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Publication Number: FHWA-HRT-12-031
Date: August 2012

 

User’s Guide: Estimation of Key PCC, Base, Subbase, and Pavement Engineering Properties From Routine Tests and Physical Characteristics

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CHAPTER 4. RIGID PAVEMENT DESIGN FEATURES MODELS

The models developed for the prediction of MEPDG-specific inputs fall under the design features category. In developing these models, the dependent variable (e.g., deltaT for JPCP design) was determined through performing several trial and error runs of the MEPDG and establishing the optimum value that minimizes the error prediction. The independent variables were obtained from the LTPP database or MEPDG calibration files.

The MEPDG design files used to generate the dependent variable data were obtained from the model calibration performed under NCHRP 1-40D, which produced the MEPDG software program version 1.0 in 2007.(4) However, minor changes and software bug fixes have been performed since then, and the official version available at the time of this study was the MEPDG software version 1.1. Therefore, these models presented under this section are valid only for use with the distress calibration model of version 1.1 of the MEPDG software. The prediction models presented here for the estimation of design feature inputs therefore may not be valid once the products of future MEPDG updates and revisions are released.

deltaT—JPCP Design

The equation developed to estimate the deltaT gradient variable can be expressed as follows:

deltaT divided by inch equals -5.27805 minus 0.00794 times TR minus 0.0826 times SW plus 0.18632 times PCCTHK plus 0.01677 times uw plus 1.14008 times w/c plus 0.01784 times latitude.

Figure 79. Equation. Prediction model 15 for deltaT/inch.

Where:

deltaT/inch = Predicted average gradient through JPCP slab, °F/inch.
TR = Difference between maximum and minimum temperature for the month of construction, °F.
SW = Slab width, ft.
PCCTHK = JPCP slab thickness, inch.
uw = Unit weight of PCC used in JPCP slab, lb/ft3.
w/c = Water to cement ratio.
latitude = Latitude of the project location, degrees.

The model considers climate (TR, latitude), design (SW, PCCTHK), and material (uw, w/c) parameters. The model statistics are presented in table 28. The model was developed with 147 data points, has an R2 value of 49.67 percent, and an RMSE of 0.3199 psi. Table 29 provides details of the range of data used to develop the model.


 

Table 28. Regression statistics for JPCP deltaT model.

Variable

DF

Estimate

Standard Error

t-value

Pr > |t|

VIF

Intercept

1

-5.27805

 

1.06943

 

-4.94

 

< 0.0001

 

0

 

TR

1

-0.00794

 

0.00396

 

-2

 

0.047

 

1.86047

 

SW

1

-0.0826

 

0.03432

 

-2.41

 

0.0174

 

1.07141

 

PCCTHK

1

0.18632

 

0.0195

 

9.55

 

< 0.0001

 

1.0642

 

uw

1

0.01677

 

0.00669

 

2.51

 

0.0133

 

1.22792

 

w/c

1

1.14008

 

0.2914

 

3.91

 

0.0001

 

1.14857

 

latitude

1

0.01784

 

0.0072

 

2.48

 

0.0144

 

1.85265

 

 

Table 29. Range of data used for JPCP deltaT model.

Parameter

Minimum

Maximum

Average

Temperature range

21.2

64.5

47.4

Slab width

12.0

14.0

12.5

PCC thickness

6.4

14.3

9.6

Unit weight

134

156

147

w/c ratio

0.27

0.72

0.46

Latitude

27.93

49.60

39.58

 

Figure 80 shows the predicted versus measured for the proposed JPCP deltaT gradient model, while figure 81 shows the residual errors. Note that the measured data here refers to the deltaT gradient determined by matching MEPDG prediction to field performance. Figure 82 shows the predicted versus measured deltaT for the model.

This graph 
is an x-y scatter plot showing the predicted versus the measured values used in the jointed plain concrete pavement (JPCP) deltaT gradient model. The x-axis shows the deltaT gradient estimated by matching the Mechanistic-Empirical Pavement Design Guide and field performance from -2.5 to 0 ºF/inch, and the y-axis shows the predicted deltaT gradient from 
-2.5 to 0 ºF/inch. The plot contains 147 points, which correspond to the data points used in the model. The graph also shows a 45-degree line that represents the line of equality. The data are shown as solid diamonds, and they appear to demonstrate a good prediction. The measured values range from -2.343 to -0.175 °F/inch. The graph also shows the model statistics as follows: N equals 147, R-squared equals 49.67 percent, and root mean square error equals 0.31992 psi.

Figure 80. Graph. Predicted versus measured for JPCP deltaT gradient model.

This graph is an x-y scatter plot showing the residual errors in the predictions of the jointed plain concrete pavement (JPCP) deltaT gradient model. The x-axis shows the predicted deltaT from -2.5 to 0 ºF/inch, and the y-axis shows the error in prediction from -2.5 to 1 ºF/inch. The points are plotted as solid diamonds, and they show no significant bias (i.e., the data are well distributed about the zero-error line). This plot illustrates a fair but acceptable error. There appears to be no trend in the data, and the trend line is almost horizontal (i.e., zero slope). The following equations are provided in the graph: y equals 3E minus 0.6x plus 4E minus 0.6 and R-squared equals 8E 
minus 12.

Figure 81. Graph. Residual errors for JPCP deltaT gradient model.

This graph shows the predicted jointed plain concrete pavement (JPCP) deltaT versus the JPCP deltaT estimated by matching Mechanistic-Empirical Pavement Design Guide (MEPDG) predictions with field data. The x-axis shows the deltaT estimated by matching MEPDG and field performance from -16 to 0 ºF, and the y-axis shows the predicted deltaT from -16 to 0 ºF. The plot is essentially an x-y scatter plot, and all data are lined at x-axis values of -12.5, -10, 
-7.5, -5, -2.5, and 0 ºF. The points cover a range of values on the y-axis. A majority of the 
points are in the range of -12.5 and -7.5 ºF. The points are represented as solid diamonds.

Figure 82. Graph. Predicted versus measured deltaT based on the JPCP deltaT gradient model.

Figure 83 through figure 89 present the sensitivity analysis performed to examine the impact of varying the model parameters on its prediction. The parameters included are temperature range, slab width, slab thickness, unit weight, w/c ratio, and latitude. For each sensitivity analysis, the variable of interest was varied while holding all other variables constant at their typical values. Typical values used in this analysis were 24 °F temperature range, 12-ft slab width, 10-inch slab thickness, 145 lb/ft3 unit weight, 0.40 w/c ratio, and 40 degrees latitude.

This graph shows the sensitivity of the predicted deltaT to temperature range during the month of construction. The x-axis shows the temperature range from 0 to 80 ºF, 
and the y-axis shows the predicted deltaT in a 10-inch slab from -15 to 0 ºF. The sensitivity is shown for temperatures ranging from 20 to 65 ºF, and the data are plotted using solid diamonds connected by a solid line. The graph shows that with increasing temperature, the predicted 
deltaT decreases.

Figure 83. Graph. Sensitivity of predicted deltaT to temperature range during month of construction.

This graph shows the sensitivity of the predicted deltaT to the slab width. The x-axis shows the slab width from 11.5 
to 14.5 ft, and the y-axis shows the predicted deltaT in a 10-inch slab from -13 to -11 ºF. The sensitivity is shown for slabs ranging from 12 to 14 ft wide, and the data are plotted using solid diamonds connected by a solid line. The graph shows that with increasing slab width, the predicted deltaT decreases.

Figure 84. Graph. Sensitivity of predicted deltaT to slab width.

This graph shows the sensitivity of the predicted deltaT to the slab thickness. The x-axis shows the slab thickness from 0 to 20 inches, and the y-axis shows the predicted deltaT in a 10-inch slab from -14 to 0 ºF. The sensitivity is shown for slab thicknesses ranging from 6 to 16 inches, and the data are plotted using solid diamonds connected by a solid line. The graph shows that with increasing slab thickness, the predicted deltaT increases; however, it remains flat from 7 to 9 inches and decreases from 6 to 7 inches.

Figure 85. Graph. Sensitivity of predicted deltaT to slab thickness.

This graph shows the sensitivity of the predicted deltaT to Portland cement concrete (PCC) slab unit weight. The 
x-axis shows the PCC unit weight from 130 to 160 lb/ft3, and the y-axis plots the predicted deltaT in a 10-inch slab from -15 to 0 ºF. The sensitivity is shown for unit weights between 
135 and 155 lb/ft3, and the data are plotted using solid diamonds connected by a solid line. The graph shows that with increasing PCC unit weight, the predicted deltaT increases.

Figure 86. Graph. Sensitivity of predicted deltaT to PCC slab unit weight.

This graph shows the sensitivity of the predicted deltaT to the Portland cement concrete (PCC) water/cement (w/c) ratio. The x-axis shows the w/c ratio, and the y-axis shows the predicted deltaT in a 10-inch slab from -15 to 0 ºF. The sensitivity is shown for w/c ratios ranging from 0.25 to 0.7, and the data are plotted using solid diamonds connected by a solid line. The graph shows that with increasing PCC w/c ratio, the predicted deltaT increases.

Figure 87. Graph. Sensitivity of predicted deltaT to PCC w/c ratio.

This graph shows the sensitivity of the predicted deltaT to the latitude of the project location. The 
x-axis shows the latitude from 0 to 60 degrees, and the y-axis shows the predicted deltaT from 
-15 to 0 ºF. The sensitivity is shown for latitudes ranging from 30 to 50 degrees, and the data are plotted using solid diamonds connected by a solid line. The graph shows that with increasing latitude, the predicted deltaT increases.

Figure 88. Graph. Sensitivity of predicted deltaT to latitude of the project location.

This graph is a bar chart showing the predicted deltaT values for jointed plain concrete pavement sections in typical Long-Term Pavement Performance sites in various locations. The data are categorized by location, which, starting from the left are Florida, Washington, Arkansas, Michigan, American Association of State Highway Officials (AASHO) site, Arizona, and Minnesota. The y-axis shows the deltaT in a 10-inch slab from 0 to -14 ºF. The values plotted are also labeled on the solid bars. The values are -11.3, -9.7, -11.4, -10.2, -9.5, -11.8, and -9.6 ºF, respectively.

Figure 89. Graph. Predicted deltaT for different locations in the United States.

The following are brief observations from these sensitivity analyses:

Using the JPCP deltaT Model

This section provides an example for the use of the JPCP deltaT model developed under this study. The section used to describe the process is the LTPP Specific Pavement Studies 2 section 04_0213 located in Maricopa County, AZ, and constructed in July 1993. The following latitude, design, and material inputs required for the deltaT prediction model can be obtained from the MEPDG inputs:

The temperature range input to this model is the difference between the mean monthly maximum and minimum temperatures for the month of July from historical climate data records (as climate data included in the MEPDG). If the user does not have this information readily available, the data to compute the temperature range can be determined from the output file of the MEPDG analysis of this section. The output file (i.e., titled “04_0213.xls”) contains a worksheet titled “Climate” with key climate data for the specific location (or the virtual climate station created). This worksheet includes the monthly climate summary with minimum and maximum temperature by month for all years of data used under the headings “Min. Temp. (°F)” and “Max. Temp. (°F),” respectively. (Note that this summary also includes “Average Temp. (°F),” “Max. Range (°F),” “Precip. (in.),” “Average Wind (mph),” “Average Sun (%),” “Number Wet Days,” and “Max. Frost (in.).” However, these data are not of relevance to the deltaT model.

For the month of July, the average minimum and maximum temperatures are 73 and 111.7 °F, respectively. The difference between these temperatures is 38.7 °F.

Using these inputs, the deltaT gradient can be calculated as -1.7457138 °F/inch. For the slab thickness of 8.3 inches, this is equivalent to a deltaT of -14.5 °F. This value is significantly higher than the default -10 °F/inch. This input can be revised in an MEPDG file and reanalyzed to evaluate the predicted transverse cracking performance.

deltaT—CRCP Design

The equation developed to estimate the CRCP deltaT gradient variable is as follows:

DeltaT divided by inch equals 12.93007 minus 0.15101 times MaxTemp minus 0.10241 times MaxTempRange plus 3.279 times Chert plus 1.55013 times Granite plus 1.40009 times Limestone plus 2.01838 times Quartzite plus 0.11299 times PCCTHK.

Figure 90. Equation. Prediction model 16 for deltaT/inch.

Where:

deltaT/inch = Predicted gradient in CRCP slab, °F/inch.
MaxTemp = Maximum temperature for the month of construction, °F.
MaxTempRange = Maximum temperature range for the month of construction, °F.
PCCTHK = JPCP slab thickness, inch.
Chert = 1 if PCC mix coarse aggregate is chert, or 0 if otherwise.
Granite = 1 if PCC mix coarse aggregate is granite, or 0 if otherwise.
Limestone = 1 if PCC mix coarse aggregate is limestone, or 0 if otherwise.
Quartzite = 1 if PCC mix coarse aggregate is quartzite, or 0 if otherwise.

The model considers climate (MaxTemp and MaxTempRange), design parameters (PCCTHK), and material (Aggregate type) parameters. The model statistics are presented in table 30. The model was developed with 35 data points, has an R2 value of 82.5 percent, and an RMSE of 0.27932 psi. Table 31 provides details of the range of data used to develop the model.

Table 30. Regression statistics for CRCP deltaT model.

Variable

DF

Estimate

Standard Error

t-Value

Pr > |t|

VIF

Intercept

1

12.93007

 

1.98459

 

6.52

 

< 0.0001

 

0

 

MaxTemp

1

-0.15101

 

0.01793

 

-8.42

 

< 0.0001

 

3.46347

 

MaxTempRange

1

-0.10241

 

0.01869

 

-5.48

 

< 0.0001

 

2.00933

 

Chert

1

3.279

 

0.30508

 

10.75

 

< 0.0001

 

2.24965

 

Granite

1

1.55013

 

0.22656

 

6.84

 

< 0.0001

 

4.96262

 

Limestone

1

1.40009

 

0.18956

 

7.39

 

< 0.0001

 

4.00053

 

Quartzite

1

2.01838

 

0.39449

 

5.12

 

< 0.0001

 

1.93773

 

PCCTHK

1

0.11299

 

0.0705

 

1.6

 

0.1207

 

1.68624

 

 


 

Table 31. Range of data used for CRCP deltaT model.

Parameter

Minimum

Maximum

Average

Maximum temperature

78.4

99.2

90.3

Temperature range

24.8

40.4

30.4

Chert

0

1

0.06

Granite

0

1

0.31

Limestone

0

1

0.46

Quartzite

0

1

0.03

PCC thickness

5.6

9.5

8.4

 

Figure 91 shows the predicted versus measured for the proposed CRCP deltaT gradient model, while figure 92 shows the residual errors. Note that the measured data here refers to the deltaT gradient determined by matching MEPDG prediction to field performance.

This graph is an 
x-y scatter plot showing the predicted versus the measured values used in the continuously reinforced concrete pavement (CRCP) deltaT model. The x-axis shows the deltaT gradient estimated by matching the Mechanistic-Empirical Pavement Design Guide and field performance from -3 to 0 ºF/inch, and the y-axis shows the predicted deltaT gradient from -3 to 0 ºF/inch. The plot contains 35 points, which correspond to the data points used in the model. The graph also shows a 45-degree line that represents the line of equality. The data are shown as solid diamonds, and they appear to demonstrate a good prediction. The measured values range from -2.67 to -0.30 °F/inch. The graph also shows the model statistics as follows: y equals 0.825x minus 0.2629 and R-squared equals 0.825.

Figure 91. Graph. Predicted versus measured for CRCP deltaT model.

This graph is an x-y scatter plot showing the residual errors in the predictions of the continuously reinforced concrete pavement (CRCP) deltaT model. The x-axis shows the deltaT gradient estimated by matching the Mechanistic-Empirical Pavement Design Guide and field performance from -2.5 to 0 ºF/inch, and the y-axis shows the predicted deltaT gradient from -2.5 to 2.5 ºF/inch. The points are plotted as solid diamonds, and they appear to show no significant bias (i.e., the data are well distributed about the zero-error line). There appears to be no trend in the data, and the trend line is almost horizontal (i.e., zero slope). The graph provides the following equations: y equals 8E minus 07x minus 8E minus 05 and R-squared equals 3E minus 12.

Figure 92. Graph. Residual errors for CRCP deltaT model.

Figure 93 through figure 96 show the sensitivity of the deltaT differential calculation to the parameters maximum temperature of the project location, maximum temperature range, CRCP slab thickness, and geographic location, respectively. The trends observed in the model—CRCP deltaT increasing with increasing maximum temperature and increasing temperature range— are reasonable. While the effect of slab thickness shows a linear relationship with the deltaT gradient, the magnitude of the coefficient for this variable results causes the deltaT differential (CRCP deltaT gradient × thickness) to assume a nonlinear relationship with the deltaT differential, peaking at about 10 inches. Figure 96 shows the deltaT predictions for projects selected from LTPP sites in Texas, Illinois, Virginia, Mississippi, Oregon, and Georgia.

This graph shows the sensitivity of the continuously reinforced concrete pavement (CRCP) deltaT prediction model to the maximum temperature. The x-axis shows the maximum temperature from 70 to 110 ºF, and the y-axis shows the predicted deltaT in a 10-inch slab from -30 to 20 ºF. The sensitivity is shown for temperature ranges from 76 to 100 ºF, and the data are plotted using solid diamonds connected by a solid line. The graph shows that with increasing temperature, the predicted deltaT decreases.

Figure 93. Graph. Effect of maximum temperature on CRCP deltaT prediction model.

This graph shows the sensitivity of the continuously reinforced concrete pavement (CRCP) deltaT prediction model to a range of temperatures. The x-axis shows the temperature range from 
20 to 50 ºF, and the y-axis shows the predicted deltaT in a 10-inch slab from -25 to 0 ºF. The sensitivity is shown for temperatures ranging from 24 to 40 ºF, and the data are plotted using solid diamonds connected by a solid line. The graph shows that with increasing temperature, 
the predicted deltaT decreases.

Figure 94. Graph. Effect of temperature range on CRCP deltaT prediction model.

This graph shows the sensitivity of the continuously reinforced concrete pavement (CRCP) deltaT prediction model to a range of slab thicknesses. The x-axis shows the slab thickness from 6 to 
14 inches, and the y-axis shows the predicted deltaT from -12.1 to -11.4 ºF. The sensitivity is shown for thicknesses ranging from 8 to 12 inches, and the data are plotted using solid diamonds connected by a solid line. The graph shows that in the range of 8 to 10 inches with increasing thickness, the predicted deltaT decreases. In the range of 10 to 12 inches with increasing thickness, the predicted deltaT increases.

Figure 95. Graph. Effect of slab thickness on CRCP deltaT prediction model.

This graph is a bar chart showing the predicted deltaT values for continuously reinforced concrete pavement (CRCP) sections in the Long-Term Pavement Performance sites in various locations. The data are categorized by the location, which, starting from the left, are Texas—cold climate, Texas—hot climate, Illinois, Mississippi, Oregon, Georgia, and Virginia. The y-axis shows the deltaT in a 10-inch slab from 0 to -40 ºF. The values plotted are also labeled on the solid bars and are -1.3, -31.0, -11.4, -1.5, -25.1, -14.5, and -12.4 ºF, respectively.

Figure 96. Graph. Effect of geographic location on CRCP deltaT prediction model.


 

The sensitivity analyses show reasonable trends but do not demonstrate that the model is robust. It is not clear, from an engineering standpoint, if the range of predicted values and their magnitudes are practical and realistic. The wide range of deltaT has a significant effect on design thickness. The data used to develop the model show very strong correlations, and it is likely that the predictions are valid, at least within a certain range of inputs. The current analyses and the data available are not adequate to determine these ranges. It is therefore recommended that this model be used with extreme caution.

Using the CRCP deltaT Model

The CRCP deltaT model shares similarities with the JPCP deltaT model. The section used to describe the process is the LTPP General Pavement Studies section in Illinois, 17_5020, which was constructed in May 1986. The CRCP thickness is 8.6 inches, and the PCC mix used a limestone aggregate. The following inputs can be directly obtained from the MEPDG input file:

The maximum temperature and maximum temperature range can be obtained by running the design file and deriving this input from the worksheet titled “Climate.” For the month of May, the maximum temperature and maximum temperature range for this location were 89.6 and 39.2 °F, respectively. Using these inputs, the CRCP deltaT gradient can be calculated as -1.3214 °F/inch. For the slab thickness of 8.6 inches, this is equivalent to a deltaT of -11.36 °F. This value is comparable to the -10-°F default. This input can be revised in an MEPDG file and reanalyzed to predict punchout development over time.


 


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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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