# Effects of Vehicular Speed on the Assessment of
## 2 Materials and Methods
### Road Surface Profiles Classification--ISO 8608  
To evaluate the road surface profiles classification according to ISO 8608 standard, the Power Spectral Density (PSD) was calculated using Welch periodogram, which is a method used for the estimation of the power of a spectral signal, based on the use of the Fast Fourier Transform (FFT). The two steps that characterize this method consist in splitting up the signal into overlapping segments and, then, windowing them with an appropriate window function. In the performed analysis,  
\begin{table}
\begin{tabular}{c c c} \hline
**Road** & **Total Length (km)** & **Number of Sections (320 m Length)** \\ \hline
01 & 28.8 & 90 \\
02 & 42.8 & 134 \\
03 & 66.2 & 207 \\
04 & 60.8 & 190 \\
**Total** & **198.6** & **621** \\ \hline \end{tabular}
\end{table}
Table 1: Length of examined roads and number of sections.  
the Hanning window and an overlapping zone equal to 50% were used. Then, the smoothing process described in the ISO 8608 standard was performed.  
Finally, through the implementation of a Matlab code, the fitted PSD was evaluated by means of the general formula Equation (3):  
\[G_{d}(n)=G_{d}(n_{0})\left(\frac{n}{n_{0}}\right)^{-w} \tag{3}\]  
where \(G_{d}\) is the displacement PSD [m\({}^{3}\)], \(n_{0}=0.1\) cycles/m is the reference spatial frequency and \"\(w\)\" is the exponent of the fitted PSD, also known as waviness (Figure 1).  
As stated by [PERSON] and [PERSON] (2016), recent road network extensive measurements, performed in some countries like Sweden ([PERSON], 2016), have revealed that for most of the roads waviness values vary between 1.5 and 3.5 with a mean value close to 2.5. Considering all the measured path of 320 m (both left and right), it was found that, for the examined profiles, the mean value of the exponent \(w\) is 3.16.  
As specified by [PERSON] and [PERSON] (2016), the two parameters that define the fitted PSD, \(G_{d}(n_{0})\), and \(w\), are independent and in particular, the second one provides information about the wavelength distribution in the spatial frequency range of interest. In fact, values greater than 2 mean that long waves are prevalent, while if the waviness (\(w\)) value is lower than 2, the short wavelengths are predominant.  
Based on the values of the \(G_{d}(n_{0})\). parameter, as found for all the examined profiles, they were classified as belonging to one of the classes (from A to H) provided by ISO 8608.  
Usually, paved road profiles hardly belong to class worse than D because road agencies set intervention thresholds (using specific ride quality index like IRI) above which optimal conditions are restored. For this reason, the ISO classes that in general should be taken into account are the first four. As is going to be shown in detail in the next section, the real roads profiles analyzed in this study belong to class A (_very good_), B (_good_), C (_average_) and D (_poor_).  
The classification proposed by ISO 8608 presents critical aspects because it does not take into account the speed at which vehicles travel on the road. Thus, it does not properly consider the different vibration levels affecting road users at different speeds, while this fact influences drivers ride quality perception. This aspect can be faced by evaluating pavement performances related to comfort levels, through both measurements inside vehicles or using simulation models. In this way a global assessment of the vertical acceleration induced on road users, due to the presence of irregularities  
Figure 1: Smoothed and Fitted Power Spectral Density (PSD) according to ISO 8608.  
on the pavement surface, can be provided. One of the available simulation models is going to be described in the next section.