A vertical cut $4\mathrm{.}15m$ high is excavated in saturated intact clay. The clay is isotropic and has an undrained shear strength of $31\mathrm{.}6k\frac{N}{m^2}$ and a saturated unit weight of $16k\frac{N}{m^3}.$

Assume that a vertical, air$-$filled tension crack forms behind the cut at $l$ distance to its crest, with a depth of $1\mathrm{.}09m.$

For the critical slope angle which is $45$ determine the factor of safety of the vertical cut, under short$-$term $($end of construction$)$ conditions.

Type your answer in three decimal places.

Hint: The free body diagram for the vertical cut is as follows. You should be able to determine the distance to the tension crack from the vertical cut $(l)$ using the given data and

slope angle $(=45).$

Calculate $W($Weight of the moving mass$)$ and $AB$ distance $($length of failure plane$).$

Considering driving and resisting forces along $AB$ failure plane determine factor of safety.