A $16-$inch diameter pipe pile with a wall thickness of $0\mathrm{.}5$ inches is driven open$-$ended in the soil conditions shown below. The axial design loads are shown below. Assuming plugged conditions, calculate the shaft resistance in the $($a$)$ clay layer, and $($b$)$ sand layer. Apply the limiting values of unit shaft resistance presented in the NAVFAC manual as needed.

For the pile in Problem $1,$ draw a free body diagram of the soil plug and assess if pugging would occur $($or not$).$