Problem No$.4$: $20$ Points

Consider a cut to be done in a homogeneous clay layer as shown in Figure $4$ 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 $=1)(6$ points$).$

b$.$ The radius of the critical circle when the factor of safety is equal to $1(7$ points$).$

c$.$ The factor of safety if the excavation is cut to a depth of $4m(7$ points$).$

Slopes in Homogeneous Clay Soil with $=0$

Use procedure defined by Terzaghi and Peck

Typically in clay soil, the failure is rotational and not translational

Factor of safety is defined as Fs $=C\frac{u}{C}dCu$ is the undrained shear strength of the soil and $Cd$ is the the amount of cohesion developed along the failure surface.

The stability factor is defined as $m=C\frac{d}{y}HY$ is the unit weight of the soil, $H$ is the height of the slope

Distinction between slope angles $>53$ degrees and less than $53$ dearees

Slopes in Homogeneous Clay Soil with $=0$

For $>53$ :

All circles are toe circles.

For ;

Toe circle $q,$

Midpoint circle $q,$

Slope circle

$q,$

Slopes in Homoaeneous Clay Soil with $=0$

Determining the radius of the critical circle when $>53$ degrees

$r=\frac{H_{cr}}{2sin*sin(\frac{}{2})}$