$($a$)$ A rectangular foundation $2\mathrm{.}2m3\mathrm{.}8m$ is to be founded $1m$

below the surface of a thick deposit of soft saturated clay.

The unit weight of the clay is $29k\frac{N}{m^3}.$ Undrained and

consolidated undrained triaxial laboratory tests established

the following soil properties:

${}_u=5,c_u=20$kPa;${}^{\text{'}}=30$ and $c^{\text{'}}=0.$

Calculate the ultimate bearing capacity of the foundation

using the Terzaghi model of shear failure for a square

foundation immediately after construction, and some years

after construction. You are given:

$q_u=c{N}_c(1+0\mathrm{.}3\frac{B}{\text{I}})+z^{**}{N}_q+0\mathrm{.}5B{N}_{}(1-0\mathrm{.}2\frac{B}{L})$

and the Chart supplied $($Fig$.$ Q$4$a$)-$ Terzaghi's bearing

capacity coefficients.

$($b$)$ Explain what the beach profile in a tailings impoundment is$,$

and explain why it is important to be able to control this

profile.