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

 

LTPP Computed Parameter: Dynamic Modulus

APPENDIX C: AMPT VERSUS TP-62

C.1 EXPERIMENTAL VERIFICATION OF AMPT AND TP-62 DIFFERENCES

To assess differences in the measured moduli determined from the AMPT and TP-62 protocols, a joint study was carried out between researchers at the Turner-Fairbank Highway Research Center (TFHRC) and NCSU. For this study, TFHRC performed dynamic modulus testing on a mixture following the AMPT TP, and NCSU performed testing on the same mixture using the TP-62 protocol.(8) In both cases, three replicates have been tested. To reduce any variability not related to the equipment and protocols, all specimens were fabricated at NCSU and randomly sampled for either AMPT testing or TP-62 testing. The details of each testing protocol are summarized in table 43.

Table 43. TP summary.
Factor AMPT TP-62
Temperature (°F) 40, 70, 100, and 130 14, 40, 70, 100, and 130
Frequency (Hz) 20, 10, 5, 1, 0.5, and 0.1 25, 10, 5, 1, 0.5, and 0.1
Microstrain target 75–125 50–75
LVDT gauge length (mm) 70 100
Load direction Bottom loading Top loading
End treatment Teflon® Greased double latex membranes
Conditioning External temperature chamber, then equalize in AMPT for 3 min Equalize for 2.5–3.0 h in test machine
Rest period between frequencies (s) 0 300
Calculations NCHRP 09-29 final 10 cycles(50) NCHRP 09-29 final five cycles(50)

°C = (°F−32)/1.8
1 inch = 25.4 mm

The mixture used for this purpose is a 0.371-inch (9.5-mm) Superpave™ mixture typically used in North Carolina for surface courses. The gradation of this mixture is given in figure 133, and the relevant volumetric properties are summarized in table 44. All tests were conducted at 5.9 percent ±0.1 percent air void levels.

Figure 133. Graph. Test mixture gradation. This figure shows a graduation mixture graph. The percent passing is shown on the y–axis from 0 to 100 percent, and the sieve size raised to the power of 0.45 is plotted on the x–axis from 0 to 3.5. The gradation for the mixture used in this study is shown along with the maximum density line and control points. The gradation falls between the control points.
Figure 133. Graph. Test mixture gradation.

Table 44. Test mixture volumetric properties.
Volumetric Property Mix Design Test Samples
Va (percent) 3.8 5.9
VMA (percent) 15.6 17.5
VFA (percent) 75.7 66.2
Asphalt content (percent) 5.2 5.2
Percent effective binder content 4.9 4.9
Dust percentage 1.2 1.2
Gmm 2.616 2.616
Bulk specific gravity of the aggregate 2.828 2.828
Effective specific gravity of the aggregate 2.855 2.855
Gb 1.035 1.035

Results from the experimental study are summarized in figure 134 and figure 135, where the average dynamic moduli from the TP-62 protocol are plotted against the average moduli from the AMPT protocol. Error bars in these figures represent a single standard deviation from the mean. From these figures, it is observed that the AMPT test results are systematically lower than those from the TP-62 protocol; the difference between the two datasets is approximately 13 percent. Statistical analysis of these values using the step-down bootstrap method has also been performed. This method is used in lieu of multiple paired t-tests due to the effect of experimentwise error rates, which results in statistical errors when making multiple comparisons. Specifically, failing to account for this error rate increases the probability of finding significance when none is present. The statistical analysis results are shown by temperature and frequency in table 45. Note that in this table, the conditions under which the means are statistically similar are bold.

Figure 134. Graph. Comparison of |E*| measured via AMPT and TP–62 protocols in arithmetic scale. This figure shows the relationship between the measured dynamic modulus (|E*|) from test protocol (TP)–62 with |E*| measured from the asphalt mixture performance tester (AMPT). The measured |E*| via AMPT is shown on the y–axis in megapascals from 0 to 3.6 × 106 psi (0 to 2.5×104 MPa) in an arithmetic scale, and the measured |E*| via TP–62 is shown on the x–axis in megapascals 0 to 3.6 × 106 psi (0 to 2.5×104 MPa) in an arithmetic scale. A solid line represents the line of equality (LOE). The dataset align with LOE, and the measured moduli from AMPT become smaller than the measured moduli from TP–62 as the value increases.
Figure 134. Graph. Comparison of |E*| measured via AMPT and TP-62 protocols in arithmetic scale.

Figure 135. Graph. Comparison of |E*| measured via AMPT and TP–62 protocols in logarithmic scale. This figure shows the relationship between the measured dynamic modulus (|E*|) from the test protocol (TP)–62 with |E*| measured from the asphalt mixture performance tester (AMPT). The measured |E*| via AMPT is shown on the y–axis in megapascals from 1×102 to 1×105 MPa in a logarithmic scale, and the measured |E*| via TP–62 is shown on the x–axis in megapascals from 1.5 × 104 to 1.5 × 107 psi (1×102 to 1×105 MPa) in a logarithmic scale. A solid line represents the line of equality (LOE). The measured moduli from AMPT are slightly smaller than the measured moduli from TP–62 along LOE.
Figure 135. Graph. Comparison of |E*| measured via AMPT and TP-62 protocols in logarithmic scale.

Table 45. Statistical summary of AMPT and TP-62 test results.
Temperature (°C) Frequency (Hz) |E*| AMPT (psi) |E*| TP-62 (psi) p-Value
4 25.00 2,145,226 2,420,540 0.032
4 10.00 1,989,606 2,284,746 0.020
4 5.00 1,838,144 2,111,129 0.030
4 1.00 1,503,747 1,726,774 0.026
4 0.50 1,359,729 1,601,117 0.019
4 0.10 1,050,375 1,234,431 0.023
21 25.00 1,030,409 1,237,696 0.020
21 10.00 899,831 1,022,446 0.023
21 5.00 785,545 881,347 0.025
21 1.00 550,882 628,569 0.033
21 0.50 468,842 524,847 0.068
21 0.10 306,841 358,120 0.057
37 25.00 385,448 464,233 0.008
37 10.00 318,540 384,219 0.010
37 5.00 263,476 330,282 0.002
37 1.00 160,938 198,110 0.008
37 0.50 130,346 167,580 0.005
37 0.10 75,190 96,587 0.011
54 25.00 153,735 177,050 0.003
54 10.00 127,039 128,097 0.801
54 5.00 102,669 101,164 0.672
54 1.00 58,086 59,737 0.377
54 0.50 42,997 48,863 0.022
54 0.10 23,863 33,547 0.005

°C = (°F−32)/1.8
1 psi = 6.86 kPa
Note: Bold text indicates conditions where means are statistically similar.

C.2 COMPARISON OF AMPT AND TP-62 PROTOCOLS WITH THE AVAILABLE DATABASE

To assess the differences observed between the two |E*| measurement protocols, a more comprehensive analysis was performed using the databases available in this study. The two AMPT and TP-62 databases were segregated based on the temperatures at which the |E*| values were measured. Because these two databases cover different ranges of parameters, it is useful to examine the distribution of the relevant parameters for the two databases. Figure 136 through figure 157 present the distribution and range of each parameter in the two databases. In figure 158 through figure 162, the measured |E*| data points available for some specific temperatures for each type of database are shown by frequency. Based on observations from these figures and the difference equation shown in equation 100, differences between the databases containing AMPT and TP-62 measurements are evident, as can be seen in table 46.

Equation 100. Calculation of the percentage of difference between AMPT and TP–62 dynamic modulus measurements. Percent difference equals the ratio of vertical line E superscript star vertical line subscript TP–62 minus vertical line E superscript star vertical line subscript AMPT divided by vertical line E superscript star vertical line subscript TP–62, multiplied by 100. (100)

Based on this description, the following differences are observed at each temperature:

Figure 136. Graph. Frequency distribution of temperature in AMPT versus TP–62 databases. This figure shows a bar graph of the data point distribution of the temperatures for the test protocol (TP)–62 and asphalt mixture performance tester (AMPT) databases. The number of data points is shown on the y–axis from 0 to 4,000, and the temperature is shown in Fahrenheit on the x–axis from 14 to 140 °F (−10 to 60 °C) in increments of 18 °F (−7.7 °C). The histogram shows that most of the AMPT data points are in the 86 °F (30 °C) range, with fewer data points in the extremes. The TP–62 data points are distributed along the x–axis with the most data points in the 50 °F (10 °C) range.
Figure 136. Graph. Frequency distribution of temperature in AMPT versus TP-62 databases.

Figure 137. Graph. Range of temperature in AMPT versus TP–62 databases. This figure shows a bar graph of the range of testing temperature for the test protocol (TP)–62 and asphalt mixture performance tester (AMPT) databases. The temperature is shown on the y–axis in Fahrenheit from 0 to 140 °F (−18 to 60 °C), and the range of minimum, average, and maximum values are shown on the x–axis. The plot shows the value of 39.2 °F (4 °C) as the minimum temperature, 86.7 °F (30.4 °C) as the average temperature, and 129.9 °F (54.4 °C) as the maximum temperature for AMPT. The plot shows 14.0 °F (−10 °C) as the minimum temperature, 69.7 °F (20.9 °C) as the average temperature, and 130.0 °F (54.4 °C) as the maximum temperature for TP–62.
Figure 137. Graph. Range of temperature in AMPT versus TP-62 databases.

Figure 138. Graph. Frequency distribution of frequency in AMPT versus TP–62 databases. This figure shows a bar graph of the data point distribution of the frequency for the test protocol (TP)–62 and asphalt mixture performance tester (AMPT) databases. The number of data points is shown on the y–axis from 0 to 3,500, and the frequency is shown on the x–axis in hertz from 0 to 25 Hz. The histogram shows that most of the AMPT data points are in the 1 Hz range, with fewer data points in the extremes. The TP–62 data points are distributed along the x–axis, with the most data points in the 1 Hz range and fewer datapoints in the extremes.
Figure 138. Graph. Frequency distribution of frequency in AMPT versus TP-62 databases.

Figure 139. Graph. Range of loading frequency in AMPT versus TP–62 databases. This figure shows a bar graph of the range of loading frequency for the test protocol (TP)–62 and asphalt mixture performance tester (AMPT) databases. The frequency is shown on the y–axis in hertz from 0 to 30 Hz, and the range of minimum, average, and maximum values are shown on the x–axis. The plot shows 0.01 Hz as the minimum frequency, 6.7 Hz as the average frequency, and 25.0 Hz as the maximum frequency for the AMPT database. The plot also shows 0.01 Hz as the minimum frequency, 6.5 Hz as the average frequency, and 25.0 Hz as the maximum frequency for the TP–62 database.
Figure 139. Graph. Range of loading frequency in AMPT versus TP-62 databases.

Figure 140. Graph. Frequency distribution of percentage retained on 3/4–inch (19.05–mm) sieve ( 34) in AMPT versus TP–62 databases. This figure shows a bar graph of the data point distribution of the percentage of aggregate retained on a three–fourths–inch (19.05–mm) sieve for the test protocol (TP)–62 and asphalt mixture performance tester (AMPT) database. The number of data points is shown on the y–axis from 0 to 7,000, and the percentage of aggregate retained on a three–fourths–inch (19.05–mm) sieve,  34, is shown n the x–axis from 0 to 35 percent in intervals of 5 percent. The histogram shows that most of the AMPT data points are in the range of 0 percent, with fewer datapoints in the high extreme. The TP–62 data points are distributed along the x–axis, with the most datapoints in the range of 0 percent and fewer datapoints in the high extreme.
Figure 140. Graph. Frequency distribution of percentage retained on ¾-inch (19.05-mm) sieve (ρ34) in AMPT versus TP-62 databases.

Figure 141. Graph. Range of percentage retained on 3/4–inch (19.05–mm) sieve (ρ34) in AMPT versus TP–62 databases. This figure shows a bar graph of the percentage range of aggregate retained on a three–fourths–inch (19.05–mm) sieve for the test protocol (TP)–62 and asphalt mixture performance tester (AMPT) databases. The percentage of aggregate retained on a three–fourths–inch (19.05–mm) sieve, ρ34, is shown on the y–axis from 0 to 35 percent, and the range of minimum, average and maximum values is shown on the x–axis. The plot shows 0 percent as the minimum percentage, 1.4 percent as the average percentage, and 11.6 percent as the maximum percentage of aggregate retained on a three–fourths–inch (19.05–mm) sieve for the AMPT database. The plot also shows 0 percent as the minimum percentage, 5.1 percent as the average percentage, and 31.0 percent as the maximum percentage of aggregate retained on a three–fourths–inch (19.05–mm) sieve for the TP–62 database.
Figure 141. Graph. Range of percentage retained on ¾-inch (19.05-mm) sieve (ρ34) in AMPT versus TP-62 databases.

Figure 142. Graph. Frequency distribution of percentage retained on 3/8–inch (9.56–mm) sieve (ρ38) in AMPT versus TP–62 databases. This figure shows a bar graph of the data point distribution of the percentage of aggregate retained on a three–eighths–inch (9.56–mm) sieve for the test protocol (TP)–62 and asphalt mixture performance tester (AMPT) databases. The number of data points is shown on the y–axis from 0 to 3,000, and the percentage of aggregate retained on a three–eighths–inch (9.56–mm) sieve, ρ38, is shown on the x–axis from 0 to 55 percent in increments of 5 percent. The histogram shows that most of the AMPT data points are in the 5 percent range, with fewer data points in the high extreme. The TP–62 data points are distributed along the x–axis, with the most number of data points in the 25 percent range and fewer datapoints in the extremes.
Figure 142. Graph. Frequency distribution of percentage retained on 3/8-inch (9.56-mm) sieve (ρ38) in AMPT versus TP-62 databases.

Figure 143. Graph. Range of percentage retained on three–eighths inch (9.56–mm) sieve (ρ38) in AMPT versus TP–62 databases. This figure shows a bar graph of the range of percentage of aggregate retained on a three–eighths–inch (9.56–mm) sieve for the test protocol (TP)–62 and asphalt mixture performance tester (AMPT) databases. The percentage of aggregate retained on a three–eighths–inch (9.56–mm) sieve, ρ38, is shown on the y–axis from 0 to 60 percent, and the range of minimum, average, and maximum values is shown on the x–axis. The plot shows 2.3 percent as the minimum percentage, 15.2 percent as the average percentage, and 45.1 percent as the maximum percentage of aggregate retained on a three–eighths–inch (9.56 mm) sieve for the AMPT database. The plot also slows 1.0 percent as the minimum percentage, 26.5 percent as the average percentage, and 55.0 percent as the maximum percentage of aggregate retained on a three–eighths–inch (9.56–mm) sieve for the TP–62 database.
Figure 143. Graph. Range of percentage retained on 3/8-inch (9.56-mm) sieve (ρ38) in AMPT versus TP-62 databases.

Figure 144. Graph. Frequency distribution of percentage retained on #4 sieve (ρ4) in AMPT versus TP–62 databases. This figure shows a bar graph of the datapoint distribution of the percentage of aggregate retained on a #4 sieve for the test protocol (TP)–62 and asphalt mixture performance tester (AMPT) databases. The number of data points is shown on the y–axis from 0 to 7,000, and the percentage of aggregate retained on a # 4 sieve, ρ4, is shown on the x–axis from 20 to 80 percent in increments of 10 percent. The histogram shows that most of the AMPT data points are in the 40 percent range, with fewer datapoints in the extremes. The TP–62 data points are distributed along the x–axis, with the most datapoints in the 60 percent range and fewer datapoints in the extremes.
Figure 144. Graph. Frequency distribution of percentage retained on #4 sieve (ρ4) in AMPT versus TP-62 databases.

Figure 145. Graph. Range of percentage retained on #4 sieve (ρ4) in AMPT versus TP–62 databases. This figure shows a bar graph of the range of percentage of aggregate retained on a #4 sieve for the test protocol (TP)–62 and asphalt mixture performance tester (AMPT) databases. The percentage of aggregate retained on #4 sieve, ρ4, is shown on the y–axis from 0 to 80 percent, and the range of minimum, average, and maximum values is shown on the x–axis. The plot shows 22.3 percent as the minimum percentage, 37.6 percent as the average percentage, and 67.4 percent as the maximum percentage of aggregate retained on a #4 sieve for the AMPT database. The plot also shows 14.0 percent as the minimum percentage, 49.5 percent as the average percentage, and 73.0 percent as the maximum percentage of aggregate retained on a #4 sieve for the TP–62 database.
Figure 145. Graph. Range of percentage retained on #4 sieve (ρ4) in AMPT versus TP-62 databases.

Figure 146. Graph. Frequency distribution of percentage passing #200 sieve (ρ200) in AMPT versus TP–62 databases. This figure shows a bar graph of the data point distribution of the percentage of aggregate retained on a #200 sieve for the test protocol (TP)–62 and asphalt mixture performance tester (AMPT) databases. The number of data points is shown on the y–axis from 0 to 3,000, and the percentage of aggregate retained on a #200 sieve, ρ200, is shown on the x–axis from 2.5 to 7.5 percent in increments of 0.5 percent. The histogram shows that most of the AMPT data points are in the 4 percent range, with fewer datapoints in the extremes. The TP–62 data points are distributed along the x–axis, with the most data points in the 5 percent range and fewer data points in the extremes.
Figure 146. Graph. Frequency distribution of percentage passing #200 sieve (ρ200) in AMPT versus TP-62 databases.

Figure 147. Graph. Range of percentage passing #200 sieve (ρ200) in AMPT versus TP–62 databases. This figure shows a bar graph of the range of percentage of aggregate retained on a #200 sieve for the test protocol (TP)–62 and asphalt mixture performance tester (AMPT) databases. The percentage of aggregate retained on a #200 sieve, ρ200, is shown on the y–axis from 0 to 8 percent, and the range of minimum, average, and maximum values is shown on the x–axis. The plot shows 2.7 percent as the minimum percentage, 4.9 percent as the average percentage, and 6.6 percent as the maximum percentage of aggregate retained on a #200 sieve for the AMPT database. The plot also shows 2.6 percent as the minimum percentage, 4.9 percent as the average percentage, and 6.6 percent as the maximum percentage of aggregate retained on a #200 sieve for the TP–62 database.
Figure 147. Graph. Range of percentage passing #200 sieve (ρ200) in AMPT versus TP-62 databases.

Figure 148. Graph. Frequency distribution of specimen air voids in AMPT versus TP–62 databases. This figure shows a bar graph of the data point distribution of the percentage of air voids for the test protocol (TP)–62 asphalt mixture performance tester (AMPT) databases. The number of data points is shown on the y–axis from 0 to 4,000, and the percentage of air voids is shown on the x–axis from 0 to 14 percent in increments of 1 percent. The histogram shows that most of the AMPT data points are in the 8 percent range, with fewer data points in the extremes. The TP–62 data points are distributed along the x–axis, with the most data points in the 7 percent range and fewer data points in the extremes.
Figure 148. Graph. Frequency distribution of specimen air voids in AMPT versus TP-62 databases.

Figure 149. Graph. Range of specimen air voids in AMPT versus TP–62 databases. This figure shows a bar graph of the range of percentage of air voids for the test protocol (TP)–62 and asphalt mixture performance tester (AMPT) databases. The percentage of air voids is shown on the y–axis from 0 to 14 percent, and the range of minimum, average, and maximum values is shown on the x–axis. The plot shows 4.5 percent as the minimum percentage, 6.9 percent as the average percentage, and 8.7 percent as the maximum percentage of air voids for the AMPT database. The plot also shows 0.7 percent as the minimum percentage, 6.4 percent as the average percentage, and 12.5 percent as the maximum percentage of air voids for the TP–62 database.
Figure 149. Graph. Range of specimen air voids in AMPT versus TP-62 databases.

Figure 150. Graph. Frequency distribution of effective binder volume in AMPT versus TP–62 databases. This figure shows a bar graph of the data point distribution of the percentage of effective asphalt content for the test protocol (TP)–62 and asphalt mixture performance tester (AMPT) databases. The number of data points is shown on the y–axis from 0 to 9,000, and the percentage of effective asphalt content is shown on the x–axis from 5 to 17 percent in increments of 3 percent. The histogram shows that most of the AMPT data points are in the 11 percent range, with fewer data points in the extremes. The TP–62 data points are distributed along the x–axis, with the most data points in the 11 percent range and fewer data points in the extremes.
Figure 150. Graph. Frequency distribution of effective binder volume in AMPT versus TP-62 databases.

Figure 151. Graph. Range of effective binder volume in AMPT versus TP–62 databases. This figure shows a bar graph of the range of percentage of effective asphalt content for the test protocol (TP)–62 and asphalt mixture performance tester (AMPT) databases. The percentage of effective asphalt content is shown on the y–axis from 0 to 16 percent, and the range of minimum, average, and maximum values is shown on the x–axis. The plot shows 4.8 percent as the minimum percentage, 9.5 percent as the average percentage, and 12.7 percent as the maximum percentage of effective asphalt content for the AMPT database. The plot also shows 6.1 percent as the minimum percentage, 10.0 percent as the average percentage, and 14.2 percent as the maximum percentage of effective asphalt content for the TP–62 database.
Figure 151. Graph. Range of effective binder volume in AMPT versus TP-62 databases.

Figure 152. Graph. Frequency distribution of voids in mineral aggregates in AMPT versus TP–62 databases. This figure shows a bar graph of the data point distribution of the percentage of voids in mineral aggregates from the test protocol (TP)–62 and asphalt mixture performance tester (AMPT) databases. The number of data points is shown on the y–axis from 0 to 6,000, and the percentage of voids in mineral aggregates is shown on the x–axis from 8 to 24 percent in increments of 4 percent. The histogram shows that most of the AMPT data points are in the 20 percent range, with fewer data points in the low extreme. The TP–62 data points are distributed along the x–axis, with the most data points in the 16 percent range and fewer data points in the extremes.
Figure 152. Graph. Frequency distribution of VMA in AMPT versus TP-62 databases.

Figure 153. Graph. Range of voids in mineral aggregates in AMPT versus TP–62 databases. This figure shows a bar graph of the range of percentage of voids in mineral aggregates for the test protocol (TP)–62 and asphalt mixture performance tester (AMPT) databases. The percentage of voids in mineral aggregates is shown on the y–axis from 0 to 25 percent, and the range of minimum, average, and maximum values is shown on the x–axis. The plot shows 9.5 percent as the minimum percentage, 16.4 percent as the average percentage, and 19.9 percent as the maximum percentage of voids in mineral aggregates for the AMPT database. The plot also shows 10.8 percent as the minimum percentage, 16.4 percent as the average percentage, and 22.2 percent as the maximum percentage of voids in mineral aggregates for the TP–62 database.
Figure 153. Graph. Range of VMA in AMPT versus TP-62 databases.

Figure 154. Graph. Frequency distribution of voids filled with asphalt in AMPT versus TP–62 databases. This figure shows a bar graph of the data point distribution of the percentage of voids filled with asphalt from the test protocol (TP)–62 and asphalt mixture performance tester (AMPT) databases. The number of data points is shown on the y–axis from 0 to 7,000, and the percentage of voids filled with asphalt is shown on the x–axis from 30 to 100 percent in increments of 10 percent starting at 30 percent. The histogram shows that most of the AMPT data points are in the 60 percent range, with fewer data points in the extremes. The TP–62 data points are distributed along the x–axis, with the most data points in the 60 percent range and fewer data points in the extremes.
Figure 154. Graph. Frequency distribution of VFA in AMPT versus TP-62 databases.

Figure 155. Graph. Range of voids filled with asphalt in AMPT versus TP–62 databases. This figure shows a bar graph of the range of percentage of voids filled with asphalt for the test protocol (TP)–62 and asphalt mixture performance tester (AMPT) databases. The percentage of voids filled with asphalt is shown on the y–axis from 0 to 100 percent, and the range of minimum, average, and maximum values is shown on the x–axis. The plot shows 42.9 percent as the minimum percentage, 58.1 percent as the average percentage, and 70.3 percent as the maximum percentage of voids filled with asphalt for the AMPT database. The plot also shows 32.8 percent as the minimum percentage, 61.9 percent as the average percentage, and 95.1 percent as the maximum percentage of voids filled with asphalt for the TP–62 database.
Figure 155. Graph. Range of  VFA in AMPT versus TP-62 databases.

Figure 156. Graph. Frequency distribution of |G*| in AMPT versus TP–62 databases. This figure shows a bar graph of the data point distribution of the dynamic shear modulus (|G*|) of asphalt binder from the test protocol (TP)–62 test protocol and asphalt mixture performance tester (AMPT) databases. The number of data points is shown on the y–axis from 0 to 3,500, and |G*| of asphalt binder is shown on the x–axis in pounds per square inch from 0.01 to 1 × 106 psi (6.9 × 10−2 to 6.9 × 106 kPa). The histogram shows that most of the AMPT data points are in the 1,000 psi range, with fewer data points in the extremes. The TP–62 data points are distributed along the x–axis, with the most data points in the 10,000 psi range and fewer data points in the extremes.
Figure 156. Graph. Frequency distribution of |G*| n AMPT versus TP-62 databases.

Figure 157. Graph. Range of |G*| in AMPT versus TP–62 databases. This figure shows a bar graph of the range of dynamic shear modulus (|G*|) of asphalt binder for the test protocol (TP)–62 and asphalt mixture performance tester (AMPT) databases. |G*| of asphalt binder is shown on the y–axis in pounds per square inch from 2 × 10−2 to 7 × 105 psi (1.4 × 10−1 to 4.8 × 106 kPa), and the range of minimum, average, and maximum values is shown on the x–axis. The plot shows 4.8 × 10−2 psi (3.3 × 10−1 kPa) as the minimum |G*|, 5.4 × 102 psi (3.7 × 103 kPa) as the average |G*|, and 1.8 × 104 psi (1.2 × 105 kPa) as the maximum |G*|of asphalt binder for the AMPT database. The plot also shows 2.9 × 10−2 psi (2 × 10−1 kPa) as the minimum |G*|, 1.4 × 104 psi (9.6 × 104 kPa) as the average |G*|, and 6.8 × 105 psi (4.7 × 106 kPa) as the maximum |G*| of asphalt binder for the TP–62 database.
Figure 157. Range of |G*| in AMPT versus TP-62 databases.

Figure 158. Graph. Percentage of difference between AMPT versus TP–62 databases based on similar ranges of different variables at 39.9 °F (4.4 °C). This figure shows a bar graph of the percentage of difference between asphalt mixture performance tester (AMPT) and test protocol (TP)–62 databases based on similar ranges of different variables at 40 °F (4.4 °C). The percentage of difference is shown on the y–axis from 30 to 65 percent. Different variables are shown on the x–axis and include percentage of aggregate retained on a three–fourths–inch (19.05–mm) sieve (ρ34), percentage of aggregate retained on a three–eighths–inch (9.56–mm) sieve (ρ38), percentage of aggregate retained on a #4 sieve (ρ4), percentage of aggregate retained on a #200 (ρ200), percentage of air voids (Va), percentage of effective asphalt content (Vbeff), percentage of voids in mineral aggregates (VMA), percentage of voids filled with asphalt (VFA), and dynamic shear modulus of asphalt binder (|G*|) in pounds per square inch. The figure shows that the percentage of difference based on different variables is mostly from 40 to 45 percent. The highest percentage of difference is related to a similar range of percentage of aggregate retained on a three–fourths–inch (19.05–mm) sieve, and the lowest percentage of difference is related to the similar range of percentage of aggregate retained on a three–eighths–inch (9.56–mm).
Figure 158. Graph. Percentage of difference between AMPT versus TP-62 databases based on similar ranges of different variables at 39.9 °F (4.4 °C).

Figure 159. Graph. Percentage of difference between AMPT versus TP–62 databases based on similar ranges of different variables at 69.9 °F (21.1 °C). This figure shows a bar graph of the percentage of difference between test protocol (TP)–62 and asphalt mixture performance tester (AMPT) databases based on similar ranges of different variables at 70 °F (21.1 °C). The percentage of difference is shown on the y–axis from 30 to 65 percent. Different variables are shown on the x–axis and include percentage of aggregate retained on a three–fourths–inch (19.05–mm) sieve (ρ34), percentage of aggregate retained on three–eighths–inch (9.56–mm) sieve (ρ38), percentage of aggregate retained on a #4 sieve (ρ4), percentage of aggregate retained on a #200 (ρ200), percentage of air voids (Va), percentage of effective asphalt content (Vbeff), percentage of voids in mineral aggregates (VMA), percentage of voids filled with asphalt (VFA), and dynamic shear modulus of asphalt binder (|G*|) in pounds per square inch. The figure shows that the percentage of difference based on the different variables is mostly from 45 to 60 percent. The highest percentage of difference is related to a similar range of percentage of effective asphalt content, and the lowest percentage of difference is related to the similar range of percentage of aggregate retained on a three–eighths–inch (9.56–mm) sieve.
Figure 159. Graph. Percentage of difference between AMPT versus TP-62 databases based on similar ranges of different variables at 69.9 °F (21.1 °C).

Figure 160. Graph. Percentage of difference between AMPT versus TP–62 databases based on similar ranges of different variables at 100 °F (37.8 °C). This figure shows a bar graph of the percentage of difference between test protocol (TP)–62 and asphalt mixture performance tester (AMPT) databases based on similar ranges of different variables at 100 °F (37.7 °C). The percentage of difference is shown on the y–axis from 30 to 65 percent. Different variables are shown on the x–axis and include percentage of aggregate retained on a three–fourths–inch (19.05–mm) sieve (ρ34), percentage of aggregate retained on a three–eighths–inch (9.56–mm) sieve (ρ38), percentage of aggregate retained on a #4 sieve (ρ4), percentage of aggregate retained on a #200 (ρ200), percentage of air voids (Va), percentage of effective asphalt content (Vbeff), percentage of voids in mineral aggregates (VMA), percentage of voids filled with asphalt (VFA), and dynamic shear modulus of asphalt binder (|G*|) in pounds per square inch. The figure shows that the percentage of difference based on the different variables is mostly from 45 to 65 percent. The highest percentage of difference is related to a similar range of percentage of effective asphalt content, and the lowest percentage of difference is related to the similar range of percentage of aggregate retained on a three–eighths–inch (9.56–mm) sieve.
Figure 160. Graph. Percentage of difference between AMPT versus TP-62 databases based on similar ranges of different variables at 100 °F (37.8 °C).

Figure 161. Graph. Percentage of difference between AMPT versus TP–62 databases based on similar ranges of different variables at 129.2 °F (54.0 °C). This figure shows a bar graph of the percentage of difference between test protocol (TP)–62 and asphalt mixture performance tester (AMPT) databases based on similar ranges of different variables at 129.2 °F (54 °C). The percentage of difference is shown on the y–axis from 30 to 65 percent. Different variables are shown on the x–axis and include percentage of aggregate retained on a three–fourths–inch (19.05–mm) sieve (ρ34), percentage of aggregate retained on a three–eighths–inch (9.56–mm) sieve (ρ38), percentage of aggregate retained on a #4 sieve (ρ4), percentage of aggregate retained on a #200 (ρ200), percentage of air voids (Va), percentage of effective asphalt content (Vbeff), percentage of voids in mineral aggregates (VMA), percentage of voids filled with asphalt (VFA), and dynamic shear modulus of asphalt binder (|(G*|) in pounds per square inch. The percentage of difference based on the different variables is mostly 45 to 65 percent. The highest percentage of difference is related to a similar range of percentage of effective asphalt content, and the lowest percentage of difference is related to the similar range of percentage of VMA.
Figure 161. Graph. Percentage of difference between AMPT versus TP-62 databases based on similar ranges of different variables at 129.2 °F (54.0 °C).

Figure 162. Graph. Percentage of difference between AMPT versus TP–62 databases based on similar ranges of different variables at 129.9 °F (54.4 °C). This figure shows a bar graph of the percentage of difference between test protocol (TP)–62 and asphalt mixture performance tester (AMPT) databases based on similar ranges of different variables at 130 °F (54.4 °C). The percentage of difference is shown on the y–axis from 30 to 65 percent. Different variables are shown on the x–axis and include percentage of aggregate retained on a three–fourths–inch (19.05–mm) sieve (ρ34), percentage of aggregate retained on a three–eighths–inch (9.56–mm) sieve (ρ38), percentage of aggregate retained on a #4 sieve (ρ4), percentage of aggregate retained on a #200 (ρ200), percentage of air voids (Va), percentage of effective asphalt content (Vbeff), percentage of voids in mineral aggregates (VMA), percentage of voids filled with asphalt (VFA), and dynamic shear modulus of asphalt binder (|(G*|) in pounds per square inch. The percentage of difference based on different variables is mostly 40 to 60 percent. The highest percentage of difference is related to a similar range of percentage of voids in mineral aggregates, and the lowest percentage of difference is related to the similar range of percentage of aggregate retained on a three–eighths–inch (9.56–mm) sieve.
Figure 162. Graph. Percentage of difference between AMPT versus TP-62 databases based on similar ranges of different variables at 129.9 °F (54.4 °C).

Table 46. Percentage of difference between AMPT versus TP-62 database based on similar ranges of different variables.
Temp (°F) 0 ≤ ρ34 ≤ 15 5 ≤ ρ38 ≤ 50 30 ≤ ρ4 ≤ 70 3 ≤ ρ200 ≤ 7 5 ≤ Va ≤ 9 8 ≤ Vbeff ≤ 14 12 ≤ VMA ≤ 20 50 ≤ VFA ≤ 80 1e-2 ≤ |G*| ≤ 1e5
40 46.08 39.80 41.14 43.54 42.75 45.65 44.81 44.29 43.60
70 59.39 47.54 51.74 57.66 57.67 60.23 59.91 58.32 57.84
100 62.63 49.53 51.35 61.61 63.38 64.49 64.36 62.66 61.95
129 45.60 51.02 49.65 46.26 N.A 63.01 46.16 52.09 46.26
130 57.55 40.76 44.14 57.46 60.50 59.99 60.54 57.93 57.83

°C = (°F−32)/1.8

Similar ranges of each variable have been considered for each temperature, and the percentage of error has been calculated based on the difference of average TP-62 versus AMPT |E*| measurements for the corresponding temperature.

C.3 EVALUATION OF AMPT VERSUS TP-62 PROTOCOLS USING ANN MODEL

A preliminary study was conducted to determine the feasibility and predictability of the ANN modeling technique relative to the existing models. This feasibility study was first conducted based on |G*| because more existing closed-form models use this parameter as their primary input parameter. The ANN models used in this preliminary study are not the final models suggested by the research team, but they are similar in form and validation. To ensure full coverage of the expected conditions, the most recent Witczak database with available measured |G*| data and a portion of the dataset obtained at NCSU with support from the NCDOT were utilized as the TP-62 training database. Also, appropriate portions of the FHWA mobile trailer database and the WRI database (from Kansas and Nevada sites) were considered as the AMPT training database (see table 47).(51,52) New parameters were not identified through this study. Instead, only those that have been used in the modified Witczak model are incorporated. For verification purposes, three different sets of independent databases were used (see table 48). As a corollary to this study, an additional ANN model was trained that uses the Hirsch model input parameters. The results from this model are given in this section, as well.

Table 47. Summary of database used for training ANN models.
Type of Database AMPT TP-62 Total
FHWA I WRI Witczak NCDOT I
Number of mixtures 409 24 106 24 563
Number of data points 7,827 500 3,180 644 12,151
Number of binders 13 8 17 5 43
Number of gradation variations 13 12 13 19 57
Number of volumetric variations 256 13 98 24 391

Note: FHWA I consists of the mixtures from 12 States

 

Table 48. Summary of the database used for verification of ANN models.
Type of Database AMPT TP-62 Total
FHWA II Citgo NCDOT II
Number of mixtures 84 8 12 104
Number of data points 1,652 168 338 2,158
Number of binders 3 2 3 8
Number of gradation variations 3 1 12 16
Number of volumetric variations 75 1 12 88

Note: FHWA II consists of the mixtures from three States in the FHWA mobile trailer database with the following site IDs: 1-IA0358, 2-WA0463, and 3-KS464.

It should be noted that the two TPs, AMPT and TP-62, were used to measure the |E*| values in the various databases. To illustrate any possible differences between the two protocols, three different ANNs were developed using the Witczak-based input parameters, as shown in table 49. G-GR pANN was trained using data from both the AMPT and TP-62 protocols, whereas AMPT pANN and TP-62 pANN models were trained using the data from AMPT only and TP-62 only. Table 49 summarizes the databases used to train and verify the ANNs.

Table 49. Description of the developed ANN Models and their validation statistics.
Model Data Used in ANN Training Description Reference Scale Statistical Parameters for Training Data Statistical Parameters for
Verification Data
AMPT TP-62 FHWA II NCDOT II Citgo
G-GR pANN FHWA I Witczak ANNs trained with modified Witczak  parameters Arithmetic Se/Sy = 0.29 R2 = 0.92 Se/Sy = 0.38 R2 = 0.86 Se/Sy = 0.33 R2 = 0.97 Se/Sy = 0.52 R2 = 0.94
WRI NCDOT I Log Se/Sy = 0.15 R2 = 0.98 Se/Sy = 0.35 R2 = 0.91 Se/Sy = 0.27 R2 = 0.96 Se/Sy = 0.59 R2 = 0.96
AMPT pANN FHWA I   Arithmetic Se/Sy = 0.24 R2 = 0.94 Se/Sy = 0.36 R2 = 0.91 Se/Sy = 0.63 R2 = 0.87 Se/Sy = 0.37 R2 = 0.88
WRI Log Se/Sy = 0.16 R2 = 0.97 Se/Sy = 0.38 R2 = 0.90 Se/Sy = 0.60 R2 = 0.89 Se/Sy = 0.48 R2 = 0.91
TP-62 pANN   Witczak Arithmetic Se/Sy = 0.34 R2 = 0.88 Se/Sy = 2.08 R2 = 0.77 Se/Sy = 0.24 R2 = 0.95 Se/Sy = 1.20 R2 = 0.97
NCDOT I Log Se/Sy = 0.18 R2 = 0.97 Se/Sy = 0.99 R2 = 0.82 Se/Sy = 0.27 R2 = 0.93 Se/Sy = 0.53 R2 = 0.99

Modified Witczak Model
    Arithmetic   Se/Sy = 0.92 R2 = 0.91 Se/Sy = 0.71 R2 = 0.91 Se/Sy = 0.64 R2 = 0.98
Log   Se/Sy = 0.58 R2 = 0.92 Se/Sy = 0.19 R2 = 0.98 Se/Sy = 0.26 R2 = 0.99
Hirsch Model     Arithmetic   Se/Sy = 0.30 R2 = 0.92 Se/Sy = 0.47 R2 = 0.97 Se/Sy = 0.11 R2 = 0.99
Log   Se/Sy = 0.39 R2 = 0.92 Se/Sy = 0.26 R2 = 0.97 Se/Sy = 0.09 R2 = 0.99
Al-Khateeb Model     Arithmetic   Se/Sy = 0.48 R2 = 0.89 Se/Sy = 0.55 R2 = 0.93 Se/Sy = 0.36 R2 = 0.93
Log   Se/Sy = 0.43 R2 = 0.92 Se/Sy = 0.40 R2 = 0.93 Se/Sy = 0.17 R2 = 0.97

Note: Blank cells indicate information is not applicable.

The ANN models perform well, as shown in figure 163 to figure 180, which display the prediction accuracies of the different models for the combined AMPT and TP-62 data (figure 163 to figure 168), TP-62 data only (figure 169 to figure 174), and AMPT data only (figure 175 to figure 180). Also, these three groups of figures show the prediction accuracies of the ANNs separately. In these three figures, the type of data (i.e., AMPT versus TP-62) used in the ANN training matches the type of data used in the verification (e.g., figure 163 shows the prediction accuracy of the G-GR pANN model trained with the combined AMPT and TP-62 data on the combined AMPT and TP-62 data, etc.). It is noted that the data used in these figures were not included in the ANN training.

Figure 181 through figure 204 further demonstrate the differences between the AMPT and the TP-62 data and their effect on the prediction accuracies of the different ANNs. FHWA II data used in figure 181 through figure 188 are obtained using the AMPT protocol. The TP-62 pANN model trained with the TP-62 data and the modified Witczak model overpredict the measured |E*| values. Figure 189 through figure 196 present the prediction results for the NCDOT II data, which were measured using the TP-62 protocol. These figures illustrate the opposite effect on the prediction bias, that is, the effect of using the TP-62 data in the ANN training and predicting the AMPT data. In this case, the AMPT pANN model, trained using the AMPT data, underpredicts the |E*| values. The G-GR pANN model provides a promising ANN-based |E*| model, and the TP-62 pANN model shows good predictions without any significant bias. With the exception of the Citgo dataset, the G-GR pANN model provides high goodness of fit and correlation, as seen in table 49. The promising feature of the G-GR pANN model is that it improves the bias of |E*| predictions, particularly at high and low temperatures. This new ANN model is more sensitive to, and thus more likely to capture, the changes in volumetric parameters than all the other existing predictive models.

The findings from figure 163 to figure 204 are summarized as follows:

Figure 163. Graph. Prediction of the combination of AMPT and TP–62 data using the modified Witczak and G–GR pANN models in arithmetic scale. This figure shows the relationship between the measured dynamic modulus (|E*|) of the asphalt mixture performance tester (AMPT) and test protocol (TP)–62 databases and |E*| from the dynamic shear modulus binder and gradation–based pilot artificial neural network (G–GR pANN) and modified Witczak predictive models. The predicted |E*| is shown on the y–axis in pounds per square inch from 0 to 1.2 × 107 psi (0 to 8.3 × 107 kPa) in an arithmetic scale. |E*| from measured data is shown on the x–axis in pounds per square inch from 0 to 1.2 × 107 psi (0 to 8.3 × 107 kPa) in an arithmetic scale. A solid line represents the line of equality (LOE). The dataset align with LOE, and the predicted moduli from the modified Witczak model become larger than the measured moduli as the value increases. The predicted moduli from the G–GR pANN model align with LOE. There are few scatter data points with the predicted moduli smaller than the measured moduli. On the bottom right of the graph, there are two equations describing the modified Witczak model: R2 equals 0.84 and Se/Sy equals 0.76. Additionally, there are two equations describing the G–GR pANN model: R2 equals 0.92, and Se/Sy equals 0.29.
Figure 163. Graph. Prediction of the combination of AMPT and TP-62 data using the modified Witczak and G-GR pANN models in arithmetic scale.

Figure 164. Graph. Prediction of the combination of AMPT and TP–62 data using the modified Witczak and G–GR pANN models in logarithmic scale. This figure shows the relationship between the measured dynamic modulus (|E*|) of the asphalt mixture performance tester (AMPT) and test protocol (TP)–62 databases and |E*| from the dynamic shear modulus binder and gradation–based pilot artificial neural network (G–GR pANN) and modified Witczak predictive models. The predicted |E*| is shown on the y–axis in pounds per square inch from 1 × 103 to 1 × 108 psi (6.9 × 103 to 6.9×108 kPa) in a logarithmic scale. |E*| from measured data is shown on the x–axis in pounds per square inch from 1 × 103 to 1 × 108 psi (6.9 × 103 to 6.9×108 kPa) in a logarithmic scale. A solid line represents the line of equality (LOE). The predictions from the modified Witczak model are larger than the measured value along LOE and become further away from it as the value decreases. The predictions from the G–GR pANN model align with LOE. On the bottom right of the graph, there are two equations describing the modified Witczak model: R2 equals 0.92 and Se/Sy equals 0.40. Additionally, there are two equations describing the G–GR pANN model: R2 equals 0.98 and Se/Sy equals 0.15.
Figure 164. Graph. Prediction of the combination of AMPT and TP-62 data using the modified Witczak and G-GR pANN models in logarithmic scale.

Figure 165. Graph. Prediction of the combination of AMPT and TP–62 data using the Hirsch model in arithmetic scale. This figure shows the relationship between the measured dynamic modulus (|E*|) of the asphalt mixture performance tester (AMPT) and test protocol (TP)–62 databases and |E*| from the Hirsch predictive model. The predicted |E*| is shown on the y–axis in pounds per square inch from 0 to 1.2 × 107 psi (0 to 8.3 × 107 kPa) in an arithmetic scale. |E*| from measured data is shown on the x–axis in pounds per square inch from 0 to 1.2 × 107 psi (0 to 8.3 × 107 kPa) in an arithmetic scale. A solid line represents the line of equality (LOE). The dataset align with LOE, and the predicted moduli become smaller than the measured moduli as the value increases. On the bottom right of the graph, there are two equations describing the Hirsch model: R2 equals 0.81 and Se/Sy equals 0.48.
Figure 165. Graph. Prediction of the combination of AMPT and TP-62 data using the Hirsch model in arithmetic scale.

Figure 166. Graph. Prediction of the combination of AMPT and TP–62 data using the Hirsch model in logarithmic scale. This figure shows the relationship between the measured dynamic modulus (|E*|) of the asphalt mixture performance tester (AMPT) and test protocol (TP)–62 databases and |E*| from the Hirsch predictive model. The predicted |E*| is shown on the y–axis in pounds per square inch from 1 × 103 to 1 × 108 psi (6.9 × 103 to 6.9 × 108 kPa) in a logarithmic scale. |E*| from measured data is shown on the x–axis in pounds per square inch from 1 × 103 to 1 × 108 psi (6.9 × 103 to 6.9 × 108 kPa) in a logarithmic scale. A solid line represents the line of equality (LOE). The dataset align with LOE, and the predicted moduli become smaller than the measured moduli as the value increases and become larger than the measured moduli as the value decreases. There is also a horizontal line at the lowest range of predictions that shows the insensitivity of this model to different input parameters. On the bottom right of the graph, there are two equations describing the Hirsch model: R2 equals 0.92 and Se/Sy equals 0.31.
Figure 166. Graph. Prediction of the combination of AMPT and TP-62 data using the Hirsch model in logarithmic scale.

Figure 167. Graph. Prediction of the combination of AMPT and TP–62 data using the Al–Khateeb model in arithmetic scale. This figure shows the relationship between the measured dynamic modulus (|E*|) of the asphalt mixture performance tester (AMPT) and test protocol (TP)–62 databases and |E*| from the Al–Khateeb predictive model. The predicted |E*| is shown on the y–axis in pounds per square inch from 0 to 1.2 × 107 psi (0 to 8.3 × 107 kPa) in an arithmetic scale. |E*| from measured data is shown on the x–axis in pounds per square inch from 0 to 1.2 × 107 psi (0 to 8.3 × 107 kPa) in an arithmetic scale. A solid line represents the line of equality (LOE). The predicted moduli become smaller than measured moduli as the value increases. On the bottom right of the graph, there are two equations describing the Al–Khateeb model: R2 equals 0.71 and Se/Sy equals 0.65.
Figure 167. Graph. Prediction of the combination of AMPT and TP-62 data using the Al-Khateeb model in arithmetic scale.

Figure 168. Graph. Prediction of the combination of AMPT and TP–62 data using the Al–Khateeb model in logarithmic scale. This figure shows the relationship between the measured dynamic modulus (|E*|) of the asphalt mixture performance tester (AMPT) and test protocol (TP)–62 databases and |E*|from the Al–Khateeb predictive model. The predicted |E*| is shown on the y–axis in pounds per square inch from 1 × 103 to 1 × 108 psi (6.9 × 103 to 6.9 × 108 kPa) in a logarithmic scale. |E*| from measured data is shown on the x–axis in pounds per square inch from 1 × 103 to 1 × 108 psi (6.9 × 103 to 6.9 × 108 kPa) in a logarithmic scale. A solid line represents the line of equality (LOE). The dataset align with LOE in the middle range, and the predicted moduli become smaller than the measured moduli as the value increases and decreases. There is also a horizontal line at the lowest range of predictions that shows the insensitivity of this model to different input parameters. On the bottom right of the graph, there are two equations describing the Al–Khateeb model: R2 equals 0.89 and Se/Sy equals 0.34.
Figure 168. Graph. Prediction of the combination of AMPT and TP-62 data using the Al-Khateeb model in logarithmic scale.

Figure 169. Graph. Prediction of the AMPT data using the modified Witczak and AMPT pANN models in arithmetic scale. This figure shows the relationship between the measured dynamic modulus (|E*|) of the asphalt mixture performance tester (AMPT) database and |E*| from the AMPT pilot artificial neural network (pANN) and modified Witczak predictive models. The predicted |E*| is shown on the y–axis in pounds per square inch from 0 to 8 × 106 psi (0 to 5.5 × 107 kPa) in an arithmetic scale. |E*| from measured data is shown on the x–axis in pounds per square inch from 0 to 8 × 106 psi (0 to 5.5 × 107 kPa) in an arithmetic scale. A solid line represents the line of equality (LOE). The dataset align with LOE, and the predicted moduli from the modified Witczak model become larger than the measured moduli as the value increases. The predicted moduli from the AMPT pANN model align with LOE. There are few scatter points with predictions larger and smaller than measured moduli. On the bottom right of the graph, there are two equations describing the modified Witczak model: R2 equals 0.86 and Se/Sy equals 1.04. Additionally, there are two equations describing the AMPT pANN model: R2 equals 0.94 and Se/Sy equals 0.24.
Figure 169. Graph. Prediction of the AMPT data using the modified Witczak and AMPT pANN models in arithmetic scale.

Figure 170. Graph. Prediction of the AMPT data using the modified Witczak and AMPT pANN models in logarithmic scale. This figure shows the relationship between the measured dynamic modulus (|E*|) of the asphalt mixture performance tester (AMPT) database and |E*| from the AMPT pilot artificial neural network (pANN) and modified Witczak predictive models. The predicted |E*| is shown 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 a logarithmic scale. |E*| from measured data is shown on the x–axis in pounds per square inch from 1 × 103 to 1 × 107 psi (6.9 × 103 to 6.9 × 107 kPa) in a logarithmic scale. A solid line represents the line of equality (LOE). The predictions from the modified Witczak model are larger than the measured value along LOE and become further away from it as the value decreases. The predictions from the AMPT pANN model align with LOE, and there are few scatter data points with predictions larger than the measured moduli. On the bottom right of the graph, there are two equations describing the modified Witczak model: R2 equals 0.93 and Se/Sy equals 0.48. Additionally, there are two equations describing the AMPT pANN model: R2 equals 0.97 and Se/Sy equals 0.16.
Figure 170. Graph. Prediction of the AMPT data using the modified Witczak and AMPT pANN models in logarithmic scale.

Figure 171. Graph. Prediction of the AMPT data using the Hirsch model in arithmetic scale. This figure shows the relationship between the measured dynamic modulus (|E*|) of the asphalt mixture performance tester (AMPT) database and |E*| from the Hirsch predictive model. The predicted |E*| is shown on the y–axis in pounds per square inch from 0 to 8 × 106 psi (0 to 5.5 × 107 kPa) in an arithmetic scale. |E*| from measured data is shown on the x–axis in pounds per square inch from 0 to 8 × 106 psi (0 to 5.5 × 107 kPa) in an arithmetic scale. A solid line represents the line of equality (LOE). The dataset align with LOE, and there are few scatter data points with predictions larger than the measured moduli. On the bottom right of the graph, there are two equations describing the Hirsch model: R2 equals 0.91 and Se/Sy equals 0.31.
Figure 171. Graph. Prediction of the AMPT data using the Hirsch model in arithmetic scale.

Figure 172. Graph. Prediction of the AMPT data using the Hirsch model in logarithmic scale. This figure shows the relationship between the measured dynamic modulus (|E*|) of the asphalt mixture performance tester (AMPT) and |E*| from the Hirsch predictive model. The predicted E*| is shown 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 a logarithmic scale. |E*| from measured data is shown on the x–axis in pounds per square inch from 1 × 103 to 1 × 107 psi (6.9 × 103 to 6.9 × 107 kPa) in a logarithmic scale. A solid line represents the line of equality (LOE). The dataset align with LOE, and the predicted moduli become larger than the measured moduli as the value decreases. There is also a horizontal line at the lowest range of predictions that shows the insensitivity of this model to different input parameters. On the bottom right of the graph, there are two equations describing the Hirsch model: R2 equals 0.93 and Se/Sy equals 0.34.
Figure 172. Graph. Prediction of the AMPT data using the Hirsch model in logarithmic scale.

Figure 173. Graph. Prediction of the AMPT data using the Al–Khateeb model in arithmetic scale. This figure shows the relationship between the measured dynamic modulus (|E*|) of the asphalt mixture performance tester (AMPT) database and |E*| from the Al–Khateeb predictive model. The predicted |E*| is shown in pounds per square inch on the y–axis from 0 to 8 × 106 psi (0 to 5.5 × 107 kPa) in an arithmetic scale. |E*| from measured data is shown on the x–axis in pounds per square inch from 0 to 8 × 106 psi (0 to 5.5 × 107 kPa) in an arithmetic scale. A solid line represents the line of equality (LOE). The predicted moduli become smaller than the measured moduli as the value increases. On the bottom right of the graph, there are two equations describing the Al–Khateeb model: R2 equals 0.88 and Se/Sy equals 0.39.
Figure 173. Graph. Prediction of the AMPT data using the Al-Khateeb model in arithmetic scale.

Figure 174. Graph. Prediction of the AMPT data using the Al–Khateeb model in logarithmic scale. This figure shows the relationship between the measured dynamic modulus (|E*|) of the asphalt mixture performance tester (AMPT) database and |E*| from the Al–Khateeb predictive model. The predicted |E*| is shown 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 a logarithmic scale. |E*| from measured data is shown on the x–axis in pounds per square inch from 1 × 103 to 1 × 107 psi (6.9 × 103 to 6.9 × 107 kPa) in a logarithmic scale. A solid line represents the line of equality (LOE). The dataset align with LOE in the middle range, and the predicted moduli become smaller than measured moduli as the value increases and decreases. There is also a horizontal line at the lowest range of predictions that shows the insensitivity of this model to different input parameters. On the bottom right of the graph, there are two equations describing the Al–Khateeb model: R2 equals 0.94 and Se/Sy equals 0.33.
Figure 174. Graph. Prediction of the AMPT data using the Al-Khateeb model in logarithmic scale.

Figure 175. Graph. Prediction of the TP–62 data using the modified Witczak and TP–62 pANN models in arithmetic scale. This figure shows the relationship between the measured dynamic modulus (|E*|) of the test protocol (TP)–62 database and |E*| from the TP–62 pilot artificial neural network (pANN) and modified Witczak predictive models. The predicted |E*| is shown on the y–axis in pounds per square inch from 0 to 1.2 × 107 psi (0 to 8.3 × 107 kPa) in an arithmetic scale. |E*| from measured data is shown on the x–axis in pounds per square inch from 0 to 1.2 × 107 psi (0 to 8.3 × 107 kPa) in an arithmetic scale. A solid line represents the line of equality (LOE). The dataset align with LOE, and the predicted moduli from the modified Witczak model become larger than the measured moduli as the value increases. The predicted moduli from the TP–62 pANN model align with LOE, and the predicted moduli become smaller than measured moduli as the value increases. On the bottom right of the graph, there are two equations describing the modified Witczak model: R2 equals 0.79 and Se/Sy equals 0.83. Additionally, there are two equations describing the AMPT pANN model: R2 equals 0.88 and Se/Sy equals 0.34.
Figure 175. Graph. Prediction of the TP-62 data using the modified Witczak and TP-62 pANN models in arithmetic scale.

Figure 176. Graph. Prediction of the TP–62 data using the modified Witczak and TP–62 pANN models in logarithmic scale. This figure shows the relationship between the measured dynamic modulus (|E*|) of the test protocol (TP)–62 database and |E*| from the TP–62 pilot artificial neural network (pANN) and modified Witczak predictive models. The predicted |E*| is shown on the y–axis in pounds per square inch from 1 × 103 to 1 × 108 psi (6.9 × 103 to 6.9 × 108 kPa) in a logarithmic scale. |E*| from measured data is shown on the x–axis in pounds per square inch from 1 × 103 to 1 × 108 psi (6.9 × 103 to 6.9 × 108 kPa) in a logarithmic scale. A solid line represents the line of equality (LOE). The predictions from the modified Witczak model are larger than the measured value along LOE. The predictions from the TP–62 pANN model align with LOE. On the bottom right of the graph, there are two equations describing the modified Witczak model: R2 equals 0.92 and Se/Sy equals 0.33. Additionally, there are two equations describing the TP–62 pANN model: R2 equals 0.97 and Se/Sy equals 0.18.
Figure 176. Graph. Prediction of the TP-62 data using the modified Witczak and TP-62 pANN models in logarithmic scale.

Figure 177. Graph. Prediction of the TP–62 data using the Hirsch model in arithmetic scale. This figure shows the relationship between the measured dynamic modulus (|E*|) of the test protocol (TP)–62 database and |E*| from the Hirsch predictive model. The predicted |E*| is shown on the y–axis in pounds per square inch from 0 to 1.2 × 107 psi (0 to 8.3 × 107 kPa) in an arithmetic scale. |E*| from measured data is shown on the x–axis in pounds per square inch from 0 to 1.2 × 107 psi (0 to 8.3 × 107 kPa) in an arithmetic scale. A solid line represents the line of equality (LOE). The dataset align with LOE, and the predicted moduli become smaller than the measured moduli as the value increases. On the bottom right of the graph, there are two equations describing the Hirsch model: R2 equals 0.79 and Se/Sy equals 0.53.
Figure 177. Graph. Prediction of the TP-62 data using the Hirsch model in arithmetic scale.

Figure 178. Prediction of the TP–62 data using the Hirsch model in logarithmic scale. This figure shows the relationship between the measured dynamic modulus (|E*|) of the test protocol (TP)–62 database and |E*| from the Hirsch predictive model. The predicted |E*| is shown on the y–axis in pounds per square inch from 1 × 103 to 1 × 108 psi (6.9 × 103 to 6.9 × 108 kPa) in a logarithmic scale. |E*| from measured data is shown on the x–axis in pounds per square inch from 1 × 103 to 1 × 108 psi (6.9 × 103 to 6.9 × 108 kPa) in a logarithmic scale. A solid line represents the line of equality (LOE). The dataset align with LOE, and the predicted moduli become smaller than the measured moduli as the value increases. There is also a horizontal line at the lowest range of predictions that shows the insensitivity of this model to different input parameters. On the bottom right of the graph, there are two equations describing the Hirsch model: R2 equals 0.92 and Se/Sy equals 0.30.
Figure 178. Graph. Prediction of the TP-62 data using the Hirsch model in logarithmic scale.

Figure 179. Graph. Prediction of the TP–62 data using the Al–Khateeb model in arithmetic scale. This figure shows the relationship between the measured dynamic modulus (|E*|) of the test protocol (TP)–62 database and |E*| from the Al–Khateeb predictive model. The predicted |E*| is shown on the y–axis in pounds per square inch from 0 to 1.2 × 107 psi (0 to 8.3 × 107 kPa) in an arithmetic scale. |E*| from measured data is shown on the x–axis in pounds per square inch from 0 to 1.2 × 107 psi (0 to 8.3 × 107 kPa) in an arithmetic scale. A solid line represents the line of equality (LOE). The predicted moduli become smaller than the measured moduli as the value increases. On the bottom right of the graph, there are two equations describing the Al–Khateeb model: R2 equals 0.75 and Se/Sy equals 0.75.
Figure 179. Graph. Prediction of the TP-62 data using the Al-Khateeb model in arithmetic scale.

Figure 180. Graph. Prediction of the TP–62 data using the Al–Khateeb model in logarithmic scale. This figure shows the relationship between the measured dynamic modulus (|E*|) of the test protocol (TP)–62 database and |E*| from the Al–Khateeb predictive model. The predicted |E*| is shown on the y–axis in pounds per square inch from 1 × 103 to 1 × 108 psi (6.9 × 103 to 6.9 × 108 kPa) in a logarithmic scale. |E*| from measured data is shown on the x–axis in pounds per square inch from 1 × 103 to 1 × 108 psi (6.9 × 103 to 6.9 × 108 kPa) in a logarithmic scale. A solid line represents the line of equality (LOE). The dataset align with LOE in the middle range, and the predicted moduli become smaller than the measured moduli as the value increases and decreases. There is also a horizontal line at the lowest range of predictions that shows the insensitivity of this model to different input parameters. On the bottom right of the graph, there are two equations describing the Al–Khateeb model: R2 equals 0.88 and Se/Sy equals 0.40.
Figure 180. Graph. Prediction of the TP-62 data using the Al-Khateeb model in logarithmic scale.

Figure 181. Graph. Prediction of the FHWA II data the using modified Witczak and G–GR pANN models in arithmetic scale. This figure shows the relationship between the measured dynamic modulus (|E*|) of the Federal Highway Administration (FHWA) II database and |E*| from the dynamic shear modulus binder and gradation–based pilot artificial neural network (G–GR pANN) and modified Witczak predictive models. The predicted |E*| is shown on the y–axis in pounds per square inch from 0 to 4 × 106 psi (0 to 2.8 × 107 kPa) in an arithmetic scale. |E*| from measured data is shown on the x–axis in pounds per square inch from 0 to 4 × 106 psi (0 to 2.8 × 107 kPa) in an arithmetic scale. A solid line represents the line of equality (LOE). The dataset align with LOE, and the predicted moduli from the modified Witczak model become larger than the measured moduli as the value increases. The predicted moduli from the G–GR pANN model align with LOE. On the bottom right of the graph, there are two equations describing the modified Witczak model: R2 equals 0.91 and Se/Sy equals 0.92. Additionally, there are two equations describing the G–GR pANN model: R2 equals 0.86 and Se/Sy equals 0.38.
Figure 181. Graph. Prediction of the FHWA II data using the modified Witczak and G-GR pANN models in arithmetic scale.

Figure 182. Graph. Prediction of the FHWA II data using the modified Witczak and G–GR pANN models in logarithmic scale. This figure shows the relationship between the measured dynamic modulus (|E*|) of the Federal Highway Administration (FHWA) II database and |E*| from the dynamic shear modulus binder and gradation–based pilot artificial neural network (G–GR pANN) and modified Witczak predictive models. The predicted |E*| is shown 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 a logarithmic scale. |E*| from measured data is shown on the x–axis in pounds per square inch from 1 × 103 to 1 × 107 psi (6.9 × 103 to 6.9 × 107 kPa) in a logarithmic scale. A solid line represents the line of equality (LOE). The predictions from the modified Witczak model are larger than the measured value along LOE. The predictions from the test protocol (TP)–62 pANN model align with LOE and become larger than the measured moduli as the value decreases. On the bottom right of the graph, there are two equations describing the modified Witczak model: R2 equals 0.92 and Se/Sy equals 0.58. Additionally, there are two equations describing the G–GR pANN model: R2 equals 0.91 and Se/Sy equals 0.35.
Figure 182. Graph. Prediction of the FHWA II data using the modified Witczak and G-GR pANN models in logarithmic scale.

Figure 183. Graph. Prediction of the FHWA II data using the AMPT pANN and TP–62 pANN models in arithmetic scale. This figure shows the relationship between the measured dynamic modulus (|E*|) of the Federal Highway Administration (FHWA) II database and |E*| from the asphalt mixture performance tester pilot artificial neural network (AMPT pANN) and test protocol (TP)–62 pANN predictive models. The predicted |E*| is shown on the y–axis in pounds per square inch from 0 to 4 × 106 psi (0 to 2.8 × 107 kPa) in an arithmetic scale. |E*| from measured data is shown in pounds per square inch on the x–axis from 0 to 4 × 106 psi (0 to 2.8 × 107 kPa) in an arithmetic scale. A solid line represents the line of equality (LOE). The predicted moduli from the AMPT pANN model align with LOE. The predicted moduli from the TP–62 pANN model become larger than the measured moduli as the value increases. On the bottom right of the graph, there are two equations describing the AMPT pANN model: R2 equals 0.91 and Se/Sy equals 0.36. Additionally, there are two equations describing the TP–62 pANN model: R2 equals 0.77 and Se/Sy equals 2.08.
Figure 183. Graph. Prediction of the FHWA II data using the AMPT pANN and TP-62 pANN models in arithmetic scale.

Figure 184. Graph. Prediction of the FHWA II data using the AMPT pANN and TP–62 pANN models in logarithmic scale. This figure shows the relationship between the measured dynamic modulus (|E*|) of the Federal Highway Administration (FHWA) II database and |E*| from the asphalt mixture performance tester pilot artificial neural network (AMPT pANN) and test protocol (TP)–62 pANN predictive models. The predicted |E*| is shown 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 a logarithmic scale. |E*| from measured data is shown on the x–axis in pounds per square inch from 1 × 103 to 1 × 107 psi (6.9 × 103 to 6.9 × 107 kPa) in a logarithmic scale. A solid line represents the line of equality (LOE). The predictions from the AMPT pANN model align with LOE and become larger than the measured moduli as the value decreases. The predictions from the TP–62 pANN model are larger than measured value along LOE. On the bottom right of the graph, there are two equations describing the AMPT pANN model: R2 equals 0.90 and Se/Sy equals 0.38. Additionally, there are two equations describing the TP–62 pANN model: R2 equals 0.82 and Se/Sy equals 0.99.
Figure 184. Graph. Prediction of the FHWA II data using the AMPT pANN and TP-62 pANN models in logarithmic scale.

Figure 185. Graph. Prediction of the FHWA II data using the Hirsch model in arithmetic scale. This figure shows the relationship between the measured dynamic modulus (|E*|) of the Federal Highway Administration (FHWA) II database and |E*| from the Hirsch predictive model. The predicted |E*| is shown on the y–axis in pounds per square inch from 0 to 4 × 106 psi (0 to 2.8 × 107 kPa) in an arithmetic scale. |E*| from measured data is shown on the x–axis in pounds per square inch from 0 to 4 × 106 psi (0 to 2.8 × 107 kPa) in an arithmetic scale. A solid line represents the line of equality (LOE). The dataset align with LOE. On the bottom right of the graph, there are two equations describing the Hirsch model: R2 equals 0.92 and Se/Sy equals 0.30.
Figure 185. Graph. Prediction of the FHWA II data using the Hirsch model in arithmetic scale.

Figure 186. Graph. Prediction of the FHWA II data using the Hirsch model in logarithmic scale. This figure shows the relationship between the measured dynamic modulus (|E*|) of the Federal Highway Administration (FHWA) II database and |E*| from the Hirsch predictive model. The predicted |E*| is shown 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 a logarithmic scale. |E*| from measured data is shown on the x–axis in pounds per square inch from 1 × 103 to 1 × 107 psi (6.9 × 103 to 6.9 × 107 kPa) in a logarithmic scale. A solid line represents the line of equality (LOE). The dataset align with LOE, and the predicted moduli become larger than the measured moduli as the value decreases. There is also a horizontal line at the lowest range of predictions that shows the insensitivity of this model to different input parameters. On the bottom right of the graph, there are two equations describing the Hirsch model: R2 equals 0.92 and Se/Sy equals 0.39.
Figure 186. Graph. Prediction of the FHWA II data using the Hirsch model in logarithmic scale.

Figure 187. Graph. Prediction of the FHWA II data using the Al–Khateeb model in arithmetic scale. This figure shows the relationship between the measured dynamic modulus (|E*|) of the Federal Highway Administration (FHWA) II database and |E*| from the Al–Khateeb predictive model. The predicted |E*| is shown on the y–axis in pounds per square inch from 0 to 4 × 106 psi (0 to 2.8 × 107 kPa) in an arithmetic scale. |E*| from measured data is shown on the x–axis in pounds per square inch from 0 to 4 × 106 psi (0 to 2.8 × 107 kPa) in an arithmetic scale. A solid line represents the line of equality (LOE). The dataset align with LOE, and the predicted moduli become smaller than the measured moduli as the value increases. On the bottom right of the graph, there are two equations describing the Al–Khateeb model: R2 equals 0.89 and Se/Sy equals 0.48.
Figure 187. Graph. Prediction of the FHWA II data using the Al-Khateeb model in arithmetic scale.

Figure 188. Graph. Prediction of the FHWA II data using the Al–Khateeb model in logarithmic scale. This figure shows the relationship between the measured dynamic modulus (|E*|) of the Federal Highway Administration (FHWA) II database and |E*| from the Al–Khateeb predictive model. The predicted |E*| is shown 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 a logarithmic scale. |E*| from measured data is shown on the x–axis in pounds per square inch from 1 × 103 to 1 × 107 psi (6.9 × 103 to 6.9 × 107 kPa) in a logarithmic scale. A solid line represents the line of equality (LOE). The dataset align with LOE, and the predicted moduli become larger than the measured moduli as the value decreases. There is also a horizontal line at the lowest range of predictions that shows the insensitivity of this model to different input parameters. On the bottom right of the graph, there are two equations describing the Al–Khateeb model: R2 equals 0.92 and Se/Sy equals 0.43.
Figure 188. Graph. Prediction of the FHWA II data using the Al-Khateeb model in logarithmic scale.

Figure 189. Graph. Prediction of the NCDOT II data using the modified Witczak and G–GR pANN models in arithmetic scale. This figure shows the relationship between the measured dynamic modulus (|E*|) of the North Carolina Department of Transportation (NCDOT) II database and |E*| from the modified Witczak and dynamic shear modulus binder and gradation–based pilot artificial neural network (G–GR pANN) predictive models. The predicted |E*| is shown on the y–axis in pounds per square inch from 0 to 1 × 107 psi (0 to 6.9 × 107 kPa) in an arithmetic scale. |E*| from measured data is shown on the x–axis in pounds per square inch from 0 to 1 × 107 psi (0 to 6.9 × 107 kPa) in an arithmetic scale. A solid line represents the line of equality (LOE). The predicted moduli from the modified Witczak model align with LOE and become larger than measured moduli as the value increases. The predicted moduli from the G–GR pANN model also align with LOE. On the bottom right of the graph, there are two equations describing the modified Witczak model: R2 equals 0.91 and Se/Sy equals 0.71. Additionally, there are two equations describing the G–GR pANN model: R2 equals 0.97 and Se/Sy equals 0.33.
Figure 189. Graph. Prediction of the NCDOT II data using the modified Witczak and G-GR pANN models in arithmetic scale.

Figure 190. Graph. Prediction of the NCDOT II data using the modified Witczak and G–GR pANN models in logarithmic scale. This figure shows the relationship between the measured dynamic modulus (|E*|) of the North Carolina Department of Transportation (NCDOT) II database and |E*| from the modified Witczak and dynamic shear modulus binder and gradation–based pilot artificial neural network (G–GR pANN) predictive models. The predicted |E*| is shown in pounds per square inch on the y–axis from 1 × 103 to 1 × 107 psi (6.9 × 103 to 6.9 × 107 kPa) in a logarithmic scale. |E*| from measured data is shown on the x–axis in pounds per square inch from 1 × 103 to 1 × 107 psi (6.9 × 103 to 6.9 × 107 kPa) in a logarithmic scale. A solid line represents the line of equality (LOE). The predictions from both predictive models align with LOE, and the predictions from the modified Witczak model become larger than the measured moduli as the value increases. On the bottom right of the graph, there are two equations describing the modified Witczak model: R2 equals 0.98 and Se/Sy equals 0.19. Additionally, there are two equations describing the G–GR pANN model: R2 equals 0.96 and Se/Sy equals 0.27.
Figure 190. Graph. Prediction of the NCDOT II data using the modified Witczak and G-GR pANN models in logarithmic scale.

Figure 191. Graph. Prediction of the NCDOT II data using the AMPT pANN and TP–62 pANN models in arithmetic scale. This figure shows the relationship between the measured dynamic modulus (|E*|) of the North Carolina Department of Transportation (NCDOT) II database and |E*| from the asphalt mixture performance tester pilot artificial neural network (AMPT pANN) and test protocol (TP)–62 pANN predictive models. The predicted |E*| is shown in pounds per square inch on the y–axis from 0 to 1 × 107 psi (0 to 6.9 × 107 kPa) in an arithmetic scale. |E*| from measured data is shown on the x–axis in pounds per square inch from 0 to 1 × 107 psi (0 to 6.9 × 107 kPa) in an arithmetic scale. A solid line represents the line of equality (LOE). The predicted moduli from the AMPT pANN model align with LOE and become smaller than measured moduli as the value increases. The predicted moduli from the TP–62 pANN model also align with LOE. On the bottom right of the graph, there are two equations describing the AMPT pANN model: R2 equals 0.87 and Se/Sy equals 0.63. Additionally, there are two equations describing the TP–62 pANN model: R2 equals 0.95 and Se/Sy equals 0.24.
Figure 191. Graph. Prediction of the NCDOT II data using the AMPT pANN and TP-62 pANN models in arithmetic scale.

Figure 192. Graph. Prediction of the NCDOT II data using the AMPT pANN and TP–62 pANN models in logarithmic scale. This figure shows the relationship between the measured dynamic modulus (|E*|) of the North Carolina Department of Transportation (NCDOT) II database and |E*| from the asphalt mixture performance tester pilot artificial neural network (AMPT pANN) and test protocol (TP)–62 pANN predictive models. The predicted |E*| is shown 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 a logarithmic scale. |E*| from measured data is shown on the x–axis in pounds per square inch from 1 × 103 to 1 × 107 psi (6.9 × 103 to 6.9 × 107 kPa) in a logarithmic scale. A solid line represents the line of equality (LOE). The predicted moduli from the AMPT pANN model align with LOE in the middle range and become smaller than measured moduli as the value increases or decreases. The predicted moduli from the TP–62 pANN model also align with LOE. On the bottom right of the graph, there are two equations describing the AMPT pANN model: R2 equals 0.89 and Se/Sy equals 0.60. Additionally, there are two equations describing the TP–62 pANN model: R2 equals 0.93 and Se/Sy equals 0.27.
Figure 192. Graph. Prediction of the NCDOT II data using the AMPT pANN and TP-62 pANN models in logarithmic scale.

Figure 193. Graph. Prediction of the NCDOT II data using the Hirsch model in arithmetic scale. This figure shows the relationship between the measured dynamic modulus (|E*|) of the North Carolina Department of Transportation (NCDOT) II database and |E*| from the Hirsch predictive model. The predicted |E*| is shown on the y–axis in pounds per square inch from 0 to 1 × 107 psi (0 to 6.9 × 107 kPa) in an arithmetic scale. |E*| from measured data is shown on the x axis in pounds per square inch from 0 to 1 × 107 psi (0 to 6.9 × 107 kPa) in an arithmetic scale. A solid line represents the line of equality (LOE). The dataset align with LOE, and the predicted moduli become smaller than measured moduli as the value increases. On the bottom right of the graph, there are two equations describing the Hirsch model: R2 equals 0.97 and Se/Sy equals 0.47.
Figure 193. Graph. Prediction of the NCDOT II data using the Hirsch model in arithmetic scale.

Figure 194. Graph. Prediction of the NCDOT II data using the Hirsch model in logarithmic scale. This figure shows the relationship between the measured dynamic modulus (|E*|) of the North Carolina Department of Transportation (NCDOT) II database and |E*| from the Hirsch predictive model. The predicted |E*| is shown 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 a logarithmic scale. |E*| from measured data is shown on the x–axis in pounds per square inch from 1 × 103 to 1 × 107 psi (6.9 × 103 to 6.9 × 107 kPa) in a logarithmic scale. A solid line represents the line of equality (LOE). The dataset align with LOE, and the predicted moduli become smaller than measured moduli as the value increases. On the bottom right of the graph, there are two equations describing the Hirsch model: R2 equals 0.97 and Se/Sy equals 0.26.
Figure 194. Graph. Prediction of the NCDOT II data using the Hirsch model in logarithmic scale.

Figure 195. Graph. Prediction of the NCDOT II data using the Al–Khateeb model in arithmetic scale. This figure shows the relationship between the measured dynamic modulus (|E*|) of the North Carolina Department of Transportation (NCDOT) II database and |E*| from the Al–Khateeb predictive model. The predicted |E*| is shown on the y–axis in pounds per square inch from 0 to 1 × 107 psi (0 to 6.9 × 107 kPa) in an arithmetic scale. |E*| from measured data is shown on the x–axis in pounds per square inch from 0 to 1 × 107 psi (0 to 6.9 × 107 kPa) in an arithmetic scale. A solid line represents the line of equality (LOE). The dataset align with LOE, and the predicted moduli become smaller than measured moduli as the value increases. On the bottom right of the graph, there are two equations describing the Al–Khateeb model: R2 equals 0.93 and Se/Sy equals 0.55.
Figure 195. Graph. Prediction of the NCDOT II data using the Al-Khateeb model in arithmetic scale.

Figure 196. Graph. Prediction of the NCDOT II data using the Al–Khateeb model in logarithmic scale. This figure shows the relationship between the measured dynamic modulus (|E*|) of the North Carolina Department of Transportation (NCDOT) II database and |E*| from the Al–Khateeb predictive model. The predicted |E*| is shown 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 a logarithmic scale. |E*| from measured data is shown on the x–axis in pounds per square inch from 1 × 103 to 1 × 107 psi (6.9 × 103 to 6.9 × 107 kPa) in a logarithmic scale. A solid line represents the line of equality (LOE). The dataset align with LOE, and the predicted moduli become smaller than measured moduli as the value decreases or increases. On the bottom right of the graph, there are two equations describing the Al–Khateeb model: R2 equals 0.93 and Se/Sy equals 0.40.
Figure 196. Graph. Prediction of the NCDOT II data using the Al-Khateeb model in logarithmic scale.

Figure 197. Graph. Prediction of the Citgo data using the modified Witczak and G–GR pANN models in arithmetic scale. This figure shows the relationship between the measured dynamic modulus (|E*|) of the Citgo database and |E*| from the modified Witczak and dynamic shear modulus binder and gradation–based pilot artificial neural network (G–GR pANN) predictive models. The predicted |E*| is shown on the y–axis in pounds per square inch from 0 to 6 × 106 psi (0 to 4.1 × 107 kPa) in an arithmetic scale. |E*| from measured data is shown on the x–axis in pounds per square inch from 0 to 6 × 106 psi (0 to 4.1 × 107 kPa) in an arithmetic scale. A solid line represents the line of equality (LOE). The predicted moduli from modified Witczak model align with LOE and become larger than measured moduli as the value increases. The predicted moduli from G–GR pANN model are distributed irregularly along LOE. On the bottom right of the graph, there are two equations describing the modified Witczak model: R2 equals 0.98 and Se/Sy equals 0.64. Additionally, there are two equations describing the G–GR pANN model: R2 equals 0.94, and Se/Sy equals 0.52.
Figure 197. Graph. Prediction of the Citgo data using the modified Witczak and G-GR pANN models in arithmetic scale.

Figure 198. Graph. Prediction of the Citgo data using the modified Witczak and G–GR pANN models in logarithmic scale. This figure shows the relationship between the measured dynamic modulus (|E*|) of the Citgo database and |E*| from the modified Witczak and dynamic shear modulus binder and gradation–based pilot artificial neural network (G–GR pANN) predictive models. The predicted |E*| is shown 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 a logarithmic scale. |E*| from measured data is shown on the x–axis in pounds per square inch from 1 × 103 to 1 × 107 psi (6.9 × 103 to 6.9 × 107 kPa) in a logarithmic scale. A solid line represents the line of equality (LOE). The predictions from the modified Witczak predictive model are greater than the measured moduli along LOE. The predicted moduli from G–GR pANN model are distributed irregularly along LOE and become more overestimated and greater than measured moduli as the value decreases. On the bottom right of the graph, there are two equations describing the modified Witczak model: R2 equals 0.99 and Se/Sy equals 0.26. Additionally, there are two equations describing the G–GR pANN model: R2 equals 0.96 and Se/Sy equals 0.59.
Figure 198. Graph. Prediction of the Citgo data using the modified Witczak and G-GR pANN models in logarithmic scale.

Figure 199. Graph. Prediction of the Citgo data using the AMPT pANN and TP–62 pANN models in arithmetic scale. This figure shows the relationship between the measured dynamic modulus (|E*|) of the Citgo database and |E*| from the asphalt mixture performance tester pilot artificial neural network (AMPT pANN) and test protocol (TP)–62 pANN predictive models. The predicted |E*| is shown on the y–axis in pounds per square inch from 0 to 6 × 106 psi (0 to 4.1 × 107 kPa) in an arithmetic scale. |E*| from measured data is shown on the x–axis in pounds per square inch from 0 to 6 × 106 psi (0 to 4.1 × 107 kPa) in an arithmetic scale. A solid line represents the line of equality (LOE). The predicted moduli from AMPT pANN model are distributed irregularly along LOE. The predicted moduli from TP–62 pANN model are larger than measured moduli along LOE and become slightly smaller as the value increases. On the bottom right of the graph, there are two equations describing the AMPT pANN model: R2 equals 0.88 and Se/Sy equals 0.37. Additionally, there are two equations describing the TP–62 pANN model: R2 equals 0.97 and Se/Sy equals 1.20.
Figure 199. Graph. Prediction of the Citgo data using the AMPT pANN and TP-62 pANN models in arithmetic scale.

Figure 200. Graph. Prediction of the Citgo data using the AMPT pANN and TP–62 pANN models in logarithmic scale. This figure shows the relationship between the measured dynamic modulus (|E*|) of the Citgo database and |E*| from the asphalt mixture performance tester pilot artificial neural network (AMPT pANN) and test protocol (TP)–62 pANN predictive models. The predicted |E*| is shown 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 a logarithmic scale. |E*| from measured data is shown on the x–axis in pounds per square inch from 1 × 103 to 1 × 107 psi (6.9 × 103 to 6.9 × 107 kPa) psi in a logarithmic scale. A solid line represents the line of equality (LOE). The predictions from AMPT pANN predictive model are distributed irregularly along LOE. The predicted moduli from the TP–62 pANN model are greater than measured moduli along LOE. On the bottom right of the graph, there are two equations describing the AMPT pANN model: R2 equals 0.91 and Se/Sy equals 0.48. Additionally, there are two equations describing the TP–62 pANN model: R2 equals 0.99 and Se/Sy equals 0.53.
Figure 200. Graph. Prediction of the Citgo data using the AMPT pANN and TP-62 pANN models in logarithmic scale.

Figure 201. Graph. Prediction of the Citgo data using the Hirsch model in arithmetic scale. This figure shows the relationship between the measured dynamic modulus (|E*|) of the Citgo database and |E*| from the Hirsch predictive model. The predicted |E*| is shown in pounds per square inch on the y–axis from 0 to 6 × 106 psi (0 to 4.1 × 107 kPa) in an arithmetic scale. |E*| from measured data is shown on the x–axis in pounds per square inch from 0 to 6 × 106 psi (0 to 4.1 × 107 kPa) in an arithmetic scale. A solid line represents the line of equality (LOE), and the dataset align with it. On the bottom right of the graph, there are two equations describing the Hirsch model: R2 equals 0.99 and Se/Sy equals 0.11.
Figure 201. Graph. Prediction of the Citgo data using the Hirsch model in arithmetic scale.

Figure 202. Graph. Prediction of the Citgo data using the Hirsch model in logarithmic scale. This figure shows the relationship between the measured dynamic modulus (|E*|) of the Citgo database and |E*| from the Hirsch predictive model. The predicted |E*| is shown 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 a logarithmic scale. |E*| from measured data is shown on the x–axis in pounds per square inch from 1 × 103 to 1 × 107 psi (6.9 × 103 to 6.9 × 107 kPa) in a logarithmic scale. A solid line represents the line of equality (LOE), and the dataset align with it. On the bottom right of the graph, there are two equations describing the Hirsch model: R2 equals 0.99 and Se/Sy equals 0.09.
Figure 202. Graph. Prediction of the Citgo data using the Hirsch model in logarithmic scale.

Figure 203. Graph. Prediction of the Citgo data using the Al–Khateeb model in arithmetic scale. This figure shows the relationship between the measured dynamic modulus (|E*|) of the Citgo database and |E*| from the Al–Khateeb predictive model. The predicted |E*| is shown on the y–axis in pounds per square inch from 0 to 6 × 106 psi (0 to 4.1 × 107 kPa) in an arithmetic scale. |E*| from measured data is shown on the x–axis in pounds per square inch from 0 to 6 × 106 psi (0 to 4.1 × 107 kPa) in an arithmetic scale. A solid line represents the line of equality (LOE). The dataset align with LOE, and the predicted moduli become smaller than measured moduli as the value increases. On the bottom right of the graph, there are two equations describing the Al–Khateeb model: R2 equals 0.93 and Se/Sy equals 0.36.
Figure 203. Graph. Prediction of the Citgo data using the Al-Khateeb model in arithmetic scale.

Figure 204. Graph. Prediction of the Citgo data using the Al–Khateeb model in logarithmic scale. This figure shows the relationship between the measured dynamic modulus (|E*|) of the Citgo database and |E*| from the Al–Khateeb predictive model. The predicted |E*| is shown 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 a logarithmic scale. |E*| from measured data is shown on the x–axis in pounds per square inch from 1 × 103 to 1 × 107 psi (6.9 × 103 to 6.9 × 107 kPa) in a logarithmic scale. A solid line represents the line of equality (LOE). The dataset align with LOE, and the predicted moduli become smaller than measured moduli as the value increases or decreases. On the bottom right of the graph, there are two equations describing the Al–Khateeb model: R2 equals 0.97 and Se/Sy equals 0.17.
Figure 204. Graph. Prediction of the Citgo data using the Al-Khateeb model in logarithmic scale.

 

 


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.
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