a$)$ Will the $\backslash (1\backslash$mathrm$\{$H$\}$: $1\backslash$mathrm$\{$~V$\}\backslash )$ slope be stable in the short$-$term without the surcharge of $250$ psf added to the ground surface? Refer to the approximate wedge stability method we discussed in class. The factor of safety $($FS$)$ on any given plane must be greater than $1\mathrm{.}3$ to be considered stable.

Your analysis must include computation of factor of safety over a range of trial failure plane orientations $(\backslash (\backslash$beta $\backslash )),$ plotting the values to find the minimum. For guidance, vary $\backslash (\backslash$boldsymbol$\{\backslash$beta$\}\backslash )$ in $5-$degree increments from $10$ degrees to $35$ degrees and plot the resulting values of FS against $\backslash (\backslash$beta $\backslash )($from the geometry of the problem, $\backslash (\backslash$beta $\backslash )$ cannot be greater than $\backslash (\backslash$alpha $\backslash )).$ Find the minimum FS and the corresponding $\backslash (\backslash$beta $\backslash )$ on the resulting curve. It may be easiest to do this on Excel.

b$)$ Will the $\backslash (1\backslash$mathrm$\{$H$\}$: $1\backslash$mathrm$\{$~V$\}\backslash )$ slope be stable in the short$-$term with the uniform surcharge of $250$ psf applied at the ground surface? You only need to determine the FS at the critical value of $\backslash (\backslash$beta $\backslash )$ determined in a$).$