Problem $2_{?}$

For the layered elastic system shown below and given that each tire is inflated to $90$ psi and has a

radius of $5$ inches,

$E_1=300ksi{v}_1=0\mathrm{.}35$

$E_2=40$ksi,$v_2=0\mathrm{.}40$

$E_3=20$ksi,$v_3=0\mathrm{.}45$

$E_4=10$ksi,$v_4=0\mathrm{.}50$

a$)$ Determine and plot the tensile strain at the bottom of the asphalt concrete layer

$(z=7\mathrm{.}99$ inch$)$ for the following radial offsets: $0,2\mathrm{.}5,5,8,11,13\mathrm{.}5,16,20,24,$ and $88$ inch. $A$

point having a radial offset of zero is located under the center of the far left tire.

b$)$ Determine and plot the compressive strain on the top of the subgrade $(z=28\mathrm{.}01)$ for the

following radial offsets: $0,2\mathrm{.}5,5,8,11,13\mathrm{.}5,16,20,24,$ and $88$ inch. A point having a radial

offset of zero is located under the center of the far left tire.

c$)$ Comment on your results regarding the location of the maximum tensile strain and the

maximum compressive strain.

d$)$ Using the Asphalt Institute fatigue cracking and rutting failure criteria presented in Huang

$(2004),$ page $98($refer to Equations $3\mathrm{.}6$ and $3\mathrm{.}7,$ respectively, in the following page$),$ determine

the life of the pavement structure $($in years$)$ if the number load repetitions is $50,000$ per year.