$($a$)$For the proposed basement shown on Figure $1,$ determine the required drawdown in the water pressure in the sand layer in order to provide a factor of safety of $2\mathrm{.}0$ against heave failure of the base of the excavation

$(25\%)$

sund level

Figure $1$

$($b$)$Determine how many pumps would be required in order to draw the water level in the sand down by the amount determined in Part $($a$)$ of this question. Assume the capacity of a single pump is $350$ litres $/$ minute and assume each pumping well is located $2$ m from the edge of the excavation. Assume the radius of influence of the pumping system is $800$ m $.$ Use the formula for flow rate $($q$)$ into a single cylindrical well from a confined aquifer of thickness $($H$)$

$k=\frac{q}{2H(h_2-h_1)}lo{g}_e(\frac{r_2}{r_1})$

where:

$h_1$ and $h_2$ are the heads at distances $r_1$ and $r_2$ from the centre of the well

NB: If you are unable to answer Part $($a$)$ just assume a sensible value of the drawdown in order to attempt this part of the question.

$(40\%)$