A cut slope $(1V$:$2H)$ for a new road is excavated to a depth of $10$ m in a deep clay layer. The clay has a saturated weight density $($or unit weight$)$ of $18k\frac{N}{m^3}$ and an undrained shear strength of $40$ kPa $.$

a$.$ Determine the global factor of safety for slope stability for the trial slip surface shown below $($ignore the formation of a tension crack$).$

b$.$ Determine the global factor of safety for slope stability when a tension crack forms $($not shown$).$ Assume the tension crack is filled with water.

c$.$ What effect does the tension crack have on the stability of the slope. Give your reasons why.

d$.$ Check the overall stability of the slope in $($b$)$ above, using the limit state approach $($i$.$e$.$ factoring the undrained shear strength by $1\mathrm{.}4).$ Comment on your result.

Note: Draw the slope to scale using graph paper and determine an appropriate area $(A_{\text{a}\text{b}\text{c}\text{a}})$ by simplifying the shape geometry.