Q$1$a$.$ A continuous foundation is to be constructed near a slope made of granular soil $($Figure $1).$ If $B=1\mathrm{.}4m,b=2m,H=5m,D_f=1\mathrm{.}4m,=30,{}^{\text{'}}=40,=20K\frac{N}{m^3}$ and FOS$=3\mathrm{.}5,$ estimate the allowable bearing capacity of the foundation.

Q$1$b$.$ Considering a similar continuous foundation is to be constructed near a slope made of granular soil with $b=3m,H=6m,D_f=1\mathrm{.}5m,=30,{}^{\text{'}}=40,=20K\frac{N}{m^3},$ and FOS $=2,$ find the appropriate $B$ value for the foundation to support a pressure $=1200K\frac{N}{m^2}.($Hint: Plot the variation of ultimate bearing capacity with respect to $B$ and find the appropriate value$).$