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-HRT-12-030
Date: August 2012

 

Estimation of Key PCC, Base, Subbase, and Pavement Engineering Properties From Routine Tests and Physical Characteristics

PDF Version (4.44 MB)

PDF files can be viewed with the Acrobat® Reader®

CHAPTER 5. MODEL DEVELOPMENT (17)

 

JPCP deltaT Gradient Model Development

It was observed that the data generated for the dependent variable, deltaT, correlated well with the material, design, and climate parameters when transformed from deltaT temperature differential to deltaT temperature gradient. This involved dividing the deltaT temperature differential by the slab thickness. A step-wise regression analysis and Cp analyses were performed to select the variables that are correlated to the dependent variable and to select the best combination of variables to develop the model. After an iterative process to optimize the model, the equation developed to estimate the deltaT gradient variable is 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 214. 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 = w/c 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 53. The model was developed with 147 data points and has an R2 value of 0.4967 percent and an RMSE value of 0.3199 psi. Table 54 provides details of the range of data used to develop the model. Figure 215 shows the predicted versus measured for the proposed JPCP deltaT gradient model, while figure 216 shows the residual errors. Note that the measured data here refer to the deltaT gradient determined by matching MEPDG prediction to field performance. Figure 217 shows the predicted versus measured deltaT for the model.

Table 53. 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

 

The model statistics for table 54 are as follows:

Table 54. 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

 

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 Fahrenheit/inch, and the y-axis shows the predicted deltaT gradient from 
-2.5 to 0 Fahrenheit/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 °F/inch.

Figure 215. 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 Fahrenheit/inch, and the y-axis shows the error in prediction from -2.5 to 1 Fahrenheit/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 216. 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 Fahrenheit,  and the y-axis shows the predicted deltaT from -16 to 0 Fahrenheit. 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 Fahrenheit. 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 Fahrenheit. The points are represented as solid diamonds.

Figure 217. Graph. Predicted versus measured deltaT based on the JPCP deltaT gradient model.

Figure 218 through figure 224 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, 12-ft slab width, 10-inch slab thickness, 145 lb/ft3 PCC 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 zero to 80 Fahrenheit, and the y-axis shows the predicted deltaT in a 10-inch slab from -15 to 0 Fahrenheit. The sensitivity is shown for temperatures ranging from 20 to 65 Fahrenheit, 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 218. 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 Fahrenheit. 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 219. 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 zero to 20 inches, and the y-axis shows the predicted deltaT  in a 10-inch slab from -14 to 0 Fahrenheit. 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 220. 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 Fahrenheit. 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 221. 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 Fahrenheit. 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 222. 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 zero to 60 degrees, and the y-axis shows the predicted deltaT  from -15 to 0 Fahrenheit. 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 223. 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 zero to -14 Fahrenheit. 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 Fahrenheit, respectively.

Figure 224. Graph. Predicted deltaT for different locations in the United States.

The following list contains brief observations from these sensitivity analyses:

 


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