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Federal Highway Administration Research and Technology
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Publication Number: FHWAHRT12030 Date: August 2012 
Publication Number:
FHWAHRT12030
Date: August 2012 
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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 stepwise regression analysis and C_{p} 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:
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 = 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 R^{2} 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.
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 
The model statistics for table 54 are as follows:
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 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, 12ft slab width, 10inch slab thickness, 145 lb/ft^{3} PCC unit weight, 0.40 w/c ratio, and 40 degrees latitude.
The following list contains brief observations from these sensitivity analyses: