planning < Transportation, highways < Transportation ... · planning < Transportation, ... Department of Civil and Environmental Engineering, ... of the CDA using the assumption of

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Another Look at Delineation of Uniform Pavement Sections

Based on FWD Deflections Data

Journal: Canadian Journal of Civil Engineering

Manuscript ID cjce-2015-0281.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

https://mc06.manuscriptcentral.com/cjce-pubs

Canadian Journal of Civil Engineering

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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: 517-353-9782; Fax: 517-432-1827; e-mail: [email protected]

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 48824

Phone: 517-355-8422; Fax: 517-432-1827; e-mail: [email protected]

Text Count = 5,848

Number of Figures and Table = 10 (Equivalent word count = 2500)

Total Word Count = 8,348

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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

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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.

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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

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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.

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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.

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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., 1 2 3, ,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 (1 2 3, ,d d d ) while the

slope of the dashed line is the overall average deflection value ( d ) of the entire project

length considered.

1

1

1 2

0

x x

x

x

A d dx d dx= +∫ ∫ (1)

0

x

xA ddx d x= = ×∫ (2)

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31 2

1 2

1 2 3

0

xx x

x x T

s s

d dx d dx d dxA

dL L

+ +

= =∫ ∫ ∫

(3)

Equation (4) can be used to calculate the difference in the two areas called cumulative

difference variable as shown in Figure 1c.

x x xZ A A= − (4)

As shown in Figure 1b, x

Z is simply the difference in cumulative area values, at a given

distance, x between the actual and project average lines. However, if thex

Z value is

plotted with distance, x then Figure 1c results. An inspection of the figure illustrates that

the location of unit boundaries always coincides with the location (along x ) where the

slope of the x

Z 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 x

Z can be determined

by using Equation(5).

1

1 1

1where; 2

n

in ni

x i i

i is

i ii i i i

d

Z d xL

d dd x d x

=

= =

−

= −

+ = =

∑∑ ∑

(5)

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The approach can be further simplified for data collection at a constant interval as shown

by Equation(6):

1

1

; where, = 1,....,

where;

k

x i

i

n

i

i

Z d kd k n

d

dn

=

=

= −

=

∑

∑ (6)

where;

id = deflection at point i

d = average deflection on the project length

k = deflection at the th

k measurement

n = 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).

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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)

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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

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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.

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2. 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.)

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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

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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.

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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

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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 1000. 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 (SNeff) 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 (Ep) and SNeff were

determined using the peak deflection and pavement layer thicknesses data based on the

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AASHTO overlay design procedure (Huang 2004). For a known pavement thickness D,

the effective modulus Ep of pavement layers above the subgrade can be estimated using

Equation (7). The do 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 (dr = 36 inches) were used to estimate the subgrade modulus (MR) by

using Equation (8). SNeff was calculated using Equation (9).

2

0

2

3

11

11

1.5

1

− + = +

+

R

Pp

RR

D

aM d

qa EED

Ma M

(7)

0.24

R

r

PM

d r= (8)

30.0045eff pSN D E= (9)

Table 2 shows the summary results for SNeff within each of the uniform section

determined based on methods 2 and 3. Assuming a required structural number (SNf) is

equal to 6 for this pavement based on the design traffic and subgrade modulus, the

structural number for an overlay (SNOL) can be determined. The SNeff for overlay design

was calculated based on 5th

percentile ( 2µ σ− ). This will ensure that only 5% of the

SNeff 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

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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

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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

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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 mass-

significance. 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 0.05.

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

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22

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

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Haider and Varma

23

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.

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24

Bennett, C. "Sectioning of Road Data for Pavement Management." Proc., 6th

International Conference on Managing Pavements, Brisbane, Australia, 19-24

October 2004.

Cafiso, S., and Di Graziano, A. (2012). "Definition of Homogenous Sections in Road

Pavement Measurements." Procedia-Social and Behavioral Sciences, 53, 1069-

1079.

Cuhadar, A., Shalaby, K., and Tasdoken, S. "Automatic Segmentation of Pavement

Condition Data using Wavelet transform." Proc., Electrical and Computer

Engineering, 2002. IEEE CCECE 2002. Canadian Conference on, IEEE, 1009-

1014.

El Gendy, A., and Shalaby, A. (2008). "Using Quality Control Charts to Segment Road

Surface Condition Data." Seventh International Conference on Managing

Pavement Assets.

El Gendy, A., Shalaby, A., and Eng, P. (2005). "Detecting Localized Roughness Using

Dynamic Segmentation." the First Annual Inter-University Symposium of

Infrastructure Management (AISIM).

Haider, S. W., Baladi, G. Y., Chatti, K., and Dean, C. M. (2010). "Effect of Pavement

Condition Data Collection Frequency on Performance Prediction." Transportation

Research Record (2153), 1, 67-80.

Haider, S. W., Chatti, K., Baladi, G. Y., and Sivaneswaran, N. (2011). "Impact of

Pavement Monitoring Frequency on Pavement Management System Decisions."

Transportation Research Record (2225), 1, 43-55.

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25

Haider, S. W., and Dwaikat, M. B. (2011). "Estimating Optimum Timings for Preventive

Maintenance Treatments to Mitigate Pavement Roughness." Transportation

Research Record, 2235, 43-53.

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), 485-493.

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), 229-233.

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), 65-73.

Thomas, F. (2003). "Statistical approach to road segmentation." Journal of transportation

engineering, 129(3), 300-308.

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), 591-598.

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Table 1 Variables names and description

Variable Description of the variables

id = Field measured performance variable (e.g. peak deflection)

x∆ = Interval between each measured value

totn = Total number of measured points

meand = Over all mean of the total field measurements

iCS = Cumulative difference of the measured field variable (calculated using equation #)

TH = Mean difference of the measured performance between two adjacent homogeneous

sections. (1)

1p = Slope of the cumulative difference curve

(2)

1p = Slope of the cumulative difference curve

minL = Minimum length of a project

minn = Number of measurement points in minimum length.

λ = Reduction factor

1n = Starting point of a subsection

un = Last point on a subsection

minλ = Minimum reduction factor

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Table 2 Effect of delineation methods on SNeff

Sections

Method 2 Method 3

Average

SNeff

Std

SNeff CoV

SNeff for

Design

Average

SNeff

Std

SNeff CoV

SNeff for

Design

1 7.94 1.32 16.6% 5.307 7.94 1.32 16.6% 5.307

2 6.80 1.53 22.5% 3.741 7.00 1.53 21.9% 3.939

3 7.40 1.58 21.4% 4.237 7.34 1.55 21.1% 4.238

4 6.29 1.49 23.7% 3.312 6.25 1.48 23.7% 3.285

5 4.37 0.92 21.0% 2.541 4.37 0.92 21.0% 2.541

6 4.46 0.21 4.7% 4.043 4.64 0.36 7.8% 3.915

7 4.67 0.31 6.6% 4.057 5.08 0.47 9.2% 4.152

8 5.11 0.46 9.0% 4.192 - - - -

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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)


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Draft

(a) Uniform response parameter

(b) Cumulative and average areas

(c) Cumulative area difference

Fig. 1 AASHTO concept of cumulative difference approach (AASHTO 1993)

Pavem

ent

Re

spon

se

Para

me

ter,

di

d1

d2

d3

x1 x2 x3=Lsx

dC

um

ula

tive

Are

a

x1 x2 x3=Lsx

xAxA

TA

x x xZ A A

x1 x2 x3=Lsx

xx

xZ

AA

0

(+)

(-)

Change Point

Change Point

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Draft

Fig. 2 Flow chart for method 2 (mean difference)

End

YesNo

Start

Parameters: Measured data:

is a new

subsection

Yes

No

, ,i totd x n

minmin

Ln

x

2

1

1 totn

mean i

itot

d dn

1

i

i k mean

k

CS d i d

(1) (1)

1 ( )

:

i o i

l u

CS p p n

i n n

min

u

totn n n

(2) (2)

1

min

( )

:

i o i

u u

CS p p n

i n n n

min

(2) (1)

1 1| |p p TH

min

u un n n :l ui n n

min1,l un n n

u

totn n

min min, ,TH L

1

No

Yes

No

Yes

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Fig. 3 Flow chart for method 3 (mean and variance differences)

End

Yes

No

Start

Parameters: Measured

data:

is a

new subsection

Yes

No

T-test

Similar meansdissimilar

means

2

, ,i totd x n

minmin

Ln

x

1

1 totn

mean i

itot

d dn

1

i

i k mean

k

CS d i d

(1) (1)

1 ( )

:

i o i

l u

CS p p n

i n n

min

u

totn n n min

u un n n :l ui n n

(2) (2)

1

min

( )

:

i o i

u u

CS p p n

i n n n

min

(2) (1)

1 1| |p p TH

min min, ,TH L

min1,l un n n

u

totn n

1

No

Yes

No

Yes

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Fig. 4 Example for comparing all delineation methods

0

10

20

30

40

50

0 50 100 150 200 250 300 350 400 450 500 550 600 650 700 750 800

De

fle

ctio

n, (m

ils)

Measurement point

Deflection data

Section means

Overall mean

0

5

10

15

20

25

30

35

-2000

-1500

-1000

-500

0

500

1000

0 50 100 150 200 250 300 350 400 450 500 550 600 650 700 750 800

De

fle

ctio

n, (m

ils)

Cu

mu

lative

su

m d

iffe

ren

ce,

(CS

D)

Measurement points

CS

Method 2

Method 3

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(a) CoV=10% (low variability)

(b) CoV=20% (medium variability)

(c) CoV=40% (high variability)

Fig. 5 Impact of variability on delineation methods

0

10

20

30

40

50

60

0 50 100 150 200 250 300 350 400 450 500 550 600 650 700 750 800 850 900 950 1000 1050 1100 1150 1200

Deflection

, (m

ils)

Measurement point

Deflection data

Section means

0

10

20

30

40

50

60

0 50 100 150 200 250 300 350 400 450 500 550 600 650 700 750 800 850 900 950 1000 1050 1100 1150 1200

De

flection

, (m

ils)

Measurement point

Deflection data

Section means

0

10

20

30

40

50

60

0 50 100 150 200 250 300 350 400 450 500 550 600 650 700 750 800 850 900 950 1000 1050 1100 1150 1200

De

fle

ctio

n, (m

ils)

Measurement point

Deflection data

Section means

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Draft

(a) Method 2 (mean difference)

(b) Method 3 (mean and variance difference)

Fig. 6 Impact of mean difference threshold and variability on delineation methods

0%

20%

40%

60%

80%

100%

0 2 4 6 8 10 12

Pe

rcen

t co

rre

ct

Threshold, (mils)

10

20

30

40

0%

20%

40%

60%

80%

100%

0 2 4 6 8 10 12

Pe

rcen

t co

rre

ct

Threshold, (mils)

10

20

30

40

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(a) Peak deflection

(b) Cumulative difference


0 100 200 300 400 500 600 700 800 900 10000

10

20

30

40

50

Station number

De

fle

ctio

n (

mils)

0 100 200 300 400 500 600 700 800 900 1000-1200

-1000

-800

-600

-400

-200

0

200

400

Station number

Cu

mu

lative

diffe

ren

ce

(m

ils)

2 1 5 4 3 6 8 7

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Draft

(a) Peak deflection

(b) Cumulative difference


0 100 200 300 400 500 600 700 800 900 10000

10

20

30

40

50

Station number

De

fle

ctio

ns (

mils)

0 100 200 300 400 500 600 700 800 900 1000-1200

-1000

-800

-600

-400

-200

0

200

400

Station number

Cu

mu

lative

diffe

ren

ce

(m

ils)

1 2 3 4 5 6 7

Page 36 of 36



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