Methodology for Estimating Life Expectancies of Highway Assets

Methodology for Estimating Life Expectancies of

Highway Assets

INTERIM REPORT I (ADDENDUM VERSION)

Kevin M. Ford

Mohammad Arman Samuel Labi

Kumares C. Sinha Arun Shirole

Paul D. Thompson

School of Civil Engineering Purdue University

West Lafayette, IN 47907

April 5, 2010 (Revised June 10, 2010)

NCHRP 08-71

Transportation Research Board NAS-NRC

Limited Use Document

This document is for use of recipient in selection of a research agency to conduct work under the National Highway Cooperative Research Program. Dissemination

of the information included therein must be approved by the NCHRP.

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ACKNOWLEDGMENTS

The preparation of this report and the development of the proposed methodologies would not have been possible without the support and efforts of Dr. Ghim Ping Raymond Ong, and Dr. Zonghzi Li. Furthermore, the research team would like to acknowledge the following individuals who have graciously shared their data and knowledge regarding state highway assets: Gregory Lockshaw, Wes Lum, Ray Tritt, and Eric Uyeno (CA); Scott Neubauer (IA); Darcy Bullock (IN); Nancy Albright, Ted Swansegar, Jon Wilcoxson, and Jeff Wolfe (KY); John Smith and John Vance (MI); Thomas Martin, Mark Nelson, and Bonnie Peterson (MN); James Burke and Li Zhang (MS); Jane Berger (ND); James Bledsoe, Joseph Jones, and David Nichols (MO); John Dourgarian and David Kuhn (NJ); Lou Adams, Michael Fay, and Scott Lagace (NY); Ginger McGovern (OK); John Coplantz, Joel Fry, Laura Hansen, Bert Hartmann, Bill Link, Carol Newvine, Marina Orlando, Mark Wills (OR); Janice Arellano, Daniel Farley, David Kuniega, Michael Long, and John Van Sickle (PA); Jennifer Brandenburg, Steve Dewitt, and Kevin Lacy (NC); Paul Annarummo, Kazem Farhoumand, and Bob Rocchio (RI); Dave Huft (SD); Larry Buttler, Rick Collins, Brian Merrill, Steve Simmons, Bryan Stampley, Brian Stanford, and Tom Yarbrough (TX); Michael Fazio, Ahmad Jaber, and Brant Whiting (UT); Tanveer Chowdhury, Brack Dunn, and Raja Shekharan (VA); Martin Kidner (WY). Finally, the research team wishes to thank Dr. Andrew Lemer for his continual support, guidance, and coordination between the Panel and the research team.

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TABLE OF CONTENTS

Page

LIST OF FIGURES .......................................................................................................................... V LIST OF TABLES .......................................................................................................................... VII CHAPTER 1 – INTRODUCTION ................................................................................................... 1

1.1 Study Background and Problem Statement ................................................................ 1 1.2 Study Objectives ......................................................................................................... 3 1.3 Scope of the Research Study ...................................................................................... 3 1.4 Summary Description of Completed and Pending Tasks ........................................... 4

CHAPTER 2 – RESULTS OF THE INFORMATION SEARCH ..... ........................................... 7

2.1 Introduction ................................................................................................................ 7 2.2 Definitions and Measures of Asset Life Expectancy ................................................. 7 2.3 Existing Approaches to Estimating Life Expectancies of Assets ............................... 8 2.4 Asset-Specific Life Expectancy Factors and Approaches ........................................ 13

2.4.1 Culverts ........................................................................................................ 13 2.4.2 Traffic Signs ................................................................................................. 14 2.4.3 Traffic Signals and Roadway Lighting ........................................................ 15 2.4.4 Pavement Markings ...................................................................................... 16 2.4.5 Noise and Crash Barriers .............................................................................. 19 2.4.6 Pavements ..................................................................................................... 22 2.4.7 Bridges .......................................................................................................... 25 2.4.8 Alternative Asset Classes (Vehicle Fleets, Equipment, and Utilities)……...30

2.5 Summary of Information Search Results……………………………………………32 CHAPTER 3 – ASSESSMENT OF DATA AVAILABILITY ....... .............................................. 33

3.1 Data Availability ....................................................................................................... 33 3.2 Geographic Representation of the Data Collected .................................................... 35 3.3 Summary of Data Collection Needs………………………………………………...39

CHAPTER 4 –METHODOLOGIES FOR LIFE EXPECTANCY ESTIMA TION .................. 40 4.1 Introduction ...............................................................................................................40 4.2 Dimensions of Analysis ............................................................................................ 40 4.3 General Methodologies ............................................................................................. 41

4.3.1 Condition-based ............................................................................................ 41 4.3.2 Interval-based ............................................................................................... 42

4.4 Specific Methodologies ............................................................................................ 43 4.4.1 Model Types ................................................................................................. 43

4.4.1.1 Linear and Non-Linear Regression Models. ................................. 43 4.4.1.2 Discrete Outcome Models ............................................................ 45 4.4.1.3 Duration Model Characteristics .................................................... 46 4.4.1.4 Markov Chains .............................................................................. 49 4.4.1.5 Miner’s Hypothesis ....................................................................... 50 4.4.1.6 Neural Networks ........................................................................... 50

4.4.2 Model Selection for Calibration ................................................................... 51 4.4.3 Model Recommendations and Results ......................................................... 53

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Page

CHAPTER 5 –METHODOLOGIES FOR SENSITIVITY ANALYSIS . ................................... 54 5.1 Introduction ............................................................................................................... 54 5.2 Methods ..................................................................................................................... 54 5.2.1 Relative Parameter Strength ......................................................................... 54 5.2.2 Marginal Effects ........................................................................................... 54 5.3 Sensitivity Plots and Results ..................................................................................... 54 CHAPTER 6 – EXAMPLE APPLICATION OF METHODOLOGIES .. .................................. 57

6.1 Introduction ............................................................................................................... 57 6.2 Example for the Condition-based Approach ............................................................. 57 6.3 Example for the Interval-based Approach ................................................................ 60 6.4 Sensitivity Analysis Example ................................................................................... 67 6.5 Summary ................................................................................................................... 70

REFERENCES ................................................................................................................................. 71

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LIST OF FIGURES

Figure Page

1: Expected use of Asset Life-Expectancies in Asset Management Decision-making .......................... 3 2: Sequence of the Research Approach showing Work Done and Remaining Work to Date ............... 4

3: Survey Results for Estimated Average Service Lives as Completed by Highway Agencies

(Morgan and Kay 2001) .................................................................................................................. 21 4: Climate Zones as determined by the Strategic Highway Research Program (SHRP) ..................... 35

5: Availability of Pavement Data (besides LTPP data) ................................................................... 3636 6: Availability of Bridge Data (in addition to NBI data which covers all 50 states) ........................... 36 7: Availability of Culvert Data (in addition to NBI data which covers all 50 states) ...................... 3737 8: Availability of Road Sign Sheeting Material Data ......................................................................... 37 9: Availability of Pavement Marking Material Data (From NTPEP) .................................................. 38 10: Availability of Crash Barrier / Guardrail Data .............................................................................. 38 11: Availability of Traffic Signal and Roadway Lighting Data .......................................................... 39

12: Condition-based Determination of Asset Service Life .................................................................. 41 13: Interval-based Determination of Asset Service Life ...................................................................... 42 14: Illustration of Asset Survival Curves using Different Performance Indicators and Different

Performance Thresholds (Irfan et al., 2009) .................................................................................. 47 15: Potential for Error due to Censored Data (Washington et al., 2003) ............................................. 49 16: Example of an Artificial Neural Network ...................................................................................... 51

17: Example of a Tornado Diagram (FHWA, 2006) ........................................................................... 55 18: Example of a Spider Diagram (Van Dorp, 2009) .......................................................................... 55 19: Residuals vs. predicted values for log(retroreflectivity) ............................................................ 59 20: Actual values vs. predicted values for log(retroreflectivity) ..................................................... 59 21: Residuals of Best Regression Model Specification (historical service life) ............................. 63

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Figure Page

22: General Survivor Curve (years) of Best Model Specification ................................................... 65 23: Survivor Curve (freeze-thaw cycles) of Best Model Specification ........................................... 65 24: Residuals of Survival Probabilities of Best Model Specification ............................................ 66 25: Residuals of Best Neural Network Model Specification ........................................................... 67 26: Tornado Diagram of Significant Predictors of Pavement Marking Retroreflectivity ................... 69 27: Spider Diagram of Significant Predictors of Pavement Marking Retroreflectivity ....................... 69

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LIST OF TABLES

Table Page 1: Determining Remaining Service Life - Mechanistic vs. Empirical Models ..................................... 9

2: Service Life Prediction Methods for Concrete Structures (Liang et al., 2002) ............................... 10

3: Mean Pavement marking Service Life in Elapsed Months by Color of Marking............................ 18 4: Estimated Service Life for Noise Barriers by Material Type (Kay et al. 2001) .............................. 20

5: Estimated Service Life for Noise Barriers by Geographic Region .................................................. 21

6: Prediction of Corrosion Time Stages (Liang et al. 2002) ................................................................ 28

7: Collected DOT Data by Asset Type ................................................................................................ 33

8: Specific Statistical Model Types ..................................................................................................... 43

9: Recommendations for Selection of Methodology for Life Expectancy Estimation ....................... 52

10: Variables Available to Model PMM performance of 1A: 2-yr Waterborne Paint......................... 57

11: Model for Pavement Marking Peformance (Retroreflectivity) on basis of Maximum Likelihood Estimates, Material – 1A: 2-yr Waterborne Paint ....................................................... 58

12: Determining Remaining Service Life of a Pavement Marking ..................................................... 60

13: Historical Service Lives of a Subset of the NBI Database ............................................................ 61

14: Best Generalized Least Squares Regression Model ....................................................................... 62

15: Best Weibull-distributed Survival Model ...................................................................................... 64

16: RMSE by Neural Network Activation Functions .......................................................................... 66

17: Normalized Parameter Strength of Significant Predictors of Pavement Marking Retroreflectivity ............................................................................................................................. 68

18: Data Statistics of Significant Predictors of Pavement Marking Retroreflectivity ........................ 68

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CHAPTER 1 – INTRODUCTION

1.1 Study Background and Problem Statement

In the current transportation environment, highway agencies grapple with conundrum of providing sustainable levels of service in terms of facility condition, safety, security, mobility, reliability, and life cycle cost in the face of aging infrastructure, increasing user expectations and funding limitations. As such, the preservation of existing highway assets (pavements, bridges, culverts, pavement markings, traffic signals and signs, roadway lighting, guardrails, etc.) continues to be a critical issue. In light of these trends, highway asset managers, as stewards of the most valuable physical assets in any state, have an urgent responsibility to apply cost-effective, life-cycle management strategies and practices that are in the best interest of taxpayers and highway users.

A vital aspect of cost-effective highway asset management is the estimation of facility life expectancies. Highway assets deteriorate with age due to the accumulated effects of usage/loading, climate, deicing chemicals, and other factors. For proper planning and programming of asset preservation and replacement activities, it is essential that the highway asset manager acquires a profound comprehension of the behavior of each asset class in terms of the pattern (and influential factors) of its deterioration and consequently its life expectancy (i.e., the length of time until the asset must be retired, replaced, or removed from service).

Factors of life expectancy include asset materials, design, and maintenance frequencies as well as the severity of the environment. For example, the use of better materials in design such as stainless steel for deck reinforcement in place of traditional carbon epoxy-coated steel could lead to longer life expectancies in a possibly more cost-effective manner; life expectancies could be shortened by heavy traffic loadings, high freeze indices, frequent freeze thaw cycles, exposure to winter de-icing salts, and other harsh conditions within the highway system environment, Furthermore, timely application of preventive maintenance and rehabilitation treatments could yield increased life expectancies for highway assets. As such, one of the motivations for this research is the expectation that asset managers can make enhanced decisions for maintaining, repairing, rehabilitating and replacing highway assets if they are better equipped with greater understanding of highway asset life expectancies. Using more reliable life expectancy estimates, highway asset managers can evaluate the impacts of alternative preservation schedules over the asset life-cycle and thus identify which life-cycle preservation policies are optimal.

As the Research Team proceeds in carrying out this research, we are continually communicating with the Research Panel and our partners in the industry to ensure that we are focused on the applicability of the developed methodology. In this context, we realize that in assessing the life expectancy of a highway asset, it is important to consider the primary reasons for which agencies replace or retire the asset. These reasons may include:

• Accommodate demands of higher traffic volume and heavier trucks, typically from new economic development;

• Reduction of the high maintenance costs associated with current design practices;

• Meet regulatory changes such as mitigating safety problems caused by poor alignment or narrow roadways and bridge decks;

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• Changes in development patterns that render a road or structure no longer needed; • Eliminate potential vulnerability inherent in the current design, e.g., fatigue damage; • Eliminate potential vulnerability to extreme events such as floods, earthquakes, or

collision; • Address deterioration that is beyond cost-effective repair/rehabilitation; • Improve asset performance through the use of new technologies. As we develop the life expectancy estimation methodologies, we are guided by the

realization that when designing a new road or bridge, agencies strive to account for these factors using the best techniques available at the time. However, many of these factors often change during the asset lifespan, especially for long-lived highway assets such as bridges. After an asset is put in service, the highway agency attempts to manage risk and deterioration through mitigation actions, maintenance, repair, and rehabilitation. There are methods for forecasting these factors, for example NCHRP Report 495 for fatigue life, hydrological and seismic studies for extreme events, and deterioration models. Thus, ideally, an agency strives to use all those techniques when considering how much longer an asset might last, and what additional life might result from agency activity. For deterioration, the agency decision to rehabilitate or replace an asset might be based on design details such as access to the deteriorated area. For example, the existence of pack rusts (corrosion that is inaccessible under gusset plates) on bridge trusses might be a reason to replace rather than repair. For pavements, subgrade failure may warrant need for reconstruction. If there is no functional reason to replace a facility, the agency will normally prefer to maintain it perpetually unless there is irreparable damage. In many cases the motivation to replace a facility is a combination of factors. It is often a matter of benefit/cost analysis in a context of funding constraints and competing projects. An agency might band-aid a facility for many years because of a lack of funding to replace it, when other parts of the network have more urgent needs. Service life is an especially useful consideration for assets when the first 4 factors listed above are not expected to come into play in the foreseeable future. The goal of the agency, then, is to extend service life indefinitely if possible, until one of the higher-level considerations takes precedence.

We are striving to consider the implementation of our study results even as the research progresses. As such, we are communicating with the agencies to ascertain how the study results could further enhance asset management decision-making. Figure 1 illustrates the possible role of asset life-expectancy estimates in highway management. Life expectancy values can help establish the year in which asset replacement will be necessary, and thus can ultimately help establish short- or long-term physical and financial work plans and program development. Also, updated values of the life expectancy of assets due to new designs, materials, operating conditions, or preservation programs can help agencies assess the feasibility of extending the time intervals between asset replacements.

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Life Expectancy Models

Determine Year of

Replacement

Physical Work Planning

Financial Work

Planning

Budget Constraints

Programming Cost Analysis

Facility Design

Policy-making for Increased Intervals between Asset

Replacements

Budgeting and Programming

Figure 1: Expected use of Asset Life-Expectancies in Asset Management Decision-making

For each of the several different asset classes under consideration in this study, we are developing a methodology by which highway asset managers can establish life expectancy values for each combination of factor levels, or life expectancy models as a function of various influential factors. The factors that are currently being investigated by the Research Team include material type, operating environment (traffic loading and climatic conditions), and past preservation history if available. This report also demonstrates how, after establishing these models for assets in their jurisdiction, asset manager could investigate the sensitivity of the asset life expectancy to changes in the levels of these factors. The life expectancy methodology being developed in this study will show how agencies could establish the probability distributions of life expectancies of their facilities. The probabilistic approaches yield robust values of asset life expectancies for reliable life-cycle cost analyses. Overall, agencies will benefit from the enhanced capability to estimate asset life expectancies so that they can better guide in-service asset management programs. 1.2 Study Objectives

The objectives of this research are to: 1. Develop a methodology for determining the life expectancies of major types of highway

assets that can be utilized in life-cycle cost analyses to assist asset replacement decisions; 2. Demonstrate the methodology’s use for the various highway asset types; 3. Develop a guidebook and accompanying resources that can be used by state and local DOTs

and other agencies. Thus, agencies will be in a better position to develop highway maintenance/preservation programs and also to assess their impact on system performance.

Consistent with the directions of the research panel, the primary emphasis of the research study is the set of highway assets besides pavements and bridges. 1.3 Scope of the Research Study

The developed methodologies will be applied to at least three asset classes to demonstrate the methodology. Consistent with the RFP, the life expectancy estimation methodology is being based on

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replacement due to irreparable condition states and extreme events. Where data are available, the Research Team is investigating historical replacements of highway assets to capture any other dominant criteria for asset replacement/reconstruction.

1.4 Summary Description of Completed and Pending Tasks

The overall study sequence, showing the tasks completed and the remaining tasks as of the reporting time, is illustrated as Figure 2.

Figure 2: Sequence of the Research showing Work Done and Remaining Work to Date

Task 1 – Information Search (July 5 – September 30, 2009) In this task, we analyzed, described, and critiqued domestic and international research in the general subject area of life expectancies on the basis of applicability, conclusiveness of findings, and usefulness for the development of life expectancy estimation methodologies. Details of the information search results are provided as Chapter 2 of this report. Task 2 – Assessment of Data Availability (September 1 - November 30, 2009) We have assessed the availability of data for the study pertaining to the following assets: culverts, traffic signs and sign structures, traffic signals, roadway lighting fixtures, noise and crash barriers/guardrails, pavement markings, pavements, and bridges. For life expectancy modeling, particular emphasis has been placed on collecting data on asset age, condition, material/design type, location, repair history, traffic loading, basic design/construction features, and geometric features. In Chapter 3 of this report, we present details of our assessment of data availability. Task 3 – Methodology for Life Expectancy Estimation (November 1, 2009 - January 31, 2010) We have developed general and specific methodologies to predict life expectancies of each asset class across various dimensions (material/structural type, climate zone, traffic loading, etc.). We

2.

Assessment

of Data

Availability

1.

Information

Search

3.

Methodology

for

Asset Life-

Expectancy Estimation

4. Sensitivity

of Life

Expectancy

Factors

6. Application of

the Developed

Methodologies

8. (a) Guidebook

Development

(b) Workshop Organization

9. Final Reporting

5. and 7.

Submit Interim

Report;

Panel Meeting;

NCHRP Comments

Receipt of Comments

from Workshop

Attendants and from

NCHRP

LEGEND

Task 95-100% completed as of current time

Task in progress as of current time

Task not yet started as of current time

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have presented methods that are based on asset condition and those that are based on time, with an emphasis on probabilistic, statistical techniques. The condition-based methods estimate life expectancy by tracking the asset deterioration curve and extrapolating to the time when a certain threshold condition state is reached. The time-based methods predict life expectancy using observed historical service lives of similar assets in the past. For each of these two methods, a variety of data analysis techniques was investigated as part of this study. These techniques, which can be replicated by highway agencies to develop life expectancies of their highway assets, include linear and non-linear regression models, discrete choice models, survival models, neural networks, fuzzy logic, and panel effects) is recommended with a final selection based on goodness-of-fit measures (residuals, validation plots, coefficients of determination, root mean square error, etc.). Details of the developed methodologies for life expectancy estimation are provided as Chapter 4 of this report. Task 4 – Sensitivity of Life Expectancy Factors (January 1 – March 31, 2010) Our developed overall methodology for life expectancy estimation includes methods by which agencies can investigate the sensitivity of asset life expectancy to influential factors. To demonstrate the sensitivity analysis methods, we used the data collected from the various participating states (herein referred to as the “study areas”) and thus identified the factors that influence the life expectancies of specific highway asset classes at these areas. These factors, which depend on the asset class under consideration, generally include traffic and climatic loading, asset dominant material and structure type, and geometric design. We are carrying out sensitivity analysis to investigate the impact of each factor on asset life expectancy with representative sensitivity plots generated through a basic spreadsheet application. We expect that as highway agencies apply our sensitivity analysis methods to their asset data, they will uncover additional factors that influence asset life expectancies in their states. These may include quality of initial construction, frequency or annual expenditure of maintenance or preventive maintenance per unit dimension or per count of the asset (for example, $/ft2, $/Nr, $/lane-mile, etc.). In Chapter 5 of this report, we provide details of the developed methodologies for investigating the sensitivity of life expectancy factors. Task 5 – Interim Report 1 and Panel Meeting (Report: March 31, 2010 and Meeting: May 1, 2010) The remainder of this report includes thorough documentation of Tasks 1 to 4, for review by the NCHRP and the study panel. This includes a discussion of the information search, an assessment of data availability from identified sources, and the methodologies we have proposed for life expectancy estimation and sensitivity analysis. In early May 2010, the Research Team and NCHRP 08-71 Panel will hold a teleconference meeting organized by the NCHRP to discuss the details of the interim report and to plan how best to move forward with the remaining tasks. Task 6 – Application of the Developed Methodology (May 1 - July 31, 2010) In Task 6, the Research Team will apply the methodologies developed in Tasks 3 and 4 for estimating life expectancies of new and in-service assets and the sensitivity of significant factors. Using data gathered in Task 2, we will demonstrate the efficacy of the alternative methodologies to quantify the effect of the influential factors of asset life expectancy. As we proceed to apply the

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developed methodologies, we will carry out due adjustments and modifications as and where necessary to enhance its usefulness and the clarity of the methodology results to the highway agencies. We will then implement the approach developed in Task 3 as a simple Excel spreadsheet model, building on the model used for sensitivity analysis in Task 4, for computing, graphing, and reporting on the combined probability density functions for overall life expectancy. Task 7 – Interim Report 2 and Panel Meeting (Report: July 31, 2010 and Meeting: September 1, 2010) We will document the methodology and application examples for estimating life expectancies of the identified highway assets, and will illustrate how life expectancies may be used in life-cycle cost analyses of new and in-service assets so as to develop maintenance/preservation programs for highway assets. Furthermore, we will describe the effects of uncertainties (e.g., whether these programs are executed as planned) on the actual performance of these assets. Approximately 1 month after the NCHRP receives the initial draft Interim Report 2, we will meet with the NCHRP project panel via teleconference and modify Interim Report 2 in response to project panel comments. Task 8 – Guidebook Development and Workshop Preparations (September 1 - December 31, 2010) In Task 8, we will develop a guidebook and other resources that will assist highway agencies to implement the methodologies we developed in previous tasks. We will organize the guidebook according to various types of applications of the methodology including project-level planning and design studies, corridor planning exercises, and integration into the management systems for the various asset classes. We will provide example applications and graphical depictions to communicate the usefulness of the product. Task 9 – Final Report Preparation and Submission (January 1 – April 4, 2011) We will submit a final report documenting the entire project. The final report will also include an outline or framework of dissemination activities and future research needed to ensure that highway agencies can use estimated asset-life expectancies as key inputs in a broader context of life-cycle maintenance and preservation planning and programming. We will submit a revised version of the guidebook based on comments from the workshop and prepare a PowerPoint slide presentation reviewing the project and its results. The final research product will also include the comprehensive database that we would have assembled for purposes of the demonstrations of the study methodologies.

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CHAPTER 2 – RESULTS OF THE INFORMATION SEARCH

2.1 Introduction

The research team has obtained and critiqued domestic and international research in the general subject area of life expectancies, not only for highway assets (culverts, signs, pavement markings, guardrail, roadside facilities, pavements, and bridges) but also for other asset classes such as utilities, vehicle fleet, and equipment. This task was focused and concise, guided by the basis of applicability of the information, conclusiveness of findings, panel suggestions, and usefulness of concepts for the development of life expectancy models.

Our search included a review of publications from the following databases/sources: International Road Research Documentation, National Technical Information Service, and Transportation Research Information Services; transportation centers in Northwestern University, University of Wisconsin, and other universities; state and local transportation agencies; and Transportation Research Board (TRB) Committees, such as ABC40 (Transportation Asset Management Committee) and ADA50 (Transportation Programming, Planning, and Systems Evaluation). The information search was carried out with the objective of determining the state-of-the-practice and state-of-the-art approaches for life expectancy estimation. The results of our search served as a pedestal for us to add our new thinking that we expect will add significantly to the state-of-the-art. Areas of the information search covered the following areas:

• definitions and measures of asset life expectancy;

• general approaches to estimating service life; • established life expectancy values for the different assets and environmental

conditions; • stratification of data for analysis (climate zone, geographic region, roadway functional

class, etc.); • statistical/econometric techniques applied to asset databases to predict service life;

• factors that affect asset life expectancies (materials, design criteria, construction quality control, and maintenance policies and practices, etc.).

2.2 Definitions and Measures of Asset Life Expectancy Asset life expectancy can be measured by physical life or service life (Chang and Garvin, 2008). Physical life is typically referred to as the time until structural failure due to accumulated traffic and/or climatic loadings or an extreme event. Service life refers to the time until an asset must be replaced due to substandard operational performance, technological improvements, regulatory changes, or changes in consumer behavior and values (Lemer, 1996). Due to the dominance of the latter measure, many agencies refer to asset life expectancy solely as “service life”. These terms are considered interchangeable and are used interchangeably throughout the rest of this report. The most common variable for expressing life expectancy is the asset age in years. However, some agencies and researchers (Shekharan and Ostrom, 2002; McManus and Metcalf, 2003) prefer to measure service life in terms of accumulated traffic loading (for pavements and pavement markings,

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bridges, and large culverts) and accumulated climatic effects (for all asset types). Due to these various measures, in this study, we are quantifying asset service life in terms of both asset age (years) and accumulated loadings experienced by the asset since its construction. 2.3 Existing Approaches to Estimating Life Expectancy of Assets With regard to the data type, there has been three general approaches are commonly applied to estimate asset service life:

1. Expert opinion – this simple approach is commonly applied by practitioners. Experienced persons who have acquired years of accumulated intimate knowledge of the in-service durations of a particular asset are solicited for their perspectives on the future longevity of a similar new or in-service asset. For example, pavement experts can provide, from their engineering judgment, the expected life of a 12-inch PCC pavement under a given set of environmental and traffic conditions. Disadvantages are that several years of experience are typically required to reach such a good level of expertise. Secondly, the true underlying causes of life expectancy of a given asset may be difficult to decipher objectively.

2. Observed historical asset lives – in this approach, analyses of past records are examined to determine the actual number of years that have elapsed between successive asset replacements or reconstructions. These service lives may be averaged for a given asset class, material type, etc., or statistical models may be developed to relate the observed service life as a function of asset and environmental attributes. This approach can help capture the influence of hard-to-measure variables such as changes in technology or economic climate. However, data on actual observed lives are difficult to obtain at highway agencies. Secondly, historical asset lives that were observed in the past may have been unduly influenced by economic conditions: in good economies, assets are likely to be replaced in shorter intervals, and vice versa, thus these observations of asset life may be biased.

3. Asset performance – the most commonly studied approach in research literature is the use of asset performance trends and thresholds. Given the performance trend and the performance thresholds, the time taken for the performance to reach the threshold is identified as the asset life expectancy. The performance trends can be modeled using mechanistic or empirical models. In empirical modeling, statistical functions are developed to describe the trajectory of asset deterioration as a function of age, and other asset and environmental attributes. In mechanistic modeling, some primary response of the asset material is measured, often using an instrument, and modeled theoretically as a function of time or accumulated repeated loadings or other environmental stimuli.

Due to the subjective nature of expert opinions, that approach is not recommended in this

study. Instead, both the observed historical asset life approach and the asset performance approach will be applied. Our data availability analysis (Task 3) showed that cross-sectional performance data are typically available for certain assets at state agencies, while historical data are often lacking but are becoming more frequently collected. In this respect, the literature is replete with a number of mechanistic and empirical models that were developed for asset life expectancy determination.

9

Examples of general methods are outlined in Table 1 and material-specific methods are listed in Table 2.

Table 1: Determining Remaining Service Life - Mechanistic vs. Empirical Models

Category Typical Methods Description Advantages Disadvantages

Mechanistic

Fatigue Test

Punchout Failures

FWD (NDT)

Uses destructive or non-

destructive test to measure

a primary response of the

asset (such as material

strength) using basic

theory. The remaining service life is

then determined by both

the current strength and

projected traffic loadings.

Destructive tests are

intrusive and thus typically

incur some damage to the

asset. Non-destructive test

typically measure the

response of the asset to a

specific level of external

stress.

Historical data on

asset attributes,

loading, or

environment are not

required.

More suited for asset

evaluation and

decision-making at

project-level.

Yields a direct and

easy means to

compare the condition

(and thus, service life)

of different assets.

Operation procedure

is standardized.

Destructive test causes damage

to a part of pavement and the

equipment is often expensive.

Non-destructive test often

requires back-calculation whose

accuracy is sometimes doubtful.

Predictive accuracy can be

compromised by sampling

locations and traffic projections.

The effects of certain influential

factors of asset condition and

life expectancy, excluded from

the mechanistic model, are

difficult to measure.

Deemed relatively less

appropriate for network-level

management.

Empirical

Regression

Neural Network

Nomograph

Life Table

Kaplan-Meier

Failure Time

Theory

Cox Proportional

Hazards

Remaining service life is

estimated using observed

historical data on asset

condition. Effects of the influential

factors that affect asset life

can be estimated directly

or indirectly.

Less expensive than

mechanistic methods

if historical data are

available.

The effects of

influential factors can

be estimated.

Relatively easy to

implement/integrate

in asset management.

Sufficient amount of historical

data are required. Thus

assessment of data availability is

critical.

Predictive accuracy hinged on

the quality of available historical

data and the model format.

Determination of the model

format usually requires

extensive field knowledge and

experience.

Adapted from Yu (2005)

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Table 2: Service Life Prediction Methods for Concrete Structures (Liang et al., 2002)

Method Influence or Application Reference

Physical-mathematical model Predicted time of tp and tcor Bazant (1979a,b)

Accelerated durability test method Prediction of the service life of a structure depended on minimum

load-carrying capacity, maximum acceptable deformation, and

permeability

Fagerlund (1979)

Evaluation of parameters of

deterioration

Use in formulating repair rehabilitation, replacement policy,

underestimated value of tcor

Cady and Weyers

(1984)

Accelerated test and mathematical

model

Prediction of concrete service life Pommersheim and

Clifton (1985)

Probabilistic view Prediction of service life of building materials and components Sjostrom (1985)

Failure probability Design life and durabilty of concrete structures Somerville (1986)

Survey data of bridge decks exposed

to deicing salt, coastal buildings, and

offshore structures

Predicted initiation time Guirguis (1987)

Systematic approach Service life prediction of building and construction materials Masters (1987)

Unsteady-state dynamic analysis

(using the semi-infinite solid

approximation and the Laplace

transformation method)

Service life prediction for external vertical walls of RC with

external thermal insulations

Fukushima (1987)

Modified version of Bazant's model Predicted time of tp Subramanian and

Wheat (1989)

Predictive service life test, aging test,

and mathematical model

Service life prediction of building materials and components Masters and Brandt

(1989)

Experimental and field tests Prediction of corrosion depth in concrete Tsaur (1989)

Expanded and Bazant model Prediction of the tp time, the corrosion cracking time, the breaking

time of bond between concrete and steel, and the steel area

losing time

Liu and Mian (1990)

Allowable limit and the state of

corrosion

Prediction of service lives of RC buildings, but the predicted results

are always overestimated

Morinaga (1990)

Predictive service life tests and long

term aging, and in-use conditions

Systematic methodology for the prediction of service life of

building materials and components

Sjostrom and

Brandt (1990)

Mathematical deterioration model

expressed the property changing as a

function of solar ultraviolet rays,

heat, and degradation factors

Service life prediction system of building materials Tomiita (1990)

Mathematical model consists of the

assessment of the annual total

damage ratio and the estimation of

the service life

To estimate the service life of a bituminous glass-fibre-reinforced

multiple waterproof roofing element

Ahoz and Akman

(1990)

Probabilistic approach Service life prediction of ferrocement roof slabs Quek et al. (1990)

Experience, deduction, accelerated

testing, mathematical modeling,

reliability, and stochastic concept

Predicting the service life of concrete Clifton (1990, 1991,

1993)

Measurement of the corrosion rate of

reinforcing steel

Prediction of service lives of RC building Morinaga (1990)

Accelerated corrosion tests and field

measurement

Measure the rate of steel corrosion in concrete Harn et al. (1991)

11

Table 2: (Continued)

Method Influence or Application Reference

Gray theory Predicts remaining service life of harbor structures Li (1992)

Implementation of Tuntti's model (considers

effect of temperature, chloride proportion, &

humidity in concrete pores (resistivity))

Influence of temperature on the service life of rebars Lopez et al. (1993)

Time-dependent reliability Service life assessment of aging concrete structures Mori&Ellingwood(1993)

Probability method Service life prediction of existing concrete bridges Qu (1995)

Reliability approach Predicts service life of concrete structures exposed to

chloride ions

Prezzi et al. (1996)

Fick's second law Predicts service life of existing concrete exposed to

marine environments

Maage et al. (1996)

Testing, structural, and economic models Service life of existing RC structures Henriksen (1996)

Generalization of the Markov Chain models

based on time-dependent reliability theory

Prediction of bridge service life Ng and Moses (1996)

Long-term economic analysis Service life prediction of concrete road bridges Brito and Branco (1996)

Calculation of prestressing cable forces from

vibro-wire gauges embedded in bridges

Service life prediction of prestressed concrete

cantilever bridge

Javor (1996)

Corrosion damage prediction using electrical

potential surveys

Service life prediction of concrete bridge deck Kriviak et al. (1996)

Utilization of measured stress spectra for

predicting fatigue accumulation and crack

propagation

Service life evaluation of steel or composite bridge;

influence of the effective traffic loading on structures

Baumgartner et al.

(1996)

Established a computer-integrated knowledge

system

Predicting the service life of steel-RC exposed chloride

ions

Bentz et al. (1996)

In situ permeability and strength testing Develop the durability-based design criteria for

concrete and assess the remaining life of existing

structures

Long and Rankin (1997)

Cumulative damage theory and accelerating

the corrosion of rebar in concrete

Service life prediction of rebar-corroded RC structure Ahmad et al. (1997)

Mathematical model for accelerated testing

for concrete structures in chloride laden

environments

Predicting the initiation time of concrete structures Liang et al. (1997, 1999a)

Mathematical model combined Fick's second

law with durability coefficient

Predicting the service life of existing RC bridges due to

carbonation

Liang et al. (1998,

1999b)

Time-variant reliability method, Monte-Carlo

simulation for finding the cumulative-time

system failure probability

Service life prediction of deteriorating concrete bridges Enright and Frangopol

(1998)

Fick's second law incorporated surface

environment, chloride transport, temperature

of surrounding medium, seasonal effects, and

construction variability

Predicting the service life of a RC structure in different

environments

Amey et al. (1998)

FBECR (fusion-bonded epoxy-coated

reinforcing steel) as a physical chloride barrier

system

FBECR is not a cost-effective corrosion protection

system when compared with bridge built with bare

steel in Virginia, because they only provide corrosion

protection for 5% of Virginia's bridge decks

Weyers et al. (1998)

Time-to-cracking model based on elasticity Corrosion cracking model is dependent on the cover

depth, properties of the concrete and steel/concrete

interface, type of corrosion products, and the size of

the reinforcing steel and is a function of the critical

weight of rust products and corrosion rate

Weyers (1998),

Liu and Weyers (1998)

12

Mechanistic methods, which pertain to laboratory or field experiments to simulate service life under accelerated, controlled conditions, are commonly used to measure the time until some specific failure mode such as material fatigue. Past experimental studies analyzing fatigue with accelerated loading have included the application of vibration theory, fatigue damage theory, fracture mechanics, the Palmgren-Miner linear damage equation, Miner’s hypothesis test, and finite element-based methods (Coetzee and Connor, 1990; South, 1994; Romanoschi et al., 1999; Lund and Alampalli, 2004; Suwito and Li, 2004; Breysse et al., 2005; Zuo et al., 2007; Samson and Marchand, 2008). These tests, however, are limited to the accuracy of the laboratory representation of real-world conditions and yield models that are largely inconsistent with the kinds of data in state highway agency databases. It is this difficulty of replicating mechanistic models on a network wide basis is what makes them relatively unsuitable, at the current time, for purposes of asset management decision-making.

Therefore, the methodologies we have developed for life expectancy estimation focuses on empirical, rather than mechanistic methods. In the literature, there have been a number of empirical methods for predicting service life. Examples from the literature, categorized by the modeling technique used, are listed below:

• Statistical regression (Linear and non-linear) o Hadiprono et al. (1988); KurdZiel and Bealey (1990); Kirk et al. (2001); Abboud et al.

(2002); Bischoff and Bullock (2002); Wolson et al. (2002); Lee et al. (2002); Flom and Darter (2005); Szary et al. (2005); Yu (2005); Zhang and Wu (2006); Halmen et al. (2008); Gedafa et al. (2009); Immaneni et al. (2009).

• Markov chains o Jiang and Sinha (1989); Estes and Frangopol (2001); Zhang et al. (2003); Hallberg

(2005); Morcous (2006); Chou et al. (2008); Ertekin et al. (2008). • Survival/reliability models

o Lin (1995); Vepa et al., (1996); ; Colucci et al. (1997); Eltahan et al. (1999); Romanoschi et al. (1999); Lounis (2000); Estes and Frangopol (2001); Shekharan and Ostrom (2002); Gharaibeh and Darter (2003); McManus and Metcalf (2003); Zwahlen et al. (2003); Akgul and Frangopol (2004); Bausano et al. (2004); Biondini et al. (2006); Saber et al. (2006); Hearn and Xi (2007); Oh et al. (2007); Yang (2007); Meegoda et al. (2008); Strauss et al. (2008); Yu et al. (2008); Sathyanarananan et al. (2008); Anastasopoulos (2009); Irfan et al. (2009).

• Machine learning/neural networks o Flintsch et al. (1997); Ferregut et al. (1999); Abdallah et al. (2000); Melhelm and

Cheng (2003); Swargam (2004); Narasinghe et al. (2006). To account for uncertainties in service life prediction, recent studies have focused on

applying stochastic approaches which are considered to be more robust. Probabilistic techniques in service life estimation can mitigate four basic types of uncertainty (Lin, 1995):

• Inherent randomness of structural characteristics (material properties, section dimensions, or loads)

• Inherent randomness of external effects (environmental conditions)

13

• Statistical uncertainty (incomplete or errant data from inspections, or errors in estimating parameters of probability models)

• Model imperfection (error created through idealized mathematical modeling attempting to describe complex physical phenomena)

We are considering the above sources of uncertainty as we proceed to enhance the developed methodology to include probabilistic analysis that generates, for each asset class, a range of life expectancy predictions instead of a single number. That way, prediction of asset life expectancy can be generated and reported with a corresponding confidence level. Common probabilistic methodologies that have been applied include survival models, Markov chains, fuzzy sets (Anoop and Rao, 2007), and Monte Carlo simulation of various statistical distributions (e.g., log-normal distributions have been applied to account for data collection errors) (Lin, 1995; Biondini et al., 2006; Oh et al., 2007; Williamson et al., 2007; Ertekin et al., 2008). Such approaches can similarly be carried over to the assessment of life cycle costs to account for uncertainties in the face of assumed discount rates and traffic growth factors (Adams et al., 2002; Christensen et al., 2008; Ertekin et al., 2008; Madanu et al., 2009). 2.4 Asset-specific Life Expectancy Factors and Approaches The developed study methodology (described in Chapter 4) is designed to be flexible, repeatable by highway agencies, and comprehensive enough to accommodate a variety of asset classes. Subsequent to our data collection, we will apply the developed methodology to demonstrate how agencies could establish life expectancy models and thus, life expectancy values or ranges, for the highway asset classes under consideration. The literature review for each asset class, including those outside the scope of this study, provided critical information on what kind of data we need to request at the subsequent stage of data collection. This review is herein summarized. 2.4.1 Culverts Culverts are a critical but often overlooked element of highway infrastructure (Broviak, 2005; McGrath et al., 2006). Fortunately, the NCHRP has funded several culvert studies including Synthesis #20 “Durability of Drainage Pipe” and #254 “Service Life of Drainage Pipe” (Gabriel and Moran, 1998). Culvert material types that have been studied include precast concrete, concrete cast-in-place, cast iron, corrugated steel, corrugated aluminum, asbestos-bonded steel, galvanized steel, brick/clay, as well as different coating materials (asbestos, aluminum, bitumen, etc.) for inner culvert walls (Jacobs, 1984, Meegoda et al., 2008). Life expectancies for such material types have previously been defined as the time to failure due to cracking of the precast concrete or corrosion perforation throughout the galvanized steel wall (Ring, 1984; Gabriel and Moran, 1998; Wyant, 2002; Markow, 2007; Halmen et al., 2008; Meegoda et al., 2008) and the use of visual condition ratings (Hadipriono et al., 1988; Wyant, 2002; Beaver and McGrath, 2005; Meegada et al., 2004, 2005, 2006, and 2008), as used in NCHRP #303 and by several state departments of transportation (such as Ohio and Utah) and the World Bank Institute. Empirical data analyses and modeling techniques have included the linear additive model (Hadiprono et al., 1988), log-linear model (Kurdziel and Bealey, 1990), multiple regression (Halmen et al., 2008), a Weibull-distributed survival model (Meegoda et al., 2008), and nomographs for

14

culvert asset durations (CalTrans, 1999). Mechanistic studies have focused on stress crack resistance in laboratory experiments using techniques such as the rate process and popelar shift methods and finite element analysis to determine the time to mechanical or chemical failure of pipe culverts (Folkman et al., 2010; Hsuan, 2010). Expert opinion has placed pipe culvert lives anywhere from 25-100 years depending on climate and construction practices (Pluimer, 2010). Therefore, more in-depth study can help narrow the range of life estimates. Factors that affect culvert life expectancy: In past studies, factors found to be significant include culvert age, culvert material type, backfill material type, presence of any pipe protection coatings or systems, pipe flow conditions, pH and electrical resistivity of the backfill soil as well as of the flowing water, chloride content, frequency and intensity of culvert inspections or maintenance, presence and type of culvert coating, topography (flat vs. rolling), etc. (Beaton, 1962; Gabriel and Moran, 1998; Halmen et al., 2008; CalTrans, 1999; Sagues et al., 2001). Mechanistic studies have found that significant life expectancy factors include antioxidants help extend life, with the amount of fill, level of antioxidants, compaction, condition state of joints, gaskets, and connections, and deflection of the pipe system (Hsuan, 2010; Pluimer, 2010). Approaches used to determine culvert life expectancy: The expert opinion and asset performance general approaches are most commonly applied to determine culvert life expectancies. Specific, statistical approaches have typically included linear and non-linear regression, duration models, and laboratory analyses (Hadiprono et al., 1988; Kurdziel and Bealey, 1990; CalTrans, 1999; Halmen et al., 2008; Meegoda et al., 2008; Hsuan, 2010; Pluimer, 2010). 2.4.2 Traffic Signs Traffic sign life expectancy is based on the condition of the sign structure and performance of the sign sheeting surface. For the sign structure, past research has established that the estimated life expectancy is influenced by the fatigue behavior of the structure type (single or double mast-arm cantilevers, box-trusses, tri-chord, and monotube) (Gilani and Whittaker, 2006; Li et al., 2006; Lucas and Cousins, 2006), the connection type (welded studs, etc.), and post material type (Griffith, 1999). Traffic sign sheeting life has been based on retroreflectivity values, commonly collected with mobile retroreflectometers, and stratified by color, ASTM sheeting type, and geographic location (Kenyon et al., 1982; Nelson and Woltman, 1985; Awadallah, 1988; Paniatti and Schwab, 1991; McGee, 1991; Bischoff and Bullock, 2002; Markow, 2007). While few studies have analyzed sign structure condition, several have investigated sign sheeting. Statistical tools including linear regression and ANOVA have been used to develop performance models for red, white, and yellow sign sheeting (Kirk et al., 2001; Bischoff and Bullock, 2002; Wolson et al., 2002). More recently, Swargam (2004) used artificial neural network and multiple linear regression analysis to assess the performance of traffic sign retroreflectivity. A synthesis study by Immaneni et al. (2009) analyzed data from various studies that estimated deterioration rates using a different data analysis and modeling techniques, and determined that

15

threshold retroreflectivity values were reached 8 to 15 years after the sign installation. Interestingly, the authors stated that the best-fitting relationships between retroreflectivity and age were generally linear. Factors that affect traffic sign life expectancy: For traffic sign structures, the life expectancy factors in past research include the structure type (single or double mast-arm cantilevers, box-trusses, tri-chord, and monotube, etc.), natural wind loading characteristics (direction and strength of local winds), truck-induced wind gusts, nature of connections (welded, threaded, etc.).

For traffic sign sheeting performance, considerations have included age, sheeting grade and type, sign size, roadway speed limit, color, precipitation, orientation to the sun and traffic, and proximity to the roadway (Black et al., 1991, 1992; Paniatti and Mace, 1993; Hawkins et al., 1996; Kirk et al., 2001; Hawkins and Carlson, 2001; Wolson et al., 2002; AASHTO, 2003; Hildebrand, 2003). Approaches used to determine traffic sign life expectancy: The asset performance general approach is commonly applied to determine life expectancies of traffic signs, using statistical approaches including linear regression and neural networks for sign sheeting (Kirk et al., 2001; Bischoff and Bullock, 2002; Wolson et al., 2002; Swargam, 2004; Immaneni et al., 2009) and finite element analysis to assess the fatigue behavior of sign structures (Gilani and Whittaker, 2006; Li et al., 2006; Lucas and Cousins, 2006).

2.4.3 Traffic Signals and Roadway Lighting Different components of traffic signals and roadway lighting systems typically reach the end of their respective service lives due to either structural failure of the support structure or component failure of bulbs and load switches. With regard to traffic signal mast arms, structural failures have been observed recently in states such as California and Texas, making the determination of service life an important matter not only for purposes of asset management but also from the perspective of road user safety. Life expectancies due to structural failure have most commonly been measured in the past on the basis of the initiation and propagation of defects such as cracks (South, 1994; Chen et al., 2001; Kloos and Bugas-Schramm, 2005; Lucas and Cousin, 2005; Schrader and Bjorkman, 2006; Markow, 2008). With respect to signal and roadway lighting bulbs, failure methods of a variety of bulb types (LED, sodium, mercury, QL, HPS, etc.) have been assessed for lumen depreciation or time until bulb burnout (Zwahlen et al., 2003; Szary et al., 2005). Statistical techniques used in these studies have included fitting of bulb longevity data using exponential and Weibull probability distributions (Zwahlen et al., 2003) and non-linear regression (Szary et al., 2005). Factors that affect traffic signal life expectancy: Factors influencing the life expectancy of the traffic signal supporting structure include local wind/gust strength, dominant wind direction with respect to the signal orientation, structure material type, type of structural connections, and climatic and weather factors (South, 1994; Chen et al., 2001;

16

Kloos and Bugas-Schramm, 2005; Lucas and Cousin, 2005; Schrader and Bjorkman, 2006; Markow, 2008). With regard to signal bulb life expectancy, significant factors include bulb type, temperature extremes, and other environmental factors (Zwahlen et al., 2003; Szary et al., 2005). For both the structure and bulbs, age, frequency of inspection, and intensity of maintenance have been found significant. Approaches used to determine traffic signal life expectancy: Generally traffic signal maintenance is conducted routinely, however some studies have modeled life expectancy based on performance using fatigue analysis and non-linear regression and duration techniques (South, 1994; Chen et al., 2001; Zwahlen et al., 2003; Kloos and Bugas-Schramm, 2005; Lucas and Cousin, 2005; Szary et al., 2005; Schrader and Bjorkman, 2006; Markow, 2008). 2.4.4 Pavement Markings The performance of pavement marking is usually expressed by its retroreflectivity. This performance index, which is a measure of the amount of light returned to drivers from their vehicle headlights through reflection from the pavement marking, is traditionally accomplished by incorporating glass beads into the marking paint at the time of manufacture or application. The reflected light provides drivers with critical information regarding the road orientation to enable the driver to navigate safely at night. Retroreflectivity is usually expressed in units called candelas/lux/square meter, which is equivalent to candelas/foot-candle/square foot (Jiang, 2008).

The performance of at least 16 different types of pavement marking materials has been tested by researchers. Most studies focus on conventional paint, waterborne paint, epoxy, polyester, and thermoplastic, the five most commonly used pavement marking materials in the United States and Canada (Migletz and Graham, 2002). Within each material type there are variations depending on bead gradation, installation application rate, and color. Past data analyses have typically stratified the marking materials by their color or orientation, the position of pavement markings, and the pavement type (NTPEP 2009). Water-based paint is now the most commonly used pavement marking material. Paint markings are typically 15 to 25 mm thick when applied. Paint drying time depends on the thickness of the application and the chemical formulation. Paint materials often have a lower initial retroreflectivity values and degrade at a faster rate than other pavement marking materials like thermoplastic, epoxy etc. So, they are usually classified as non-durable marking materials. Paint markings can last 3 months to 2 years or more depending on the traffic volume, snowplow frequency, application quality, and other factors (Zhang, 2009).

Glass beads in pavement marking are either pre-mixed into the paint or dropped onto the waterborne paint while the marking is wet to provide retroreflectivity. Such glass beads are dropped on top of freshly applied conventional paints and durable materials such as epoxies. In some cases, portions of the beads are mixed in with paint before it is applied (pre-mixed paint). Glass beads can also be untreated or treated. Treated glass beads have a coating on their surface that enables the bead to sink into the paint, while the untreated beads float on the surface. Having a portion of the beads on the surface and in the paint allow continued retroreflectivity as the paint wears. The proper application of beads is the key in creating the marking’s retroreflectivity (Jiang, 2008).

17

In good management practice, pavement markings are replaced after their useful life is reached. At present, there are no objective standards in place to estimate the life expectancy of pavement markings. However, FHWA’s delineation handbook suggests that durability, color, and retroreflectivity of the markings could be indicative measures (Sathyanarayan et al., 2008). NCHRP Synthesis of Highway Practice 306 (2002) reported that in making pavement marking decisions, state DOTs have either relied on the judgment of maintenance personnel or adopted a fixed-time schedule for replacement: policies specified how and when pavement markings were to be replaced. At certain agencies, decisions are performance-based: field inspections are used to evaluate retroreflectivity, durability, and color performance to determine whether markings should be replaced. At highway agencies, there is increasing use retroreflectometers, both handheld and mobile, to measure retroreflectivity at any time (Migletz and Graham, 2002). The service life of the pavement marking is said to have ‘expired’ when the marking retroreflectivity falls below a specified threshold level.

In response to a Congressional mandate (Department of Transportation and Related Agencies Appropriations Act, 1993), the FHWA is developing minimum retroreflectivity requirements for pavement markings. Various studies, however, have suggested that the threshold level of retroreflectivity, based on driver judgment and preference, should be between 70 and 180 mcd/m2/lux (Abboud and Bowman, 2002; Sathyanarayanan et al., 2008). Migletz and Graham (2002) reported earlier recommendation by FHWA on minimum retroreflectivity level of pavement marking. Those reported values along with calculated mean service lives of different types of pavement markings are presented in Table 3. However, due to the lack of consensus on consistent thresholds, marking life expectancies has not been established from a consistent viewpoint and thus the benefits and consequences of different policies and investment scenarios (application scheduling and material type) remain unclear (Abboud and Bowman, 2002; Markow, 2008).

It is worthy to note from our information search that statistical modeling techniques applied to determination of pavement marking service life have included linear regression model (Lee et al., 1999; Migletz et al., 2001), exponential regression analysis (Abboud and Bowman, 2002), smoothing spline and time series model (Zhang and Wu, 2005), weibull-distributed survival model (Sathyanarayan et al., 2008), multiple linear regression models (Sitzabee et al., 2009), and linear mixed effect model (Zhang, 2009). In most of the studies, predictive models to estimate rate of pavement marking degradation were developed considering mainly waterborne and thermoplastic paints.

Sathyanarayan et al. (2008) and Zhang and Wu (2005) used data from NTPEP test decks while Sitzabee et al. (2009) and Zhang (2009) worked with datasets in North Carolina. Migletz et al. (2001) studied data on pavement marking performance from 85 sites across 19 states; Abboud and Bowman (2002) and Lee et al. (1999) studied data from Alabama and Michigan respectively. However, Zhang (2009) pointed to the replicability limitations of the data from NTPEP test decks such as the transverse orientation of pavement marking in test decks as opposed to longitudinal orientation of edge lines and skip lines in the in-service pavements.

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Table 3: Mean Pavement Marking Service Life in Elapsed Months by Color of Marking Pavement Marking Color Marking Service Life in Elapsed Months

(sample size) by Roadway Type/Speed

Minimum Retroreflectivity (mcd/m2/lux)

as Recommended by FHWA

Non-freeway Non-freeway Freeway Non-freeway Non-freeway Freeway

≤40 mph ≥45 mph >55 mph ≤40 mph ≥45 mph >55 mph

White 39.0 (6) 33.0 (27) 16.9 (54) 85 100 150

White with RRPMs or Lighting 54.0 (6) 54.6 (27) 43.6 (66) 30 35 70

Yellow 39.6 (5) 35.9 (19) 23.4 (28) 55 65 100

Yellow with RRPMs or Lighting 50.6 (5) 46.8 (19) 35.9 (32) 30 35 70

Source: (Migletz and Graham, 2002)

Although a number of explanatory variables were included in these studies, the response

variable was solely retroreflectivity of the pavement marking which was measured by mobile retroreflectometer. A study conducted by Washington State Transportation Center (TRAC) in 2004 utilized a vehicle-mounted retroreflectometer to take measurements on approximately 80 test sections throughout Washington State. The resulting retroreflectivity values from roadways with similar average annual daily traffic (AADT) and environments displayed a significant amount of variability (Kopf 2004). Migletz et al. (2001) also concluded that there was much variation in the performance of identical pavement marking materials at different sites. The variation was due to differences in roadway type, region of the country, marking specifications, quality control, and winter maintenance. They used cumulative traffic passage (CTP) as the explanatory variable which was the cumulative sum of the AADT values over time. Earlier study by Lee et al. (1999) in Michigan developed linear regression model with age in days as the explanatory variable. R2 value was found to be 0.14 for thermoplastic. They concluded that snowfall was highly correlated to deterioration of pavement marking due to snowplowing. However, AADT, speed limit, and percent truck traffic were found to be insignificant factors. Abboud and Bowman (2002) used vehicle exposure, a product of AADT and time, as the explanatory variable and after analyzing retroreflectivity measurements collected at 827 test sites along 520 miles of rural highways in Alabama, they developed logarithmic regression model. The R2 values were 0.58 and 0.31 for thermoplastics and paints, respectively.

Sathyanarayanan et al (2008) developed weibull-distributed survival model that included time as the only predicted variable. Sitzabee et al. (2009) developed a number of multiple linear regression models for thermoplastic and paints and those models had three independent variables (time, initial retroreflectivity, and AADT) as well as line type and color. The R2 values were in the range of 0.38-0.60. Recently, Zhang (2009) has developed linear mixed effect model for longitudinal pavement marking in North Carolina taking into consideration explanatory variables like type of pavements, glass bead density, and of course, age of pavement marking. Factors that affect pavement marking life expectancy: Our information search established that the factors affecting the life expectancy of pavement marking include material type, bead gradations, installation application rates and quality, color, pavement surface type, and roadway positions (centerline, edge), as well as environmental and operational conditions such as annual precipitation, frequency of snow plowing, ultraviolet degradation of color, placement procedure, traffic volume and vehicle class distribution, and traffic speed sections

19

(constant sections vs. acceleration/deceleration sections) (Bowman et al., 1992; Fish, 1996; Harrison and Thamer, 1999; Henry et al., 1999; Migletz et al., 2001; Migletz and Graham, 2002; Parker, 2002; Parker and Meja, 2003; Kopf, 2004; Zhang and Wu, 2006; Jiang, 2008; Lee et al., 2008; Maurer and Bemanian, 2008; Sathyanarayanan et al., 2008). Approaches used to determine pavement marking life expectancy: Like other non-traditional assets, pavement markings tend to be replaced as part of a routine maintenance schedule. However, performance-based linear and non-linear regression and duration models have been calibrated to predict pavement marking life (Lee et al., 1999; Migletz et al., 2001; Abboud and Bowman, 2002; Zhang and Wu, 2005; Sathyanarayan et al., 2008; Sitzabee et al., 2009; Zhang, 2009).

2.4.5 Noise and Crash Barriers Life expectancies of roadside appurtenances such as guardrails and noise barriers have received relatively little attention in the literature despite their importance in reducing severe injuries and reducing noise pollution, respectively. At least one researchers states that some agencies have treated noise barriers, guardrails, signs, signals, etc. as perpetual assets, but such policies have been found to be ineffective (Jha and Abdullah, 2006). From a survey of state transportation agencies, it was found by Li and Madanu (2006) that: only 30% of agencies randomly sample guardrails to determine condition; only 14% of agencies have established a performance index for guardrails; and the primary goal of the agency was to maximize useful service life of the asset.

Investments involving guardrails and other types of crash barriers are typically assessed through cost-effectiveness analysis such as the incremental benefit-cost approach. The Transportation Research Board (TRB) developed the Roadside Safety Analysis Program (RSAP), as part of NCHRP Report 492, specifically for this purpose. This program consists of four modules: encroachment prediction, crash prediction, crash severity prediction, and benefit-cost analysis (Mak et al., 2003). Additionally the performance of safety appurtenances can be evaluated using the recommendations of NCHRP Report 350 and NCHRP Report 490 (Ray et al., 2003; Mak et al., 2003).

The effectiveness of noise barriers is generally evaluated in terms of attenuation. The extent of attenuation, through reflection and absorption, depends on the material used and design features of the barriers. Evaluation guidelines for technical performance have been published by the Highway Innovative Technology Evaluation Center (HITEC) and design guidelines published by Hong Kong’s Environmental Protection Department (Kay et al., 2001; Government of the Hong Kong SAR, 2003).

In the Kay et al. (2001) and Morgan and Kay (2001) studies, eleven different noise barrier materials types (the majority of which are concrete) have been analyzed with regards to their life expectancy in Illinois. Compared to other materials, steel barriers and tropical hardwood and were found to deteriorate shortly after installation; steel barriers deteriorated due to water forming in pockets within the barrier leading to corrosion; and wood barriers due to shrinkage of the material resulting in warping and differential settlement (Kay et al., 2001). Durisol barriers have similarly been found to deteriorate rapidly in Pennsylvania (Hughes and Somers, 2000). Kay et al. (2001) contend that the actual service lives of noise barriers constructed of slowly-deteriorating materials are difficult to determine because they are relatively new to the highway system, typically less than 30

20

years in age. The noise barrier with the longest expected service life and most advantageous properties is considered to be the earth berm because it is relatively maintenance free; has no potential for graffiti degradation, fire damage, or vehicle damage; and has efficient acoustic and aesthetic properties. However, right-of-way may be an issue for installation (Kay et al., 2001) because the wide base of berms requires greater right-of-way width. Service lives for all noise barrier types studied in Illinois are summarized in Table 4.

Table 4: Estimated Service Life for Noise Barriers by Material Type (Kay et al. 2001)

Noise Barrier Material Type Average Service Life (yrs)

Earth Berm 50

Fanwall Precast Concrete 50

Glued Laminated Wood 25

Precast Concrete Cantilever Barrier 50

Precast/Prestressed Concrete Cantilever Barrier 50

Noishield Steel <1

Noishield Aluminum 25

Tropical Hardwood <1-8 initially, 25-30 after re-design

Durisol 25

Precast Concrete Post and Panel Barrier 60

Carsonite Barrier 50

To extend noise barrier service lives maintenance activities, such as painting, are required.

The determination of when to perform such an activity, however, depends on data collection and management strategies.

With roadside appurtenances, data collection and management is a particular challenge. Inspection schedules for barriers are variable, with some states using random sampling to extrapolate asset condition (Li and Madanu, 2006). To handle the challenge of collecting safety hardware data, the Idaho Transportation Department developed the Geographic Roadway Application for Information Location (GRAIL). This system combines video-logging with GPS location, curvature, and length data; the New Mexico and Virginia DOTs similarly uses video-logging. The California DOT (CalTrans) focuses as well on collecting construction data such as how much time is spent working on an asset and what materials and equipment are being used. Storing data is another challenge. For instance, Florida DOT utilizes a single large database called the Roadway Characteristics Inventory (RCI) to store barrier and other data; the Maryland SHA utilizes several separate databases integrated into a shared route system; the Tennessee DOT uses an ORACLE database with a graphic interface (Li and Madanu, 2006). Crash barrier deterioration has been modeled using a Markovian approach with a genetic algorithm for optimization and an adaptive approach to mitigate uncertainties in inspection schedules (Jha and Abdullah, 2006). Probabilistic survival curves have also been developed for guardrails and

other safety hardware (Jha and Abdullah, 2006). material, with wood guardrail posts hav

Noise barrier service lives are currently predicted survey of expected service lives for all noise barriers completed by highway agencies is summarized in Figure 3 (Morgan and Kay, 2001geographic region.

Figure 3: Survey Results for Estimated Average Service LivesHighway Agencies (Morgan and Kay

Table 5: Estimated Service Life for

Region

20 years

Midwest 1

Northwest 0

Southwest 4

Southeast 2

Northeast 1

Source: Morgan and Kay (2001)

Factors that affect noise and crash barrierThese include age, percent length/area of classification/geometric characteristics, pavement condition, accident frequency/severity, barriers (Cardrone, 1963; McCrum and Arnold, 1980; 2006). For sound barriers, performance is a function of receiver and source locations, traffic volume and mix, and time of day, and the s

30 Years; 12%

40 Years; 8%

50 Years; 21%

e (Jha and Abdullah, 2006). Experience shows that service life vawood guardrail posts having a service life of approximately 30 years (Gatchell, 1968).

Noise barrier service lives are currently predicted mostly on the basis of esurvey of expected service lives for all noise barriers completed by highway agencies is summarized

Morgan and Kay, 2001). Table 5 shows a further breakdown of survey results by

Survey Results for Estimated Average Service Lives of Noise Barriers ighway Agencies (Morgan and Kay 2001)

Estimated Service Life for Noise Barriers by Geographic Region

Number Reporting Estimated Service Life

years 25 years 30 years 40 years 50 years

1 2 1 0

1 0 0 0

0 0 0 1

2 0 1 1

1 1 0 3

2001)

noise and crash barrier life expectancy: age, percent length/area of exposed or distressed area,

classification/geometric characteristics, construction techniques/quality (particularly of joints)dent frequency/severity, climate/weather, and traffic volume

Cardrone, 1963; McCrum and Arnold, 1980; Jha and Abdullah, 2006; Li and Madanu, For sound barriers, performance is a function of receiver and source locations, traffic volume

, and the service life of these assets is heavily influenced by the levels of

20 Years; 33%

25 Years; 21%

30 Years; 12%

40 Years; 8%

50 Years; 21%

80 Years; 4%

21

Experience shows that service life varies, by a service life of approximately 30 years (Gatchell, 1968).

mostly on the basis of expert opinion; a survey of expected service lives for all noise barriers completed by highway agencies is summarized

shows a further breakdown of survey results by

of Noise Barriers as Completed by

Noise Barriers by Geographic Region

80 years

0

0

0

0

1

distressed area, material type, road /quality (particularly of joints),

, and traffic volume for crash Jha and Abdullah, 2006; Li and Madanu,

For sound barriers, performance is a function of receiver and source locations, traffic volume these assets is heavily influenced by the levels of

20 Years; 33%

22

precipitation, construction quality (particularly of joints), barrier material type, geographic region, and design details (Kay et al., 2001). Approaches used to determine noise and crash barrier life expectancy: Noise and crash barriers service lives are primarily determined using either expert opinion, however duration models and Markoviian approaches have been applied using a performance-based approach (Gatchell, 1968; Kay et al., 2001; Morgan and Kay, 2001; Jha and Abdullah, 2006). 2.4.6 Pavements

Compared to other asset classes, a relatively large number of research studies have been carried out to predict the life expectancies of pavements. This has been done for different pavement surface material types (rigid, flexible, composite) and different subtypes within each type. Pavement life expectancies are typically measured on the basis of both functional performance indicators such as IRI and PCR (Shiyab et al., 2006) and structural performance indicators such as deflection (Vepa et al., 1996; Zaghloul and Elfino, 2000; Shiyab et al., 2006; Roberts et al., 2007).

Analysis of pavement performance data (for purposes including life expectancy determination) are usually stratified by some combination of climate zone, pavement type, type of construction, treatment type, travel speed, and functional class to reduce heterogeneity (Baker et al., 1998; Al-Suleiman and Shiyab, 2003; Gharaibeh and Darter, 2003; Bausano et al., 2004; Labi and Sinha, 2005). For grouping assets by climate zone, it is recommended to use statistical cluster analysis and Delphi techniques (Colluci et al., 1997). Mechanistic models of pavement performance and thus, life expectancy have been developed at accelerated pavement testing centers nationwide (Breysse et al., 2005; Miradi and Molenaar, 2007; von Quintus et al., 2007). These tests generally involve accelerated aging on the basis of expected traffic loadings. De Pont et al. (1999), among others, analyzed pavement life on the basis of field tests for trucks with various suspensions and for both static and dynamic load. Shekharan and Ostrom (2002) and McManus and Metcalf (2003) developed reliability curves based on traffic loading.

Empirical methods used to estimate pavement service life directly have included the development of non-linear regression models (Lee et al., 2002; Flom and Darter, 2005; Gedafa et al., 2009), artificial neural networks (Ferregut et al., 1999; Abdallah et al., 2000), hazard (typically of the Cox proportional or log-logistic form) or survival models (typically of the Weibull form) (Vepa et al., 1996; Colucci et al., 1997; Romanoschi et al., 1999; Gharaibeh and Darter, 2003; Bausano et al., 2004; Yang, 2007; Yu et al., 2008; Anastasopoulos, 2009; Irfan et al., 2009), interface constitutive model (Ziari and Khabiri, 2005), and probability tables and curves based on various distress indices (Fwa, 1991; Chen et al., 1994). Survival analysis in particular is commonly applied because it eases data collection requirements; the technique takes into account the duration period during which observations are collected, instead of having to wait until a pavement fails (Eltahan et al., 1999).

Overlay service life can be estimated separately with guidelines outline by the American Association of Highway State Transportation Officials (AASHTO); two approaches are generally used: the traditional approach for new pavements and the AASHTO approach for existing pavements (Easa, 1990; Fwa, 1991; Irfan et al., 2009).

23

More typically, planners use statistical and econometric techniques to predict pavement condition or some specific distress; the remaining service life is then the amount of time from the last major treatment until a trigger/threshold value is reached (Ping and He, 1998; Park and Kim, 2003; Gartin and Saboundjian, 2005; Anastasopoulos, 2009). The distress could be either functional/serviceability-related or structural (Vepa et al., 1996). The prediction of pavement condition is more common because it readily allows for a change in policy (i.e., a change in the magnitude of the trigger value). Pavement condition has been modeled using linear regression, Markov Chains, Bayesian statistics, mechanistic-empirical models, artificial neural networks, three-stage least squares, and seemingly unrelated regression (Chou et al., 2008; Anastasopoulos, 2009). Mechanistic-empirical models, however, have been proven susceptible to transferability issues (Gramajo et al., 2007). Remaining pavement strength has been modeled using discrete-time Markov models (Abaza and Murad, 2009). Garcia-Diaz and Allison (1984) recommended a discriminant analysis approach to determine the most influential distress types of pavement longevity.

Other studies have focused specifically on the extension of service life and cost effectiveness of specific rehabilitation or maintenance treatments (Smtih et al., 1997; Eltahan et al., 1999; Rao et al., 1999; Lee et al., 2002; Rajagopal and Minkarah, 2003; Bausano et al., 2004; Labi et al., 2005; Labi and Sinha, 2005; Romero and Anderson, 2005; Labi et al, 2007; Cuelho et al., 2006; Irfan et al., 2009; Khurshid et al., 2009). The timing of the treatment is of essential importance; studies have shown that a preventative maintenance approach extends the remaining service life (Flom and Darter, 2005; Schuler and Schmidt, 2009). Treatment service life can be determined directly from field measurements (typically non-destructive testing (NDT) or accelerated pavement testing (APT)), laboratory tests, or by using post-treatment performance models; however, such models are sensitive to the selected performance measure (e.g., IRI, PCR, PQI, rut depth) and corresponding trigger value (Eltahan et al., 1999; Rao et al., 1999; Romanoschi et al., 1999; Rajagopal and Minkarah, 2003; Labi and Sinha, 2005; Shiyam et al., 2006; Labi et al., 2007; Prozzi and Guo, 2008; Irfan et al., 2009). NDT has become a more common approach for determining service life data, particularly by way of deflection-based methods (Vepa et al., 1996; Zaghloul and Elfino, 2000; Park and Kim, 2003; Roberts et al., 2007; Werkmeister and Alabaster, 2007; Gedafa et al., 2009)

With predicted service life values, these results then have to be incorporated into the pavement management system. The Arizona Department of Transportation have begun using artificial neural networks to select pavement projects at the network level based on a priority rating of uniformly broken up pavement sections (Flintsch et al., 1997). The Kansas Department of Transportation incorporates a sigmoidal econometric prediction model with a network optimization system and annual condition surveys (Gedafa et al., 2009). The decision of when to select a pavement for rehabilitation based on service life has significant economic implications. Due to high maintenance costs of traditional pavements, studies have more recently been evaluating perpetual pavements with their rut- and fatigue-resistant layers; use of these pavements can ease decision-making with structural lives in excess of fifty years (Walubita, 2007).

Due to emerging changes in pavement design approaches, such as the AASHTO Mechanistic-Empirical Pavement Design Guide (MEPDG) (Gramajo et al., 2007; Walubita, 2007; Zuo et al., 2007), the next generation of pavements are expected to have life expectancies that differ from those of present-day pavements. The MEPDG evaluates pavement structures using mechanistic-

24

empirical principles, on the basis of project-specific traffic, climate, and materials data for estimating damage accumulation over a specified pavement service life. Factors that affect pavement life expectancy: Pavement life expectancy factors include surface type (rigid, flexible, and composite) and thickness, construction quality, traffic loading and speeds, structure and overlay age, accumulated climate effects, subgrade moisture conditions, and frequency and intensity of pavement maintenance and rehabilitation (Attoh-Okine and Roddis, 1993; Vepa et al., 1996; Baker et al., 1998; Gharaibeh and Darter, 2003).

For pavement constructed using bituminous asphalt mixes, a number of factors related to fatigue failure have been identified to be influential to the life expectancy (Breysse et al., 2005; Coetzee and Connor, 1990). Environmental effects such as the temperature averaging period, temperature gradient in the asphalt, and timing and duration of wet base and subgrade conditions have similarly been found significant for flexible pavements (Zuo et al., 2007). The life expectancy of pavements constructed using porous asphalt was found to be influenced by mixture properties (Miradi and Molenaar, 2007). The quality and characteristics of aggregates, level of bonding, layer properties, and degree of compaction are additional factors that must be considered when predicting the service life of asphalt (Witczak and Bell, 1978; Noureldin, 1997; Ziari and Khabiri, 2005). Due to such characteristics, different asphalt mixtures have different life expectancies (e.g., dense-graded conventional asphalt concrete and gap-graded asphalt rubber hot mix); the quality and thickness of the pavement base material is also influential (Raad et al., 1993; Romanoschi et al., 1999). The service life hot mix asphalt pavements was studied by Von Quintus et al. (2007).

For non-overlaid continuously reinforced concrete pavements, early-age crack distribution patterns, coarse aggregate type, and the presence of a swelling subgrade have been found significant for predicting remaining service life (Easley and Dossey, 1994; Dossey et al., 1996). For other types of materials used for constructing pavements assets, the traffic speed, precipitation, and drainage properties have been found to be significant in determining service life (Huntington and Ksaibati, 2007).

The information search showed that studies on pavement asset life expectancy have utilized a wide range of pavement performance indicators including pavement structural condition (PSC), visual condition index (VCI), distress points/index (particularly rutting, punchouts, transverse, fatigue, and D-cracking distresses), pavement quality indicator (PQI), measures of roughness (i.e., international roughness index (IRI), dynamic load index (DLI), and road quality index (RQI)), effective structural number, center deflection (Fwa, 1991; Attoh-Okine and Roddis, 1994; Henning et al., 1997; Baker et al., 1998; Abdallah et al., 2000; Kuo et al., 2000; Lee et al., 2002; Al-Suleiman and Shiyab, 2003; Gharaibeh and Darter, 2003; Baladi, 2006; Huntington and Ksaibati, 2007; Chou et al., 2008; Gedafa et al., 2009). Approaches used to determine pavement life expectancy: Given the extensive amount of data collected by pavement-managing agencies, life expectancy is generally determined via performance-based methods. Both mechanistic and empirical data have led to the common development of linear and non-linear regression models, Markov chains, duration

25

models, neural networks, and interface and finite element analyses (Garcia-Diaz and Allison, 1984; Fwa, 1991; Chen et al., 1994; Vepa et al., 1996; Colucci et al., 1997; Ping and He, 1998; De Pont et al., 1999; Eltahan et al., 1999; Ferregut et al., 1999; Romanoschi et al., 1999; Abdallah et al., 2000; Lee et al., 2002; Shekharan and Ostrom, 2002; Gharaibeh and Darter, 2003; McManus and Metcalf, 2003; Park and Kim, 2003; Bausano et al., 2004; Breysse et al., 2005; Flom and Darter, 2005; Gartin and Saboundjian, 2005; Ziari and Khabiri, 2005; Gramajo et al., 2007; Miradi and Molenaar, 2007; Von Quintus et al., 2007; Yang, 2007; Chou et al., 2008; Yu et al., 2008; Abaza and Murad, 2009; Anastasopoulos, 2009; Gedafa et al., 2009; Irfan et al., 2009). 2.4.7 Bridges Given the current highway environment which is characterized by funding limitations, agencies seek to wring out maximum service lives from their existing highway assets through stop gap measures such as rehabilitation and maintenance. However, there are safety and economic risks in unduly delaying reconstruction. This state of affairs becomes more stark upon the realization that nearly a third of the bridges in the United States are considered deficient and will require over a billion dollars a year to bring up to acceptable performance levels (Estes and Frangopol, 2001). It is therefore critical for agencies to be equipped with analytical tools that would enable them to estimate the remaining life expectancies of their highway assets such as bridges.

Bridge life expectancies are often predicted through the forecasting of discrete condition ratings (e.g., NBI nine point scale), with a preset threshold, or trigger, rating. Triggers in bridge management, which are key to establishing service lives of bridges, have been determined using reliability analysis (Lin, 1995). Chang and Garvin (2008) investigated the inherent trade-offs in different levels of activity triggers in terms of bridge quality and service life.

A more basic method is to rely on visual inspection; Fitch et al. (1995) developed a linear regression model to relate visual condition ratings to actual physical damage. This was based on a survey of engineers at Snowbelt states whose expert opinions were solicited regarding the appropriate times to apply specific treatments. In studies of that kind, the performance indicator used to express the trigger is of importance: a change in trigger value can lead to significant changes not only in the asset service life, but also in the investment consequences in terms of the life cycle costs. For example, there is a trade-off relationship between safety costs and service life costs; the strategy to minimize accidents may not be the same as the strategy to extend service life, therefore a multi-objective genetic algorithm (MOGA) can be used (Furuta et al., 2003; Van Noortwijk and Frangopol, 2004).

Empirical methods that have been applied to predict overall bridge service life have included survival probability curves (Lin, 1995; Lounis, 2000; Estes and Frangopol, 2001; Akgul and Frangopol, 2004; Biondini et al., 2006; Saber et al., 2006; Oh et al., 2007; Strauss et al., 2008), linear and non-linear regression (Rodriguez et al., 2005), neural networks (Narasinghe et al., 2006), ordered probit models (Rodriguez et al., 2005), constitutive models using the Lamb wave technique (Desai, 2001), and Markov chains (Jiang and Sinha, 1989; Estes and Frangopol, 2001; Zhang et al., 2003; Hallberg, 2005; Morcous, 2006; Ertekin et al., 2008).

Other studies have focused on the life expectancy of individual bridge components (deck, overlay, substructure, etc.). Service life can then be looked at as a series or parallel system. A series

26

system would mean that once a single component falls below a corresponding trigger value, the service life is reached; a parallel system would mean that the service life is reached once all components fail (Lin, 1995; Estes and Frangopol, 2001). With a series system, it is particularly important to be aware of all component deterioration levels; for instance, minor maintenance procedures such as painting can reduce service life if deferred (Testa and Yanev, 2002). In Pontis 5.2, the life expectancies of individual elements are combined by simulating element deterioration and traffic growth over a long period of time, and accumulating the separate maintenance, mitigation, and functional needs until a cost threshold is reached.

Bridge decks are the most commonly studied component of bridges (Bettigole, 1989; Adams, 2002; Kirkpatrick et al., 2002). It has been claimed that deck service life tends to be one-half that of the overall bridge structure (Bettigole, 1990). Even within different deck types, life expectancies vary. For instance, decks with waterproofing membranes were found to have longer service lives than bare decks; decks with epoxy-coated or galvanized reinforcement typically outlast plain reinforcement decks by 5 years (Hearn and Xi, 2007). Decks in entirety, and wearing surfaces in particular, have had service lives modeled using survivor curves taking the form of Rayleigh and exponential distributions (Hearn and Xi, 2007). However, deck service lives have been found to vary by geographic location, depending on external factors such as climate and weather patterns (Hearn and Xi, 2007). While decks bear the brunt of the loading, expansion joints are also a concern because if these are not closed, further deterioration can occur. Purvis (2003) outlines joint treatments that could be used to extend the life of bridge decks. The service life of bridge coating has been modeled separately (Zemajtis and Weyers, 1995). The success of treatments on individual bridge components is also variable, as evident by the scattered treatment life estimates provided during a national survey for the Strategic Highway Research Program Project C-103 (Chamberlin and Weyers, 1991).

Data for such approaches are typically collected during bridge inspections conducted every two years, as mandated by AASHTO (Lin, 1995; Lund and Alampalli, 2004; Zhou, 2006; Hearn and Xi, 2007). However, Caner et al. (2008) developed a framework to predict the remaining service life based on a single condition assessment and the age of a bridge. Models of inspection data are then usually assessed by some combination of geographic location, bridge type, traffic volume, rehabilitation history, and by environmental considerations to reduce heterogeneity (Estes and Frangopol, 2001; Rodriguez et al., 2005).

Mechanistic models are also commonly applied to predict service life as a function of

corrosion. Corrosion occurs in three stages (Liang et al., 2002): 1. Initiation time – The time for chloride ions to penetrate the concrete surface and onto the

passive film surrounding the reinforcement. 2. Depassivation time – The time for the chlorides, transported to the steel by the alkaline

hydrated cement matrix, to locally destroy the passive film leading to pitting corrosion 3. Propagation or corrosion time – The time when corrosion products form until cracking,

spalling, or sufficient structural damage occurs.

Generally, the first two stages are modeled together and can jointly be considered as the initiation time. Attempts to model these time stages are shown in Table the service life is then the sum of the two time periods.

27

The most common for predicting corrosion stage times is Fick’s law (Daigle et al., 2008). The recommended approach is outlined in NCHRP Report 588 (Sohanghpurwala, 2006a).

Models for describing the progression of other defects (and thus the asset service life) have included finite element analysis (e.g., to model crack growth) (Lu and de Boer, 2006; Samson and Marchand, 2008) and fatigue analysis (e.g., application of Miner’s hypothesis) (Lipkus and Brasic, 2007). Fatigue life of steel bridges can be calculated using the AASHTO Guide Specifications for Fatigue Evaluation of Existing Steel Bridges; the time of occurrence of the failure mechanism described in the AASHTO guide, has also been modeled (Lund and Alampalli, 2004; Metzge and Huckelbridge, 2006).

The primary obstacle in bridge life expectancy predictions are the uncertainties regarding unknown material properties, corrosion initiation and propagation times, structural dimensions, loading, structural resistance, environmental conditions, inspection techniques, limited observations, environmental, time to corrosion, and corrosion rate, material properties, geometrical parameters, area and location of the reinforcement, material diffusivity and damage rates and the use of idealized models (Lin, 1995; Val et al., 2000; Biondini et al., 2006; Anoop and Rao, 2007; Williamson et al., 2007; Ertekin et al., 2008). Various software packages have been developed to predict bridge service life. The Wisconsin Highway Research Program developed a spreadsheet tool to construct performance curves, estimate service lives, and optimize life-cycle costs by selecting a trigger value for various treatments including patching, concrete or asphaltic overlays, and reconstructed bridge decks with epoxy coated bars (Hyman and Hughes, 1983; Adams et al., 2002). NCHRP 463 developed a similar bridge life-cycle cost analysis (BLCCA) spreadsheet to help select between bridge preservation alternatives (Hawk, 2003). NCHRP 14-15, nearing completion, will further present rigorous methods for capturing maintenance management system data and applying the information to models predicting treatment effectiveness. Other software has focused on predicting time-to-corrosion service lives such as the Life-365 program (Hooton et al., 2009). Lin (1995) developed an interface combining reliability-based (i.e., MCREL) and optimization (i.e., ADS) programs. SLAB-D is another reliability-based software package (Daigle et al., 2008). The most commonly applied bridge management software include PONTIS and Bridgit which apply Markov-chain models (Morcous, 2006). The Indiana Bridge Management System (IBMS) is also available to ease decision-making (Saito and Sinha, 1990). Knowledge of factors influencing bridge life expectancy are essential for life-cycle decisions in bridge management. With models to predict remaining service lives, asset managers can determine which bridges require a treatment and when. Knowing the causes of deterioration can also influence preservation strategies. For instance, to slow the ingress of chlorides in concrete structures, planners have used low-permeability concretes, polymer overlays, deck sealers, increased concrete cover depth, cathodic protection, and looked into alternative reinforcements (Kirkpatrick et al., 2002). Cope and Labi (2009) studied the effects on service life and life cycle costs for stainless steel and other high strength reinforcements.

28

Table 6: Prediction of Corrosion Time Stages (Liang et al. 2002) Time Prediction

Method Formula Reference

Initiation Time, t1

Weyers ���, �� = �√� 1 − erf � �2������

Weyers (1998)

LZCL ���, �� = �� + ������ − ���erfc � �2���������

Liang et al. (2001)

Hookham

� = ��� �! + �"� Hookham (1992)

AJMF ���, �� = #� $�1 + �!2���� erfc � �2�����

− � ��%���� ��&'/)*+�,

(1)

Amey et al. (1998)

���, �� = #√� $��&'/)*+� − �√%�%���� erfc � �2�����,

(2) Guirguis � = -.��

Guirguis (1987)

Bazant

� = -12�� /0 -

1 − 1�∗�345

!

Bazant (1979b)

Propagation time, tcor

Bazant ��67 = 8�67 �9 Δ�∗;7 , Δ�∗ = 2<′� -� >??

Bazant (1979b)

Modified Bazant ��67 = 8�67 �9 Δ�∗

;7 , Δ�∗ = <′� @2 A-�B + 1C >??

Proposed

CW ��67 = 2~5 years Cady and Weyers (1984)

Liu ��67 = J�7��!2#?

J�7�� = 8�67 $% -<′�K L �M! + N!M! − N! − O�� + PQ� � + J��8�� ,

#? = 0.098 1V %�W�677 , V = 0.57

Liu (1996)

Faraday’s Law ��67 = >8��YZ[W�677

Fontana (1987) Mangat and Elgarf (1999)

29

Factors that affect bridge life expectancy: The factors that influence the life expectancy of concrete bridges are similar but not identical to those that influence the life expectancy of steel bridges. For concrete bridges, the factors include freeze index, cumulative precipitation, span length, age since last treatment, overall age, superstructure material type, construction technique, wearing surface type, bond strength of overlay with bridge deck, number of spans, highway functional class, repair history, deck area and percent distressed area (i.e., spalled or delaminated), evaluation methodologies, traffic volume, wheel locations, and accumulated truck load (Chamberlain and Meyers, 1991; Adams et al., 2002; Testa and Yanev, 2002; Rodriguez et al., 2005; Chang and Garvin, 2008). Of these, freeze index is considered the most influential (Rodriguez et al., 2005). Truck loading, in particular, has been studied extensively (Saber et al., 2006; Chang and Garvin, 2008). In terms of bridge material type, deterioration of concrete bridges can occur due to corrosion, fatigue, temperature, and/or collision causing change in strength and stiffness (Lin, 1995). Primarily, concrete deterioration is caused by corrosion of reinforcement steel which in turn is a function of chloride concentration, diffusion coefficient, average depth of bar cover, size and spacing of reinforcement, concrete type, type of curing, amount of air entrainment, carbonation, and water-to-cement ratio (Estes and Frangopol, 2001; Adams et al., 2002; Kirkpatrick et al., 2002; Liang et al., 2002; Melhelm and Cheng, 2003; Nowalk and Szerszen, 2004; Sohanghpurwala, 2006b; Hearn and Xi, 2007; Oh et al., 2007; Wood and Dean, 2007; Daigle et al., 2008; Parameswaran, 2008). Chlorides reduce alkalinity of water solution leading to rust (i.e., corrosion process), which expands, effectively causing a loss in reinforcement area, leading to distresses in the bridge deck. Chloride content is a function of concrete age, roadway functional class, and salt rate from either bodies of water or de-icing chemicals during winter maintenance (Adams et al., 2002). Chloride content is considered low at concentrations less than 2.4 kg/m3, moderate when between 2.4 and 4.7 kg/m3, high when between 4.7 and 5.9 kg/m3, and severe when above 5.9 kg/m3 (Liang et al., 2002).

In the case of steel bridges, deterioration trends (and hence, life expectancy) have been found to be influenced by the bridge age, volume of truck traffic, truck size distributions and configuration, and weight, cumulative precipitation, freeze index, road classification, type of wearing surface, degradation of individual component, fatigue durability, span length, and number of hot days (Rodriguez et al., 2005; Lu and de Boer, 2006; Lund and Alampalli, 2004; Lipkus and Brasic, 2007). The main cause of deterioration in masonry arch bridges are axle loads (Narasinghe et al., 2006).

Approaches used to determine bridge life expectancy: As with pavements, bridges have been studied extensively in the past and typically have life expectancies determined by performance. Mechanistic and empirical models are commonly applied including finite element and fatigue analysis, time to corrosion analyses, discrete choice models, linear and non-linear regression, Markov chains, duration models, and neural networks (). Jiang and Sinha, 1989; Fitch et al., 1995; Lin, 1995; Lounis, 2000; Desai, 2001; Estes and Frangopol, 2001; Liang et al., 2002; Zhang et al., 2003; Akgul and Frangopol, 2004; Hallberg, 2005; Rodriguez et al., 2005; Biondini et al., 2006; Morcous, 2006; Saber et al., 2006; Narasinghe et al., 2006; Hearn and Xi, 2007; Oh et al., 2007; Chang and Garvin, 2008; Ertekin et al., 2008; Strauss et al., 2008

30

2.4.8 Alternative Asset Classes (Vehicle Fleets, Equipment, and Utilities) To further learn of how life expectancies are determined, a brief literature review of alternative asset classes (e.g., vehicle fleets, equipment, and utilities) was conducted. Primarily, it was found that service life estimates for these other asset classes are based on expert opinion and historical financial records. In the fleet management field, expert opinion and historical records are primarily utilized to determine a range of life expectancies for different vehicle classifications. Based on this range, federal regulations are often enforced on government vehicles. For instance, the U.S. federal government requires that vehicles meet a minimum number of years or miles before being replaced (e.g., 3 years or 60,000 miles for sedans/station wagons and 6 years or 50,000 miles for light trucks), unless extensive mechanical repairs are needed (Treasury Board of Canada Secretariat, 2007). Surveys of fleet managers across the United States and Canada found that on average: business fleets survive 82,000+ miles or 4+ years, government/public-sector fleets survive 100,000+ miles or 7+ years, and private utility fleets survive 103,000+ miles or 5+ years (Treasury Board of Canada Secretariat, 2007; Fleet Management, 2008). The use of two standards is duly noted for this research. Highway assets can be considered to need replacement due to multiple measures other than age, including the accumulation of climatic or traffic loadings. Construction equipment service lives are typically determined through either expert opinion or analyses of historical cost records. For equipment, life expectancies are considered to be reached when a unit is no longer profitable. Therefore, economic service life is often studied with life cycle cost assumptions for interest rates, tax rates, etc. One past study did a statistical analysis of economic service life of tower cranes, concrete mixers, and hoists in which the annual equivalent equipment costs as a percentage of purchase price was calculated over a range of years, the service life was then taken once as the time until a threshold value was reached (Selinger, 1983). A similar methodology, described in Chapter 4, is proposed in this research. Selinger (1983) also noted that a range of service life estimates should be developed based on varying assumptions. Considering this fact, the research team has developed methodologies to conduct sensitivity analyses and will develop ranges of estimates based on probabilistic techniques.

The need for accurate equipment service lives has become increasingly apparent through the recent developments of management systems. Depending on equipment lives, warranties, and other factors, an agency must decide upon a certain level of mechanic staffing. The Missouri DOT has most notably been working on developing models to help optimize the level of staffing as a function of equipment life and repair needs (Fluharty, 2000). Effective maintenance management systems can help achieve cost savings through both optimal staffing and performing preventative maintenance to extend equipment life (Fluharty, 2000). Likewise, through the determination of highway asset life expectancies, asset management systems can be run more effectively to help lower costs. As with most non-traditional assets, utility service lives are calculated through expert opinion and historical records. For instance when predicting the service life of wooden utility poles, one past study analyzed both purchasing records, to determine the time until replacement (an interval-based approach), and survey results of agency experts (Morell, 2008). Typically, it was found that experts tend to underestimate the service life of utility poles, yet results vary widely due to various factors that may lead to pole replacement such as decay, upgrades becoming available, road widening, car/pole interactions, and storm damage. The condition-based service life of such poles is a factor of: the material specification, quality of treatment, climatic conditions, and maintenance. Similarly, for our study, it is important to recognize the existence of alternative rationales for asset replacement, as well as to try to collect data on material types, climate conditions, and levels of maintenance. Given the importance of setting pole replacement and inspection intervals, studies have started focusing on

31

GIS inventory databases to help track pole locations, material types, and other factors (Quiroga and Pina, 2003).

There have been numerous different methodological approaches to predict the condition of drainage pipes and majority of those use operation research tools like linear programming, dynamic programming and Markov chain methods. The use of cohort survival model for infrastructure deterioration can be traced back to 1987 and sewer deterioration can also be described by a cohort survival mode where cohorts are sewers of the same period of construction and those share few other characteristics like material, diameter, bedding and sub soil characteristics. Survival curves can be used to forecast number of years a particular sewer may take to enter a critical condition (Baur and Herz, 2002). The Factor Method by ISO (1997) is another method used to estimate service life of built components. This method multiplies the reference service life of the component by factors affecting it. The value of these factors can be determined by using a Delphi process or by individual experience. Flourentzou et al. (1999) divided the life of every built element into four subjective condition states: good, fair, poor, and needs replacement and they used field data to estimate the age distribution of a component in any condition state. Then they estimated the time replacement and the expected costs by using conditional probabilities. Abraham et al. (1998) as well as Kathula and McKim (1999) modeled the deterioration of sanitary sewers using Markov Chain while Ariaratnam et al. (1999) used a multinomial logit model to model the performance of sewer network.

In recent years, Ana and Bauwens (2007) described a review of selected sewer asset management decision-support tools, notably those used in performance modeling. The tools included Baik Model, used in the USA, Bengassem and Bennis model, used in Canada, and Hasegawa et al. model, used in Japan. The Baik model estimates the transition probabilities of different condition states in Markov chain-based deterioration models, using an ordered probit model (Baik et al., 2006). The Baik Model estimates transition probabilities and in doing so, it requires data from the condition assessments of the existing system. Internal inspection is required for structural assessment, while the model is used for hydraulic assessment. The pipe condition rating is calculated based on maintenance and structural points which are evaluated using criteria like deformation, presence of roots etc. The Bengassem and Bennis model, as reported by Ana and Bauwens (2007), is a combination of structural inspection and hydraulic simulation to evaluate the condition of the components of the sewer network. Later, fuzzy theory is applied at the pipe sections level to integrate all the evaluation factors, to come up with a performance assessment of the sewer network. Finally, Hasegawa et al. (1999) model estimates the degree of necessity of repairs for existing sewer pipes. This model is based on four points, namely a decrease in flow capacity, road collapse possibility, sewer overflow and flooding as influenced by inflow/infiltration, and an increase in treatment cost due to inflow/infiltration. These models use a number of data to predict the performance of sewer network.

Factors considered while modeling the performance of sewer network include material, age, type, diameter, thickness, shape, slope, defects, and roughness of pipe, depth and location, soil and groundwater, type of joints, flow and leakage, date of construction and repair history, traffic or road condition etc. 2.5 Summary of Information Search Results From past studies, the research team has obtained various definitions and measures of life expectancy, determined significant life expectancy factors, as well as identify general approaches and specific, statistical techniques used to determine life expectancies for a variety of highway assets.

An asset is considered to reach its life expectancy when it has either physically deteriorated to an acceptable condition or is no longer useful in terms of the service it provides. Measures of life expectancy are typically the asset’s age in years at the time the asset reaches its life expectancy.

32

However, service life has also been found to be measured in terms of accumulated traffic loading and climatic effects. General factors that have been found to be the most significant in predicting asset life have included:

• Asset characteristics (age, construction/design type, predominant material, structure type, size, color, etc.)

• Site characteristics (climate, weather, soil classification, soil chemistry, proximity to coast, etc.)

• Traffic/Loading characteristics (traffic volume, speed, % trucks, etc.) • Repair history (maintenance/rehabilitation intensities and frequencies, etc.)

Therefore, the research team has focused its data collection efforts on obtaining such information. In the application step, this list can be further narrowed down to more specific, significant factors for which agencies should focus their resources towards obtaining data. Approaches used in the past to determine life expectancy has generally fallen into three categories:

• Expert opinion • Observed historical asset lives

• Asset performance Adaptations, particularly of the latter two approaches, are highlighted in more depth in Chapter 4. The most common statistical techniques applied to these approaches have included various forms of:

• Statistical regression (Linear and non-linear)

• Markov chains • Survival/reliability models • Machine learning/neural networks

Having learned from these findings, the remainder of the report will focus on the availability of data, recommended life expectancy and sensitivity methodologies, as well as demonstrations of the methodologies.

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CHAPTER 3 – ASSESSMENT OF DATA AVAILABILITY

3.1 Data Availability To date, data sources for this project include state transportation agencies, AASHTO’s National Transportation Product Evaluation Program (NTPEP), the National Bridge Inventory (NBI) database, the FHWA-managed Strategic Highway Research Program’s Long-Term Pavement Performance study (LTPP), the National Oceanic and Atmospheric Administration (NOAA), for climate data, and the Natural Resources Conservation Service (NRCS) for soil data. Even as the research team proceeds to the next stage of the research, we are continuing to solicit data at state highway agencies in order to have a stronger basis for demonstrating our developed methodologies. The data collection is particularly focused on lesser-studied assets such as traffic signs and signals, roadway lighting, and guardrails and also on hard-to-obtain data items such as asset maintenance/repair histories. State DOTs that have provided data so far are listed in Table 7.

Also, the following states have expressed a willingness to share additional data: California, Missouri, New York, North Carolina, and Utah.

Table 7: Collected DOT Data by Asset Type ASSET TYPE SOURCE(S)

Pavement Colorado*, Florida*, Indiana, Virginia, New York, North

Carolina, North Dakota, Ohio*, Oregon, South Dakota

Bridge Illinois, Iowa, Minnesota, Rhode Island, Vermont,

Virginia, New Jersey*

Culvert Illinois, Minnesota, New York, Pennsylvania, Vermont,

Virginia

Pavement Marking Mississippi, Pennsylvania, Utah

Traffic Sign Arizona, Florida, Indiana, Louisiana, Minnesota, New

Jersey*, New York*, North Carolina, Rhode Island*,

Virginia*

Crash Barriers / Guardrails Pennsylvania*, Wisconsin

Traffic Signals and Roadway Lighting Kentucky*, New Jersey*, Pennsylvania*, Rhode Island

Noise Barriers N/A

• The data provided lacks certain key data items such as asset condition or age.

Where different measures of asset condition (e.g., culvert visual condition rating) exist

between the states, universal measures will be applied with clearly defined condition states. While several state agencies have been cooperative, it has become apparent that without

established asset management systems little historical data is available for non-bridge and non-pavement assets. As noted in Table 7, data provided by some highway agencies are difficult to use in this study because they lack certain key data items such as asset age or condition or historical replacement data. Oftentimes, DOTs maintain only an inventory of assets without condition ratings. Also, there are those that maintain the current condition and do not archive historical data beyond a

34

year or more. As such, several of the state agency databases lack information on maintenance histories (this is particularly the case with assets that have relatively infrequent inspection rates). In many databases, the most recent preservation activity is available for most pavement, bridge, and culvert assets. Therefore, additional data collection will be critical for developing robust models for the lesser studied assets. To increase our dataset size, the research team has offered to sift through rough databases for needed information and to calibrate state-specific models in exchange for copies of asset databases. In addition to state databases, data from national databases such as the NTPEP are being analyzed. Using the NTPEP Datamine service, traffic safety, construction, and maintenance data can be obtained at http://data.ntpep.org/home/index.asp. Arizona, Florida, Louisiana, Minnesota, Mississippi, North Carolina, Pennsylvania, Utah, Virginia, and Wisconsin all have provided data for the past ten years to the program. The database includes climate data (temperature, precipitation, and humidity), location data, material data (e.g., for traffic signs - type of sheeting material, composition, and color), inspection data (interval, retroreflectivity, luminance, cracking, blistering, appearance, and shrinkage), etc. Historical pavement marking and traffic sign retroreflectivity data, as well as weather data, are considered to be of great use. However, the database currently lacks traffic data. The research team is in the process of trying to obtain such information for the test sites.

The National Bridge Inventory (NBI) database for bridges and large culverts (which consists of geographic information, structural and material types, traffic loadings, age, condition ratings, reconstruction history, etc.) is being analyzed. Data from the periods of 1992-2009 for all fifty states are currently available with new structural inspection data reported at least every two years.

With regard to pavement data, the Strategic Highway Research Program-developed Long-Term Pavement Performance (LTPP) database, now managed by the FHWA, is being used for data collection. This database contains thousands of observations for pavements across the United States with data on pavement structural composition, material properties, traffic loading, climatic conditions, pavement conditions, construction/maintenance factors, and design features. Using the data on asset location (longitude and latitude) provided by the state and national asset databases, the research team obtained appropriate climate and soil data from the National Oceanic and Atmospheric Administration (NOAA) and the National Resources Conservation Service (NRCS) data platforms, respectively. From the NOAA database, thirty year annual normals (averages) are available at the climate divisional level (approximately 8 per state) consisting of average temperatures, precipitation values, and heating and cooling degree-days. In addition, using the primary data available at the NOAA data platform, we are calculating the average number of freeze-thaw cycles for each climate division, and predominant wind direction, speed, and peak wind gusts are available by city. The NOAA also maintains an extreme-event database consisting of historical records of floods, tornadoes, etc. with information including the magnitude of the event, when it occurred, and property damage from the event.

From the NRCS database, various soil properties are available at the soil survey area level (each area is approximately represented by a county). Soil properties of interest to the research team include soil pH, liquid limit, plasticity index, soil erodibility, salinity, sodium absorption, cation exchange capacity, percent calcium carbonate, gypsum, sand, silt, and clay, potential for frost action, risk of corrosion of steel structures or rebar, and ponding and flooding durations and frequencies.

35

3.2 Geographic Representation of the Data Collected To enhance the implementability of the developed methodologies, the Research Team seeks to demonstrate the capability of the methodologies using data from a geographically diverse set of states. Where enough data exists in each region, the research team is stratifying the data into groups that will minimize heterogeneity within each group and maximize heterogeneity between each group. More efficient statistical/econometric models can be developed for assets sharing similar climatic, material, and traffic characteristics, as well as repair histories. Climate zones, such as those shown in Figure 4 are particularly important for this research study because freeze-thaw cycles and precipitation have been found to be one of the main causes of deterioration across all assets. On the basis of collected data to date (which are presented in Table 7), geographic representations of data availability at the time of reporting are highlighted in the Figures 5 to 11.

Figure 4: Climate Zones as determined by the Strategic Highway Research Program (SHRP)

36

Figure 5: Availability of Pavement Data (besides LTPP data)

Figure 6: Availability of Bridge Data (besides NBI data which covers all 50 states)

37

Figure 7: Availability of Culvert Data (in addition to NBI data which covers all 50 states)

Figure 8: Availability of Road Sign Sheeting Material Data

38

Figure 9: Availability of Pavement Marking Material Data (From NTPEP)

Figure 10: Availability of Crash Barrier / Guardrail Data

39

Figure 11: Availability of Traffic Signal and Roadway Lighting Data

As seen in Figure 7 and Figure 10, data from the southern and western geographic regions is currently lacking for culverts and safety appurtenances. Pavement marking data from Pennsylvania, Mississippi, and Utah are readily available via National Transportation Product Evaluation Program (NTPEP), but these lack specific location data and traffic data (Figure 9). Also, pavement marking data on assets at the Midwest region are still not available and are being aggressively sought by the Research Team. The case for traffic signal and roadway lighting data is similar: the data collected so far are incomplete (key data items such as condition or age is missing or historical replacement data is not available). The Research Team has reinforced its data collection efforts to acquire data of this kind for the study. 3.3 Summary of Data Collection Needs Based on the geographic representation of the collected data, the research team is now focusing upon obtaining the following information from the southern and western regions of the United States:

1. historical replacement data (if available) 2. a condition rating or performance measure with a corresponding age 3. material and/or structural type of the asset 4. the county the asset is located in (so as to lookup climate, soil, and extreme event data from

other sources) 5. maintenance history of the assets 6. traffic loadings (for applicable assets) 7. any other additional data that may be readily available and easily transferable

40

CHAPTER 4 –METHODOLOGIES FOR LIFE EXPECTANCY

ESTIMATION

4.1 Introduction In this Chapter, we present the methodologies we have developed for life expectancy estimation. The methodologies can be applied across different dimensions to accommodate the variability of different geographic locations and asset material and structural types. The analysis was carried out on the basis of general and specific methodologies. Then for each type of methodology, the analysis occurs at three levels of dimensions that are outlined in the following section. The chapter discusses the dimensions of the analysis and describes the underlying general and specific methodologies for the analysis. 4.2 Dimensions of Analysis To determine the service life of any asset, three levels of dimension of analysis are considered in this study: the first dimension relates to the basic asset attributes; the second dimension relates to the nature of the data; and the third attribute relates to the modeling techniques. First level dimensions

• Asset class or type (e.g., bridge, crash barrier, culvert, pavement, pavement marking, roadway lighting, traffic sign, traffic signal)

• Structural type (e.g., for culverts: box/frame, pipe, etc.) • Material type (e.g., for culverts: concrete, steel, etc.)

Second level dimensions

• General methodology (i.e., condition-based, interval-based) • Nature of dependent variable (i.e., discrete, continuous) • Nature of data (i.e., cross-sectional, time-series, panel)

• Geographic representation of data (e.g., SHRP Climate zone, FHWA district number, state-specific)

• Explanatory variables available (e.g., AADT, frequency of preservation activities) Third level dimensions

• Model specification type (i.e., deterministic, probabilistic) • Specific methodology (i.e., (non)linear regression, discrete choice models, duration models,

Markov chains, neural networks) • Goodness-of-fit (GOF) measures (e.g., R2, validation plots, RMSE)

Based on the selections made at each level, different approaches in the following dimensions may

be recommended. For instance, if an asset manager would like to predict the service life of a steel, box culvert (1st level), then a condition-based approach to predict a discrete visual condition rating

41

may be applied given the lack of historical replacement data (2nd level), which would then suggest that a discrete choice model may be the most appropriate (3rd level). Further detail on such condition-based methods and other general approaches are provided in the chapter. Before we proceed to provide details on the dimensions, we discuss the general and specific methodologies for the life expectancy analysis. 4.3 General Methodologies Two general methodologies are proposed: condition-based and interval-based. The condition-based approach relies on the prediction of an asset’s physical or operational condition as a function of age and other explanatory variables. The service life would then be represented as the time at which an asset reaches a level of irreparable damage. The interval-based approach relies on the direct prediction of time until an asset needs to be retired, replaced, or removed from service due to poor performance/condition, the occurrence of an extreme event (e.g., flood), or some other dominating criteria. Selecting between the methodologies will be a function of data availability, agency preferences, and the goodness-of-fit of the models used in each approach. 4.3.1 Condition-based Through a condition-based approach, agencies would have the flexibility to assess how service life changes given different thresholds in performance, as well as the ability to identify the most significant factors influencing the physical or operational performance of an asset. Generally speaking, this approach involves the prediction of a deterioration curve such as that shown in Figure 12.

Figure 12: Condition-based Determination of Asset Service Life

The asset life is then measured from the time of construction or reconstruction until the time

that asset performance falls below an agency-established threshold level. Such a level would

42

represent a state of irreparable damage, that is, at that point, the application of any maintenance/rehabilitation activity would not be enough to effectively extend the life of the asset. This approach is considered particularly effective for agencies lacking historical replacement data that are needed for an interval-based approach. Such data is typically not available to transportation agencies due to the lack of an asset management unit, poor bookkeeping, and/or the loss of hand-written records (particularly for assets with longer service lives). Given that many DOTs at least maintain a database reflecting the current condition of their assets, more observations are available to be studied using a condition-based approach leading to the development of more accurate models. Various measures of condition can be assessed, these can be classified as either continuous performance measures (e.g., retroreflectivity) or discrete condition states (e.g., visual condition rating). For assets with multiple feasible measures of condition (e.g., pavements – IRI, PSR, rutting index), service life can be taken as the minimum amount of time until any one of the measures reaches an established threshold. 4.3.2 Interval-based Alternatively, an interval-based method can be applied to predict service life using any of the following approaches:

• Observed historical average lives of assets in a given class • Time until an extreme event (e.g., flood, earthquake) is considered likely to occur based on

annual, historical records • Time until maintaining asset is no longer considered financially viable

Historical average life ( Figure 13) in particular will be useful to validate any developed models. As with the condition-based approach, the minimum amount of time until any ‘failure mode’ (e.g., extreme event, accumulated damage) will be considered the service life of the asset.

Reconstruction, Y Construction, X

Service Life

Year TX Year

Year TY

Figure 13: Interval-based Determination of Asset Service Life The interval-based method is more direct but also requires less commonly available data (i.e., historical replacement or asset valuation data) as well as increased uncertainty in terms of predicting extreme events. Both condition-based and interval-based approaches are being applied in this study.

43

4.4 Specific Methodologies To predict service life using any one of the general methodologies, the Research Team is applying a portfolio of statistical methods of varying complexity, to make a recommendation based on goodness-of-fit measures. The final selection of appropriate model types will depend upon data availability, nature of the data (i.e., cross-sectional, time-series, or panel) and dependent variable (i.e., continuous or discrete), and preferred model specification type (i.e., deterministic or probabilistic). In general, probabilistic models are preferred, so as to add robustness, quantify uncertainty, and add reliability to life-cycle cost analyses. Based on these classifications, and drawing on research team experience and reviewed literature, the model types in Table 8 are deemed appropriate.

Table 8: Specific Statistical Model Types

Continuous Discrete

Deterministic - Non-linear regression models

- Linear regression models

- Miner’s hypothesis

Probabilistic - Duration models

- Neural networks

- Discrete outcome models

- Markov chains

For any reason, some agencies may prefer to use specific analytical techniques. For example, an agency may insist on using continuous models to model data of a discrete nature (e.g., linear regression of ordinal asset condition ratings). While, the Research Team recognizes the inherent limitations of such an approach, some agencies feel comfortable in such practices which may not be sound from a theoretical perspective but may be found practical, for example, using linear regression to model discrete data would imply that it is acceptable to interpret values that lie between specific ordinal levels. A very specific example is a linear regression model that predicts a NBI condition rating of 5.6 for an asset: this could inform an agency that a bridge will likely be either in a condition state of rating 5 or 6 given the set of explanatory variables. A brief review of such model types, including our selected model subtypes (based on expert opinion and the completed literature review), and final model selection criteria and results are herein provided. 4.4.1 Model Types 4.4.1.1 Linear and Non-linear Regression Models Linear and non-linear regression models are the most commonly applied by agencies due to their simplicity, clarity of results, and ability to be calibrated with widely available software such as MS Excel. Such models, in our case, can be applied to predict a continuous performance measure (condition-based) as a function of age and other variables, or to directly predict service life as a function of explanatory variables (interval-based). Latent variable and adaptive approaches can also be examined; that is, predict condition as a function of past performance and characteristics. Using a system of linear equations, we can also estimate discrete/continuous models. Various model functional forms and types can be applied, including:

44

Polynomial

\ = ]Q + ^ ]���_�`a

If n =1, then Linear If n =2, then Quadratic If n =3, then Cubic

Exponential/Logistic

\ = b]Q + ^ V�]�&c_

�`ad� for k = −1 or 1

If k = 1, then Exponential If k = –1, then Logistic Gompertz

\ = ^ g�V�hcic_�`a

Where: Y represents a dependent variable ci, αi, and βi represent estimable parameters and xi represents an independent variable For linear models, various model subtypes can be calibrated, including: ordinary, indirect, generalized, two-stage, and three-stage least squares, instrumental variables, limited and full information maximum likelihood, and seemingly unrelated regression. The most efficient and consistent of these models are the system equation methods commonly applied for simultaneous equations, as opposed to single equation methods: (i.e., ordinary least squares (OLS), indirect least squares (ILS), instrumental variables (IV), two-stage least squares (2SLS), and limited information maximum likelihood (LIML)). System equation methods include three-stage least squares (3SLS), seemingly unrelated regression estimation (SURE), and full information maximum likelihood (FIML). Such models are better suited for dealing with serial correlation problems (i.e., lack of independence among explanatory variables), heteroskedasticity (i.e., variables with non-constant standard deviations), and mitigating errors created by endogenous variables (i.e., variables where there is not a unidirectional causal relationship from the independent variable to the dependent variable) (Washington et al, 2003).

In 3SLS, least squares regression is performed in three stages: (1) get 2SLS estimates of the model system, (2) use the 2SLS estimates to compute residuals to determine cross-equation correlations, and (3) use generalized least squares (GLS) to estimate model parameters as similarly done in SURE (Washington et al., 2003). Simply put, 3SLS relies on multiple rounds of OLS to

45

predict instrument variables (i.e., suspected endogenous variables) which in turn predict the dependent variable. This process results in a more efficient and consistent linear regression model.

Of this set of model subtypes, the 3SLS approach is recommended for this study, however we will also calibrate OLS models due to agencies being more familiar and comfortable with such equations. For panel data, we will add random effects to account for correlation (e.g., multiple inspections for a single structure). Despite their simplicity to interpret (particularly for linear regression), there are disadvantages to this general model type. Linear regression methods are only appropriate when the dependent variable has a linear relationship with the explanatory variables, which is typically not the case in transportation. For instance in pavements, asset deterioration tends to increase exponentially with higher accumulations of traffic loadings. Furthermore, such models are deterministic, providing agencies with only a point estimate that does not reflect the true uncertainty of the model. For non-linear models, it is far more difficult to develop a set of significant independent variables. While these models may result in higher coefficients of determination (R2), they typically lack in explanatory power due to the inclusion of fewer significant variables. 4.4.1.2 Discrete Outcome Models Given the use of discrete condition ratings and functional classifications, it is considered more appropriate to apply discrete outcome models. Based on an assumed distribution, these models can be used to calculate the probability of an asset being in any condition state. For instance, the probability of a bridge being in any condition state of the NBI rating scale (0-worst to 9-best) in any future year can be calculated using these models. Such models also simplify sensitivity analysis, through the analysis of marginal effects (i.e., how probability of a condition state changes given a unit change in one of the inputs), and can be used for panel, ordered, and/or nested data. Model subtypes are typically of the probit or logit form, and can be in any of the following forms:

• ordered (e.g., NBI condition rating) or unordered (e.g., bridge status – functionally obsolete, structurally deficient, satisfactory condition),

• nested (e.g., predict status of all concretes bridge at first level, then predict status of pre-tensioned concrete bridges and post-tensioned concrete bridges at the second nest level), or

• incorporate mixed, fixed, or random effects (to account for asset heterogeneity) for panel data.

Probit models assume normally distributed variates whereas logit models assume extreme value distributions. Depending on the data, similar results may be obtained. Probit

j�\�� = k A]���_ − ]�la���la�_m B = 1√2% n Koj A− 12 p!B Pphc&cq�hcrs&�crs�qt�u

46

Logit j�\�� = Koj �]����∑ Koj �]����_�`a

With regard to predicting service life, the ordered logit models with random effects subtype

is preferred for ordered condition ratings and the multinomial logit model subtype is recommended for unordered data. Because our discrete conditions are not binary, the logit specification is preferred given that the outcome probabilities of the multionomial probit are not closed form and estimation of the likelihood function requires numerical integration (Washington et al., 2003). The most common extreme value distribution (i.e., Gumbel distribution) has the simplifying property where the maximums of randomly drawn values are also extreme value distributed, unlike the normal distribution (Washington et al., 2003). These models, however, are only appropriate if the assumed distribution accurately reflects the data. Furthermore, with discrete models in general there is a potential for aggregation bias. That is, two culverts may each have a condition rating of say 4 but one may be nearly in a condition state of rating 3 while the other is nearly in a condition state of rating 5. This loss of generality may cause some errors in model calibration. Visual condition ratings in particular may add uncertainty as well, given that one person may consider a bridge to be in a condition state of 4 while another believes it to be in a condition state of 3. As a result, the model predictions may be biased, given the subjective nature of the condition inspections, fuzzy logic may be appropriate to apply so as to improve model estimates. With fuzzy logic, degrees of being in each condition state are assigned, as opposed to classical set theory where an asset is either in one condition state or another. For our project, we are paying particular attention to explain exactly what we consider each condition state to be. 4.4.1.3 Duration Model Characteristics Duration (or reliability) analysis is a probabilistic approach for predicting the likelihood of a continuous dependent variable ‘surviving’ at any given unit of time. Generally, these models produce hazard or survival curves such as those presented in Figure 14. A hazard curve would be the inverse relationship (in fact, the hazard rate is the derivative of the survivor curve), with an increased hazard corresponding to a lower survival probability.

47

Figure 14: Illustration of Asset Survival Curves using different Performance Indicators and Different Performance Thresholds (Irfan et al. 2009)

As shown in Figure 14, we are developing these curves to predict the probability of each

asset surviving based on a variety of dependent variables. Duration models can be non-parametric, semi-parametric, or fully-parametric. Non-parametric methods (e.g., product-limit or life table) are rarely applied because they do not retain the parametric assumption of the covariate influence; however they may be appropriate when there is little knowledge of the functional form of the hazard or if a small number of observations is obtained (Washington et al., 2003). Semi-parametric models (e.g., Cox proportional-hazards) account for covariate influence and are appropriate when the underlying distribution of the data is unknown, making this approach more flexible. Fully-parametric models (e.g., gamma, exponential, Weibull, log-logistic, log-normal, Gompertz), are generally recommended for this study due to the benefits in model efficiency and in reducing bias, but are dependent on the data fitting the assigned distribution. The Cox model approach takes the following form, similar to the logit model:

ℎ���� = Koj �]����∑ Koj �]x�x�xyzc

Where: j represents durations greater than or equal to ti Ri represents the set of observations

48

The Weibull model subtype, with gamma heterogeneity (to capture unobserved effects across the population), and the log-logistic hazard model subtype, using maximum likelihood estimation, will both be evaluated as well. The Weibull distribution is a more generalized form of the exponential distribution that allows for more flexible means of capturing duration dependence; however the model requires hazards to be monotonic over time; the log-logistic distribution allows for non-monotonic hazard functions, while serving as an approximation to the lognormal distribution (Washington et al., 2003). The density functions for Weibull and log-logistic are as follows:

Weibull: ��{9W�|: <��� = .j�.��~�aKoj�−�.��~� �M�M�P: ℎ��� = .j�.��~�a�������

Where: survival function, ��� = �1 + ��.��~��s� , with θ representing a gamma heterogeneity capturing term

Also, P (>0) denotes probability, λ (> 0) is a parameter), and t is some specified time. Moreover, density function, f(t)=dF(t)/dt ; hazard function, h(t)=f(t)/[1-F(t)]; and survivor function, S(t)=P(T ≥ t); while, F(t) = P(T<t); T is a random variable. Log-logistic (with parameter, λ > 0 and P > 0):

��{9W�|: <��� = .j�.��~�a�1 + �.��~�!

�M�M�P: ℎ��� = .j�.��~�a�1 + �.��~�

The Weibull model form is monotone increasing in duration when P>1, monotone decreasing

when P<1, and reduces to the exponential distribution when P=1; the log-logistic model form has the hazard increasing in duration from zero to an inflection point and subsequently decreases toward zero, when P<1 the monotone is decreasing in duration, and when P=1 the hazard is monotone decreasing from the λ parameter.

The main disadvantage of this approach, other than its statistical complexity, is the presence

of censored data (Figure 15).

49

Figure 15: Potential for Error due to Censored Data (Washington et al., 2003)

Data can be either left-censored, right-censored, both left and right censored, not captured, or completely captured over the observational period. Censored data are problematic in that they can lead to more biased estimates. For our project: left-censored data (e.g., t4) would indicate that the actual initial construction or reconstruction year is not observed but the time of replacement is; right-censored data (e.g., t5) would indicate that we know when the asset was built but it has not been replaced during the time of observation; both types of censoring would represent data (e.g., t2) where neither the construction/reconstruction year and year of replacement is observed; data not captured (e.g., t1) would be those for which no construction or replacement data is available; and the completely captured data would represent those assets for which we know both when a structure was built and replaced (e.g., t3). Right censored data are less problematic and can readily be accounted for in hazard-based models, however left censored data add additional complexity to the likelihood function. The semi- and fully-parametric techniques will help to reduce any bias from such censoring. 4.4.1.4 Markov Chains Markov-chains are one of the more common approaches in modeling bridge service lives, where the transitional probability of a condition rating changing is assessed. The advantages of Markov-chains are that they can account for uncertainty, initial conditions, and are efficient for larger networks; disadvantages include that they are discrete, deterioration of components are described in visual terms only, assume constant inspection periods, system condition is not considered, and they do not rely on past data, if a first order Markov-chain is used (Morcous, 2006; Van Noortwijk and Frangopol, 2004). To overcome the assumption of constant inspection periods, Bayesian techniques can be applied (Morcous, 2006).

Markov chain models are appropriate for discrete data that undergo transitions from one condition state to the next. The models predict the probability of transitioning, ��x = Pr�Y�la = j|Y� = i�

Observations

Time

a b

1

2

3

4

5

t1

t2

t3

t4

t5

Observational Period

50

with the assumption that the future condition is independent of the past conditions. This assumption, however, is generally not realistic, at least solely based on past condition. Therefore sets of explanatory variables (can be latent) are needed to predict the probabilities (typically of probit or logit form). Furthermore, the transition probabilities may change with age, therefore multiple transition matrices may be developed using statistical techniques or expert opinion. Bayesian techniques could be used to update transition probabilities as well.

The main disadvantage, however, is the assumption of only a single condition stage switches. That is, Markov chains assume that a bridge in NBI condition state 7 cannot become condition state 5 at the next inspection, but first must experience a condition state of 6. For assets where inspections are not as frequent, this approach may not be appropriate. 4.4.1.5 Miner’s Hypothesis Fatigue-based models generally rely on Miner’s Hypothesis:

^ {��� = ���`a

Where: n represents the accumulation of loads over cycle i, N represents the maximum allowable load cycles, and C represents the fractional life when C is assumed to be 1.

For our project, this basic hypothesis can be used to represent service life in terms of other measures, such as traffic and climate loads. Based on other models, we can predict the service life in terms of years, and then identify the accumulated traffic or climate loads at this time (N). An agency knowing the current accumulation of such loads (n) could then estimate the service life assuming a C of 1. The main disadvantage of this approach is that service life is a deterministic estimate and may vary greatly between the identified asset dimensions. 4.4.1.6 Neural Networks In recent years, this approach has become more common among researchers. Essentially, this non-linear, adaptive model predicts conditions based on what it has ‘learned’ (pattern identification) from past data. Statistically, an artificial neural network is a non-linear form of 3SLS, where instruments are predicted to predict future events (Figure 16).

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Figure 16: Example of an Artificial Neural Network

To facilitate learning, such models are typically Bayesian-based. This approach updates

estimates (i.e., posterior means) by applying weighted averages based on previous estimates (i.e., prior means). Typically, these weights are based on the number of observations. Activation functions within the network have included hyperbolic tangent, log-sigmoid, and bipolar-sigmoid functions. Such approaches have been found to work well with noisy data and are relatively quick; however, such techniques are better suited for smaller databases (Melhem and Cheng, 2003). These models require more sophisticated software to develop (e.g., Palisade’s @Risk Neural Tools, NeuroXL) and can sometimes be used as a ‘black box’ (i.e., prediction process unknown but assumed appropriate). However, the ability to ‘learn’ makes these models particularly useful to asset managers. 4.4.2 Model Selection for Calibration To summarize, we are calibrating the model subtypes to predict the various measures of condition-based service life (Table), and interval-based service life (OLS and 3SLS for historical life predictions and Miner’s Hypothesis for alternative measures of life). In addition, for panel data, the Research Team are exploring the applicability of random effects and fuzzy logic to discrete, ordered condition states.

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Table 9: Recommendations for Selection of Methodology for Life Expectancy Estimation Asset Type Dependent Variable(s) Model Subtypes

Bridges NBI sufficiency rating OLS & 3SLS regression models; Cox, Weibull, & Log-logistic

duration models; Artificial Neural Networks

NBI component ratings Ordered Logit; Markov Chain

Culverts Visual condition rating Ordered Logit; Markov Chain

Health index rating OLS & 3SLS regression models; Cox, Weibull, & Log-logistic

duration models; Artificial Neural Networks

Crash barriers LOS rating Ordered Logit; Markov Chain

Pavements IRI, Rut Depth, PCR OLS & 3SLS regression models; Cox, Weibull, & Log-logistic

duration models; Artificial Neural Networks

Pavement Markings Retroreflectivity OLS & 3SLS regression models; Cox, Weibull, & Log-logistic

duration models; Artificial Neural Networks

Roadway Lighting LOS rating Ordered Logit; Markov Chain

Percent bulb outages OLS & 3SLS regression models; Cox, Weibull, & Log-logistic

duration models; Artificial Neural Networks

Traffic Signals Burned out or operating

bulb

Binary logit

Traffic Signs Sign surface

retroreflectivity

OLS & 3SLS regression models; Cox, Weibull, & Log-logistic

duration models; Artificial Neural Networks

Sign structure LOS Ordered Logit; Markov Chain

For the probability of a service life being reached due to an extreme event, we will apply

simple probability theory to historical data. For example, via the NOAA database we can calculate the probability of a flood occurring in any given year as the number of floods over a time span divided by that time span. The probability of a flood over the predicted service life is then represented by: j�K������ KO�{� �O�� 9��OWg� �W<�� = �1 − ��� 7��� ��L Where: p represents the probability of an extreme event occurring in any given year (total

number of historical events in county / interval of historical county database) Once this probability exceeds an agency-set threshold value, then the service life is reached.

Given the rarity of such events, this calculation is not expected to dominate (i.e., be less than other service life estimates). However, as discussed in the section, we can combine probabilistic estimates into a combined survivor curve. With these calculations of service life, we can then make a single model recommendation for each asset that agencies can use to predict the life expectancies of their assets.

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4.4.3 Model Recommendations and Results Given the various model calibrations, the Research Team will recommend a decision support system involving sets of models that provide asset managers with the necessary equations needed to predict service life. The Team will also provide average estimates of service life that we developed for purposes of demonstrating the study methodology, using the collected data. To facilitate service life calculations, we will develop an Excel spreadsheet for agencies to input location data and asset characteristics. As a result, the spreadsheet will provide an expected value for service life using deterministic methods or provide a range of service life values according to different confidence levels using probabilistic methods.

In addition, for probabilistic models we will develop survivor curves that account for the uncertainties associated with each failure mode (i.e., extreme event, irreparable damage). That is, the overall probability of failure at any age in time is:

j�[ ∪ �� = j�[� + j��� − j�[ ∩ ��

Where: Event A represents the probability of the service life being reached at any point in time due to irreparable damage (e.g., retroreflectivity threshold reached) and Event B represents the probability of an extreme event occurring.

This overall, condition-based survivor curve can then be compared to a historical, interval-

based survivor curve for each asset with sufficient data. The two curves are expected to match quite closely. Any differences between the curves can be interpreted as either: improvement of design/construction practices over time, inaccuracies in calibrated models, different condition variables and/or thresholds than used in the past, replacements occurring due to economic or technological developments, and the practice of simultaneous replacement (e.g., while replacing a pavement section, contractors may also replace signs still in an adequate condition state). Model recommendations will be based on an assortment of goodness-of-fit measures (GOF). Primarily, model selections will be based on the residuals of our model predictions from each subtype’s best model calibration. That is, the error between observed values and model estimates for each observation. The best overall model type will be the one for which the root mean squared error (RMSE) is minimized. The best model calibration subtype will be a function of adjusted or McFadden R2 value, Durbin-Watson statistic (measure of autocorrelation and heteroskedasticity), t-statistics of parameter estimates (used to identify significant life expectancy factors), intuitiveness of parameter signs, independence and number of explanatory variables, lack of omitted variables, number of observations, log-likelihood function values, and significance of test statistics (e.g., random effects test statistic).

To add further insight regarding the influence of service life factors, a methodology for conducting sensitivity analysis is outlined in the following chapter.

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CHAPTER 5 –METHODOLOGIES FOR SENSITIVITY

ANALYSIS

5.1 Introduction After having identified the factors that influence asset life expectancy, we are carrying out as in-depth analysis to assess the sensitivity of each variable. Through the approach outlined in this chapter, agencies will be able to quantify the influence of changes in service life factors so as to better guide in-service asset management programs. As we intensify our data collection regarding preservation history, we are paying attention to how best we can measure the sensitivity of asset life expectancy to the frequency and intensity of maintenance and preservation activities. 5.2 Methods 5.2.1 Relative Parameter Strength For linear regression models, the sensitivity of life expectancy factors can be interpreted directly on the basis of the estimated parameter (coefficient). For every unit change in the input, the output varies by the magnitude of the coefficient. For interval-based models this output will be the service life; for condition-based models this output will be the asset performance measure or condition rating. To determine the relative strength of each factor, the parameter estimate will be normalized to account for differing units (Parameter estimate * Mean value of observations). The largest value will represent the most influential factor in determining the service life or asset condition. 5.2.2 Marginal Effects For probabilistic models, the sensitivity of factors can be analyzed through marginal effects. That is, the change in probability of some condition state occurring given some unit change in an explanatory variable. For instance, with an ordered logit model predicting an NBI condition rating as a function of bridge age, we can assess how the probability of a bridge being in a given condition state changes for a unit change in age. 5.3 Sensitivity Plots and Results For non-linear models and those with less direct interpretations of sensitivity, we will focus more on developing sensitivity plots. Tornado diagrams (Figure 17), spider diagrams (Figure 18), and plots of significant explanatory variables vs. the dependent variable will be completed.

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Figure 17: Example of a Tornado Diagram (FHWA, 2006)

Figure 18: Example of a Spider Diagram (Van Dorp, 2009)

Tornado and spider diagrams are constructed through the use of a one-way sensitivity analysis (i.e., vary one input and assess the change in the output when all other inputs are set at their respective average values). The tornado diagram, in particular, further identifies the factors that have either a positive or negative effect on the outcome. Those variables with the largest range of outputs are considered the most influential. Using the same spreadsheet application briefly referenced in the previous chapter, we are implementing the tested models in order to provide a framework for repeatable sensitivity analyses and for generating reports of the results. The spreadsheet will provide a place to enter sample data; to

Variable 1 Variable 1

Variable 2

. . . . . . . . . . . . . . Variable n

Range of Outcomes

Percent Change in Input Value

Output Value

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implement the various sub-models for performance forecasting; and to combine the separate models into an overall prediction of service life. It is anticipated that the spreadsheet model will be self-contained and will require little or no Visual Basic programming. The intention is to use worksheet formulas and built-in Excel statistical capabilities to demonstrate the models.

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CHAPTER 6 – EXAMPLE APPLICATION OF

METHODOLOGIES

6.1 Introduction To demonstrate the proposed methodologies, service life estimates based on preliminary condition-based and interval-based models have been prepared using a portion of the collected data. The condition-based example predicts the service life of pavement markings, from the NTPEP database, as the time until an irreparable retroreflectivity level is reached. The interval-based example predicts the historical service life of large culverts sampled from the NBI database. Subsequent sections of this chapter provide detail on the applications of each general approach. 6.2 Example for the Condition-based Approach Waterborne paints are most commonly used for pavement markings given their low initial cost and environmental ‘friendliness’. In this example, we analyze historical data for a certain type of waterborne pavement marking paint,1A: 2 year waterborne paint tested on Pennsylvania test decks, set up as part of the National Transportation Product Evaluation Program (NTPEP). From this data a deterioration model predicting retroreflectivity values is herein developed. From the model, the service life of the marking can be determined as the time the retroreflectivity takes to reach an unacceptable value – at that point, this pavement asset will need to be replaced. From the NTPEP database and using additional climate information from National Climatic Data Center (NCDC), a database containing data on various factors that may influence the performance of pavement marking is developed. These data include age, color, material properties of the paint including glass bead properties, installation conditions, climatic exposure, traffic exposure, snowplowing activities etc. The most significant of these factors, as determined by calibrating regression models, are listed in Table 10.

Table 10: Variables Available to Model PMM performance of 1A: 2-yr Waterborne Paint

Variable Description

Indicator for color; white=1, yellow=0

Inspection interval in months

Skip retroreflectivity (Dependent variable)

Bead content

Thickness, in mm

Bead weight, lb/gal

Bead coat; Moisture proof or Moisture coating =1, rest =0

No-track dry time (in minutes)

Humidity during installation

Wind speed during installation

Number days with maximum temperature greater than or equal to 90 deg. F in a month

Number days with minimum temperature less than or equal to 32 deg. F in a month

Monthly mean temp in deg. F

Total precipitation in a month, in inches

AADT, in thousand vpd

Snowplowing; yes=1, no=0

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Initially, an Ordinary Least Squares (OLS) regression model was attempted; however the model was plagued by autocorrelation problems as reflected by a low Durbin-Watson statistic. Therefore, an autoregression procedure was performed to help mitigate the correlation problems. The model was developed using data from NTPEP data mine and its applicability in places other than Pennsylvania is yet to be tested. The results of the final model are presented in Table 11.

Table 11: Model for Pavement Marking Performance (Retroreflectivity) on basis of Maximum Likelihood Estimates, Material - 1A: 2-yr Waterborne Paint

Variable Description Estimated

Parameter

t statistic Comment

Dependent Variable: ln(retroreflectivity)

Constant 3.85 26.65

Indicator for color; white=1, yellow=0 0.53 33.61

Age in months -0.056 -117.94

Bead content -0.0002 -10.39 Material properties

Thickness, in mm 0.038 18.51

Bead weight, lb/gal -0.00016 -3.29

Bead coat; Moisture proof coating =1, rest =0 0.00016 5.56

No-track dry time (in minutes) -0.00018 -2.77 Installation condition

Humidity during installation, in percent -0.0044 -4.00

Wind speed during installation, in mph 0.0045 3.91

No of days max T=>90 F in a month 0.0135 19.38 Climatic condition

(as experienced) No of days min T=<32 F in a month 0.01 12.49

Monthly mean temp in F -0.01 -28.59

Total precipitation in a month, in inches -0.01 -8.76

AADT, in thousand vpd 0.1309 10.71 Traffic Condition

Snowplowing; yes=1, no=0 -0.1841 -16.95

AR1=-0.8545 (t=-207.57)

Durbin-Watson = 2.1123

Number of Observations = 16492

R2 = 0.78

The residual plots in Figure 19 shows an almost horizontal band centered at 0 while the

Figure 20 shows the statistical fit of the final model. In this model, the variables that were found to positively affect the performance of pavement markings include: white color, higher wind speeds during installation, thickness of marking, etc. On the other hand, the factors that negatively affected the performance of pavement markings included: higher ages, greater bead weight, higher humidity during installation of the marking, snowplowing frequency, etc. The results suggest that the influence of certain factors on pavement marking performance (and thus, on the asset life expectancy) requires further analysis. A example is traffic volume in terms of the average annual daily traffic (AADT). For example, AADT values typically remain fairly constant over the relatively short life span of pavement marking which ranges from 1 to 3 years and thus may fail to show as a significant variable. Thus, it would be more prudent to use accumulated traffic since the marking installation instead of annual traffic.

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Figure 19: Residuals vs. predicted values for log(retroreflectivity)

Figure 20: Actual values vs. predicted values for log(retroreflectivity) NTPEP data mine also contains test data on other types of pavement marking materials,

namely 1B: 3-year Waterborne, 2A: 2-year Solvent Borne, 3A: Thermoplastic, 3B: Preformed Thermoplastic, 3E: Durable Tapes, 3G: Methyl Methacrylate, 4: Temporary Tape, 5A: 2-year Experimental, and 5B: 3-year Experimental etc. Degradation models for these materials will be developed. After the performance (degradation) model is developed, the remaining service life of the pavement marking is estimated by substituting the performance threshold (minimum retroreflectivity value) for pavement marking into the model. Considering the current model described in Table 11 for a given set of placement, climate and traffic scenarios, it is herein assumed that the asset manager seeks to predict the remaining service life (RSL) of a 6 month old white, 1A pavement marking in Union County, PA. Further, assume that the marking has a thickness of 20 mm with moisture-proof coating and beads weighing 25 lb/gal and bead content = 34.5. The markings were laid under the

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following weather conditions: wind speed = 6 mph, humidity = 50, and ‘no-track’ dry time = 3 min. Given the climate of the site, the agency performs winter snowplowing during winter (Nov-March). Using AADT of 11,000 vehicles per day and with 30 year norms the agency may calculate retroreflectivity expected in the subsequent months. If the agency considers the pavement markings to need replacement at a retroreflectivity threshold of 100 cd/m2/lux then Table 12 shows the remaining life expectancy of the pavement marking to be 17 months (23 months – current age of 6 months).

Table 12: Determining Remaining Service Life of a Pavement Marking

Age (month) DT90 DT32 MNTM TPCP Snowplow Retroreflectivity

January 7 0 28 29.7 1.36 1 320.19

February 8 0 27 26.7 4.26 1 300.04

March 9 0 25 35.9 5.44 1 250.67

April 10 0 7 52.6 2.9 0 206.57

May 11 0 1 55 3.98 0 177.65

June 12 5 0 70.9 2.66 0 153.78

July 13 3 0 72.5 4.03 0 137.39

August 14 0 0 68.1 1.98 0 133.06

September 15 3 0 64.9 3.09 0 133.78

October 16 0 0 50.1 1.52 0 143.08

November 17 0 2 40 1.57 1 126.95

December 18 0 7 30.7 3.95 1 135.24

January 19 0 28 29.7 1.36 1 163.52

February 20 0 27 26.7 4.26 1 153.23

March 21 0 25 35.9 5.44 1 128.01

April 22 0 7 52.6 2.9 0 105.49

May 23 0 1 55 3.98 0 90.72

June 24 5 0 70.9 2.66 0 78.53

• Note, in this example the retroreflectivity level is found to decrease with time until at later stage when a slight bump in performance is noticed. This may be due to the delayed exposure of glass beads embedded in the paint.

Similarly, if an agency decides to apply different thresholds, the remaining service life (RSL) can still be determined. For instance, if an agency has established a threshold of 80 md/m2/lux, then the RSL is estimated to be 18 months; if an agency prefers a threshold of 150 md/m2/lux, then the estimated RSL is 15 months. 6.3 Example for the Interval-based Approach

For this example, historical service life (time from year built until year reconstructed) is analyzed using values reported in the NBI database from the period of 1992 through 2009. Data from four states have been compiled including Indiana, New Mexico, South Carolina, and Wyoming, each representing one of the four major climate zones as designated by the SHRP. Within this sample of the NBI database, 786 observations are available, representing nearly 800 different structures that

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have a recorded lifespan. Basic data statistics for these observations including the range and average observed historical lives are presented in Table 13.

Table 13: Historical Service Lives of a Subset of the NBI Database OBSERVED

SERVICE LIVES

Indiana

(116 obs.)

New Mexico

(331 obs.)

South Carolina

(249 obs.)

Wyoming

(90 obs.)

Subset Total

(786 obs.)

Minimum 1 year 2 years 7 years 6 years 1 year

Average 33 years 33 years 37 years 39 years 35 years

Maximum 97 years 73 years 76 years 75 years 97 years

Based on the subset, observed service life values are fairly consistent across the states with a 16%

difference between the average values. Of this subset, Wyoming culverts tend to last the longest on average, which is intuitive given the relatively dry climate in that state. Considering the continuous nature of the dependent variable (historical service life) regression, survival, and neural network models were developed. The independent variables investigated include:

• Roadway type: o Functional class (used as a proxy for missing historical AADT values), maintenance

agency, and rural/urban classification; • Climate normals by climate division:

o Average temperature, precipitation, annual freeze thaw cycles, and heating/cooling degree days;

• Average soil characteristics by soil survey area: o Cation exchange capacity, soil pH, % sand, silt, clay, and calcium carbonate,

plasticity index, liquid limit, soil erodibility, and ratings of potential for frost action and risk of corrosion.

Statistical analyses were then conducted to decide the best specification by model type. The results of the best regression specification are shown in Table 14.

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Table 14: Best Generalized Least Squares Regression Model (historical service life) Independent Variable Parameter Estimate t-statistic

Constant 237.550 1.857

Interstate indicator variable (1 if culvert located on interstate system, 0

otherwise) -15.510 -8.791

Rural geographic region indicator variable (1 if culvert located in rural

setting, 0 otherwise) 2.982 2.129

Annual average temperature (°F) -3.042 -1.660

Annual average heating degree days -0.885E-02 -1.486

Annual average freeze-thaw cycles -0.518E-01 -1.413

Soil reaction (pH) -0.128E-01 -3.684

% sand 4.177 2.607

Potential for Frost Action (1 if low, 2 if moderate, 3 if high) -0.191 -3.072

Cation exchange capacity (meq/100g) -0.611E-02 -1.812

Plasticity Index -1.063 -3.916

RMSE 16.1

Adjusted R2

0.13

Durbin Watson Statistic 1.34

For this model, a negative parameter suggests a tendency to reduce service life, while a

positive parameter indicates an increase in service life. All estimated parameters were found to be significant above the 90% confidence interval. The average annual temperature was found to have the strongest parameter estimate (after normalizing for units) suggesting that at areas of higher temperatures or greater number of annual heating degree-days, culverts seem to have shorter service lives. It can also be seen, that interstate highway culverts, and those experiencing and greater frequency of freeze-thaw cycles had lower service lives. Similarly, areas with a high potential for frost freeze, higher pH, cation exchange capacity, and plasticity index also had shorter service lives. Culverts in areas with higher sand concentrations tended to have longer service lives – this seems intuitive because granular soils generally perform better as structural foundations compared to cohesive soils. Also, the results suggest that culverts in rural locations last longer than those in urban locations: a plausible reason is the higher traffic volumes encountered on rural highway sections.

However, autocorrelation problems, as indicated by the Durbin Watson statistic and a low R2 value suggest that there is too much variability in service life estimates, particularly for culvert assets that have shorter-than-average and longer-than-average lives (Figure 21).

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Figure 21: Residuals of Best Regression Model Specification

Given the variability of the life expectancy estimates yielded by the linear model (as reflected in the Durban Watson statistic), a survival model may be more appropriate for the NBI culvert data. Thus, the Research Team proceeded to develop a survival model using different alternative mathematical functional forms. The functional form consistent with the Weibull distribution was found to best describe the progression of hazards of the sample, with negative parameters indicating an increased hazard and hence lower survival probability and positive parameters indicating a decreased hazard with a higher survival probability (Table 15).

-80

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Table 15: Best Weibull-distributed Survival Model Independent Variable Parameter Estimate t-statistic

Interstate indicator variable (1 if culvert located on interstate system, 0

otherwise) -0.560 -9.756

Rural geographic region indicator variable (1 if culvert located in rural

setting, 0 otherwise) 0.842E-01 1.828

Annual average temperature (°F) 0.582E-01 10.001

Annual average heating degree days 0.116E-03 5.308

Annual average cooling degree days -0.471E-03 -3.647

Soil reaction (pH) 0.184 3.395

% clay -0.161E-01 -1.826

% sand -0.708E-02 -3.073

Potential for Frost Action (1 if low, 2 if moderate, 3 if high) -0.585E-03 -4.113

Risk of corrosion to Uncoated steel (1 if low, 2 if moderate, 3 if high) -0.188 -2.102

Cation exchange capacity (meq/100g) -0.188E-03 -1.640

Sigma (ancillary parameter for survival) 0.309 34.042

Lambda parameter 0.032

P parameter 3.234

RMSE 0.02

Log likelihood function -660

Again, all variables were found to be significant at the 90% confidence level, however in this

model, a few seemingly unintuitive parameter signs are observed. For example, the duration model suggests that culverts at areas of higher temperatures tend to have longer service lives; and culverts founded on granular foundations (larger percentages of sand) are associated with lower service life. The Research Team is investigating the data more closely to ascertain the need for additional techniques and is reviewing the literature more closely to identify the a-priori expectations of the model parameter directions. In any case, the results show that different model functional forms, for the same dataset, can yield results that are not consistent. The important lesson is the cultivated ability to explain any such inconsistencies. From the duration model, the sample culverts were found to generally survive 12.75 years with 95% probability; 22.57 years with 75% probability; 31.70 years with 50% probability; and 44.52 years with 25% probability (Figure22).

Similarly, from the duration model, the sample culverts were found to generally survive 893freeze-thaw (f-t) cycles with 95% probability; 2,583 f-t cycles with 75% probability; 4,531 cycles with 50% probability; and 7,446 f-t cycles with 25% probability (Figure 23).

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Figure 22: General Survivor Curve (years) of Best Model Specification

Figure 23: General Survivor Curve (freeze-thaw cycles) of Best Model Specification

Using the model parameter estimates, we can also calculate remaining service life using

Miner’s hypothesis. For instance, consider an asset manager who seeks to the appropriate time to replace a 35 year old culvert structure in Henry County, Indiana. Now assume the agency decides that the asset should be replaced when there is a 75% of reaching an undesirable level of service (or a 25% chance of surviving) in the next year due to accumulated freeze-thaw cycles. From the curves, we can expect this asset to last 7,446 freeze-thaw cycles. Given the climate of Henry County, Indiana, we expect approximately 116 freeze-thaw cycles per year. Over a 35-year period, it is therefore anticipated that the structure has survived 4,060 freeze-thaw cycles. Therefore, the structure is 55% (4,060/7,446) into its service life with 45% remaining, which is approximately another 29 years.

Residuals of the actual versus estimated survival probabilities by observation show a relatively close fit for most observations (within ±0.05).

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Figure 24: Residuals of Survival Probabilities of Best Model Specification

A final approach to estimate service life is through the use of artificial neural networks. To determine the best model subtype, the Research Team tested five activation functions (zero-based log-sigmoid, threshold, hyperbolic tangent, log-sigmoid, bipolar sigmoid) using initial weights and a learning rate = 0.3, momentum = 0.6 and no neurons in the hidden layer. The trained networks were found to have the following RMSE values by activation function (Table 16). By this measure, the hyperbolic tangent activation function was found to yield the most accurate predictions (Figure 25).

Table 16: RMSE by Neural Network Activation Function

Activation Function RMSE (%)

Zero-based log-sigmoid 1.6

Threshold 1.2

Hyperbolic tangent 1.1

Log-sigmoid 2.9

Bipolar sigmoid 3.3

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Figure 25: Residuals of Best Neural Network Model Specification Based on the residuals of each model specification, the neural network approach is recommended for forecasting, with 93% of the predictions being accurate within ±2 years. For those agencies interested in survival probabilities and identifying significant life expectancy factors a Weibull distributed model is recommended. To further demonstrate the proposed methodologies, sensitivity analyses of significant factors from the condition-based linear regression model are presented in the following section. 6.4 Sensitivity Analysis Example An example sensitivity analysis of the condition-based regression model follows. To assess the general strength of each significant variable, normalized parameter estimates can be calculated by making all coefficients unitless (multiplying by average values fro non-dummy variables). As a result, the most significant factors are found to be (1) AADT, (2) age, and (3) thickness (Table 17).

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Table 17: Normalized Parameter Strength of Significant Predictors of Pavement Marking Retroreflectivity

Variable Description Normalized Parameter Strength

AADT, in thousand vpd 1.50

Age in months 0.71

Thickness, in mm 0.66

Monthly mean temp in deg. F 0.61

Indicator for color; white=1, yellow=0 0.53

Snowplowing; yes=1, no=0 0.18

Humidity during installation 0.15

Total precipitation in a month, in inches 0.04

Number days with maximum temperature

greater than or equal to 90 deg. F in a month 0.03

Number days with minimum temperature less

than or equal to 32 deg. F in a month 0.03

Wind speed during installation 0.02

Bead content 0.01

Bead weight, lb/gal 1.07E-03

No-track dry time (in minutes) 2.68E-04

Bead coat; Moisture proof or Moisture coating

=1, rest =0 1.60E-04

In addition, agencies can conduct one-way sensitivity analyses, as we have demonstrated here

for each significant variable in the linear regression model. By holding variables at their mean values and varying one variable at a time from their minimum observed values to their maximum observed values (Table 18), the range of retroreflectivity values were observed (Figure 26).

Table 18: Data Statistics of Significant Predictors of Pavement Marking Retroreflectivity Variable Minimum Average Maximum

Age (months) 0 12.7 36

Thickness (mm) 15 17.3 30

AADT (1000 vpd) 10 11.4 13.5

Color (1 if white, 0 otherwise) 0 -- 1

Monthly Temp. (°F) 39.9 61.0 75

Number of Days with Temp. ≥ 90°F 0 2.6 15

Number of Days with Temp. ≤ 32°F 0 3.1 20

Humidity 19 35.1 68

Snowplowing (1 if yes, 0 otherwise) 0 -- 1

Precipitation (in.) 1.2 3.6 8.6

Wind Speed at Installation (mph) 2 3.8 6

Moisture-proof Bead Coating (1 if yes, 0 otherwise) 0 -- 1

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Figure 26: Tornado Diagram of Significant Predictors of Pavement Marking Retroreflectivity

Figure 27: Spider Diagram of Significant Predictors of Pavement Marking Retroreflectivity

From the diagram, it is clear that given the expected ranges of each variable age is the most

significant factor in predicting retroreflectivity, followed by thickness, AADT, and color respectively. Similarly, the sensitivity of retroreflectivity can be represented by a spider diagram (Figure 27), showing how retroreflectivity predictions change given a percent change in the inputs. Similar plots can be completed with respect to the predicted service life as determined by an agency’s minimum threshold value.

-300 -200 -100 0 100 200

Change in Retroreflectivity

Va

ria

ble

Age (months)

Thickness (mm)

AADT (1000 vpd)

Color

Monthly Temp. (°F)

Number of Days with Temp. ≥ 90°F

Number of Days with Temp. ≤ 32°F

Humidity

Snowplowing

Precipitation (in.)

0

50

100

150

200

250

300

350

-200 -100 0 100 200

Re

tro

refl

ect

ivit

y

% Change in Variable

Age (months)

Moisture-proof Bead

Coating

Thickness (mm)

Bead Weight (lb/gal)

No-track Dry Time

(min)

Humidity

70

6.5 Summary Using the proposed methodologies, further improved per panel comments, the remainder of the project will be spent on (1) applying the approaches to the collected data and (2) preparing resources to help demonstrate and report on relevant findings.

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