## 3 Case Study Calculation
### Pavement Unewemess Deterioration  
The progression of unevenness deterioration can be mathematically described using degradation models. These models serve as the cornerstone of asset valuation, as they can predict the technical condition of individual assets within a road network.  
Mathematically derived degradation functions are employed to predict pavement serviceability throughout its service life. These functions express changes in surface characteristics over time or, preferably, in relation to load cycles. The general shape of the degradation function illustrates the relationship between the relative value of a surface characteristic and either time or the number of load repetitions. Degradation models can be derived through experimental testing on an accelerated pavement testing (APT) facility shown in Figure 5, which simulates traffic loads and climatic parameters at a 1:1 ratio on a test pavement section. Alternatively, they can be developed based on long-term measurements of existing pavements using data archived in road inventories collected over the past 20 years. In our research, we applied both methods, so the degradation functions presented in this study were fitted using data obtained from APT experiments and long-term pavement monitoring, with model accuracy assessed through standard  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameter** & **AC16-L Recyclate** & **AC16-L** \\ \hline A0 & \(-\)38.2918 & \(-\)25.5616 \\ A1 & \(-\)10.9971 & \(-\)8.0090 \\ b & \(-\)0.0909 & \(-\)0.1249 \\ \(\varepsilon\)6 & 93.85 & 114.61 \\ Structural Life Expectancy (DAL 106) & 1.1 & 1.4 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Fatigue parameters of different mixtures are shown in Figures 3 and 4.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multicolumn{5}{c}{**Samples of Complex Modulus for Different Temperatures (MPa)**} \\ \hline
**Frequency (Hz)** & \(-\)**10 \({}^{\circ}\)C** & **0 \({}^{\circ}\)C** & **10 \({}^{\circ}\)C** & **15 \({}^{\circ}\)C** & **27 \({}^{\circ}\)C** \\ \hline
1 Hz & 14,523 & 10,920 & 7059 & 4685 & 1599 \\
5 Hz & 16,450 & 13,259 & 9169 & 6719 & 2920 \\
10 Hz & 17,388 & 14,250 & 9998 & 7575 & 3565 \\
15 Hz & 17,519 & 14,659 & 10,428 & 8019 & 3939 \\
20 Hz & 17,751 & 15,121 & 10,800 & 8436 & 4343 \\ \hline \end{tabular}
\end{table}
Table 3: Complex modulus of AC11 measured at different frequencies.  
regression diagnostics such as \(\mathrm{R}^{2}\) values to ensure adequate representation of observed deterioration trends.  
Measurements of transverse and longitudinal unevenness, skid resistance, and macro-texture were taken every 100,000 load cycles. Figure 6 illustrates the evaluation of transverse unevenness (RUT).  
Unevenness is measured using profile levelling combined with a Bibus VX element scanner, which creates a highly accurate 3D point cloud scan (with precision up to 0.1 mm). Before each scanner measurement, contrast powder paint is applied to the pavement surface to enhance imaging, and positioning targets are placed to enable the handheld scanner to determine the point cloud's position. The scanner outputs both transverse and longitudinal unevenness measurements, as shown in Figures 6 and 7.  
The mathematical expression of the derived transverse unevenness is given in Figure 8.  
Figure 5: APT facility.  
Figure 6: Transverse evaluation of track depth measured by the Bibus scanner (RUT).