A square foundation with dimensions $1$m x $1$m has to be constructed on a dense sand. The unit weight and the static angle of friction of the soil can be assigned representative values of $19\mathrm{.}4$ kN$/$m$3$ and $36\mathrm{.}5$ degrees, respectively. The foundation may occasionally be subjected to a maximum dynamic load of $650$ kN increasing at a moderate rate. Determine the required minimum depth $($Df$)$ of the shallow foundation using a safety factor of $3.$

Df $=\_\_\_\_\_\_$m