$5\mathrm{.}14$ A continuous foundation with a width of $1$ m is located on a slope made of clay soil. Refer to Figure $5\mathrm{.}19$ and let $D_f=1m,H=4m,b=2m,=16\mathrm{.}8k\frac{N}{m^3},c=c_u=68k\frac{N}{m^2},=0,$ and $=60.$

a$.$ Determine the allowable bearing capacity of the foundation. Let $FS=3.$

b$.$ Plot a graph of the ultimate bearing capacity $q_u$ if $b$ is changed from $0$ to $6$ m $.$

Figure $5\mathrm{.}19$ Shallow foundation on top of a slope