GEORGIA DOT RESEARCH PROJECT 17-28 FINAL REPORT
BRIDGE ASSET VALUATION UTILIZING CONDITION STATES OBTAINED FROM
ELEMENT-BASED INSPECTION INVENTORIES AND
DEPRECIATION MODELS OVER THE LIFE CYCLE OF THE ASSETS
OFFICE OF PERFORMANCE-BASED MANAGEMENT AND RESEARCH 15 KENNEDY DRIVE FOREST PARK, GA 30297-2534
TECHNICAL REPORT STANDARD TITLE PAGE
1. Report No.: FHWA-GA-19-1728
2. Government Accession No.:
3. Recipient's Catalog No.:
4. Title and Subtitle: Bridge Asset Valuation Utilizing Condition States Obtained from Element-Based Inspection Inventories and Depreciation Models over the Life Cycle of the Assets
5. Report Date: August 2019
6. Performing Organization Code:
7. Author(s): Mi G. Chorzepa, Ph.D., P.E. Stephan Durham, Ph.D., P.E. S. Sonny Kim, Ph.D., P.E. O. Brian Oyegbile, Ph.D. Candidate
8. Performing Organization Report No.:
9. Performing Organization Name and Address: University of Georgia College of Engineering Driftmier Engineering Center, Athens, GA 30602
10. Work Unit No.:
11. Contract or Grant No.: PI#0012795
12. Sponsoring Agency Name and Address: Georgia Department of Transportation Office of Performance-Based Management and Research 15 Kennedy Drive Forest Park, GA 30297-2534
13. Type of Report and Period Covered: Final; November 2017 August 2019
14. Sponsoring Agency Code:
15. Supplementary Notes: Prepared in cooperation with the U.S. Department of Transportation, Federal Highway Administration.
16. Abstract:
This report evaluates the element-based bridge inspection data assembled by the Georgia Department of Transportation
(GDOT) for the past four years (2015-2018). The primary goals of this study are to evaluate bridge asset values for
use in Georgia and identify value engineering methodologies that optimize spending on a bridge. Through this study,
the research team has developed deterioration models for bridge elements by classifying bridges in 12 age bins and
has assessed bridge deterioration predictions in terms of health index using weight factors available in the literature.
Discrepancies exist in deterioration prediction models developed from element-based and National Bridge Inventory
(NBI) data. These differences are anticipated as element-based data offers far more detailed information. Furthermore,
two important parameters, a lifecycle and a threshold health index, determine bridge deterioration predictions in terms
of Modified Health Index (MHI). A conjoint analysis further adjusts MHIs to reflect three attributes--geographic
location, age, and presence of a waterway--that affect bridge deterioration. Finally, the adjusted MHIs quantify bridge
asset values. In this report, bridge asset value defines a benefit used for a benefit-cost analysis. The cost includes the
initial project cost as well as maintenance costs. This report estimates the total value of bridges and culverts in Georgia
at $30 billion. In addition, the benefit-cost assessment process presented in this report enables an engineering and
economic analysis over the lifecycle of bridges in Georgia. The research team recommends that GDOT incorporates
its network priority plan and factor in element dependencies for assessing bridge health indices, in order to optimize
long-term returns on investments.
17. Keywords:
18. Distribution Statement:
Asset Valuation, Bridge, Health index, Modified Health Index, Deterioration,
Element, Element Based, Inspection, Life Cycle, National Bridge Inventory
19. Security Classif. (of this report):
20. Security Classif. (of this page):
21. No. of Pages: 22. Price:
Unclassified Form DOT 1700.7 (8-69)
Unclassified
101
N/A
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GDOT Research Project No. 17-28
BRIDGE ASSET VALUATION UTILIZING CONDITION STATES OBTAINED FROM ELEMENT-BASED INSPECTION INVENTORIES AND
DEPRECIATION MODELS OVER THE LIFE CYCLE OF THE ASSETS
Final Report
By
Mi G. Chorzepa, Ph.D., P.E. Associate Professor of Civil Engineering
Stephan Durham, Ph.D., P.E. Professor of Civil Engineering
S. Sonny Kim, Ph.D., P.E. Associate Professor of Civil Engineering
O. Brian Oyegbile Ph.D. Candidate
University of Georgia College of Engineering
Contract with
Georgia Department of Transportation
In cooperation with
U.S. Department of Transportation Federal Highway Administration
August 2019
The contents of this report reflect the views of the authors, who are responsible for the facts and accuracy of the data presented herein. The contents do not necessarily reflect the official views of the Georgia Department of Transportation or the Federal Highway Administration. This report does not constitute a standard, specification, or regulation.
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TABLE OF CONTENTS
Page
LIST OF TABLES ........................................................................................................... vi
LIST OF FIGURES ........................................................................................................ vii
EXECUTIVE SUMMARY ........................................................................................... viii
ACKNOWLEDGEMENTS ..............................................................................................x
1. INTRODUCTION ......................................................................................................1
1.1 OVERVIEW ................................................................................................................1 1.2 RESEARCH NEEDS .....................................................................................................2
1.2.1 Quantifying Bridge Asset Value .........................................................................................................2 1.2.2 Enhancing Long-term Bridge Asset Management Plans....................................................................2 1.2.3 Optimizing Computation of Bridge Element Health Index.................................................................3
1.3 PROJECT SIGNIFICANCE AND SCOPE..........................................................................4 1.4 OBJECTIVES ..............................................................................................................4
2. LITERATURE REVIEW ..........................................................................................6
2.1 U.S. TRANSPORTATION AGENCIES' ASSET VALUATION PROCESS ...............................6 2.2 BRIDGE ASSET DETERIORATION PREDICTION TECHNIQUES ........................................8 2.3 MARKOVIAN BRIDGE DETERIORATION MODELS .........................................................9 2.4 EVOLUTION OF MODIFIED BRIDGE HEALTH INDEX ...................................................11
2.4.1 Bridge Health Index Developed by Caltrans in 1990's....................................................................11 2.4.2 Denver Bridge Health Index Developed by Jiang and Rens in 2000 ...............................................13 2.4.3 Revised Health Index for FDOT by Sobanjo and Thompson in 2016 ..............................................18 2.4.4 Modified Bridge Health Index (MHI) Developed by VDOT in 2016 ...............................................18
3. PRELIMINARY DATA ANALYSIS .....................................................................20
3.1 INTRODUCTION ..........................................................................................................20 3.2 DATA CHARACTERIZATION .......................................................................................20 3.3 DATA QUALITY ASSESSMENT....................................................................................22 3.4 DATA PROCESSING ....................................................................................................24
4. DETERIORATION MODELS FOR EACH BRIDGE ELEMENT....................26
4.1 METHOD....................................................................................................................26
4.1.1 Create Age Groups with the Latest (2018) Element-based Inspection Data....................................27 4.1.2 Aggregate Element Health Indexes Using the Age-bin-based Approach.........................................27 4.1.3 Develop Deterioration Curves for Each Element Using Markovian Model ....................................29
4.2 RESULTS - ELEMENT PERFORMANCE PREDICTIONS ...................................................29
4.2.1 Mathematical Expression for Describing Element Performance Predictions..................................29 4.2.2 Deterioration Curves for Each Element...........................................................................................30
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5. DETERIORATION MODELS FOR EACH BRIDGE.........................................37 5.1 METHOD....................................................................................................................37
5.1.1 Aggregated Element Health Indexes by Cost-based Weight Factors...............................................37 5.1.2 Deterioration Curves for Each Bridge Using a Markovian Model..................................................39
5.2 RESULTS BRIDGE PERFORMANCE PREDICTIONS .....................................................39
5.2.1 Mathematical Equations for Describing Bridge Overall Health Indexes ........................................39 5.2.2 Deterioration Curves for Bridges and Culverts ...............................................................................39
6. COMPARISION OF NBI AND ELEMENT-BASED CONDITION SCORES .43 6.1 METHOD....................................................................................................................43 6.2 RESULTS ELEMENT VS. NBI-BASED PREDICTIONS ..................................................45
7. COMPUATION OF MODIFIED HEALTH INDEX ...........................................47 7.1 OVERALL APPROACH ................................................................................................47 7.2 MHI PROJECTIONS ....................................................................................................48
8. BRIDGE ASSET VALUATION .............................................................................51 8.1 CONJOINT ANALYSIS .................................................................................................51 8.2 CONJOINT MODIFIED HEALTH INDEX ........................................................................52 8.3 BRIDGE VALUATION..................................................................................................55 8.4 BENEFIT-COST ANALYSIS .........................................................................................58
9. LIMITATIONS.........................................................................................................61 10. CONCLUSIONS .......................................................................................................62 11. FUTURE STUDY AND RECOMMENDATIONS................................................64 REFERENCES .................................................................................................................66 APPENDICES ..................................................................................................................71
APPENDIX A SAMPLE ELEMENT-BASED BRIDGE INSPECTION RECORDS. .....................72 APPENDIX B ELEMENT NUMBERS, COUNTS, AND DESCRIPTION. ..................................73 APPENDIX C ELEMENT DETERIORATION PREDICTION MODELS FOR GEORGIA. ............76 APPENDIX D ELEMENT VERSUS NBI-BASED BRIDGE DETERIORATION PREDICTIONS. .83 APPENDIX E MHI PREDICTIONS AND ASSOCIATED PARAMETERS. ...............................89 APPENDIX F LIST OF ELECTRONIC SUBMITTALS. ........................................................101
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LIST OF TABLES
Table No.
Page
Table 1 Valuation Techniques (Herabat, Amekudzi, & Sirirangsi, 2002)........................7 Table 2 Element-Based Inspections in 14 States as of September 2014. .......................13 Table 3 Bridge Condition Indices (CI). ..........................................................................18 Table 4 Condition State Definitions (AASHTO, 2013)..................................................23 Table 5 Element Inspection Records for Selected Bridges in Georgia...........................24 Table 6 Bridges by Age Bin............................................................................................27 Table 7 Age-Bin-Based Health Index Predictions for Selected Elements......................28 Table 8 Equations for Describing Time-Dependent Element Health Index. ..................33 Table 9 Element Weight Factors in Age Bin 1930 for Bridge Number 32150490. .......37 Table 10 Selected Equations for Describing Bridge Performance Over Time. ..............40 Table 11 Discretization of 2 Using Percentages at a Significance Level of 0.05.........45 Table 12 Description of Discretized 2 in Form of Percentages. ...................................45 Table 13 Parameters Considered for Modified Health Index. ........................................48 Table 14 Summary of Findings for Parameters Affecting MHIs. ..................................48 Table 15 Attribute Preferences and Attribute-Worths. ...................................................53 Table 16 Attribute Worths (%) From a Conjoint Analysis.............................................53
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LIST OF FIGURES
Figure No.
Page
Figure 1 Performance Distribution of Bridges in Denver (Jiang & Rens, 2010a)..........14 Figure 2 Linear and Nonlinear Coefficients for Weighing Condition States. ................15 Figure 3 Linear Step Curve for Calculating Adjustment Factor.....................................15 Figure 4 Failure/Repair Cost-Based (C-B) BHIs and DBHI (Jiang & Rens, 2010b). ....17 Figure 5 Process for Determining a Modified Health Index...........................................19 Figure 6 VDOT's Modified Health Index (VDOT, 2016)..............................................19 Figure 7 Bridge and Element Counts in the GA Bridge Inventory.................................21 Figure 8 Extraction of Year Built/Reconstructed from NBI...........................................25 Figure 9 Linear and Nonlinear Condition Index Coefficients (Inkoom et al., 2017). ....28 Figure 10 Deck and Slab Elements in Georgia. ..............................................................30 Figure 11 Twelve (12) Inspection Areas in Georgia. .....................................................32 Figure 12 Health Index Normalized by the Number of Bridges.....................................32 Figure 13 FDOT Bridge Element Important Weights (Sobanjo & Thompson, 2016). ..38 Figure 14 Health Index Predictions of 14,039 Bridges and Culverts in Georgia. ..........41 Figure 15 Health Index Predictions of 9,019 Bridges Only in Georgia..........................41 Figure 16 Typical Bridge Condition Over Time (FHWA, 2018a). ................................42 Figure 17 Process Chart for the Chi-Square Test. ..........................................................44 Figure 18 Chi-Square Percentage (% Error) in Each Age Bin. ......................................46 Figure 19 MHI Predictions for Bridges and Culverts in Georgia. ..................................50 Figure 20 Difference Between MHI and HI for Bridges and Culverts in Georgia.........50 Figure 21 Modified Health Indexes before a Conjoint Analysis. ...................................54 Figure 22 Modified Health Indexes After a Conjoint Analysis. .....................................54 Figure 23 Valuation of All Bridges and Culverts. ..........................................................55 Figure 24 Valuation of Bridges Only..............................................................................56 Figure 25 Valuation of Culverts Only. ...........................................................................57 Figure 26 Sample Cash Flow Diagram of Two Bridges (Illustration Only)...................59 Figure 27 Benefit-Cost Analysis Framework. ................................................................60
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EXECUTIVE SUMMARY This study evaluates the element-based bridge inspection data assembled by the Georgia Department of Transportation (GDOT) for the past four years (2015-2018) and identifies a value engineering methodology for assisting GDOT with long-term transportation asset management plans (TAMP). Element-based inspection records include a quantitative assessment of bridge elements in accordance with the American Association of State Highway and Transportation Officials (AASHTO) Manual for Bridge Element Inspection (2013). Therefore, when aggregated, they provide an evidence-based and quantitative assessment of bridges' overall health.
Elements refer to commonly recognized structural components that constitute a bridge. This study focuses on an evaluation of Bridge Health Index (BHI), a weighted average of bridge element health indexes. Accordingly, element weight factors determine an overall BHI. The study team has provisionally adopted the Florida Department of Transportation's (FDOT's) weight factors (Sobanjo and Thompson, 2016) in this study. They incorporate relative importance and cost of elements. Sample element-based inspection records, element descriptions, and element deterioration predictions are presented (see Appendices A through C). Subsequently, element-based bridge overall deterioration predictions are presented. When compared to the National Bridge Inventory (NBI)-based bridge performance predictions (see GDOT RP 18-30 final report, 2019), discrepancies exist (see Appendix D). This is reasonable because detailed quantitative data, as provided by element-based inspection records, are expected to yield predictions with higher rates of deterioration.
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Furthermore, additional attributes such as lifecycle and threshold health index are considered to compute Modified Health Indexes (MHIs). Bridge deterioration predictions are developed in terms of MHIs (see Appendix E). Finally, a conjoint analysis identifies attributes that negatively affect bridge health and adjusts MHIs (refer to as `conjoint MHIs'). Consequently, conjoint MHIs are multiplied by the total project cost (NBI Item No. 96) to calculate bridge asset values. The report defines the asset value as a benefit compared against cost in a benefit-cost analysis. Bridges and culverts in Georgia have an estimated asset worth of $30 billion. Therefore, once bridge maintenance costs are defined, the benefit-cost assessment process presented in this report should enable an engineering and economic analysis over a lifecycle for approximately 15,000 bridges in Georgia. Lastly, it is recommended that GDOT considers other key features such as its network priority plan and element dependencies when conducting bridge health assessments.
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ACKNOWLEDGEMENTS The University of Georgia greatly appreciates the financial support provided by the Georgia Department of Transportation (GDOT) for this work. The authors would like to thank the personnel at GDOT who assisted with this study. A special thanks to Mr. Clayton Bennett, P.E. (Bridge Maintenance Unit), Mr. Bob O'Daniels (Bridge Maintenance Unit), Richard Williams (Construction Bidding), and Mr. David Jared, P.E. (Performance-based Management and Research), for their research support and provision of pertinent information. Special thanks also to Mrs. Supriya Kamatkar, the project manager, who advised the research team in successfully performing the study and helped coordinate project meetings with GDOT's bridge maintenance unit. Finally, Adara Dodson (MS in Engineering, The University of Georgia) is acknowledged for her significant contribution to the conjoint analysis presented in Section 8.
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1. INTRODUCTION
1.1 Overview Asset valuation is the "assignment of monetary value to physical infrastructure based on its size, age, condition, replacement cost, and original cost to construct" (FHWA, 2016). Assigning a monetary value to bridges underscores the substantial value dedicated to the asset as public wealth or equity (CIPFA, 2013). Bridge asset valuation can provide a very strong justification for promoting an efficient balance between maintaining well-performing assets and repairing/replacing deteriorating assets while working within budget constraints (Matteo, Milton, & Springer, 2016; Weldemicael, Li, & Redd, 2018).
Bridge condition rating is a major variable for determining asset valuation. Transportation agencies are interested in the long-term performance (condition) of bridges because the effects of bridge management programs rarely manifest in the short-term. Bridge deterioration models are expected to capture long-term bridge condition rating projections and quantify devaluation.
Bridge preservation, rehabilitation, and replacement costs often represent a lump sum of overall bridge cost per unit size. Alternatively, the sum of major components' unit costs represents the total maintenance cost. Construction bidding often involves a combination of these two approaches. Anticipating the cost of bridge maintenance remains challenging, however, due to inherent variations in bridge element performance. This study focuses on bridge asset valuation rather than quantifying maintenance costs. This report shows how the study team develops bridge deterioration prediction models, computes Modified Health Indexes (MHIs), and quantifies bridge asset values (or benefits) for a benefit-cost analysis.
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1.2 Research Needs
1.2.1 Quantifying Bridge Asset Value Asset values must be adjusted upward each year to reflect returns on investments (e.g., rehabilitations). In order to capture the full effects of bridge deterioration and maintenance investments, it is necessary to consider potential changes in the bridge asset values over a long-term financial period--10 years or longer, which is consistent with the Moving Ahead for Progress in the 21st Century Act (MAP-21) requirements. GDOT should be able to optimize returns on investments by quantifying bridge health indexes (BHIs) as well as associated equities (Fereshtehnejad & Shafieezadeh, 2018; Ghahari, Volovski, Alqadhi, & Alinizzi, 2018; Inkoom, Sobanjo, Thompson, Kerr, & Twumasi-Boakye, 2017; Miller, 2017; Miyamoto, Kawamura, & Ong, 2002; Santos, Ferreira, Flintsch, & Cerezo, 2018).
1.2.2 Enhancing Long-term Bridge Asset Management Plans State highway agencies increasingly recognize the need to develop bridge management plans in a more efficient and cost-effective way (Bocchini & Frangopol, 2011; Bu, Lee, Guan, Loo, & Blumenstein, 2014; Hasan, Setunge, Law, & Koay, 2015). GDOT's efficiency strategies and other productivity-enhanced attributes should improve transportation asset management plans (TAMP). MAP-21 (FHWA, 2018b) defines asset management as follows: "Asset management is a strategic and systematic process of operating, maintaining, and improving physical assets, with a focus on engineering and economic analysis based upon quality information, to identify a structured sequence of maintenance, preservation, repair, rehabilitation, and replacement actions that will achieve and sustain a desired state of good repair over the lifecycle of the assets at minimum practicable cost." - Title 23, United States Code (U.S.C.), 101(a)(2)
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While TAMPs constitute a major undertaking for bridge management agencies, the content and complexity of these plans tend to vary. Several factors affect TAMPs: geographical locations, number and characteristics of bridges in a network, performance requirements, etc. In the United States, each state must develop a riskbased asset management plan to improve or preserve the condition of bridge assets and the performance of the system in compliance with MAP-21 Legislation (FHWA, 2018c).
One of the most critical aspects of bridge asset management plans is the Major Repairs and Rehabilitation (MRR) requirements for each bridge. Bridge replacement is an expensive decision and thus must be supported by a sound engineering benefit-cost analysis. Despite significant progress over the past two to three decades culminating in the development of bridge management programs (e.g., AASHTOWare BrM software) to support decision-making, a substantial need for improvements remains (Inkoom & Sobanjo, 2018; Inkoom et al., 2017; Jiang & Rens, 2010a).
In summary, GDOT will need to optimize its decision-making process to meet annual performance requirements and to effectively manage a large infrastructure asset such as bridges. In doing so, GDOT will need to consider the various risks affecting bridge performance, such as high traffic volumes, wetting and drying cycles, freezing and thawing attacks, the level of exposure to deicing salts and wet environments, aging and quality/durability of construction materials, and more (Chorzepa et al., 2016; Hu, Daganzo, & Madanat, 2015; Saeidpour, Chorzepa, Christian, & Durham, 2018).
1.2.3 Optimizing Computation of Bridge Element Health Index Variations in bridge conditions exist due to inherent differences in factors that can potentially influence bridge performance. While highly accurate bridge element construction costs can be obtained from relevant sources, predicting future bridge
3
conditions remains strenuous. For example, linear element condition state weighting factors initially adopted in the AASHTOWare BrM software to compute element health index may not necessarily predict bridge conditions across the United States. As a result, weight factor adjustments based on each state's element inspection records have been recommended (Inkoom et al., 2017; Jiang & Rens, 2010a, 2010b).
1.3 Project Significance and Scope GDOT has the TAMP in place to meet MAP-21 requirements. This study allows GDOT to evaluate options for enhancing the TAMP long-term and research `asset valuation' processes which reflect bridge conditions and their potential benefits. The deterioration models and forecasting scenarios identified through this study can better support estimates of long-term investment needs to guide decision-making.
The asset valuation developed in this study is expected to: 1. assess GDOT's bridge equity (present and future values of bridges) in terms of
bridge conditions as the basis for engineering decisions; and 2. create an engineering benefit-cost analysis framework.
1.4 Objectives This study aims to advance the concept that physical assets have financial value. A sound engineering analysis and reliable financial planning support GDOT's long-term TAMP. This overall goal is consistent with MAP-21 objectives.
The primary objectives of this study are to evaluate bridge asset values for use in Georgia and identify value engineering methodologies that optimize spending on a bridge.
The specific goals of this special research study are to: 1. identify deterioration models for bridge elements utilizing available GDOT
resources (e.g., annual element inspection records);
4
2. develop a process for determining BHI in terms of element-based condition states documented over the past 4 years; and
3. assign monetary values to bridges based on age, element condition, replacement cost, and original construction cost.
5
2. LITERATURE REVIEW
2.1 U.S. Transportation Agencies' Asset Valuation Process Assets are valued at historical cost under the Governmental Accounting Standards Board (GASB) Statement 34 deterioration approach. GASB 34 requires agencies to value assets only based on their original construction costs, known as historic costs (FHWA, 2016). As a result, a 20-year-old bridge restored nearly to "as new" condition would be reported on the agency's balance sheet at a depreciated value. Although the asset may have been maintained and rehabilitated, its value will continue to decline and could reach a value of zero in 75 years. Therefore, the use of historic costs underestimates the intrinsic value of U.S. infrastructure (FHWA, 2016) and thus makes this asset valuation technique largely irrelevant to U.S. transportation asset management.
Recently developed asset management plans recognize that historic costs have limited value for making infrastructure investment decisions (FHWA, 2016). Accordingly, transportation agencies have started reporting replacement costs which are more meaningful to decision makers. Most agencies report fair values of transportation assets, not historic costs. When estimating fair values, transportation agencies may consider transportation asset characteristics such as condition and location. Asset valuation methods that rely on deteriorated replacement costs and fair market values may appear attractive to bridge asset managers; however, transitioning away from the historical asset valuation method remains challenging due to complexities involved in processing element-based bridge inspection data. Table 1 shows selected asset valuation techniques applicable to transportation infrastructure.
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Table 1 Valuation Techniques (Herabat, Amekudzi, & Sirirangsi, 2002).
Valuation Techniques
Cost-based
Description
Derives pavement value from replacement cost, physical deterioration, physical & economic obsolescence.
Applications/Limitations
Useful for valuing assets which are not frequently sold in the market or where no market exists. Relates pavement value with its performance and time.
Productivity Realized Value or Income Capitalization
Option Value
Relative Value
Market Comparison
Based on the net present value of benefit stream of the pavement/highway for its remaining life.
Derives pavement value under certain circumstances, e.g., specific number of cumulative ESALs* of minimum acceptable level of roughness. Estimates value by comparison with other pavements based on common attributes such as traffic volume, etc. Based on market price by comparison with recent sales of pavements and highways.
Appropriate for toll highway by discounting its future cash flow. Possible to apply with public pavement/highway by studying current or future benefit of a pavement. Requires several assumptions. Can be applied as a decisionmaking tool for maintenance or rehabilitation investments.
Applicable to toll highway and public highway by estimating value based on traffic volume.
Applicable to highway sales. Only few pavements/highways are sold in an open market.
*ESAL - Equivalent Single Axle Load.
Among the valuation techniques shown above, a cost-based asset valuation approach is most applicable to the objectives of this study. Therefore, this study focuses on developing a cost-based asset valuation approach for bridges in Georgia. The costbased bridge asset valuation approach is based on element inspection records and utilizes MHIs determined from bridge deterioration prediction models. MHIs measure the equity of each bridge over a projected consumption period. Sections 2.2 and 2.3
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present techniques (i.e., deterministic and stochastic models) for building MHI deterioration prediction models. Section 2.4 provides a critical review on measuring BHIs.
2.2 Bridge Asset Deterioration Prediction Techniques Several models exist for quantifying bridge deterioration rates. Bridge inspection data have been collected and analyzed since the early 1970's to assist decision makers in predicting the likelihood of future changes in bridge conditions. A statistical approach is often adopted to investigate structural performance trends in individual elements (Chang & Maguire, 2016). A predictive model that can describe the future state of a bridge component has enabled state agencies to prioritize and deploy resources to where they are most needed. A reliable future condition estimate is expected to directly improve emergency response, management, and budget allocation (Bu, Lee, Guan, & Loo, 2013; Bu, Son, et al., 2013; DeStefano & Grivas, 1998; Huang, Ong, & Alahakoon, 2015; Khatami, Shafei, & Smadi, 2016).
MAP-21 establishes a performance- and outcome-based program to help state agencies invest resources in projects that "collectively will make progress towards the achievement of the national goals." MAP-21 represents a strong commitment to a datadriven, risk-based approach to asset management in the United States. Pursuant to 23 U.S.C.150(c)(3)(A), transportation agencies are required to develop TAMPs which must contain deterioration models, as elaborated in 23 C.F.R. 515.17 and MAP-21 1106 (C.F.R., 2017; Campbell, Perry, Connor, & Lloyd, 2016; FHWA, 2018b; U.S.C., 2018).
At present, cutting-edge bridge management systems classify bridge deterioration models into two major categories: deterministic models and stochastic models (Agrawal, Kawaguchi, & Chen, 2010; Li, Sun, & Ning, 2014). For deterministic
8
models, the measure of bridge condition is expressed without probabilistic considerations, whereas a stochastic approach reflects the uncertainties that each bridge condition represents.
Deterministic models assume that bridge deterioration is certain, and thus a regression analysis is commonly used to determine a decay rate. They generally describe a relationship between factors affecting the facility's deterioration (e.g., bridge age) and condition using a mathematical or a statistical formulation. These models calculate predicted conditions deterministically by ignoring the random error in predictions (Huang et al., 2015; Li et al., 2014; Morcous, Lounis, & Mirza, 2003). Such models aim to further improve the overall predictive performance of a system (Huang et al., 2015).
This study uses a stochastic modeling approach, more suitable for handling a large network of bridges: approximately 15,000 in-service Georgia bridges. Moreover, a stochastic approach enables more realistic deterioration models (Chang & Maguire, 2016). The Markovian modeling technique, a special stochastic approach long used for bridge deterioration modeling, is described in Section 2.3.
2.3 Markovian Bridge Deterioration Models Markovian bridge deterioration models forecast BHIs based on the concept of condition transitions from one state to another state during a transition period. The Markov-chain approach is a special case of the Markov-process with discrete time and state parameters. These models have been employed by most state-of-the-art bridge management systems (BMS), such as AASHTOWare BrM, BRIDGIT, and Ontario Bridge Management System (OBMS) (Bu, Lee, Guan, Blumenstein, & Loo, 2011). Bridge deterioration models based on the Markov-chain approach assume a static condition or progressive deterioration to a lower condition state. For example, in
9
PONTIS (now AASHTOWare BrM), bridge element deterioration is typically modeled as annual transition estimates across four discrete condition states.
There are two assumptions made in the Markov-chain process. First, the future state of a stochastic process depends only on the present condition (namely, a state independence assumption). Second, the transition probability between two states should be constant. A constant inspection period, where inspections are performed at predefined and fixed-time intervals, is required (Grussing, 2015; Li et al., 2014). The major advantages of the Markov-process (Almeida, Teixeira, & Delgado, 2015; Chang & Maguire, 2016; Huang et al., 2015) are as follows:
It can reflect a stochastic bridge deterioration process based on variables such as initial conditions, assessment errors, and inherent uncertainties;
A future-state prediction is based on the present state enabling an incremental approach; and
It can be applied to a large network of bridges.
The procedure for developing Markovian bridge deterioration models is well documented in the literature (Agrawal et al., 2010; Bu et al., 2011; Cavalline, Whelan, Tempest, Goyal, & Ramsey, 2015; Morcous, 2006). The most significant task in the Markov-chain process is to determine a transition probability matrix, P, which quantifies the probabilities of condition state transitions (Li et al., 2014).
Element-based health indexes (0 to 100) in the 2013 AASHTO Bridge Manual are distributed across four possible bridge element states. Condition states 1 and 4 correspond to the best and worst conditions, respectively. A change in condition state is assumed to occur at discrete time intervals that align with routine inspection periods. Consequently, the components, , of the probability matrix, P, represent bridge elements transitioning from state to state during a specified period (see Equation
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2.1). The transition matrix has zero values below the diagonal because it is assumed that deterioration takes place without rehabilitation. Thus, the probability of an improvement at any state is assumed to be zero (Cavalline et al., 2015). The values above the diagonal matrix indicate transitions to `immediately' lower condition states. System states are "mutually exclusive and collectively exhaustive" after each transition so that the sum of each row is the unity (Chang & Maguire, 2016).
1
0
0
0 0
0
1
0
1
0
0
0
. 2.1
2.4 Evolution of Modified Bridge Health Index
2.4.1 Bridge Health Index Developed by Caltrans in 1990's In the 1990's, the California Department of Transportation (Caltrans) managed 12,656 bridges with an estimated asset value of more than $35 billion. Caltrans developed a versatile diagnostic tool, the California Bridge Health Index (BHI). BHI is a singlenumber assessment of bridge condition based on the bridge's economic worth as determined by an element-level inspection (Shepard & Johnson, 2001). It generally varies from 0 (worst condition) to 100 (best condition).
Contrary to the Federal Highway Administration's (FHWA's) sufficiency rating, a BHI quantitatively measures structural health conditions. Due to the growing popularity and advantages of BHIs, more state departments of transportation (DOTs) have adopted an element-based inspection (see Table 2) procedure to quantify bridge health. The main advantage of a BHI is that each bridge element has an initial asset value of 100 when newly constructed. An element may deteriorate to a lower condition state, reducing its asset value (Inkoom et al., 2017; Shepard & Johnson, 2001). To
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account for the deterioration in asset value over time, the Caltrans BHI assigns important weights (or coefficients) to element quantities in four condition states.
Element quantities and important weights are primarily used for measuring an overall BHI for a network of bridges based on identified condition states (Shepard & Johnson, 2001). Important weights are factors that quantify the contribution of each condition state and bridge element that make up a complete bridge. Thus, two important weight factors exist: (1) a weight factor for measuring weights of each of four condition states within an element and (2) a weight factor given to each bridge element that constitutes a bridge (Croop et al., 2017; Fereshtehnejad, Hur, & Shafieezadeh, 2017; Shepard & Johnson, 2001). Resource allocations for MRR largely depend on how accurately important weights can represent the condition of each bridge element and ultimately bridge structures (Inkoom & Sobanjo, 2018; Inkoom et al., 2017; Jiang & Rens, 2010a, 2010b; Shepard & Johnson, 2001).
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Table 2 Element-Based Inspections in 14 States as of September 2014.
State Wyoming
Performing element level inspections
before MAP21?
Yes
Uses ADE1 or NBE2/ BME3 sub elements?
Yes
Collecting defects?
No
State has a bridge
management program?
Yes
Bridge Management System (BMS)
software
AASHTOWare
New York
Yes
No
No
Yes
In house database
Texas
Yes
No
Yes
Yes
In house database
(PonTex)
California
Yes
Yes
Yes
Yes
AASHTOWare
Georgia
Yes
Yes
Yes
Yes
AgileAssets
Florida
Yes
Yes
No
Yes
AASHTOWare
Montana
Yes
Yes
No
Yes
Under
development
Kentucky
Yes
Yes
Yes
Yes
AASHTOWare
North Dakota
Yes
Yes
Yes
Yes
AASHTOWare
Iowa
Yes
Yes
Yes
Yes
In house database
(SIIMS)
Michigan
Yes
Yes
No
Yes
AASHTOWare
Wisconsin
Yes
Yes
Yes
Yes
In house database
(HSIS)
Missouri
No
No
No
No
None
Ohio
No
Yes
No
Yes
Bentley SMS
1 Agency Developed Elements.
2 National Bridge Elements (AASHTO, 2013): "Primary structural components of bridges necessary to
determine the overall condition and safety of the primary load carrying members."
3 Bridge Management Elements (AASHTO, 2013): "Components of bridges such as joints, wearing
surfaces, and protective coating systems and deck/slab protection systems that are typically managed by
agencies utilizing Bridge Management Systems."
Note: This table is taken from a report (Campbell, Perry, Connor, & Lloyd, 2016).
2.4.2 Denver Bridge Health Index Developed by Jiang and Rens in 2000 After analyzing Caltrans BHIs for bridges in Denver, Colorado, Jiang and Rens (2010a, 2010b) concluded that the Caltrans BHI was often subject to a municipality's imprecise cost data. Even though most of the bridges had been in use for many years and needed rehabilitation, Caltrans BHIs indicated excellent performance: approximately 90% of Denver's bridges had a BHI between 90 and 100 (see Figure 1).
13
(a) Failure-Cost BHI
(b) Repair-Cost BHI
Figure 1 Performance Distribution of Bridges in Denver (Jiang & Rens,
2010a).
Jiang and Rens (2010a) also indicated that the Caltrans BHI was not sensitive
to the general deterioration of bridge elements. Furthermore, the element health index,
the product of weight and element quantity, did not indicate the effect of element
damage on bridge health and function. The result of this study served as the basis for
developing an alternate BHI methodology, called "Denver BHI." Jiang and Rens
(2010a) introduced new weight coefficients and proposed Denver BHI as follows:
100%
. 2.2
. 2.3
100%
. 2.4
where,
is the health index assigned to each element;
is the quantity of the element in sth condition state;
is the nonlinear health index coefficient corresponding to the sth condition state;
is the adjusted weight coefficient of element e; is the adjustment factor of element e; is the weight coefficient assigned to each element;
14
is the health index assigned to each bridge (i.e., Denver BHI); and
are fractional values calculated as follows, where s is the index of the condition
state; and n is shown in Figure 2 (Jiang and Ren, 2010b).
1
. 2.5
Figure 2 Linear and Nonlinear Coefficients for Weighing Condition States.
Figure 3 Linear Step Curve for Calculating Adjustment Factor. 15
The concept of BHI originated with the California Department of Transportation (Caltrans). Its bridge management program software, Pontis, has been adopted by AASHTO and developed into the AASHTOWare Bridge Management software (BrM). The old (Pontis) system determined BHIs based on Failure-Cost (FC) or Repair-Cost (RC). The new Denver BHI approach is based on the application of nonlinear index coefficients of condition states (see Figure 2) and adjustment factors (see Figure 3) to obtain a new BHI.
Weight coefficients are determined based on expert opinions. Weight coefficients define the contribution and relative importance of each element to the health and functionality of a bridge. In Caltrans' BHI, it is a function of element costs. The weight coefficients developed for Denver BHI assign numerical values to each of the AASHTO elements (2013). Table 3 shows zones created based on condition index used to interpret the Denver BHI. The computation of health index using the Denver BHI (DBHI) method generally results in a lower health index compared to the two costbased approaches as shown in Figure 4.
16
Figure 4 Failure/Repair Cost-Based (C-B) BHIs and DBHI (Jiang & Rens, 2010b).
17
Table 3 Bridge Condition Indices (CI).
CI zones Action
Immediate action not required (71-100)
Economic analysis of repair alternatives recommended to determine appropriate maintenance action (41-70)
Value 85 100
CI scales
Condition description
Excellent no noticeable defects, some aging or wear visible.
70 84
Very good only minor deterioration or defects evident.
55 69 Good some deterioration or defects evident, function not impaired.
`40 54 Fair moderate deterioration, function not seriously impaired.
25 39 Poor serious deterioration in at least some portion of structure, function
Detailed evaluation
seriously impaired.
required to determine the
need for RR&R, safety
10 24 Very poor extensive deterioration,
evaluation recommended (0-40)
barely functional.
0 9 Failed general failure or failure of a
major component, no longer
functional.
Note: RR&R - Resurfacing, Restoration and Rehabilitation.
2.4.3 Revised Health Index for FDOT by Sobanjo and Thompson in 2016 Sobanjo and Thompson (2016) investigated various approaches for weighing FDOT's health indexes. Specifically, the researchers considered (1) element replacement costs; (2) element long-term costs; (3) vulnerability to hazard risks; and (4) element definition in terms of class, category, and type (Sobanjo & Thompson, 2016). As a result, a revised health index incorporating new element importance factors was proposed.
2.4.4 Modified Bridge Health Index (MHI) Developed by VDOT in 2016 An MHI is a measure of bridge health condition that considers the influence of average bridge life on the long-term performance of bridge assets. Thus, computing an MHI requires deterioration curves for bridge elements (see Figure 5). Once MHIs are
18
determined for bridge elements as shown in Figure 6, Eq. (2.6) determines an overall MHI for a bridge:
Historical deterioration data
for each bridge element
Deterioration models for each bridge element
MHI for each bridge element (MHIElement )
Overall MHI, MHIOverall, for each
bridge
Bridge element replacement values
Figure 5 Process for Determining a Modified Health Index.
Average life: 20% in CS4
For a 30-year in service bridge
MHI = 100*(70-30)/70 = 57
Average life is ~ 70 Years
Figure 6 VDOT's Modified Health Index (VDOT, 2016).
MHI
MHI
ReplacementValue
ReplacementValue
. 2.6
19
3. PRELIMINARY DATA ANALYSIS 3.1 Introduction Element-based bridge inspection data include quantitative assessment of each bridge element in four condition states (see Table 4). Table 5 illustrates how quantities are specified in the data. Appendix A also illustrates numerical quantities in four condition states. Such quantitative evaluation allows decision makers to measure the extent of deterioration, determine current asset value, and prepare successful bridge management plans (AASHTO, 2013). Each condition state aggregates the cumulative effects of relevant defects. Thus, a preliminary data analysis is conducted to understand bridge element performance. It also ensures that element-based inspection data are sufficient (in terms of quality and format) as an input file for Matlab (The MathWorks, Inc., 1994 2018), which is the primary software used for this study. Although Matlab was the primary analysis software for developing deterioration predictions shown in Sections 4 and 5, the key features presented in Sections 7 and 8 are captured by a Microsoft Excel application (see Appendix F.1). 3.2 Data Characterization This section describes the characteristics of element-based bridge inspection records in Georgia. The purpose of data characterization is to obtain valuable information on the element inspection records that are relevant to bridge asset valuation.
20
Bridge count Element count
3000
80
2015
2016
2017 2018
70
2500
60
2000 50
1500
40
30 1000
20 500
10
0
0
2020 2010 2000 1990 1980 1970 1960 1950 1940 1930 1920 1910
Year constructed (x > Year x-10)
Figure 7 Bridge and Element Counts in the GA Bridge Inventory.
Notes: Read the y-axis on the left for hatched bars and the one on the right for line graphs. Read the x-axis for Year 2020 x values range from 2010 to just below 2020.
As shown in Figure 7, a total of four element inspection data sets (referred to as "Tapes" for 2015 through 2018) have been collected since GDOT started its elementbased bridge inspection program in 2015. These data sets include 46,176 (in Tape 2015); 83,370 (in Tape 2016); 87,624 (in Tape 2017); and 88,030 (in Tape 2018) element-level inspection records. Similarly, they include 87 (in Tape 2015), 86 (in Tape 2016), 85 (in Tape 2017), and 85 (in Tape 2018) bridge elements.
The number of bridges constructed in the past 100 years varies (see Figure 7). Most bridges were constructed from 1961-2010, and fewer bridges have been constructed since 2010. This may be attributed to the `Fix-it-First' highway management strategy in the United States (Kahn & Levinson, 2011; Schanzenbach, Nunn, & Nantz, 2017). This strategy is based on the notion that conducting early and
21
regular maintenance yields higher returns on investments and thus prioritizes maintenance, repair, and rehabilitation over new infrastructure construction (or replacement) projects.
Figure 7 also shows a steady increase in the number of bridge elements. Changes in element counts may be attributed to advancement in bridge design and construction techniques in the past 50 to 100 years. Since the late 1960's, there have been tremendous improvements in the computational techniques available for bridge analysis and design, as well as in construction materials (Biernacki et al., 2017; Ngo, 2018; Schanzenbach et al., 2017) and technologies.
3.3 Data Quality Assessment Table 4 shows the four condition states defined in the AASHTO element inspection manual (2013). Appendix A shows typical GDOT element-based bridge inspection data. The quality assessment performed in this study is based on experience gained from the National Bridge Inventory (NBI) condition rating analysis (see GDOT RP 1830 final report, 2019), where bridges and components with incomplete entries were found and screened out. This analysis concluded with 46,176 (in Tape 2015); 83,370 (in Tape 2016); 87,624 (in Tape 2017); and 88,030 (in Tape 2018) element inspection records. Overall, these records are found to be complete with a few anomalies (i.e., incomplete and missing data and changes in element number assignments) observed in the 2015 and 2016 datasets.
22
Table 4 Condition State Definitions (AASHTO, 2013).
Defects Delamination/ Spall/Patched
Area (1080)
Exposed Rebar (1090)
Efflorescence/ Rust Staining
(1120) Cracking (RC
and Other) (1130)
Abrasion/Wear (PSC/RC) (1190)
Damage (7000)
Condition States for Element 12, Reinforced Concrete Deck
1
2
3
4
None
Delaminated. Spall Spall greater
1 in. or less deep or than 1 in. deep or
6 in. or less in greater than 6 in.
diameter. Patched
diameter.
area that is sound. Patched area that
is unsound or
showing distress.
None
Present without measurable section
loss.
Does not warrant structural review.
Present with measurable section loss but does not warrant structural
review.
The condition warrants a
structural review to determine the effect on strength or serviceability of the element or
bridge;
None
Surface white
Heavy build-up
or,
without build-up or
with rust
leaching without rust staining.
staining.
a structural review has been
None or insignificant
cracks
Unsealed moderate width cracks or
unsealed moderate pattern (map)
cracking. Cracks from 0.012 to 0.05
Wide cracks or heavy pattern (map) cracking. Cracks greater than 0.05 inches
wide.
completed and the defects
impact strength or serviceability of the element or
bridge.
inches wide.
No abrasion Abrasion or wearing Coarse aggregate
or wearing has exposed coarse is loose or has
aggregate but the popped out of
aggregate remains
the concrete
secure in the
matrix due to
concrete.
abrasion or wear.
Not
The element has The element has The element has
applicable impact damage. The impact damage. impact damage.
specific damage
The specific
The specific
caused by the
damage caused damage caused
impact has been
by the impact by the impact has
captured in
has been
been captured in
condition state 2
captured in condition state 4
under the
condition state 3
under the
appropriate material defect entry.
under the appropriate
appropriate material defect
material defect entry.
entry.
23
3.4 Data Processing Unfortunately, element-based inspection data are not self-reliant. That is, there are important bridge variables that are comprehensively captured in the NBI but not captured by element-based inspection data. Among others, construction years are not available in the element inspection inventory (`Tape') as shown in Table 5. Therefore, element-based inspection data do not replace NBI data; rather, it is a supplementary data set that provides more details on each element's quantitative condition. In Section 6, element inspection-based and NBI-based condition scores are compared.
Table 5 Element Inspection Records for Selected Bridges in Georgia.
STATE STRUCNUM EN TOTALQTY CS1 CS2 CS3 CS4
13
12105430 12
19393 19393 0
0
0
13
12105430 515
21426 21426 0
0
0
13
12105430 515
36
36
0
0
0
13
12105430 234
190
188 2
0
0
13
8100450 215
62
55
7
0
0
13
3150100 110
1956
1956 0
0
0
13
2101220
12
5630
5216 414 0
0
13
14100010 215
112
100 12 0
0
13
14100010 331
206
206 0
0
0
13
14100010 234
104
74 30 0
0
13
30350140 301
120
0
0 120 0
Other relevant attributes in the NBI include structure number, designated as STRUCNUM (Item no. 8); year built, designated as YEAR BUILT (Item no. 27); and year reconstructed (Item no. 106). In this study, NBI data for 2017 and Tape data for 2018 are used for the analysis. The Excel program (see Appendix F.1) developed for this study can process any combination of standardized NBI and Tape (or elementbased) data.
The following three steps are used for data processing: (1) extract year built from NBI data;
24
(2) replace year built by the year reconstructed if the year reconstructed is greater than year built; and (3) align bridge identification numbers (IDs) in NBI data with bridge IDs in Tape (or element-based) data to extract year built/reconstructed.
This process is illustrated in Figure 8 with the first five rows of the elementbased bridge inspection data from Table 5. There is a total number of 14,863 bridges in NBI 2017 and 14,684 bridges in Tape 2018. This querying process returns a total number of 14,039 bridges. It should be noted that NBI 2018 data was not available when this study was conducted.
Tape for further analysis
STATE STRUCNUM EN TOTALQTY CS1 CS2 CS3 CS4 EPN YEAR BUILT
13 12105430 12 19393 19393 0 0 0
1977
13 12105430 515 21426 21426 0 0 0 107 1977
13 12105430 515
36
36 0 0 0 311 1977
13 12105430 234 190
188 2 0 0
1977
13 8100450 215
62
55 7 0 0
1960
Link NBI and Tape to extract year built/reconstructed for bridges in Tape
NBI STRUCNUM YEAR BUILT 12105430 1977
8100450 1960 8100490 1982 8100500 1982 8100510 1935
Tape STRUCNUM 12105430 12105430 12105430 12105430
8100450
Tape with year built/reconstruction STRUCNUM YEAR BUILT 12105430 1977 12105430 1977 12105430 1977 12105430 1977 8100450 1960
Note: EN = Element Number, and `EPN' indicates the parent element number. Figure 8 Extraction of Year Built/Reconstructed from NBI.
25
4. DETERIORATION MODELS FOR EACH BRIDGE ELEMENT
4.1 Method The bridge asset valuation method implemented in this study uses the MHI computed from a deterioration model for each bridge. Therefore, bridge element deterioration models must be developed to determine health indexes and MHIs (see Sections 5 and 7). This approach is also consistent with Title 23 of the United States Code 150(c)(3)(A) (U.S.C., 2018) and Title 23 of the Code of Federal Regulations 515.17 (C.F.R., 2017). The granularity of element-based inspection data enables the development of deterioration models at element level. These models are more quantitative and informative than the ones derived from the traditional NBI overall condition-rating-based approach.
However, the element-based approach has its deficiencies at this time. The main shortcoming relates to a lack of sufficient records. Many bridge authorities worldwide have similar problems using a BMS for accurate predictions of long-term bridge performance and budget planning (Bu, Son, et al., 2013; Jeong, Kim, Lee, & Lee, 2017). While some state DOTs have collected element inspection data since the mid1990's, most have only assembled element inspection data since 2013, in compliance with the MAP-21 Legislation. GDOT falls into the second category and started the element-based inspection of all bridges in 2015 to comply with the FHWA's element inspection requirements in Title 23 of the United States Code 144(b). Additionally, GDOT has sustained NBI inspection data for all bridges.
GDOT has collected bridge element inspection data since 2015, yielding two inspection records per bridge between 2015 and 2018, resulting from a biennial inspection process. Based on the experience of the authors, these inspection records are insufficient for developing meaningful deterioration models when a conventional
26
approach is used. As an alternative method, this study has developed an age-bin-based approach for generating bridge deterioration models. This process must be validated once sufficient element-based inspection data are gathered. This study primarily utilizes GDOT's element inspection records between 2015 and 2018. Sections 4.1.1 through 4.1.3 provide the key steps involved in the age-bin-based approach.
4.1.1 Create Age Groups with the Latest (2018) Element-based Inspection Data The 14,039 bridges obtained in Section 3.4 are categorized into 13 age groups corresponding to construction eras (Table 6). The authors reviewed the data in the age bin, 1900 (Year built <=1900), and decided not to use the bin due to insufficient data (see Figure 7).
Table 6 Bridges by Age Bin.
Age category 1 2
3 4
Age bin
2020 2010 2000 1990 1980 1970 1960 1950 1940 1930 1920 1910 1900
Description
2011<=Year built<=2020 2001<=Year built<=2010 1991<=Year built<=2000 1981<=Year built<=1990 1971<=Year built<=1980 1961<=Year built<=1970 1951<=Year built<=1960 1941<=Year built<=1950 1931<=Year built<=1940 1921<=Year built<=1930 1911<=Year built<=1920 1901<=Year built<=1910
Year built <=1900
4.1.2 Aggregate Element Health Indexes Using the Age-bin-based Approach The computation of bridge element health indexes follows the procedure described in Sections 2.3 and 2.4. Figure 9 shows the linear and nonlinear coefficients for element condition states, which are currently used to compute bridge element health indexes, as
27
obtained from the relevant literature (Inkoom et al., 2017). Based on results from the preliminary analysis of bridge elements in Georgia, nonlinear pessimistic coefficients, (100, 55, 25, 0), are determined suitable condition state weighting factors (or coefficients) for computing element health indexes (HIs). The coefficients yield the `Pessimistic 2' model shown in Figure 9, and they are considered pessimistic because the quantities in condition states 1 and 2 (good and fair conditions) are given higher weight factors than those for condition states 3 and 4 (poor and severe conditions) in calculating the HIs.
The computed element health indexes are then grouped according to the 12 age bins described in Section 4.1.1. Element health indexes within age bins represent element performance scores over the last 100 years (Table 7).
Figure 9 Linear and Nonlinear Condition Index Coefficients (Inkoom et al., 2017).
Table 7 Age-Bin-Based Health Index Predictions for Selected Elements.
Element #
12 38 107 205 215
2020
99.47 99.92 99.16 98.00 99.19
2010
98.43 97.41 98.43 97.09 98.23
2000
97.35 94.04 95.62 93.78 97.25
1990
92.90 95.77 97.20 93.61 95.97
1980
88.01 92.55 96.52 95.73 94.96
Health Index 1970 1960 1950
79.33 74.64 70.91 85.83 81.17 99.44 94.21 87.79 79.71 89.45 80.87 71.83 94.71 92.89 89.56
1940
73.46 68.84 78.72 90.38 83.72
1930
88.49 77.43 81.54 76.82 81.27
1920
84.30 67.26 81.60 42.93 62.92
1910
76.36 55.00 73.44 59.69 53.63
28
4.1.3 Develop Deterioration Curves for Each Element Using Markovian Model As discussed in Section 2.3, a successful implementation of the Markovian approach for developing a deterioration model requires condition state transition probabilities for each element. In this study, a data-driven analysis using GDOT's element inspection data captures transition percentages in element health indexes. This process estimates transition probability by measuring a proportion of the number of element condition state changes to the total number of states before the change (Chang & Maguire, 2016; Grussing, 2015; Morcous, 2006). This study uses the following optimization method, governed by the following equation (Chang & Maguire, 2016):
| , , | subject to 0 1 for = 1,2, 3, .. , . (4.1) where, denotes minimization; N denotes the number of bridges or elements belonging to a subset; is the number of condition states (= 4 in this study); , is the observed health index at an th age bin of th bridge; , is the predicted health index; and is the optimization function to minimize the difference between , (the observed health index) and , (the predicted health index).
For each transition probability matrix (see Eq. 2.1), three unknowns ( , ... . ) must be estimated by minimizing the sum of errors between predicted and aggregated health indexes. Section 4.2 presents the outcome of this analysis.
4.2 Results - Element Performance Predictions The age-bin approach yields a time-dependent health index history for each element.
4.2.1 Mathematical Expression for Describing Element Performance Predictions Table 8 shows the mathematical equations describing time-dependent element health indexes and lists diagonal components (P11, P22, P33, P44) of the transition probabilities for bridge elements.
29
4.2.2 Deterioration Curves for Each Element Long-term performance of bridge elements greatly influences the overall health of bridges in Georgia. For example, in Figure 10, a steel deck with corrugated material in a highly corrosive marine environment will deteriorate at a much faster rate than a reinforced concrete deck. Thus, bridge element deterioration models are invaluable for the development of short- and long-term plans for Georgia. Appendix C presents deterioration predictions for the remaining bridge elements in Georgia.
RC = Reinforced Concrete; P/S = Prestressed/Precast; conc = concrete; and Steel deck with corrugated = steel deck with corrugated panels Figure 10 Deck and Slab Elements in Georgia.
Note: In the brackets, the presence of each element within the Deck & Slab category is shown as a percentage.
Figure 10 illustrates the overall performance of deck and slab elements. In reviewing the figure, it is important to recognize that Georgia's bridge inventory
30
consists of approximately 60% reinforced concrete decks (Element #12). Based on these results, long-term performance of bridge elements is mainly dependent on the following factors: (1) material type and properties; (2) resistance to environmental factors, e.g., corrosion; (3) areas of applications, e.g., under water, surface, or concealed; and (4) design type. In reviewing the element-level deterioration prediction models in Appendix C, it is also important to recognize that the number of elements affects the results. Figures 11 and 12 show that Element #12's health scores vary each year, particularly for Inspection Area #6, when normalized by the number of elements (see Figure 12).
31
Figure 11 Twelve (12) Inspection Areas in Georgia.
Figure 12 Health Index Normalized by the Number of Bridges (Element No. 12). 32
Category
Decks and Slabs
Girders Stringer Trusses/Arches
Table 8 Equations for Describing Time-Dependent Element Health Index.
Element key
12 13 15 16 28 29 30 31 38 54 60 65 102 104 105 106 107 109 110 111 113 115 117 120
135
141
Deterioration equation (Time T in Years)
0.1511 2.4490 6.9678T 94.2513 0.1092 1.4851 5.1516T 101.4598 0.4884 6.0982 20.0941T 81.4156 0.1530 1.2990 4.6632T 103.5154 0.4265 4.0447 5.7860T 100.4697 0.1226 0.9684 4.8706T 103.8687 0.5547 7.2746 20.8149T 82.3411 0.1666 1.9874 3.1748T 94.3892 0.1355 1.1674 0.7712T 99.8981 0.1192 2.1480 4.9265T 94.6867 0.1439 2.8658 15.4903T 115.0714 0.6910 8.9121 34.3159T 127.6112 0.2733 0.6392 2.0611T 95.3792 0.1818 2.1016 7.1032T 104.1719 0.3058 3.9018 14.2819T 111.8641 0.2391 2.3433 7.7390T 105.5500 0.1793 1.8265 6.1996T 103.9503 0.0048 0.0280 0.0829T 100.0693 0.0184 0.0247 0.6066T 97.7558 0.2454 2.6258 9.4648T 108.3868 0.3022 5.7739 30.3880T 130.2841 0.3162 3.5916 14.1909T 108.5664 0.4058 7.0331 25.7675T 77.5086 0.0764 1.1226 8.0852T 108.1244
0.3726 4.8292 8.0359T 94.8630 0.0136 0.5720 11.6083T 111.0455
Transition probabilities
P11 P22 P33 P44
0.9849 0.0049 0.7814 1.0000 0.9998 0.0000 0.0000 1.0000 0.9949 0.0527 0.8042 1.0000 0.9839 0.9323 0.8596 1.0000 0.9942 0.0000 0.0000 1.0000 0.9825 0.0023 0.9268 1.0000 0.9735 0.3872 0.1274 1.0000 0.9827 0.0000 0.0000 1.0000 0.9972 0.0000 0.0000 1.0000 0.9748 0.0114 0.8600 1.0000 0.9988 0.0000 0.0000 1.0000 0.9893 0.0008 0.9839 1.0000 0.9639 0.8947 0.7985 1.0000 0.9968 0.1156 0.9680 1.0000 0.9989 0.0034 0.9660 1.0000 0.9896 0.2662 0.9320 1.0000 0.9936 0.0579 0.7892 1.0000 0.9999 0.0000 0.0000 1.0000 0.9971 0.0242 0.7580 1.0000 0.9924 0.0648 0.7871 1.0000 0.9984 0.0000 0.0000 1.0000 0.9817 0.0000 0.9684 1.0000 0.9559 0.8862 0.7874 1.0000 0.9888 0.0000 0.0000 1.0000
0.9446 0.0032 0.7394 1.0000
0.9225 0.0000 0.9937 1.0000
33
Category Trusses/Arches Floor Beams & Miscellaneous Superstructure
Elements
Columns/Pier Walls
Abutments
Piles/Pier Caps/Footings
Table 8 Continued Equations for Describing Time-Dependent Element Health Index.
Deterioration equation
Transition probabilities
Element key
(Time T in Years)
P11
P22
P33 P44
144
0.2997 2.8672 2.0216T 103.0959
0.9510 0.0000 0.0000 1.0000
145
0.0136 0.5720 11.6083T 111.0455
0.9225 0.0000 0.9937 1.0000
147
0.2575 4.0389 11.7925T 91.7796
0.9766 0.0166 0.8501 1.0000
152
0.2929 5.4006 27.6338T 127.6848
0.9992 0.0000 0.0000 1.0000
155
1.0000 11.2215 18.5911T 27.3454
0.0000 0.0755 0.0008 1.0000
156
0.2142 3.1530 6.4074T 97.1074
0.9718 0.0026 0.7784 1.0000
161
0.1660 3.6218 24.6024T 123.4673
0.9752 0.0000 0.0000 1.0000
162
0.3427 3.5559 6.2069T 98.0005
0.9916 0.0000 0.0000 1.0000
202
0.2229 2.7735 15.8273T 116.0349
0.9645 0.0125 0.9809 1.0000
203
1.6130 19.1205 54.1177T 60.2429
0.9520 0.0212 0.4622 1.0000
204
0.0410 0.4741 1.3183T 99.0977
0.9996 0.0282 0.7751 1.0000
205
0.1974 1.8931 6.4979T 102.9826
0.9895 0.0184 0.8380 1.0000
206
0.5789 8.7546 43.1680T 143.6437
0.9797 0.0000 0.0000 1.0000
210
0.1867 2.1425 4.7253T 94.4143
0.9927 0.0000 0.0000 1.0000
211
0.3867 4.8406 17.5379T 111.2257
0.9959 0.0475 0.8097 1.0000
213
0.3624 5.4961 24.2161T 108.9389
0.9914 0.0000 0.0000 1.0000
215
0.0501 0.5681 2.8296T 101.7064
0.9958 0.0000 0.0000 1.0000
216
0.0368 0.3911 3.0559T 102.2274
0.9932 0.0000 0.0000 1.0000
217
0.1438 2.5721 14.8861T 113.1101
0.9921 0.1507 0.3741 1.0000
218
0.0999 0.8046 0.5969T 102.1581
0.9963 0.0000 0.0000 1.0000
219
0.5122 8.5317 41.0527T 123.9565
0.7899 0.0000 0.9999 1.0000
220
0.6389 10.1743 2.8321T 135.1197
0.9223 0.0000 0.0000 1.0000
225
0.0093 1.5020 15.8565T 115.5996
0.9895 0.0000 0.0000 1.0000
226
0.1297 1.3238 7.8336T 104.4685
0.9718 0.0052 0.9838 1.0000
227
0.3511 3.7013 3.9339T 96.3666
0.9602 0.0328 0.8830 1.0000
228
0.1313 2.7077 18.0713T 114.9383
0.9805 0.0000 0.0000 1.0000
229
0.7298 9.8749 39.9382T 132.1143
0.9823 0.0000 0.9859 1.0000
231
0.7233 11.1874 52.2665T 142.4373 0.9803 0.0000 0.0000 1.0000
34
Category Piles/Pier Caps/Footings Culverts
Joints
Bearings
Railings
Table 8 Continued Equations for Describing Time-Dependent Element Health Index.
Deterioration equation
Transition probabilities
Element key
(Time T in Years)
P11
P22 P33 P44
233
0.2144 2.0851 7.4290T 105.5556
0.9882 0.0477 0.9307 1.0000
234
0.0294 0.2793 1.4889T 100.7699
0.9965 0.0309 0.7773 1.0000
235
0.1744 2.1612 9.3287T 108.7321
0.9938 0.0563 0.7901 1.0000
236
0.1402 0.5315 15.7073T 116.7351
0.9606 0.0000 0.9999 1.0000
240
0.0842 2.3358 18.6154T 114.8947
0.9732 0.1743 0.4373 1.0000
241
0.0136 0.0723 2.9892T 100.0298
0.9887 0.0000 0.0000 1.0000
243
0.4643 7.2809 34.7551T 134.1467
0.9933 0.0000 0.0000 1.0000
244
0.4346 7.1332 35.6148T 131.7878
0.9905 0.0008 0.0002 1.0000
245
0.1813 2.4789 2.3095T 101.1617
0.9695 0.3609 0.3189 1.0000
300
0.4704 6.6107 29.3921T 112.2405
0.9764 0.1710 0.6086 1.0000
301
0.1202 2.1401 15.9017T 109.8458
0.9693 0.1029 0.2788 1.0000
302
0.0154 2.4377 18.5906T 104.2560
0.9936 0.1302 0.5132 1.0000
303
1.0185 14.2996 64.5428T 158.1630
0.9545 0.0320 0.6716 1.0000
304
0.0565 2.2024 17.4749T 117.9738
0.9913 0.0000 0.0000 1.0000
305
0.3536 3.6514 11.9816T 105.1657
0.9868 0.0346 0.8587 1.0000
306
0.0053 0.5761 4.1493T 95.4245
0.9406 0.0221 0.6084 1.0000
310
0.0055 0.1459 0.5291T 99.6494
0.9967 0.0766 0.9125 1.0000
311
0.0025 0.3854 0.8707T 91.6961
0.9868 0.0000 0.0000 1.0000
312
0.1135 1.3667 4.1231T 96.7693
0.9988 0.2028 0.2218 1.0000
313
0.1253 1.4890 7.3435T 102.3654
0.9883 0.0000 0.0000 1.0000
314
0.0836 0.8993 7.4061T 107.9560
0.9729 0.1267 0.9880 1.0000
315
0.3162 3.5916 14.1909T 108.5664
0.9817 0.0000 0.9684 1.0000
316
0.5684 6.8948 25.3556T 120.6585
0.9903 0.2095 0.9605 1.0000
330
0.4342 4.8417 15.4665T 112.1704
0.9957 0.0490 0.8068 1.0000
331
0.0497 0.6634 2.8795T 101.8070
0.9983 0.1223 0.3533 1.0000
332
0.0316 1.1579 10.0941T 109.6748
0.9917 0.0000 0.0000 1.0000
333
0.6065 6.9569 22.9647T 119.0347
0.9951 0.0512 0.8047 1.0000
334
0.6813 7.5481 23.6620T 119.1135
0.9942 0.0606 0.8077 1.0000
35
Table 8 Continued Equations for Describing Time-Dependent Element Health Index.
Deterioration equation
Transition probabilities
Category
Element key
(Time T in Years)
P11 P22 P33 P44
Wearing Surface and Protective Coating
510 515
521
0.0737 0.2595
0.1805
0.9915 2.9795
2.0346
2.5419T 95.5164 12.8247T 107.3627
6.5042T 105.3158
0.9947 0.0000 0.0000 1.0000 0.9775 0.0137 0.9853 1.0000 0.9987 0.0303 0.8144 1.0000
36
5. DETERIORATION MODELS FOR EACH BRIDGE
5.1 Method
5.1.1 Aggregated Element Health Indexes by Cost-based Weight Factors
A weighted average of element health indexes determines an overall BHI. This study utilizes bridge element importance weights recommended for the management of bridges in Florida (see Figure 13). Element weights are determined based on element replacement costs, long-term costs, hazard vulnerability, and engineering judgment
(Sobanjo & Thompson, 2016).
Element weights generally represent the relative contributions of each element
to the overall structural health of a bridge. This study introduces the concept of dynamic
element weights (DEW) to re-scale the weighted health index by 100. For instance,
consider a bridge (#32150490) with associated elements in age bin 1930 (Table 9). The
BHI is computed as the weighted values of element health indexes in each age bin. The
weighted average is 121 and is generally greater than 100. The dynamic health index is
calculated as the product of element health index and its dynamic weight. This study
aggregates dynamic health indexes for elements in age bins between years 1920 and 2020.
Table 9 Element Weight Factors in Age Bin 1930 for Bridge Number 32150490.
Element key
Health index (HI)
301
61.36
234
88.42
227
44.29
331
81.27
16
71.54
110
78.37
215
81.27
Bridge HI
Element weight (EW)
Dynamic element weight (DEW=HI*EW/100)
12.00 13.00 11.00 14.00 25.00 33.00 13.00
121.00
7.36 11.49 4.87 11.38 17.89 25.86 10.57
89.42
Element health
(HI* EW)
736.32 1149.46
487.19 1137.78
1788.5 2586.21 1056.51 8941.97
73.90
Dynamic element health (HI* DEW)
451.81 1016.35
215.78 924.67 1279.49 2026.81 858.63
6773.54 75.75
37
Figure 13 FDOT Bridge Element Important Weights (Sobanjo & Thompson, 2016). 38
5.1.2 Deterioration Curves for Each Bridge Using a Markovian Model Deterioration curves for bridges in Georgia are developed using the Markovian approach. 5.2 Results Bridge Performance Predictions 5.2.1 Mathematical Equations for Describing Bridge Overall Health Indexes Similar to element performance prediction models, Table 10 shows the mathematical expressions for describing overall BHIs and lists transition probabilities for selected bridges in each age category. The bridges are selected at random to discuss the outcome. Mathematical expressions for the remaining bridges are electronically submitted (see Appendix F.2).
5.2.2 Deterioration Curves for Bridges and Culverts Deterioration models for 14,039 bridge structures have been developed. This number includes 9,019 bridges and 5,020 culverts. Figures 14 and 15 show the deterioration curves for both bridges and culverts and bridges only, respectively, in each of the 12 age categories, respectively. The deterioration curves for `one-element' bridge structures (i.e., culverts only) are shown in Appendix C.
39
Age category
2020 2010 2000 1990 1980 1970 1960 1950 1940 1930 1920 1910
Structure number
25750600 1350580 31950370 6550670 25950340 2102100 6500610 6701020 9950410 29150240 300110 15700210 31550290 10550020 26950110
9350170
23300450 8150340 13950020 15700090 11150070 10550220 21501270 12100470
Table 10 Selected Equations for Describing Bridge Performance Over Time.
Year built/reconstructed
2017 2016 2010 2002 2000 1995 1989 1986 1980 1977 1968 1964 1960 1951 1950
1945
1940 1932 1929 1929 1918 1915 1910 1905
Deterioration equation (Time T in Years)
0.0791 1.4434 6.0551T 91.8810 0.0791 1.4434 6.0551T 91.8810 0.0791 1.4434 6.0551T 91.8810 0.1639 1.4450 6.5851T 93.6358 0.0791 1.4434 6.0551T 91.8810 0.0791 1.4434 6.0551T 91.8810 0.0791 1.4434 6.0551T 91.8810 0.1639 1.4450 6.5851T 93.6358 0.1639 1.4450 6.5851T 93.6358 0.1639 1.4450 6.5851T 93.6358 0.0791 1.4434 6.0551T 91.8810 0.1639 1.4450 6.5851T 93.6358 0.1639 1.4450 6.5851T 93.6358 0.1639 1.4450 6.5851T 93.6358 0.1639 1.4450 6.5851T 93.6358
0.1639 1.4450 6.5851T 93.6358
0.1639 1.4450 6.5851T 93.6358 0.1639 1.4450 6.5851T 93.6358 0.1639 1.4450 6.5851T 93.6358 0.0786 1.1420 2.7693T 93.7727 0.1639 1.4450 6.5851T 93.6358 0.1639 1.4450 6.5851T 93.6358 0.0786 1.1420 2.7693T 993.7727 0.0786 1.1420 2.7693T 993.7727
Transition probabilities
P11
P22 P33 P44
0.9950 0.9950 0.9950 0.9711 0.9950 0.9950 0.9950 0.9711 0.9711 0.9950 0.9711 0.9711 0.9711 0.9711 0.9711
0.9711
0.9711 0.9711 0.9711 0.9911 0.9711 0.9711 0.9911 0.9911
0.0426 0.0426 0.0426 0.0243 0.0426 0.0426 0.0426 0.0243 0.0243 0.0426 0.0243 0.0243 0.0243 0.0243 0.0243
0.0243
0.0243 0.0243 0.0243 0.1605 0.0243 0.0243 0.1605 0.1605
0.8023 0.8023 0.8023 0.7431 0.8023 0.8023 0.8023 0.7431 0.7431 0.8023 0.7431 0.7431 0.7431 0.7431 0.7431
0.7431
0.7431 0.7431 0.7431 0.4670 0.7431 0.7431 0.4670 0.4670
1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000
1.0000
1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000
40
Figure 14 Health Index Predictions of 14,039 Bridges and Culverts in Georgia.
Figure 15 Health Index Predictions of 9,019 Bridges Only in Georgia. 41
Culverts generally have a faster deterioration rate than bridges (Perrin & Dwivedi, 2006). Therefore, Figure 14 can be misleading when reviewing the predictions for bridges and culverts together. In Figure 15, the HI predictions of bridges are isolated from Figure 14. Figure 15 indicates that older bridges yield slightly higher deterioration rates, which is reasonable based on Figure 16 and agrees with previous research (Bulusu & Sinha, 1997; Morcous, Rivard, & Hanna, 2002; Qiao et al., 2016). In Figure 15, the uniquely slower deterioration of bridge structures in age categories 1920 and 1910 may be attributed to increased attention to maintenance over their service life and/or other reasons such as the limited number of bridges.
Figure 16 Typical Bridge Condition Over Time (FHWA, 2018a).
42
6. COMPARISION OF NBI AND ELEMENT-BASED CONDITION SCORES
6.1 Method
A Chi-square goodness of fit test is performed to compare element-based bridge
deterioration models (developed based on FDOT's weight factors) and NBI condition-
rating-based bridge deterioration models (see GDOT RP 18-30 final report, 2019) for a
network of bridges in Georgia. The formula for the Chi-square distribution is given as (Bu,
Lee, et al., 2013; Bu et al., 2014):
2
2
1
. 6.1
where, 2 = Chi-square distribution with k - 1 degrees of freedom (DOF); = value of
condition rating in year predicted using the element-based models, = value of
condition rating in year predicted using NBI condition-rating-based models; and =
number of prediction years.
The approach to the Chi-square hypothesis testing is shown in Figure 17. The test
is performed using two bridge deterioration models (element-based and NBI condition-
rating-based). NBI condition ratings are rescaled to a 100-point scale (e.g., an NBI
condition rating of 9 is scaled to 100), while the health indexes are reduced by 22%. This
reduction is necessary for a fair comparison as will be evident in Section 6.2. NBI
condition-rating-based models are aggregated using Eq. (6.2) to determine a blended
general condition rating (Blended GCR) as proposed by the Virginia DOT (VDOT, 2017):
Blended GCR 0.25 Deck GCR 0.35 Superstructure GCR
0.40 Substructure GCR
. 6.2
43
Element-based Method
Element-based (EB) bridge deterioration models Categorization into age bins
Selecting input models for Chi-square
Selected EB bridge deterioration models,
Chisquare
Selected NBI bridge deterioration models,
Link and extract common bridges Selection
Bridges common to EB and NBI
Selecting input models for Chi-square
Categorization into age bins
NBI
NBI bridge deterioration models
Figure 17 Process Chart for the Chi-Square Test.
The difference between the Chi-square and the critical threshold values evaluates the null hypothesis: the two models are not correlated. The larger the difference between the Chi-square and the critical values, the closer the predictions between the Chi-square test parameters (i.e., and ).
44
6.2 Results Element vs. NBI-based Predictions Overall, element-based bridge prediction models yield steeper depreciation curves (see Appendix D). Due to this discrepancy, the two prediction models are not well correlated although they have similar trends. The outcomes of the hypothesis test for 9,019 bridges are presented in Table 11, which summarizes the distribution of discretized Chi-square values at 99 DOFs, a Chi-square critical value of 123.23, and a significance level ( = 0.05).
Table 11 Discretization of Using Percentages at a Significance Level of 0.05.
Bridge Count in Each Age Category
percentage
2020
2010
2000
1990
1980
1970
1960
1950
1940
1930
1920
1910
1900
10
128 366 301 255 98 61 53
13 0
0
0
0
20
112 245 192 169 76 70 59 3
8
3
0
0
0
30
25 135 70 71 41 33 42 14 8
6
0
0
0
40
18 85 72 67 29 20 25 11 9
2
0
0
0
50
13 31 27 33 25 19 18 7
5
2
0
0
0
60
3 21 18 31 13 9 19 4
2
4
2
0
0
70
2 28 12 20 10 14 15 2
3
2
2
0
0
80
4 29 13 18 13 7 18 1
4
2
3
0
0
90
4 16 11 14 7
3 11 1
1
2
1
1
0
100
2 25 8 16 14 7 11 2
3
1
1
1
0
>100
68 467 635 874 979 1023 794 269 155 48 18 1
2
Note: percentage = Chi-square percentage.
Table 12 Description of Discretized in Form of Percentages.
percentage
10 20 30 40 50 60 70 80 90 100 >100
Description
0<= percentage <=10 11<= percentage <=20 21<= percentage <=30 31<= percentage <=40 41<= percentage <=50 51<= percentage <=60 61<= percentage <=70 71<= percentage <=80 81<= percentage <=90 91<= percentage <=100
percentage >=101
45
Table 12 gives the discretized Chi-square percentage values. Equation (6.3) is used to calculate the Chi-square in the form of a percentage. Figure 18 shows the percentage error the NBI and element-based data are not correlated.
Chi-square percentage
100
. 6.3
Figure 18 Chi-Square Percentage (% Error) in Each Age Bin. 46
7. COMPUATION OF MODIFIED HEALTH INDEX
7.1 Overall Approach Section 6 concludes that discrepancies may exist between NBI and element-based data. Title 23 of the United States Code 150(c)(3), in compliance with MAP-21 Legislation, requires state DOTs to establish, as part of their governance of performance measures, "minimum standards for States to use in developing and operating bridge and pavement management system". For bridges on the National Highway System (NHS), Title 23 of the United States Code 119(f) stipulates that no more than 10% of the total NHS bridge deck area be structurally deficient (U.S.C., 2018). However, other important factors for measuring bridge performance such as the average life cycle must be considered. Therefore, three major modeling parameters are considered when computing MHIs for Georgia (see Table 13):
1. Deterioration prediction model for each bridge 2. Threshold health index 3. End of service life for each bridge
The Virginia DOT determines MHIs based on the latest replacement costs of elements and a bridge life cycle as the service year when 20% of its elements are in condition state 4. Due to GDOT's active bridge maintenance program and a favorable environment, such a state is rather hard to reach. Therefore, bridge life cycle is defined as the service year in which 50 - 60% of the bridge's highest health index (=100) is consumed. Bridges with the majority of their elements in condition state 3 might have outlived their service life although less than 20% of their quantities remain in condition state 4. MHI is computed using the procedure shown in Section 2.4.4.
47
A total of 12 MHI prediction cases are studied: 6 bridges-only and 6 bridges/culverts consisting of 2 service life periods (70 and 100) with 3 threshold health indexes (50, 45, and 40). Table 13 summarizes the parameters. The findings from this parameter study are presented in Appendix E.
Table 13 Parameters Considered for Modified Health Index.
Model #
Threshold MHI
Life cycle
Description
Varies Service year when 50% of a bridge has deteriorated
Model 1
50
(70 & 100) in each life cycle
Varies Service year when 45% of a bridge has deteriorated
Model 2
45
(70 & 100) in each life cycle
Varies Service year when 40%* of a bridge has deteriorated
Model 3
40
(70 & 100*) in each life cycle
Note: * indicates parameters selected for Section 7.2.
7.2 MHI Projections The three models shown in Table 13 are studied, and Model 3 with the 100-year life cycle option is selected for bridge asset valuation. Model 3 generally gives higher MHIs and lower deterioration rates. Table 14 presents a summary of findings. Appendix E includes MHI predictions using the three models. Overall, increasing the end of bridges' service life from 70 to 100 increases MHIs, and increasing the threshold MHI also increases deterioration rates.
Table 14 Summary of Findings for Parameters Affecting MHIs.
Parameter
Life cycle Threshold MHI
Parameter trend
Increases Increases
MHI
Increases Decreases
48
MHI deterioration rate
Decreases Increases
Figure 19 shows MHI predictions using Model 3. Figure 20 illustrates the difference between MHIs and health indexes. Overall, the health indexes (HIs) are larger than MHIs. Therefore, MHIs are subtracted from HIs to show the changes in HIs (see Figures E.13-E.24). Over time, this difference reduces for recently constructed bridges (age categories 1990 to 2020), whereas old bridge structures experience a marginal health index change.
49
Figure 19 MHI Predictions for Bridges and Culverts in Georgia.
Figure 20 Difference Between MHI and HI for Bridges and Culverts in Georgia. Note: The `change in MHI' on the y-axis is computed by the following: HI - MHI. 50
8. BRIDGE ASSET VALUATION
8.1 Conjoint Analysis Health indexes assist GDOT in determining overall bridge conditions as well as in making engineering decisions about maintenance or replacement. However, a health index does not take into account environmental and indirect factors. Attributes such as location and age are not best indicated in health indexes.
A conjoint analysis captures important attributes and creates a system to apply them to health indexes. It offers a regression method used to capture preferences in a data set through means of a survey that measures preferences and trade-offs respondents identify in response to leading questions about attributes. Trade-offs signify what an individual is willing to sacrifice for an aspect they deem important. A conjoint analysis determines what combination of attributes respondents value most highly. In this study, attributes most detrimental to bridge health are ranked the highest (see Table 15). The expected outcomes are attribute-worths, a quantitative representation of preferences and trade-offs, that are subsequently used to determine scaling factors for MHIs (see Table 16).
In this study, three attributes are selected: construction year, geographic location, and presence of a waterway. Based on NBI condition-rating-based depreciation curves (see GDOT RP 18-30 final report, 2019) for bridges in different regions of Georgia, location has an influence on health. Geographic location is included because bridges in colder regions, or regions with extreme cold weather conditions, appear to deteriorate faster than those in "normal" weather conditions such as the Central region. Furthermore, the presence of a waterway and age affect bridge elements, yielding a faster deterioration.
51
In a hypothetical example, when one assumes that an old bridge deck element located in North Georgia and crossing a waterway has an element health score of 70, and also considers that another relatively newer non-waterway bridge located in Central Georgia has a health score of 70. Generally, the two health indexes are weighted equally for determining the overall bridge condition. However, these elements deteriorate at different rates based on a combination of attribute-worths (e.g., location, age, presence of waterway). Therefore, a conjoint analysis applies attribute-worths to bridges in order to consider how location, age, and the presence of a waterway affect deterioration rates. As a result, this method provides a more accurate health score. Table 15 shows attribute rankings and total attribute scores from a conjoint analysis. The scaled attribute-worths range between zero and one. Table 16 summarizes the outcomes and reveals the most influential attributes (old, northern, and waterway conditions) affecting a bridge's health score.
8.2 Conjoint Modified Health Index In Section 7, it was concluded that Model 3 (with a 100-year life cycle and a threshold MHI of 40) is the most reasonable for Georgia's bridges. Therefore, the MHIs using Model 3 are used to factor in the attribute-worths determined in Section 8.1. The following equation is used to determine MHIconjoint:
MHIconjoint = Modified Health Index -10 x Attribute-Worth
(Eq. 8.1)
In Eq. 8.1, the scaled attribute-worths (see the last column in Table 15) from a conjoint analysis are assumed to alter the health index value by a maximum of 10 points. Figures 21 and 22 illustrate how the MHIs change before and after a conjoint analysis, respectively.
52
YR < 2020 (x1)
1 1 0 0 1 1 1 0 1 0 0 0 0 0 0 0 0 0
YR < 2000 (x2)
0 0 1 1 0 0 0 1 0 1 1 0 0 1 0 0 0 0
Table 15 Attribute Preferences and Attribute-Worths.
YR < 1980 (x3)
Northern Central
(x4)
(x5)
Coastal (x6)
Waterway (x7)
NonWaterway
(x8)
Rank (y)
Total score
0
0
1
0
0
1
1
0.44
0
0
0
1
0
1
2
0.51
0
0
1
0
0
1
3
0.51
0
0
0
1
0
1
4
0.58
0
1
0
0
0
1
5
0.83
0
0
1
0
1
0
6
1.03
0
0
0
1
1
0
7
1.1
0
1
0
0
0
1
8
0.9
0
1
0
0
1
0
9
1.42
0
0
1
0
1
0
10
1.1
0
0
0
1
1
0
11
1.17
1
0
1
0
0
1
12
1.2
1
0
0
1
0
1
13
1.27
0
1
0
0
1
0
14
1.49
1
0
1
0
1
0
15
1.79
1
1
0
0
0
1
16
1.59
1
0
0
1
1
0
17
1.87
1
1
0
0
1
0
18
2.18
(scaled) Attribute
-worth 0.00 0.04 0.04 0.08 0.22 0.34 0.38 0.26 0.56 0.38 0.42 0.44 0.48 0.60 0.78 0.66 0.82 1.00
Attribute
Attribute worth (%) Total (%)
Table 16 Attribute Worths (%) From a Conjoint Analysis.
YR < 2020 (x1)
YR < 2000 (x2)
YR < 1980 (x3)
Central (x5)
Coastal (x6)
Northern (x4)
Nonwaterway
(x8)
Waterway (x7)
5%
13%
82%
18%
25%
57%
20%
80%
100%
100%
100%
53
Figure 21 Modified Health Indexes before a Conjoint Analysis. Note: The frequency indicates the number of bridges.
Figure 22 Modified Health Indexes After a Conjoint Analysis. 54
8.3 Bridge Valuation The total construction cost of each bridge in the NBI (Item #96 Total Project Cost) is multiplied by MHIconjoint to assign a monetary value. Figure 23 illustrates the distribution of Georgia's bridge asset value, totaling nearly $30 billion. A majority of culverts are at an asset value (or benefit) range below $0.2 million (or $200,000); however, another group of bridges (around 1800 bridges) is valued between $1 million and $2 million. Figures 24 and 25 present asset values for bridges (a total of $28 billion) and culverts (a total of $2 billion), respectively.
Figure 23 Valuation of All Bridges and Culverts. 55
Figure 24 Valuation of Bridges Only. 56
(a) X-axis scale identical to bridges only.
(b) X-axis scale revised for clarity. Figure 25 Valuation of Culverts Only.
57
8.4 Benefit-Cost Analysis The terms, `benefit-cost' and `cost-benefit', are often interchangeably used. However, the term, `benefit-cost' is intentionally used in this report in order to emphasize the importance of evaluating a benefit-cost ratio. Bridge asset value quantifies a benefit, and it is weighed against service-time costs. In this study, the benefit and cost are determined as follows:
Benefit: Bridge asset value determined from Section 8.3. Cost: Net present value of initial construction and maintenance costs
In a hypothetical example, bridge IDs `21300180' and `12104760' are two bridges in the database with recorded maintenance costs for both sources, NBI and GDOT Construction Bidding (2011-2017). Bridge 21300180's construction cost was defined as $1,278,000. Meanwhile, Bridge 12104760 had a construction cost of $1,383,000. Bridge 21300180's health index is currently at 78.10 after modification. Based on the analysis in Section 8.3, the benefit of Bridge 21300180 is: (78.10/100) $1,278,000.00 = $998,118.00. The last instance of maintenance was in 2016. Bridge 12104760 exhibited maintenance performed between 1958 and 2018. Its current health index is 92.81 after modification. The last recorded maintenance was performed in 2016. The bridge's excellent health score appears to be attributed to the regular maintenance performed. The benefit of Bridge 12104760 is: (92.81/100) $1,383,000 = $1,283,562.30.
The costs are gathered from the NBI database as well as GDOT Construction Bidding (2011-2017). The cash flow analysis, shown in Figure 26, illustrates these expenses over the bridges' lifetimes. In this figure, the maintenance cost information electronically documented and available to the research team is used. However, for most Georgia bridges, NBI maintenance cost entries appear to be unrealistically repetitive (e.g.,
58
approximately $1.4M recurring between 2013 and 2016) and in some cases higher than costs reported by GDOT Construction Bidding. Between 1958 and 2018, Bridge 12104760 had 5 recorded instances of maintenance, 2 of which were unique values. Therefore, the present value of the maintenance and rehabilitation/repair cost is hypothetically assumed $5,834,374.09 and $9,073,800.00 for Bridges 21300180 and 12104760, respectively.
Figure 26 Sample Cash Flow Diagram of Two Bridges (Illustration Only). Based on the cost assumptions, the benefit-to-cost ratio is 0.11
($998,118.00/$9,073,800.00) and 0.22 ($1,283,562.30/$5,834,374.09) for Bridge 21300180 and Bridge 12104760, respectively. In this hypothetical example, it has been more beneficial to maintain Bridge 12104760 although returns on future investments will need to be investigated in a similar manner.
59
Finally, Figure 27 shows a hypothetical scenario where the benefit-cost analysis in Year 10 is used for decision-making.
(a) Rehabilitate Option.
(b) Replace Option. Figure 27 Benefit-Cost Analysis Framework.
60
9. LIMITATIONS The major limitation of this study relates to element-level inspection records collected over a short period of time. The state of Georgia presently has four years of bridge element inspection records, which amounts to insufficient data to meaningfully develop bridge deterioration models using a conventional approach. This study, however, introduced an age-bin-based approach to develop deterioration models for elements and bridges.
The bridge deterioration models presented in this study represent the long-term performance of bridges having the same type and number of bridge elements, irrespective of their locations in Georgia. A conjoint analysis presented in Section 8 captures the effect of geographic location and other attributes. Overall, bridge deterioration prediction models are expected to improve as additional element-based bridge inspection data become available. Finally, cost evaluations for the proposed benefit-cost analysis are expected to improve as more element cost data become available.
61
10. CONCLUSIONS
Through this study, the research team has developed deterioration prediction models for bridge elements and bridges, assessed bridge health indexes (BHIs) and MHIs, developed bridge deterioration prediction models in terms of MHIs, and determined bridge asset values (or benefits). Based on the findings of this study, the following conclusions are made: 1. The projected long-term performance of bridge elements, particularly decks and
girders, shows strong correlations with two important factors, namely: (1) design types (i.e., prestressed and reinforced concrete) and (2) material types (i.e., concrete, steel, and timber). In terms of design, prestressed concrete members as a whole yield the best long-term asset values. For material types, bridge elements with concrete materials tend to lose their values at slower rates than those with other materials (see Appendix C). 2. Culverts (see Figure C.10) overall have faster deterioration rates, in the range between 35 and 85% HI reductions in 70 years, than bridges (see Figure 15) showing about 1525% HI reductions over 70 years, regardless of age. Steel culverts depreciate relatively faster (see Figure C.10) although only less than 10% of the culverts are made of steel. 3. Most bridge elements' deterioration rates tend to be slower as time passes (see Appendix C). This prediction trend is not anticipated but consistent with the findings of a previous study (GDOT RP 18-30, 2019). 4. MHI predictions generated by age groups show that bridges in the newer age groups (e.g., 2020 and 2010) deteriorate slightly faster than bridges in the older age groups (1950 - 1910) (see Figures E.1 through E.12).
62
5. The results of the Chi-square test accept the null hypothesis that the element- and NBIbased bridge condition prediction models are not correlated; element-based BHIs are generally 22% higher than NBI condition scores when rescaled to the 100-scale.
6. Similar to NBI deterioration models (see GDOT RP 18-30 final report, 2019), elementbased forecasting trends indicate that bridges deteriorate slower as time passes (see Appendix D), which is not expected. That is, deterioration curves are steeper in the short term.
7. GDOT manages a significant bridge asset (approximately $30 billion) worth maintaining and investing in.
8. Bridge asset values determined through this study represent benefits for an engineering benefit-cost analysis.
63
11. FUTURE STUDY AND RECOMMENDATIONS
The following recommendations are made:
1. Bridge element deterioration models (Appendix C) are valuable for future investment and design decisions. Thus, it is important to recognize that the element numbers (see Appendix B) must be correctly identified by inspectors. It is strongly recommended that GDOT creates an inspectors' manual that gives specific instructions with picture illustrations.
2. The bridge deterioration models presented in this study represent the long-term performance of bridges having the same type and number of bridge elements, irrespective of their locations in Georgia. Although a conjoint analysis considers the location, age, and presence of waterways for valuation, additional parameters that affect deterioration rates must be considered in the future.
3. Usage must be quantified by establishing a relationship between GDOT's traffic counts and deterioration rates. GDOT has a network prioritization plan for interstates and state routes. Critical, high, medium, and low priority routes exist based on traffic volume, size, and proximity to shelter. It is strongly recommended that GDOT considers this strategic priority plan when measuring BHIs, as well as Weigh-In-Motion (WIM) data.
4. Due to inherent variation in bridge element performance, it is highly recommended that future research considers alternative approaches for determining element weights that are more consistent with the experience of GDOT's bridge maintenance unit.
5. Research on establishing inter-dependencies among bridge elements is highly recommended. Element weight factors drive strategic priorities. As a result, weighted
64
element condition scores determine an overall BHI. A new asset management program such as AASHTOWare BrM needs element weight factors. Most state transportation agencies use replacement cost for evaluating element weight factors. For Georgia, a more strategic approach is recommended: GDOT should factor in dependent element relationships and show the effect of maintenance investments. In turn, this approach will reflect increases in health indexes and optimize long-term returns on investments (ROIs). 6. The discrepancy between NBI and element-based bridge condition ratings is observed (see Appendix D). If GDOT were to maintain both NBI and element-based inspection records, consistent criteria must be applied to close the gap. 7. Finally, annual maintenance actions/spending on each bridge need to be documented and analyzed. In addition, bridge condition improvements and associated costs need to be digitally documented to fully realize the advantages of the benefit-cost analysis (see Section 8.4) for decision-making.
65
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APPENDICES
71
Appendix A Sample Element-Based Bridge Inspection Records.
Table A.1 Typical GDOT Element-Based Bridge Inspection Data for Bridge ID:
100140.
Element key
12 215 301 311 234 225 107 313 331 515 (107*) 515 (225) 515 (311) 515 (313)
Unit
ft. ft. Sq.ft. ft. ft. ft. ea. ea. ft. Sq.ft. Sq.ft. Sq.ft. Sq.ft.
Element
quantity
6069 52 208 28 156 24 756 16 378 4528 10200 28 16
Condition states
CS1 CS2 CS3 CS4
5887 179 3
52
182
26
9
7 12
156
24
741 5 10
4
2 10
363 15
4528
10200
11
17
4
2 10
Note: *The element number in parentheses, 107Steel Open Girder/Beamfor example, indicates the parent element for 515steel protective coatings. See Appendix B for element description.
Table A.2 Element-Based Inspection Record for Colorado Bridge D-03-V-150
(Jiang & Rens, 2010a).
Element
Condition states
Element key Unit quantity CS1
CS2 CS3 CS4 CS5
14
in. 8,895.28 8,895.28
0
0
0
0
101
in. 1,444.76 1,300.28 144.48 0
0
106
in.
176.48 176.48
0
0
0
210
ft.
164.59 164.59
0
0
0
215
ft.
27.43
27.43
0
0
0
234
in.
175.26
0
175.26 0
0
305
in.
27.43
27.43
0
0
314
ea.
86
27
4
55
326
ea.
4
4
0
0
331
ea. 874.78 874.78
0
0
0
333
ea. 569.98 569.98
0
0
334
ea. 722.38 633.38
0
89 0
0
338
ea. 722.38 722.38
0
0
0
72
Appendix B Element Numbers, Counts, and Description.
Table B.1 Element Numbers, Counts, Description, and Category.
EN Count Description
12 5557 Reinforced Concrete Deck
13
18 Prestressed Concrete Deck
15
351 Prestressed Concrete Top Flange
16 2559 Reinforced Concrete Top Flange
28
10 Steel Deck with Open Grid
29
4 Steel Deck with Concrete Filled Grid
30
46 Steel Deck with Corrugated/Orthotropic/Etc. Panels
31
287 Timber Deck
38
555 Reinforced Concrete Slab
54
1 Timber Slab
60
16 Other Deck
65
28 Other Slab
102
7 Steel Closed Web/Box Girder
104 384 Prestressed Concrete Closed Web/Box Girder
105
26 Reinforced Concrete Closed Web/Box Girder
106
5 Other Closed Web/Box Girder
107 3107 Steel Open Girder/Beam
109 2460 Prestressed Concrete Open Girder/Beam
110 2769 Reinforced Concrete Open Girder/Beam
111 105 Timber Open Girder/Beam
113
56 Steel Stringer
115
2 Prestressed Concrete Stringer
117
14 Timber Stringer
120
31 Steel Truss
135
4 Timber Truss
141
1 Steel Arch
144
49 Reinforced Concrete Arch
145
2 Masonry Arch
147
2 Steel Main Cables
152
47 Steel Floor Beam
156
5 Timber Floor Beam
161
9 Steel Pin and Pin & Hanger Assembly or both
162
15 Steel Gusset Plate
Category
Decks and Slabs
Girders
Stringer
Trusses/ Arches Floor Beams & Miscellaneous Superstructure Elements
73
Table B.1 Continued Element Numbers, Counts, Description, and Category.
EN Count Description
Category
202 65 Steel Column
203 4 Other Column
204 36 Prestressed Concrete Column
205 4164 Reinforced Concrete Column
Columns/Pier
206 15 Timber Column
Walls
210 398 Reinforced Concrete Pier Wall
211 16 Other Pier Wall
213 38 Masonry Pier Wall
215 8691 Reinforced Concrete Abutment
216 126 Timber Abutment
217 124 Masonry Abutment
Abutments
218 69 Other Abutments
225 1997 Steel Pile
226 1583 Prestressed Concrete Pile
227 172 Reinforced Concrete Pile
Piles
228 566 Timber Pile
229 1 Other Pile
220 415 Reinforced Concrete Pile Cap/Footing
231 179 Steel Pier Cap
233 8 Prestressed Concrete Pier Cap
Pier Caps
234 7532 Reinforced Concrete Pier Cap
and Footings
235 128 Timber Pier Cap
236 1 Other Pier Cap
240 552 Steel Culvert
241 5047 Reinforced Concrete Culvert
243 30 Other Culvert
Culverts
244 4 Masonry Culvert
245 2 Prestressed Concrete Culvert
300 228 Strip Seal Expansion Joint
301 7241 Pourable Joint Seal
302 1207 Compression Joint Seal
303 172 Assemble Joint with Seal
Joints
304 53 Open Expansion Joint
305 147 Assemble Joint without Seal
306 18 Other Joint
74
Table B.1 Continued Element Numbers, Counts, Description, and Category.
EN Count Description
Category
310 3011 Elastomeric Bearing
311 2289 Movable Bearing
312 123 Enclosed/Concealed Bearing
313 2244 Fixed Bearing
Bearings
314 119 Pot Bearing
315 1 Disk Bearing
316 54 Other Bearing
330 2005 Metal Bridge Railing
331 6924 Reinforced Concrete Bridge Railing
332 85 Timber Bridge Railing
Railings
333 107 Other Bridge Railing
334 19 Masonry Bridge Railing
510 1790 Wearing Surfaces
Wearing Surface
515 9583 Steel Protective Coatings
Protective Coat
521 47 Concrete Protective Coatings
etc.
75
Appendix C Element Deterioration Prediction Models for Georgia.
RC = Reinforced concrete; P/S conc = Prestressed concrete; conc = concrete; and Steel deck with corrugated = steel deck with corrugated panels
Figure C.1 Deck and Slab Elements in Georgia. Note: In the brackets, the presence of each element within the category is shown as a
percentage.
P/S conc = Prestressed concrete; R/conc = Reinforced concrete; and conc = concrete
Figure C.2 Girders in Georgia. 76
P/S conc = Prestressed concrete
Figure C.3 Stringer Elements.
R/conc = Reinforced concrete
Figure C.4 Trusses and Arches. 77
Figure C.5 Floor Beams and Miscellaneous Superstructure Elements.
coln = column; P/S conc = Prestressed concrete; and R/conc = Reinforced concrete
Figure C.6 Columns and Pier Walls. 78
R/conc = Reinforced concrete
Figure C.7 Abutments.
P/S conc = Prestressed concrete and R/conc = Reinforced concrete
Figure C.8 Piles. 79
R/conc = Reinforced concrete and P/S conc = Prestressed concrete
Figure C.9 Pier Caps and Footings.
R/conc = Reinforced concrete and P/S conc = Prestressed concrete
Figure C.10 Culverts. 80
Pour = Pourable; Comp = Compression; Assemb = Assembly; exp = expansion; and jnt = joint
Figure C.11 Joints in Georgia.
Figure C.12 Bearings in Georgia. 81
R/conc = Reinforced concrete Figure C.13 Railings in Georgia.
Conc = Concrete
Figure C.14 Wearing Surface and Protective Coating in Georgia. 82
Appendix D Element versus NBI-Based Bridge Deterioration Predictions.
Figure D.1 Element-Based vs. NBI-Based Bridge Deterioration Models (Age Bin 2020).
Note: NBI condition ratings are rescaled to the 100-scale (e.g., an NBI condition rating of 9 is scaled to 100), and the health indexes are reduced by 22% for a fair comparison.
Figure D.2 Element-Based vs. NBI-Based Bridge Deterioration Models (Age Bin 2010). 83
Figure D.3 Element-Based vs. NBI-Based Bridge Deterioration Models (Age Bin 2000).
Figure D.4 Element-Based vs. NBI-Based Bridge Deterioration Models (Age Bin 1990). 84
Figure D.5 Element-Based vs. NBI-Based Bridge Deterioration Models (Age Bin 1980).
Figure D.6 Element-Based vs. NBI-Based Bridge Deterioration Models (Age Bin 1970). 85
Figure D.7 Element-Based vs. NBI-Based Bridge Deterioration Models (Age Bin 1960).
Figure D.8 Element-Based vs. NBI-Based Bridge Deterioration Models (Age Bin 1950). 86
Figure D.9 Element-Based vs. NBI-Based Bridge Deterioration Models (Age Bin 1940).
Figure D.10 Element-Based vs. NBI-Based Bridge Deterioration Models (Age Bin 1930). 87
Figure D.11 Element-Based vs. NBI-Based Bridge Deterioration Models (Age Bin 1920).
Figure D.12 Element-Based vs. NBI-Based Bridge Deterioration Models (Age Bin 1910). 88
Appendix E MHI Predictions and Associated Parameters.
Figure E.1 Model 1 MHI Predictions for Bridges & Culverts (100yr & Threshold=50).
Figure E.2 Model 1 MHI Predictions for Bridges & Culverts (70yr & Threshold=50). 89
Figure E.3 Model 1 MHI Predictions for Bridges Only (100yr & Threshold=50).
Figure E.4 Model 1 MHI Predictions for Bridges Only (70yr & Threshold=50). 90
Figure E.5 Model 2 MHI Predictions for Bridges & Culverts (100yr & Threshold=45).
Figure E.6 Model 2 MHI Predictions for Bridges & Culverts (70yr & Threshold=45). 91
Figure E.7 Model 2 MHI Predictions for Bridges Only (100yr & Threshold=45).
Figure E.8 Model 2 MHI Predictions for Bridges Only (70yr & Threshold=45). 92
Figure E.9 Model 3 MHI Predictions for Bridges & Culverts (100yr & Threshold=40).
Figure E.10 Model 3 MHI Predictions for Bridges & Culverts (70yr & Threshold=40). 93
Figure E.11 Model 3 MHI Predictions for Bridges Only (100yr & Threshold=40).
Figure E.12 Model 3 MHI Predictions for Bridges Only (70yr & Threshold=40). 94
Figure E.13 Health Indexes (HIs) - Modified Health Indexes (MHIs) of Bridges & Culverts for Model 1 (100yr & Threshold=50).
Figure E.14 Health Indexes (HIs) - Modified Health Indexes (MHIs) of Bridges & Culverts for Model 1 (70yr & Threshold=50). 95
Figure E.15 Health Indexes (HIs) - Modified Health Indexes (MHIs) of Bridges Only for Model 1 (100yr & Threshold=50).
Figure E.16 Health Indexes (HIs) - Modified Health Indexes (MHIs) of Bridges Only for Model 1 (70yr & Threshold=50). 96
Figure E.17 Health Indexes (HIs) - Modified Health Indexes (MHIs) of Bridges and Culverts for Model 2 (100yr & Threshold=45).
Figure E.18 Health Indexes (HIs) - Modified Health Indexes (MHIs) of Bridges and Culverts for Model 2 (70yr & Threshold=45). 97
Figure E.19 Health Indexes (HIs) - Modified Health Indexes (MHIs) of Bridges Only for Model 2 (100yr & Threshold=45).
Figure E.20 Health Indexes (HIs) - Modified Health Indexes (MHIs) of Bridges Only for Model 2 (70yr & Threshold=45). 98
Figure E.21 Health Indexes (HIs) - Modified Health Indexes (MHIs) of Bridges & Culverts for Model 3 (100yr & Threshold=40).
Figure E.22 Health Indexes (HIs) - Modified Health Indexes (MHIs) of Bridges & Culverts for Model 3 (70yr & Threshold=40). 99
Figure E.23 Health Indexes (HIs) - Modified Health Indexes (MHIs) of Bridges Only for Model 3 (100yr & Threshold=40).
Figure E.24 Health Indexes (HIs) - Modified Health Indexes (MHIs) of Bridges Only for Model 3 (70yr & Threshold=40). 100
Appendix F List of Electronic Submittals. F.1 Microsoft EXCEL application for calculating bridge MHIs and asset values. F.2 Microsoft EXCEL spreadsheet summarizing a mathematical formula for describing each bridge's depreciation prediction in terms of health index for all Georgia bridges.
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