A $400mm$ square$-$section concrete pile is driven to an embedded depth of $12m$ in a

cohesive soil, which has the following properties:

$c_u=35+4\mathrm{.}2$kPa $(wherez=$ depth below surface$)$

$=20k\frac{N}{m^3}$

The groundwater level is at a depth of $3m.$

Calculate:

$($a$)$ the design load capacity for the pile, adopting the following factors of safety: $3\mathrm{.}0$

against end$-$bearing, $1\mathrm{.}5$ against shaft resistance failure and $2\mathrm{.}5$ against overall

shear failure; and

$($b$)$ the safe load capacity for a square group of nine of these piles in this soil, when

spaced at $2\mathrm{.}25m$ centres and adopting a factor of safety of $2\mathrm{.}5$ against group

failure.

What is the efficiency of the group?

$[15$ marks$]$