Example $14\mathrm{.}11$: A foundation, $2\mathrm{.}0$ m square is installed $1\mathrm{.}2$ m below the surface of a uniform

sandy gravel having a density of $19\mathrm{.}2k\frac{N}{m^3},$ above the water table and a submerged density of

$10\mathrm{.}1k\frac{N}{m^3}.$ The strength parameters with respect to effective stress are $c^{\text{'}}=0$ and ${}^{\text{'}}=30.$

Find the gross ultimate bearing capacity for the following conditions:

$($i$)$ Water table is well below the base of the foundation $($i$.$e$.,$ the whole of the rupture

zone is above the water table$)$;

$($ii$)$ Water table rises to the level of the base of the foundation; and

$($iii$)$ the water table rises to ground level.

$($For $=30,$ Terzaghi gives $N_q=22$ and $N_{}=20)$