PROBLEM SET $2.$ ASPHALT VOLUMETRIC METHOD $(30$ pts$)$

To determine the optimum asphalt binder content, mixtures were prepared using four different asphalt binder contents and compacted to $\backslash (\backslash$mathrm$\{$N$\}\_\{\backslash$text $\{$des $\}\}\backslash )$ using the Superpave gyratory compactor. The volumetric results on the compacted samples are as follows:

Based on the information given for each binder content, calculate and plot the following. To receive full credit, you must show calculations and cite which equations were used. Create three scatter plots, each with the appropriate x $-$axis $($percent binder$)$ and y $-$axis scale $($listed below$)$ on the plots.

$-$ Air voids $(4$ pts$)$

$-$ The voids in the mineral aggregate $($VMA$)(4$ pts$)$

$-$ The voids filled with asphalt $($VFA$)(4$ pts$)$

Determine the optimum binder content for this mixture $(4$ pts$).$ Determine the VMA and VFA at the optimum binder content $(4$ pts $).$ Determine the Dust$-$to$-$Effective Binder Ratio, D$/$B$,$ at the optimum binder content if the gradation shows $\backslash (4\mathrm{.}5\backslash \%\backslash )$ passing the $\backslash$#$200$ sieve $(5$ pts $).$ Based on the volumetrics determined, explain if this mixture meet the requirements for a $19-$mm nominal maximum size mixture to be placed on a road designed for $20$ million ESALs? $(5$ pts$)$