The retaining wall shown in figure is supporting a horizontal backfill having a unit weight of $18\mathrm{.}88k\frac{N}{m^3}$ with an angle of friction of $37.$ Foundation soil ultimate bearing capacity is $470$kPa. Unit weight of concrete is $23\mathrm{.}6k\frac{N}{m^3}$

a$)$ Compute the factor of safety against sliding considering passive earth pressure at the toe. Ans:$2\mathrm{.}94$

b$)$ Compute factor of safety against overturning. Ans:$3\mathrm{.}66$

c$)$ Compute the factor of safety against bearing failure. Ans:$3\mathrm{.}47$