Please give solution step by step in detail $($Don$\text{'}$t skip mathamatical equations$)$

Question $1$:

A Plain Jointed Concrete Pavement is to be designed using the AASHTO $93$ Pavement Design Method to

withstand a traffic of $10,000,000$ ESALs. The slabs are connected longitudinally and transversally using

dowel and tie bars and asphalt shoulders were used. The geotechnical investigation conducted before

the construction indicated that the subgrade is composed of clay with high plasticity $($Class $CH$ according

to USCS$)$ and that the bedrock layer was found at five feet from the surface of the subgrade.

The following information and design assumptions are available:

Concrete slab: $E_c=3\mathrm{.}8{10}^6,S_c^{\text{'}}=650$

Unbound Granular Subbase: $D_{SB}=12$ in$.,$ EsB $=30,000$ psi.

Resilient Modulus of the Subgrade: $M_R=4,000$ psi.

Initial Serviceability index value: $p_i=4\mathrm{.}5$

Terminal Serviceability index value: $p_1=2\mathrm{.}5$

Reliability and Standard Deviation: $R=90\%$ and $S_0=0\mathrm{.}3$

The quality of the drainage is good and the pavement is exposed to moisture level approaching saturation

for $15\%$ of the time.

Determine the thickness of the concrete slab to withstand the projected traffic. Assume reasonably any

missing information and justify your assumptions.