# Glass Beads for Road Markings: Surface Damage and Retroreflection Decay Study
## 1 Introduction  
One of the basic yet highly effective safety features on majority of paved roads are road markings (RM). These special types of industrial maintenance coatings must be considered systems comprising a base (paint) layer and a retroreflective layer, and only their cooperation furnishes the functional RM [1]. While many materials can be used for the base layer [2], the retroreflective layer always consists of glass beads (GB) that are partially embedded in it. GB protect the base layer from abrasion [3] and simultaneously provide retroreflectivity, which can be perceived by drivers at night when other visual cues are limited [4]. Retroreflectivity, measured through coefficient of retroreflected luminance (R\({}_{\text{L}}\)) and expressed in the unit of millicandela per square metre per lux (mcd/m\({}^{2}\)/lx), is the key parameter defining quality and service life of RM, because in vast majority of cases it fails first and indicates the need for their renewal [5]. For road safety, retroreflectivity is critical because the number and severity of accidents that occur in darkness is disproportionally higher as compared to daytime, despite much lower traffic loads [6]. Indeed, studies have shown that increase in R\({}_{\text{L}}\) is associated with lower accident rate on unlit roads at night inthe absence of other interfering factors [7; 8], even though some researchers have pointed out weaknesses of such analyses [9]. The influence of RM on driver behaviour and thus on road safety was recently reviewed [10]. Interestingly, eye movements of drivers were also preliminarily reported as being correlated with \(\mathrm{R_{L}}\)[11]; sadly, no further exploration of this interesting issue has been reported so far. Because the visibility of RM depends on the contrast ratio [12; 13], it is critical not only for human drivers, but also for machine vision technology that is utilised for advanced driver assistance systems (ADAS) and thus for the emerging technology of automated vehicles [14; 15; 16; 17]. The quality of RM, particularly \(\mathrm{R_{L}}\) and the resulting contrast ratio, have been repeatedly associated with the reliability of ADAS depending on machine vision [18; 19; 20; 21; 22]; in contrast, poor quality of RM has been reported to have contributed to several recent severe crashes of vehicles travelling in autonomous mode [23]. The recent report that discarded the importance of \(\mathrm{R_{L}}\) and instead found a sole correlation of machine vision reliability with daytime visibility did not consider that at night the \(\mathrm{R_{L}}\) can increase the contrast ratio [24]. Indeed, research has shown that the contrast ratio at night was consistently higher than during daytime, which was likely due to its enhancement through \(\mathrm{R_{L}}\)[25]. While researchers were often analysing various environmental and traffic parameters in an attempt to find the optimum performance model for RM [26; 27], only very small part of their attention was given to GB, which appeared to be treated as ingredients of RM so uniform that no particular consideration was needed. Furthermore, the vast majority of reports ignored the possibility of using GB other than those with refractive index (RI) of 1.5 [28; 29]; however, other types of GB with higher RI are readily available and can furnish exceptional \(\mathrm{R_{L}}\)[30; 31; 32; 33; 34]. The issue of \(\mathrm{R_{L}}\) loss due to GB damage has been ignored in the literature; the theoretical calculations of \(\mathrm{R_{L}}\) and GB embedment in the base layer assumed that the surface of the GB was perfect [35; 36]. Recently, GB damage under vehicular traffic was addressed for the first time by us [37], prompted by earlier results from field measurements of \(\mathrm{R_{L}}\): after winter, despite the presence of GB properly embedded in the paint layer, the \(\mathrm{R_{L}}\) was low, albeit only in the direction of the traffic flow [38].