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Federal Highway Administration Research and Technology
Coordinating, Developing, and Delivering Highway Transportation Innovations
REPORT 
This report is an archived publication and may contain dated technical, contact, and link information 

Publication Number: FHWAHRT12031 Date: August 2012 
Publication Number: FHWAHRT12031 Date: August 2012 
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The models developed for the prediction of MEPDGspecific 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 140D, 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.
The equation developed to estimate the deltaT gradient variable can be expressed as follows:
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/ft^{3}.
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 R^{2} 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 
tvalue 
P_{r} > 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.
Figure 80. Graph. Predicted versus measured for JPCP deltaT gradient model.
Figure 81. Graph. Residual errors for JPCP deltaT gradient model.
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, 12ft slab width, 10inch slab thickness, 145 lb/ft^{3} unit weight, 0.40 w/c ratio, and 40 degrees latitude.
Figure 83. Graph. Sensitivity of predicted deltaT to temperature range during month of construction.
Figure 84. Graph. Sensitivity of predicted deltaT to slab width.
Figure 85. Graph. Sensitivity of predicted deltaT to slab thickness.
Figure 86. Graph. Sensitivity of predicted deltaT to PCC slab unit weight.
Figure 87. Graph. Sensitivity of predicted deltaT to PCC w/c ratio.
Figure 88. Graph. Sensitivity of predicted deltaT to latitude of the project location.
Figure 89. Graph. Predicted deltaT for different locations in the United States.
The following are brief observations from these sensitivity analyses:
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.
The equation developed to estimate the CRCP deltaT gradient variable is as follows:
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 R^{2} 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 
tValue 
P_{r} > 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.
Figure 91. Graph. Predicted versus measured for CRCP deltaT model.
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.
Figure 93. Graph. Effect of maximum temperature on CRCP deltaT prediction model.
Figure 94. Graph. Effect of temperature range on CRCP deltaT prediction model.
Figure 95. Graph. Effect of slab thickness on CRCP deltaT prediction model.
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.
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.