HW $3$ Flexible Pavement Design $(20$ points$)$: You are designing a pavement with a $20-$year design ESAL value of $20$ million and a subgrade Mr of $7\mathrm{.}5$ ksi $.$ Local requirements include $\backslash (95\backslash \%\backslash )$ reliability, a standard deviation of $0\mathrm{.}35,$ and a total serviceability loss of $2$ PSI. Prepare the following pavement designs:

a$)$ Design $1$: Full$-$depth asphalt $($Mr$1=380$ksi$)$

b$)$ Design $2$: Asphalt over aggregate base $($Mr$1=380$ksi, Mr$2=21$ksi$)$

c$)$ Design $3$: Asphalt over aggregate base over subbase $($Mr$1\backslash (=380\backslash$mathrm$\{$ksi$\},\backslash$mathrm$\{$Mr$\}2=21\backslash$mathrm$\{$ksi$\}\backslash ),$ Mr$3=11$ksi$)$

d$)$ Given the following unit weights and unit costs per ton of material, which design is the most cost$-$effective per lane mile? $($Assume a $12-$ft lane and an excavation cost of $\backslash (\backslash$$ $5\backslash )$ per cubic yard.$)$