Example $14\mathrm{.}15$: A column carries a load of $1000$ kN $.$ The soil is a dry sand weighing $19k\frac{N}{m^3}$

and having an angle of internal friction of $40.$ A minimum factor of safety of $2\mathrm{.}5$ is required

and Terzaghi factors are required to be used. $(N_{}=42$ and $N_q=21).$

$($i$)$ Find the size of a square footing, if placed at the ground surface; and,

$($ii$)$ Find the size of a square footing required if it is placed at $1$ m below ground surface

with water table at ground surface. Assume ${}_{\text{s}\text{a}\text{t}}=21k\frac{N}{m^3}.$