## 3 Material Characterization Results
### Glass Bead Characterization  
The glass beads' size distribution and shape characteristics were evaluated according to the procedure of AASHTO R98 ([PERSON], 2016). Figures 5-7 present the grain size distributions, thickness-to-length distributions, and sphericity distributions, respectively, for each glass bead composition and application rate. Figure 5: Grain size distributions of glass beads. Figure 6: Thickness-to-length ratio (b/l) distributions of glass beads. The size distributions of the glass beads (Figure 5) present a large variation due to their gradations or manufacturers. The glass bead compositions \(\delta\)-7030T, \(\delta\)-5050T, and \(\delta\)-3070T present larger particles than the other compositions. Regarding the other compositions, \(\beta\)-100 Br and \(\omega\)-100 Br present the smallest particles, but all the compositions present similar size distributions. The distributions of the thickness-to-length ratio (b/I) in Figure 6 show that compositions \(\delta\)-7030T, \(\delta\)-5050T, and \(\delta\)-3070T present the same distribution of thickness-to-length ratio, with around 78% of round particles (b/I higher than 0.85), as required by AASHTO R98 [26]. The compositions \(\varepsilon\)-7030 Br and \(\omega\)-100 Br present 70% and 65% of particles with b/I higher than 0.85, while the other compositions present less than 50% of round particles. Regarding the sphericity distribution in Figure 7, all glass beads present poor shape properties considering the threshold of sphericity required by AASHTO R98 [26] to classify the particles as round (SPHT \(>\) 0.93), since all the compositions present less than 10% of round particles. Therefore, the lack of sphericity that all these glass beads present may lead to low retroreflectivity values when they are applied on the pavement markings [8,33]. Since the results of the glass bead characterization are distribution curves, the analysis of results is mainly qualitative. However, to compare the glass beads' composition and use their characteristics as variables in the statistical model, some parameters were obtained from the distributions of the grain size, thickness-to-length ratio, and sphericity to discretize the results. The size distribution of glass beads was evaluated considering whether the composition is well graded, or not, by the coefficients of uniformity (C\({}_{\text{U}}\)) and curvature (C\({}_{\text{C}}\)) commonly employed in soil mechanics for analyzing granular materials [34,35]. The coefficient of uniformity is defined by Equation (1):  
\[\text{C}_{\text{U}}=\frac{\text{D}_{\text{I}0}}{\text{D}_{60}}, \tag{1}\]  
where D\({}_{\text{I}0}\) and D\({}_{\text{I}0}\) correspond to the diameter (particle size) at which 10% and 60% of particles are smaller, respectively. The coefficient of uniformity (C\({}_{\text{U}}\)) evaluates the uniformity of a granular material. The material is considered uniform if C\({}_{\text{U}}\) is lower than 2, i.e., the particles' size distribution is concentrated at one size range. The coefficient of curvature (C\({}_{\text{C}}\)) is described by Equation (2):  
\[\text{C}_{\text{C}}=\frac{\text{D}_{\text{I}0}^{2}}{\text{D}_{\text{I}0}\times \text{D}_{60}}, \tag{2}\]  
where D\({}_{\text{I}0}\) corresponds to the diameter (particle size) at which 30% of particles are smaller. The coefficient of curvature (C\({}_{\text{C}}\)) identifies whether the particles' size distribution of the granular  
Figure 7: Sphericity (SPHT) distributions of glass beads. materials is continuous or not, i.e., presents a proportional percentage of several particle sizes. The material presents a continuous distribution if C\({}_{\text{C}}\) is between 1 and 3. Continuous distribution characterizes well-graded sands and aggregates because it presents particles with several diameters that cause interlock and package between grains since the smaller particles will fill the voids between the larger particles [36].