$(50$ total points$)$ Using the AASHTO flexible pavement design procedure, design a flexible pavement for an interstate highway. The projected $30-$year design traffic in the truck lane is $5{10}^6$ ESALs. The resilient modulus of the asphalt concrete has been determined to be $400$ ksi $.$ The local state agency is recommending a high reliability $(90\%)$ and a maximum change in present serviceability of $2\mathrm{.}0$ for this design since it is a critical truck route. A crushed stone material for the base is going to be used for one potential design alternative. It has a resilient modulus of $30$ ksi $.$ The locally available granular subbase material has a resilient modulus of $15$ ksi $.$ The drainage of the base is fair while the subbase material has poor drainage characteristics. The base material approaches saturation $5\%$ of the time, while the subbase material is saturated $25\%$ of the time. The seasonal resilient moduli of the soil have been determined to be $20$ ksi in the winter, $5$ ksi in early spring $/$ late fall, and $8$ ksi in the summer months.

a$.(20$ points$)$ What is the required thickness of the asphalt concrete layer, granular base layer, and granular subbase material to satisfy the above design criteria?

b$.(10$ points$)$ For a full depth asphalt concrete design, what is the required thickness of the AC layer for this problem?

c$.(10$ points$)$ What is the full depth AC thickness if the design reliability is only $85\%$ for this project?

d$.(10$ points$)$ What is the AC$,$ base, and subbase thickness for $95\%$ reliability, if the traffic prediction is $50{10}^6$ instead of $20{10}^6$ ESALs?