A square foundation $($B x B$)$ has to be constructed $1\mathrm{.}2$ m below the ground surface. Assume that following properties:

y $=16\mathrm{.}50$ kN$/$m$3$

ysat $=18\mathrm{.}45$ kN$/$m$3$

$=30$ Degree

C$=10$ kN$/$m$2$

The water table is $0\mathrm{.}50$ m below the bottom of the footing. The gross allowable load with factor of safety of $3\mathrm{.}00$ is $665$ kN$.$ Determine the size of the foundation.