Example $9\mathrm{.}3$: An embankment $10$ m high is inclined at an angle of $36$ to the horizontal. A

stability analysis by the method of slices gives the following forces per running meter:

$$ Shearing forces $=450kN$

$$ Normal forces $=900kN$

$$ Neutral forces $=216kN$

The length of the failure arc is $27$ m $.$ Laboratory tests on the soil indicate the effective

values $c^{\text{'}}$ and ${}^{\text{'}}$ as $20k\frac{N}{m^2}$ and $18$ respectively.

Determine the factor of safety of the slope with respect to $($a$)$ shearing strength and $($b$)$

cohesion.