Example $14\mathrm{.}19$: Calculate the ultimate bearing capacity, according to the Brinch Hansen's

method, of a rectangular footing $2m3m,$ at a depth of $1$ m in a soil for which $=18k\frac{N}{m^2},$

$c=20k\frac{N}{m^2},$ and $=20.$ The ground water table is lower than $3$ m from the surface. The total

vertical load is $1350$ kN and the total horizontal load is $75$ kN at the base of the footing.

Hansen's factors for $=20$ are $N_c=14\mathrm{.}83,N_q=6\mathrm{.}40,$ and $N_{}=3\mathrm{.}54.$ Determine also the factor

safety.