## 6 FWD Back-Calculation and Frequency-Temperature Correction  
The layered elastic analysis program LEAF in the BAKFAA back-calculation software [33] was employed in this study to perform back-calculation of the FWD data obtained at the four test road sections. Because the surface layers such as OGAC, PAC, and SMA were functional layers and overly thin, they were combined with DGAC to form a single layer for the convenience of back-calculation and improvement of convergence. In Sections 1 and 2, the OGAC was integrated with DGAC to form a single layer; the OGAC and SMA in Section 3 were integrated with DGAC to form a single layer; and the PAC and SMA of Section 4 were integrated with DGAC to form a single layer. Figure 12 illustrates the adjusted cross-sections used in the back-calculation. This study considered the loading duration of the FWD as 29 ms, corresponding to an approximate frequency of 17.24 Hz [34]. Since FWD tests were conducted at different temperatures and the  
Figure 11: Dynamic modulus master curve. Figure 12: Schematic of layers used in back-calculation analysis. modulus of asphalt material layer is related to temperature, the back-calculated modulus of the asphalt layer could not be directly compared with those obtained by the dynamic modulus test. Therefore, the back-calculated modulus values of asphalt layer had to undergo frequency-temperature correction. This study employed the frequency-temperature shift factors obtained by the dynamic modulus test to perform temperature correction for back-calculation at various temperatures. Figure 13 illustrates the frequency-temperature correction flowchart, while Figure 14 presents a schematic plot of the frequency-temperature correction. Firstly, FWD back-calculation at different temperatures was performed to obtain the modulus of the asphalt material layer represented by the dots in Figure 14. This study used the temperature from the middle of the asphalt material layer and the temperature was evaluated by the temperature model as shown in Equation (3). According to the determined temperature, the frequency-temperature shift factor can be obtained through the dynamic modulus test (Equations (5) and (6)). The back  
Figure 15 illustrates a comparison of the dynamic modulus master curve of DGAC and the back-calculated modulus of that layer with frequency-temperature correction. The solid line is the master curve of DGAC obtained from the dynamic modulus test, while the dotted lines indicate the \(\pm\)30% range of the master curve. Table 6 summarizes the percentage of the back-calculated DGAC results that fell within this \(\pm\)30% range. The results show that the back-calculated modulus of DGAC with frequency-temperature correction had more than 70% within the \(\pm\)30% range, except for cross-section 1. Figure 16 shows a comparison of the dynamic modulus master curve of the BTB and the modulus values obtained by FWD back-calculation with frequency-temperature correction. Table 7 presents the percentage of back-calculated BTB results that fell within the \(\pm\)30% range of the dynamic modulus master curve. The results show that more than 85% of back-calculated moduli fell within this range. These results indicate that the proposed frequency-temperature correction can efficiently correct the FWD back-calculated modulus of asphalt material at different temperatures. Figure 15: _Cont._  
Figure 15: Comparison between the dynamic modulus master curve and FWD back-calculated results for DGAC layer. \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & \multicolumn{2}{c}{**DGAC**} & & \\ \hline  & **Section 1** & **Section 2** & **Section 3** & **Section 4** \\ \hline Number of data & 66 & 66 & 66 & 66 \\ Number of data within \(\pm\)30\% & 30 & 48 & 56 & 55 \\ Percentage of data within the range & 45.45\% & 72.73\% & 84.85\% & 83.33\% \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Range distribution of the back-calculated results for the DGAC layer. _Appl. Sci._**2020**, _10_, 132