G$3.$ A $14m$ deep canal is to be cut through a saturated clay having an undrained shear strength of $40$kPa and bulk unit weight of $18k\frac{N}{m^3}.$ By considering the slip circle shown, and assuming tension cracks up to a depth $3\mathrm{.}6m$ below the ground surface, calculate the short$-$term stability of the slope under the following conditions:

$($a$)$ Canal and tension cracks dry; no surcharge.

$($b$)$ Water of depth $8m$ in the canal; tension cracks filled with rain water; no surcharge.

$($c$)$ A surcharge of $20k\frac{N}{m^2}$ applied uniformly at the ground surface in addition to condition $($b$),$ assuming this not to affect the depth of tension cracks.

Calculate moments due to the weight of soil by dividing the sliding mass into six horizontal layers of suitable thickness.