Problem $1(15$ Points$)$

A $12-$in wide concrete wall carries axial $DL=10\frac{k}{f}t$ and $LL=8\frac{k}{f}.$ The wall is supported on continuous footing. The wall is founded $3$ ft below ground surface $($Fig$.1).$

Fig. $1$

a$)$ Just draw the failure surface of anticipated bearing capacity failure.b$)$ Calculate the friction angle of the silty sand soil using the given $N_{60}$ and the effective vertical stress at $10$ ft below the back ground surface.

c$)$ Determine the ultimate bearing capacity $(q{u}_u)$ of the footing if the footing width $(B)=4ft.$

d$)$ If the footing width $($B$)=4ft$ and the footing bearing capacity resistance factor $=0\mathrm{.}45,$ is this a safe design against the factored axial loads $)($show calculations$)?($Neglect the weight of the footing$)$