Consider precast concrete driven piles to support a column load of $500$ kips $(350$ dead load $+150$ live load$)$ at the ground surface. The soil conditions and the proposed pile are shown in the figure below. Piles are $36\mathrm{.}0$ ft in length and $1\mathrm{.}25$ ft in diameter. Estimate the following:

$-$ The geotechnical capacity of the individual pile.

$-$ The structural capacity of the individual pile. Use compressive strength of $4$ ksi for the concrete.

$-$ The number of piles required to support the column. Use load factors of $1\mathrm{.}2$ for dead load and $1\mathrm{.}6$ for live load. Use resistance factors of $0\mathrm{.}30$ for both end bearing and skin friction.

$-$ The geotechnical capacity of the pile group. Use spacings of $3$ times the pile diameter. Verify the adequacy of the group capacity.

$-$ The immediate settlements of the individual pile and the pile group.

$-$ The long$-$term settlement of the silty clay layer.