Problem $1[10$ points$]$

A flexible pavement has a $4-$inch hot$-$mix asphaltic concrete wearing surface, a $7-$inch densegraded crushed stone base, and a $10-$inch crushed stone subbase. The pavement is on a soil

with a resilient modulus of $5,000$ lb$/$in$2$

$.$ The pavement was designed with $90\%$ reliability, an

overall standard deviation of $0\mathrm{.}4,$ and a $\backslash$Delta PSI of $2\mathrm{.}0($a TSI of $2\mathrm{.}5).$ The drainage coefficients

are $0\mathrm{.}9$ and $0\mathrm{.}8$ for the base and subbase, respectively. How many $25-$kip single$-$axle loads

can be carried before the pavement reaches its TSI $($with given reliability$)?$