Question $2$:

A $4\mathrm{.}0m5\mathrm{.}0m$ footing is built in sand at the water table in the soil profile shown below.

If a load of $300$ kN is applied to the footing, calculate the primary consolidation settlement

of the footing under this load. Use Simpson's rule to calculate the average stress change

within the clay layer when you're trying to solve for the final stress within the clay layer.

$($Hint: You can estimate the vertical stress change due to the applied load using the $2$:$1$

Approximate method$)$

Soil properties are given below:

Sand: $,{}_{\text{d}\text{r}\text{y}}=17\mathrm{.}1k\frac{N}{m^3},{}_{\text{s}\text{a}\text{t}}=19\mathrm{.}7k\frac{N}{m^3}$

Clay: Normally consolidated

Moisture content $=30\%,Gs=2\mathrm{.}65,LL=40$