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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: FHWA-HRT-12-030 Date: August 2012 |
Publication Number: FHWA-HRT-12-030 Date: August 2012 |
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The models developed for the prediction of MEPDG-specific inputs are in the design features category. As explained earlier in this chapter, it was never intended for inclusion in the LTPP database, nor was the need for inclusion clearly foreseen at the time of designing the LTPP database. The data formulation for developing these models is model type 3, wherein the dependent variable (e.g., the design feature deltaT for JPCP design) is determined through several trial and error runs of the MEPDG and establishing the optimum value that minimizes the error prediction.
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. Version 1.1 was used in the generation of the dependent variables for the models included in this study.
Therefore, the models developed to predict the design features variables are valid only for use with the distress calibration model of version 1.1 of the MEPDG software. At the time this report was written, the MEPDG is being recalibrated under ongoing project NCHRP 20-07/Task 288. This recalibration effort will make the necessary updates to the CTE values used in the rigid pavement model calibrations and will handle the various updates and software bug fixes since the release of MEPDG version 1.0.
The prediction models presented in this report for the estimation of design feature inputs therefore may not be valid once the products of NCHRP 20-07/Task 288 are released. The information provided in this section should be considered as a description of a viable method to develop design feature input models. This effort has to be repeated after the release of the NCHRP 20-07/Task 288 products.
Both the JPCP transverse fatigue distress model and JPCP mean joint faulting were considered for use as the basis for selecting the optimum deltaT with minimized errors. However, JPCP transverse fatigue cracking prediction data correlated well with the material, climate, and design elements to develop the deltaT prediction model. The procedure used to determine the value of the dependent variable in the analysis entailed the following steps.
Step 1: Run MEPDG Calibration Files for a Range of deltaT Values:
The transverse cracking model in the MEPDG was calibrated using 300 design projects at a deltaT value of -10 °F. Each of these calibration files were run at deltaT values of -2.5, -5.0, -7.5, -10, -12.5, and -15 °F. The number of deltaT levels (six) and the range (-2.5 to -15 °F) were selected based on practical considerations of the time required to perform this analysis as well as to maintain the bounds of the predicted value within a reasonable range.
Step 2: Compile Predicted Cracking Data for All Ages:
Field-measured cracking at different ages was available for all the sections used in the calibration models. MEPDG-predicted damage and cracking data were extracted for ages corresponding to field data measurements. Table 50 shows a sample for cracking data extraction for section 01_3028.
Pavement Age (Years) |
Measured Field Cracking (Percent) |
Predicted Cracking (Percent) |
|||||
deltaT = -15 |
deltaT = -12.5 |
deltaT = -10 |
deltaT = -7.5 |
deltaT = -5 |
deltaT = -2.5 |
||
20.31507 |
0 |
20.8 |
4.3 |
1 |
0.7 |
3 |
12.8 |
21.84384 |
0 |
26.9 |
5.2 |
1.2 |
0.9 |
3.6 |
14.7 |
26.52329 |
4 |
48.9 |
9.3 |
2.2 |
1.6 |
6.8 |
23.3 |
28.87123 |
4 |
57.7 |
11.7 |
2.8 |
2 |
8.6 |
27.6 |
32.72329 |
8 |
70.1 |
16.8 |
4.2 |
3.1 |
12.7 |
36 |
Step 3: Calculate Errors and Determine Optimal deltaT for Each Section:
The predicted cracking for each level of deltaT (as shown in table 50) was compared against the field data to compute errors for each age. The sum of squared errors was then computed for each age and for each level of deltaT. Table 51 shows an example of error calculation for section 01_3028.
Pavement Age (Years) |
Measured Field Cracking (Percent) |
Squared Error Calculation |
|||||
deltaT = -15 |
deltaT = -12.5 |
deltaT = -10 |
deltaT = -7.5 |
deltaT = -5 |
deltaT = -2.5 |
||
20.31507 |
0 |
432.64 |
18.49 |
1 |
0.49 |
9 |
163.84 |
21.84384 |
0 |
723.61 |
27.04 |
1.44 |
0.81 |
12.96 |
216.09 |
26.52329 |
4 |
2,016.01 |
28.09 |
3.24 |
5.76 |
7.84 |
372.49 |
28.87123 |
4 |
2,883.69 |
59.29 |
1.44 |
4 |
21.16 |
556.96 |
32.72329 |
8 |
3,856.41 |
77.44 |
14.44 |
24.01 |
22.09 |
784 |
Sum of squared errors |
9,912.36 |
210.35 |
21.56 |
35.07 |
73.05 |
2,093.38 |
Note: The bold text in the squared error calculation section indicates the minimum sum of squared error for all ages.
The minimum sum of squared error for all ages, a value of 21.56 as highlighted in table 51, is observed for a deltaT of -10 °F in this case. The value -10 °F is therefore the dependent variable for this section. The same procedure was repeated for all 301 JPCP sections to develop a list of optimum temperatures, or dependent variables, for each calibration file.
The example presented in table 51 used a straightforward process to select the deltaT value. The sum of squared errors reached a minimum value for a value of -10 °F. However, there were cases where the sum of squared errors did not provide a clear choice for the selection of an optimal value. As shown in table 52, scenarios A and B are assigned a value of -10 and -12.5 °F, respectively. Scenario C represents a case where the measured cracking was zero percent for all ages, and the predicted cracking also was zero at all values of deltaT. Scenario D represents a case where the minimum error was achieved at the bounds of the selected range (i.e., at -15 °F). A higher deltaT can result in smaller errors, but the extent of data that could be appropriately included in the analyses by evaluating higher deltaT values was minimal. Therefore, all cases that resulted in error trends as represented by scenarios C and D were deleted from the dataset used for the statistical analyses. The dataset used in the statistical analyses contained 147 JPCP sections.
Scenario |
Sum of Squared Errors |
deltaT at Minimum Error (°F) |
|||||
deltaT = -15 |
deltaT = -12.5 |
deltaT = -10 |
deltaT = -7.5 |
deltaT = -5 |
deltaT = -2.5 |
||
A |
19,824.72 |
420.7 |
43.12 |
70.14 |
146.1 |
4,186.76 |
-10 |
B |
5.39 |
2.6 |
28.18 |
405.83 |
2,655.08 |
8,924.36 |
-12.5 |
C |
0 |
0 |
0 |
0 |
0 |
0 |
Cannot be determined |
D |
12,600.71 |
13,032.5 |
13,097.05 |
13,111.56 |
13,111.56 |
13,111.56 |
-15 |