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Publication Number: FHWA-RD-98-156
Date: FEBRUARY 1999

Volume 2, Chapter 4

Introduction

A second method used to demonstrate the Level 1 PRS prototype specification involved developing general pay factor charts for typical designs within a chosen SHA. As a follow-up to the original shadow field trial, the research team developed Level 1 pay factor charts representative of three typical pavement designs used in Iowa. The objectives of this exercise were twofold:

  1. To demonstrate how the Level 1 prototype approach can be used by a SHA to develop pay factor charts for commonly used designs—each chart being specific to a particular road classification and climatic region.
  1. To illustrate an example of the trends that may occur between different pay factor charts developed for different pavement classes.

This chapter explains the details of selecting the different pavement designs, the development of the respective pay factor charts, an analysis of the observed trends within and between the developed charts, and the conclusions and recommendations resulting from this exercise.

Defining Three Different Pavement Designs

The first step was the selection of three typical PCC pavement designs used in Iowa. Each pavement design was selected to be specific to an assumed traffic level representing medium, heavy, or very heavy traffic. All three pavement designs were assumed to have a 40-year design life. The chosen cumulative ESAL values (over the 40-year design lives) for each of the chosen traffic classifications consisted of the following:

Definition of Pavement Performance

For the development of these pay factor charts, pavement performance was defined in terms of all of the four available distress indicators (i.e., transverse slab cracking, transverse joint faulting, transverse joint spalling, and pavement smoothness over time).

Selection of Acceptance Quality Characteristics

For the three chosen typical designs, Level 1 pay factor charts were developed for each of the following four AQC’s:

Selection of Representative Constant Values

The representative constant values required to simulate the corresponding pay factor charts (for the three chosen designs) were determined based on information provided by Iowa SHA personnel. Values for the climatic-related variables and unit costs were assumed to be the same as those used at the original PRS field trial conducted in Wapello County, Iowa, in 1996 (see chapter 2 of this volume). More information on the selection of constant variables is presented in chapter 5 of volume I, in the section titled Identification of Constant Variable Values. The specific values chosen to represent each of the three typical designs are presented in table 71. (Note: The constant inputs presented in table 71 are those required by the old distress prediction models used in the prototype PaveSpec software.(1-3) These variables differ slightly from those constant values required by the new distress indicator models included in the revised PaveSpec 2.0 software [as shown in figure 1 of volume I].)

Table 71. Chosen constant variable values for the required PRS inputs for three typical pavement designs in Iowa.

Variable

Design 1 (Medium Traffic)

Design 2 (Heavy Traffic)

Design 3 (Very Heavy Traffic)

Project Information
Pavement Type

Doweled, JPCP

Road Location

Rural Setting

Highway Type

Undivided

Divided

Divided

Design Life

40 years

No. of Lanes in One Direction

1

2

2

Lane Width

3.7 m

Joint Spacing

6.1 m

Traffic Information
Total Design Traffic

2.5 MESAL’s

7.5 MESAL’s

30.0 MESAL’s

Initial Year Traffic

62,500 ESAL’s

187,500 ESAL’s

750,000 ESAL’s

Traffic Growth Type

Simple Linear Trend

Materials and Climatic Information
Annual Temperature Range

22 ºC

Freezing Index

750 degree-days

Average Annual Precipitation

81.3 cm

Projected Annual Freeze-Thaw Cycles (at 7.6 cm below the pavement surface)

12

Salt Present

Yes

Joint Sealant Type

Liquid Asphalt

Slab Support Information
Base Type

Granular

Modulus of Subgrade Reaction

40.7 MPa/m

Subgrade Soil Type

Fine-grained (AASHTO A4-A7)

Presence of Longitudinal Subdrains

Yes

Load Transfer Information
Dowel Bar Diameter

3.2 cm

3.8 cm

3.8 cm

Presence of Tied PCC Shoulder

Yes

Cost Information
Construction Bid, Traffic Lanes (based on $86.32/m3)

$17.89/m2

$20.08/m2

$23.32/m2

Cost of Asphalt Overlay

$10.76/m2

Cost of Patching a Joint

$95.68/m2

Cost of Replacing a Slab

$83.72/m2

Assumed Asphalt Overlay Life

20 years

Selection of AQC Target Values

Four different AQC’s were chosen to demonstrate the Level 1 PRS approach for each of the three typical designs. These included 28-day flexural strength (third-point loading), slab thickness, plastic entrained air content (using a pressure meter), and initial smoothness (measured using a 5.1-mm blanking band). The AQC target means and standard deviations for each of the three designs were estimated by interpreting the current Iowa construction specifications. These values were determined using the same procedures utilized in determining the target values at the original Iowa field trial in 1996 (see the section titled Definition of the Required As-Designed AQC Target Values in chapter 2 of this volume). The chosen AQC as-designed target means and standard deviations are presented in table 72 (the actual specification design thickness means are shown as a comparative reference).

Table 72. Chosen AQC as-designed target values for three typical pavement designs in Iowa.

AQC

Design 1 (Medium Traffic)

Design 2 (Heavy Traffic)

Design 3 (Very Heavy Traffic)

28-day Flexural Strength (third-point loading)
PRS Target Mean

4.48 MPa

PRS Target Std Dev

0.45 MPa

Slab Thickness
Specification Design Mean

203 mm

229 mm

267 mm

PRS Target Mean

207 mm

233 mm

271 mm

PRS Target Std Dev

6 mm

Entrained Air Content
PRS Target Mean

7.0%

PRS Target Std Dev

0.5%

Initial Smoothness (5.1-mm blanking band)
PRS Target Mean

79 m/km

PRS Target Std Dev

16 mm/km

Selection of Simulation Parameters

A number of simulation-related parameters are required to simulate LCC’s representing the as-designed and as-constructed pavement lots. The individual Level 1 AQC pay factor charts were simulated using the following simulation parameters:

These simulation parameters are used in conjunction with the defined constant variable values and selected AQC target values to generate the preconstruction output.

Simulation of AQC Pay Factor Charts and Corresponding Pay Factor Equations

The final step in the specification development process involves the development of the preconstruction output. For the Level 1 specification, this involves constructing individual pay factor charts (and corresponding pay factor equations) for the four AQC’s. Individual AQC pay factors may be computed using these equations by knowing the as-constructed AQC lot means and standard deviations. (Note: Each pay factor chart is specific to the chosen constant values, target means, and standard deviations.)

Step-by-Step Procedure Used to Develop Individual Level 1 AQC Pay Factor Curves

The following step-by-step procedure was used to develop Level 1 pay factor charts and corresponding pay factor equations for the three typical Iowa designs. (Note: Each of these steps is accomplished using the PaveSpec PRS demonstration software.)

  1. Define the number of sublots per lot. As mentioned previously, four sublots
  1. Define the number of samples per sublot. A sampling frequency of four samples per sublot was used for each of the four AQC’s. In a Level 1 PRS, we assume that all of the material in a lot is represented by the same statistical population. Based on this assumption, the total sample size N may be represented by the number of sublots, n, times the number of samples per sublot. Therefore, the total sample size N was 16 for the case of 4 sublots.
  1. Define the Level 1 AQC target means and standard deviations. The Level 1 target as-designed AQC means and standard deviations for the three typical designs were defined in table 72.
  1. Choose a range of as-constructed means for each AQC. Reasonable ranges of AQC means are selected that will define the values used in the PaveSpec simulations. These chosen ranges of AQC simulation means (based on the chosen AQC target values for each of the three designs) are presented in table 73.

    Table 73. As-constructed AQC simulation mean ranges for the three typical

    AQC

    Design 1 (Medium Traffic)

    Design 2 (Heavy Traffic)

    Design 3 (Very Heavy Traffic)

    28-day Flexural Strength (third-point loading), MPa

    3.78 – 5.18

    Slab Thickness, mm

    187 – 227

    213 – 253

    251 – 291

    Entrained Air Content, %

    0.0 – 7.0

    Initial Smoothness (5.1-mm blanking band), mm/km

    0 – 240

  1. Choose specific as-constructed AQC standard deviation levels for the simulation of pay factor curves. The pay factor curves not only depend on the as-constructed AQC mean, but the as-constructed AQC standard deviation as well. Table 74 contains the three different standard deviation levels chosen (for each AQC) representing very good, good, and poor AQC quality control. These different levels of AQC standard deviation are used in the simulation of individual AQC pay

    Table 74. As-constructed AQC standard deviation levels for simulation

    AQC

    Design 1 (Medium Traffic)

    Design 2 (Heavy Traffic)

    Design 3 (Very Heavy Traffic)

    28-day flexural strength (third-point loading), MPa

    0.00, 0.45, 0.90

    Slab thickness, mm

    0, 6, 13

    Entrained air content, %

    0.0, 0.5, 1.5

    Initial smoothness (5.1-mm blanking band), mm/km

    0, 16, 79

  1. Simulate the target as-designed LCC’s. In order to calculate pay factors for different hypothetical levels of as-constructed AQC quality, the target as-designed LCC’s had to first be simulated. The PaveSpec specification simulation software was used to estimate target as-designed LCC means (for each of the 3 chosen designs) from 100 simulation lots, for the case of 4 sublots per lot and 4 AQC samples per sublot. Each individual lot was simulated by randomly selecting AQC samples from the target value distributions summarized in table 72. The simulations were conducted using an 80-year analysis life (twice the 40-year design life) and include 5 percent of the calculated user costs. The resulting simulated Level 1 mean as-designed LCC values (for the case of four sublots) for the three respective typical designs, were

To better demonstrate the PRS method, the estimated typical distresses over time associated with each of the three Iowa designs (reflecting the chosen constant inputs and the AQC target means only) are presented in figure 14. These distresses reflect the predicted first overlay application at year 33 for Designs 1 and 2, and year 30 for design 3. The M & R plan defined for the original Iowa field trial was also used here.

Enlarge Figure 1

Figure 14. Estimated typical as-designed distresses over time associated with each of the three typical designs (reflecting the chosen constant inputs and the AQC target means only).
Enlarge Figure 1
Enlarge Figure 1
Enlarge Figure 1
  1. Simulate as-constructed LCC’s and calculate an independent AQC pay factor for each hypothetical as-constructed mean/standard deviation pair. The hypothetical as-constructed mean/as-constructed standard deviation pair values (coming from combinations of means and standard deviations defined in steps 5 and 6, respectively) were used to define individual simulation sessions in the PaveSpec software. Each AQC was investigated independently for each session (for example, if strength was being investigated, all of the other AQC as-constructed means and standard deviations were set equal to the target values). Each pair was used in PaveSpec to simulate a corresponding LCCCON. A pay factor was calculated for each pair using equation 5. The simulated pay factors (from PaveSpec) are summarized by AQC in tables 75 through 77.

Table 75. Design 1 (medium traffic)—simulated Level 1 pay factors for four sublots and four samples per sublot (lot sample size N=16).

As-Constructed Means

Simulated pay factors at different as-constructed standard deviations, %

28-day Flexural Strength (third-point loading), MPa

SD = 0.00 MPa

SD = 0.45 MPa

SD = 0.90 MPa

3.78

48.6

47.3

43.4

4.48

101.3

100.0

93.4

5.18

128.8

127.9

123.8

Slab Thickness, mm

SD = 0 mm

SD = 6 mm

SD = 13 mm

187

49.8

48.8

46.6

207

99.2

100.0

98.1

227

126.9

127.2

126.6

Entrained Air Content, %

SD = 0.0%

SD = 0.5%

SD = 1.5%

2.0

67.4

66.8

66.0

7.0

101.8

100.0

97.5

Initial Smoothness (0.0-mm blanking band), mm/km

SD = 0 mm/km

SD = 16 mm/km

SD = 79 mm/km

0

112.5

112.5

110.8

79

100.6

100.0

99.2

240

58.6

58.2

57.3


Table 76. Design 2 (heavy traffic)—simulated Level 1 pay factors for four sublots and four samples per sublot (lot sample size N=16).

As-Constructed Means

Simulated pay factors at different as-constructed standard deviations, %

28-day Flexural Strength (third-point loading), MPa

SD = 0.00 MPa

SD = 0.45 MPa

SD = 0.90 MPa

3.78

70.9

67.7

61.6

4.48

100.5

100.0

94.9

5.18

115.9

116.1

113.5

Slab Thickness, mm

SD = 0 mm

SD = 6 mm

SD = 13 mm

213

74.7

73.4

71.5

233

100.7

100.0

99.5

253

114.4

114.3

114.0

Entrained Air Content, %

SD = 0.0%

SD = 0.5%

SD = 1.5%

2.0

77.1

76.9

76.7

7.0

101.0

100.0

98.5

Initial Smoothness (0.0-mm blanking band), mm/km

SD = 0 mm/km

SD = 16 mm/km

SD = 79 mm/km

0

107.1

107.1

106.0

79

100.5

100.0

99.9

240

79.1

78.8

78.4


Table 77. Design 3 (Very Heavy Traffic)—simulated Level 1 pay factors for four sublots and four samples per sublot (lot sample size N=16).

As-Constructed Means

Simulated pay factors at different as-constructed standard deviations, %

28-day Flexural Strength (third-point loading), MPa

SD = 0.00 MPa

SD = 0.45 MPa

SD = 0.90 MPa

3.78

74.1

72.3

67.7

4.48

101.7

100.0

93.6

5.18

119.0

118.1

114.0

Slab Thickness, mm

SD = 0 mm

SD = 6 mm

SD = 13 mm

251

79.1

78.7

76.7

271

100.7

100.0

99.2

291

116.4

116.0

115.8

Entrained Air Content, %

SD = 0.0%

SD = 0.5%

SD = 1.5%

2.0

85.4

84.6

83.8

7.0

100.6

100.0

99.1

Initial Smoothness (0.0-mm blanking band), mm/km

SD = 0 mm/km

SD = 16 mm/km

SD = 79 mm/km

0

106.6

105.2

103.4

79

100.4

100.0

99.3

240

84.9

84.6

84.2

  1. Plot charts of pay factor vs. AQC mean. The simulated pay factors determined in step 7 can easily be graphed as a function of the AQC mean. Each AQC pay factor chart contains three different curves corresponding to the three different standard deviation levels chosen in step 5. Best-fit regression equations were fit through each individual pay factor curve representing one chosen as-constructed AQC standard deviation. Figures 15 through 17 contain AQC pay factor charts representing the three typical Iowa pavement designs. The best-fit pay factor regression equations (at different as-constructed AQC standard deviations) for the three chosen typical designs are summarized in tables 78 through 80. (Note: All of these charts and pay factor equations are specific to the assumed simulation parameters of four sublots per lot and four AQC samples per sublot.)
Enlarge Figure 1 Figure 15. Design 1 (medium traffic)—simulated Level 1 individual AQC pay factor charts for the case of four sublots per lot and four samples per sublot (lot sample size N=16).

Enlarge Figure 1 Figure 16. Design 2 (heavy traffic)—simulated Level 1 individual AQC pay factor charts for the case of four sublots per lot and four samples per sublot (lot sample size N=16).

Enlarge Figure 1 Figure 17. Design 3 (very heavy traffic)—simulated Level 1 individual AQC pay factor charts for the case of four sublots per lot and four samples per sublot (lot sample size N=16).

Table 78. Design 1 (medium traffic)—Level 1 AQC best-fit regression equations for the case of four sublots per lot and four samples per sublot (lot sample size N=16).

AQC

As-Constructed Standard Deviation

Pay Factor Regression Equation, x = mean value
28-day Flexural Strength (third-point loading)

0.00 MPa

PFS-(x, 0.00) = –25.7189x2 + 287.7179x – 671.4876

0.45 MPa

PFS-(x, 0.45) = –25.3191x2 + 284.4695x – 666.2597

0.90 MPa

PFS-(x, 0.90) = –19.9880x2 + 236.5143x – 565.0175
Slab Thickness

0 mm

PFT-(x, 0) = –2.7195E-02x2 + 13.1846x – 1464.7132

6 mm

PFT-(x, 6) = –2.8791E-02x2 + 13.8807x – 1540.1355

13 mm

PFT-(x, 13) = –2.8768E-02x2 + 13.9090x – 1548.3911
Plastic Entrained Air-Content (for 0 to 7% only)

0.0%

PFA-(x, 0.0) = 6.8683x + 53.6719

0.5%

PFA-(x, 0.5) = 6.64x + 53.52

1.5%

PFA-(x, 1.5) = 6.315x + 53.335
Initial Smoothness

0 mm/km

PFSM-(x, 0) = –4.6066E-04x2 – 0.1139x + 112.45

16 mm/km

PFSM-(x, 16) = –4.2248E-04x2 – 0.1246x + 112.48

79 mm/km

PFSM-(x, 79) = –4.7001E-04x2 – 0.1100x + 110.8

Table 79. Design 2 (heavy traffic)—Level 1 AQC best-fit regression equations for the case of four sublots per lot and four samples per sublot (lot sample size N=16).

AQC

As-Constructed Standard Deviation

Pay Factor Regression Equation, x = mean value
28-day Flexural Strength (third-point loading)

0.00 MPa

PFS-(x, 0.00) = –14.5726x2 + 162.7450x – 336.0902

0.45 MPa

PFS-(x, 0.45) = –16.5210x2 + 182.6422x – 386.6551

0.90 MPa

PFS-(x, 0.90) = –15.0809x2 + 172.2030x – 373.8903
Slab Thickness

0 mm

PFT-(x, 0) = –1.5438E-02x2 + 8.1861x – 968.5134

6 mm

PFT-(x, 6) = –1.6236E-02x2 + 8.5896x – 1019.5902

13 mm

PFT-(x, 13) = –1.6794E-02x2 + 8.8875x – 1059.5914
Plastic Entrained Air-Content (for 0 to 7% only)

0.0%

PFA-(x, 0.0) = 4.7850x + 67.5050

0.5%

PFA-(x, 0.5) = 4.6183x + 67.6719

1.5%

PFA-(x, 1.5) = 4.3700x + 67.9200
Initial Smoothness

0 mm/km

PFSM-(x, 0) = –2.0616E-04x2 – 0.0673x + 107.10

16 mm/km

PFSM-(x, 16) = –1.7625E-04x2 – 0.0753x + 107.05

79 mm/km

PFSM-(x, 79) = –2.3768E-04x2 – 0.0579x + 105.95

Table 80. Design 3 (very heavy traffic)—Level 1 AQC best-fit regression equations for the case of four sublots per lot and four samples per sublot (lot sample size N=16).

AQC

As-Constructed Standard Deviation

Pay Factor Regression Equation, x = mean value
28-day Flexural Strength (third-point loading)

0.00 MPa

PFS-(x, 0.00) = –10.5255x2 + 126.3893x – 253.3085

0.45 MPa

PFS-(x, 0.45) = –9.8374x2 + 120.8210x – 243.8380

0.90 MPa

PFS-(x, 0.90) = –5.4613x2 + 82.0068x – 164.2257
Slab Thickness

0 mm

PFT-(x, 0) = –7.4090E-03x2 + 4.9484x – 696.1730

6 mm

PFT-(x, 6) = –7.2153E-03x2 + 4.8425x – 682.2020

13 mm

PFT-(x, 13) = –7.5020E-03x2 + 5.0440x – 716.7401
Plastic Entrained Air-Content (for 0 to 7% only)

0.0%

PFA-(x, 0.0) = 3.0383x + 79.3319

0.5%

PFA-(x, 0.5) = 3.0733x + 78.4869

1.5%

PFA-(x, 1.5) = 3.0583x + 77.7019
Initial Smoothness

0 mm/km

PFSM-(x, 0) = –7.3172E-05x2 – 0.0727x + 106.60

16 mm/km

PFSM-(x, 16) = –1.2338E-04x2 – 0.0561x + 105.20

79 mm/km

PFSM-(x, 79) = –1.7278E-04x2 – 0.0384x + 103.40


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.
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