Skip to contentUnited States Department of Transportation - Federal Highway Administration FHWA Home
Research Home   |   Pavements Home
Report
This report is an archived publication and may contain dated technical, contact, and link information
Publication Number: FHWA-RD-03-041

Evaluation and Analysis of LTPP Pavement Layer Thickness Data

Previous | Table of Contents | Next

The main purpose of this chapter is to characterize the extent of differences in the layer thickness data between as-designed and as-constructed (measured) thicknesses for the newly constructed SPS layers. Only these new SPS layers have design thicknesses accurately documented.

Data sources for the analysis are discussed first, followed by an overview of as-designed thicknesses for the newly constructed SPS layers. After that, typical thickness deviations from the target thicknesses are summarized, as well as their distribution types. Finally, the results of the statistical analysis are presented.

Data Sources

Two thickness data sources with multiple measurements on a given layer exist in the LTPP database:

According to the SPS construction guidelines [35-40], rod and level survey measurements are to be taken at a minimum of five offset locations (edge, outer wheel path, midlane, inner wheel path, and inside edge of lane) at longitudinal intervals no greater than 15 m (50 ft). Typically, 55 elevation measurements are available for each regular SPS test section.

The number of cores taken at each section depends on experiment and layer type and is defined in the corresponding Sampling and Testing Guide [6-11]. The number of cores per section ranges between 1 and 9.

All sections with available thickness data in either one of these tables are studied to quantify as-designed versus as-constructed variations in layer thickness.

For the section/layer combination, an analysis cell is defined to represent a specific layer in a test section, for which the target thickness was documented. The following fields from TST_L05B or EXPERIMENT_SECTION table in LTPP database along with the design target layer thickness define a unique analysis cell:

Design Thicknesses

For newly constructed SPS layers, the design thicknesses are defined in the corresponding SPS Experimental Designs [12-17]. The design thicknesses are available for the following layer types:

The design thicknesses for all these SPS experiments and layer types are presented in tables 38 through 43.

Table 38. Design layer thicknesses for the SPS-1 experiment.

SHRP_ID

Design Layer Thickness, mm (in)

DGAB

PATB

DGATB

SB

0101

203 (8)

   

178 (7)

0102

305 (12)

   

102 (4)

0103

   

203 (8)

102 (4)

0104

   

305 (12)

178 (7)

0105

102 (4)

 

102 (4)

102 (4)

0106

102 (4)

 

203 (8)

178 (7)

0107

102 (4)

102 (4)

 

102 (4)

0108

203 (8)

102 (4)

 

178 (7)

0109

305 (12)

102 (4)

 

178 (7)

0110

 

102 (4)

102 (4)

178 (7)

0111

 

102 (4)

203 (8)

102 (4)

0112

 

102 (4)

305 (12)

102 (4)

0113

203 (8)

   

102 (4)

0114

305 (12)

   

178 (7)

0115

   

203 (8)

178 (7)

0116

   

305 (12)

102 (4)

0117

102 (4)

 

102 (4)

178 (7)

0118

102 (4)

 

203 (8)

102 (4)

0119

102 (4)

102 (4)

 

178 (7)

0120

203 (8)

102 (4)

 

102 (4)

0121

305 (12)

102 (4)

 

102 (4)

0122

 

102 (4)

102 (4)

102 (4)

0123

 

102 (4)

203 (8)

178 (7)

0124

 

102 (4)

305 (12)

178 (7)



Table 39. Design layer thicknesses for the SPS-2 experiment.

SHRP_ID

Design Layer Thickness, mm (in)

DGAB

PATB

LC

PCC

0201

152 (6)

   

203 (8)

0202

152 (6)

   

203 (8)

0203

152 (6)

   

279 (11)

0204

152 (6)

   

279 (11)

0205

   

152 (6)

203 (8)

0206

   

152 (6)

203 (8)

0207

   

152 (6)

279 (11)

0208

   

152 (6)

279 (11)

0209

102 (4)

102 (4)

 

203 (8)

0210

102 (4)

102 (4)

 

203 (8)

0211

102 (4)

102 (4)

 

279 (11)

0212

102 (4)

102 (4)

 

279 (11)

0213

152 (6)

   

203 (8)

0214

152 (6)

   

203 (8)

0215

152 (6)

   

279 (11)

0216

152 (6)

   

279 (11)

0217

   

152 (6)

203 (8)

0218

   

152 (6)

203 (8)

0219

   

152 (6)

279 (11)

0220

   

152 (6)

279 (11)

0221

102 (4)

102 (4)

 

203 (8)

0222

102 (4)

102 (4)

 

203 (8)

0223

102 (4)

102 (4)

 

279 (11)

0224

102 (4)

102 (4)

 

279 (11)



Table 40. Design layer thicknesses for the SPS-5 experiment.

SHRP_ID

Design Layer Thickness, mm (in)

SB

0501

0

0502

51 (2)

0503

127 (5)

0504

127 (5)

0505

51 (2)

0506

51 (2)

0507

127 (5)

0508

127 (5)

0509

51 (2)



Table 41. Design layer thicknesses for the SPS-6 experiment.

SHRP_ID

Design Layer Thickness, mm (in)

SB

0601

0

0602

0

0603

102 (4)

0604

102 (4)

0605

0

0606

102 (4)

0607

102 (4)

0608

203 (8)



Table 42. Design layer thicknesses for the SPS-7 experiment.

SHRP_ID

Design Layer Thickness, mm (in)

PCC

0701

0

0702

76 (3)

0703

76 (3)

0704

76 (3)

0705

76 (3)

0706

127 (5)

0707

127 (5)

0708

127 (5)

0709

127 (5)



Table 43. Design layer thicknesses for the SPS-8 experiment.

SHRP_ID

Design Layer Thickness, mm (in)

DGAB

PCC

SB

0801

203 (8)

 

102 (4)

0802

305 (12)

 

178 (7)

0803

203 (8)

 

102 (4)

0804

305 (12)

 

178 (7)

0805

203 (8)

 

102 (4)

0806

305 (12)

 

179 (7)

0807

152 (6)

203 (8)

 

0808

152 (6)

279 (11)

 

0809

152 (6)

203 (8)

 

0810

152 (6)

279 (11)

 

0811

152 (6)

203 (8)

 

0812

152 (6)

279 (11)

 

Study Methodology

For both the elevation and core as-constructed thickness measurements, typical mean layer thickness deviations are established by the following:

Descriptive Summary Statistics of the Thickness Deviations

The mean thickness difference between as-designed and as-constructed thicknesses was computed for each layer using both core and elevation thickness measurements.

The following statistical indicators were computed:

The analyses were done separately for the thickness data obtained from core measurements and for the data from elevation measurements.

Layer Thickness Deviation Distribution Type

Mean thickness deviations from layers or sections were analyzed to determine whether they follow typical statistical distributions. Skewness and kurtosis analyses were conducted for this purpose, using the methodology outlined in chapter 5.

Percentage Distribution of the Individual Measurements

To evaluate the variation between as-designed and as-constructed thicknesses, deviations of the individual measurements in relation to the target values are computed for each analysis cell. These deviations are then summarized into three deviation levels: 6.35 mm (0.25 in), 12.7 mm (0.5 in), and 25.4 mm (1 in), for different material types and target thickness values.

This evaluation provides information regarding variations between as-constructed and as-designed thicknesses at individual measurement level.

Statistical Analysis of Sample Measurement Means

Statistical analysis is performed to evaluate variations for each analysis cell. The goal of statistical analysis is to assess deviation of the measurement population means from the target thicknesses. Two types of the thickness comparison are performed for both data sources:

Two-sided t-tests with 95 percent confidence level for each section and layer, to determine whether the differences between as-designed and as-constructed thicknesses are significant.

Figure 45 in page 90 shows the two-sided (i.e., equal sign) hypothesis test equations for elevation and core thickness data. For the elevation data hypothesis test, the null hypothesis: the difference between the mean elevation thickness and the target design thickness is zero versus the alternative hypothesis: the difference is not zero. Similarly, for the core data hypothesis test, the null hypothesis: the difference between the mean core thickness and the target design thickness is zero versus the alternative hypothesis: the difference is not zero.

Figure 45: Equation. The null and alternative hypotheses for two-sided t-test.

The null hypothesis for this test is that average of core or elevation thickness data is equal to the target thickness, i.e.: If the null hypothesis is rejected (i.e., the result of the two-sided t-test is significant), then the measured mean thickness is different from the design thickness at the 95 percent confidence level. On the other hand, if the null hypothesis is not rejected or the test result is not significant, then there is no evidence that the measured mean thickness is different from the design value.

One-sided t-tests with 95 percent confidence level for the difference between as-designed thickness and the mean as-constructed thickness and for tolerance level of 6.35 mm (0.25 in), 12.7 mm (0.5 in), and 25.4 mm (1 in). The null hypothesis is that the absolute value of the difference between the mean and target thickness is less than or equal to the tolerance level with the alternative hypothesis being that the absolute value of the difference is greater than the tolerance level. For example, for elevation data, for allowance of 6.35 mm (0.25 in), the null and alternative hypotheses are:

Figure 46 in page 90 shows the one-sided (i.e., greater or less than sign) hypothesis test equation for elevation thickness data with tolerance of 6.35 mm. The null hypothesis: the absolute value of the difference between the mean elevation thickness and the target design thickness is less than or equal to 6.35 mm versus the alternative hypothesis: the absolute difference is greater than 6.35 mm.

Figure 46: Equation. The null and alternative hypothesis for one-sided t-test.

If the null hypothesis is rejected (i.e., the result the one-sided t-test is significant), then the measured mean thickness deviates from the design thickness by more than the specified allowance (in this example 6.35 mm) at a 95 percent confidence level. On the other hand, if the null hypothesis is not rejected or the test result is not significant, then there is no evidence that the measured mean thickness deviates from the designed value by more than the specified allowance value, in other words, that the mean thickness is within the allowance value (in this case 6.35 mm) from the designed thickness.

Typical Deviations between Mean Measured and the Design Thicknesses

Descriptive Summary Statistics

Mean layer thickness data for SPS experimental sections with newly constructed layers were obtained from the TST_AC01_LAYER and TST_PC06 tables (core thickness), and from the SPS*_LAYER_THICKNESS tables (elevation thickness), to compute measured thickness deviation from the design value. The analysis was done for the sets of data grouped by target design thickness, material, and layer type. The following statistical indicators were computed:

The analyses were done separately for the thickness data obtained from core measurements and for the data from elevation measurements. Table 44 summarizes layer thickness deviations by different layer and material types based on analysis of elevation measurements. Table 45 summarizes mean core examination layer thickness deviations from their designed values by different layer and material types.

Figures 47 through 61 present the frequency distributions of the thickness deviations for different layer types and target thicknesses for both core and elevation thickness measurements.

The following observations are made based on these summary statistics:

Table 44. Summary of differences between mean elevation thickness measurements and target thicknesses.

Mat. Type

Target Thickness

Total Number of Sections

Mean Difference

Standard Deviation

Min.

Difference

Max. Difference

mm

in

mm

in

mm

in

mm

in

mm

in

DGAB

102

4

84

0.4

0.01

10.3

0.40

-28.6

-1.13

33.4

1.32

152

6

55

-1.2

-0.05

14.4

0.57

-51.5

-2.03

38.2

1.51

203

8

40

0.9

0.04

12.7

0.50

-26.8

-1.05

45.2

1.78

305

12

40

-6.0

-0.24

30.0

1.18

-173.3

-6.82

34.9

1.37

DGATB

102

4

27

1.8

0.07

8.0

0.31

-12.0

-0.47

21.1

0.83

203

8

42

0.5

0.02

16.3

0.64

-62.5

-2.46

28.9

1.14

305

12

28

-2.1

-0.08

15.9

0.63

-35.1

-1.38

38.1

1.50

LC

152

6

48

5.5

0.22

10.6

0.42

-25.8

-1.02

36.9

1.45

PATB

102

4

129

1.2

0.05

10.5

0.41

-17.1

-0.67

41.9

1.65

PCC

76

3

12

18.2

0.72

11.5

0.45

3.4

0.13

42.6

1.68

127

5

12

16.5

0.65

11.6

0.46

5.1

0.20

39.0

1.53

203

8

76

5.4

0.21

12.2

0.48

-32.6

-1.28

53.3

2.10

279

11

77

4.7

0.18

11.0

0.43

-24.8

-0.98

39.0

1.54

SB

51

2

46

4.8

0.19

19.9

0.78

-27.8

-1.10

67.9

2.67

102

4

125

-2.2

-0.09

18.5

0.73

-58.9

-2.32

31.7

1.25

127

5

46

-4.4

-0.17

20.1

0.79

-70.6

-2.78

38.3

1.51

178

7

95

-8.2

-0.32

23.9

0.94

-73.3

-2.89

59.4

2.34

203

8

7

-2.7

-0.11

22.9

0.90

-36.9

-1.45

36.3

1.43



Table 45. Summary of differences between mean core thickness measurements and target thicknesses.

Mat. Type

Target Thickness

Total Number of Sections

Mean Difference

Standard Deviation

Min.

Difference

Max. Difference

mm

in

mm

in

mm

in

mm

in

mm

in

DGATB

102

4

22

-0.9

-0.04

10.9

0.43

-22.9

-0.90

20.3

0.80

203

8

34

1.1

0.04

21.5

0.85

-64.3

-2.53

38.1

1.50

305

12

22

-5.4

-0.21

25.1

0.99

-88.9

-3.50

21.0

0.83

LC

152

6

36

8.2

0.32

12.6

0.50

-19.1

-0.75

38.9

1.53

PATB

102

4

32

-19.7

-0.78

39.4

1.55

-87.2

-3.43

113.5

4.47

PCC

76

3

10

20.3

0.80

10.7

0.42

5.9

0.23

35.9

1.41

127

5

12

13.4

0.53

13.5

0.53

-9.9

-0.39

37.1

1.46

203

8

71

9.8

0.39

14.0

0.55

-22.5

-0.89

52.3

2.06

279

11

71

-0.7

-0.03

28.3

1.12

-94.7

-3.73

31.8

1.25

SB

51

2

45

16.2

0.64

21.4

0.84

-17.1

-0.68

59.7

2.35

102

4

114

5.2

0.20

17.0

0.67

-63.5

-2.50

47.0

1.85

127

5

47

9.1

0.36

23.6

0.93

-39.4

-1.55

73.2

2.88

178

7

94

-4.3

-0.17

21.8

0.86

-96.5

-3.80

65.4

2.58

203

8

6

-18.4

-0.73

51.6

2.03

-118.1

-4.65

16.5

0.65


These summary statistics for the differences between as-designed and mean as-constructed layer thicknesses can be used as benchmarks for use in pavement design reliability and other research studies.


Figure 47 in page 93 shows four charts for the deviations of the mean elevation-measured dense graded aggregate base layer thickness from four target thicknesses: 102, 152, 203 and 305 mm, respectively. The horizontal axis of each chart is the deviation between the mean elevation-measured thickness of a section and the corresponding target thickness, ranging from -25.4 mm to 25.4 mm or more with 6.3-mm increment. The vertical axis of each chart is the number of sections that fall into the deviation range on the horizontal axis. All the four frequency distributions appear to be normal.



Figure 47: Chart. The Frequency distribution of mean thickness deviations for all four target thicknesses of the DGAB layer.


Figure 48 in page 94 shows the chart for the deviation of the mean elevation- and core-measured dense graded asphalt-treated base layer thickness from the target thickness of 102 mm. The horizontal axis of the chart is the deviation between the mean elevation-measured thickness of a section and the corresponding target thickness, ranging from -25.4 mm to 25.4 mm or more with 6.3-mm increment. The vertical axis of the chart is the number of sections that fall into the deviation range on the horizontal axis. The frequency distributions of the elevation and the core layer thickness deviations are juxtaposed side by side on the same scale. The frequency distribution of the elevation deviations appears to skew to the right while the distribution of the core deviations appears to be normal.

Figure 48: Chart. Frequency distribution of elevation and core thickness measurements deviations for DGATB with 102-mm (4-in) target thickness.


Figure 49 in page 94 shows the chart for the deviation of the mean elevation- and core-measured dense graded asphalt-treated base layer thickness from the target thickness of 203 mm.  The horizontal axis of the chart is the deviation between the mean elevation-measured thickness of a section and the corresponding target thickness, ranging from -25.4 mm to 25.4 mm or more with 6.3-mm increment.  The vertical axis of the chart is the number of sections that fall into the deviation range on the horizontal axis.  The frequency distributions of the elevation and the core layer thickness deviations are juxtaposed side by side on the same scale.  The frequency distribution of the elevation deviations appears to be normal while the distribution of the core deviations appears to be uniform.

Figure 49: Chart. Frequency distribution of elevation and core thickness measurements deviations for DGATB with 203-mm (8-in) target thickness.
Figure 50 in page 95 shows the chart for the deviation of the mean elevation- and core-measured dense graded asphalt-treated base layer thickness from the target thickness of 305 mm.  The horizontal axis of the chart is the deviation between the mean elevation-measured thickness of a section and the corresponding target thickness, ranging from -25.4 mm to 25.4 mm or more with 6.3-mm increment.  The vertical axis of the chart is the number of sections that fall into the deviation range on the horizontal axis.  The frequency distributions of the elevation and the core layer thickness deviations are juxtaposed side by side on the same scale.  The frequency distribution of the elevation deviations appears to skew to the left while the distribution of the core deviations appears to be uniform.

Figure 50: Chart. Frequency distribution of elevation and core thickness measurements deviations for DGATB with 305-mm (12-in) target thickness.

Figure 51 in page 95 shows the chart for the deviation of the mean elevation- and core-measured lean concrete base layer thickness from the target thickness of 152 mm.  The horizontal axis of the chart is the deviation between the mean elevation-measured thickness of a section and the corresponding target thickness, ranging from -25.4 mm to 25.4 mm or more with 6.3-mm increment.  The vertical axis of the chart is the number of sections that fall into the deviation range on the horizontal axis.  The frequency distributions of the elevation and the core layer thickness deviations are juxtaposed side by side on the same scale.  The frequency distribution of the elevation deviations appears to be normal with a higher peak while the distribution of the core deviations appears to be normal with a flat peak.

Figure 51: Chart. Frequency distribution of elevation and core thickness measurements deviations for LC with 152-mm (6-in) target thickness.
Figure 52 in page 96 shows the chart for the deviation of the mean elevation- and core-measured permeable asphalt-treated base layer thickness from the target thickness of 102 mm.  The horizontal axis of the chart is the deviation between the mean elevation-measured thickness of a section and the corresponding target thickness, ranging from -25.4 mm to 25.4 mm or more with 6.3-mm increment.  The vertical axis of the chart is the number of sections that fall into the deviation range on the horizontal axis.  The frequency distributions of the elevation and the core layer thickness deviations are juxtaposed side by side on the same scale.  The frequency distribution of the elevation deviations appears to be normal and skew to the right while the distribution of the core deviations appears to be decreasing from the left to the right.

Figure 52: Chart. Frequency distribution of elevation and core thickness measurements deviations for PATB with 102-mm (4-in) target thickness.
Figure 53 in page 96 shows the chart for the deviation of the mean elevation- and core-measured PCC surface layer thickness from the target thickness of 76 mm.  The horizontal axis of the chart is the deviation between the mean elevation-measured thickness of a section and the corresponding target thickness, ranging from -25.4 mm to 25.4 mm or more with 6.3-mm increment.  The vertical axis of the chart is the number of sections that fall into the deviation range on the horizontal axis.  The frequency distributions of the elevation and the core layer thickness deviations are juxtaposed side by side on the same scale.  Both frequency distributions of the elevation and core deviations appear to be normal but shifted to the upper end of the horizontal axis.

Figure 53: Chart. Frequency distribution of elevation and core thickness measurements deviations for PCC with 76-mm (3-in) target thickness


Figure 54 in page 97 shows the chart for the deviation of the mean elevation- and core-measured PCC surface layer thickness from the target thickness of 127 mm.  The horizontal axis of the chart is the deviation between the mean elevation-measured thickness of a section and the corresponding target thickness, ranging from -25.4 mm to 25.4 mm or more with 6.3-mm increment.  The vertical axis of the chart is the number of sections that fall into the deviation range on the horizontal axis.  The frequency distributions of the elevation and the core layer thickness deviations are juxtaposed side by side on the same scale.  The frequency distribution of the elevation deviations appears to be normal but shifted to the right end of the horizontal axis while the distribution of the core deviations appears to be normal and shifted to the right end of the horizontal axis and skew to the left.

Figure 54: Chart. Frequency distribution of elevation and core thickness measurements deviations for PCC with 127-mm (5-in) target thickness.


Figure 55 in page 97 shows the chart for the deviation of the mean elevation- and core-measured PCC surface layer thickness from the target thickness of 203 mm.  The horizontal axis of the chart is the deviation between the mean elevation-measured thickness of a section and the corresponding target thickness, ranging from -25.4 mm to 25.4 mm or more with 6.3-mm increment.  The vertical axis of the chart is the number of sections that fall into the deviation range on the horizontal axis.  The frequency distributions of the elevation and the core layer thickness deviations are juxtaposed side by side on the same scale.  The frequency distribution of the elevation deviations appears to be normal and evenly spread over the horizontal axis but with the peak in the upper half of the horizontal axis while the distribution of the core deviations appears to be normal with a flat peak and skew to the left.

Figure 55: Chart. Frequency distribution of elevation and core thickness measurements deviations for PCC with 203-mm (8-in) target thickness.


Figure 56 in page 98 shows the chart for the deviation of the mean elevation- and core-measured PCC surface layer thickness from the target thickness of 279 mm.  The horizontal axis of the chart is the deviation between the mean elevation-measured thickness of a section and the corresponding target thickness, ranging from -25.4 mm to 25.4 mm or more with 6.3-mm increment.  The vertical axis of the chart is the number of sections that fall into the deviation range on the horizontal axis.  The frequency distributions of the elevation and the core layer thickness deviations are juxtaposed side by side on the same scale.  The frequency distribution of the elevation deviations appears to be normal while the distribution of the core deviations appears to be normal and skew to the left with outliers in the deviation range below -2.54 mm.

Figure 56: Chart. Frequency distribution of elevation and core thickness measurements deviations for PCC with 279-mm (11-in) target thickness.


Figure 57 in page 98 shows the chart for the deviation of the mean elevation- and core-measured surface and binder layer thickness from the target thickness of 203 mm.  The horizontal axis of the chart is the deviation between the mean elevation-measured thickness of a section and the corresponding target thickness, ranging from -25.4 mm to 25.4 mm or more with 6.3-mm increment.  The vertical axis of the chart is the number of sections that fall into the deviation range on the horizontal axis.  The frequency distributions of the elevation and the core layer thickness deviations are juxtaposed side by side on the same scale.  The frequency distribution of the elevation deviations appears to be normal and evenly spread over the horizontal axis but with the peak in the upper half of the horizontal axis while the distribution of the core deviations appears to be normal with a flat peak and skew to the left.

Figure 57: Chart. Frequency distribution of elevation and core thickness measurements deviations for SB with 51-mm (2-in) target thickness.


Figure 58 in page 99 shows the chart for the deviation of the mean elevation- and core-measured surface and binder layer thickness from the target thickness of 102 mm.  The horizontal axis of the chart is the deviation between the mean elevation-measured thickness of a section and the corresponding target thickness, ranging from -25.4 mm to 25.4 mm or more with 6.3-mm increment.  The vertical axis of the chart is the number of sections that fall into the deviation range on the horizontal axis.  The frequency distributions of the elevation and the core layer thickness deviations are juxtaposed side by side on the same scale.  The frequency distribution of the elevation deviations appears to be normal with a spike in the deviation range below -2.54 mm while the distribution of the core deviations appears to be normal.

Figure 58: Chart. Frequency distribution of elevation and core thickness measurements deviations for SB with 102-mm (4-in) target thickness.


Figure 59 in page 99 shows the chart for the deviation of the mean elevation- and core-measured surface and binder layer thickness from the target thickness of 127 mm.  The horizontal axis of the chart is the deviation between the mean elevation-measured thickness of a section and the corresponding target thickness, ranging from -25.4 mm to 25.4 mm or more with 6.3-mm increment.  The vertical axis of the chart is the number of sections that fall into the deviation range on the horizontal axis.  The frequency distributions of the elevation and the core layer thickness deviations are juxtaposed side by side on the same scale.  The frequency distribution of the elevation deviations appears to be normal with a spike in the deviation range below -2.54 mm while the distribution of the core deviations appears to be normal with a spike in the deviation range above 2.54 mm.

Figure 59: Chart. Frequency distribution of elevation and core thickness measurements deviations for SB with 127-mm (5-in) target thickness.


Figure 60 in page 100 shows the chart for the deviation of the mean elevation- and core-measured surface and binder layer thickness from the target thickness of 178 mm.  The horizontal axis of the chart is the deviation between the mean elevation-measured thickness of a section and the corresponding target thickness, ranging from -25.4 mm to 25.4 mm or more with 6.3-mm increment.  The vertical axis of the chart is the number of sections that fall into the deviation range on the horizontal axis.  The frequency distributions of the elevation and the core layer thickness deviations are juxtaposed side by side on the same scale.  The frequency distribution of the elevation deviations appears to be normal with a spike in the deviation range below -2.54 mm while the distribution of the core deviations appears to be normal with a spike in the deviation range below -2.54 mm.

Figure 60: Chart. Frequency distribution of elevation and core thickness measurements deviations for SB with 178-mm (7-in) target thickness.
Figure 61 in page 100 shows the chart for the deviation of the mean elevation- and core-measured surface and binder layer thickness from the target thickness of 203 mm.  The horizontal axis of the chart is the deviation between the mean elevation-measured thickness of a section and the corresponding target thickness, ranging from -25.4 mm to 25.4 mm or more with 6.3-mm increment.  The vertical axis of the chart is the number of sections that fall into the deviation range on the horizontal axis.  The frequency distributions of the elevation and the core layer thickness deviations are juxtaposed side by side on the same scale.  The frequency distribution of the elevation deviations appears to be normal while the distribution of the core deviations appears to be normal with a spike in the deviation range below -2.54 mm.

Figure 61: Chart. Frequency distribution of elevation and core thickness measurements deviations for S with 203-mm (8-in) target thickness.

Layer Thickness Deviation Distribution Type

Mean thickness deviations from layers or sections were analyzed to determine whether they follow typical statistical distributions. Skewness and kurtosis analyses were conducted for this purpose. The statistical test results are presented in table 46 for both the elevation and core mean layer thicknesses. Examples of the thickness deviation distributions are shown in figures 62 and 63.

Table 46. Distribution of the mean thickness deviations from the design thickness based on kurtosis and skewness tests.

Mat. Type

Target Thickness

Elevation Measurement Data

Core Examination Data

mm

in

No. Layers

Distribution Type

No. Layers

Distribution Type

DGAB

102

4

84

Normal

No Data

152

6

55

Wide spread and skewed left

203

8

40

Wide spread and skewed right

305

12

40

Wide spread and skewed left

DGATB

102

4

27

Normal

22

Normal

203

8

42

Wide spread and skewed left

34

Normal

305

12

28

Normal

22

Wide spread and skewed left

LC

152

6

48

Normal

36

Normal

PATB

102

4

129

Skewed right

32

Normal

PCC

76

3

12

Normal

10

Normal

127

5

12

Normal

12

Normal

203

8

76

Wide Spread

71

Normal

279

11

77

Normal

71

Wide spread and skewed left

SB

51

2

46

Skewed right

45

Normal

102

4

125

Skewed left

114

Wide spread and skewed left

127

5

46

Normal

47

Normal

178

7

95

Skewed left

94

Wide spread and skewed left

203

8

7

Not enough data

6

Not enough data

As shown in table 46, there are some discrepancies between the distribution types drawn from elevation data and core data. For the layers with both elevation and core data, the distribution of the thickness deviation derived from the core data is normal for more layer type and design thicknesses than from the elevation data.

The conclusions drawn from both the descriptive statistics and the kurtosis and skewness tests of their distribution types will be useful for pavement designers and researchers. They will be especially useful in reliability based mechanistic-empirical pavement performance analysis and design.


Figure 62 in page 102 shows an example normally distributed chart for the deviation of the mean elevation-measured lean concrete base layer thickness from the target thickness of 152 mm.  The horizontal axis of the chart is the deviation between the mean elevation-measured thickness of a section and the corresponding target thickness, ranging from -44.5 mm to 50.8 mm with 6.3-mm increment.

Figure 62: Chart. Example of normally distributed thickness deviations (elevation data, LC, target thickness 152 mm [6 in]).

Figure 63 in page 102 shows an example skew-distributed chart for the deviation of the mean core-measured PCC surface layer thickness from the target thickness of 279 mm.  The horizontal axis of the chart is the deviation between the mean elevation-measured thickness of a section and the corresponding target thickness, ranging from -101.6 mm to 50.8 mm with 6.3-mm increment.  The distribution of the deviations appears to skew to the right.

Figure 63: Chart. Example of a skewed distribution for layer thickness deviation (core data, PCC, target thickness 279 mm [11 in]).

Statistical Analysis of Elevation Measurements

Analysis of the Percentage Distribution

The overall percentage distribution of elevation measurements as a function of the three tolerance levels is presented in table 47.

Table 47. Percentage distribution summary of the elevation thickness measurements.

Measured Layer Thickness, t

Difference Between As-Constructed and As-Designed Thickness

Diff = 6.35 mm (0.25 in)

Diff = 12.7 mm (0.5 in)

Diff = 25.4 mm (1.0 in)

Number of Measurements

Percent of Measurements

Number of Measurements

Percent of Measurements

Number of Measurements

Percent of Measurements

t <
TV1 - Diff

15557 30.30 8481 16.52 3656 7.12

t within
TV ± Diff

17788 34.65 32542 63.38 44324 86.33

t >
TV + Diff

17996 35.05 10318 20.10 3361 6.55

Total

51341 100 51341 100 51341 100
Notes: 1Target value

The distribution of measurements by layer type for tolerance levels of 6.35 mm (0.25 in), 12.7 mm (0.5 in), and 25.4 mm (1 in) are presented in tables 48, 49, and 50, respectively.

Table 48. Percentage distribution of individual elevation measurements by layer type and design thickness for a tolerance level of 6.35 mm (0.25 in).

Layer Type

Target Thickness

Thickness
<TV-6.35 mm (0.25 in)

Thickness Within
TV ± 6.35 mm (0.25 in)

Thickness
>TV+6.35 mm (0.25 in)

Total

Number of Measurem.

mm

in

Number of Measurem.

Percent of Measurem.

Number of Measurem.

Percent of Measurem.

Number of Measurem.

Percent of Measurem.

DGAB

102

4

1376

31.9

1686

39.0

1256

29.1

4318

152

6

820

31.1

1046

39.7

772

29.3

2638

203

8

675

32.0

679

32.2

756

35.8

2110

305

12

809

37.8

722

33.7

609

28.5

2140

DGATB

102

4

370

25.9

597

41.8

461

32.3

1428

203

8

700

30.3

700

30.3

907

39.3

2307

305

12

570

37.6

499

32.9

446

29.4

1515

LC

152

6

342

13.9

1034

42.1

1082

44.0

2458

PATB

102

4

2059

30.6

2554

37.9

2124

31.5

6737

PCC

76

3

7

1.5

96

21.0

355

77.5

458

127

5

10

2.2

85

18.5

365

79.3

460

203

8

706

18.5

1296

33.9

1821

47.6

3823

279

11

713

18.3

1460

37.5

1721

44.2

3894

SB

51

2

655

27.3

810

33.8

932

38.9

2397

102

4

2286

33.9

2203

32.6

2259

33.5

6748

127

5

1107

46.2

617

25.8

671

28.0

2395

178

7

2201

42.9

1589

30.9

1345

26.2

5135

203

8

151

39.7

115

30.3

114

30.0

380

Total

   

15557

30.3

17788

34.6

17996

35.1

51341



Table 49. Percentage distribution of individual elevation measurements by layer type and design thickness for a tolerance level of 12.7 mm (0.5 in).

Layer Type

Target Thickness

Thickness

<TV-12.7 mm (0.5 in)

Thickness Within
TV ±
12.7 mm (0.5 in)

Thickness
>TV+12.7 mm (0.5 in)

Total

Number of Measurem.

mm

in

Number of Measurem.

Percent of Measurem.

Number of Measurem.

Percent of Measurem.

Number of Measurem.

Percent of Measurem.

DGAB

102

4

589

13.6

2990

69.2

739

17.1

4318

152

6

447

16.9

1796

68.1

395

15.0

2638

203

8

425

20.1

1284

60.9

401

19.0

2110

305

12

560

26.2

1168

54.6

412

19.3

2140

DGATB

102

4

104

7.3

1087

76.1

237

16.6

1428

203

8

384

16.6

1419

61.5

504

21.8

2307

305

12

370

24.4

851

56.2

294

19.4

1515

LC

152

6

168

6.8

1661

67.6

629

25.6

2458

PATB

102

4

790

11.7

4774

70.9

1173

17.4

6737

PCC

76

3

2

0.4

159

34.7

297

64.8

458

127

5

2

0.4

214

46.5

244

53.0

460

203

8

323

8.4

2549

66.7

951

24.9

3823

279

11

338

8.7

2745

70.5

811

20.8

3894

SB

51

2

374

15.6

1420

59.2

603

25.2

2397

102

4

1360

20.2

4031

59.7

1357

20.1

6748

127

5

747

31.2

1241

51.8

407

17.0

2395

178

7

1380

26.9

2971

57.9

784

15.3

5135

203

8

118

31.1

182

47.9

80

21.1

380

Total

   

8481

16.5

32542

63.4

10318

20.1

51341



Table 50. Percentage distribution of individual elevation measurements by layer type and design thickness for a tolerance level of 25.4 mm (1 in).

Layer Type

Target Thickness

Mean Thickness
< TV-25.4 mm (1in)

Mean Thickness Within TV ± 25.4 mm (1in)

Mean Thickness >TV+25.4 mm (1in)

Total Number of Measurem.

mm

in

Number of Measurem.

Percent of Measurem.

Number of Measurem.

Percent of Measurem.

Number of Measurem.

Percent of Measurem.

DGAB

102

4

181

4.2

3910

90.6

227

5.3

4318

152

6

187

7.1

2310

87.6

141

5.3

2638

203

8

124

5.9

1807

85.6

179

8.5

2110

305

12

260

12.1

1688

78.9

192

9.0

2140

DGATB

102

4

9

0.6

1403

98.2

16

1.1

1428

203

8

134

5.8

2038

88.3

135

5.9

2307

305

12

170

11.2

1249

82.4

96

6.3

1515

LC

152

6

33

1.3

2228

90.6

197

8.0

2458

PATB

102

4

108

1.6

6378

94.7

251

3.7

6737

PCC

76

3

0

0.0

308

67.2

150

32.8

458

127

5

0

0.0

336

73.0

124

27.0

460

203

8

64

1.7

3474

90.9

285

7.5

3823

279

11

45

1.2

3593

92.3

256

6.6

3894

SB

51

2

72

3.0

1970

82.2

355

14.8

2397

102

4

925

13.7

5512

81.7

311

4.6

6748

127

5

298

12.4

1866

77.9

231

9.6

2395

178

7

983

19.1

3987

77.6

165

3.2

5135

203

8

63

16.6

267

70.3

50

13.2

380

Total

   

3656

7.1

44324

86.3

3361

6.5

51341

The graphical presentations of percentage distributions of elevation measurements are shown in figures 64, 65, and 66 for different tolerance levels.

The following conclusions may be drawn based on the percentage distributions of the elevation measurements:


Figure 64 in page 106 shows a chart for the percentage distribution of deviations of the mean elevation-measured layer thickness for six material types including DGAB, DGATB, LC, PATB, PCC, and SB from the corresponding target thickness listed in Table 48 in page 104.  The percentage is determined by the number of deviations that are below, within, or above the tolerance level (TV) of 6.35 mm divided by the total number of deviations from the corresponding target thickness. The horizontal axis of the chart is the corresponding target thicknesses for each of the six material types.  The vertical axis is the percentage of deviations that are below, within, or above the TV of 6.35 mm, which are displayed as a vertical bar of 100 percent in total, consisting of black (below the TV of 6.35 mm), blank (within the TV of 6.35 mm), and gray (above the TV of 6.35 mm) percentages.  On average for the six material types, about 30.3 percent of the deviations are below the TV of 6.35 mm; about 34.6 percent of the deviations are within the TV of 6.35 mm; and about 35.1 percent of the deviations are above the TV of 6.35 mm.

Figure 64: Chart. Percentage distribution of the elevation measurements for a tolerance level of 6.35 mm (0.25 in) for different material types and design thicknesses.

Figure 65 in page 106 shows a chart for the percentage distribution of deviations of the mean elevation-measured layer thickness for six material types including DGAB, DGATB, LC, PATB, PCC, and SB from the corresponding target thickness listed in Table 49 in page 104.  The percentage is determined by the number of deviations that are below, within, or above the tolerance level (TV) of 12.7 mm divided by the total number of deviations from the corresponding target thickness. The horizontal axis of the chart is the corresponding target thicknesses listed in for each of the six material types.  The vertical axis is the percentage of deviations that are below, within, or above the TV of 12.7 mm, which are displayed as a vertical bar of 100 percent in total, consisting of black (below the TV of 12.7 mm), blank (within the TV of 12.7 mm), and gray (above the TV of 12.7 mm) percentages.  On average for the six material types, about 16.5 percent of the deviations are below the TV of 12.7 mm; about 63.4 percent of the deviations are within the TV of 12.7 mm; and about 20.1 percent of the deviations are above the TV of 12.7 mm.

Figure 65: Chart. Percentage distribution of the elevation measurements for a tolerance level of 12.7 mm (0.5 in) for different material types and design thicknesses.

Figure 66 in page 106 shows a chart for the percentage distribution of deviations of the mean elevation-measured layer thickness for six material types including DGAB, DGATB, LC, PATB, PCC, and SB from the corresponding target thickness listed in Table 50 in page 105.  The percentage is determined by the number of deviations that are below, within, or above the tolerance level (TV) of 25.4 mm divided by the total number of deviations from the corresponding target thickness. The horizontal axis of the chart is the corresponding target thicknesses for each of the six material types.  The vertical axis is the percentage of deviations that are below, within, or above the TV of 25.4 mm, which are displayed as a vertical bar of 100 percent in total, consisting of black (below the TV of 25.4 mm), blank (within the TV of 25.4 mm), and gray (above the TV of 25.4 mm) percentages.  On average for the six material types, about 7.1 percent of the deviations are below the TV of 25.4 mm; about 86.3 percent of the deviations are within the TV of 25.4 mm; and about 6.5 percent of the deviations are above the TV of 25.4 mm.

Figure 66: Chart. Percentage distribution of the elevation measurements for a tolerance level of 25.4 mm (1 in) for different material types and design thicknesses.

Statistical Analysis of the Elevation Measurements

Two-sided t-test

After removing the outlying data points (as discussed in chapter 4), t-tests are performed to evaluate whether the mean constructed thicknesses are close to the designed thicknesses. Many of these tests are highly significant, meaning that the mean constructed thickness is significantly different from the designed thickness.

The following notes apply to tables 51 to 56 and tables 61 to 66:

Results of two-sided t-test with 95 percent confidence are presented in table 51. The results of the two-sided t-tests by layer material type and target thickness are given in table 52.

Table 51. Summary of the results of the two-sided t-tests (95 percent confidence level) using elevation measurements.

Mean Thickness

Number of Layers

Percentage of Layers

Significantly lower than the target value

357

36.10

No significant difference from the target value

196

19.82

Significantly higher than the target value

436

44.08

Total

989

100

The following observations are based on the results of the two-sided t-test for the elevation measurements:

Table 52. Results of the two-sided t-test for different material types (95 percent confidence level) by layer type and design thickness using elevation measurements.

Layer Type

Target Thickness

Significantly Lower than the Target Value

No Significant Difference

Significantly Higher than the Target Value

Total

Number of Sections

mm

in

Number of Sections

Percent of Sections

Number of Sections

Percent of Sections

Number of Sections

Percent of Sections

DGAB

102

4

28

33.3

27

32.1

29

34.5

84

152

6

20

36.4

14

25.5

21

38.2

55

203

8

12

30.0

15

37.5

13

32.5

40

305

12

16

40.0

13

32.5

11

27.5

40

DGATB

102

4

10

37.0

5

18.5

12

44.4

27

203

8

15

35.7

12

28.6

15

35.7

42

305

12

14

50.0

3

10.7

11

39.3

28

LC

152

6

9

18.8

11

22.9

28

58.3

48

PATB

102

4

48

37.2

26

20.2

55

42.6

129

PCC

76

3

0

0.0

0

0.0

12

100.0

12

127

5

0

0.0

0

0.0

12

100.0

12

203

8

20

26.3

11

14.5

45

59.2

76

279

11

16

20.8

21

27.3

40

51.9

77

SB

51

2

19

41.3

4

8.7

23

50.0

46

102

4

50

40.0

16

12.8

59

47.2

125

127

5

29

63.0

2

4.3

15

32.6

46

178

7

48

50.5

14

14.7

33

34.7

95

203

8

3

42.9

2

28.6

2

28.6

7

Total

   

357

36.1

196

19.8

436

44.1

989

One-sided t-test

Three one-sided t-tests with a confidence level of 95 percent were performed to evaluate whether the absolute differences between as-constructed and as-designed thicknesses are greater than 6.35 mm (0.25 in), 12.7 mm (0.5 in), and 25.4 mm (1 in), respectively. The results of the overall analysis of all data points for all layers are presented in table 53.

The results of the analysis by layer material type for different tolerance levels are presented in tables 54 to 56.

Table 53. Summary of the results of one-sided t-tests using elevation measurements.

Level of Significance (TV - Target Value)

Difference Between the Mean As-Constructed and As-Designed Thickness

6.35 mm (0.25 in)

12.7 mm (0.5 in)

25.4 mm (1.0 in)

Number of Layers

Percent of Layers

Number of Layers

Percent of Layers

Number of Layers

Percent of Layers

Significantly lower than TV

181

18.3

102

10.3

50

5.1

No significant difference from the TV

562

56.8

760

76.8

908

91.8

Significantly higher than TV

246

26.9

127

12.8

31

3.1

Total

989

100

989

100

989

100



Table 54. Results of one-sided t-test for tolerance level of 6.35 mm (0.25 in) by layer type and design thickness using elevation measurements.

Layer Type

Target Thickness

Mean Thickness <TV-6.35 mm (0.25 in)

Mean Thickness Within TV ± 6.35 mm (0.25 in)

Mean Thickness >TV+6.35 mm (0.25 in)

Total Number of Sections

mm

in

Number of Sections

Percent of Sections

Number of Sections

Percent of Sections

Number of Sections

Percent of Sections

DGAB

102

4

12

14.3

59

70.2

13

15.5

84

152

6

9

16.4

40

72.7

6

10.9

55

203

8

5

12.5

28

70.0

7

17.5

40

305

12

9

22.5

25

62.5

6

15.0

40

DGATB

102

4

3

11.1

20

74.1

4

14.8

27

203

8

8

19.0

22

52.4

12

28.6

42

305

12

8

28.6

12

42.9

8

28.6

28

LC

152

6

3

6.3

28

58.3

17

35.4

48

PATB

102

4

21

16.3

81

62.8

27

20.9

129

PCC

76

3

0

0.0

2

16.7

10

83.3

12

127

5

0

0.0

3

25.0

9

75.0

12

203

8

5

6.6

41

53.9

30

39.5

76

279

11

8

10.4

44

57.1

25

32.5

77

SB

51

2

9

19.6

24

52.2

13

28.3

46

102

4

31

24.8

65

52.0

29

23.2

125

127

5

19

41.3

17

37.0

10

21.7

46

178

7

29

30.5

47

49.5

19

20.0

95

203

8

2

28.6

4

57.1

1

14.3

7

Total

   

181

18.3

562

56.8

246

24.9

989



Table 55. Results of one-sided t-tests for tolerance level of 12.7 mm (0.5 in) by layer type and design thickness using elevation measurements.

Layer Type

Target Thickness

Mean Thickness <TV-12.7 mm (0.5 in)

Mean Thickness Within TV ± 12.7 mm (0.5 in)

Mean Thickness >TV+12.7 mm (0.5 in)

Total Number of Sections

mm

in

Number of Sections

Percent of Sections

Number of Sections

Percent of Sections

Number of Sections

Percent of Sections

DGAB

102

4

5

6.0

73

86.9

6

7.1

84

152

6

6

10.9

47

85.5

2

3.6

55

203

8

3

7.5

33

82.5

4

10.0

40

305

12

6

15.0

32

80.0

2

5.0

40

DGATB

102

4

0

0.0

25

92.6

2

7.4

27

203

8

5

11.9

29

69.0

8

19.0

42

305

12

6

21.4

19

67.9

3

10.7

28

LC

152

6

1

2.1

40

83.3

7

14.6

48

PATB

102

4

5

3.9

111

86.0

13

10.1

129

PCC

76

3

0

0.0

7

58.3

5

41.7

12

127

5

0

0.0

6

50.0

6

50.0

12

203

8

4

5.3

60

78.9

12

15.8

76

279

11

2

2.6

62

80.5

13

16.9

77

SB

51

2

6

13.0

29

63.0

11

23.9

46

102

4

20

16.0

88

70.4

17

13.6

125

127

5

10

21.7

29

63.0

7

15.2

46

178

7

21

22.1

66

69.5

8

8.4

95

203

8

2

28.6

4

57.1

1

14.3

7

Total

   

102

10.3

760

76.8

127

12.8

989



Table 56. Results of one-sided t-test for tolerance level of 25.4 mm (1 in) by layer type and design thickness using elevation measurements.

Layer Type

Target Thickness

Mean Thickness

<TV-25.4 mm (1in)

Mean Thickness Within

TV ± 25.4 mm (1 in)

Mean Thickness

>TV+25.4 mm (1in)

Total

Number of Sections

mm

in

Number of Sections

Percent of Sections

Number of Sections

Percent of Sections

Number of Sections

Percent of Sections

DGAB

102

4

0

0.0

83

98.8

1

1.2

84

152

6

4

7.3

50

90.9

1

1.8

55

203

8

0

0.0

39

97.5

1

2.5

40

305

12

2

5.0

38

95.0

0

0.0

40

DGATB

102

4

0

0.0

27

100.0

0

0.0

27

203

8

2

4.8

39

92.9

1

2.4

42

305

12

1

3.6

26

92.9

1

3.6

28

LC

152

6

0

0.0

46

95.8

2

4.2

48

PATB

102

4

0

0.0

127

98.4

2

1.6

129

PCC

76

3

0

0.0

10

83.3

2

16.7

12

127

5

0

0.0

10

83.3

2

16.7

12

203

8

1

1.3

73

96.1

2

2.6

76

279

11

0

0.0

75

97.4

2

2.6

77

SB

51

2

0

0.0

41

89.1

5

10.9

46

102

4

18

14.4

104

83.2

3

2.4

125

127

5

4

8.7

39

84.8

3

6.5

46

178

7

17

17.9

76

80.0

2

2.1

95

203

8

1

14.3

5

71.4

1

14.3

7

Total

   

50

5.1

908

91.8

31

3.1

989

The results of the one-sided t-tests for the elevation measurements are shown in figures 67, 68, and 69 for the three different tolerance levels.

The following observations are drawn based on the results of the one-sided t-test for the elevation measurements:

Follow this link for a full description

Figure 67: Chart. Results of one-sided t-tests for the differences between mean elevation and design thicknesses for a tolerance level of 6.35 mm (0.25 in).

Follow this link for a full description

Figure 68: Chart. Results of one-sided t-tests for the differences between mean elevation and design thicknesses for a tolerance level of 12.7 mm (0.5 in).

Follow this link for a full description

Figure 69: Chart. Results of one-sided t-tests for the differences between mean elevation and design thicknesses for a tolerance level of 25.4 mm (1 in).

Statistical Analysis of the Core Thickness Data

Analysis of the Percentage Distribution

The percentage distribution of core data as a function of different tolerance levels is presented in table 57.

Table 57. Summary of the percentage distribution of the individual core thickness measurements versus the design thickness.

Measured Layer Thickness t

Difference Between As-Constructed and As-Designed

Diff = 6.35 mm (0.25 in)

Diff = 12.7 mm (0.5 in)

Diff = 25.4 mm (1.0 in)

Number of Measurements

Percent of Measurements

Number of Measurements

Percent of Measurements

Number of Measurements

Percent of Measurements

t <
TV1 - Diff

617

19.04

368

11.35

179

5.52

t within
TV ± Diff

1117

34.46

2026

62.51

2720

83.92

t >
TV + Diff

1507

46.50

847

26.13

342

10.55

Total

3241

100

3241

100

3241

100

Notes: 1Target value

The distributions of measurements by layer type for tolerance levels of 6.35 mm (0.25 in), 12.7 mm (0.5 in), and 25.4 mm (1 in) are presented in tables 58, 59, and 60 for different layer types and target thickness values.

Table 58. Percentage distribution of core thickness measurements by layer type and design thickness for a tolerance level of 6.35 mm (0.25 in).

Layer Type

Target Thickness

Thickness

<TV-6.35 mm (0.25 in)

Thickness Within

TV ± 6.35 mm (0.25 in)

Thickness

>TV+6.35 mm (0.25 in)

Total

Number of Cores

mm

in

Number of Cores

Percent of Cores

Number of Cores

Percent of Cores

Number of Cores

Percent of Cores

DGATB

102

4

23

25.0

46

50.0

23

25.0

92

203

8

42

29.6

46

32.4

54

38.0

142

305

12

36

40.4

20

22.5

33

37.1

89

LC

152

6

24

13.2

50

27.5

108

59.3

182

PATB

102

4

86

60.6

39

27.5

17

12.0

142

PCC

76

3

   

5

6.8

68

93.2

73

127

5

11

6.8

26

16.1

124

77.0

161

203

8

48

10.2

159

33.8

263

56.0

470

279

11

67

15.2

182

41.4

191

43.4

440

SB

51

2

10

6.0

63

38.0

93

56.0

166

102

4

63

11.8

213

39.9

258

48.3

534

127

5

64

22.1

85

29.4

140

48.4

289

178

7

134

30.5

180

41.0

125

28.5

439

203

8

9

40.9

3

13.6

10

45.5

22

Total

   

617

19.0

1117

34.5

1507

46.5

3241



Table 59. Percentage distribution of core thickness measurements by layer type and design thickness for a tolerance level of 12.7 mm (0.5 in).

Layer Type

Target Thickness

Thickness <TV-12.7 mm (0.5 in)

Thickness Within TV ± 12.7 mm (0.5 in)

Thickness >TV+12.7 mm (0.5 in)

Total Number of Cores

mm

in

Number of Cores

Percent of Cores

Number of Cores

Percent of Cores

Number of Cores

Percent of Cores

DGATB

102

4

8

8.7

76

82.6

8

8.7

92

203

8

22

15.5

90

63.4

30

21.1

142

305

12

28

31.5

40

44.9

21

23.6

89

LC

152

6

15

8.2

105

57.7

62

34.1

182

PATB

102

4

69

48.6

63

44.4

10

7.0

142

PCC

76

3

0

0.0

25

34.2

48

65.8

73

127

5

8

5.0

66

41.0

87

54.0

161

203

8

24

5.1

300

63.8

146

31.1

470

279

11

38

8.6

315

71.6

87

19.8

440

SB

51

2

4

2.4

96

57.8

66

39.8

166

102

4

29

5.4

387

72.5

118

22.1

534

127

5

22

7.6

166

57.4

101

34.9

289

178

7

93

21.2

290

66.1

56

12.8

439

203

8

8

36.4

7

31.8

7

31.8

22

Total

   

368

11.4

2026

62.5

847

26.1

3241



Table 60. Percentage distribution of core thickness measurements by layer type and design thickness for a tolerance level of 25.4 mm (1 in).

Layer Type

Target Thickness

Thickness
TV-25.4 mm (1 in)

Thickness Within
TV ± 25.4 mm (1 in)

Thickness
>TV+25.4 mm (1 in)

Total
Number of Cores

mm

in

Number of Cores

Percent of Cores

Number of Cores

Percent of Cores

Number of Cores

Percent of Cores

DGATB

102

4

2

2.2

90

97.8

0

0.0

92

203

8

10

7.0

123

86.6

9

6.3

142

305

12

15

16.9

70

78.7

4

4.5

89

LC

152

6

2

1.1

171

94.0

9

4.9

182

PATB

102

4

45

31.7

90

63.4

7

4.9

142

PCC

76

3

0

0.0

51

69.9

22

30.1

73

127

5

0

0.0

123

76.4

38

23.6

161

203

8

10

2.1

419

89.1

41

8.7

470

279

11

32

7.3

387

88.0

21

4.8

440

SB

51

2

0

0.0

123

74.1

43

25.9

166

102

4

13

2.4

476

89.1

45

8.4

534

127

5

7

2.4

205

70.9

77

26.6

289

178

7

37

8.4

379

86.3

23

5.2

439

203

8

6

27.3

13

59.1

3

13.6

22

Total

   

179

5.5

2720

83.9

342

10.6

3241


The graphical presentation of the percentage distributions of core thickness measurements is shown in figures 70, 71, and 72 for the three different tolerance levels.

The following are observed based on the percentage distributions of the individual core thickness measurements:


Follow this link for a full description

Figure 70: Chart. Percentage distribution of core measurements by layer type and design thickness for a tolerance level of 6.35 mm (0.25 in).

Follow this link for a full description

Figure 71: Chart. Percentage distribution of core measurements by layer type and design thickness for a tolerance level of 12.7 mm (0.5 in).

Follow this link for a full description

Figure 72: Chart. Percentage distribution of core measurements by layer type and design thickness for a tolerance level of 25.4 mm (1 in).

Statistical Analysis of the Core Data

Two-sided t-test

The results of the two-sided t-tests with 95 percent confidence are presented in table 61. The distribution of differences by different surface type and target thickness is presented in table 62.

Table 61. Summary of the results of the two-sided t-test (95 percent confidence level) using core thickness data.

Difference

Number of Layers

Percentage of Layers

Significantly lower than the target value

90

15.38

No significant difference from the target value

268

45.81

Significantly higher than the target value

227

38.80

Total

585

100



Table 62. Distribution of differences by layer type and design thickness (two-sided t-test, 95 percent confidence level) using core thickness data.

Layer Type

Target Thickness

Significantly Lower than the Target Value

No Significant Difference

Significantly Higher than the Target Value

Total

Number of Sections

mm

in

Number of Sections

Percent of Sections

Number of Sections

Percent of Sections

Number of Sections

Percent of Sections

DGATB

102

4

3

15.8

15

78.9

1

5.3

19

203

8

5

16.1

16

51.6

10

32.3

31

305

12

3

15.8

11

57.9

5

26.3

19

LC

152

6

2

5.7

13

37.1

20

57.1

35

PATB

102

4

13

41.9

15

48.4

3

9.7

31

PCC

76

3

0

0.0

2

20.0

8

80.0

10

127

5

1

8.3

2

16.7

9

75.0

12

203

8

6

8.5

21

29.6

44

62.0

71

279

11

12

17.1

32

45.7

26

37.1

70

SB

51

2

3

7.7

18

46.2

18

46.2

39

102

4

13

11.8

49

44.5

48

43.6

110

127

5

11

23.9

15

32.6

20

43.5

46

178

7

17

19.8

54

62.8

15

17.4

86

203

8

1

16.7

5

83.3

0

0.0

6

Total

   

90

15.4

268

45.8

227

38.8

585

The following are observed based on the results of the two-sided t-test for the core thickness measurements:

One-sided t-test

Three one-sided t-tests (95 percent confidence level) were performed to check whether the difference between as-constructed and as-designed thickness is lower than 6.35 mm (0.25 in), 12.7 mm (0.5 in), and 25.4 mm (1 in), respectively. The results of the overall analysis of all data points for all layers are summarized in table 63.

The results of the analysis by layer type for different tolerance levels are presented in tables 64 through 66.

Table 63. Summary of the results of the one-sided t-tests using core thickness data.

Level of Significance

Difference Between As-Constructed and As-Designed Thickness

6.35 mm (0.25 in)

12.7 mm (0.5 in)

25.4 mm (1.0 in)

Number of Layers

Percent of Layers

Number of Layers

Percent of Layers

Number of Layers

Percent of Layers

Significantly lower than the target value

58

9.91

34

5.81

22

3.76

No significant difference from the target value

378

64.62

473

80.85

533

91.11

Significantly higher than the target value

149

25.47

78

13.33

30

5.13

Total

585

100

585

100

585

100



Table 64. Results of the one-sided t-test (95 percent confidence level) by layer type and design thickness for tolerance level of 6.35 mm (0.25 in) using core thickness data.

Layer Type

Target Thickness

Mean Thickness <TV-6.35 mm (0.25 in)

Mean Thickness Within TV ± 6.35 mm (0.25 in)

Mean Thickness >TV+6.35 mm (0.25 in)

Total Number of Sections

mm

in

Number of Sections

Percent of Sections

Number of Sections

Percent of Sections

Number of Sections

Percent of Sections

DGATB

102

4

1

5.3

17

89.5

1

5.3

19

203

8

4

12.9

20

64.5

7

22.6

31

305

12

3

15.8

12

63.2

4

21.1

19

LC

152

6

2

5.7

22

62.9

11

31.4

35

PATB

102

4

13

41.9

16

51.6

2

6.5

31

PCC

76

3

0

0.0

2

20.0

8

80.0

10

127

5

0

0.0

5

41.7

7

58.3

12

203

8

2

2.8

40

56.3

29

40.8

71

279

11

6

8.6

50

71.4

14

20.0

70

SB

51

2

1

2.6

20

51.3

18

46.2

39

102

4

7

6.4

75

68.2

28

25.5

110

127

5

5

10.9

27

58.7

14

30.4

46

178

7

12

14.0

68

79.1

6

7.0

86

203

8

2

33.3

4

66.7

0

0.0

6

Total

   

58

9.9

378

64.6

149

25.5

585



Table 65. Results of the one-sided t-test (95 percent confidence level) by layer type and design thickness for tolerance level of 12.7 mm (0.5 in) using core examination data.

Layer Type

Target Thickness

Mean Thickness <TV-12.7 mm (0.5 in)

Mean Thickness Within TV ± 12.7 mm (0.5 in)

Mean Thickness >TV+12.7 mm (0.5 in)

Total Number of Sections

mm

in

Number of Sections

Percent of Sections

Number of Sections

Percent of Sections

Number of Sections

Percent of Sections

DGATB

102

4

0

0.0

18

94.7

1

5.3

19

203

8

0

0.0

27

87.1

4

12.9

31

305

12

2

10.5

14

73.7

3

15.8

19

LC

152

6

0

0.0

27

77.1

8

22.9

35

PATB

102

4

10

32.3

20

64.5

1

3.2

31

PCC

76

3

0

0.0

4

40.0

6

60.0

10

127

5

0

0.0

6

50.0

6

50.0

12

203

8

1

1.4

58

81.7

12

16.9

71

279

11

6

8.6

59

84.3

5

7.1

70

SB

51

2

0

0.0

29

74.4

10

25.6

39

102

4

5

4.5

97

88.2

8

7.3

110

127

5

1

2.2

33

71.7

12

26.1

46

178

7

7

8.1

77

89.5

2

2.3

86

203

8

2

33.3

4

66.7

0

0.0

6

Total

   

34

5.8

473

80.9

78

13.3

585



Table 66. Results of the one-sided t-test (95 percent confidence level) by layer type and design thickness for tolerance level of 25.4 mm (1 in) using core examination data.

Layer Type

Target Thickness

Mean Thickness <TV-25.4 mm (1 in)

Mean Thickness Within TV ± 25.4 mm (1 in)

Mean Thickness >TV+25.4 mm (1 in)

Total Number of Sections

mm

in

Number of Sections

Percent of Sections

Number of Sections

Percent of Sections

Number of Sections

Percent of Sections

DGATB

102

4

0

0.0

19

100.0

0

0.0

19

203

8

0

0.0

31

100.0

0

0.0

31

305

12

1

5.3

18

94.7

0

0.0

19

LC

152

6

0

0.0

34

97.1

1

2.9

35

PATB

102

4

7

22.6

23

74.2

1

3.2

31

PCC

76

3

0

0.0

8

80.0

2

20.0

10

127

5

0

0.0

10

83.3

2

16.7

12

203

8

0

0.0

68

95.8

3

4.2

71

279

11

6

8.6

64

91.4

0

0.0

70

SB

51

2

0

0.0

32

82.1

7

17.9

39

102

4

3

2.7

103

93.6

4

3.6

110

127

5

0

0.0

37

80.4

9

19.6

46

178

7

4

4.7

81

94.2

1

1.2

86

203

8

1

16.7

5

83.3

0

0.0

6

Total

   

22

3.8

533

91.1

30

5.1

585

The graphical presentations of one sided t-test results of core thickness measurements are shown in figures 73, 74, and 75 for the three different tolerance levels.

The following conclusions may be drawn based on results of the t-test for the core thickness measurements:


Follow this link for a full description

Figure 73: Chart. Results of one-sided t-tests for the differences between core measurements and design thicknesses for tolerance level of 6.35 mm (0.25 in).


Follow this link for a full description

Figure 74: Chart. Results of one-sided t-tests for the differences between mean core and design thicknesses by layer type and design thickness for tolerance level of 12.7 mm (0.5 in).


Follow this link for a full description

Figure 75: Chart. Results of one-sided t-tests for the differences between mean core and design thickness by layer type and design thickness for tolerance level of 25.4 mm (1 in).

Summary

In this chapter, the as-constructed core and elevation grid layer thickness measurements were compared to the design thicknesses for newly constructed SPS layers.

The mean thickness difference between as-designed and as-constructed thicknesses was computed for each layer using both core and elevation thickness measurements and typical thickness deviations from the target thicknesses are summarized, as well as their distribution types.

For both data sources, two types of comparisons are made in relation to their as-designed thicknesses or target values. First, both data sources were evaluated for the percentage of individual measurements either within or outside specific values from the target thickness. Second, a statistical analysis was performed to compare the measured mean thickness values with the designed values. Two types of the thickness comparisons are performed for both data sources. The two-sided t-test with 95 percent confidence level was used for each section and layer to determine whether differences between as-designed and as-constructed thicknesses are significant. One-sided t-tests with 95 percent confidence level were used for each layer to determine if the difference between as-designed thickness and the mean as-constructed thickness had significant allowances of more than 6.35 mm (0.25 in), 12.7 mm (0.5 in), and 25.4 mm (1 in), respectively.

Based on the analysis of both data sources, the following conclusions can be made:

A comparison between analysis results from the elevation and core thickness measurements shows that the percentage of measurements within the selected limits is approximately the same for all three tolerance levels. However, the percentage of measurements lower than the target value is consistently higher for core measurements than for elevation grid measurements.

Based on elevation measurements, it is observed that more than 70 percent of sections with DGAB have as-constructed thickness within ±6.35 mm (0.25 in) from the design value.

Previous | Table of Contents | Next


The Federal Highway Administration (FHWA) is a part of the U.S. Department of Transportation and is headquartered in Washington, D.C., with field offices across the United States. is a major agency of the U.S. Department of Transportation (DOT).
The Federal Highway Administration (FHWA) is a part of the U.S. Department of Transportation and is headquartered in Washington, D.C., with field offices across the United States. is a major agency of the U.S. Department of Transportation (DOT). Provide leadership and technology for the delivery of long life pavements that meet our customers needs and are safe, cost effective, and can be effectively maintained. Federal Highway Administration's (FHWA) R&T Web site portal, which provides access to or information about the Agency’s R&T program, projects, partnerships, publications, and results.
FHWA
United States Department of Transportation - Federal Highway Administration