Problem No$.3$: $30$ Points

Consider a cut to be done in a homogeneous clay layer as shown in Figure $3$ with its sides rising at an angle $=53$ degrees.

The undrained shear strength of the clay layer is $16k\frac{N}{m^2}$ and the unit weight of the clay is $18k\frac{N}{m^3}.$

Determine the following:

a$.$ The maximum depth of the excavation $(H)$ to remain stable $($Factor of safety $=1(10$ points$).$

b$.$ The radius of the critical circle when the factor of safety is equal to $1(10$ points$).$

c$.$ The factor of safety if the excavation is cut to a depth of $4m(10$ points$).$