## 5 Results
### The IRI Approach for Gravel Pavement  
Methodically, the velocities of SM and USM in a vertical direction of the Golden car model are determined and used for calculating the IRI value (Equation (8)). The second column in Table 1 shows the IRI values of the different states of the gravel pavement at a driving speed of 80 km/h, as provided in the ASTM [80]. Under the deteriorating road pavement condition, the IRI values change inconsistently; the highest IRI value (7.28 m/km) is obtained under PS-2 condition, while the lowest IRI value (5.51 m/km) is obtained under PS-3 condition. This is not in line with the visually observed (Figure 3) trends of pavement roughness deterioration from PS-1 to PS-3. To analyse the resulting distribution of IRI values concerning pavement condition, the vertical velocities of SM and USM were calculated. Table 1 shows the calculated RMS values of the SM and USM velocities in vertical directions. The RMS is calculated as follows:  
\[\text{RMS}_{z_{i}}=\big{[}\frac{1}{T}\int_{0}^{T}\dot{z_{i}}^{2}\,dt\big{]}^{ 1/2}, \tag{15}\]  
where \(T\) is the duration of the evaluated road profile (s) and \(i\) is the indicator for the SM or USM depending on the calculated parameter (\(\dot{z}_{sm}\) or \(\dot{z}_{ussm}\)). The values presented in Table 1 show that the RMS of the SM velocity increases along with consistent deterioration of the road pavement condition (from PS-1 to PS-3), but the RMS value of the USM velocity is unevenly distributed (such as the IRI values). The SM movement is inhibited by suspension elements (mainly dampers). At the same time, the USM interacts with the gravel pavement through the types, for which stiffness (\(k_{t}\)) is around ten times higher than that of suspension (\(k_{s}\)). As a result, the USM moves faster than the SM and has a more significant effect on calculating the IRI. These results indicate that the calculated IRI values are not suitable for analysing gravel pavements in which the wavelengths of the dominant length in the mega-texture area are formed. Similar results of higher sensitivity of wheel holder vibrations to the IRI value as compared with vehicle frame vibrations have been captured following measurements of reconstructed urban roads with cobblestone and asphalt pavements in [85]. The IRI values of the gravel pavement are determined by simulating a quarter car model as a vehicle moving at a speed of 80 km/h. Due to comfort and sufficient stability, the tested road section of gravel pavement is characterised by lower driving speeds. Therefore, the IRI values were calculated for a broader (30-90 km/h) speed range (Figure 5a). \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Pavement State**} & \multirow{2}{*}{**IRI, m/km**} & \multicolumn{2}{c}{**Velocity RMS, m/s**} \\ \cline{3-4}  & & **SM** & **USM** \\ \hline PS-1 & 6.33 & 0.0283 & 0.1821 \\ \hline PS-2 & 7.28 & 0.0313 & 0.2303 \\ \hline PS-3 & 5.51 & 0.0378 & 0.1530 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The estimated IRI values of the analysed gravel pavement. The received IRI values are significantly higher at lower speeds because the same road section is covered over a longer time duration, leading to higher accumulated suspension displacement in the IRI calculation. In this case, the distribution value at a given speed under a certain gravel pavement condition rather than the IRI absolute value is analysed. Figure 5a shows that, at lower speeds (30 and 40 km/h), the IRI values increase along with road pavement deterioration from PS-1 to PS-3. At speeds above 45 km/h, the distribution of the IRI values changes; the values of IRI\({}_{\text{PS-3}}\) corresponding to the worst gravel pavement condition become lower than the values of IRI\({}_{\text{PS-2}}\), whereas, at speeds above 55 km/h, the values of IRI\({}_{\text{IPS-3}}\) are the same as the worst gravel pavement condition and become lower than that of IRI\({}_{\text{IPS-1}}\) (under the best-quality gravel pavement state).