Problem $3(50$ points$)$

A $12"$ diameter $($D$)$ concrete pile is planned to be used to carry an actual load of

$7,500$ pounds. The soil at the site is granular with effective friction angle ${}^{\text{'}}$ of $30$

and no cohesion. The unit weight of the soil is $120l\frac{b}{f}{t}^3.$ There is no ground water

table at this site. Considering only the skin friction resistance of the pile $($ignore the

tip resistance$),$ use Coyle and Costello $(1988)$ method to determine the length of

the pile that will provide an ultimate capacity providing a factor of safety in the range

of $4$ to $3($not more nor less$).$