The column loads: $500,900,$ and $1200$ kN $,$ are to be carried by suitable foundation. Standard Penetration tests were conducted in four bore holes $(BH)$ at the building site, and the observed N $-$values are given below:

$\backslash$table$[[$Depth $(m),0\mathrm{.}75,1\mathrm{.}50,2\mathrm{.}25,3\mathrm{.}00,3\mathrm{.}75,4\mathrm{.}50,6\mathrm{.}00,7\mathrm{.}50,9\mathrm{.}0,10\mathrm{.}5],[$BH # $1,$N $-$value,$15,17,21,22,25,29,16,31,27,40],[$BH # $2,$N $-$value,$18,21,19,22,24,27,21,33,25,48],[BH$#$3,$N $-$value,$16,15,18,20,22,21,19,36,35,43],[$BH # $4,$N $-$value,$14,18,20,21,26,26,24,28,38,42]]$

The site has predominantly sandy soil$/$silty sand layers. The water table exists at surface in peak monsoon.

a$)$ If it is an individual footing, footings are proposed to be located at a depth of $1$ m in a sandy deposit having saturated unit weight of $18k\frac{N}{m^3}.$ Determine the size of footing for each column assuming a factor of safety of $2\mathrm{.}5.$

b$)$ If it is proposed to use pile foundation of $500$ mm diameter, and $8$ m length how many piles are required for each column?