A strip foundation $2\mathrm{.}0m$ wide is located at a depth of $2\mathrm{.}0m$ in a stiff clay of

saturated unit weight $21k\frac{N}{m^3}.$ The undrained shear strength is uniform with

depth, with $c_u=120$kPa. Determine the undrained bearing capacity of the

foundation under the following conditions:

$($a$)$ the foundation is constructed in level ground;

$($b$)$ a cutting at a gradient of $1$:$2$ is subsequently made adjacent to the

foundation, with the crest $1\mathrm{.}5m$ from the edge of the foundation.