includes several factors such as safety, serviceability, obsolescence, and importance
for public use [Hadavi, 1998]. Although the states use different criteria for
allocating funds for their bridge infrastructure, historically, bridges with a
sufficiency rating of 50.0 and less are eligible for federal replacement funding.
21


Bridges with a sufficiency rating greater than 50.0 are eligible for rehabilitation
only, unless the cost of rehabilitation exceeds the replacement costs [Lonco, 1996].
The standard form of the structure inventory and appraisal sheet required by
the NBIS includes information about items that are not relevant in determining the
condition of the structure. Moreover the methodology does not include other
important factors. As a consequence, the sufficiency rating used by the Federal
Highway Administration for allocating funds does not reflect the real condition of
the structure. A study conducted by the United States General Accounting Office
about the methodology to determine bridge needs showed that other important
factors should be included for a more realistic eligibility process [Hadavi, 1998;
Amer el al., 1986]. Some of these factors are the importance of the structure for the
economy, volume of traffic, detour length, and ADT x detour length. New
methodologies using indexes based in the condition of individual elements of the
bridges, instead of main components, are recently being adopted [Hooks and
Romack, 1998].
For a more effective and realistic allocation of resources the deterioration
curves for the main components of the bridge structures need be determined. The
integration of other factors related to the achievement of optimal policies in BMSs
also need to be considered.
22


4. Deterioration Model
4.1 Markovian Model
The determination of the future condition of structures in a bridge network
will permit a proactive administration of the network. The prediction of the
deterioration progress in the bridge components helps prevent structural problems
and failures. An optimized allocation of funds cannot be achieved without the use
of deterioration models. When a certain period of time has elapsed after the
deterioration process starts the rate of deterioration increases. From this moment
on, in a relatively short period of time, the component in which the deterioration
occurs will be no longer able to sustain the loads it was designed to carry. This
increase in the rate of deterioration shows the importance of a precise prediction of
the deterioration level.
Models for condition ratings prediction are commonly referred as
deterioration models [Glagola, 1992; Scherer and Glagola, 1994; Bulusu and Sinha,
1997]. Recent publications emphasize that the decrease in the condition ratings may
not accurately represent the deterioration process [Heam and Shim, 1997; Hearn and
Shim, 1998], In fact, the condition ratings are intended to capture the deterioration
process. In this work the decrease in the condition ratings will be considered
23


intrinsically associated with the deterioration process. This relation can be inferred
after analyzing the condition rating guidelines where the word deterioration is used
in the description of five condition ratings (Table 3.1). Therefore, the deterioration
growth determines a decrease on the bridge condition rating. Figure 4.1 shows an
example of condition rating versus time relationship referenced by the U.S. Army
Corps of Engineers [REMR, 1996].
Figure 4.1 Decrease of condition rating with the age of the component.
24


Different methodologies have been used in the prediction of bridge
deterioration. Examples of the application of Bayesian approach, binary probit
model, and Markovian method can be found in the literature [Buluso and Sinha,
1997; White and White, 1989; Sherer and Glagola, 1994], The Markovian chain
approach has been used in several models for bridge and road analysis [Scherer and
Glagola, 1994], According to this methodology the transition probability matrices
are computed by using regression methods for each group of bridges with similar
characteristics. The bridges are grouped according to characteristics that can induce
related deterioration such as bridge age, bridge type, environment, and ADT.
The City and County of Denver, Colorado occupies an area of approximately
150 square miles and in this area the CCD is in charge of maintaining the entire
infrastructure, which includes around 750 bridges. About 250 bridges are under the
jurisdiction of the CCD since 1986 and are biennially inspected. From this group a
subset of 160 bridges that contain at least one decrease in the condition ratings will
be used in this work. APPENDIX B summarizes the information used in the bridge
classification and the condition ratings of the main components of the bridge (58 -
deck, 59 superstructure, and 60 substructure). The inspections took place every
two years since 1986 to 1996; therefore, five transition periods of two years will be
analyzed in this work.
25


Since the prediction model will analyze the deterioration in a biennial basis,
transitions occurring in periods longer than two years will not be considered in this
analysis. The bridge condition ratings always decrease as the age of the bridge
increases as a consequence of its use and by the influence of other factors -
therefore, the condition ratings in the biennial intervals always remain unchanged or
decrease. As a consequence, any increase in the condition ratings will be
considered to result from any maintenance action taken during the two year interval
between the consecutive inspections. The modeling of the repairs and maintenance
actions in the bridges will be later discussed.
The Markovian model can only be applied to a database with a finite number
of states if the transition from a present state to the future state does not depend
upon the previous history of the structure [White and White, 1989; Glagola, 1992],
This property, known as Markovian property, implies that the transition from a
present to the next future state is not influenced by the previous state. The
verification of this property can be done by the analysis of 3 state sequences of
condition ratings in two periods of 2 years. Some examples of verification of the
Markovian property for the three components of the bridge are given below. For the
next sections the two definitions will be used in the examples:
TrXYZ is defined as the number of 3-state sequences where Z is the past state,
Y is the present state, and X the future state, and
26


TrXY is defined as the number of 2-state sequences where Y is the past state
and X is the present state.
Difference is defined as 100*1 TrXVz /TrX'Y1 TrX2Y2Z 2/TrX2Y21, where
1 2
the superscripts indicate different 3-state sequences with X = X .
4.1.1 Deck:
In this example the influence of the past state (5 or 6) in the decrease from
present state 5 to future state 4 will be analyzed. Defining:
Tr455: number of 3-state sequences where 5 is the past state, 5 is the present
state, and 4 the future state (Table 4.1);
Tr456: number of 3-state sequences where 6 is the past state, 5 is the present
state, and 4 the future state (Table 4.1);
Tr55: number of 2-state sequences where 5 is the past state, and 5 is the
present state (Table 4.1);
Tr56: number of 2-state sequences where 6 is the past state, and 5 is the
present state (Table 4.1);
Difference: 100*1 Tr455/Tr55 Tr456/Tr56 I.
Table 4.1
Tr455 = 1 Tr55 = 18 Tr455/Tr55 = 0.0556
Tr456 = 0 Tr56 = 2 Tr456/Tr56 = 0.0000
Difference: 5.56%
The small 5.56% difference in the results (Table 4.1) indicates that the transition
from state 5 to state 4 is not influenced by the previous state 5 or 6.
27


Following the same methodology and definitions to analyze the influence of
the past state (6 or 7) to the future state 6, the following results are found:
Tr666: number of 3-state sequences where 6 is the past state, 6 is the present
state, and 6 the future state (Table 4.2);
Tr667: number of 3-state sequences where 7 is the past state, 6 is the present
state, and 6 the future state (Table 4.2);
Tr66: number of 2-state sequences where 6 is the past state, and 6 is the
present state (Table 4.2);
Tr67: number of 2-state sequences where 7 is the past state, and 6 is the
present state (Table 4.2);
Difference: 100*1 Tr666/Tr66-Tr667/Tr67 I.
Table 4.2
Tr666 = 63 Tr66= 63 Tr666/Tr66 = 1.0000
Tr667 = 3 Tr67 = 3 Tr667/Tr67 = 1.0000
Difference: o o r->
Again, the difference of 0.00% (Table 4.2) shows that the permanence of the
structures on state 6 is not influenced by the previous state 6 or 7.
Applying the same procedure to investigate the influence of the past state (7
or 8) to the future state 6:
Tr677: number of 3-state sequences where 7 is the past state, 7 is the present
state, and 6 the future state (Table 4.3);
28


Tr678: number of 3-state sequences where 8 is the past state, 7 is the present
state, and 6 the future state (Table 4.3);
Tr77: number of 2-state sequences where 7 is the past state, and 7 is the
present state (Table 4.3);
Tr78: number of 2-state sequences where 8 is the past state, and 7 is the
present state (Table 4.3);
Difference: 100*1 1x661/1x11 Tr678ATr78 I.
Table 4.3
Tr677 = 4 Tr77 = 193 Tr677/Tr77 = 0.0207
Tr678 = 2 Tr78= 20 Tr678/Tr78 = 0.1000
Difference: 7.93%
One more time, the minimal difference of 7.93% (Table 4.3) suggests that the
previous states of 6 or 7 do not influence the transition to future state 6.
The results show that the transition from a present state to a future state does
not depend upon the previous state. This indicates that the deck indeed satisfies the
Markovian property.
4.1.2 Superstructure:
Tables 4.4 and 4.5 indicate superstructure results:
29


Table 4.4
Tr455 = 0 Tr55 = 15 Tr455/Tr55 = 0.0000
Tr456 = 0 Tr56 = 3 Tr456/Tr56 = 0.0000
Difference: 3.00%
Table 4.5
Tr566 = 0 Tr66 = 35 Tr566/Tr66 = 0.0000
Tr567 = 1 Tr67 = 7 Tr567/Tr67 = 0.1429
Difference: 14.29%
The low differences of 0.00% (Table 4.4) and 14.29% (Table 4.5) for the
superstructure indicate adherence to the Markovian property.
4.1.3 Substructure:
For the substructure, the results are shown in Tables 4.6 and 4.7 :
Table 4.6
Tr566 = 1 Tr66 = 48 Tr566/Tr66 = 0.0208
Tr567 = 0 Tr67 = 3 Tr567/Tr67 = 0.0000
Difference: 2.08%
Table 4.7
Tr788= 13 Tr88 =55 Tr788/Tr88 = 0.2364
Tr789 = 1 Tr89 = 7 Tr789/Tr89 = 0.1429
Difference: 9.35%
30


The differences of 2.08% (Table 4.6) and 9.35% (Table 4.7) again suggest the
validation of the Markovian property.
The results presented in Sections 4.1.1 to 4.1.3 indicate that the condition
ratings of the deck, superstructure, and substructure for the period of time
considered in this analysis satisfy the Markovian property.
4.2 Transition Matrices
The following Sections present two steps that need to be taken for the
calculation of deterioration curves. The adequacy of the deterioration curves to
reflect the behavior of the bridges strongly depends upon these steps.
4.2.1 - Classification Schemes
The arrangement of the bridges into different groups according to
classification schemes is an important factor in the analysis of the deterioration.
The deterioration of each bridge component (deck, superstructure, and substructure)
in each group will be analyzed separately. The bridge characteristics that affect the
deterioration are used to classify the structures into groups. The factors usually
employed that can induce related behavior of the deteriorating bridge structures
include: age, bridge type, deck type, number of spans, environment, and average
daily traffic. The configuration of the classification schemes is limited by the
31


number of bridges in each subgroup. A small number of bridges in a subgroup do
not constitute a representative set for the determination of transition probability.
With only a few bridges at a determined condition rating in any period of time it is
likely to have each bridge deteriorating to the same lower condition rating a
spurious absorbing state would be created. This occurs when the number of bridges
is not large enough to reflect the probabilistic behavior of the deteriorating
structures in the bridge network. With a large number of bridges in a data set it is
more probable to have some bridges with the same rating and other bridges with
lower ratings for future inspections. Therefore by increasing the number of bridges
with any particular condition rating the spurious absorbing states can be avoided.
Because of the limitations in the number of data available from the bridge
inspections, only two classification schemes were used. Spurious condition states
were created by using classification schemes that use more than one parameter. For
example, in a classification scheme that groups the bridges according the ADT
(10,000 as a threshold) and age (3 age groups) simultaneously several spurious
absorbing states were found in the 6 subgroups generated. As a consequence, in
order to avoid spurious absorbing states, each classification scheme considers only
one parameter to divide the bridges in subgroups and is described below.
The first classification scheme considered the bridges divided into three
groups according to the year they were constructed.
32


1. bridges built before 1960,
2. bridges built from 1960 and before 1980, and
3. bridges built in 1980 and after.
The second classification scheme grouped the bridges in accordance with the
average daily traffic into two groups.
1. bridges with ADT less than 10,000, and
2. bridges with ADT equal to 10,000 or more.
Almost all the structures had their ADT measured in 1991 or 1992. Although the
value of the ADT can have slight variations for different years the effect of these
changes in the ADT did not affect the classification schemes. Therefore no
corrections were made for the measured ADT of the structures.
Whenever the data was insufficient to be used in the deterioration model the
information from all the structures without classification schemes was used.
The matrices in Figure 4.2 summarize the number of transitions in the five
consecutive two years intervals considered in the model, i.e. from 1986 to 1996.
The condition ratings 0, 1, and 2 were not considered because the structures are
usually replaced when the condition rating of its components reach these values.
Although the deterioration model is based on a group of 160 bridges, since
this constitutes a representative subset (about 80%) of the inspected structures, the
33


deterioration model can be applied to any bridge in the CCD. For the application of
the model to any other bridge the ADT, year of construction, in addition to the
condition ratings for any one year must be provided. The ADT and the date of
construction are used to classify the bridge whereas the one year condition ratings
are used to predict future conditions. All 160 bridges used in this study are
represented in the matrices shown in Figure 4.2.
The ratings and the indexes of the columns and rows are shown in each
matrix. The entries represent the total number of condition ratings that changed or
remained the same for all the 2.year periods considered. The zero entries in the
upper triangle of the matrices indicate that any increase of condition ratings was not
considered. The diagonal elements correspond to the ratings that remained
unchanged in consecutive inspections. The row 7, last row, in the last matrix (60
substructure) has the following elements:
Ratings 3 4 5 6 7 8 9
1 2 3 4 5 6 7
9 7 0 0 0 0 3 11 5
The notation a The element a<7i7)=5 corresponds to five bridges that had the ratings for their
substructures unchanged in consecutive inspections. In the same row the elements
a(7,6)= 11 and a<7>5)=3 show that eleven substructures changed their ratings from 9 to 8
34


in consecutive inspections and that three substructures changed the condition ratings
from 9 to 7, respectively.
58 deck
Ratings 3 4 5 6 7 8 9
1 2 3 4 5 6 7
3 1 0 0 0 0 0 0 0
4 2 1 8 0 0 0 0 0
5 3 0 3 27 0 0 0 0
6 4 0 0 2 95 0 0 0
7 5 0 0 0 7 285 0 0
8 6 0 0 0 0 22 45 0
9 7 0 0 0 0 5 11 5
59 superstructure
Ratings 3 4 5 6 7 8 9
1 2 3 4 5 6 7
3 1 9 0 0 0 0 0 0
4 2 1 6 0 0 0 0 0
5 3 0 0 25 0 0 0 0
6 4 0 0 4 55 0 0 0
7 5 0 0 0 11 263 0 0
8 6 0 0 0 1 14 88 0
9 7 0 0 0 0 1 16 15
60 substructure
Ratings 3 4 5 6 7 8 9
1 2 3 4 5 6 7
3 1 4 0 0 0 0 0 0
4 2 1 8 0 0 0 0 0
5 3 0 4 29 0 0 0 0
6 4 1 1 2 81 0 0 0
7 5 1 0 1 9 245 0 0
8 6 0 0 0 1 18 87 0
9 7 0 0 0 0 3 11 5
Figure 4.2 Transitions of condition ratings for the deck,
substructure, and superstructure for all bridges. The lines
and columns of the matrices are indicated in gray.
35


Some data distortions were found in the matrices in Figure 4.2:
Row 3 in the matrix of the superstructure condition rating transitions indicates
that all 25 structures will remain in the same state (condition rating 5) instead of
deteriorating to a lower condition rating this state is called absorbing state.
Since this behavior cannot be true, i.e. the superstructure of the bridges will
deteriorate and reach condition rating lower than 5, is was assumed that the
deterioration from the rating 5 to lower ratings would happen with the same
probability the bridges will deteriorate from state 6 to lower states. Therefore,
a<3,2)= a<4,3)=4, and a^^p ap4p55.
The elements a^jpl and apipl in the substructure matrix were not considered
and were set equal to zero. These elements represent the transition from
condition rating 6 to 3, and 7 to 3, respectively. Since a progressive decrease in
the condition ratings is expected this decrease of more than 2 in the condition
ratings in consecutive years was assumed to be consequence of a specific
problem, such as an impact, in these two structures.
In the matrices with the transitions of condition ratings (in the classification
schemes) whenever there were not enough transitions, or in the occurrence of
spurious absorbing states, data from the matrices in Figure 4.2 was used. Appendix
C shows details of the changes made in the transition matrices. These modifications
to the matrices were necessary in order to obtain the transition probability matrices.
36


4.2.2 - Transition Probability Matrices
The transition probability matrices, or probability matrices, represent the
probability of changes in the condition ratings to a lower value or remaining the
same. Figure 4.3 shows a generic transition probability matrix.
Ratings 3 4 5 6 7 8 9
1 2 3 4 5 6 7
3 1 an.i> 0 0 0 0 0 0
4 2 3an ^2.2) 0 0 0 0 0
5 3 3(3.n 3(3.2) 3(3.3) 0 0 0 0
6 4 0 3(4.2) 3(4.3) 3(4.4) 0 0 0
7 5 0 0 3(3.3) 3(5.4) 3(5.5) 0 0
8 6 0 0 0 3(6.4) 3(6.5) 3(6.6) 0
9 7 0 0 0 0 3(7,5) 3(7.7) 3(7.7)
Figure 4.3 Generic transition probability matrix.
The elements am) represent the probability of changes in the condition
ratings from a state n+2 to a state m+2. The element a<3j) indicates the likelihood of
a transition from a condition rating 5 (3+2) to a condition rating 3 (1+2). The zeroes
entries in the upper triangle indicates the impossibility of changes in the condition
ratings to higher values than the in the previous inspections. Since change of more
than 2 in the 0-9 condition rating scale in consecutive years will not be considered
in the deterioration model, the elements am+2 were set equal to zero
[Jiang et al., 1988].
37


After eliminating the data distortions, i.e. spurious absorbing states and rows
with all entries equal to zero, the transition probabilities were obtained by the
application of two methodologies. If the size of the sample (the total number of
transitions in each row) was equal to or greater than 30 a Poisson mass function was
employed to determine the probability of the transitions. If the size of the sample
was less than 30 the probability was determined by the ratio between each element
and the size of the sample. For example, in the row 7 in the last matrix (60
substructure) the total number of elements is 19:
Ratings 3 4 5 6 7 8 9
1 2 3 4 5 6 7
9 7 0 0 0 0 3 11 5
the probability of a decrease from a condition rating 9 to 7 is 3/19 = 0.158. Further
explanation about these procedures to determine the probabilities can be found in
other works [Glagola, 1992; Jiang et al., 1988].
The transition probability matrices represent the likelihood of the changes in
the condition states in a period of two years. Since the condition state 3 is the
minimum value considered in this analysis this is the state to which all the
components of the bridges tend to deteriorate. Therefore, the state 3 is a absorbing
state and the element a(ij) in the transition probability matrices is always equal to
1, which implies that the likelihood of a change to a lower state is zero and that all
38


the bridges in this state will not deteriorate further. Figure 4.4 shows the transition
probability matrix for the deck of the bridges with ADT less than 10,000.
58 deck
Ratings 3 4 5 6 7 8 9
I 2 3 4 5 6 7
3 1 1.000 0.000 0.000 0.000 0.000 0.000 0.000
4 2 0.200 0.800 0.000 0.000 0.000 0.000 0.000
5 3 0.000 0.200 0.800 0.000 0.000 0.000 0.000
6 4 0.000 0.000 0.014 0.985 0.000 0.000 0.000
7 5 0.000 0.000 0.000 0.020 0.980 0.000 0.000
8 6 0.000 0.000 0.003 0.033 0.222 0.741 0.000
9 7 0.000 0.000 0.000 0.000 0.067 0.600 0.333
Figure 4.4 Transition probability matrix for the
deck of the bridges with ADT less than 10,000.
In this matrix the elements represent the likelihood of the changes in the condition
ratings. Line 5 is shown below:
Ratings 3 4 5 6 7 8 9
1 2 3 4 5 6 7
7 5 0.000 0.000 0.000 0.020 0.980 0.000 0.000
The elements a<5,D= a<5,2)= a^jpO.OOO indicate that the probability of a decrease in
the condition rating from 7 to 5, 4, or 3 is null. Element a<5,4)=0.020 shows the
probability of a change in the condition rating from 7 to 6. The probability that a
deck in this group will remain with a condition rating 7 in the next 2 years is
a<5,5)0.980. The elements a<5,6) and a^j) are equal to zero because a deck will never
improve its condition unless a maintenance action is taken, i.e. the structures
monotonically deteriorate as the age increases [Jiang et al. 1988]. Appendix C
39


contains the transition matrices for all the subgroups of each classification scheme
used in this work.
4.3 Deterioration Curves
The transition matrices represent the probability of the occurrence of
transitions of condition states. If the condition of a bridge is defined at any time, its
future condition can be calculated by multiplying the matrices by the vector that
represents the condition of the bridge. After calculating the condition of all bridges,
the global condition of the bridge network can be evaluated.
Defining the initial condition vector for a bridge as following:
Ratings 3 4 5 6 7 8 9
1 2 3 4 5 6 7
Initial state 0 0 0 0 0 0 1
the initial condition vector of the main components of a new bridge would be:
p = [0 00000 1]
where the element a7 =1 corresponds to a condition rating 9 for the deck,
superstructure, or substructure. The appropriate subgroup of the bridge being
analyzed needs to be determined. After this classification, the transition probability
matrix can be used to forecast the future condition states for the main components
40


on a two-year interval basis. The future condition states are obtained multiplying
the initial condition vector by the transition probability matrix M:
p0 = [00 0000 1]
pi = p0 M
P2 = pi M = po M2
Pn = Po M"
where M represents the transition probability matrix, and pn is the condition state
vector after n periods of two years. The condition of each bridge component can be
calculated by the sum of the elements of pn R, where R is the vector of the
condition ratings.
In the example below the transition probability matrix for the bridges built
from 1960 and before 1980 (Figure 4.5) was used to determine the deterioration
curve of the substructure of a new bridge. The results are summarized in Table 4.8.
The deterioration curve with the decrease of the substructure condition rating, for a
60 years period is shown in Figure 4.6.
The deterioration curve shown in the Figure 4.6 markedly denotes a bias to
assign condition ratings 8 in the second inspection after the construction of the
bridge.
41


Ratings 3 4 5 6 7 8 9
1 2 3 4 5 6 7
3 1 1.000 0.000 0.000 0.000 0.000 0.000 0.000
4 2 0.111 0.889 0.000 0.000 0.000 0.000 0.000
5 3 0.007 0.107 0.886 0.000 0.000 0.000 0.000
6 4 0.000 0.001 0.045 0.953 0.000 0.000 0.000
7 5 0.000 0.000 0.001 0.041 0.958 0.000 0.000
8 6 0.000 0.000 0.001 0.011 0.138 0.850 0.000
9 7 0.000 0.000 0.000 0.000 0.158 0.579 0.263
Figure 4.5 Transition probability matrix for the substructure
of bridges built between 1960 and 1980.
The condition ratings 7 and 6 assigned to structures in a good or satisfactory
condition (Table 2.1), have more inertia these states have the highest probability
to remain at the same condition. For this reason, in the main diagonal of the
transition matrix (Figure 4.5), the elements a<4,4) and a^) are less than the element
ad,D=l .000 which is an absorbing state. A similar behavior was found in the
analysis of the deck and superstructure. Other deterioration curves for the
remaining classification schemes can be found in Appendix D.
The modeling of the maintenance actions can be performed in the same way
as the deterioration. The maintenance action can be associated with increments in
the condition ratings therefore upper triangular transition probability matrices
would be obtained. The creation of these matrices depends upon the availability of
historical records about the maintenance actions. A more complex task is the
42


analysis of costs associated with the actions. In this case, since the bridge
population includes several different types of structures, an individual
Table 4.8 Condition rating vectors and condition
ratings of the substructure for a 60 year analysis.
Year Condition rating vectors Rating
0 0 0 0 0 0 0 1.0000 9.0000
2 0 0 0 0 0.1580 0.5790 0.2630 8.1050
4 0 0 0.0009 0.0167 0.2975 0.6155 0.0692 7.7341
6 0 0.0002 0.0034 0.0475 0.3979 0.5324 0.0182 7.5108
8 0.0000 0.0007 0.0074 0.0874 0.4623 0.4365 0.0048 7.3352
10 0.0001 0.0018 0.0131 0.1322 0.4981 0.3520 0.0013 7.1799
12 0.0003 0.0038 0.0201 0.1786 0.5124 0.2823 0.0003 7.0367
14 0.0008 0.0066 0.0283 0.2244 0.5110 0.2260 0.0001 6.9027
16 0.0016 0.0103 0.0373 0.2678 0.4985 0.1809 0.0000 6.7763
18 0.0029 0.0151 0.0469 0.3078 0.4783 0.1447 0.0000 6.6563
20 0.0048 0.0207 0.0567 0.3437 0.4532 0.1158 0.0000 6.5418
22 0.0074 0.0272 0.0665 0.3752 0.4252 0.0926 0.0000 6.4321
24 0.0108 0.0344 0.0761 0.4023 0.3957 0.0741 0.0000 6.3265
26 0.0151 0.0422 0.0852 0.4249 0.3658 0.0593 0.0000 6.2245
28 0.0204 0.0505 0.0939 0.4433 0.3363 0.0474 0.0000 6.1256
30 0.0267 0.0591 0.1018 0.4577 0.3078 0.0379 0.0000 6.0294
32 0.0341 0.0678 0.1090 0.4683 0.2806 0.0303 0.0000 5.9355
34 0.0425 0.0766 0.1155 0.4756 0.2549 0.0243 0.0000 5.8438
36 0.0521 0.0853 0.1211 0.4798 0.2310 0.0194 0.0000 5.7541
38 0.0628 0.0938 0.1259 0.4812 0.2088 0.0155 0.0000 5.6661
40 0.0745 0.1019 0.1299 0.4803 0.1883 0.0124 0.0000 5.5798
42 0.0872 0.1097 0.1331 0.4772 0.1695 0.0099 0.0000 5.4951
44 0.1010 0.1169 0.1356 0.4722 0.1523 0.0080 0.0000 5.4119
46 0.1156 0.1237 0.1373 0.4657 0.1367 0.0064 0.0000 5.3303
48 0.1310 0.1298 0.1384 0.4579 0.1225 0.0051 0.0000 5.2502
50 0.1473 0.1354 0.1389 0.4489 0.1097 0.0041 0.0000 5.1716
52 0.1642 0.1403 0.1388 0.4390 0.0981 0.0033 0.0000 5.0945
54 0.1817 0.1446 0.1382 0.4283 0.0877 0.0026 0.0000 5.0190
56 0.1998 0.1482 0.1372 0.4170 0.0783 0.0021 0.0000 4.9450
58 0.2183 0.1512 0.1357 0.4053 0.0699 0.0017 0.0000 4.8726
60 0.2372 0.1536 0.1339 0.3933 0.0623 0.0013 0.0000 4.8019
43


Deterioration curve: substructure
Figure 4.6 Deterioration curve of the substructure for a period of 60 years.
analysis of each structure would be required. Unfortunately, unavailability of
detailed information regarding the expenses in the bridge network created an
obstacle to the development of the maintenance model. Further information about
maintenance transition matrices can be found in Glagola (1992).
The deterioration curves are currently being used to establish priorities in the
application of resources in the maintenance of the bridge network in the CCD. The
44


Users Manual of the computer program that was developed to administrate the
bridge network at CCD is presented in Appendix E. The pilot study for the creation
of a BMS on a GIS platform permits the registration of detailed maintenance
information of the bridges [Rens et al., 1998].
45


5. Nondestructive Evaluation and Bridge Management Systems
5.1 Overview
In the visual inspection of the main components of the bridge the inspector
carries out a subjective operation. When the inspector assigns an overall condition
rating (Table 2.1) to the deck, superstructure, or substructure the inspector makes an
idiosyncratic decision. The past experience of the inspector plays an important rule
in this operation. The subjective decision in the condition rating assignment may
deliver a good indicator of the general condition of the bridge but cannot be the only
parameter for decisions on maintenance actions.
Another intrinsic characteristic of the condition ratings is its limitation to
convey the particular problems of each bridge. A condition rating 7, for example,
can be associated with many different problems in concrete, steel, or timber bridges.
Condition ratings are limited information that do not address particular problems of
the structures nor convey complex deterioration processes commonly found in
bridges. Condition ratings are qualitative information based on subjective opinions
independent of the implications of deterioration. These limitations in the condition
ratings constitute a matter of great concern to researchers of BMSs and are referred
46


in many works as a critical problem [Shepard, 1998; Hearn and Shim, 1998; Hearn
and Shim; 1998b].
New methodologies for bridge inspections and new condition ratings have
been introduced in recent years. Inspections based on standardized Commonly
Recognized (CoRe) elements have been developed and accepted as an alternative to
the NBI conditions ratings since 1995 [Shepard, 1998]. The Pontis bridge
management system, which has been developed under the auspices of the FWHA
and adopted by several state Departments of Transportation in the United States,
uses new 4-state and 5-state condition ratings scales based on the CoRe elements
[Heam and Shim, 1997]. Procedures to convert CoRe element data into NBI
condition ratings have been successfully developed and officially accepted by the
FHWA [Heam et ai, 1997; Shepard, 1998], Although these new condition ratings
are more accurate than the NBI condition ratings and undoubtedly capture the
deterioration process more precisely, they also have some limitations.
The importance of applying more powerful and accurate tools as a
supplement of the visual inspection has been addressed in the BITM [Hartle et al.
1990]. The Manual refers to NDE techniques in the Chapter 15 Advanced
Inspection Techniques. Two of the applications of NDE listed in the BITM are:
Evaluation of defects found in the visual inspections;
47


Inspection of components that cannot be readily evaluated using visual
inspection;
In the brief description about the NDE techniques in the BITM no reference is made
of any association of applying NDE technology to condition ratings.
NDE techniques have many advantages when compared with other
conventional inspection techniques:
No damage or sacrifice of specimens is required;
NDE techniques can be applied for in-service inspections;
NDE techniques allow early detection of flaws and defects;
Depending upon the method a very precise characterization of the defect extent
can be achieved;
Nevertheless, because of their complexity there are several obstacles to the
application of NDE techniques in bridge management systems:
NDE results are complex and provide detailed information;
Experience is required to handle NDE equipment;
Expertise is necessary for interpretation of NDE results;
NDE output usually consists of quantitative information;
In order to permit a direct association of condition states and NDE results
and to allow an integration of NDE and BMSs, Hearn and Shim have proposed new
condition states corresponding to states of the member service life [Hearn and Shim,
48


1997; 1998, and 1998b]. The proposed five condition states (protected, exposed,
vulnerable, attacked, and damaged) are each mutually exclusive, detectable by the
application of NDE techniques, and are associated with repair or maintenance
actions. The condition ratings can be used in parallel definitions for different
deterioration processes. In the application of the NDE methods thresholds are
defined to indicate probabilistic transitions of condition states [Hearn and Shim,
1998],
Although the proposed methods represent an advance in the association of
NDE and BMSs several deficiencies restrict its application in any bridge inspection
which are detailed below:
Visual inspection, which constitutes the must important tool in bridge
inspection, is not considered in the proposed condition states. The importance
of visual inspection in BMSs cannot be overemphasized. In citing an
anonymous adage Eighty percent of the defects are found by visual
inspection Bray and Stanley (1997) well stress the importance of this method.
Some common forms of deterioration (such as cracking, wear, efflorescence,
potholes, scaling, and pop-outs) do not require NDE techniques to be detected
and evaluated. Visual inspection techniques are a very powerful methodology
that needs to precede the application of NDE methods. While visual inspection
also requires experience and training, the costs associated with its application
49


are less than expenditures with advanced NDE techniques. The use of NDE is
more likely to provide additional information about a defect which existence is
already suspected. NDE techniques should not be regarded as a diagnostic
technique in itself [Minor et al. 1988].
The method depends entirely upon application of NDE technology. For the
application of the method it would be necessary to use several different NDE
methods to make any distinguishing differences between the condition states.
Each different deterioration process requires a unique set of NDE methods to be
evaluated. Considerable time and expenditures would be required to apply such
a large set of different NDE methods in each inspection. Although application
of NDE can be most advantageous in quantifying defects, it is possible to
increase the sensitivity of detection to the point where identification of flaws is
either false or confusing [Manning, 1985]. Havadi (1997) states that it is
generally very expensive and is considered a waste of valuable resources to
allocate a large budget for NDE inspection of every bridge at this time.
The probabilistic definition of the thresholds for the interpretation of the NDE
results can lead to erroneous or inconclusive results. For example, in the
application of half-cell potential test to determine the corrosion activity of the
reinforcing steel (ASTM C 876-91) no conclusion can be accomplished if
potentials are in the range of -0.20 to -0.35 V CSE (ASTM C 876-91; X. 1.1.2).
According to the ASTM standard this test can not be applied to epoxy coated
50


reinforced concrete and the measurements need to be interpreted by experienced
personnel. It is often necessary to use data other than half-cell potential
measurements to draw conclusions about corrosion activity. Even though the
half-cell potential measurement is a very simple NDE method its application is
not a straightforward process. Naive use of NDE technologies without
knowledge of its limitations or without appropriate expertise in the interpretation
of the results surely leads to erroneous results. Other NDE methods such as
acoustic emission, impact-echo, ultrasonic, ground penetration radar, and
tomography demand much more expertise and experience for their application.
The application of NDE methods must be preceded by visual inspection and
be restrained to a subset of structures in the bridge network. The techniques need to
address specific problems in the bridges. Although there is a fundamental
difference between the qualitative results from a visual inspection and the
quantitative output by applying NDE methods, the visual condition ratings can be
used to help assess the severity of the deterioration process. Therefore, the divorce
between the visual and NDE inspections cannot be ignored in any bridge inspection
program.
Prior to the application of an NDE method the more adequate technology for
the problem needs to be determined. The type, severity, and extension of the
51


deterioration are parameters that help the selection of the more appropriate NDE
method in each group of deteriorated bridges.
5.2 Deterioration models and NDE methods
The probabilistic deterioration models models to forecast the decrease in
the condition ratings, such as the Markovian model can play an important rule in
the application of the NDE methods. The severity and extent of the degradation can
be estimated from the probabilistic deterioration curves. According to the budget
restraints, thresholds based in the condition ratings can be determined. For
example, in the NBI condition rating scale (Table 2.1) a rating 3 (serious condition)
usually is an alert to replace the structure. In this scale, according to the availability
of resources a condition rating of 4 (poor condition) or 5 (fair condition) could
signalize an application of an NDE method.
A methodology to apply NDE based upon NBI condition ratings can be
easily adapted to other condition rating scales. In each system, the ratings that
address degradation processes that can be evaluated by NDE techniques need to be
determined. Since this approach can be used with different condition rating scales
the available historic information used in the deterioration model adopted will not
be disregarded. Widely used in any deterioration model, the historic databases are a
precious fount of information that can not be ignored. The information in any
52


database reflects the factors that determine rates of deterioration including regional
environment conditions. Many times these databases contain information regarding
several years of inspections and the decision on the adoption of other condition
rating scales needs to be cautiously analyzed.
5.3 Types of deterioration and NDE methods
Information about the severity and extent of the deterioration process can be
partially obtained from the deterioration curves. Another very useful source of
information is the inspection reports. The reports contain detailed information about
the type, position, and extent of the deterioration. Before the application of any
NDE method the inspection notes need to be studied and the more appropriate NDE
technique needs to be defined. Photographs taken during the inspections that are
contained in the inspection reports can help define the NDE method to evaluate the
deterioration.
The deterioration processes most commonly found in the bridge network
need to be determined for each material (timber, concrete, or steel) used in bridge
construction. The pertinent NDE techniques can be defined and applied after the
deterioration type for each material is defined. The results obtained by the
application of the NDE method will be taken into account in the assignment of the
condition rating for the component. Therefore, the NDE method will be used to
53


accurately determine the extension and implications of the deterioration. It is
important to emphasize that the dissociation between NDE techniques and BMSs
will be eliminated with the interpretation of the results and rating of the component.
The transformation of the complex NDE output into data that can be used in BMSs
(i.e. a condition rating) will take place in the assignment of a more accurate rating
for the component.
5.4 Integration of NDE and BMS
NDE methods can be integrated in the deterioration model of BMSs after
determining threshold condition states and types of deterioration. The proposed
methodology to integrate NDE and BMS, from now on referred as Bridge
Evaluation using Nondestructive Testing BENT, can be summarized as follows:
1. Determination of the subset of the bridge network where the NDE tests will be
performed. This operation implies the definition of a threshold condition rating.
Deterioration models can be used to forecast future condition ratings. The
structures that fall below the threshold in any determined time period (present or
future) will be analyzed for the application of NDE techniques.
2. Determination of the most common and critical types of deterioration according
to the component and material. The definition of the types of deterioration must
be connected to an associated NDE method that will be used in its evaluation.
54


3. Definition of the NDE method for each type of deterioration for each material.
It is reasonable to choose methods that are already in advanced stage of
development and acceptance. Methods in early stages of research and
development are usually more expensive and less reliable.
4. Application of the NDE methods in the inspection of the selected bridges.
During the field inspection, the selected NDE methods will be applied to assess
each deterioration process detected in the bridges. This operation needs to be
performed by trained personnel with experience in the use of the selected
methods.
5. Rating of the component. The condition rating assigned to the component must
consider the information from the NDE results. The personnel responsible for
the application of the NDE technique must report the results to the inspector.
The extent and implications of the deterioration must be reflected in the
condition rating.
An interpretation of the NDE results prior to the condition rating assignment
is a necessary step to integrate the use of NDE methods and BMSs. Interpretation
of NDE results requires knowledge about the physical phenomena reproduced in the
application of the NDE method. Expertise in the investigation of the results is
required. Hearn and Shim (1998a) suggest three parameters to evaluate the
performance of the NDE methods applied to a bridge inspection: accuracy,
55


variability, and uncertainty. To obtain quality results when applying NDE methods,
adjustments related to these three parameters may be necessary. In addition to
training and experience, the interpretation of the NDE results may require ingenuity
and art. Ingenuous understanding of the results can lead to untrue conclusions.
Although this analysis can not be performed in an automatic fashion and effect in
the interpretation of the NDE output will be required it is an essential step in the
integration of NDE and BMS.
Since costs are associated with introduction of NDE methods in the
inspections it is advantageous to select NDE techniques that can be applied in a
large number of structures. Some methods are more versatile and can be applied to
assess different deterioration types. The impact-echo method, for example, can be
used to determinate plate thickness, cracks, delaminations, and voids in grouted
ducts [Sansalone and Streett, 1997].
56


6. Nondestructive Evaluation Applied to Concrete Bridge Inspection
6.1 Introduction
This Chapter presents an application of the BENT methodology developed
in Chapter 5. The development of the method here will be restrained to concrete
bridges. The use of the method in steel or timber bridges can be performed in a
similar way but for these materials other deterioration processes will occur and
consequently other NDE techniques will be required.
Some important aspects of the evaluation of concrete components in bridges
were addressed by Miller and Parekh (1994) who performed destructive testing of a
deteriorated prestressed beam. The authors call the attention to the lack of clear
guidelines and methods to evaluate the strength of deteriorated members. Two of
the conclusions of the authors are of great importance for bridge inspections
associated with BMSs:
The AASHTO Code was not conservative for the deteriorated beam tested. The
ultimate moment for the beam in test was found to be 8% lower than the
moment predicted by the ASSHTO Code.
The failure of the deteriorated beam occurred suddenly while a ductile behavior
was observed in an undamaged beam that was also tested.
57


These conclusions help reiterate the importance of applying new tools in bridge
inspection to prevent failures.
The NDE methods that will be described in Chapter 6 address some of the
demands of each state Department of Transportation (DOT) in the United States.
Surveys about the use of applications of nondestructive inspections in the DOTs
were conducted in 1993 [Rens et. al., 1997] and 1996 [Rens and Transue, 1998].
Questionnaires sent to the 50 DOTs in the 1996 survey yielded more than 80%
response rate and according to the respondents around 90% use some kind of NDE
technique. Information about the concerns of the respondents in the 1996 survey are
compiled in Tables 6.1 and 6.2 [from Rens and Transue, 1998]:
Table 6.1 Information required in evaluation of concrete structures.
Information concerning concrete members Number of respondents who require (desire) this information
Rebar information 32
Location of flaws 27
Strength 21
Stress state 7
Loss of prestress strength 3
Tendon corrosion 1
Other 4
Prestress strength loss and tendon deterioration are worthy of special attention
because these deterioration processes were not prompted in the questionnaires, both
58


Table 6.2 Problematic concrete members.
Type of member Number of respondents who find these members problematic to evaluate
Decks 30
Bridge piers 23
Column caps 21
Abutments 12
Prestress strands 8
Girders/beams 6
Other 4
are from write-in comments of several respondents. Since tendons are highly-
stressed elements even small corrosion can cause brittle failure, as reported in the
destructive testing of a deteriorated prestressed beam by Miller and Parekh (1994).
The necessity of ways to inspect concrete other than visual inspection was
addressed in a specific question in the work of Rens and Transue: Do you perceive a
need to assess concrete (beyond visual inspection)? More than 90% of the
respondents of the 1996 survey gave a positive answer [Rens and Transue, 1998].
Another question referred to future developments of the NDE techniques: Is
there an NDE application that is in need of further research and development? The
answers indicated need of further progress in several areas in concrete, steel, and
timber inspection. The answers referring to concrete inspection are listed below
[Rens and Transue, 1998]:
59


Table 6.3 Further development needs general.
1 Refinements of the existing technology
2 Adaptation of NDE to civil engineering field conditions
3 Faster inspection process and simplified interpretation of results
4 Elimination of operator-depending results
5 Acoustic emission inspection techniques
Table 6.4 Further development needs reinforced and prestressed concrete.
1 Direct measurement of in-place concrete strength
2 In-place concrete deterioration
3 Concrete deck evaluation through bituminous pavement
4 Live load stress in both steel and concrete
5 Size of subsurface flaws
6 Crack detection and crack growth
7 Prestress strand condition
8 Steel corrosion in prestressed concrete
9 Prestressed concrete girders
10 Prestress strands in deck units
11 Condition of epoxy-coated steel that is embedded in prestressed concrete girders
12 Corrosion detection of prestress and post-tension strands
6.2 - General guidelines on the use of NDE techniques
The application of the NDE methods must be preceded by visual inspection.
NDE technology can be used to obtain additional information of deterioration
processes already identified or suspected to exist by the inspector [Minor et al.,
1988], Some of the methods can only be carried out by experienced personnel. In
60


some cases it may be necessary to apply more than one NDE method to identify and
characterize the deterioration.
Although visual inspection is sometimes referred to as an NDE technique
this important method will not be directly addressed in this work. This technique
has been applied for bridge inspections for decades and extensive references are
available [Hartle et al., 1990; Minor et al., 1988]. The use of visual inspection must
be prior to the application of other NDE methods. Vibration analysis, a minor NDE
technique, is not even considered an NDE method by many individuals [Rens et al.,
1997], this method will also be excluded.
6.3 - Development of the BENT method
This section brings details of steps 1, 2, and 3 of Section 5.4 of Chapter 5.
Since the two final steps are strongly dependent upon the structure and budget
constraints of the agency responsible for the bridge network administration they will
not be detailed in this work.
Step 1 Determination of the bridges to be inspected with NDE methods:
The determination of the bridges that will be inspected with NDE equipment can be
based on present or future condition ratings of the bridges. The future condition
ratings can be evaluated by the use of deterioration models. In this example, the
61


Markovian deterioration model described in Chapter 4 was used to determine the
critical structures in the year 2010. Table 6.5 shows the most critical structures
(minimum condition rating less than 4) in ascending order:
Table 6.5 Critical structures in the CCD (year 2010).
- CRITICAL BRIDGES INFORMATION --------------------------
structure | number | 1. 58 | deck | 59 | superstr | 60 | substruc | 1. minimum rating
1 D-02-PR-060 3.408022 3.000000 1 3.696441 3.000000
D-02-PR-120 5.675444 5.566893 3.000000 3.000000
D-03-V-090 3.107374 5.367710 3.000000 3.000000
D-03-V-110 3.787109 3.000000 3.000000 3.000000
D-16-LG-160 5.811832 3.000000 5.496465 3.000000
D-01-CC-282 3.183142 3.042235 3.696441 3.042235
D-03-V-050 3.308331 3.056314 3.850279 3.056314
D-03-V-060 3.107374 4.226426 3.775328 3.107374
D-03-V-030 3.249360 4.220438 3.861733 3.249360
D-27-MP-110 6.885425 3.339520 5.496465 3.339520
D-01-CC-270 5.729345 6.348860 3.392696 3.392696
D-02-PR-100 4.154667 5.211925 3.392696 3.392696
D-09-CLC-010 5.675444 6.743075 3.438846 3.438846
D-01-CC-310 5.729345 5.211925 4.058598 4.058598
In the year 2010 a total of 13 bridges will have at least one of the main
components (deck, superstructure, or substructure) with a condition rating less than
4. Since these will be the most critical structures at that time, NDE techniques will
be applied in their inspection to precisely determine the extension of the
deterioration of each component. The appropriate maintenance actions that can be
proactively taken at present (1998) can then be determined.
Step 2 Determination of the deterioration mechanisms:
62


After a detailed analysis of the biennial inspection reports of the 13 bridges in Table
6.5 several types of deterioration mechanisms were identified. In the analysis of the
inspection reports the photographs play a very important role in helping identify the
different types of deterioration. Even detailed written descriptions of the
deterioration on the bridges can not provide explicit information as the photographs
do. Appendix E shows a total of 20 photographs indicating the main deterioration
processes in the 13 bridges. Each of the following deterioration processes was
found to occur in many of the selected bridges.
/. Efflorescence: Efflorescence is an indicator of contaminated concrete. It is
caused by crystallization of soluble salts carried to the surface by moisture in the
concrete [Hartle et ai, 1990]. Efflorescence is therefore a consequence of
moisture absorption and flow. Calcium carbonate, an almost insoluble product,
is the most common efflorescent salt found on concrete [St John et ai, 1998],
The passage of water can dissolve solids formed during the hydration of the
cement and may cause serious disintegration of concrete [Troxell et al., 1968].
Efflorescence may be an indicator of this process. Since one of the main factors
that affect corrosion on the reinforcing steel is concrete permeability,
efflorescence may be an evidence of incipient corrosion. The presence of rust
stains on the efflorescence (efflorescence is usually white) is a stronger indicator
of reinforcing steel corrosion. Furthermore, many aspects of the durability of
concrete depend upon the quality of the surface layer [St John et ai, 1998].
63


NDE methods to assess the condition of the reinforcing steel and to evaluate
distributed concrete damage can be used in concrete regions with intense
efflorescence. Photographs 1 through 5 (Appendix E) show examples of
efflorescence on the bottom of bridge decks.
2. Cracking: Hairline cracks are common in reinforced concrete and generally
have no effect on the structural performance of the structure. Medium and large
cracks are relevant but their importance depends upon many factors (such as
position on the structure, crack growth, length, and origin). In prestressed
concrete cracks are usually associated with serious problems. Since prestressed
concrete is subjected to high compression, no cracks should be visible [Minor et
al., 1988], Efflorescence frequently occurs in the regions where cracks take
place. In the analysis of the isolated cracks, by helping to determine their extent
and cause, NDE techniques can be useful in the investigation of their
implications. In shallow covered reinforcing steel corrosion-induced cracks can
occur. Freeze-thaw cycles induce closely spaced cracks parallel to the concrete
surface, these cracks, only visible in cores, are usually associated with scaling
[Minor et al. 1988], Distributed damage in concrete due to freeze-thaw cycles
can be estimated by utilizing NDE techniques. Photographs 4 through 10
(Appendix E) present several different types of cracks found in the 13
deteriorated bridges.
64


3. Delamination and spall: Delamination is the separation of layers of concrete
close to the surface. This frequently occurring concrete deterioration
mechanism is usually a result of corrosion in the outermost reinforcing steel and
can be observed in decks, columns, piers, and column caps. As the process
continues, a rupture between the delaminated region and the main component
can occur which results in a spall. This deterioration can be identified by the
sound produced when tapping concrete with a hammer. Delaminated regions
will produce a hollow or dead sound. In asphalt covered decks the
identification of the delamination by the sound it gives off is a difficult task.
Methods for the measurement of delaminations in bridge decks overlaid with
bituminous mixtures are not provided in the ASTM standards [ASTM C-4580-
86]. NDE techniques can be used to determine the depth and extent of the
delaminations as well as the presence of the reinforcing steel underneath the
delaminated areas. Examples of delamination and spall in the 13 bridges can be
found in photographs 11 through 20 (Appendix E).
Step 3 Definition of the NDE methods for each type of deterioration:
The definition of the most suitable NDE method to be used in the analysis of the
deteriorating bridges is a critical step to the application of the proposed BENT
methodology. Table 6.6 presents the capabilities of several NDE methods in the
investigation of the three major types of deterioration previously identified. The
65


effectiveness of the methods under field conditions is an important factor that needs
to be taken into account. The characteristics of the methods that determine their
adequacy to the use in the inspection of the bridges are briefly described in the next
sections.
Table 6.6 Adequacy of NDE methods in the investigation of the
deterioration in the bridges [G = good; F = fair; P = poor].
NDE Technique Efflorescence Cracking Delamination and spall
Acoustic emission P P P
Electrical methods P P F
Impact-echo P G G
Magnetic methods G F F
Radar P P G
Sonic methods P P G
Surface hardness methods P P P
Thermography P P G
Acoustic tomography F F G
Ultrasonic F F F
Acoustic emission: This passive NDE method is based on transient elastic wave
propagation generated by the rapid release of energy within a material [Rens et al.,
1997]. A property known as the Kaiser effect is used to detect crack propagation
through acoustic emission (AE). The Kaiser effect states that emission of acoustic
waves occurs only if a load surpassing the previous maximum load is applied to the
structure. Therefore the AE waves depend upon the past history of the structure.
But, for concrete structures, the Kaiser effect may not be a reliable indicator of the
66


loading history [Malhotra and Carino, 1991]. Recent applications of AE for early
detection of corrosion in reinforcing steel have been reported [Li et al., 1998].
Although the technique can detect corrosion earlier than other methods (such as
half-cell potential measurements) no field experiments have been yet documented.
Techniques for identifying crack location, type, and orientation by the analysis of
AE have achieved promising results in laboratory experiments [Ohtsu 1995, Ohtsu
et al., 1998], Despite encouraging laboratory results, difficulties in using AE under
field conditions may restrict its application in bridge inspections. Furthermore, AE
usually requires continuous monitoring which is not appropriate in structures with
high levels of deterioration.
Electrical methods: The most common electrical method used in field inspection -
half-cell potential measurements can yield information about corrosion activity.
The application of the method is limited to uncoated reinforcing steel. Test
equipment and procedures can be found in ASTM standard C 876-91. This method
gives no information about the rate of corrosion. In addition, the results may be
influenced by temperature. The half-cell potential measurement is the only NDE test
available for direct measurement of corrosion activity [Manning, 1985]. Since
delamination usually occurs as a consequence of reinforcing steel corrosion activity
this method may be applicable to assess delamination causes.
67


Impact-echo: This recently developed method has several applications in the
assessment of different concrete deterioration processes. The impact-echo method
is based on the analysis of the longitudinal stress waves generated by the impact of
ball bearings on the concrete surface. The method eliminates the need of a sending
transducer and uses a broadband receiving transducer to detect normal
displacements. Graphics of amplitude versus frequency, obtained by Fourier
transform methods, are used in the detection of flaws [Sansalone and Streett, 1997],
Each type of flaw shape gives off a characteristic type of response. Different
structural element shapes produce different responses when subjected to impact
[Sansalone, 1997]. This method can be used to detect delaminations in concrete
slabs with or without overlays [Sansalone and Carino, 1989; Sansalone and Streett,
1997], Other applications include characterization of surface-opening cracks,
measurements of concrete pavement thickness, detection of voids in grouted tendon
ducts, and analysis of interfacial bond quality in concrete [Sansalone et ai, 1997;
Sansalone et ai, 1998; Jaeger et ai, 1996; Lin and Sansalone, 1996; Lin et al.,
1996; Sansalone and Streett, 1997]. A standard procedure for measuring the
longitudinal wave speed and the thickness of concrete plates has been submitted to
the ASTM [Sansalone and Streett, 1997].
Magnetic methods: Magnetic devices (pachometers) can be used to determine the
position of the reinforcing steel. Inadequate cover is often associated with corrosion
68


induced deterioration. The use of magnetic methods may not be possible in heavily
reinforced bridge members (such as columns and beams) because the effect of other
bars cannot be eliminated [Manning, 1985]. Pachometers can be beneficial to
determine the depth and position of the outermost bars in efflorescent regions,
corrosion induced cracks, and delaminated areas.
Radar: Radar technology is a very efficient way to detect delamination in bridge
decks. Radar is an effective method to measure delamination of asphalt-covered
decks as well as the thickness of the cover. Although moisture can reduce the
effectiveness of this method, its use does not depend upon other weather conditions.
This method can also be used to examine the condition of the top flange of box
beams [Hartle et al., 1990], The use of dual frequency radar allows more accurate
characterization of the defects [SlatonBarker and Wallace, 1997], New technologies
that permit assessment of bridge decks at traffic speed combined with automated
signal processing and imaging are currently under development [Chase, 1998],
Sonic methods: Two standardized methods based on sounding can be used to detect
delamination on concrete decks [ASTM D 4580-86], The first method utilizes an
electro-mechanical apparatus to tap the concrete and record the sound produced.
The second method, called chain-drag, consists of dragging a chain on the concrete
deck and noting the hollow sounds produced when a delaminated area is reached.
69


Both methods have their accuracy decreased when applied over asphalt covered
surfaces [Hartle et al., 1990], On vertical surfaces, hammers can be used to tap the
concrete surface. The main advantage of the chain-drag is its low cost.
Surface hardness method: Although surface hardness methods are well established
and relatively inexpensive they have a limited application in assessing distressed
structures. ASTM standard C 803-90 and C 805-85 bring the methodology to the
application of the penetration resistance and rebound hammer methods,
respectively. Since these methods only evaluate the surface of the concrete they
have a limited use in massive structures. Furthermore, these methods are considered
usable only in relatively new structures [Minor et al., 1988], For the use in old
concrete, direct correlation with compressive strength of cores is necessary
[Malhotra and Carino, 1991].
Thermography: This method is based on the principle that subsurface anomalies in
the material affect the heat flow through the material [Malhotra and Carino, 1991].
Discontinuities, such as delaminations, interrupt the heat transfer through the
concrete. In periods of heating, the surface temperature of delaminated areas is
higher than the temperature of the surrounding concrete [Manning, 1985]. Sensitive
infrared systems are used to detect the differences in the surface temperatures.
Through the analysis of the temperature on the surface, the delaminated areas as
70


well as the depth of the delamination can be identified. The main advantage of this
technique is its efficiency in large area assessments [Rens et al., 1997], Asphalt
overlays reduce the temperature differentials associated with delaminations. This
also introduces the possibility of overlay debonding which can cause a thermal
anomaly [Maser and Roddis, 1990].
Acoustic tomography: It is possible to use the same equipment that is used in
ultrasonic testing to perform tomographic analysis of concrete [Chang and Wang,
1997; Transue et al., 1997]. The method uses a large number of pulse velocity
readings obtained on the exterior of the structure and delivers the map of velocities
in the interior through the application of reconstruction algorithms [Schuller and
Atkinson, 1995]. Gamma ray tomography can accurately detect many different
phases of reinforced concrete deterioration but the applicability of use on large
structures has not yet been determined [Martz et al., 1994]. Although acoustic
tomography is not as accurate as X-ray or gamma ray systems (a tendency to smear
the anomalies over a larger area has been observed) the costs are comparatively
small. The feasibility of the method to the analysis of concrete has been
demonstrated but additional research is needed to develop standardized procedures
in its application [Schuller and Woodham, 1996]. Acoustic tomography has been
used to detect cracks in massive concrete structures. The presence of cracks induces
velocity anomalies [Rhazi, 1997].
71


Ultrasonic: This method consists of measuring the time the ultrasonic pulses need
to travel through concrete members. Transducers are used for the generation and
reception of pulses. The detection of cracks and voids depends upon the
lengthening of the travel path between the transducers. With a longer path, the time
of transmission increases. The presence of reinforcement influences the application
of the method because the velocity of the pulses can be 20 to 90 percent higher than
in plain concrete [Manning, 1985]. The application of this method may be
restrained to members that permit direct transmissions since highway structures are
usually heavily reinforced [Manning, 1985], An ASTM standard (C 597-83) to use
pulse velocity in concrete brings information about the application of this method.
The measurements of the pulse speed can be used to determine the quality of
concrete compressive strength [Krautkramer and Krautkramer, 1990]. Some
literature reports that the decrease in the pulse amplitude (ultrasonic attenuation) is a
more sensitive and reliable parameter to determine distributed cracking in the
concrete than pulse velocity [Suaris and Fernando, 1987; Selleck et al., 1996]. A
newly developed approach to the application of ultrasound in structural inspections
is called direct-sequence spread-spectrum ultrasonic evaluation (DSSSUE) and has
been tested in bridge components [Wormley et al., 1995; Rens et al., 1997].
Although this technique has been successfully used it is not appropriate to be
applied in localized problems. This is because it performs a global analysis of the
72


structure which detects several changes in the system properties at once.
Furthermore permanently mounted transducers may be required to prevent
variations due to couplant changes [Wormley et al., 1995].
For the evaluation of the deterioration types (efflorescence, cracking, delamination,
and spall) found in the 13 bridges (Table 6.5) the more adequate NDE techniques
are impact-echo, acoustic tomogaphy, and ultrasound. Obviously the expenditures
associated with the application of these techniques is a very important factor that
needs to be taken into account. As previously stated, steps 4 (Application of the
NDE methods in the inspection of the selected bridges) and 5 (Rating of the
component) will not be analyzed in this thesis because they are strongly related to
the restraints of the agency in charge of the bridge management.
73


7. Summary, Conclusions, and Recommendations for Further Work
7.1 Summary
This thesis proposes a methodology for the application of NDE techniques in
BMSs. The BENT method explained in Chapter 5 is intended to overcome the
difficulties associated with the use of NDE in BMSs. According to the method the
divorce between NDE output and the BMS environment can be disregarded if one
uses appropriate criteria to apply NDE methods to the structures. The BENT
methodology implies the application of procedures to evaluate the deterioration of
the bridges at a future time. In addition, this thesis developed and applied a
Markovian deterioration model.
7.2 Conclusions
The main conclusion of this work is the feasibility of the application of NDE
in bridge inspections in BMSs. It is important to emphasize the role of the NDE
tools as complementary and not a substitute for visual inspection. At present stages
of development several NDE methods are already mature for use in the biennial
bridge inspections. The extent of their use for a larger number of structures in a
BMS can be defined according to deterioration curves. NDE methods are very
powerful tools but since their application is usually associated with high
74


expenditures, the criteria for their use must be carefully studied. Another important
factor in the use of NDE is the interpretation of the results. Misleading
interpretations can produce disastrous policies in bridge management
administration.
7.3 Recommendations for further work:
The BENT methodology presented in this work can be applied to concrete,
steel, and timber bridges. Only concrete bridges were addressed in this work.
Therefore a more in depth study of the deterioration processes in concrete, as well
as a review of the NDE methods for the inspection of steel and timber need to be
accomplished. More precise information about actual applications of NDE
techniques also needs to be acquired. The inclusion of case studies based on actual
application of NDE techniques on the CCD bridges will bring more information
about the benefits and restrictions of the BENT method. In order to obtain precise
information about the benefits of the application of NDE methods in BMSs it is
also necessary to determine the costs associated with it.
The use of monitoring techniques in bridges can improve information about
the general condition and safety of structures. To apply these techniques monitors
are installed to measure bridge temperatures, strains, rotations and displacements
during long periods of time. In recent years, these instrumented monitoring
75


techniques have experienced some development and their importance has increased
[Hunt et al., 1997; Giurgiutiu and Rogers, 1998]. The use of these techniques in
BMSs would lead to a much more precise analysis of the health of the bridge
components. The association of monitoring output and BMSs is a promising and
but very challenging task.
The further development of various NDE methods may be the most
important factor in the application of NDE to BMSs. The standardization of NDE
techniques plays a capital rule in their use. Schuller and Woodham (1996)
addressed the demands for standardization in the Working Group Report of the 3rd
Conference of Nondestructive Evaluation of Civil Structures and Materials. In this
work, several mature methods that should be considered for standardization were
listed. The Report emphasizes the importance of standardization to the acceptance
of NDE methods for general use by industry.
Rens and Transue (1998) identified further development needs of NDE
methods in state highway agencies in the United States. The Federal Highway
Administration created the FHWA Nondestructive Evaluation Validation Center to
analyze the factors that affect the reliability and performance of NDE methods in
bridge inspections [Washer, 1998]. Chase (1998) reports several newly developed
NDE techniques to be used in highway bridges. This is evidence that the demands
76


identified in the state highway agencies will soon be met. The application of NDE
in bridge inspections, although not in a systematic fashion, constitutes current
practice in several agencies. Its importance is, therefore, already recognized.
Large-scale NDE use in biennial bridge inspections, as a supplement to visual
inspection, is now only a matter of time.
77


Appendix A
Structure Inventory and Appraisal Sheet
The Structure Inventory and Appraisal Sheet with information of one structure
inspected in 1996 in the City and County of Denver is shown on the next page. The
following fields were used in the classification schemes:
Field 8 Structure number;
Field 27 Year built;
Field 29 ADT;
Field 58 Condition rating: Deck;
Field 59 Condition rating: Superstructure;
Field 60 Condition rating: Substructure;
Further information about this document can be found in Hartle et al. 1990.
78


L
STRUCTURE INVENTORY AND APPRAISAL SHEET
Colorado Department of Transportation
8.
132
Str No: D-01-CC-080
Ord No: 310025.
.. State: 088
12. Hwy Region Eng/Maint: 68
3. County Code: 31
4. Place Code: 20000
5. Inv Route on: 151014170
6. Feature Intersected on:
CHERRY CREEK
7. Facility on Carried Str:
ARAPAHOE ST
8. Structure No: D-01-CC-080
9. Location:
ARAPAHOE AT SPEER BLVD
10. Max vert clr-inv rte: 9999
11. Milepoint Log: 0.
136. Hiway Section: Z [
16. Latitude: 39' 44.9"
17. Longitude: 104' 59.9"
19. By-Pass Detour Length: 1
20. Toll: 3
21. Maint Responsibility: 5
22. Owner: 4
26. Functional Classification: 17
27. Year Built: 1957
28. Lanes On-Under Str: 3 0
29. ADT on: 6367
30. Year of ADT on: 92
31. Design Load: 5
33. Bridge Median: 0
A ClrAuf 42
35! Str Flared Y/l N/0: 0
38-40. Navigation Control: 00000
41. Str Open or Closed: R
129. Load posting: 000
42. Type Service: 5 5
43. Structure: 21
120. CDOT Str Type: CSC 2
44. Approach Spam Type: 0 0
45. No. Spans-Main: 2
46. No. Spams-Approach: 0
47. Horizontal Clear on: 40.
48. Max Span Length: 65
49. Structure Length: 131
50. Sidewalk: 5. 12.
51. Bridge Roadway Width: 40.
52. Deck Width (out to out): 62.
53. Min Vert OH Cl: 99' 99*
54. Min Vert Under Cl: N O' 0"
55. Min Lat Under clr rt: N 99.9
56. Min Lat Under clr It: 0.
64. Operating Rating: 271
66. Inventory Rating: 243
66A. Girder Rating: 71
66S. Slab Rating Indicator: S
75. Type of Work:
76. Lgth of Str Impvmt:
91. Inspection Freq: 24
92. Crit Feature Insp: N N N
93. Crit Feature Insp Date:
94. Bridge Impvmt Cost: $ ,000
95. Rdwav Impvmt Cost: $ ,000
96. Total Project Cost: $ ,000
97. Yr of Impvmt Cost Est:
98. Border Bridge:
99. Border Bridge Str No:
100. Def Hwy Designation: 0
101. Parallel Str Design: N
102. Direction of Traffic: 2
103. Temp Str of Traffic:
104. Hwy Sys of the Inv Rte: 1
106. Yr Reconstructed : 0
107. Deck Str Type: 1
108. Wearing Surface: 600
109. Ave Dally Truck Traf: 4
110. Designated Natl Network: 0
111. Pier or Abutment Protect:
112. NBIS Bridge Length: Y
113. Scour Critical Bridges: 8
114. Future ADT: 7000
115. Year of Future ADT: 16
121. Minor Str Indicator: 6
133. Special Equipment: 0
Under Conditions
Inv. Route: 000 00000 0
Feature Intersected:
NA
Max Vert clr-in: 99'99"
Milepoint-log: 0.
Bypass Detour Lgth: 0
Functional Class: 0
ADT Under: 0
Year of ADT: 0
Total Horiz Clr: 0.
Def Hwy Designation: 0
Hwy Sys of the Inv Rte: 0
Average Daily Truck Traf:
Designated Natl Network: 0
Highway Sect Indicator: X
205.
206.
210.
211.
219.
226.
229.
230.
247.
300.
304.
309,
310
315
CDOT Form #442a 1/96: Page 1
79


8. Str No: D-01-CC-080
132. Ord No: 310025.
Inspection Summary
32. Approach Roadway: 43
36. Safety Features: 0000
58. Deck: 6
59. Superstructure: 6
60. Substructure: 7
61. Channel: 7
62. Culvert: N
67. Structure Condition: 6
68. Deck Geometry: 4
69. Underclearance: N
70. Load Capacity: 5
71. Waterway: 7
72. Approaches: 6
90a. Inspection Date: 07/15/96
90b. Inspection Team: L
122. Inspection Indicator: 0E
137. Sufficiency Rating: 79.4
138 . SD/FO Indicator: NO
Mlsc Information
18a. Range:
18b. Township:
18c. Section:
37. Historical Significance: 5
123 . Maintanance Patrol: 0
124. Expansion Device: A
125. Bridge Rail Type: O 0
130. Rating Date: 07/26/96
134 . Vertical Clearance (NB/EB):
dir-X max-99'99" - min- O' 0"
135. Vertical Clearance (SB/WB):
dirX max-99'99" - min- O' 0"
139. Posting Map Color: 0
140 . Batch ID Number: 031005
141. Funding Category: X
142 . Funding Status: 0
80


Appendix B
Database
Information used in the classification schemes and condition ratings of the
deck (58), supersructure (59), and substructure (60) are presented in this Appendix.
The three first fields correspond to the structural number of each bridge. A total of
160 bridges were used in this work.
An entry M was used whenever the information was not available. In the
DECK column a number 1 correspond to concrete deck and 2 to timber deck.
81


I
!
CLAOSFICATION FACTORS 64 TJ TT TT 44 44
f gr6up NO ADT YEAR A0TT DECK Timer iUUi 4* 44 46 5* 46 46 61 5* 46 u 49 66 5 4* o6 ii 46
1 D-01- cc- 020A 4560 92 4 1 1984 2 7 8 7 7 8 7 7 e 7 7 8 7 7 8 8 8 9 B
2 Ml- cc- 030A 10596 92 5 1 1984 2 7 8 7 7 8 7 7 e 7 7 8 7 7 8 8 7 9 8
3 D-01- cc- 040A 12725 92 5 1 1984 2 7 8 7 7 8 7 7 6 7 7 8 8 7 8 8 8 7 8
4 0-01- cc- 050 21328 92 5 1 1981 2 7 7 7 7 8 7 7 6 7 6 6 8 8 8 8 9 7 8
5 D-01- cc- 080 6367 92 4 1 1957 2 6 6 7 6 6 7 6 6 7 6 5 7 6 3 7 6 3 7
e 0-01- cc- 090 370 92 4 1 1912 2 -1 -1 -1 -1 -1 -1 2 2 3 3 3 4 2 3 5 3 2 3
7 0-01- cc- 100 7407 92 5 1 1976 2 6 7 7 6 7 7 6 7 7 6 7 7 7 7 8 7 8 8
t D-01- cc- 110A 0985 92 5 1 1985 1 7 7 7 7 6 7 7 6 7 7 7 8 8 7 6 9 7 8
D-01- cc- 120 12 92 -1 1 1950 2 6 6 6 6 6 6 6 6 5 6 6 5 6 fi fi fi fi fi
10 0-01- cc- 140 7628 92 6 1 1956 2 6 7 6 6 7 6 6 7 6 6 6 6 6 5 6 6 6 fi
11 D-01- cc- 150 13239 92 6 1 1986 2 7 7 7 7 8 7 7 8 7 7 8 7 8 8 6 8 8 8
12 D-01- cc- 180 7640 92 4 1 1986 2 7 7 7 7 7 7 6 7 7 6 7 7 7 7 7 8 7 7
13 D-01- cc- 168 2940 92 4 1 1990 1 7 6 8 7 8 8 8 8 8 8 8 8 -1 -1 -1 -1 -1 -1
14 D-01- cc- 170A 22899 92 6 1 1990 1 8 8 8 8 7 8 e 7 8 8 8 6 5 3 fi 5 4 fi
15 0-01- cc- 180A 21364 92 5 1 1989 1 7 8 7 7 8 7 7 8 7 7 8 8 8 9 9 -1 -1 -1
14 0-01- cc- 190 21773 92 5 1 1958 2 7 5 6 7 5 6 7 5 6 7 5 6 7 fi fi fi fi fi
17 0-01- cc- 200 17387 92 5 1 1956 2 6 5 7 6 5 7 6 5 7 6 5 7 fi 4 7 fi 4 7
11 0-01- cc- 210A 3514 92 6 1 1986 1 7 7 8 7 7 8 8 8 8 8 8 8 9 9 9 -1 -1 -1
1t D-01- cc- 22QA 9996 92 6 1 1985 7 7 7 7 7 7 7 8 7 7 8 8 7 8 8 9 8 8
20 D-01- cc- 230A 6504 92 6 1 1987 ; 7 7 7 7 7 7 7 7 7 7 7 6 7 7 6 7 3 fi
21 D-01- cc- 240A 4978 92 6 1 1987 2 7 7 8 7 7 8 7 7 6 8 7 8 8 9 8 8 9 R
22 0-01- cc- 250 6732 92 5 1 1957 2 6 7 7 6 7 7 6 7 7 6 7 7 fi 7 7 fi 7 7
23 0-01- cc- 26QA 7874 92 5 1 1963 2 7 7 7 7 7 7 7 7 7 7 7 7 7 7 A 7 7 8
24 0-01- cc- 270 21822 92 5 1 1957 3 6 7 4 6 7 4 6 7 4 5 7 4 5 7 4 5 7 fi
25 04)1- cc- 281 17721 92 5 1 1974 1 5 7 7 5 7 7 5 7 7 5 7 7 5 7 7 fi 7 7
20 0-01- cc- 282 19651 86 1 r 1922 2 -f -t -T -T -f -1 -1 -1 1 -1 -1 -1 4 4 fi fi 4 fi
27 D-01- cc- 282A 21197 92 5 1 1989 1 7 8 8 7 6 8 7 8 8 8 8 8 .j -1 .1 .j
2* D-01- cc- 310 20634 92 6 1 1956 3 6 6 5 6 5 5 6 5 5 6 5 5 fi S S fi fi fi
20 0-01- cc- 320 27159 92 5 1 1964 3 6 7 6 6 7 5 6 7 5 6 7 5 fi 7 S 6 7 7
30 0-02- PR- 010 3233 92 4 i 1965 4 6 7 7 7 7 7 7 7 7 7 7 6 7 7 7 7 6
31 0-02- PR- 040 13100 92 5 1 1976 2 6 7 7 6 7 7 6 8 7 6 e 7 fi 9 7 9 7
32 0-02- PR- 050 2140 92 4 1 1974 2 7 6 7 7 6 7 7 6 7 6 8 7 fi 8 7 fi 8 9
33 0-02- PR- 060 1785 06 -1 t 1887 2 -1 -1 -1 -1 -J -1 -1 -1 -1 -1 -1 -1 5 3 fi fi 3 fi
34 0-02- PR- 060A 1410 92 6 1 1992 2 8 9 9 9 9 9 9 9 9 1 -1 -1 -1 -1 -1 -1 -1 -1
35 0-02- PR- 070 2997 92 6 1 1974 2 7 8 8 7 8 8 7 8 8 7 8 8 7 8 8 7 9 8
39 D-02- PR- 090 23567 92 5 1 1955 4 5 6 5 5 6 5 5 6 5 5 fi 5 fi fi fi fi fl fi
37 0-02- PR- 100 18112 92 5 i 1955 4 5 6 4 5 6 4 5 6 4 5 6 4 5 fi fi fi fi fi
30 0-02- PR- 120 3247 92 4 1 1966 2 6 6 3 6 6 7 6 6 7 6 6 7 8 7 ft 8 8
30 0-02- PR- 13QA 1722 92 4 1 1968 3 7 7 7 7 7 7 7 7 7 7 8 8 8 8 8 1 -1 -1
40 0-02- PR- 150 15374 92 6 1 1929 3 7 7 7 7 7 7 7 7 7 7 7 6 7 8 7 7 8 7
41 0-02- PR- 220 220 92 6 1 1958 4 7 7 6 7 7 6 7 7 6 6 6 5 fi fi fi fl fi fi
42 0-02- PR- 250 10179 92 6 i 1956 2 7 7 7 7 7 7 7 7 7 7 7 7 7 8 7 7 8 9
43 M2- PR- 260 40266 92 5 1 1966 2 7 7 7 7 7 7 7 7 7 7 7 8 7 7 8 8 7 9
44 M3- V- 010 11162 92 4 i 1978 11 7 7 6 7 7 6 7 7 6 6 7 6 fi 7 4 fi 7 4
D-03- V- 030 17543 86 -1 i 1929 52 -1 -1 -1 -1 -1 4 5 5 4 5 5 6 fi fi 3 fi fi
44 0-03- V- 040 1794 66 -1 1 1939 11 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 fi 7 fi fi 7 fi
47 0-03- V- 050 14050 86 -1 1 1970 86 -1 -1 1 -1 -1 -1 -1 -1 4 4 5 4 4 fi 4 3 3
40 M3- V- 060 1992 86 -1 i 1909 18 1 -1 -1 -1 -1 -1 -1 -1 4 6 6 4 fi fi 4 fi
40 0-03- V- 080 5844 66 -1 i 1924 89 -1 -1 -1 -1 -1 3 3 3 4 3 3 4 3 3 4 3
SO M3- V- 090 3975 96 -1 i 1963 23 -1 -1 -1 -1 -1 -1 -1 -1 4 6 3 5 fi fi fi fi fi
51 0-03- V- too 19384 86 .1 1 1889 61 -1 -1 -1 -1 -1 .1 -1 -1 -1 -1 -1 4 ? 4 4 7 fi
52 D-03- V- 110 15664 86 -1 i 1957 39 -1 -1 1 .1 -1 -1 -1 -1 -1 -1 -1 -1 fi 3 3 fi 3 3
S3 M3- V- 15QA 12714 92 6 1 1985 19 7 8 6 7 8 6 7 8 6 7 8 fi 7 8 fi 7 9 R
54 0-03- V- 160 26074 92 5 1 1950 19 6 5 6 8 5 6 -1 -1 -1 6 5 6 fi fi fi fi fi fi
55 D-03- V- 161 23212 92 5 i 1985 16 5 5 6 5 5 8 5 5 6 5 5 6 fi fi S fi fi
50 0-03- V- 170 26074 92 5 1 1965 1 7 7 6 7 7 8 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1
57 0-03- V- 180 30200 91 5 i 1972 9 7 7 7 7 7 5 -1 -1 -1 -1 -1 -1
St 0-04- BOST- 055 23567 92 5 1 1990 1 7 8 8 7 9 8 8 9 A 9 9 9 -1 -1 -1 -1 -1
50 0-04- BOST- 056 18112 92 5 1 1990 1 7 8 8 7 9 8 6 9 9 9 9 9 1 -1 -1 -1 -1 -1
00 0-04- BOST- 065 388 92 5 1 1965 1 6 7 6 6 7 6 6 7 6 6 6 6 fl fi fi 7 fi
01 M4- BOST- 100 298 92 6 i 1984 2 7 8 6 7 8 8 -1 -1 -1 7 8 8 8 9 8 ft 8 8
02 0-04- BOST- 110 8354 91 6 1 1904 2 7 7 6 7 7 e 7 7 9 8 8 8 8 8 8 8 9 9
a 0-04- BOST- 150 1488 94 6 i 1992 2 7 7 7 7 7 7 7 7 7 -1 -1 -1 -1 -1 -1 -1 -1
04 D-04- BOST- 151 1632 94 6 i 1992 2 7 7 6 7 7 6 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1
06 0-04- BOST- 160 4000 91 .1 i 1992 2 8 6 8 9 9 8 9 9 9 -1 -t -1 -1 -1 -1 -1
00 0-04- BOST- 161 4000 91 -1 1 1992 2 8 8 8 9 9 9 9 9 9 -1 -1 -1 -1 -1 -1 -1 -1 -1
07 0-05- RO- 060 26074 92 5 1 1956 1 -1 -1 -1 -1 -1 -1 7 7 6 7 7 6 7 7 8 6 7 fi
OS 005- RO- 005 350 92 5 i 1985 1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 8 8 8 fi 7 fi
90 0-05- RRBR- 020E 2000 92 -1 2 1925 4 7 7 6 7 7 7 7 7 7 -1 -1 -1 -1 -1 -1 -1
70 0-05- RRBR- 020W 2000 92 -1 2 1925 4 7 6 8 7 6 7 7 6 7 -1 -1 -1 -1 -1 -1 -1 -1 -1
71 005- RRBR- 030 2000 91 -1 2 1916 -1 7 7 7 7 7 7 7 7 7 -1 -1 -1 -1
72 005- RRBR- 070 15000 91 -1 2 1978 3 7 7 7 7 7 7 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1
73 005- RRBR- 060 15000 91 -1 1 1825 3 7 6 7 7 6 7 7 7 7 -1 -1 -1 -1 -1 -1 -1 -1 -1
74 005- RRBR- 091 9100 91 -1 1 1837 3 7 6 7 7 5 7 7 5 7 -1 -1 -1 -1 -1 -1 -1 -1 -1
75 005- RRBR- 092 9100 91 -1 1 1937 3 7 6 7 7 7 7 7 7 7 -1 -1 -1 -1 -1 -1 -1 -1 -1
70 005- RRBR- 097 2000 93 5 1 1995 3 8 8 8 9 9 9 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1
77 D-OS- RRBR- 096 2000 93 $ 1 1995 2 8 6 8 9 9 9 -1 -1 -1 -1 -1 -1 -t -1 -1 -1 -1 -1
70 005- RRBR- 101 24000 91 -1 2 1910 2 7 7 6 7 7 6 7 7 6 -1 -1 -1 -1 -1 -1 -1 -1 -1
82


l_Z!_ M8- RRBR- 102 24000 91 -1 2 1910 2 7 7 6 7 7 6 7 7 6 -1 .1 -1 -1 -1 -1 -1 -1 -1
to D-05- RRBR- 103 24000 91 -1 2 1910 2 7 6 6 7 7 6 7 7 6 -i -1 -1 -1 -1 -1 -1 -1 -1
81 D-05- RRBR- 110 8354 91 -1 1 1964 2 7 8 8 7 8 8 7 8 8 -1 -1 -1 -1 -1 -1 -1 -1 -1
82 0-05- RRBR- 120 8354 91 -1 2 1984 2 7 0 8 7 8 8 7 8 8 -1 -1 .1 1 -1 -1 -1 -1 -1
t3 0-05- RRBR- 131 4200 91 -1 1 1926 3 7 7 7 7 7 7 7 4 7 -1 -1 -1 -1 -1 -1 -1 1 -1
84 0-05- RRBR- 132 4200 91 -1 1 1926 3 7 7 7 7 7 7 7 4 7 -i -1 -1 -1 -1 -1 -1 -1 .1
85 0-05- RRBR- 140 4000 91 5 1 1992 : 8 8 8 7 7 7 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1
88 0-06- BORR- 040 23567 92 5 1 1990 t 7 8 8 7 9 8 7 9 7 9 9 9 -1 -1 -1 -1 -1 -1
87 0-06- 80RR- 050 18112 92 5 1 1990 1 7 8 9 7 9 8 7 9 7 9 9 9 -1 .1 -1 -1 -1 -1
88 0-07- PO 040 9600 91 -1 1 1978 3 7 8 1 7 8 7 7 8 7 -1 -1 -1 -1 -1 -1 -1 -1 1
tl 007- PO- 060 9800 91 -1 1 1982 3 8 6 8 8 8 8 8 8 8 -1 -1 -1 -1 -1 -1 .1 -1 -1
90 0-07- PO- 070 10300 91 1 1 1956 1 8 8 8 8 8 8 8 8 8 -1 -1 -1 -1 -1 .1 -1 -1 -1
91 0-07- PO- 080 22000 91 .1 1 1962 1 8 8 8 8 8 8 6 8 6 -1 -1 -1 -1 -1 -1 -1 -1 -1
92 0-07- PO- 090 22000 91 -1 1 1985 1 8 8 8 8 8 8 8 8 8 -1 -1 -1 -1 -1 -1 -1 -1 -1
93 0-07- PO- 110 10300 91 -1 1 1982 1 8 8 8 6 8 6 8 8 8 -1 -1 -1 -1 -1 1 -1 -1 -1
94 0-07- PO- 120 9600 91 -1 1 1969 3 7 B 7 7 8 7 7 8 7 -1 -1 -1 -1 -1 -1 -1 -1 -1
95 0-07- PO- 128 9600 91 -1 1 1969 4 6 7 7 6 7 7 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1
90 0-07- PO- 130 33000 91 -1 1 1981 3 7 7 7 7 7 7 7 7 7 -1 -1 -1 -1 -1 -1 -1 -1 -1
97 0-07- PO- 142 9800 91 -1 1 1978 1 7 7 7 7 7 7 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 1 -1
98 0-07- PO- 160 2400 91 -1 1 1966 1 6 7 7 6 7 7 6 7 7 -1 -1 .1 1 -1 -1 1 -1 -1
91 0-07- PO- 180 6400 91 -1 1 1979 3 7 7 7 7 7 7 7 7 7 -1 -1 .1 -1 -1 -1 -1 -1 -1
100 0-07- PO- 200 6354 91 -1 1 1958 1 8 7 8 8 7 8 8 7 8 -1 1 .1 1 -1 -1 -1 .1 -1
101 0-07- PO- 230 10300 91 -1 1 1982 : 7 7 7 7 7 7 7 7 7 -1 -1 -1 .1 .1 -1 -1 .1
102 0-07- PO- 270 9800 91 -1 1 1963 3 8 8 8 8 8 8 6 8 e -1 -1 -1 -1 .1 -1 -1 -1 -1
103 0-07- PO- 300 13000 91 -1 1 1983 1 8 8 8 8 8 8 8 8 8 -1 -t 1 -1 -1 -1 -1 -1 -1
104 007- PO- 310 10000 91 -1 1 1980 4 -1 -1 1 7 7 8 7 8 8 -1 -1 -1 1 -1 -1 -1 -1 -1
106 0-07- PO- 320 10000 91 -1 1 1980 4 -1 -1 -1 7 7 8 7 7 7 -1 -1 -1 -1 -1 -1 -1 -1 -1
100 007- PO- 330 4000 91 -1 1 1992 2 8 6 8 9 9 9 9 9 9 -1 -1 -1 -1 -1 -1 -1 -1 -1
107 CM7- PO- 340 4000 91 .1 1 1992 2 8 8 8 9 8 8 9 9 9 -1 -1 -1 -1 -1 -1 -1 -1 -1
100 007- PO- 350 1000 93 -1 t 1990 4 8 8 8 e 8 8 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1
100 007- PO- 360 1000 93 -1 1 1970 3 7 8 8 8 8 8 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 .1
110 0-07- RRO- 060 18112 92 5 1 1990 1 -1 -1 -1 -1 -1 -1 7 9 7 9 9 9 -1 -1 -1 -1 -1 -1
111 007- wwu- 090 9100 91 -1 1 1980 3 7 7 7 7 7 7 7 7 7 -1 -1 -1 -1 -1 -1 -1 -1 -1
112 0-09- CLC- 010 5170 92 6 1 1969 2 6 7 4 6 7 6 5 6 6 5 6 6 5 6 7 A 7 7
113 010- HC- 120 6132 92 4 1 1952 1 7 6 7 7 6 6 7 6 6 7 6 6 7 6 A 8 A A
114 010- HC- 160 19367 92 6 1 1955 1 8 7 6 7 7 7 7 7 7 7 7 A 7 7 A 7 7 A
115 010- iHC- 170 8758 92 4 1 1975 1 7 7 7 7 7 7 7 7 7 7 7 6 7 7 6 7 7 A
110 D-1D- HC- 180 18777 92 5 1 1964 1 7 7 6 7 7 6 7 7 6 8 7 6 9 7 8 7 7 7
117 010- HC- 190 10358 92 6 1 1964 1 7 7 6 7 7 6 7 7 6 7 7 6 7 7 6 8 7 A
118 010- HC- 240 10753 92 6 1 1964 1 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7
110 0-10- HC- 261 18397 92 6 1 1981 1 7 7 7 7 7 7 7 7 7 6 7 7 7 7 8 8 8 A
120 010- HC- 290 10 94 -1 1 1983 1 7 8 7 7 8 7 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1
121 010- HC- 330 6039 92 4 1 1972 1 -1 -1 -1 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7
122 011- GG- 200 15702 92 5 1 1971 1 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 9 8 8
123 013- HGE- 050 25 92 .1 1 1967 1 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 ;
124 013- HGE- 060 291 92 2 1 1967 1 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7
125 013- HGE- 070 6 92 -1 1 1967 1 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7
120 013- HGE- 060 315 92 2 1 1967 1 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7
127 013- HGE- 090 12 92 -1 1 1967 1 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7
128 013- HGE- 100 188 92 2 1 1967 1 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7
129 013- HGE- 110 296 92 2 1 1967 1 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7
130 013- HGE- 120 343 92 2 1 1967 1 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7
131 013- HGE- 130 260 92 2 1 1967 1 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7
132 013- HGE- 140 16 92 -1 1 1967 1 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7
133 013- HGE- 150 381 92 2 1 1967 1 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7
134 013- HGE- 160 294 92 2 1 1967 1 7 7 7 7 7 7 7 7 7 7 7 7 A 7 7 A 7 7
135 013- HGE- 200 487 92 2 1 1967 2 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7
138 013- HGE- 210 430 92 2 1 1967 2 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7
137 013- HGE- 230 12 92 -1 1 1967 2 7 7 6 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7
138 013- HGE- 250 237 92 2 1 1967 2 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 i
138 013- HGE- 260 224 92 2 1 1967 2 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7
140 013- HGE- 270 554 92 2 1 1967 2 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7
141 0-13- HGE- 2B0 438 92 2 1 1967 1 7 7 7 7 7 7 7 7 7 -1 -1 -1 A 7 7 A 7 7
142 016- LG- 130 793 92 2 1 1975 1 7 7 7 7 7 7 7 7 8 8 7 8 8 6 8 A 8 f
143 016- LG- 160 71 92 -1 1 1950 1 6 3 6 8 3 5 6 3 5 6 3 f> -1 -1 -1 -1 -1 -1
144 019- SC- 010 3631 92 2 1 1973 3 6 6 7 6 6 7 6 6 7 6 8 A A A A A A 1
146 019- SC- 030 3625 92 2 1 1955 10 6 7 7 6 7 7 6 7 7 6 6 A A 7 A A 7 7
140 019- SC- 05OA 5064 92 4 1 1968 4 6 8 8 8 8 8 8 8 8 -1 -1 -1 -1 -1 -1 -1 -1 -1
147 020 MB- 780A 10 91 -1 1 1965 1 9 9 9 8 8 A 8 8 8 8 n 8 -1 -1 -1 -1 -1 -1
140 020 MB- 790 12642 96 2 1 1996 3 -1 -1 -1 -1 -1 -1 8 6 7 8 4 4 -1 -1 -1 -1 -1 -1
140 020 MBO 040 10 91 -1 1 1986 1 8 6 7 6 6 7 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1
160 025- FC- 020 2016 92 2 1 1965 1 6 7 5 6 7 5 6 7 5 6 7 5 -1 -1 -1 -1 -1 -1
161 025- FC- 030 8161 92 2 1 1985 1 7 7 6 7 7 6 7 7 6 7 7 f -1 -1 1 -1 -1 -1
152 027- MP- 010 134 92 2 2 1938 1 7 6 7 7 6 7 7 6 7 7 7 7 -1 -1 -1 -1 -1 -1
153 027- MP- 030 18 92 -1 2 1960 1 7 5 7 7 5 7 7 6 7 7 7 7 -1 -1 -1 -1 -1 -
154 027- MP- 070 103 92 2 2 1980 1 7 7 7 7 7 7 7 7 7 7 7 7 -1 -1 -1 -1 -1 -1
156 027- MP- 090 70 92 -1 2 1965 1 6 6 7 6 6 7 6 6 7 6 6 7 -1 -1 -1 -1 -1 -1
150 0-27- MP- 100 3 92 -1 1 1970 1 8 8 8 8 8 8 8 8 8 6 8 8 -1 -1 -1 -1 -1 -1
157 027- MP- 110 3 92 -1 2 1940 1 6 4 6 8 4 7 8 4 7 5 4 7 -1 -1 -1 -1 -1 .1
158 027- MP- 120 10 92 -1 2 1940 1 8 6 6 8 6 6 8 f 6 4 A A -1 -1 -1 -1 -1 -1
160 027- MP- 130 7 92 -1 2 1972 1 6 7 7 7 7 7 7 7 7 -1 -1 -1 -1 -1 -1 -1 -1 -1
180 027- MP- 220 25 91 -1 1 1940 1 6 6 6 6 6 6 6 6 e -1 -1 -1 -1 -1 -1 -1 -1 -1
83


Appendix C
Data and Transition Matrices
Two classification schemes were used in this work:
Scheme 1:
1. A bridges built before 1960,
2. B bridges built from 1960 and before 1980, and
3. C bridges built in 1980 and after.
Scheme 2:
1. L bridges with ADT less than 10,000, and
2. H bridges with ADT equal to 10,000 or more.
After the classification of the structures according the age and ADT the
matrices with the transitions in the condition ratings were obtained (Figures 1 to 5).
Several matrices lack information about the transition in some of the condition
ratings. In order to avoid spurious absorbing states these matrices were completed
with a scheme that includes all the structures in the database (Figure 6). The
modified matrices can be found in Figures 7 to 11. In the superstructure matrix the
entries a^) and a^^) were set equal to the elements a^) and 3(4,4). This substitution
was necessary to eliminate a spurious absorbing state (elements a<3,2) and a<3,3) were 0
84


was necessary to eliminate a spurious absorbing state (elements a<3,2) and a^) were 0
and 25, respectively, before the substitution). The substitution implies that for the
superstructure deteriorates from 5 to 4 with the same probability that it deteriorates
from 6 to 5.
The transition probability matrices for both classification schemes are shown
in Figures 12 to 16.
85


Classification schemes for Markovian Model for Bridge Deterioration
Scheme 1A
58 deck
Ratings 3 4 5 6 7 8 9
1 2 3 4 5 6 7
3 i 0 0 0 0 0 0 0
4 1 6 0 0 0 0 0
5 0 2 14 0 0 0 0
6 4 0 0 0 48 0 0 0
7 5 0 0 0 1 51 0 0
8 ... 6 0 0 0 0 1 8 0
9 7 0 0 0 0 0 0 0
Total
59 superstructure
Ratings 3 4 5 6 7 8 9
1 2 3 4 5 6 7
3 1 9 0 0 0 0 0 0
4 " 2 0 5 0 0 0 0 0
5 3 0 0 19 0 0 0 0
6 4 0 0 3 34 0 0 0
7 5 0 0 0 5 46 0 0
8 $ 0 0 0 0 2 4 0
9 7 0 0 0 0 0 0 0
Total
60 substructure
Ratings 3 4 5 6 7 8 9
1 2 3 4 5 6 7
3 1 4 0 0 0 0 0 0
4 :>12 1 7 0 0 0 0 0
5 V: 3 0 4 22 0 0 0 0
6 " 4 0 0 2 39 0 0 0
7 5 0 0 0 6 44 0 0
8 $ 0 0 0 0 1 4 0
9 __1 0 0 0 0 0 0 0
Total
0
7
16
48
52
9
0
132
9
5
19
37
51
6
0
127
4
8
26
41
50
5
0
134
Figure C.l
86


Classification schemes for Markovian Model for Bridge Deterioration
Scheme IB
58 deck
Ratings 3 4 5 6 7 8 9
2 .VS-:: 3 4 5 : 6 7
3 ' 1 0 0 0 0 0 0 0
4 2 0 2 0 0 0 0 0
5 0 1 12 0 0 0 0
6 *rv :4 0 0 2 46 0 0 0
7 W,#5 0 0 0 4 151 0 0
8 *7,^6 0 0 0 0 4 5 0
9 * 7 0 0 0 0 1 0 0
Total
0
2
13
48
155
9
1
228
59 superstructure
Ratings 3 4 5 6 7 8 9
?r 2 v -3 4 '5 :,v. 6 7
3 -v 1 0 0 0 0 0 0 0
4 0 1 0 0 0 0 0
5 fcvte'SSS 0 0 6 0 0 0 0
6 0 0 1 16 0 0 0
7 0 0 0 4 174 0 0
8 - $ 0 0 0 1 4 23 0
9 n 0 0 0 0 0 0 0
Total
60 substructure
Ratings 3 4 5 6 7 8 9
1 2 -* -3 .fu. 5 6 >7
3 0 0 0 0 0 0 0
4 0 1 0 0 0 0 0
5 0 0 7 0 0 0 0
6 1 1 0 35 0 0 0
7 1 0 1 3 154 0 0
8 ^.7-6 0 0 0 0 6 15 0
9 src\:&?l 0 0 0 0 0 0 0
Total
0
1
6
17
178
28
0
230
0
1
7
37
159
21
0
225
Figure C.2
87


Classification schemes for Markovian Model for Bridge Deterioration
Scheme 1C
58 deck
Ratings 3 4 5 6 7 8 9
1 2 3 4 5 6 7
3 0 0 0 0 0 0 0
4 2 0 0 0 0 0 0 0
5 -.* "-3 0 0 1 0 0 0 0
6 0 0 0 1 0 0 0
7 m-^5 0 0 0 2 83 0 0
8 0 0 0 0 17 32 0
9 v.: 7 0 0 0 0 4 11 5
Total
59 superstructure
Ratings 3 4 5 6 7 8 9
~ 1 2 - 3 - 4 5 6 7
3 1 0 0 0 0 0 0 0
4 '-&v 2 1 0 0 0 0 0 0
5 3 0 0 0 0 0 0 0
6 -%r. . ,-4 0 0 0 5 0 0 0
7 0 0 0 2 43 0 0
8 $ 0 0 0 0 8 61 0
9 > 7 0 0 0 0 1 16 15
Total
60 substructure
Ratings 3 4 5 6 7 8 9
1 2 3 v 4 4 -5 6 7
3 1 0 0 0 0 0 0 0
4 2 0 0 0 0 0 0 0
5 - 3 0 0 0 0 0 0 0
6 '^4 0 0 0 7 0 0 0
7 '*' 5 0 0 0 0 47 0 0
8 . 6 0 0 0 1 11 68 0
9 *7 0 0 0 0 3 11 5
Total
0
0
1
1
85
49
20
156
0
1
0
5
45
69
32
152
0
0
0
7
47
80
19
153
Figure C.3
88


Classification schemes for Markovian Model for Bridge Deterioration
Scheme H
58 deck
Ratines 3 4 5 6 7 8 9
"I 2 3 4 5 6 7
3 .' 1 0 0 0 0 0 0 0
4 0 4 0 0 0 0 0
5 vrf? 0 2 23 0 0 0 0
6 0 0 1 28 0 0 0
7 0 0 0 3 90 0 0
8 "6 0 0 0 0 10 17 0
9 7 0 0 0 0 4 2 0
Total
59 superstructure
Ratines 3 4 5 6 7 8 9
' 1 2 3 4 5 6 7
3 1 1 0 0 0 0 0 0
4 : 2 1 3 0 0 0 0 0
5 3 0 0 21 0 0 0 0
6 4 0 0 2 14 0 0 0
7 '< 5 0 0 0 3 77 0 0
8 ; $ 0 0 0 0 8 37 0
9 7 0 0 0 0 0 7 9
Total
60 substructure
Ratings 3 4 s 6 7 8 9
1 2 3 4 5 '?' $ * 7
3 i T 1 0 0 0 0 0 0
4 2 0 8 0 0 0 0 0
5 3 0 3 18 0 0 0 0
6 - 4 0 0 1 40 0 0 0
7 0 0 1 3 56 0 0
8 -6 0 0 0 1 9 32 0
9 -r 7 0 0 0 0 3 3 1
Total
0
4
25
29
93
27
6
184
1
4
21
16
80
45
16
183
1
8
21
41
60
42
7
180
Figure C.4
89