$($a$)$ A client wishes to construct piled foundations in a thick deposit of medium

dense cohesionless sand.

The sand has an angle of internal friction, ${}^{\text{'}}=33$ and a saturated unit

weight ${}_{\text{s}\text{a}\text{t}}=20k\frac{N}{m^3}.$ The groundwater table is at the ground surface.

Note that the ultimate pile capacity, $Q_f$ is given by:

$Q_f=A_b({}_{v0}^{\text{'}}{N}_q)+A_s(K_s{}_v^{\text{'}}tan{}^{\text{'}})$

Take $Nq$ as $48,{}^{\text{'}}={}^{\text{'}}-5,Ks=1-sin{}^{\text{'}}$

If the piles are straight sided with a pile diameter of $0\mathrm{.}6m$ :

i$)$ Formulate an expression for $Q_f$ in terms of the pile length $L.$

marks$]$

ii$)$ Calculate the length of pile required for a factor of safety, $F=2\mathrm{.}5,$ if the

safe working load is to be $P_s=700kN.$