$3.$ A $14$m thick sand deposit consisting of $5\%$ fines as shown in Figure is densified by vibrocompaction method using a probe, water jet and horizontal vibration. The process of deep densification is carried out on a square pattern with a spacing of $1\mathrm{.}8$ m centre$-$to$-$centre. The maximum void ratio of the sand despoit is $1\mathrm{.}02$ and the minimum void ratio is $0\mathrm{.}60.$ From the Standard Penetration Test $($SPT$),$ average N$60$ values obtained at the different depths of the deposit before the densification are shown in table. The groundwater table $($GWT$)$ is at $3\mathrm{.}0$m below the ground surface $($GL$).$ The unit weight of water is $9\mathrm{.}81$ kN$/$m$3.$

$3$a$)$ Determine the average void ratio of the sand deposit before densification by the vibrocompaction method.

$3$b$)$ Calculate the required volume of the backfill material for one compaction point to improve the sand deposit in part $($a$)$ by assuming that the densification process did not cause any settlement of the ground surface. The average N$60$ after densification is $20$ for the entire depth of the sand deposit.

$3$c$)$ Describe briefly the influences of the fines content in the sand deposit on the result of the densification process by the vibrocompaction method. State the reason$($s$).$