Problem $4$

A cut slope in a soft clay makes an angle of $75$ to the horizontal line as shown in the below figure. The soil properties are: $=17\mathrm{.}3k\frac{N}{m^3},=0^0$ and $c_u=31\mathrm{.}1$kPa.

a$)$ Determine the maximum depth $(H_{cr})$ up to which the excavation can be carried out.

b$)$ Find the radius of the critical failure surface $($assuming the failure surface is circular$)$ when the factor of safety is $F{S}_s=1.$ Find the distance BC$.$