Prediction of remaining service life of pavements

Transcription

1 The University of Toledo The University of Toledo Digital Repository Theses and Dissertations 2010 Prediction of remaining service life of pavements Chaitanya Kumar Balla The University of Toledo Follow this and additional works at: Recommended Citation Balla, Chaitanya Kumar, "Prediction of remaining service life of pavements" (2010). Theses and Dissertations This Thesis is brought to you for free and open access by The University of Toledo Digital Repository. It has been accepted for inclusion in Theses and Dissertations by an authorized administrator of The University of Toledo Digital Repository. For more information, please see the repository's About page.

2 A Thesis entitled Prediction of Remaining Service Life of Pavements by Chaitanya Kumar Balla Submitted to the Graduate Faculty as partial fulfillment of the requirements for the Master of Science Degree in Engineering Dr. Eddie Yein Juin Chou, Committee Chair Dr. Azadeh Parvin, Committee Member Dr. George J. Murnen, Committee Member Dr. Patricia Komuniecki, Dean College of Graduate Studies The University of Toledo August 2010

3 Copyright 2010 This document is copyrighted material. Under copyright law, no parts of this document may be reproduced without the expressed permission of the author.

4 An Abstract of Prediction of Remaining Service Life of Pavements by Chaitanya Kumar Balla Submitted as partial fulfillment of the requirements for the Master of Science in Engineering The University of Toledo August 2010 Pavement management is a process that helps to maintain a pavement network in a safe and serviceable condition in a cost effective manner. A key component of an effective pavement management system is its ability to predict the remaining service life of pavements. Remaining service life of pavements can be predicted using the present pavement condition and the latest rehabilitation action performed on that particular pavement. Survival curves are often developed to obtain remaining service life of a pavement family. The objectives of this study are to determine the average service life of pavements and to predict their remaining service life. Remaining Service Life is defined as the projected number of years until rehabilitation is required. iii

5 The pavement condition data in the form of Pavement Condition Rating (PCR) were used to develop Kaplan-Meier survival curves for different PCR thresholds. PCR 60 was considered as the terminal condition and the average service life of pavement network was calculated as the area under PCR 60 survival curve. Derived performance curves for all the survival probabilities were developed between pavement age and PCR using the Weibull approximation of the Kaplan-Meier survival curves. Derived performance curves were employed to determine the remaining service life of individual pavements based on current age and PCR. PCR curves were also developed for individual PCR thresholds between RSL and pavement age by using the Weibull approximation of the Kaplan-Meier survival curves to better understand the relationship between RSL, PCR and pavement age. Average service life of the pavement network and remaining service life of individual pavements obtained from this study can be used to assist in pavement rehabilitation decision making and budget allocation. iv

6 This thesis is dedicated to my mother, Tejovathi Perisetti, to my father, Late Venkateswarlu Balla, and to my sister, Dr. Purnima Sobha Balla v

7 ACKNOWLEDGEMENTS I would like to take this opportunity to express my deepest sense of gratitude to my advisor, Dr. Eddie Yein Juin Chou for his invaluable guidance, motivation, constant encouragement, tolerance, and financial support without which this dissertation could not have this shape. I would also like to thank Dr. Azadeh Parvin, and Dr. George J. Murnen for agreeing to be my committee members for their inputs, support, and guidance. I would also like to acknowledge the City of Toledo for funding this study and for providing rehabilitation data. I would like to thank my colleagues and friends Debargha Datta, Dr. Haricharan Pulugurta, and Praneeth Nimmatoori for their generous suggestions, inputs, and encouragement. I would also like to thank all my friends for their support, special thanks to Abdul, Amanesh, Anil, Ashok, Bivash, Ishan, Jatin, Jun, Madhura, Parth, Prabhu, Shravan, Sri Hari, Shuo, Thihal, and Varun. Finally, I would like to thank my mother and my sister; for their unceasing support, morale, love, and encouragement they provided me in course of my thesis. They are always been my moral support in every sphere of my life. I could not have made it this far without them. vi

8 TABLE OF CONTENTS Abstract... iii ACKNOWLEDGEMENTS... vi TABLE OF CONTENTS... vii LIST OF TABLES...x LIST OF FIGURES... xi 1. INTRODUCTION Introduction Statement of Problem: Objectives of the study: LITERATURE REVIEW Pavement Management System Prediction Levels in Pavement Management: Pavement Condition Factors That Could Affect Pavement Condition Treatment Type Materials Traffic Loading Pavement Thickness Climate...14 vii

9 2.3.7 Condition Prior to Treatment Prediction Methods Remaining Service Life (RSL): DATA AND METHODOLOGY Introduction Calculation of Pavement Condition Rating (PCR) Methodology Survival Curve Kaplan-Meier method Example Extrapolation of incomplete survival curve using Weibull distribution function Example Derived Performance Curve Remaining Service Life Example RESULTS AND DISCUSSIONS Introduction Survival Curve Calculation of Survival Probability Kaplan Meier method Weibull approximation of Kaplan-Meier method Remaining Service Life Median Remaining Service Life Remaining Service Life by PCR and Age...61 viii

10 4.5 PCR Curves Results Conclusions SUMMARY, CONCLUSIONS, AND RECOMMENDATIONS Summary Conclusions Recommendation Future Recommendations...73 APPENDIX A...74 APPENDIX B...75 References :...76 ix

11 LIST OF TABLES Table 3.1 Number of PCR collected Pavement Miles at different ages...24 Table 3.2 Pavement Lane Miles reached PCR Table 3.3 Calculation of Pt and S(t) for PCR Table 3.4 Kaplan - Meier Survival Curve and Weibull Curve Data for PCR Table 4.1 Pavement Lane Miles reached to each PCR Threshold at different ages..44 Table 4.2 Pavement Lane Miles that were not reached to each PCR Threshold at any respective ages...46 Table 4.3 Kaplan Meier Survival Curve Data, Calculation of pt and S (t)...47 Table 4.4 Kaplan Meier Survival Curve Data for PCR Table 4.5 Linear Regression Solution in Microsoft Excel...50 Table 4.6 Calculated S (t) values by using Weibull distribution...52 Table 4.7 Remaining Service Life...57 Table 4.8 Pavement Age at different PCR values...58 x

12 LIST OF FIGURES Figure 2.1 Calculating RSL for an Individual Condition Index...20 Figure 3.1 Toledo City and Major Streets...22 Figure 3.2 Pavement miles with rehabilitation data...23 Figure 3.2 PCR collected Frequency Plot of Pavement Age Vs Number of Pavements/miles...25 Figure 3.3 Pavement Condition Rating (PCR) Scale...28 Figure 3.4 Kaplan Meier, Survival Probability Vs Pavement Age for PCR Figure 3.5 Weibull Survival Curve, Pavement Age Vs Survival Probability...39 Figure 3.6 Example Figure to find Remaining Service Life at 6 years Figure 4.1 Kaplan Meier Survival Curve...48 Figure 4.2 Weibull approximation of Kaplan Meier Survival Curve...53 Figure 4.3 Average service Life of a pavement lane mile to reach PCR Figure 4.4 Probable Life Curve...56 Figure 4.5 Derived Performance Curve for different percentile of pavement sections59 Figure 4.6 Calculating Median Remaining Service Life...60 Figure 4.7 Calculating Remaining Service Life by PCR and Age...62 Figure 4.8 RSL variation for PCR Figure 4.9 Pavement Condition Rating Curves...64 xi

13 Figure PCR and RSL Miles...65 Figure 4.11 Visual representation of 2009 PCR data for Toledo City...66 Figure 4.12 Visual representation of 2009 RSL data for Toledo City...67 xii

14 CHAPTER 1 INTRODUCTION This chapter introduces the need for the prediction of remaining service life for pavements and states the objectives of the study. 1.1 Introduction Transportation contributes to the economic, industrial, social and cultural development of any country. It plays a vital role for the economic development of any region or nation, since development of transportation facilities raises living standards, and improves the aggregate community values. The major goal of any transportation system is the safe, rapid, and convenient movement of people and goods from one place to another in order to enhance economic activity and development (Gedafa D. B. 2008). In the United States, transportation over the course of its historical development has been fundamentally influenced and shaped by legislation (Gedafa D. B. 2008). Whereas technical advances have made it possible to transport people and goods in a more efficient manner, major improvements in the transportation industry have been shaped by the larger institutional systematic frame work that determines present and future needs and seeks to give them cost effective yet far-reaching solutions (Gedafa D. B. 2008). Because, human beings are surrounded by three basic mediums i.e. land, water and air; the modes of transportation 1

15 are also connected with these three mediums for the movement. Among the major modes of transportation, transportation by road is the only mode, which provides maximum service in terms of accessibility and mobility. Roads are the dominant means of transportation in many countries today (Mitchell and Maree 1994). As roads play an essential role in achievement of government s overall social, economic, security, and developmental goals, much capital has been expended in developing extensive road networks worldwide. The United States road network of major highways includes almost four million miles of pavement (FHWA 1993). This pavement network forms a significant portion of the national transportation infrastructure and represents a cumulative investment of hundreds of billions of dollars over several decades (Gedafa D. B. 2008). To preserve the investment spent on this huge network of pavement, extensive maintenance and repair activities are necessary, with the intention of using funds optimally. With a large network of highways in place, a highway engineer s concern is shifted from construction to maintenance (T.S. Vepa et al 1996). It has been said that one dollar invested in preventive maintenance at the appropriate time in the life of a pavement can save $3 to $4 in future rehabilitation costs (Geoffroy 1996). For facilitating the management of the existing network, pavement management systems (PMSs) have evolved over the last three decades. With increasingly limited national funds for transportation infrastructure preservation and renewal, there has been a growing need for strategic management of the national pavement network to preserve this large capital investment. 2

16 Initially this strategic need led to the concept of increasing pavement life with the help of Maintenance and Rehabilitation (M&R) activities. M & R activities are the activities that are primarily concentrated on sealing surface cracks and potholes on pavement surfaces so that they will be less likely to propagate further to endanger the stability of the structure of the pavement (Joseph E. Ponniah et al 1996). The future performance of a highway depends upon the suitability of the applied treatment, timing of treatment, and quality of maintenance treatment it receives. Effective sealing of cracks and joints is necessary to reduce the amount of water entering the pavement structure and causing accelerated damage (Joseph E. Ponniah et al 1996). To address the problem of managing M&R activities, the Intermodal Surface Transportation Efficiency Act (ISTEA) was passed in ISTEA s mandates include the development and implementation of various infrastructure and monitoring systems; pavement, bridge, highway safety, traffic-congestion, public transportation facilities and equipment, and intermodal facilities and management systems. The goal is to optimize available funds in preserving the national transportation infrastructure. Consequently, in order to qualify for federal funds, states and their local jurisdictions were to implement working infrastructure management systems, consisting of all seven mandated categories (Amekudzi and Attoh-Okine 1996). Proper management of the system requires the collection, analysis, and interpretation of factual data relating to construction and maintenance activities. Prediction of the future 3

17 condition of each pavement as well as that of the entire network is an essential element of a management system (T.S. Vepa et al 1996). A Pavement management system requires prediction of pavement life. Pavement life can be defined by two terms, service life and remaining service life. Service life can be defined as a measure in years from construction to first rehabilitation or from the last completed work to the next. Rehabilitation work may be defined as the reconstruction or resurfacing of present pavement. Service life of a pavement is the time elapsed between two successive constructions performed on a particular pavement. Both service life and remaining service life of pavement can serve as tools for PMS. The purpose of remaining service life of a pavement is to help pavement management system assessing pavement s current and projected condition, determine budget needs to maintain the average condition of pavement above an accepted level, prioritize projects, and optimize spending of maintenance funds. The evaluation of remaining service life is necessary to make optimal use of the structural capacity of the in-service pavement. It simply represents the useful life left in the pavement until a failure condition is reached. Knowledge of remaining service life facilitates decision making in regard to strategies for reconstruction-rehabilitation of roads, thereby leading to the efficient use of existing resources. Prediction of remaining service life is important because prediction of future pavement condition is one of the most important functions of a PMS, i.e. when the pavement will reach its terminal condition which requires rehabilitation. 4

18 The measurement and prediction of pavement condition is a critical element of any pavement management system (PMS). Pavement condition rating (PCR), a composite statistic derived from functional and structural conditions, is used as one measure of serviceability (George et al 1989). Pavement serviceability or ride quality indices have also been widely applied to monitor pavement performance and deterioration for pavement rehabilitation, design, and other purposes. It is known that the ride quality or serviceability index of roads can be explained mainly by the vertical jerk experienced by raters sitting in a moving vehicle (Chiu Liu et al 1998). 1.2 Statement of Problem: Remaining service life (RSL) is the number of years that a pavement will be functionally and structurally in an acceptable condition with only routine maintenance. This combines severity and extent of different distresses and rates of deterioration. RSL also requires development of a performance model and establishment of a threshold value for each distress measurement. Based on the threshold value, current distress level, and deterioration model, time for each distress to reach the threshold value can be computed (Baladi 1991). Calculating remaining life has been a complex task, to say the least. Existing methods rely on various concepts from purely empirical to truly mechanistic. The lack of adequate performance prediction models has been the major impediment in predicting remaining life (T.S. Vepa et al 1996). Calculating RSL has been a complex task due to lack of adequate performance prediction models required for determining 5

19 timing of the rehabilitation project. The failure of a pavement can be categorized as structural or functional failure. In the functional failure-based approach, the remaining life is computed on the basis of the performance of the pavement (for example, serviceability or ride ability). A structural failure-based approach requires the structural stability of pavement, such as pavement deflection data and visual condition data (PCR). In the functional failure-based approach for estimating remaining life, the decrease in the performance index with age or traffic is charted in conjunction with a functional failure criterion. Alternatively, the structural failure-based approach makes use of fatigue principles, which requires the effective thickness or modulus derived from in situ measurements (T. S. Vepa et al 1996). The structural failure method and performance of the pavement (functional failure method) requires historical data, which is not always available. Most pavements have the current pavement condition data. Statistical models are based on data collected from test roads located at diverse geographical locations. The LTTP test project is a rather extreme example, with pavement sections monitored throughout the entire United States. However, due to the enormous cost to construct and monitor pavements, the number of LTPP sites in Ohio is rather limited. Therefore, a more practical and sensible approach is to be developed in predicting remaining service life of pavement in a region. Since, it is difficult to maintain the historical pavement performance data for each pavement section, it is required to establish a performance model for individual pavement sections. Thus, this study was initiated to assess the feasibility in predicting remaining service life by 6

20 using survivor curves of groups of pavements based on its age and current condition rating. 1.3 Objectives of the study: The main objectives of this study are: 1. To develop a remaining service life (RSL) model using the survivor curve method. 2. Analyze the average service life of pavements from RSL obtained from the survivor curve. 3. To develop PCR curves to establish a relationship between pavement age, condition rating, and remaining service life. 7

21 CHAPTER 2 LITERATURE REVIEW This chapter describes the past research work that was performed to predict the remaining service life of pavements and the possible method that can be used for the current dataset. 2.1 Pavement Management System The pavement management system (PMS) was first conceived in the late 1960s to 1970s as a result of pioneering work by Hudson et al (1968) and Finn et al (1977) in the United States, and by Haas (1977) in Canada. AASHTO (1990) defines PMS as follows: A PMS is a set of tools or methods that assist decision makers in finding optimum strategies for providing, evaluating, and maintaining pavements in a serviceable condition over a period of time. The products and information that can be obtained and used from a PMS include planning, design, construction, maintenance, budgeting, scheduling, performance evaluation, and research (Hugo et al 1989; AASHTO 1990). The goal of a PMS is to yield the best possible value for available funds in providing and operating smooth, safe, and economical pavements (Lee and Hudson 1985). The functions of a PMS is to improve the efficiency of decision making, to expand the scope and provide feedback on the consequences of the decisions, to facilitate coordination of activities within the 8

22 agency, and to ensure consistency of decisions made at different levels within the same organization (Haas et al 1994). A PMS provides a systematic, consistent method for selecting maintenance and rehabilitation (M&R) needs and determining priorities and the optimal time of repair by predicting future pavement conditions (Shahin 2005). 2.2 Prediction Levels in Pavement Management: To determine the direction and specificity of project development and planning, decisions can be carried out at two management levels depending on the choice of the decision maker. Those two management levels are network level and project level (Panigrahi 2004). Network-level management focuses on determination and allocation of funds to maintain pavement above a specified minimum operational standard. So, at the network level, prediction model uses include condition forecasting, budget planning, inspection scheduling, and work planning. One of the most important network uses of prediction models is to conduct what if analyses, to study the effects of various budget levels on future pavement condition (Shahin 1994). Project-level management decides which specific road to repair, and the timing and method of repair. So, prediction models at the project level are used to select specific rehabilitation alternatives to meet expected traffic and climatic conditions (Shahin 1994). Detailed consideration is also given to alternative conditions, M&R assignments, and unit costs for a particular section of project within the overall program. This level of 9

23 management involves assessing causes of pavement deterioration, determining potential solutions, assessing effectiveness of alternative repair techniques, and selecting solution and design parameters. The purpose of project level management is to provide the most cost-effective feasible original design, maintenance, and rehabilitation or reconstruction strategy possible for a selected section of pavement for the available funds (AASHTO 2001). Different management levels will need different condition prediction models. Since the main purpose of network-level management is to maintain the overall road network above a specified minimum operational standard with limited budget, it does not focus on how a specific road deteriorates. Therefore, a survival time analysis based on historical condition data is often employed to predict the remaining service life of pavement. The need to reasonably allocate funds requires the factors that affect pavement deterioration be considered. Such consideration can be accomplished by introducing these factors as parameters in prediction models. For any pavement management system, prediction of pavement condition is the first and foremost thing to be determined. Pavement condition can be defined by various indices. 2.3 Pavement Condition Pavement condition is a generic phrase to describe the ability of a pavement to sustain a certain level of serviceability under given traffic loadings. It is usually represented by various types of condition indices such as Present Serviceability Index (PSI), Present 10

24 Serviceability Rating (PSR), Mean Panel Rating (MPR), Pavement Condition Index (PCI), Pavement Condition Rating (PCR), Ride Number (RN), Profile Index (PI), and International Roughness Index (IRI). These indices can be classified into two categories: roughness-based and distress-based. Roughness is defined as the variation in surface elevation that induces vibrations in traversing vehicles in ASTM E867. It has been recognized as an important measure of road performance since the 1940 s and can be measured using either direct or indirect methods (Huang 1993). Several commonly used roughness measures are IRI, RN, and PI. Distress-based condition ratings, for example, PCI and PCR, evaluate the comprehensive condition of a road by categorizing a pavement s surface distresses by type, frequency, and extent. Each distress is manually inspected for representative pavement sections. A score is assigned to each distress found according to its frequency and severity. Distresses are weighted according to their importance to the pavement. A PCI or PCR pavement condition is obtained by subtracting the sum of all distresses from 100 (Shahin 1994). Thus, both PCI and PCR are numerical ratings of the pavement condition that range from 0 to 100, with 0 being the worst possible condition and 100 being the best possible condition. The Ohio Department of Transportation has been employing PCR as the condition index for its highway systems since 1985 (Morse and Miller 2004). 11

25 2.3.1 Factors That Could Affect Pavement Condition There are a number of variables that affect the deterioration of pavements. These major factors affecting pavement performance are considered in pavement design procedures. For accurate prediction, the same factors should be considered in condition prediction models (Lytton 1987). These factors include treatment type, materials, traffic loading, pavement structure, climates and pavement condition prior to the treatment. In practice, the choice of factors is also limited by data availability. Prediction models can only be developed based on available data. Those factors are discussed briefly in the following sections Treatment Type Various treatments can be performed on a pavement. Major treatments usually are new construction and minor treatments are overlays on existing pavement. There are three types of new constructions: rigid, flexible, and composite. Rigid pavement uses concrete as the main pavement material. Flexible pavement uses asphalt concrete as the main surface material. Composite pavement typically consists of asphalt overlays on an existing rigid pavement. Each treatment type is considered to have its own deterioration behavior and forms a unique pavement family Materials Pavement performance is affected by material characteristics. Pavements with the same design structure in different geographical areas may have different performances due to the following reasons: (1) different specifications may be applied during design; (2) the 12

26 aggregate type and its mechanical property may vary regionally; (3) the subgrade modulus may vary from section to section. In addition, the construction quality may also affect the strength and durability of a structure. These factors should be considered not only in the pavement design but also in condition prediction. However, for this study, very limited information about materials is available. Thus analysis of their effects on pavement performance cannot be performed in this study Traffic Loading Three types of traffic data; Average Daily Traffic (ADT), Average Daily Truck Traffic (ADTT), and Equivalent Single Axle Load (ESAL) are usually collected by transportation agencies. ESAL value converts all traffic into an equivalent damage done by the passing of a single 18,000-pound axle. Since higher traffic loadings will cause more damage to the pavement, design procedures generally account for increased traffic loading with increased pavement thickness. The effect of traffic loading on pavement performance should be considered whenever appropriate Pavement Thickness Pavement thickness is a major factor that could affect pavement performance. The thickness of a treatment is usually determined by specific design procedure and should be considered in pavement condition prediction models. 13

27 2.3.6 Climate Temperature, snowfall, and precipitation affect pavement performance as pavement materials may deteriorate faster in more severe climatic conditions. Climate effects should be included in pavement condition prediction models Condition Prior to Treatment Pavement condition prior to rehabilitation may affect pavement performance. It may be hypothesized that pavements in better condition prior to overlay may perform better than those pavements with worse prior condition. Pavement condition rating (PCR), which accounts for various distresses, represents the overall pavement condition. STRD, which stands for structural deduct, is an indicator of the overall remaining structural capacity of a pavement. These two quantities may be considered during condition prediction modeling. 2.4 Prediction Methods Methods for predicting pavement conditions can be generally classified into three categories according to the format of the mathematical representation: deterministic, probabilistic and other methods such as neural network method. Deterministic regression is perhaps the most popular prediction model in pavement condition prediction studies. It is usually expressed as a regression equation with the dependent variable being the condition index and independent variables being the age of the pavement, pavement type, and other influential factors. Several regression equations 14

28 might be developed - one for each family of pavements. A family is a group of pavements that have similar characteristics and thus are expected to deteriorate similarly. According to the need, family determination can be subjective or based on potential explanatory variables such as pavement type, repair alternative, and traffic loading (Shahin 1994). Linear and non-linear regression analysis is often used in developing deterministic prediction models (Lytton 1987). Power curve (Chan et al 1997) and sigmoidal curve (Sadek et al 1996) are the most popular non-linear regression formats in predicting pavement conditions. B-spline approximation was also employed to seek potential improvements for condition prediction (Shahin et al 1987). However, most non-linear models used in pavement condition prediction can be converted into linear models by variable transformation (Laird and Ware 2004). Prior knowledge of the factors that affect performance is essential in developing reasonable empirical models. Unlike deterministic models, probabilistic models predict the pavement condition with certain probability. The result from such a model is usually a probability distribution but not a fixed number. A probabilistic model can easily take the previous condition into account for the current condition prediction (Lytton 1987). Thus, it has some advantages over a deterministic model especially for overlays on an old pavement. 2.5 Remaining Service Life (RSL): The remaining service life (RSL) is the anticipated number of years that a pavement is in acceptable condition to accumulate enough functional or structural distress under normal conditions, given that no further maintenance is performed or distress points equal to an 15

29 as defined threshold value (Baladi 1991). RSL is calculated from the condition of the asset during that year and the projected number of years until rehabilitation is required. Once RSL is estimated for each pavement section in the network, the sections are grouped into different categories (Dicdican et al 2004). It combines the severity and extent of different distresses and the rate of deterioration. It requires development of a performance model and establishment of a threshold value for each distress type. Based on these threshold values, the current distress level and deterioration model for each particular distress, and time for each distress to reach the threshold value, can be computed. The shortest of these time periods is the RSL of the pavement section (Baladi 1991). The definition of the threshold values depends on the criteria used to control longterm network conditions (Kuo et al 1992). Existing methods rely on various concepts from purely empirical to truly mechanistic. Lack of adequate performance prediction models has been the major impediment in predicting remaining life (Vepa et al 1996). Remaining service life (RSL) can be estimated in many different ways. Some researchers tried to estimate pavement remaining service life from fatigue test (Witczak and Bell 1978, Carson and Rose 1980, Huang 1993, McNerney et al 1997). Other researchers correlated the number of punchout failures per mile to the remaining ESALs, equivalently the remaining life, for continuously reinforced concrete (Dossey et al 1996). Artificial Neural Network was also applied in estimating the RSL by researchers in Texas (Ferregut et al 1999, Abdallah et al 2001). In 1986, AASHTO proposed an important method to estimate the RSL for overlay design. In this method, the RSL of the existing pavement is estimated using the Non-destructive Test (NDT). The current pavement 16

30 layer elastic modulus is back-calculated from the deflection data. Then, the existing pavement condition is related to its initial structural capacity by a condition factor, C x. The RSL of overlaid pavements, which is expressed as a function of the value of C x, was calculated based on the projected future traffic applications and the ultimate number of repetitions to failure time (Zhou et al 1989). The advantage of this mechanistic method is that historical traffic data are not required. A main drawback of this method is that it requires the back calculation of the subgrade moduli, which is highly variable; therefore, a very large number of deflection data would be required. Yet another commonly used method to estimate the RSL of a pavement is to use the performance regression model. By predefining the terminal condition, for example, PCR of 70, it is possible to back calculate the age to reach that condition. Then, the RSL is determined by subtracting the current age from the back calculated age. The most popular method to estimate RSL is the survival time analysis, which is considered a probabilistic model. This method was employed to obtain the RSL for pavements in the United States as early as in 1940 s (Winfrey and Farrell 1941). Survival curves were developed for pavements built in each calendar year from 1903 to 1937 in 46 states using the life table method. According to Winfrey and Farrell (1941), the distribution of survival times is divided into a certain number of equal intervals, e.g. 1 year or half a year. For each interval, the mileage of pavement sections still in service at the beginning of the respective interval, the mileage of pavement sections that were out of service at the end of the respective interval, and the mileage of pavement sections that 17

31 were lost (for example, a road was completely out of service) during the respective interval are counted. Survival probability of each interval is calculated by dividing the remaining mileage by the total mileage entered for the respective interval. Survival curve is formed by drawing the probability versus the time interval in a chronological order. The remaining service life can be estimated by extrapolating the survival curve to zero percent survival. The life table method has been extensively used in the analysis of pavement RSL (Gronberg et al 1956, Winfrey and Howell 1967). The Kaplan-Meier method, which is also called the product-limit method (Kaplan et al 1958) is another procedure often used to generate survival curves. In the Kaplan-Meier method, the probability of survival to time t is expressed as the product of the survival of each year till time t. The Kaplan-Meier method and the life table method are identical if the intervals of the life table contain at most one observation. Survival curves method, which assumes an underlying failure distribution of the data, is an alternative to analyze RSL (Prozzi and Madanat 2000). Because survival function is now expressed explicitly in terms of a certain parametric distribution function, it is possible to estimate the coefficients of those parameters, or in other words, the effects of influential factors. However, the need to assume the underlying distribution introduces another problem, that is, the shape of the data may not be described by a known distribution. This is the major limitation of this method. 18

32 RSL is used for future planning and budgeting purposes. This is not only useful for timing a major rehabilitation but also assists managers in forecasting long-term needs of the network. The evaluation of RSL is necessary to make optimal use of the structural capacity of in-service pavements. Knowledge of RSL facilitates decision making in regard to strategies for reconstruction-rehabilitation of roads, thereby leading to efficient use of existing resources (Vepa et al 1996). Accurate RSL models improve the process of allocating funds and resources for maintenance and rehabilitation of asphalt pavements (Romanoschi and Metcalf 2000). To calculate RSL for a pavement section, the agency needs its current condition, a definition of serviceable condition, and a mechanism to predict deterioration of the pavement condition. Figure 2.1 shows the information required to calculate RSL. 19

33 Condition Index Present Condition Performance Curve Serviceable Condition Threshold Value Remaining Service Life Time (Years) Figure 2.1 Calculating RSL for an Individual Condition Index 20

34 CHAPTER 3 DATA AND METHODOLOGY This chapter describes the data used and the methodology adapted to predict the remaining service life of pavements. 3.1 Introduction Monte Carlo (or stochastic) modeling techniques have long been used for exploring the impact of uncertainty. In its purest sense, Monte Carlo simulation employs a mathematical model that interjects randomness between limits to determine a probabilistic or likely outcome. Typically, this result is in the form of a probability distribution, the shape of which lends insight into what is likely to occur if the modeled course of action is pursued. In this chapter data used in this study is described and the methodology used to predict the remaining service life is also discussed. 21

35 3.2 Data The City of Toledo is divided into six districts. Its road system has a total of 1121 miles and is divided into Major Streets and Residential Streets according to their importance, location and traffic carried. There are a total of 356 miles of major streets and 765 miles of residential streets. Major streets of Toledo are further divided into state routes and county routes. Figure 3.1 Toledo City and Major Streets The data used to demonstrate the methodology are detailed pavement condition and project history of Major streets of Toledo. Detailed Pavement condition is obtained in 22

36 the form of Pavement Condition Rating (PCR) from the Ohio Department of Transportation (ODOT) for both state routes and county routes. ODOT has maintained state routes Pavement Condition Rating data and project history data since 1985 and county routes data for every alternate year since 2003 i.e. for years 2003, 2005, 2007 and For county routes, the City of Toledo maintains the project history data. Figure 3.1 shows the City of Toledo and its Major streets. In order to know the PCR data variation with age the pavement age must be known. Out of 356 miles of major streets pavement rehabilitation data is available for 199 miles. Figure 3.2 shows the number of unique miles with the rehabilitation data in major streets category of City of Toledo. 157 Miles, 45% 199 Miles, 55% Rehabilitated Others Figure 3.2 Pavement miles with rehabilitation data 23

37 In order to know the PCR data variation with age we need to know the pavement age. This is possible by taking the construction year for a particular pavement as zero. Table 3.1 shows the tabulated number of pavement miles with PCR data at each age. Table 3.1 Number of PCR collected Pavement Miles at different ages Age Miles

38 Figure 3.2 shows the frequency plot of number of pavement miles with PCR data according to their age. Number of Pavement Miles Pavement Age Figure 3.2 PCR collected Frequency Plot of Pavement Age Vs Number of Pavements/miles 3.3 Calculation of Pavement Condition Rating (PCR) Pavement Condition Rating (PCR) is a distress based rating which evaluates the comprehensive condition of a road by categorizing 14 different distresses: raveling, bleeding, patching, surface disintegration / debonding, rutting, map cracking, base failure, settlements, transverse cracks, wheel track cracking, longitudinal cracking, edge cracking, pressure damage / upheaval, and crack sealing deficiency. 25

39 The rating method is based upon the visual inspection of pavement distress. The rating method provides a procedure for uniformly identifying and describing, in terms of severity and extent, pavement distress. The mathematical expression for pavement condition rating (PCR) provides an index reflecting the composite effects of varying distress types, severity, and extent upon the overall condition of the pavement. The model for computing PCR is based upon the summation of deducts points for each type of observable distress. Deduct values are a function of distress type, severity, and extent. Deduction for each distress type is calculated by multiplying distress weight times the weights for severity and extent of distress. Distress weight is the maximum number of deductible points for each distress type. The mathematical expression for PCR is as follows. PCR = Deduct i n I = 1 Eq (3.1) Where, n = number of observable distresses, and Deduct = (Weight for distress) (Weight for severity) (Weight for Extent) The Appendix A & Appendix B describe various distresses for local flexible pavement adopted by ODOT for establishing their severity and extent. Three levels of severity (Low, Medium and High) and three levels of extent (Occasional, Frequent, and Extensive) are defined. 26

40 To illustrate the method for calculating PCR, consider the distress raveling in a hypothetical local asphalt pavement. If the severity of this distress in the pavement is Medium and extent is Frequent, then, the deduct points for Raveling in the pavement would be equal to [(10) (0.6) (0.8)] or 4.8. If an extensive amount of medium severity Surface Disintegration is also observed the deduct points for this distress would be equal to [(5) (0.6) (1)] or 3.0. According to equation 3.1, PCR for the pavement based upon these two distresses would be equal to [100 ( )] or To know the pavement behavior with age, the PCR values must be plotted according to age of the pavement. To get the age of pavement the construction year of the pavement must be known. After subtracting the latest constructed year from the present year the age of the pavement can be obtained. In the current study, construction year of the pavements in City of Toledo was obtained from Ohio Department of Transportation (ODOT) and City of Toledo. Table 3.1 shows the number of pavement sections reconstructed in each year. Figure 3.3 illustrates the PCR scale adopted in this study and the descriptive condition of a pavement associated with the various ranges of the PCR values. The scale has a range from 0 to 100; a PCR of 100 represents a perfect pavement with no observable distress and a PCR of 0 represents a pavement with all distress present at their High levels of severity and Extensive levels of extent. 27

41 Figure 3.3 Pavement Condition Rating (PCR) Scale 28

42 3.4 Methodology This section describes the method used to predict the remaining service life (RSL) for the pavement data described in section Survival Curve Changes in the pavement age can be described by using survival curves. Survival curves give the percentage of pavement sections that last a certain number of years before a terminal event. Survival curves can be constructed for an individual pavement or a pavement population. An individual survival curve plots the probability that an individual pavement section will remain in service as a function of age. A population survival curve plots the fraction of pavement population that remains in service as a function of age. When a pavement section fails, then it will be out of the system. The height of the curve begins at one and declines as age and time increase. The slope of the curve depends on the rate of pavement failures, with steeper decreases in periods of higher rate of pavement failures Kaplan-Meier method In this study, the Kaplan-Meier method is used to calculate the survival probability using available historical PCR data. According to Kaplan-Meier, the survival probability at a given year is a multiplication of each of the preceding year s conditional probability of failure. The conditional probability of failure in a particular year is calculated by dividing the number of failures occurring in that year by the number of pavements at risk 29

43 of failure at the beginning of that year. The conditional probability p t of surviving th t year after having survived 1 t years is calculated as: p t = th th Number of pavements failed in interval t year and t + 1 year, Eq (3.2) Number of pavements at risk of failure begining of t year 1 th The probability of survival to time t, S(t) is calculated as: S ( t) = p1 p2.... Eq (3.3) p t The graph of S(t) versus the t gives the Kaplan-Meier survival curves. In the current study, survival analysis is used to determine: (1) average age of pavement network before its terminal condition; and (2) the remaining service life of pavements Example Let the PCR of 60 be the criterion for failure of a pavement. That means when a pavement reaches PCR of 60, that pavement has failed and will be out of the system. Table 3.2 shows the number of miles of pavements in City of Toledo that reached PCR 60 at each age. Total number of lane miles of pavements in the data set is If in year 6, the number of lane miles of pavements falling to a PCR 60 is 1.40 and the cumulative number of lane miles of pavements that reached PCR 60 at this age is 2.65 miles (0.44 miles miles miles). That means, total number of lane miles of pavements that have not reached PCR 60 at this age is = Using equation 3.2, the conditional probability pt can be calculated as described below. 30

44 p th Number of pavements failed in interval 6 year and 7 = 1 Number of pavements at risk of failure begining of 6 6 th th year year Table 3.2 Pavement Lane Miles reached PCR 60 Pavement Age Lane Miles reached PCR

45 2.65 p 6 = 1 = Similarly, 4.06 p 7 = 1 = Probability of survival to time t for year 6 can be calculated by using equation 3.3 S (6) = = 0.99 By using the above illustration, S (t) values for all the pavement ages are obtained and are given in Table

46 Age Table 3.3 Calculation of Pt and S(t) for PCR 60 Pavement Lane Miles reached PCR 60 Pavement Lane Miles at risk of failure Pt S(t)

47 Figure 3.4 shows the plot of Kaplan-Meier curve for the data given in Table Survival Probability, S(t) Pavement Age Figure 3.4 Kaplan Meier, Survival Probability Vs Pavement Age for PCR Extrapolation of incomplete survival curve using Weibull distribution function A Kaplan-Meier survival curve cannot be completed for the incomplete pavement condition data. To get unbiased estimates from a stub survival curve, the tail of the survival curve should be extrapolated to reach zero survival probability (Reilly 1998). A 34

48 Kaplan-Meier survival curve can be extrapolated to zero survival probability by using the Weibull survival function. The Weibull survival function that is given by: B Age S(t) = e A. Eq (3.4) Where S (t) is the survival probability at an age, Age in years. A is the scale parameter that determines the spread of the Weibull curve; and B is the shape parameter, which determines the shape of the Weibull curve. The parameters A and B are estimated by reducing the residual sum of squares. Then the Weibull survival function becomes Age B A ln S(t) = ln e Eq (3.5) B Age ln S( t) = Eq (3.6) A B 1 Age ln = Eq (3.7) S( t) A B 1 Age ln ln = S t ln Eq (3.8) ( ) A 1 ln ln S ( t) = B [ ln( Age) ln( A) ] Eq (3.9) 35

49 1 ln ln = B ln S( t) ( Age) B ln( A) Eq (3.10) It is in linear form and is similar to, y = mx + C Eq (3.11) Where, X = ln ( Age) m = B C C m C = B ln ( A) = m ln( A) ln( A) = A = e Eq (3.12) m y y e ln ln ln = e = e S( t = e Eq (3.13) S( t) S( t) S( t) y y e = ) By using the linear regression option in Microsoft Excel, the solutions for B and C are found and A obtained from the relation in equation Example In Table 3.3, the calculated conditional probability of survival to time t, is shown by using the Kaplan-Meier method described in section This example shows how to extrapolate the incomplete survival curve using Weibull distribution. By using the X and y values from the equation (3.11) and equation (3.13) respectively, the linear equation is solved by using the Regression option in Microsoft Excel as illustrated below. Tools > Data Analysis. Then regression option is selected in the pop up window. 36

50 Regression analysis gives the result of the right hand side of the linear equation. This is the y column in Table 3.4. Table 3.4 shows the calculated Weibull curve data for the corresponding Kaplan-Meier survival curve data for PCR 60. Weibull probability of survival to time, S(t) is found by using equation (3.13). Figure 3.5 shows the generated Weibull curve for the data and calculation shown in this example. From Figure 3.5 it is observed that Weibull distribution function closely approximates the Kaplan-Meier Survival Curve. 37

51 Table 3.4 Kaplan - Meier Survival Curve and Weibull Curve Data for PCR 60 Kaplan - Meier Survival Curve Data Weibull Curve Data Age Pavement Lane Miles reached PCR 60 Pavement Lane Miles at risk of failure Pt S(t) ln(age) y S(t)

52 Kaplan-Meier Survival Curve Weibull Curve Survival Probability, S(t) Pavement Age Figure 3.5 Weibull Survival Curve, Pavement Age Vs Survival Probability Derived Performance Curve Derived performance curves were drawn between pavement age and PCR for different survival probabilities for different PCR values of 95, 90, 85, 80, 75, 70, 65, and 60 by using the Weibull approximation of Kaplan-Meier survival curves which was described in sections and

53 3.4.5 Remaining Service Life Remaining service life (RSL) is another important parameter for network level pavement management. Generally, a RSL distribution of a road network is constructed to analyze the impact of M&R actions on the future condition, to optimize and prioritize the M&R actions, to determine life-cycle cost, and to obtain the feedback on current M&R strategies. A uniform RSL distribution is an indication of an ideal M&R policy. RSL is defined as the amount of time in years from a specified time (usually the latest survey year) to the year when the pavement reaches a threshold or requires the next treatment. Since the pavements will be at different ages at the latest condition survey year, the RSL changes at each age. According to Winfrey (1967) and Reilly (1998), the RSL is determined as the ratio of area under the complete survival curve to the right of an age to survival probability at that age. For example, the remaining service life of a pavement that is currently x years old can be calculated as: Area under survival curve to the right of x years RSL x =. Eq (3.14) Survival probablity at x years Example By using the Weibull survival curve data from Example and using the Remaining Service Life equation as given in equation 3.14 the remaining service life curve is established. By using the equation 3.14, Remaining Service Life for a pavement network to reach PCR 60 at the age of 6 years can be established as explained below. 40

54 RSL 6 = Area under survivalcurve to the right of 6 years (shadedarea in Figure 3.6) Survivalprobablityat 6 years Survival Probability, S(t) Pavement Age Figure 3.6 Example Figure to find Remaining Service Life at 6 years. Area under Weibull Survival Curve to the right of 6 years is units and 0.99 is the corresponding survival probability. From equation (3.14) remaining service life for pavement network to reach PCR 60 at the age of 6 years is i.e years

55 CHAPTER 4 RESULTS AND DISCUSSIONS In this chapter, the remaining service lives (RSL) of the City of Toledo major streets were determined by the derived performance curves as described in chapter Introduction Remaining service life is an important parameter in making decisions regarding pavement rehabilitation. As discussed in chapter 3, the Kaplan-Meir method with the Weibull approximation can be used to determine the pavement s remaining service life by using survival curves. In this chapter, by using the data described in chapter 3, remaining service life is estimated for an entire pavement network by taking PCR 60 as the terminal condition and individual pavement RSL is estimated by using derived performance curves. PCR curves were also derived from Weibull approximation of Kaplan-Meier survival curves for individual PCR values between pavement age and RSL to better understand the relationship between PCR, pavement age, and RSL. 42

56 4.2 Survival Curve In the current study, survival curves were developed for different PCR thresholds based on the Kaplan-Meier method using available historical pavement rehabilitation data, and PCR data described in chapter 3. Survival curves give the percentage of pavement lane miles that last a certain number of years before a terminal event. Using the method explained in section 3.4 for each individual PCR threshold, pavement lane miles were separated based on their age and the details are given in Table 4.1 and the frequency plot between pavement age and number of miles is given in Figure

57 Table 4.1 Pavement Lane Miles reached to each PCR Threshold at different ages Age PCR 95 PCR 90 Pavement Lane Miles Reached PCR PCR PCR PCR PCR 65 PCR Calculation of Survival Probability This section describes the calculation of survival probability for different PCR thresholds by using the method described in chapter 3. 44

58 4.3.1 Kaplan Meier method In this study, the Kaplan-Meier method is used to calculate survival probability. In order to calculate the survival probability according to Kaplan-Meier method, by using the data shown in Table 4.1, conditional probability needs to be calculated. Conditional probability at any age is the percentage of pavement lane miles that has not reached a corresponding PCR threshold in a particular year. Before calculating conditional probability it is necessary to calculate the number of lane miles of pavement length that has survived by not reaching a particular PCR threshold. Table 4.2 shows the number of pavement miles that were not reached to each PCR threshold at any respective age. The Probability of survival to time S(t) is the product of present year conditional probability and the previous year probability of survival to time. 45

59 Table 4.2 Pavement Lane Miles that were not reached to each PCR Threshold at Age PCR 95 PCR 90 any respective ages Pavement Lane Miles Not Reached PCR PCR PCR PCR PCR 65 PCR The conditional probability p t and probability of survival to time S (t), calculated by using equations 3.3 and 3.4 and are given in Table

60 Table 4.3 Kaplan Meier Survival Curve Data, Calculation of pt and S (t) Age PCR 95 PCR 90 PCR 85 PCR 80 PCR 75 PCR 70 PCR 65 PCR 60 Pt S(t) Pt S(t) Pt S(t) Pt S(t) Pt S(t) Pt S(t) Pt S(t) Pt S(t) The graph of S(t) versus the t gives the Kaplan-Meier survival curves. Figure 4.1 shows the Kaplan Meier survival curves generated for each PCR threshold by using PCR data and is obtained by plotting the values given in Table 4.3. One can observe that survival curve for PCR 60 is incomplete because of the incomplete data. According to Reilly (1998), average service life is the service life of a group of 47

61 pavements which is calculated as the area under the complete survival curve. In this case, since the survival curve for PCR 60 is incomplete, the area under this survival curve is infinity, which means the average service life of a particular pavement to reach PCR 60 is infinity. Survival Probability Pavement Age Figure 4.1 Kaplan Meier Survival Curve According to Reilly (1998), to get unbiased estimates from a Kaplan - Meier survival curve, the tail of the survival curve should be extrapolated to reach zero survival probability. The Kaplan-Meier survival curve can be fitted with a curve to extrapolate it to zero survival probability. In the current study, the Weibull distribution function is used to complete the curve. 48

62 4.3.2 Weibull approximation of Kaplan-Meier method Table 4.4 shows the Kaplan Meier survival curve data for pavement lane miles reaching PCR 60. Age Table 4.4 Kaplan Meier Survival Curve Data for PCR 60 Pavement Lane Miles reached PCR 60 Pavement Lane Miles at risk of failure Pt S(t) ln(age) ln(ln(1/s(t)))

63 Table 4.3 also shows the values of ln (Age) and ln (ln (1/S(t))), which is useful in calculating the scale parameters A and B in the Weibull survival function given in equation 3.9. Table 4.5 shows the linear regression solution for equation (3.11) and equation (3.13) by using the method described in section Multiple R R Square 0.99 Adjusted R Square 0.99 Standard Error 0.19 Observations 17 Table 4.5 Linear Regression Solution in Microsoft Excel SUMMARY OUTPUT Regression Statistics ANOVA df SS MS F Significance F Regression E-17 Residual Total Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% Intercept E X Variable E By using the intercept and X variable from Table 4.4 and applying them in equations 3.11, 3.12 and 3.13, the scale parameters A, B and modified S (t) are obtained. Table 4.6 shows the calculated S (t) by using the parameters stated in Table

64 The parameters A and B for equation 3.4 are estimated by using the regression function in Microsoft Excel. The Weibull survival function is: 4.24 Age S(t) = e. Eq (4.1) 51

65 Age Table 4.6 Calculated S (t) values by using Weibull distribution Kaplan - Meier Survival Curve Data Pavement Lane Miles reached PCR 60 Pavement Lane Miles at risk of failure Weibull Curve Data Pt S(t) ln(age) y S(t)

66 Figure 4.2 shows the aforementioned Weibull approximation to the Kaplan Meier survival curves for different PCR thresholds such as 95, 90, 85, 80, 75, 70, 65, and 60. It can be seen that the Weibull fit shows more reasonable estimates to the survival probabilities as it closely follows the Kaplan Meier survival curve. 1 Survival Probability Pavement Age, Years St 90-St 85-St 80-St 75-St 70-St 65-St 60-St Figure 4.2 Weibull approximation of Kaplan Meier Survival Curve 2 The R-square ( R ) is a statistical term expressing how good the regression equation is at predicting the dependent variable. If perfectly predict the value of another term. If not help you know the other term at all. 2 R is 1.0 then given the value of one term, you can 2 R is 0.0, then knowing one term doesn't 53

67 2 R is most often used in linear regression. Given a set of data points, linear regression gives a formula for the line most closely matching those points. It also gives an to say how well the resulting line matches the original data points. 2 R value The 2 R obtained for the model is 0.99, which indicates high accuracy of the fitted Weibull model. The average service life for each PCR threshold is obtained by looking at the corresponding age to the 50 percent survival probability. For example, from figure 4.3, average service life of a pavement lane mile to reach PCR 60 is 15.2 years. The next section describes how the aforementioned survival curves can be used to determine the remaining service life. 1 Survival Probability Pavement Age, Years Figure 4.3 Average service Life of a pavement lane mile to reach PCR 60 54

68 4.4 Remaining Service Life Remaining service life (RSL) is another important parameter for network level pavement management. According to equation 3.14, it is obvious that RSL for a pavement that is zero years old i.e. newly rehabilitated is exactly the average service life. A probable service life curve (Reilly 1998) is then derived from the survival curve and the RSL. A probable service life curve shows the probable service life for pavements at any age. Figure 4.4 shows the Weibull survival function and probable life curve and RSL illustration for a pavement that is 15 years old. 55

69 PCR 60 Survival Curve Probable Service Life Survival Probability Age, 15 Years RSL, 4.4 Years Pavement Age, Years Figure 4.4 Probable Life Curve Table 4.7 shows the average RSL and probable life values derived from the survival curve. It can be seen from Table 4.7 that the average service life of a newly rehabilitated pavement is 15.2 years. 56

70 Table 4.7 Remaining Service Life Age, Years Average RSL Probable Service Life From Table 4.7 it can be seen that the probable service life is increasing with the age as average remaining service life is decreasing. Also, one can observe from Figure 4.4 that as the age of the pavement increases remaining service life decreases. Remaining Service 57

71 Life decreases with the decrease in Survival Probability. Therefore, Remaining Service Life is directly proportional to the survival probability and indirectly proportional to the age of the pavement. To explain the remaining service life calculation more clearly, it is necessary to establish performance curves between PCR and pavement age. Table 4.8 shows the pavement age calculated between survival probability and PCR. Values in Table 4.8 were calculated using the Weibull approximation of Kaplan-Meier survival curves shown in Figure 4.2. Table 4.8 Pavement Age at different PCR values PCR Pavement Age (Percentile) By using the data in Table 4.8, derived performance curves were drawn between PCR values and pavement age for different percentile values of survival probability. Figure 4.5 shows the drawn derived performance curves using the data in Table

72 100 Pavement Condition Rating (PCR) th Percentile 5th Percentile 50th Percentile Pavement Age Figure 4.5 Derived Performance Curve for different percentile of pavement sections Figure 4.5 can be used for calculating the remaining service life using the PCR values. For example, if a particular pavement s PCR value is known, then its age can be calculated by selecting the appropriate derived performance curve from Figure Median Remaining Service Life Median remaining service life is the remaining service life calculated by following the 50 th percentile performance curve or the 0.5 survival probability. 59

73 100 Pavement Condition Rating (PCR) th Percentile 5th Percentile 50th Percentile RSL = = 5.3 years Pavement Age Figure 4.6 Calculating Median Remaining Service Life In this section, calculation of median remaining service life is described for the Airport Hwy section between Fearing Blvd and Detroit Ave. In calculating the median service life, the terminal PCR is taken as 60 and from the Figure 4.6, one can see that the median percentile (50 th Percentile) age at PCR 60 is 15.3 years. In Figure 4.6, Remaining Service Life calculation of the above pavement is explained. The Airport Hwy section between Fearing Blvd and Detroit Ave was constructed before 1993 and its latest PCR was 70 which was collected in the year Since the latest construction year was before the latest PCR data collected year, the consider 2009 PCR value is considered to calculate its remaining service life in the year Using the 50 th 60

74 percentile derived performance curve, the median RSL in the year 2009 for the Airport Hwy section is found based on its 2009 PCR value as 5.3 years. In calculating the remaining service life, 50 th percentile curve is taken and hence the calculated remaining service life is called as median remaining service life. Considering 50 th percentile deterioration is acceptable if the construction year of that particular pavement is unknown. But, it makes sense to consider the percentile deterioration curve that represents the construction year and current condition rating of a particular pavement section. The next section describes the calculation of remaining service life by following the deterioration curve which represents both construction year and condition rating Remaining Service Life by PCR and Age In Figure 4.7, remaining service life calculation of the Hill Ave section from Bonaparte Drive to Clarion Ave is explained. The Hill Ave section from Bonaparte Drive to Clarion Ave was constructed in 2004 and its latest PCR was 80 which was collected in the year Hence the age of this pavement section in the PCR data collection year is 5 years. Since the latest construction year was before the latest PCR data collected year, 2009 PCR value may be used to calculate its remaining service life in the year

75 100 Pavement Condition Rating (PCR) th Percentile 5th Percentile 85th Percentile RSL = = 5.9 years Pavement Age Figure 4.7 Calculating Remaining Service Life by PCR and Age Based on the pavement age and its PCR value, the 85 th percentile performance curve may be considered. By using 85 th percentile performance curve, RSL in the year 2009 for the Hill Ave section based on its 2009 PCR value as 5.9 years. 4.5 PCR Curves Based on derived performance curves shown in Figure 4.5 and the method described in section 4.4.2, we can observe that RSL varies for any particular PCR value. For example, for a pavement section which has PCR of 65, its RSL varies from minimum value of 0.8 years to a maximum value of 6 years. This was explained in figure

76 th Percentile Pavement Condition Rating (PCR) th Percentile RSL Min = = 0.8 years RSL Max = = 6 years Pavement Age Figure 4.8 RSL variation for PCR 65 PCR curves were developed between pavement age and remaining service life for different PCR values and are shown in Figure

77 Remaining Service Life PCR 90 - PCR 85 - PCR 80 - PCR 75 - PCR 70 - PCR 65 - PCR Pavement Age Figure 4.9 Pavement Condition Rating Curves From Figure 4.9, it is observed that for each PCR value there is a wide range of remaining service life and pavement age values. Also, remaining service life increases with the pavement age for any individual PCR. For example, considering a PCR 65, its remaining service life varies from 0.8 years to 6 years. It can be explained, if a pavement attains 65 PCR in its 5 th year that means its deterioration rate is faster and hence it has only 1 more year left to achieve PCR 60. On the other hand, if a pavement attains 65 PCR in its 19 th year that means its deterioration rate is slower than the pavement which reaches to 65 PCR in 5 years hence it has the remaining service life of 6 years. 64

78 4.6 Results Figure 4.10 shows the 2009 PCR and corresponding RSL miles calculated based on the method described in section for the City of Toledo. For sections which do not have rehabilitation data and have only PCR data RSL is calculated by following the 50 th percentile curve by using the method described in section % 95% 90% 85% 80% 75% 70% 65% 60% 55% 50% 45% 40% 35% 30% 25% 20% 15% 10% 5% 0% 85.2 Miles 96.4 Miles Miles Miles Miles Miles 10 > Miles Miles Miles Miles 69.7 Miles PCR 2009 RSL Figure PCR and RSL Miles Figure 4.11 shows the visual presentation of 2009 PCR data for all Toledo City streets. 65

79 Figure 4.11 Visual representation of 2009 PCR data for Toledo City Figure 4.12 shows the visual representation of 2009 RSL data for all City of Toledo streets. Converting Figure 4.11 to Figure 4.12 all the streets with a PCR 60 or below have RSL 0. In this study, the terminal condition was taken as PCR 60. That means when a pavement section reaches PCR 60 it has failed and attains RSL 0. 66

80 Figure 4.12 Visual representation of 2009 RSL data for Toledo City 4.7 Conclusions In this study, the Kaplan Meier method is used to predict remaining service life for pavement sections and the terminal PCR which describes when the pavement is out of the system was assumed as 60. In the Kaplan-Meier method, survival curves were developed by using the pavement rehabilitation and condition data. Average service life, defined as the time taken by a newly rehabilitated pavement section to reach a terminal condition i.e. PCR 60, is then calculated as the area under the survival curve. Also, it was observed that there are 67

81 pavement sections that are still surviving at the end of the analysis period i.e Hence, the survival curve does not reach zero percent survival, and resulting in an incomplete survival curve (Reilly 1998). Completing the survival curve is important because the area under incomplete survival curve is infinite that means the average service life of a pavement is infinite. In order to fix the incomplete survival curve and to force the survival curve to reach zero percent survival probability, survival curves were fitted with the Weibull function to complete the survival curve before computing the average service life. Then, the remaining service life was computed by using the methodology proposed by Reilly (1998). It was observed that the remaining service life calculated is for a group of pavements and not for individual pavements. Hence, the requirement is to determine the remaining service lives of individual pavements based on the latest PCR values and age. Therefore, derived performance curves were developed between the PCR and the pavement age to predict the remaining service life of individual PCR values. In this dataset there are two types of pavement sections. Some pavement sections have only the condition rating and some pavement sections have both construction date and pavement condition rating. Remaining service life for pavement sections which have only condition rating can be calculated by following 50 th percentile performance curve. But, for pavement sections which have both construction date and pavement condition rating it is necessary to follow 68

82 the performance curve which suits their construction date and latest pavement condition rating. Based on derived performance curves, PCR curves were developed which describes the variation of remaining service life variation according to the pavement age. From the PCR curves, it is observed that remaining service life increases with the pavement age for any particular PCR. This is because if a pavement achieves a particular PCR at a lower age than another pavement section has lower remaining service life. The average service life and the remaining service life obtained by using the Kaplan- Meier method can be used to determine the impact of M&R actions on future condition, to optimize and prioritize the M&R actions, to determine life-cycle cost, and to obtain the feedback on current M&R strategies. 69

83 CHAPTER 5 SUMMARY, CONCLUSIONS, AND RECOMMENDATIONS This chapter gives the summary, conclusions and future recommendations based on the results obtained from chapter Summary Remaining Service Life prediction plays an important role in pavement management. Survival curves are often used to obtain estimation of remaining service life of pavements. Pavement service life is affected by various factors, such as construction quality and materials, traffic loadings, climates, pavement thickness, and pavement condition prior to the previous repair. The most commonly used method to determine the service life of pavement is Kaplan-Meier method. The data used in this study is detailed pavement condition and rehabilitation data. Detailed pavement condition data in the form of Pavement Condition Rating (PCR) was obtained from Ohio Department of Transportation (ODOT) and rehabilitation data was also obtained from both ODOT and City of Toledo. 70

84 Using the available data, survival curve was drawn to find the service life for a group of pavements by assuming a terminal PCR of 60. Since the available rehabilitation data is incomplete, the developed survival curve is incomplete. The Weibull approximation was used to complete the survival curve and then individual survival curves were drawn for different PCR values to determine the remaining service life for groups of pavement sections with different PCR values. From the survival curves drawn for different PCR values, derived performance curves and PCR curves were drawn to determine the remaining service life for individual pavements and to better explain the remaining service life variation with pavement age. From the PCR curves it was observed that remaining service life increases with increase in pavement age. 5.2 Conclusions As a result of this study, the following conclusions were made: 1. Using incomplete data results in infinite average service life for the Kaplan Meier survival curve, which means survival probability never reaches a zero value. 2. To complete the survival curve, the Weibull approximation was used to complete the incomplete survival curve and the constants of Weibull survival curve were obtained by using regression analysis. 71

85 3. R-square value of Weibull survival curve is 0.99 which means the Weibull survival curve is a very good fit for the stub survival curve. 4. Since the assumed terminal PCR is 60 hence the average service life to reach PCR 60 is the average service life of pavement sections in the selected data set. According to Reilly (1998) the average service life to reach PCR 60 is the area under the survival curve for PCR 60. In the current dataset, average service life for PCR 60 is 15.2 years. 5. Derived performance curves were drawn using the Weibull approximation of the Kaplan-Meier survival curves. These curves were useful in predicting the remaining service life of pavement sections with respect to their PCR values. 6. To better understand the remaining service life variation, PCR curves were drawn. From PCR curves it is clearly understood that remaining service life increases with the pavement age. This is because, if a pavement takes less time to reach a particular PCR, it has less remaining service life than a pavement that takes more time to reach the same PCR value. 5.3 Recommendation In this study, it was found that the Weibull method can be used to approximate the Kaplan Meier method in predicting the remaining service life of pavements. It is found that the pavements in City of Toledo on average deteriorate to a PCR value of 60 in about 72

86 15.2 years. Also, it is recommended to use PCR curves shown in figure 4.8 to predict the RSL for any pavement section in the City of Toledo. 5.4 Future Recommendations As an extension to this study, it was recommended to study the cost effectiveness of the time and type of treatment to increase the average pavement condition and to lessen the percentage of pavements with 0 remaining service life in for City of Toledo. 73

87 APPENDIX A ASPHALT SURFACE RATING FORM FOR LOCAL STREETS 74

88 APPENDIX B PAVEMENT CONDITION RATING FORM FOR LOCAL STREETS 75