Consider the following $3-$layer pavement structure: Asphalt concrete surface course $($AC$)$ with a resilient modulus of $0\mathrm{.}5$ million psi, and a poisson's ratio of $0\mathrm{.}4$ ; a crushed stone base course $(BC)$ with a resilient modulus of $18000$ and a poisson's ratio of $0\mathrm{.}35$ ; and a silty subgrade with a resilient modulus of $5000,$ and a poisson's ratio of $0\mathrm{.}25.$ Assume reasonable values for all other parameters.

The loading is done by a $18-$kip single axle load with dual tires. Assume that the dual tire load is applied at the same point $(9000lb).$ Find all parameters underneath this load.

Perform the analysis for $3$ base course thicknesses $,$ and $24$ inches$),$ and $3$ AC thicknesses $(3,6,$ and $9$ inches$),$ which means a total of $9$ analyses. Each time, record the maximum values of the following parameters $($i$)$ the horizontal tensile strain at the bottom of the asphalt, and $($ii$)$ the vertical compressive strain on the subgrade. Present the following:

$(1)$ Results in tabular form

$(2)$ Plot subgrade strain $($y$-$axis$)$ versus $AC$ thickness $($x$-$axis$)$ and generate three curves one for each BC thickness

$(3)$ On the same page, plot the horizontal tensile strain at the bottom of the asphalt $($y$-$axis$)$ versus the $AC$ thickness $($x$-$axis$).$ The $AC$ scale should be the same as the AC scale used in $(2).$

$(4)$ Say you want to limit the subgrade strain to $4{10}^{-4}$ inch$/$inch$.$ What are the various design alternatives i$.$e$.$ the combination of $AC$ and $BC$ thicknesses that will achieve this objective.