$$ A rigid pavement is being designed with the same parameters as used in Problem $4\mathrm{.}5.$ The modulus of subgrade reaction is $300$ lb$/$in$3$ and the slab thickness is determined to be $8\mathrm{.}5$ inches. The load transfer coefficient is $3\mathrm{.}0,$ the drainage coefficient is $1\mathrm{.}0,$ and the modulus of elasticity is $4$ million lb$/$in$2.$ What is the design modulus of rupture? $($Assume that any parameters not given in this problem are the same as those given in Problem $4\mathrm{.}5.)$

Problum $4\mathrm{.}5$ you do not need to answer $4\mathrm{.}5$

$4\mathrm{.}5$ A flexible pavement was designed for the following daily traffic with a $12-$year design life: $1300$ single axles at $8000lb$ each, $900$ tandem axles at $15,000lb$ each, $20$ single axles at $40,000$ lb each, and $200$ tandem axles at $40,000$ lb each. The highway was designed with $4$ inches of HMA wearing surface,

$4$ inches of hot$-$mix asphaltic base, and $8$ inches of crushed stone subbase. The reliability was $70\%,$ overall standard deviation was $0\mathrm{.}5,$ PSI was $2\mathrm{.}0($with a TSI of $2\mathrm{.}5),$ and all drainage coefficients were $1\mathrm{.}0.$ What was the soil resilient modulus of the subgrade used in design?