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Federal Highway Administration Research and Technology
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Publication Number: FHWARD03041 
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This chapter summarizes the results from the evaluation of the thickness data variability indicators based on core thickness measurements and field elevation measurements (SPS only). Typical LTPP layer thickness variability values are summarized by different layer and material types.
The chapter also presents the summary of the comparisons of layer thickness variances and means obtained based on the core and elevation thickness measurements for newly constructed SPS sections for different layer types, material types, and target thicknesses.
Layer thickness summary statistics such as average, minimum, maximum, standard deviation, and coefficient of variation (COV) serve as indicators of layer thickness variability along the section. For GPS sections, most of these values could be obtained from the LTPP database tables INV_LAYER and RHB_LAYER. These summary statistics were provided by the highway agencies and could be either estimated or computed. No additional information on how summary statistics were derived for these tables is available. For the SPS sections, layer thickness summary statistics could be obtained from the SPS*_LAYER tables. These values were computed from the elevation shots measurements. The SPS*_LAYER tables do not contain summary information on the number of data points used to derive the statistics. No information is available on whether all these data points were used to compute summary statistics or whether some "outlier" points were excluded.
Due to limited information on how the layer thickness summary statistic measures provided in the INV_LAYER, RHB_LAYER, and SPS*_LAYER tables were developed, it was not possible to determine whether statistical indices available in these tables were obtained using similar procedures and whether a comparable number of samples were used to derive the statistical indices. Based on this limitation, no crosstable comparison of layer thickness variability indicators available in these tables was carried out in this study
.Alternatively, layer thickness summary statistics could be computed using LTPP layer thickness data obtained from individual core measurements or from elevation measurements. The following data sources are available in the LTPP database:
Figure 12 shows schematically where core samples and elevation layer thickness measurements were obtained along the LTPP sections. Core data were obtained for both GPS and SPS sections, while elevation measurements were obtained only for the newly constructed SPS sections.
Data Assessment and Exclusion of Erroneous Data Points
Two different data sources were used in the analysis of layer thickness variability reasonableness:
Core elevation measurements are available for both GPS and SPS sections, while elevation measurements are available only for the SPS sections. Analysis of layer thickness variability reasonableness was carried out separately for each data source, and the results of analysis obtained from different sources then were compared.
Prior to the statistical analysis, erroneous layer thicknesses measurements were identified and excluded. Several different error sources were identified in the course of this study. Details of erroneous data evaluation are included in the discussion of analyses carried out using data from each data source.
Thickness Variability Indicators
To compare the thickness information at a layer level in lieu of individual measurement level, the following summary statistics from individual measurements were computed for each pavement layer:
COV provides a good measure of whether the dispersion of layer thickness values around the established mean thickness value is large or small. The COV is computed as a ratio between standard deviation and the mean thickness value.

Figure 13: Equation. Definition of coefficient of variation.
Thickness Variability Reasonableness Criteria
Criteria established under an LTPP material study [31] were adopted to evaluate the reasonableness of the thickness variability measures, as following:
The analysis is based on evaluation of the layer thickness variation reasonableness for individual LTPP sections and individual layers within the section. Under the LTPP material study [31], the core thickness data for individual layers from the LTPP tables TST_AC01_LAYER and TST_PC06 were evaluated to exclude erroneous data points and to compute summary statistics. These summary statistics were used in this study to evaluate reasonableness of the layer thickness variability indicators for individual layers.
Prior to the analysis, LTPP sections and individual layers with computed summary statistics were correlated with data elements in the TST_L05B table describing experiment, layer, and material types.
The criteria established in the referenced study [31] were used to evaluate the reasonableness of layer thickness variability indicators for each layer that had data in either the TST_AC01_LAYER or TST_PC06 table and in the TST_L05B table. The results of the layer thickness variability evaluation are presented in table 19 for different LTPP experiments, layers, and material types.
Layer Type  Experiment  Number of Sections  Percentage of Sections with Acceptable Layer Thickness Variations  

With Data  With COV > 20 %  With SD > 8 mm  
PCC Overlay  GPS9  24  7  70.8  
SPS7  29  10  65.5  
PCC Original Surface  GPS3  126  22  82.5  
GPS4  61  12  80.3  
GPS5  84  9  89.3  
GPS7  43  6  86.0  
GPS9  24  5  79.2  
SPS2  139  40  71.2  
SPS6  50  1  98.0  
SPS7  30  5  83.3  
SPS8  2  0  100.0  
SPS9  18  1  94.4  
LC  SPS2  35  7  80.0  
AC Original Surface  GPS1  229  9  94.3  
GPS2  139  9  93.5  
GPS6  143  21  85.3  
SPS1  134  2  98.5  
SPS3  252  39  84.5  
SPS5  133  14  89.5  
SPS8  18  0  100.0  
SPS9  25  1  96.0  
AC Binder  GPS1  147  3  98.0  
GPS2  83  6  92.8  
GPS3  2  0  100.0  
GPS6  125  20  84.0  
GPS7  41  8  80.5  
GPS_9  2  1  50.0  
SPS1  110  8  92.7  
SPS3  118  16  86.4  
SPS5  150  22  85.3  
SPS6  11  1  90.9  
SPS8  11  0  100.0  
SPS9  19  1  94.7  
AC Overlay  GPS6  204  25  87.7  
GPS7  57  4  93.0  
SPS1  6  1  83.3  
SPS3  51  11  78.4  
SPS5  96  6  93.8  
SPS6  20  3  85.0  
SPS8  7  0  100.0  
ATB  GPS1  2  0  100.0  
GPS2  52  1  98.1  
GPS3  7  1  85.7  
GPS4  1  0  100.0  
GPS5  20  1  95.0  
GPS6  8  1  87.5  
SPS1  102  15  85.3  
SPS3  24  3  87.5  
SPS5  13  0  100.0  
Total  3227  257  125  88.2 
Core Thickness Data Availability and Assessment for Newly Constructed SPS Layers
For the newly constructed SPS layers with a documented target thickness, thickness measurements are available from both core examination and elevation measurements. Layer thickness summary statistics computed for the newly constructed SPS layers were compared to the elevation measurements data, as discussed later in this chapter.
To reflect the most recent LTPP data upload status for the newly constructed SPS layers with a specified target thickness, the core thickness data were evaluated again with erroneous data points excluded and summary statistics computed for each layer and each analysis cell. A summary of the available core thickness data for SPS experimental sections is presented in table 20.
Layer Type  Experiment  Number of Records (measurements)  Number of Sections with Data 

DGATB  SPS1  323  78 
PATB  SPS1  142  32 
SPS2  0  0  
LC  SPS2  182  36 
PCC  SPS2  894  140 
SPS7  235  22  
SPS8  16  2  
SB  SPS1  759  170 
SPS5  455  92  
SPS6  99  26  
SPS8  137  18  
Total  3242  616 
Using the threestandard deviation criterion, one core thickness record was identified as erroneous (Section 220708, PCC layer) and was eliminated from the analysis at the project level. The measured core thicknesses for this layer are between 140 mm (5.5 in) and 149 mm (5.85 in), except for the excluded core measurement that was 198 mm (7.8 in).
For SPS newly constructed layers, elevation measurements were taken throughout the section of the final finished surface. The measurements normally are made at five offset points at 152m (500ft) spacing along the section.
This big number of elevation thickness measurements available at each layer level makes them a good candidate for thickness variability evaluation. One additional advantage of these thickness measurements is that their layer design or target thickness is known to the research team. As a result, the thickness variability values can be compared and summarized for different target values.
Elevation Data Availability
The availability of elevation data in SPS*_LAYER_THICKNESS tables by layer type and number of sections are presented in table 21.
Layer Type  Experiment  Number of Records (measurements)  Number of Sections with Data 

DGAB  SPS1  5295  97 
SPS2  4050  85  
SPS8  1863  38  
DGATB  SPS1  5250  97 
PATB  SPS1  4496  83 
SPS2  2242  47  
LC  SPS2  2242  47 
PCC  SPS2  6955  140 
SPS7  918  24  
SPS8  763  14  
SB  SPS1  9138  167 
SPS5  4856  93  
SPS6  1933  40  
SPS8  1202  24  
Total  51419  997 
The total number of records at Level E in the SPS*_LAYER_THICKNESS tables was 51,419 at the time of the study.
Exclusion of the Erroneous Data Points
Prior to the data analysis, 78 erroneous data points were excluded before the analysis because of data inconsistency. The following list summarizes data inconsistencies found during review of the data from the SPS*_LAYER_THICKNESS tables:
These erroneous thickness values were reported to the FHWA for further investigation.
Additionally, data points that deviated by more than three standard deviations from the mean were considered as potentially erroneous and were excluded from the analysis data set. Analysis of sections with outliers revealed that most of these sections had one outlier per section; some had two outliers, and a few three or four outliers. In all, 202 data points were excluded from further analysis. The summary of outlier analysis is presented in the table 22. A total of 51,139 records were used in the statistical analysis.
Number of Outliers per Layer  Number of Layers  Total  

With Outliers  With Other Excluded Points  
1  162  5  167 
2  15  3  18 
3  2  2  4 
4  1  1  
6  1  1  
55  1  1  
Total number of layers  180  12  192 
Total number of outlier records  202  78  280 
The number of outliers summarized by different layer types is presented in table 23.
Layer Type  Number of Records (Measurements)  Total Number of Records (Measurements)  Percent of Records (Measurements) 

DGAB  46  11208  0.41 
DGATB  18  5250  0.34 
PATB  23  6738  0.34 
LC  8  2458  0.33 
PCC  35  8636  0.41 
SB  72  17129  0.42 
Total  202  51419  0.39 
The highest percentage of the sections with outliers is for AC and PCC surface layers and unbound base, while the lowest percentage is for LC base, PATB, and DGATB.
Analysis of Layer Thickness Variation
Elevation measurements obtained after each layer construction were used to conduct analysis of layer variation reasonableness. Table 24 provides summary of the layer thickness variation reasonableness evaluation results for all SPS sections.
Layer Type  Experiment  Number of Sections  Percentage of Sections with Acceptable Layer Thickness Variations  

With Data  With COV > 20 %  With SD > 8 mm  
DGAB  SPS1  97  5  94.8  
SPS2  84  2  97.6  
SPS8  38  3  92.1  
DGATB  SPS1  97  0  100.0  
PATB  SPS1  83  1  98.8  
SPS2  46  0  100.0  
LC  SPS2  48  26  45.8  
PCC  SPS2  139  61  56.1  
SPS7  24  14  41.7  
SPS8  14  12  14.3  
SB  SPS1  167  2  98.8  
SPS5  92  12  87.0  
SPS6  36  0  100.0  
SPS8  24  1  95.8 
For all material types except for PCC and LC the percentage of acceptable data is very close to or above 90 percent. For PCC and LC material types this percentage is below 60.
To estimate typical values for layer thickness variability indicators, layer thickness data for SPS experimental sections were obtained from TST_AC01_LAYER and TST_PC06 tables (core thickness), and from SPS*_LAYER_THICKNESS tables (elevation thickness). The analyses were done separately for the thickness data obtained from core measurements and for the data from elevation measurements. Table 25 summarizes layer thickness COV and standard deviations by layer and material types obtained for PCC and AC layers from GPS and SPS sections based on the analysis of core thickness data. Table 26 summarizes layer thickness COV and standard deviations by layer and material types obtained for the newly constructed SPS sections based on analysis of elevation measurements. The COV and standard deviation values from the tables 25 and 26 could be used as approximate estimates of the expected layer thickness variability along the project for a given material and layer type.
Experiment Type  Description  Number of Analysis Layers  Mean COV, %  Min COV, %  Max COV, %  Mean St. dev., mm  Min St. dev., mm  Max St. dev., mm 

GPS  AC Binder  396  10.10  0.78  83.19  7.46  0.87  110.28 
DGATB  88  6.83  1.02  46.92  8.34  1.30  61.38  
AC Surface  506  9.76  0.70  93.24  5.44  0.52  107.46  
AC Overlay  259  10.68  1.48  59.92  5.44  0.87  44.90  
SPS  AC Binder  382  10.41  0.62  71.38  7.89  1.27  95.19 
ATB  139  12.66  0.85  184.88  14.79  1.47  135.97  
AC Surface  488  10.21  0.69  64.28  5.34  1.14  45.58  
AC Overlay  160  10.70  0.72  70.71  4.90  1.14  25.85  
GPS  PCC  336  2.36  0.40  10.92  5.44  1.04  31.14 
PCC Overlay  24  2.92  0.55  13.10  6.22  1.04  20.74  
SPS  LC  34  4.62  1.12  23.38  7.37  1.80  38.80 
PCC  233  2.66  0.51  27.97  6.31  1.14  65.21  
PCC Overlay  29  5.19  1.61  12.59  7.22  2.19  14.63 
Material Type  Number of Analysis Layers  Mean COV, %  Min COV, %  MaxCOV, %  Mean St. Dev., mm  Min St. Dev., mm  Max St. Dev., mm 

DGAB  219  8.78  1.90  37.44  13.00  3.20  55.76 
DGATB  97  5.31  1.79  15.10  9.50  3.87  24.48 
LC  48  5.69  2.55  20.33  8.96  3.81  32.38 
PATB  129  8.74  3.45  21.21  8.91  3.59  20.41 
PCC  177  4.18  0.98  17.98  8.61  2.88  22.96 
SB  319  8.32  2.01  35.80  8.41  2.47  21.10 
For the newly constructed SPS layers (layers that were constructed during the LTPP program and were monitored by the LTPP team), both elevation and core thickness measurements are available in the LTPP database. These two measurement methods employ different measuring techniques. The objective of this section is to evaluate if the means and the variances derived from these two methods are significantly different from each other at the projectlevel. Thus, the analysis is based on evaluation of statistical indicators derived for each layer of each SPS section. Only newly constructed SPS layers were used in the analysis.
Analysis Methodology
The normality of distribution of elevation data was tested and it was concluded that for a majority of sections and for all material types the distribution is normal. The detailed results are presented in chapter 5. In this analysis it was assumed that core thickness measurements have also normal distribution, because they represent different sort of the measurements for the same kind of data.
The variances and means of layer thickness data were obtained for each newly constructed layer from each SPS section from two different data sources, elevation and core thickness measurements, were compared to determine the level of agreement.
Two statistical procedures were utilized to perform the comparison of elevation and core thickness measurements:
Analysis Data Set
Elevation data for bound asphalt and concrete layers were available for 770 individual layers, while core data were available for only 616 layers. However, both elevation and core thickness data were available for only 498 asphalt and concrete layers. For 118 layers, only core data were available and for 272 layers only elevation data were available. Additionally, for 15 layers only one core measurement per layer was available. Therefore, the total number of asphalt and concrete layers used in the analysis was 483. Table 27 presents the summary of data availability.
Layer Type  Experiment  Number of Layers with both Elevation and Core Data 

DGATB  SPS1  59 
PATB  SPS1  30 
SPS2    
LC  SPS2  31 
PCC  SPS2  123 
SPS7  15  
SPS8  2  
SB  SPS1  134 
SPS5  60  
SPS6  15  
SPS8  14  
Total  483 
Comparison of the Standard Deviation and COV Values
Figure 16 provides a comparison of the standard deviations computed from core thickness measurements versus standard deviations computed from elevation thickness for all the layers. For the standard deviation values below 10 mm, the standard deviations computed from the core thickness data are lower than the standard deviations computed from the elevation measurements in most cases. However, for standard deviations above 10 mm, the standard deviations from the core data are higher than the standard deviations computed from the elevation measurements for a significant number of cases. For the majority of the elevation data, the standard deviation is below 20 mm.
Overall, 321 layers (66.5 percent) had a standard deviation computed from the elevation measurements higher than the standard deviation computed from the core measurements. Figure 16 indicates that, for a few sections, the variation of core thickness was very high as compared to the elevationdetermined thickness. However, the differences between the standard deviations were not statistically significant (99 percent confidence level) for a large majority of the sections.
Figure 17 provides a comparison between the COV values computed from the elevation and core thickness data sets. Over 80 percent of the COV values computed using each data set are below 10 percent. However, a small percentage of sections show low COV computed from one data source and high COV computed using the other data source, i.e. high COVs for elevation measurements and low COVs for core thickness measurements for the same section, or vice versa.
Comparison of the Variances
Table 28 presents the results of the comparison of variances. Sections were grouped by material type, experiment number, target thickness, and subbase type. For more than 80 percent of the sections, the differences between variances obtained from elevation and core thickness measurements were not statistically significant (99 percent confidence level). This percentage is even higher for DGATB and LC layers (about 90 percent).
The greatest differences of variance values were observed for PATB and some analysis cells with PCC and SB layers, and the lowest differences were observed for DGATB and LC layers.
Material Type  EXP.  Target Thickness  Subbase  Variance  Total Number of Sections  

Equal  Unequal  
mm  in  Number of Sections  Percent of Sections  Number of Sections  Percent of Sections  
DGATB  SPS1  102  4  12  80.0  3  20.0  15  
203  8  25  92.6  2  7.4  27  
305  12  16  94.1  1  5.9  17  
PATB  SPS1  102  4  22  73.3  8  26.7  30  
LC  SPS2  152  6  28  90.3  3  9.7  31  
PCC  SPS2  203  8  S^{1}  17  77.3  5  22.7  22 
W^{2}  35  89.7  4  10.3  39  
279  11  S  15  68.2  7  31.8  22  
W  35  87.5  5  12.5  40  
SPS7  76  3  S  6  85.7  1  14.3  7  
127  5  S  4  50.0  4  50.0  8  
SPS8  203  8  W  1  100.0  0  0.0  1  
279  11  W  1  100.0  0  0.0  1  
SB  SPS1  102  4  S  33  82.5  7  17.5  40 
W  25  86.2  4  13.8  29  
178  7  S  32  86.5  5  13.5  37  
W  20  71.4  8  28.6  28  
SPS5  51  2  S  24  85.7  4  14.3  28  
127  5  S  23  71.9  9  38.1  32  
SPS6  102  4  S  12  100.0  0  0.0  12  
203  8  S  1  33.3  2  66.7  3  
SPS8  102  4  W  5  71.4  2  28.6  7  
178  7  W  5  71.4  2  28.6  7  
Total  397  82.2  86  17.8  483  
Notes: S  "Strong" subbase (DGATB, LC). W  "Weak" subbase (DGAB, PATB). 
Comparison of the Means
The mean layer thicknesses computed from elevations and those computed from core samples were compared using the ttest at a 95 percent confidence level and assuming either equal or unequal variances, based on the Ftest results, presented in table 28. The results of the ttests are presented in table 29.
Material Type  Exp.  Target Thicknesses  Subbase  No Significant Difference between Elevation and Core Thickness  Significant Difference between Elevation and Core Thickness  Total Number of Sections  

mm  in  Number of Sections  Percent of Sections  Number of Sections  Percent of Sections  
DGATB  SPS1  102  4  9  60.0  6  40.0  15  
SPS1  203  8  20  74.1  7  25.9  27  
SPS1  305  12  8  47.1  9  52.9  17  
LC  SPS2  152  6  20  64.5  11  35.5  31  
PATB  SPS1  102  4  12  40.0  18  60.0  30  
PCC  SPS2  203  8  S  14  63.6  8  36.4  22 
SPS2  W  16  41.0  23  59.0  39  
SPS2  279  11  S  10  45.5  12  54.5  22  
SPS2  W  16  40.0  24  60.0  40  
SPS7  76  3  S  3  42.9  4  57.1  7  
SPS7  127  5  S  5  62.5  3  37.5  8  
SPS8  203  8  W  0  0.0  1  100.0  1  
SPS8  279  11  W  1  100.0  0  0.0  1  
SB  SPS1  102  4  S  19  47.5  21  52.5  40 
SPS1  W  10  34.5  19  65.5  29  
SPS1  178  7  S  11  29.7  26  70.3  37  
SPS1  W  13  46.4  15  53.6  28  
SPS5  51  2  S  10  35.7  18  64.3  28  
SPS5  127  5  S  12  37.5  20  62.5  32  
SPS6  102  4  S  9  75.0  3  25.0  12  
SPS6  203  8  S  2  66.7  1  33.3  3  
SPS8  102  4  W  3  42.9  4  57.1  7  
SPS8  178  7  W  4  57.1  3  42.9  7  
Total  47.0  256  53.0  483  
Notes: S  "Strong" subbase (DGATB, LC). W  "Weak" subbase (DGAB, PATB). 
Based on the ttest results, the mean thicknesses computed from the core measurements are not different from those computed from the elevation measurements at a 95 percent confidence level for 227 (47 percent) of all layers analyzed. The opposite is true for the remaining 256 layers analyzed (53 percent).
Figure 18 presents aggregated results of the statistical analysis of the differences between elevation and core thickness measurements. More than 60 percent of the layers with DGATB and LC had no significant difference between elevation and core thickness data. This percentage is about 40 for PATB, PCC, and SB layers.
In this chapter, the layer thickness variability indicators available in the LTPP database were reviewed. A discussion about the limitations of the available data was provided. In addition, new layer thickness variability indicators (mean, range, standard deviation, COV, and variance) were developed based on the core thickness measurements and field elevation measurements (SPS only) from the most recent LTPP database upload (release 11.5 version NT3.0, obtained on June 8, 2001).
Evaluation of Layer Thickness Variability Reasonableness
Using layer thickness summary statistics, reasonableness of the layer thickness variability data was evaluated. The purpose of the analysis was to compare layer thickness variation for each section and each layer with the benchmark layer thickness variability values. The analysis results indicated that over 88 percent of layers have layer thickness variability indicators below the benchmark values.
Additionally, typical values and ranges of layer thickness variability indicators for different layer and material types were computed. These typical values could serve as approximate estimates of the expected layer thickness variability for the projectlevel analysis and design.
Excessive Variability in Layer Thickness
For the layer thickness data obtained from the core measurements, 257 layers (10.0 percent) from the TST_AC01_LAYER table and 125 layers (18.8 percent) from the TST_PC06 table had excessive variability in the layer thickness data even after outliers were removed.
For the layer thickness data obtained from the elevation measurements, 139 layers (14.1 percent) from the SPS*_LAYER tables had excessive variability in the layer thickness data even after outliers were removed.
No remedial action was taken for the identified records. However, comment codes were assigned in the analysis summary table to the records containing such data. To determine the reasons for excessive variability, individual core samples should be reviewed.
Comparison of Layer Thickness Variability Indicators from Different Data Sources
Statistical comparisons were made between the layer thickness variances and means obtained from the core and elevation thickness measurements. Only data for newly constructed SPS sections were utilized. The results of the analysis are as follows: