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Publication Number: FHWA-HRT-10-035
Date: September 2011

 

LTPP Computed Parameter: Dynamic Modulus

6.0 PREDICTION OF |E*| FOR LTPP LAYERS

6.1 MODEL PRIORITIZATION AND DECISION TREE DEVELOPMENT

The developed ANN models were ranked based on the performance of each model for an independent dataset that contains all of the required input parameters to be used in the different models. The decision tree in figure 60 is the result of this prioritization and was used to populate the LTPP database. As suspected at the outset of this project, the MR ANN model yields the best prediction possible and is the preferred model. This finding is not surprising given that the MR ANN model takes actual mixture measured quantities as input. The intuition is also supported in the fitting statistics shown in the figures presented in section 5.0. If MR data are not available, the next preferred model is the VV ANN model. Although the VV ANN shows poorer fitting statistics than the GV ANN model in terms of logarithmic space, it shows better statistics in terms of arithmetic space. The arithmetic statistics were used to rank these models because the moduli values are expressed and utilized in terms of their arithmetic value. Of the three ANN models, GV ANN received the lowest ranking. However, GV-PAR outranked the VV-grade because the model GV-PAR uses measurements taken directly from the material of interest. The VV-grade model uses viscosity values representative of the binder grade.

Figure 60. Illustration. Decision tree applied to population of LTPP database based on ranking of ANN models. This figure shows the decision tree developed based on ranking of different artificial neural network (ANN) models. The diagram has eight levels. At the top level, the user has available information on temperature and frequency of interest for a modulus prediction. In the second level, the user determines if the information available includes resilient modulus (MR). If resilient modulus is available, then the user proceeds to use the MR ANN model, using the time temperature shift factor. If resilient modulus is not available, then the user proceeds to the next level. In the third level, the user determines if the information available includes enough measures of viscosity to get the A and VTS values and also volumetric properties. If the viscosity and volumetric properties are available, then the user proceeds to use the viscosity–based (VV) ANN mode. If the viscosity and volumetric properties are not available, then the user proceeds to the next level. In the fourth level, the user determines if the information available includes the binder shear modulus and volumetric properties at consistent age. If binder shear modulus is available, then the user proceeds to use the binder shear modulus based (GV) ANN model, using the time temperature shift factor and isochronal analysis to process the data. If dynamic shear modulus and volumetric properties are not available, then the user proceeds to the next level. In the fifth level, the user determines if the information available includes the binder shear modulus and volumetric properties at inconsistent aging condition of rolling thin film oven and pressure aging vessel. If binder shear modulus is available, then the user proceeds to use the binder shear modulus based artificial neural network (GV PAR ANN) model, using the time temperature shift factor, processing the binder measurement for inconsistent aging conditions using PAR model and the isochronal analysis. If dynamic shear modulus and volumetric properties are not available, then the user proceeds to the next level. In the sixth level, the user determines if the information available includes binder grade representative of the viscosity values, and volumetric properties. If the binder grade and volumetric properties are available, then the user proceeds to use the VV–Grade ANN model, if the binder grade and volumetric properties are not available then the user proceeds to the next level. If the information needed to be used in the ranking models were not available, no prediction would be possible. In the seventh level, the user determines if the data needed for each predictive model need to be processed by surrogate models explained in each level. In the eighth level, the prediction models used to populate the long–term pavement program (LTPP) database are listed based on the ranking of ANN models as MR, VV, GV, GV–PAR, VV–Grade, and if no information available the user has to choose “No Prediction Possible.” In this level, the decision tree is applied on available information on temperature and frequency of interest to populate the LTPP database based on ranking of ANN models.
Figure 60. Illustration. Decision tree applied to population of LTPP database based on ranking of ANN models.

The input sets available for each section are different. Consequently, the models that can be utilized for a given section may differ. All the models that can be used for a specific section have been identified. If any of the inputs are outside the range of the calibration data, then the model for that section is considered to be a violated model, and predictions with it may or may not be reasonable. Any available model that does not violate the input range criteria is used as the predictive model for that section. In cases where only two violated models are available, the model for that section must be decided manually by the user.

6.2 DATA QC

Two sets of internal QC checks were applied to the |E*| data produced for submission to the LTPP database. The first QC check was used on the input values. All the other QCs were used to check the output |E*| predictions. In the following sections, each of these QC criteria is described. The work criterion is implied but not explicitly stated for each of these checks. The quality grading system referenced is different than the standard record status definition used in the LTPP database. For example, data assigned an “A” by the research team represent the highest quality data, whereas the LTPP convention assigns an “E” to the highest quality data. The research team established strict QC checks for these data to ensure that only the highest quality data were assigned an “A” grade. The data that did not achieve an “A” grade should be used with caution, and users should be fully aware that the data did not pass the QC check. All predictions are included in the database so users can determine whether or not the data are suitable for their needs. In addition, FHWA can revise the criteria used in the QC checks as deemed appropriate based on the opinions of their experts.

6.2.1 QC #1

QC #1 checks for a violation of the input range used in each model based on the input ranges of the calibration dataset, as seen in (see table 24). Figure 61 through figure 65 show example predictions of |E*| in two sections where violations of the input criteria have been detected. This check is performed on a line-by-line basis, meaning that each time a modulus is predicted, the input parameters are checked. Lines that pass the QC check receive a grade of “A,” whereas those that do not pass the QC check receive a grade of “F.”

For the layers where |E*| predictions are estimated using the MR ANN model but QC #1 is violated, the mastercurve created appears visually continuous (see figure 61 and figure 62). The reason for this appearance is that the output of this model is the mastercurve itself. However, the output of the other two ANN models is the estimation of |E*| under a specific condition. In this case, a violation of QC #1 may create a clear error in the mastercurve, as demonstrated in figure 63 through figure 65. The acceptable range of input parameters is shown for the three ANN models in table 24. These models do not estimate the information needed to create the mastercurve.

Table 24. Input ranges of different ANN models.
Model Range Parameter
MR 5 °C (GPa) MR 25 °C (GPa) MR 40 °C (GPa) fR (Hz) Viscosity (109 P) VMA (percent) VFA (percent) |G*|  (psi) Log(|E*|) (psi)
MR Min 4.8003 1.081 0.3789            
Max 34.053 15.411 6.8637
VV-grade1 Min       0.01 1.99E-06 9.51 32.82   3.52
Max 25 2.70E+01 34.64 95.07 6.82
GV-PAR1 Min           9.51 32.82 2.93E-02 3.52
Max 22.21 95.07 6.76E+05 6.81

°C = (°F-32)/1.8
1 Pas = 10 P
1 psi = 6.86 kPa
1 Indicates that VV-grade and GV-PAR have the same range of input.
Note: Blank cells indicate that the input parameter is not required in the model.

Figure 61. Graph. Example of the effect of a violation of QC #1 for MR ANN model in semi–log scale. This figure shows dynamic modulus (|E*|) on the y–axis in pounds per square inch from 0 to 4 × 106 psi (0 to 2.8 × 107 kPa) in arithmetic scale and reduced frequency on the x–axis in hertz from 1×10−8 to 1×104 Hz in logarithmic scale for the resilient modulus artificial neural network (MR ANN) model. Predicted |E*| values for a combination of five temperatures and six frequencies are shown in mastercurve form. The input data for these predictions violate quality control (QC) #1, and the results show that the data shift to form a continuous curve.
Figure 61. Graph. Example of the effect of a violation of QC #1 for MR ANN model in
semi-log scale.

Figure 62. Graph. Example of the effect of a violation of QC #1 for MR ANN model in log–log scale. This figure shows dynamic modulus (|E*|) on the y–axis in pounds per square inch from 1 × 103 to 1 × 107 psi (6.9 × 103 to 6.9 × 107 kPa) in logarithmic scale and reduced frequency on the x–axis in hertz from 1×10−8 to 1×104 Hz in logarithmic scale for the resilient modulus artificial neural network (MR ANN) model. Predicted |E*| values for a combination of five temperatures and six frequencies are shown in mastercurve form. The input data for these predictions violate quality control (QC) #1, and the results show that the data shift to form a continuous curve.
Figure 62. Graph. Example of the effect of a violation of QC #1 for MR ANN model in log-log scale.

Figure 63. Graph. Example of the effect of a violation of QC #1 for VV ANN model in semi–log scale. This figure shows dynamic modulus (|E*|) on the y–axis in pounds per square inch from 0×100 to 3×106 psi in arithmetic scale and reduced frequency on the x–axis in hertz from 1×10−5 to 1×1010 Hz in logarithmic scale for the viscosity–based artificial neural network (VV ANN) model. Predicted |E*| values for a combination of five temperatures and six frequencies are shown in mastercurve form. The input data for these predictions violated quality control (QC) #1, and the results show that the data do not shift to form a continuous curve.
Figure 63. Graph. Example of the effect of a violation of QC #1 for VV ANN model in semi-log scale.

Figure 64. Graph. Example of the effect of a violation of QC #1 for VV ANN model in log–log scale. This figure shows dynamic modulus (|E*|) on the y–axis in pounds per square inch from 1×103 to 1×107 psi in logarithmic scale and reduced frequency on the x–axis in hertz from 1×10−5 to 1×1010 Hz in logarithmic scale for the viscosity–based artificial neural network (VV ANN) model. Predicted |E*| values for a combination of five temperatures and six frequencies are shown in mastercurve form. The input data for these predictions violate quality control (QC) #1, and the results show that the data do not shift to form a continuous curve.
Figure 64. Graph. Example of the effect of a violation of QC #1 for VV ANN model in log-log scale.

Figure 65. Graph. Example of the effect of a violation of QC #1 for case of VV ANN model unshifted data. This figure shows dynamic modulus (|E*|) on the y–axis in pounds per square inch from 1 × 102 to 1 × 107 psi (6.9 × 102 to 6.9 × 107 kPa) in logarithmic scale and frequency on the x–axis in hertz from 0.01 to 100 Hz in arithmetic scale for the viscosity–based artificial neural network (VV ANN) model. Predicted |E*| values segregated by five temperatures and for six frequencies in each temperature are shown. The input data for these predictions violate quality control (QC) #1.
Figure 65. Graph. Example of the effect of a violation of QC #1 for VV ANN model unshifted data.

6.2.2 QC #2

QC #2 checks the trends of |E*| as a function of temperature and frequency. It is expected that |E*| decreases as the temperature increases and the loading frequency decreases. Figure 66 through figure 68 show sample cases of a QC #2 violation. In these examples, the predicted |E*| value at 40 °F (4.4 °C) and 25 Hz is smaller than the predicted value at 40 °F (4.4 °C) and 10 Hz. Similar to QC #1, this QC check is performed line-by-line; the lines that pass receive a grade of “A,” and those that fail receive a grade of “F.”

Figure 66. Graph. Example of the effect of a violation of QC #2 in semi–log scale. This figure shows dynamic modulus (|E*|) on the y–axis in pounds per square inch from 0 to 5 × 106 psi (0 to 3.4 × 107 kPa) in arithmetic scale and reduced frequency on the x–axis in hertz from 1 × 10−6 to 1×108 Hz in logarithmic scale. Predicted |E*| values for a combination of five temperatures and six frequencies are shown in mastercurve form. The input data for these predictions violate quality control (QC) #2, and the results show that the data do not shift to form a continuous curve.
Figure 66. Graph. Example of the effect of a violation of QC #2 in semi-log scale.

Figure 67. Example of the effect of a violation of QC #2 in log–log scale. This figure shows dynamic modulus (|E*|) on the y–axis in pounds per square inch from 1 × 103 to 1 × 107 psi (6.9 × 103 to 6.9 × 107 kPa)  in logarithmic scale and reduced frequency on the x–axis in hertz from 1×10−6 to 1×108 Hz in logarithmic scale. Predicted |E*| values for a combination of five temperatures and six frequencies are shown in mastercurve form. The input data for these predictions violate quality control (QC) #2, and the results show that the data do not shift to form a continuous curve.
Figure 67. Graph. Example of the effect of a violation of QC #2 in log-log scale.

Figure 68. Example of the effect of a violation of QC #2 unshifted data. This figure shows dynamic modulus (|E*|) on the y–axis in pounds per square inch from 1 × 102 to 1 × 107 psi (6.9 × 102 to 6.9 × 107 kPa) in logarithmic scale and frequency on the x–axis in hertz from 0.01 to 100 Hz in arithmetic scale. Predicted |E*| values segregated by five temperatures for six frequencies in each temperature are shown. The input data for these predictions violate quality control (QC) #2.
Figure 68. Graph. Example of the effect of a violation of QC #2 unshifted data.

6.2.3 QC #3

The typical percentage of difference between 0.1 Hz at one temperature and 25 Hz at the next warmest temperature is checked using QC #3. Equation 51 states the percentage of difference and a typical value of this term based on the available data in this study. Figure 69 through figure 71 show the violation of QC #3 in one of the sections. For this particular section, a violation occurred between 40 and 70 °F (4.4 and 21.1 °C). For this sample case, at 0.1 Hz and 40 °F (4.4 °C), the modulus is equal to 1.29 x 106 psi (8.85 x 106 kPa). At 25 Hz and 70 °F (21.1 °C), the modulus is equal to 8.28 x 105 psi (56.8 x 105 kPa), which is a percentage difference of 55.4 percent.

Equation 51. Calculation of the percentage of difference. Percent difference equals the difference lower temperature at 0.1 Hz minus higher temperature at 25 Hz divided by e higher temperature at 25 Hz (51)

Unlike the previous QC checks, QC #3 is performed on the basis of temperature. For example, if the percentage of difference between 14 and 40 °F (-10 and 4.4 °C) exceeds 25 percent, then all of the predictions at 14 °F (-10 °C) would receive a grade of “F.”

Figure 69. Example of the effect of a violation of QC #3 in semi–log scale. This figure shows dynamic modulus (|E*|) on the y–axis in pounds per square inch from 0 to 4 × 106 psi (0 to 2.8 × 107 kPa) psi in arithmetic scale and reduced frequency on the x–axis in hertz from 1×10−6 to 1×108 Hz in logarithmic scale. Predicted |E*| values for a combination of five temperatures and six frequencies are shown in mastercurve form. The input data for these predictions violate quality control (QC) #3, and the results show that the data do not shift to form a continuous curve.
Figure 69. Graph. Example of the effect of a violation of QC #3 in semi-log scale.

Figure 70. Example of the effect of a violation of QC #3 in log–log scale. This figure shows dynamic modulus (|E*|) on the y–axis in pounds per square inch from 1 × 103 to 1 × 107 psi (6.9 × 103 to 6.9 × 107 kPa) in logarithmic scale and reduced frequency on the x–axis in hertz from 1×10−6 to 1×108 Hz in logarithmic scale. Predicted |E*| values for a combination of five temperatures and six frequencies are shown in mastercurve form. The input data for these predictions violate quality control (QC) #3, and the results show that the data do not shift to form a continuous curve.
Figure 70. Graph. Example of the effect of a violation of QC #3 in log-log scale.

Figure 71. Example of the effect of a violation of QC #3 unshifted data. This figure shows dynamic modulus (|E*|) on the y–axis in pounds per square inch from 1 × 102 to 1 × 107 psi (6.9 × 102 to 6.9 × 107 kPa) in logarithmic scale and frequency on the x–axis in hertz from 0.01 to 100 Hz in arithmetic scale. Predicted |E*| values segregated by five temperatures for six frequencies in each temperature are shown. The input data for these predictions violate quality control (QC) #3.
Figure 71. Graph. Example of the effect of a violation of QC #3 unshifted data.

6.2.4 QC #4

in QC #4, the difference in |E*| values predicted between 0.1 Hz at one temperature and 0.1 Hz at the next warmest temperature is checked to see if appropriate trends with regard to temperature and modulus hold. Sample cases of QC #4 violation are shown in figure 72 through figure 74. For the data in these figures, |E*| at 0.1 Hz and 40 °F (4.4 °C) is smaller than |E*| at 0.1 Hz and 70 °F (21.1 °C). In the case shown in these figures, this situation has led to a discontinuous mastercurve because the optimization algorithm becomes confused when the modulus does not decrease as the temperature increases. Similar to QC #3, QC #4 is applied on a temperature basis.

Figure 72. Example of the effect of a violation of QC #4 in semi–log scale. This figure shows dynamic modulus (|E*|) on the y–axis in pounds per square inch from 0 to 5 × 106 psi (0 to 3.4 × 107 kPa) in arithmetic scale and reduced frequency on the x–axis in hertz from 1×10−6 to 1×106 Hz in logarithmic scale. Predicted |E*| values for a combination of five temperatures and six frequencies are shown in mastercurve form. The input data for these predictions violate quality control (QC) #4, and the results show that the data do not shift to form a continuous curve.
Figure 72. Graph. Example of the effect of a violation of QC #4 in semi-log scale.

Figure 73. Example of the effect of a violation of QC #4 in log–log scale. This figure shows dynamic modulus (|E*|) on the y–axis in pounds per square inch from 1 × 103 to 1 × 107 psi (6.9 × 103 to 6.9 × 107 kPa) in logarithmic scale and reduced frequency on the x–axis in hertz from 1×10−6 to 1×106 Hz in logarithmic scale. Predicted |E*| values for a combination of five temperatures and six frequencies are shown in mastercurve form. The input data for these predictions violate quality control (QC) #4, and the results show that the data do not shift to form a continuous curve.
Figure 73. Graph. Example of the effect of a violation of QC #4 in log-log scale.

Figure 74. Example of the effect of a violation of QC #4 unshifted data. This figure shows dynamic modulus (|E*|) on the y–axis in pounds per square inch from 1 × 102 to 1 × 107 psi (6.9 × 102 to 6.9 × 107 kPa) in logarithmic scale and frequency on the x–axis in hertz from 0.01 to 100 Hz in arithmetic scale. Predicted |E*| values segregated by five temperatures for six frequencies in each temperature are shown. The input data for these predictions violate quality control (QC) #4.
Figure 74. Graph. Example of the effect of a violation of QC #4 unshifted data.

6.2.5 QC #5

QC #5 checks the range of shift factor values in the output predictions against typical values. This check is used to indicate potential problems with the mastercurve generation process. The limits identified and subsequently used are as follows:

The output parameters of interest from the ANNACAP software are SHIFT_FACTOR COEFFICIENT 1 (α1), SHIFT_FACTOR_COEFFICIENT 2 (α2), and SHIFT_FACTOR_COEFFICIENT 3 (α3). The shift factor is computed using equation 52 as follows:

Equation 52. Calculation of shift factor. The logarithmic base 10 parenthesis a subscript T end parenthesis equals alpha subscript 1 times T squared plus alpha subscript 2 times T plus alpha subscript 3. (52)

Because the goal of this QC criterion is to judge the mastercurve generation process, only shift factor values at extreme temperatures need to be examined. Note that because the MR ANN model predicts the mastercurve directly, any predictions made with this model will automatically pass QC #5 without the need for calculation. When this QC is not passed, the entire section (at all temperatures) receives a grade of “F.”

Figure 75 through figure 77 show violations of QC #5. In these cases, the shift factor at 14 °F (-10 °C) is equal to 7.03. This effect results in a visual discontinuity in the mastercurve between the 14- and 40-°F (-10- and 4.4-°C) datasets.

Figure 75. Example of the effect of a violation of QC #5 in semi–log scale. This figure shows dynamic modulus (|E*|) on the y–axis in pounds per square inch from 0 to 4 × 106 psi (0 to 2.8 × 107 kPa) in arithmetic scale and reduced frequency on the x–axis in hertz from 1×10−6 to 1×109 Hz in logarithmic scale. Predicted |E*| values for a combination of five temperatures and six frequencies are shown in mastercurve form. The input data for these predictions violate quality control (QC) #5, and the results show that the data do not shift to form a continuous curve.
Figure 75. Graph. Example of the effect of a violation of QC #5 in semi-log scale.

Figure 76. Example of the effect of a violation of QC #5 in log–log scale. This figure shows dynamic modulus (|E*|) on the y–axis in pounds per square inch from 1 × 103 to 1 × 107 psi (6.9 × 103 to 6.9 × 107 kPa) in logarithmic scale and reduced frequency on the x–axis in hertz from 1×10−6 to 1×109 Hz in logarithmic scale. Predicted |E*| values for a combination of five temperatures and six frequencies are shown in mastercurve form. The input data for these predictions violate quality control (QC) #5, and the results show that the data do not shift to form a continuous curve.
Figure 76. Graph. Example of the effect of a violation of QC #5 in log-log scale.

Figure 77. Example of the effect of a violation of QC #5 unshifted data. This figure shows dynamic modulus (|E*|) on the y–axis in pounds per square inch from 1 × 102 to 1 × 107 psi (6.9 × 102 to 6.9 × 107 kPa) in logarithmic scale and frequency on the x–axis in hertz from 0.01 to 100 Hz in arithmetic scale. Predicted |E*| values segregated by five temperatures for six frequencies in each temperature are shown. The input data for these predictions violate quality control (QC) #5.
Figure 77. Graph. Example of the effect of a violation of QC #5 unshifted data.

6.2.6 QC #6

In an earlier version of the ANN models developed for this study, some cases had inputs within the calibration input range, but the |E*| predictions obtained values of the limits of the calibration data. In some other cases, |E*| did not change with varying temperature and frequency. QC #6 was expected to be the last QC check, but after improving the ANN models, the problem no longer exists. Nevertheless, the check is performed on the data. The limiting |E*| values used to judge whether a given prediction passes this QC check are given in table 25. Like QC #1 and QC #2, this QC check is applied line-by-line.

Table 25. Limiting |E*| values used for QC #6.
Model Upper Limit (psi) Lower Limit (psi)
MR ANN N/A N/A
VV ANN 5,888,437 3,311.311
GV ANN 6,456,542 3,311.311

1 psi = 6.86 kPa
N/A indicates that data are not available.

6.2.7 QC #7

Similar to QC #5, QC #7 is designed to judge the mastercurve generation process. Each time a mastercurve is generated, fitting statistics are computed. These statistics include the Se/Sy (of combined predictions), and R2. According to the draft standard for mastercurve generation using AASHTO TP-62 data, the explained variance should be greater than 0.99, and the ratio of Se/Sy should be less than 0.05.(42) When these limits are exceeded, QC #7 is triggered, and the layer fails. Because the MR ANN model predicts the mastercurve directly, any predictions made with this model will automatically pass QC #7 without the need for calculation. Equations 53–55 are used to compute the necessary statistical parameters. Whenever this QC is violated, the entire section receives a grade of “F.”

Equation 53. Calculation of standard error. S subscript e equals the square root of the summation from i equals 1 to n of the difference between bracket parenthesis logarithmic base 10 of vertical line E superscript star vertical line subscript ANN end parenthesis subscript i minus parenthesis logarithmic base 10 of vertical line E superscript star vertical line subscript fit end parenthesis subscript i, end bracket, squared, divided by 23. (53)

Where:

23 = Number of temperature/frequency combinations used minus the number of fitting parameters minus 1.
(log|E*|ANN)i = Logarithm of the modulus determined from the ANN models at a particular temperature frequency combination.
(log|E*|fit)i = Logarithm of the modulus determined from the optimized sigmoidal fit.
Equation 54. Calculation of standard deviation. S subscript y equals the square root of the summation from i equals 1 to n of the difference between bracket parenthesis logarithmic base 10 of vertical line E superscript star vertical line subscript ANN end parenthesis subscript i minus parenthesis logarithmic base 10 of vertical line E superscript star vertical line end parenthesis subscript avg end bracket, squared, divided by 29. (54)

Where:

29 = Number of temperature/frequency combinations used minus 1.
(log|E*|avg)i = Logarithm of the average modulus determined from the ANN models for a given layer.
Equation 55. Calculation of correlation coefficient. R squared equals 1 minus parenthesis 23 end parenthesis times S subscript e, squared divided by parenthesis 29 end parenthesis times S subscript y, squared. (55)

6.3 Contractor Judgment

The NCSU researchers used a combination of the above QC factors to judge the quality of the modulus prediction for an individual modulus prediction. If QCs #1, #3, #4, and #6 all pass, then the section receives a grade of “A.” If QC #1 fails but QCs #3, #4, and #6 all pass, then the modulus receives a grade of “C,” which means the predicted moduli are questionable. Otherwise, the modulus receives a grade of “F.”

6.4 Contractor Mastercurve Judgment

QCs #5 and #7 are used to judge the quality of the calibrated mastercurve and shift factor function. When both QCs pass, the section receives a grade of “A,” but when both fail, the section receives a grade of “F.” If one passes and one fails, then the mastercurve and shift factor function values are questionable, and the section receives a grade of “C.”

6.5 Prediction Statistics

The LTPP database contains information for a total of 1,806 layers that meet the criteria described in section 3.4 of this report. These layers have binder data available at a combination of different aging conditions including unaged or original-, RTFO-, PAV-, or field-aged. In the field-aged data, 2,223 records are available because some layers' properties may have been measured at different dates. The total resulting number of records is 7,641. Using the combined ANN models and requisite QC checks, modulus values were predicted for 363 records/layers in the original-aged level, 469 records/layers in the RTFO-aged level, 1 record/layer in the PAV level, and 503 records in the field-aged level. These numbers translate to predictions for 17.5 percent of the total number of records available. However, these records are distributed in such a way that a higher percentage of the layers have some sort of valid prediction. Of the 1,806 layers in the database, 1,010, or 56 percent, have a modulus prediction at some aging condition. Of these 1,010 layers, 615, or 34 percent of the total 1,806 layers, have completely reasonable predictions (i.e., an “A” grade), and 89, or 4.9 percent of the total 1,806 layers, have unreasonable predictions (i.e., an “F” grade). The remaining 306 layers (17 percent of the 1,806 layers) have questionable predictions (i.e., a “C” grade). Thus, the total percentage of layers with a completely valid or questionable prediction is 51 percent. Table 26 shows the summarized statistics of the population effort. Although it cannot be interpreted directly from this table, the majority of the valid records were populated using the MR ANN model followed next by the VV-grade ANN model and the VV ANN model.

Table 26. Statistics of LTPP data populated with |E*|.
Populated LTPP data Aging Condition Total
Original RTFO PAV Field
Number of records 1,806 1,806 1,806 2,223 7,641
Number of populated records 363 469 1 503 1,336
Number of records by contractor individual judgment grade Grade A 147 252 0 465 864
Grade C 0 1 1 38 40
Grade F 216 216 0 0 432
Number of records by contractor mastercurve judgment grade Grade A 44 142 0 0 186
Grade C 211 237 0 503 951
Grade F 108 90 1 0 199
Populated records using MR 5 0 0 503 508
Populated records using VV 358 59 0 0 417
Populated records using GV 0 0 1 0 1
Populated records using GV-PAR 0 2 0 0 2
Populated records using VV-grade 0 408 0 0 408
Number of populated layers 1,010
Number of layers with valid and questionable predictions 921
Number of layers with fully valid predictions 615
Number of layers with failed predictions 89

6.6 LTPP Database Additions

As a result of this project, nine tables were included in the LTPP database to document the inputs used in the dynamic modulus models as well as resultant predictions.(20) The tables were added to the materials testing module (i.e., TST) of the LTPP database. Each table is described below. It should be noted that inputs from the LTPP database as well as outputs from the models are in units that are consistent with popular convention, but both SI and English units are used in the tables.

Table 27. Structure and format of the TST_ESTAR_MASTER table.
Field Name Field Description
ESTAR_LINK Generic key for linking ESTAR data
STATE_CODE Numerical code for State or province. U.S. codes are consistent with Federal Information Processing Standards
SHRP_ID Test section identification number assigned by LTPP program. Must be combined with STATE_CODE to be unique
LAYER_NO Unique sequential number assigned to pavement layers starting with layer 1 as the deepest layer (subgrade)
PROJECT_ID The four-character identifier for the SPS project used to identify elements of information which are common to all sections in that project
PROJECT_LAYER_CODE Sequential alphabetic code assigned to identify group project-wide layers
PREDICTIVE_MODEL Code indicating the predictive model used to generate ESTAR estimates
CONSTRUCTION_DATE Construction date of the layer
SAMPLE_TYPE_ESTAR Code indicating the aging condition of the samples used for inputs into the ESTAR predictive models
SAMPLE_DATE Sampling date if field-aged
SAMPLE_AGE Sample age if field-aged
RECORD_STATUS Code indicating the general quality of the data as outlined, based on the level of QC checks described in the Database User Reference Guide(10)
Table 28. Structure and format of the TST_ESTAR_MODULUS table
Field Name Field Description
ESTAR_LINK Generic key for linking ESTAR data
TEMPERATURE Temperature of modulus prediction
FREQUENCY Frequency of modulus prediction
ESTAR Predicted dynamic modulus
RECORD_STATUS Code indicating the general quality of the data as outlined, based on the level of QC checks described in the Database User Reference Guide(10)
Table 29. Structure and format of the TST_ESTAR_MODULUS_COEFF table.
Field Name Field Description
ESTAR_LINK Generic key for linking ESTAR data
SIGMOIDAL_COEFF_1 Sigmoidal fitting function coefficient delta
SIGMOIDAL_COEFF_2 Sigmoidal fitting function coefficient alpha
SIGMOIDAL_COEFF_3 Sigmoidal fitting function coefficient beta
SIGMOIDAL_COEFF_4 Sigmoidal fitting function coefficient gamma
SHIFT_FACTOR_COEFF_1 Shift factor fitting function coefficient alpha 1
SHIFT_FACTOR_COEFF_2 Shift factor fitting function coefficient alpha 2
SHIFT_FACTOR_COEFF_3 Shift factor fitting function coefficient alpha 3
MASTERCURVE_QUALITY Code indicating the general quality of the mastercurve generation process. Pass if explained variance is greater than 0.99 and ratio of standard error to standard deviation is less than 0.05
RECORD_STATUS Code indicating the general quality of the data as outlined based on the level of QC checks described in the Database User Reference Guide(10)
Table 30. Structure and format of the TST_ESTAR_GSTAR_INPUT table.
Field Name Field Description
ESTAR_LINK Generic key for linking ESTAR data
TEMPERATURE Temperature of modulus prediction
FREQUENCY Frequency of modulus prediction
GSTAR Binder shear modulus used for G* ANN model
RECORD_STATUS Code indicating the general quality of the data as outlined based on the level of QC checks described in the Database User Reference Guide(10)
Table 31. Structure and format of the TST_ESTAR_GSTAR_CAM_COEFF table.
Field Name Field Description
ESTAR_LINK Generic key for linking ESTAR data.
CAM_COEFF_1 CAM fitting function coefficient Gg
CAM_COEFF_2 CAM fitting function coefficient wc
CAM_COEFF_3 CAM fitting function coefficient k
CAM_COEFF_4 CAM fitting function coefficient me
RECORD_STATUS Code indicating the general quality of the data as outlined based on the level of QC checks described in the Database User Reference Guide(10)
Table 32. Structure and format of the TST_ESTAR_VOLUM_INPUT table.
Field Name Field Description
ESTAR_LINK Generic key for linking ESTAR data
VMA Voids in mineral aggregate as a percent of total volume
VFA Voids filled with asphalt as a percent of VMA
RECORD_STATUS Code indicating the general quality of the data as outlined, based on the level of QC checks described in the Database User Reference Guide(10)
Table 33. Structure and format of the TST_ESTAR_VISC_INPUT table.
Field Name Field Description
ESTAR_LINK Generic key for linking ESTAR data
TEMPERATURE Temperature of modulus prediction
VISCOSITY Voids filled with asphalt as a percent of VMA
RECORD_STATUS Code indicating the general quality of the data as outlined, based on the level of QC checks described in the Database User Reference Guide(10)
Table 34. Structure and format of the TST_ESTAR_VISC_MODEL_COEFF table.
Field Name Field Description
ESTAR_LINK Generic key for linking ESTAR data
VISC_A Viscosity model intercept
VISC_VTS Viscosity model slope
RECORD_STATUS Code indicating the general quality of the data as outlined, based on the level of QC checks described in the Database User Reference Guide(10)
Table 35. Structure and format of the TST_ESTAR_MR_INPUT table.
Field Name Field Description
ESTAR_LINK Generic key for linking ESTAR data
MR_5C Resilient modulus at 5 °C
MR_25C Resilient modulus at 25 °C
MR_40C Resilient modulus at 40 °C
RECORD_STATUS Code indicating the general quality of the data asoutlined, based on the level of QC checks described in the Database UserReference Guide(10)

°C = (°F−32)/1.8

QC checks were developed to be applied to the LTPP database. These checks include many of the internal checks developed as part of this study as well as additional checks deemed appropriate. As such, the data available in the LTPP database have been subjected to both the research team's internal QC checks and the LTPP database QC checks. Figure 78 shows the ANN models and their appropriate input and output tables.

Figure 78. Illustration. ANN models and their appropriate input and output tables. This diagram shows the flow of data from the input tables to the artificial neural network (ANN) models to the output tables. The top of the illustration shows the VISC_MODEL_COEFF table flowing into the VISC_INPUT table and the GSTAR_CAM_COEFF table flowing into the GSTAR_INPUT table. At the next level, four tables (MR_INPUT, VISC_INPUT, VOLUM_INPUT, and GSTAR_INPUT) flow into five ANN models (MR, VV, GV, GV–PAR, VV–Grade). Those five ANN models all flow into the MODULUS output table. The MODULUS output table flows into the MODULUS_COEFF table.
Figure 78. Illustration. ANN models and their appropriate input and output tables.

 

 


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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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