## 4 Test Site Results: Statistical Analysis
### Results Analysis
However, an evaluation of glass beads' size and gradation beyond the granulometric curves or even the quantification of different beads' gradation on retroreflectivity was not found in the literature. Therefore, the evaluation of the coefficients related to \(\text{C}_{\text{U}}\) and \(\text{C}_{\text{C}}\) is important to understand the grain size distribution contribution to retroreflectivity. Since there is an interaction between \(\text{C}_{\text{U}}\) and \(\text{C}_{\text{C}}\), their impact on retroreflectivity must be evaluated simultaneously. A higher coefficient of uniformity indicates a large range of sizes for glass beads, while higher coefficient of curvature indicates the equivalent distribution of several particles' sizes. The increase in retroreflectivity related to higher \(\text{C}_{\text{U}}\) and \(\text{C}_{\text{C}}\) values shows the importance of selecting well graded glass beads. The improvement of retroreflectivity occurs due to the distribution of several glass bead sizes on the pavement markings' surface since the larger particles fall on the paint surface first, and then the smaller particles fill the voids between the larger beads, which expands the area of the markings covered with glass beads. Thus, there is a higher area available to reflect light and improve the night visibility of pavement markings [10]. Supposing a glass bead sample with \(\text{X}_{\text{CU}}\) = 1.700, an increase in \(\text{X}_{\text{CC}}\) by 0.1 will improve the retroreflectivity, on average, by 8.71%. The difference between the \(\text{R}_{\text{L}}\) before (\(\text{X}_{\text{CC}_{1}}=1.0\)) and after the \(\text{C}_{\text{C}}\) increase (\(\text{X}_{\text{CC}_{2}}=1.1\)) may be calculated as \(\exp\left[(\theta_{4}\times\text{X}_{\text{CU}}+\theta_{5}\times\text{X}_{ \text{CC}_{2}}-\theta_{8}\times\text{X}_{\text{CU}}\times\text{X}_{\text{CC} _{2}})-(\theta_{4}\times\text{X}_{\text{CU}}+\theta_{5}\times\text{X}_{\text{ CC}_{1}}-\theta_{8}\times\text{X}_{\text{CU}}\times\text{X}_{\text{CC}_{1}}) \right]-1=\exp\left[(6.652\times 1.700+9.055\times 1.1-4.841\times 1.700\times 1.1)-(6.652\times 1.700+9.055\times 1.0-4.841\times 1.700\times 1.0)\right]-1=8.71\%\). Regarding the paint's characteristics, the effect of the variable \(\text{X}_{\text{v,sol}}\) on the retroreflectivity is analyzed considering the different time periods in which the retroreflectivity was measured. An increase of one unit in the volume of solids leads to an average decrease in retroreflectivity of 0.23% when measured within 20 days after the application of the pavement marking. However, this decrease is not statistically significant (\(p\)-value = 0.404). The volume solids of paints are associated with pavement markings' durability. The estimates of the parameters of the time intervals obtained at the model adjustment show that the decrease in retroreflectivity over time depends on the volume solids. Supposing a pavement marking using a paint with \(\text{V}.\text{sol}=62.0\), the retroreflectivity decreases, on average, by 24.38% (\(\exp\left(\theta_{4}\times\text{X}_{\text{t}2}+\theta_{7,2}\times\text{X}_{ \text{t}2}\times\text{X}_{\text{V},\text{sol}}\right)-1=\exp(-5.850\times 1+0.0 90\times 1\times 62)-1=0.2438) at the time interval \(\text{X}_{\text{t,2}}\)= (20, 40) when compared to the initial time interval. Analogously, the time interval \(\text{X}_{\text{t,3}}\) = (40, 60) presents, on average, 43.50% lower retroreflectivity values. Regarding the other time intervals, the reduction in retroreflectivity is, on average, 62.36% for \(\text{X}_{\text{t,4}}\) = (60, 80], 63.51% for \(\text{X}_{\text{t,5}}\) = (80,100], 74.08% for \(\text{X}_{\text{t,6}}\) = (100,200], 80.30% for \(\text{X}_{\text{t,7}}\) = (200,300], and 74.64% for \(\text{X}_{\text{t,8}}\) = (300,800). The volume solids is an important characteristic because it evaluates the percentage of paint's volume without the volatile fraction, thus representing the percentage of the dried paint's thickness compared to the wet thickness.