Canadian Journal of Civil Engineering. Another Look at Delineation of Uniform Pavement Sections Based on FWD Deflections Data

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1 Another Look at Delineation of Uniform Pavement Sections Based on FWD Deflections Data Journal: Manuscript ID cjce r1 Manuscript Type: Article Date Submitted by the Author: 18-Sep-2015 Complete List of Authors: Haider, Syed; Michigan State University, Civil and Environmental Engineering Varma, Sudhir; Michigan State University, Civil and Environmental Engineering Keyword: planning < Transportation, highways < Transportation, design < type of paper to review

2 Page 1 of 36 Another Look at Delineation of Uniform Pavement Sections Based on FWD Deflections Data Syed Waqar Haider, Ph.D, P.E. Associate Professor (Corresponding Author) Department of Civil and Environmental Engineering, Michigan State University, Engineering Building, 428 S. Shaw Lane, Room 3546, East Lansing, MI 48824, Phone: ; Fax: ; syedwaqa@egr.msu.edu and Sudhir Varma, Ph.D Graduate Research Assistant, Department of Civil and Environmental Engineering, Michigan State University, Engineering Building, 428 S. Shaw Lane, Room 3552, East Lansing, MI Phone: ; Fax: ; varmasud@egr.msu.edu Text Count = 5,848 Number of Figures and Table = 10 (Equivalent word count = 2500) Total Word Count = 8,348

3 Page 2 of 36 Another Look at Delineation of Uniform Pavement Sections Based on FWD Deflections Data ABSTRACT The large amount of data commonly used to characterize the pavement surface and structural conditions offer a challenge to practitioners making decisions about the representative value of a particular parameter for design. While a large number of observations along the length of a road allow a better quantification of the expected value and variance of a parameter, basing a design on an average parameter along the project length, it will typically be uneconomical and less reliable. Therefore, pavement surface and structural condition data along a project length needs to be delineated into uniform sections. The design can be performed individually for each of these uniform sections to achieve economy without compromising reliability level. This paper documents delineation methods that explicitly address the problem of segmentation of measurement series obtained from FWD deflections. Modifications in the existing AASHTO delineation procedure were incorporated to address the mean differences and the local variability. The results of delineation show that the AASHTO methodology ignores the local variations along the project length which may not be valid from a practical standpoint while designing rehabilitation or preservation strategies. The inclusion of restrictions on mean difference and section length resulted in better delineation than the AASHTO method but it could be sensitive to local variations of the deflections within a section. The delineation approach can handle the local deflection variations within a section if appropriate constraints on the local variations are imposed. The results from the delineation of field deflections showed that the restrictions on mean difference, minimum section length and location variability are vital to delineate the 2

4 Page 3 of 36 project length into appropriate homogenous sections which can be different from each other from both statistical and practical viewpoints. Keywords: Delineation, Uniform sections, Homogenous sections, FWD deflections, Rehabilitation design. 3

5 Page 4 of 36 INTRODUCTION Generally two types of evaluations are conducted for pavement rehabilitation: (a) surface condition assessment, and (b) structural condition evaluation. The data collected from such evaluations play a key role in decision making regarding the treatment type selection and timing to fix an existing pavement (Haider and Dwaikat 2011; Haider and Dwaikat 2012). The surface condition assessment data includes the type, extent and severity of surface distresses while the structural condition data (i.e., surface deflections and material properties) are used to assess the existing structural capacity of pavements. Decisions about maintenance, rehabilitation or preservation action to extend the life of the pavements in the network relies on the combination of functional or structural distresses observed on those sections. Pavement surface condition is comprised of load-related distresses such as fatigue cracking and rutting, and functional distresses (non-load-related) such as transverse and block cracking, ride quality etc. Pavement surface condition information is an integral part of any pavement management system (PMS). On the other hand, falling weight deflectometer (FWD) deflections are typically utilized at the project level to assess the structural capacity of existing pavements. While deflection data can be used to evaluate the construction quality of a newly constructed road, those are generally helpful to backcalculate the existing layer moduli of asphalt, base/subbase, and subgrade layers for designing an overlay thickness to meet anticipated traffic for the extended life. However, only structurally sound pavements may be considered as candidates for pavement preservation. Both types of data (surface conditions and deflections) are typically reported over a unit length of a pavement; typical unit length for data collection purposes 4

6 Page 5 of 36 in the US is 0.1 mile (528 ft). Further, some of the surface condition data are collected continuously (sensor-measured, e.g., IRI and rutting) while others are collected at discrete locations (e.g., deflections, coring or boring etc.) (Haider et al. 2010; Haider et al. 2011). Such data are used for designing new roads (reconstruction), or selecting rehabilitation actions on existing roads. The large amount of data commonly used to characterize the pavement surface and structural conditions offer a challenge to practitioners making decisions about the representative value of a particular parameter for design. While a large number of observations along the length of a road allow a better quantification of the expected value and variance of a parameter, basing a design on an average parameter along the project length, it will typically be uneconomical and less reliable. Therefore, pavement surface and structural condition data along a long stretch of pavement needs to be delineated into sections which are relatively uniform, referred to as homogeneous sections, for which the design is performed individually. This results in economy in design without compromising reliability level (Misra and Das 2003). Currently, highway agencies need to identify homogeneous sections when planning maintenance actions. In fact, identifying candidate sections for maintenance or rehabilitation is essentially a task of determining which parts of the measurement series (surface and structural condition data) exceed certain threshold values, and ensuring that these sections are not too short to be meaningful candidates for actions such as repaving (Thomas 2004). However, the large amount of data collected by road profilers can be used for more than just identifying sections that fail some minimal requirements. Furthermore, evaluating and comparing the information from different locations over time in these measurement series allows for a systematic monitoring of the road surfaces. 5

7 Page 6 of 36 In general, a prerequisite for most of the delineation analyses is to identify the parts of the measurement series that are homogeneous with respect to a particular criterion (Thomas 2004). However, the criteria selection and how best to combine different existing segments of the road into a single uniform one will depend on the unique problem at hand (Bennett 2004). While several criteria are available to accomplish the same objective of determining uniform sections, the results could be different. The main objectives of the paper are to review the existing delineation methods and develop a procedure that addresses various shortcomings in the existing AASHTO delineation methodology by considering the (a) mean differences for surface deflections, and (b) local variations in the measured deflections between adjacent pavement sections. In order to accomplish the above mentioned objectives, this paper documents a delineation method that explicitly addresses the problem of segmentation of measurement series obtained from FWD deflections. First, a review of the method recommended in AASHTO (AASHTO 1993; AASHTO 2008) is presented. Further, some extensions necessary to make the AASHTO delineation procedure a fully automatic method suitable for the large amount of data are discussed. Second, additional modifications in the existing AASHTO procedure were incorporated to address the mean differences and the local variability. The modified algorithms are documented along with examples to demonstrate their accuracy and efficiency. Finally, examples are presented to analyze the peak deflection data from actual field projects to demonstrate the application of the developed methodology. 6

8 Page 7 of 36 BACKGROUND The AASHTO design guide documents a straightforward and powerful analytical method for delineating statistically homogenous units from pavement response measurements along a highway system (AASHTO 1993). The method is described the cumulative difference approach (CDA). The approach can be used for a wide variety of measured pavement response variables such as deflection, serviceability, surface roughness in terms of IRI, skid resistance, pavement distress indices, etc. Figure 1 shows the overall concept of the CDA using the assumption of a continuous and constant deflection (pavement structural response) within various intervals along a project length. The simplified scenario in Figure 1a shows three unique pavement sections having different deflection magnitudes (i.e., d, d, d ) while d represent the overall average deflection on the entire project. The cumulative areas under deflections for individual sections and overall average deflections can be calculated using Equations (1) through (3) and are shown in Figure 1b. It should be noted that the slopes (derivatives) of the cumulative area curves are simply the deflection for each unit ( d, d, d ) while the slope of the dashed line is the overall average deflection value ( d ) of the entire project length considered. x x1 A = d dx+ d dx 0 x (1) 1 2 x1 x Ax = ddx= d x (2) 0 7

9 Page 8 of 36 d x1 x2 0 x3 d dx+ d dx+ d dx x1 x A 2 T = = L L s s (3) Equation (4) can be used to calculate the difference in the two areas called cumulative difference variable as shown in Figure 1c. Zx = Ax Ax (4) As shown in Figure 1b, Z x is simply the difference in cumulative area values, at a given distance, x between the actual and project average lines. However, if the Z value is plotted with distance, x then Figure 1c results. An inspection of the figure illustrates that x the location of unit boundaries always coincides with the location (along x ) where the slope of the Z x function changes algebraic signs (i.e., from negative to positive or vice versa). This fundamental concept is the ultimate basis used to analytically determine the boundary location for the analysis units (AASHTO 1993). However, in practice, the pavement response parameters (peak deflections in this paper) are never constant and have inherent variability with distance due to changes in construction and material properties along the project length. Therefore, in order to apply the CDA to real data, a numerical difference approach is recommended by AASHTO and by using Equation(5). Z x can be determined n d Z d x n i n i= 1 x = i i i= 1 Ls i= 1 d + d where; d = x = d x 2 i 1 i i i i i (5) 8

10 Page 9 of 36 The approach can be further simplified for data collection at a constant interval as shown by Equation(6): k Z = d kd ; where, k = 1,..., n x i= 1 where; d = i n i= 1 n d i (6) where; d i = d = deflection at point i average deflection on the project length k = n = deflection at the th k measurement total number of measurements The AASHTO CDA method is simple and can be suitable as an algorithm for a computer program. However, due to subjectivity due visual inspection of results involved in the final selection of homogenous sections, it may offer certain limitations in delineation. Since, the method relies on the change of cumulative sum (CS) slope for identifying uniform sections; it fails to recognize the variability of the parameter within the homogenous sections. Therefore, for practical purposes, it is recognized that some constraints need to be placed in the CDA algorithms on the delineation unit to filter out higher variability, and to have homogeneous units that will be viable rehabilitation projects. As a result, two types of constraints have been considered: (a) minimum segment length, and (b) minimum difference in mean parameter for delineation (e.g., rut depth, IRI, peak surface deflections etc.) between adjacent segments (Misra and Das 2003; Ping et al. 1999). 9

11 Page 10 of 36 For the minimum segment length criterion, it is important to consider the intended application of the data. Certainly, the lower the minimum segment length, the better the chances of minimizing the variability within delineated segments which will result in establishing more uniform segments. However, in practice, there is a limit to how short a section length can get in order to establish a viable rehabilitation project. Therefore, it is advantageous to combine very short segments with other segments to form longer segments for the purposes of overlay design and construction. On the other hand, in order to consider practical and operational mean differences of the parameter considered for delineating adjacent segments, the mean difference should be consistent with the observed variability of the parameter within uniform pavement segments. In other words, the mean difference should be dissimilar enough to trigger a different design or a treatment. It should be noted that such practical mean difference magnitude will depend upon the type of the parameter used for delineation. For example, the mean difference of 1 mil for peak deflection between adjacent segments may not trigger a different treatment while a mean difference value of 4 mils may be practical enough to produce different pavement rehabilitation or preservation treatment. In light of above mentioned limitations of the CDA method, several modifications have been proposed. Bennet highlighted different sectioning needs for pavement management and documented the differences between sectioning of roads and analysis sections based on data sources (Bennett 2004). Thomas provided an elaborated literature on the-state-of-the-practice for generating homogenous road sections based on surface measurements (Thomas 2004). He documented available methods for road segments such as (a) cumulative differences, (b) absolute differences in sliding mean values, and (c) 10

12 Page 11 of 36 Bayesian segmentation algorithm. Several issues were highlighted and described for all of these methods. It was reported that a successful implementation of the CDA rests upon development of sensible criteria to interpret the calculated series of cumulative differences. It is likely that any criteria that work well for a wide range of measurement series will be data-dependent, for example, by explicitly accounting for the variability in a particular measurement series under study. Unfortunately, such dependencies on the data under study inevitably destroy the most attractive feature of CDA, namely, the already mentioned simplicity in calculation (because the exact criteria have to be calculated from the data) (Thomas 2004). On the other hand, when data smoothing is utilized, it disguises the information about sudden changes in a measurement series because (a) a suspected change in the measurement series is abrupt, the information about the location of that change is clearest by comparing its immediate neighbors, and (b) averaging of measurements corrupts this pure information in the neighborhood of that location by mixing values from both sides of the suspected change. Therefore, smoothing a measurement series by a sliding mean might be expected to do more harm than good when the task is to identify the location of a sudden change (Thomas 2004). While the statistical methods such as Bayesian algorithm (Thomas 2003; Thomas 2005) often provides a good approximation of more involved processes and will consequently render satisfying results even when the model assumptions do not hold exactly, the algorithm should be expected to fail in cases of seriously violated model assumptions. Several other researchers have used some modifications of the CDA approach and suggested several improvements in the procedure for identifying homogenous or uniform sections. For example, Misra and Das (Misra and Das 2003) suggested an improved yet 11

13 Page 12 of 36 simplistic methodology for identification of homogeneous sections based on a combined approach of classification and regression tree (CART) and exhaustive search. Cafiso and Graziano (Cafiso and Di Graziano 2012) proposed a methodology to detect a change point by searching those points to minimize the sum of the squared errors respect to the series of data. Gendy and Shalaby (El Gendy et al. 2005) proposed two methods for segmentation to divide the roughness profile into segments which have a specified IRI range. They used absolute difference and combining segment approaches to establish uniform sections based on IRI. The same authors also looked the fundamental concepts of the quality control charts and their suitability for segmentation (El Gendy and Shalaby 2008). Shalaby and Tasdoken (Cuhadar et al. 2002) used a new algorithm based on wavelet transform for automated segmentation of the pavement-condition data. They developed a de-noising scheme to remove random noise caused by the collection device and random extreme distress in the pavement while essentially preserving the important information followed by a singularity detection-based segmentation algorithm. From the above discussion of the literature on the detection of uniform or homogenous pavement sections based on different response parameters, the following take home points can be established: 1. The segmentation procedure should be able to consider the practical or operational aspects, i.e., the mean difference in the response parameter. Such attentions for practical mean differences among delineated pavement sections are important when the uniform sections are to be used for rehabilitation design or for preservation treatment selections. 12

14 Page 13 of The procedure should also be able to detect the local variations in the response parameter to reduce the risk of failure and increase the reliability of the selected rehabilitation or preservation treatment. 3. The methodology should be robust and simple enough for practical application. The new delineation methodology developed in this paper is documented below along with some examples to demonstrate its application by using the deflection data. DELINEATION METHODOLOGY In this paper, three delineation methods are considered (1) the AASHTO cumulative difference approach (CDA), (2) a delineation approach which considers the mean difference, and (3) a delineation methodology which considers the mean difference and local variability. All the above approaches consider the impact of minimum section length (as a constraint) while establishing uniform sections based on FWD deflection data. The main purpose of including multiple approaches is to compare the results among those and recommend a practical and robust methodology for identifying homogenous sections for preserving or rehabilitating an existing flexible pavement. It should be noted that selection of mean difference of response parameter (in this case peak deflection) between adjacent sections will depend on the: a. Practical or operational significance of the mean difference for peak deflection. For example, a mean difference of 2 to 3 mils between adjacent sections may trigger a different preservation or rehabilitation treatment depending on traffic and condition of an existing pavement structure. However, the mean difference practical magnitude will depend on the response parameter to be considered for delineation (e.g., IRI, friction, rutting etc.) 13

15 Page 14 of 36 b. The mean difference will also depend on the overall variability of deflections along the project length. For example, if a mean difference of more than the observed maximum difference in deflections is selected, there will be only one uniform or homogenous pavement section. The CDA approach (AASHTO 1993) as described in the background section (method 1) was used to analyze deflection data. The algorithms for methods 2 and 3 developed in this paper are shown in Figures 2 and 3, respectively. The cumulative sum for peak deflections is calculated based on Equation (6) for the project length. In method 2, the adjacent sections (e.g. section 1 followed by the section 2) are chosen based on the minimum length specified and the slope of the cumulative sum is calculated by fitting a linear line for both. It should be noted that the difference between the slopes for two adjacent sections is same as the difference between their mean deflections. If the mean deflection difference is less than a specified threshold, the adjacent sections are combined and compared with next minimum length. On the other hand, if the mean difference between sections 1 and 2 is more than the specified threshold, then section 2 is reduced in length by a factor,λ, and then the new section 2 is compared with section 1. The length reduction factor is used to find the change point within the minimum length specified. The threshold (i.e., mean difference) criteria will be again checked to establish that the two adjacent sections should be combined or considered as separate sections. The process is iterative and will terminate when the entire project length ends (see Figure 2). A similar algorithm to method 2 is utilized for method 3 but this time the mean difference is tested statistically with 95% confidence to consider the impact of local variability. A t- test (with pooled variance) was used when variance between adjacent sections is 14

16 Page 15 of 36 statistically similar; otherwise a t-test with unequal variances is used. The process is also iterative and will terminate when the entire project length ends (see Figure 3). Table 1 shows the variables names and descriptions used in both methods shown in Figures 2 and 3. Comparison of Different Delineation Methods To illustrate the differences between the three methods described above, an example of project delineation is shown in Figure 4. Figure 4a shows simulated peak deflections for a project. The deflections data were simulated based on randomly generated normal distributions with varying means and standard deviations. As shown in the figure, the deflection data shows six (6) separate sections in the entire project length. Figure 4b shows the delineation results based on the three methods. Based on the AASHTO delineation method, the entire project length is divided into three uniform sections (0 to 400, 400 to 650, and 650 to 800). Applying method 2 results in seven uniform sections (0 to 200, 200 to 400, 400 to 450, 450 to 500, 500 to 650, 650 to 700, and 700 to 800). The AASHTO method does not consider the variability between adjacent sections because slope of cumulative sum does not change signs. For example, it ignored to delineate between stations 0 to 400. Since, method 2 is based on the mean difference; it captures any significant change in slope. Method 3 gave the exact delineation for the simulated sections. The method 2 results are better than those of the AASHTO method but method 2 could be sensitive to local variations of the deflections within a section. Since, method 3 also considers the local variations of deflections while delineating the deflection data; it can overcome the problem of local variations within a section. This simple example shows the robustness of the method 3. 15

17 Page 16 of 36 Impact of Mean Difference and Local Variability on Delineation Methods In order to verify the effectiveness of methods 2 and 3, deflection data were simulated for a wide range of local variability with a specified number of sections (i.e., six homogenous sections). The maximum and minimum differences between the average deflections on adjacent sections were 22 and 10 mils, respectively. In addition, the delineation was performed based on different thresholds (mean differences) to evaluate its impact under different variability. Figure 5 shows the variability in the simulated deflection data for a realization. However, the simulation was carried out for a total of 1000 cases to determine the distribution for a number of homogenous sections with different delineation methods. Figures 6a and 6b show the percent of correct uniform sections determined by methods 2 and 3, respectively. The result of method 2 indicates that percentage of correct delineation depends on the threshold value (i.e., the mean difference between adjacent sections) and local variability of deflections within each homogenous section. If the threshold is less than 4 mils, method 2 fails to delineate the correct number of sections, especially when the local variability is high. Similarly, when the threshold is more than 9 mils, the error for identifying correct percentage of sections increases (see Figure 6a). It seems that when the threshold is too low, method 2 will delineate higher number of sections because of the local variations. On the other hand, if the threshold is too high, the method will under predict the number of correct homogenous sections. Since, method 3 considers the local variations in deflections; it is more robust at lower threshold values than method 2. However, it also under predicts for higher threshold values (see Figure 6b). From these results, it can be suggested that the 16

18 Page 17 of 36 method 3 is more efficient and robust than method 2, irrespective of local variations and threshold values. Application of the Developed Methodology The measured deflection data for a 200 km (125 miles) highway section at spacing of 200 m were used to demonstrate the application of the developed delineation methods. Figure 7a shows the peak deflection variations along the entire project. Using method 2, the project is delineated into 8 uniform sections (see Figure 7b). On the other hand, when method 3 is used the same project length is delineated into 7 uniform sections based on the peak deflections (see Figure 8). It can be seen from the deflection data along the length in Figure 8a that the peak deflections show high variations between stations 840 to Since, method 2 is only based on the mean difference of peak deflection for delineation; it is more sensitive to the local variation and does not consider variations statistically. Thus it resulted in multiple sections between the stations. However, method 3 considers the local variations in deflections because of the application of statistical methods (95% confidence for the mean difference), and thus is a more rational way of considering variability. Therefore, there are only two uniform sections between the stations as compared to three given by method 2. In order to evaluate the practical implication of the delineation, effective structural number (SN eff ) was calculated for the project length based on deflections. The Falling Weight Deflectometer (FWD) deflection data were analyzed for each station to characterize the structural capacity. The effective pavement modulus (E p ) and SN eff were determined using the peak deflection and pavement layer thicknesses data based on the 17

19 Page 18 of 36 AASHTO overlay design procedure (Huang 2004). For a known pavement thickness D, the effective modulus E p of pavement layers above the subgrade can be estimated using Equation (7). The d o is the deflection measured at the center of the load plate and q is the pressure on the loading plate. The deflections at the sensor located 36 inch from the center of the load (d r = 36 inches) were used to estimate the subgrade modulus (M R ) by using Equation (8). SN eff was calculated using Equation (9). M Rd qa D 1+ 1 a = E P D Ep 1+ 3 M R a M R 2 (7) M R 0.24P = (8) d r r SN eff = (9) D 3 Ep Table 2 shows the summary results for SN eff within each of the uniform section determined based on methods 2 and 3. Assuming a required structural number (SN f ) is equal to 6 for this pavement based on the design traffic and subgrade modulus, the structural number for an overlay (SN OL ) can be determined. The SN eff for overlay design was calculated based on 5 th percentile ( µ 2σ ). This will ensure that only 5% of the SN eff will be below the design value. Based on the results of delineation for method 2, difference in the overlay thicknesses is 0.03 inch between sections 6 and 7. If one assumes that 0.5 inch overlay thickness difference is practical for uniform sections delineation from cost point of view, then delineation of sections 6 and 7 does not make 18

20 Page 19 of 36 practical sense. The delineation results based on method 3 show that sections 6 and 7 obtained from method 2 should be combined which also makes practically sense. It should be noted that delineation of uniform sections based on method 3 show the difference in overlay thicknesses for adjacent sections more than 0.5 inch. DISCUSSION OF RESULTS The results from different delineation approaches show that the number and boundaries (i.e., change points) of homogeneous pavement sections may vary for a same project with a single response measure. While the AASHTO (AASHTO 1993) approach for delineation is simple and easy to use, it ignores the impact of local variations in the response measure. In addition, one may need judgement to determine an effective delineation based on visual inspection of the cumulative differences. However, the approach can be adopted with caveats for different response parameters (e.g., IRI, rutting, deflections, etc.). For an effective delineation methodology, the homogenous segments should be based on the: (a) practical or operational aspects i.e., the mean difference in the response parameter. Such consideration is essential when the uniform sections are to be used for rehabilitation design or preservation treatment selections, (b) the procedure should detect the local variations in the response parameter to reduce the risk of failure and increase the reliability of the selected rehabilitation or preservation treatment, (c) methodology should be robust and simple enough for practical application. The new delineation methodology developed in this paper addresses most of the above mentioned attributes. Two new approaches were developed and demonstrated for delineating project length based on FWD deflection data. Method 2 used a mean difference in peak deflections between adjacent sections to determine the change point 19

21 Page 20 of 36 while method 3 considered the mean differences which are tested statistically with 95% confidence to consider the impact of local variability. Both methods are iterative and will terminate when the entire project length ends. The results of simulations for both developed algorithms show that: 1. The percentage of correct delineation depends on the threshold value (i.e., the mean difference between adjacent sections) and local variability of deflections within each homogenous section for method 2. For the simulated deflection data, if the threshold is very low, the method fails to delineate correct number of sections (i.e., will give higher number of uniform sections), especially when the local variability is high. Similarly, a very high threshold will also result in higher error in delineation (i.e., under predicts the number of sections). 2. Since, method 3 considers the local variations in deflections; it is more robust at lower threshold values than method 2. However, it also under predicts for higher threshold values. From the above findings, it can be suggested that method 3 is more efficient and robust than method 2, irrespective of local variations and threshold values. The selection of mean difference of deflections (i.e., the threshold) between adjacent sections will depend on the: (a) practical or operational significance of the mean difference for peak deflection, (b) mean difference will also depend on the overall variability of deflections along the project length. However, the mean difference practical magnitude will depend on the response parameter to be considered for delineation (e.g., IRI, friction, rutting etc.). The developed delineation methodology was applied to the FWD deflections conducted on a highway project. The results of delineation show that method 3 was able 20

22 Page 21 of 36 to delineate the project length into appropriate homogenous sections which were found to differ from each other from both statistical and practical viewpoints. The developed delineation methods employed the restrictions: (a) a threshold for the minimal length of resulting sections, and (b) minimal differences of arithmetic mean values of resulting adjacent sections. In addition, method 3 uses two-sided t-tests to assess the statistical significance of differences in mean values. At least two conceptual problems are associated with t-testing as reported in the literature (Thomas 2004): 1. A standard t-test requires the measurements to be statistically independent (conditionally on the common mean), something which is not the case for the measurement series. These measurements typically exhibit pronounced first-order autocorrelation, thus violating the assumptions in a standard t-test. 2. Applying t-tests repeatedly a large number of times in different parts of a long measurement may associate such a procedure with problems of masssignificance. In other words, the type I error rate (i.e., comparison-wise error rate for the experiment) may be much larger than assumed value of It is true that spatial correlation will contribute to the violation of independence assumption for a standard t-test. In pavements, the spatial autocorrelation will be a concern for measurement series to characterize the surface characteristics such as IRI, rutting, friction etc. However, for surface deflections (shows the pavement structural capacity) such problem may not be as severe as some of the other surface characteristics. In addition, minor violation of such assumption will not significantly change the conclusions. In fact, the results of the demonstrative example from the field deflections show that the method is robust enough to give meaningful statistical significance which 21

23 Page 22 of 36 passes the test of operational and practical significance. Further, the simulated deflections data used to validate the developed methodology were generated as independent normally distributed random variable; therefore, no spatial correlation is expected. It is also valid that multiple mean comparisons can be susceptible to problem of mass-significance. However, in the developed methodology, only two adjacent sections were considered for statistical testing at a time i.e., the means from a single section was not compared with different pavement sections at the same time. The authors feel that such mean comparisons will not be significantly impacted by mass-significance. CONCLUSIONS More data along the length of a road are appropriate in quantifying the parameter expected value and variability, however; if design is based on the data of a particular parameter of the whole project length, it will lead to an uneconomical design. Therefore, pavement surface and structural condition data along a long stretch of road needs to be delineated into sections which are relatively uniform, referred to as homogeneous sections and the design performed individually for each of these homogeneous sections. This results in economical design without compromising reliability level. The paper documents delineation methods that explicitly address the problem of segmentation of measurement series obtained from FWD deflections. Extensions necessary to make the AASHTO delineation procedure a fully automatic method suitable for the large amount of data are discussed. Modifications in the existing AASHTO delineation procedure were incorporated to address the mean differences and the local variability. The modified algorithms are documented along with examples to demonstrate their accuracy and efficiency. Examples are presented to analyze the peak deflection data 22

24 Page 23 of 36 from actual field projects to demonstrate the application of the developed methodology. The results of the analyses show that the AASHTO methodology (i.e. method 1) ignores the local variations along the project length while delineating the homogenous sections. Such delineated uniform sections may not be valid from a practical standpoint while designing rehabilitation or preservation strategies. The results of method 2 are better than those of the AASHTO method but method 2 could be sensitive to local variations of the deflections within a section. Since, method 3 also considers the local variations of deflections while delineating the deflection data; it can overcome the problem of local variations within a section. The simulation results confirmed that the method 3 is more efficient and robust than method 2, irrespective of local variations and threshold values. When the developed delineation methods were applied to field deflections, the results showed that method 3 is able to delineate the project length into appropriate homogenous sections which were found to be different from each other from both statistical and practical viewpoints. REFERENCES AASHTO (1993). "AASHTO Guide for Design of Pavement Structures, Appendix J: Analysis Unit Delineation by Cumulative Differences." American Association of State Highway and Transportation Officials, Washington, D.C. AASHTO (2008). "Mechanistic-Empirical Pavement Design Guide: A Manual of Practice: Interim Edition." American Association of State Highway and Transportation Officials. 23

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26 Page 25 of 36 Haider, S. W., and Dwaikat, M. B. (2011). "Estimating Optimum Timings for Preventive Maintenance Treatments to Mitigate Pavement Roughness." Transportation Research Record, 2235, Haider, S. W., and Dwaikat, M. B. (2012). "Estimating Optimum Timings for Treatments on Flexible pavements with Surface Rutting." Journal of Transportation Engineering, 139(5), Huang, Y. H. (2004). Pavement Analysis and Design, Pearson Prentice Hall, Upper Saddle River, NJ. Misra, R., and Das, A. (2003). "Identification of homogeneous sections from road data." International Journal of Pavement Engineering, 4(4), Ping, W. V., Yang, Z., Gan, L., and Dietrich, B. (1999). "Development of procedure for automated segmentation of pavement rut data." Transportation Research Record: Journal of the Transportation Research Board, 1655(1), Thomas, F. (2003). "Statistical approach to road segmentation." Journal of transportation engineering, 129(3), Thomas, F. (2004). "Generating Homogenous Road Sections Based on Surface Measurements: Available Methods." 2nd Eurpean Pavement and Asset Management Conference. Thomas, F. (2005). "Automated road segmentation using a Bayesian algorithm." Journal of transportation engineering, 131(8),

27 Page 26 of 36 Table 1 Variables names and description Variable Description of the variables d i = Field measured performance variable (e.g. peak deflection) x = Interval between each measured value n = Total number of measured points tot d = Over all mean of the total field measurements mean CS = Cumulative difference of the measured field variable (calculated using equation #) i Mean difference of the measured performance between two adjacent homogeneous TH = sections. p = Slope of the cumulative difference curve (1) 1 (2) p 1 = Slope of the cumulative difference curve L = Minimum length of a project min n = Number of measurement points in minimum length. min λ= Reduction factor 1 n = Starting point of a subsection u n = Last point on a subsection λ = Minimum reduction factor min 26

28 Page 27 of 36 Table 2 Effect of delineation methods on SNeff Method 2 Method 3 Sections Average Std SN CoV eff for Average Std SN CoV eff for SN eff SN eff Design SN eff SN eff Design % % % % % % % % % % % % % % %

29 Page 28 of 36 List of Figures Fig. 1 AASHTO concept of cumulative difference approach (AASHTO 1993) Fig. 2 Flow chart for method 2 (mean difference) Fig. 3 Flow chart for method 3 (mean and variance differences) Fig. 4 Example for comparing all delineation methods Fig. 5 Impact of variability on delineation methods Fig. 6 Impact of mean difference threshold and variability on delineation methods Fig. 7 Example of delineating uniform section based on peak deflection (Method 2) Fig. 8 Example of delineating uniform section based on peak deflection (Method 3) 28

30 Pavement Response Parameter, di Cumulative Area Page 29 of 36 d 1 d 2 d d 3 x 1 x x 2 x 3 =L s (a) Uniform response parameter A T A A x x Z A A x x x x 1 x x 2 x 3 =L s (b) Cumulative and average areas (+) Change Point Z x A x A x 0 x 1 x x 2 x 3 =L s (-) Change Point (c) Cumulative area difference Fig. 1 AASHTO concept of cumulative difference approach (AASHTO 1993)

31 Page 30 of 36 Start Measured data: d, x, n i tot Parameters: TH,, L min min n min Lmin x d mean n n 1 tot tot i 1 d i i CS d i d i k mean k 1 l u n 1, n n min u n n tot Yes End l u i n : n is a new subsection No min Yes No (1) (1) CSi po p1 ( ni ) l i n : n u No 1 u ntot n nmin Yes CS p p ( n ) (2) (2) i o 1 i u u i n : n n min u u n n nmin 2 No p p TH (2) (1) 1 1 Yes Fig. 2 Flow chart for method 2 (mean difference)

32 Page 31 of 36 Measured data: di, x, ntot n min Start Lmin x Parameters: TH,, L min min d mean n n 1 tot tot i 1 d i i CS d i d i k mean k 1 l u n 1, n n min u n n tot No Yes End (1) (1) CSi po p1 ( ni ) l i n : n u l u i n : n is a new subsection No min No Yes 1 u u u ntot n nmin n n nmin Yes CS p p ( n ) (2) (2) i o 1 i u u i n : n n min 2 dissimilar means p p TH (2) (1) 1 1 No T-test Yes Similar means Fig. 3 Flow chart for method 3 (mean and variance differences)

33 Cumulative sum difference, (CSD) Deflection, (mils) Deflection, (mils) Page 32 of Deflection data Section means Overall mean Measurement point CS 500 Method 2 30 Method Measurement points 0 Fig. 4 Example for comparing all delineation methods

34 Deflection, (mils) Deflection, (mils) Deflection, (mils) Page 33 of Deflection data Section means Measurement point (a) CoV=10% (low variability) Deflection data Section means Measurement point Deflection data Section means (b) CoV=20% (medium variability) Measurement point (c) CoV=40% (high variability) Fig. 5 Impact of variability on delineation methods

35 Percent correct Percent correct Page 34 of % 80% 60% % 20% 0% Threshold, (mils) (a) Method 2 (mean difference) 100% 80% 60% % 20% 0% Threshold, (mils) (b) Method 3 (mean and variance difference) Fig. 6 Impact of mean difference threshold and variability on delineation methods

36 Cumulative difference (mils) Deflection (mils) Page 35 of Station number (a) Peak deflection Station number (b) Cumulative difference Fig. 7 Example of delineating uniform section based on peak deflection (Method 2)

37 Cumulative difference (mils) Deflections (mils) Page 36 of Station number (a) Peak deflection Station number (b) Cumulative difference Fig. 8 Example of delineating uniform section based on peak deflection (Method 3)