# Glass Beads for Road Markings: Surface Damage and Retroreflection Decay Study
## 3 Methodology
### Service Life Prediction  
Prediction of the point of failure and, consequently, the service life of RM is difficult, and no universal formula has been found despite numerous attempts [26]. One of the more reliable methods is the fitting of R\({}_{\rm L}\) decay data to an exponential curve [57]. Because the conditions during the tests were stable, without clearly defined periods of more and less heavy damage (like those occurring, for example, during summer and winter), multiple piecewise analyses were not needed [58].  
For service life prediction from the abrasive testing was used Equation (1), where \(R_{L}\)--retroreflectivity (in mcd/m\({}^{2}\)/lx) at specified number of drum rotations \(x\), \(R_{\rm o}\)--maximum calculated R\({}_{\rm L}\) (in mcd/m\({}^{2}\)/lx), \(e\)--the base of natural logarithm, \(C\)--dimensionless exponential decay coefficient per specified number of rotations, and \(x\)--number of drum rotations. The use of \(R_{\rm o}\) instead of the maximum measured R\({}_{\rm L}\) was appropriate within this dataset, where the utilisation of the maximum measured value would have led to completely inaccurate service life predictions, departing too far from the measured values; such choices, which to people not familiar with RM may appear to be 'data massaging',  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Sample** & **Standard** & **70\% Premium + 30\% High Index** & **High Index** \\ \hline Sample Code & \(SF^{t}\) & \(SH^{t}\) & \(HI^{t}\) \\ \hline Glass beads: & Size & & \\ Standard (type \(SF\)) & 600–850 μm & 100\% & – & – \\ Premium (type \(SP\)) & 600–1400 μm & – & 70\% & – \\ High index (type \(HI\)) & 300–850 μm & – & 30\% & 100\% \\ \hline \hline \end{tabular}
\end{table}
Table 3: Turntable evaluation: glass bead mixtures (weight percentages).  
are often necessary in this field and do not affect the reliability and truthfulness of the results. The data fit coefficient \(\mathrm{R}^{2}\) was also calculated. To remain consistent with the recommended minimum \(\mathrm{R_{L}}\)[59; 60], its drop to \(150\,\mathrm{mcd/m^{2}/lx}\) was considered the limit of usable service life.  
\[R_{L}=R_{a}e^{Cx} \tag{1}\]  
Unfortunately, the testing facility operating the turntable set the failure limit at a very high level of \(500\,\mathrm{mcd/m^{2}/lx}\), which forced the utilisation of a linear decay prediction only, despite possible errors mainly associated with the absence of sufficient data and the initial measurement inaccuracies caused by the phenomenon of the initial \(\mathrm{R_{L}}\) increase [61; 62]. Consequently, for the turntable testing, service life was estimated according to Equation (2), where \(R_{L}\)--retroreflectivity (in \(\mathrm{mcd/m^{2}/lx}\)) at specific number of tyre passes \(p\), \(D\)--dimensionless linear decay coefficient for the specified number of tyre passes, \(p\)--number of tyre passes, and \(R_{m}\)--maximum measured \(\mathrm{R_{L}}\) (in \(\mathrm{mcd/m^{2}/lx}\)). The \(\mathrm{R}^{2}\) was not calculated because it was meaningless with the available dataset, in which the \(\mathrm{R_{L}}\) varied at the beginning because of the aforementioned initial increase phenomenon.  
\[R_{L}=Dp+R_{m} \tag{2}\]