Q$5.($a$)$ A footing is founded above a soil strata as shown in Figure Q$\mathrm{.}5($a$).$ Groundwater is assumed to be at $4$ m below the ground. The unit weight of the sand above and below water table is $18k\frac{N}{m^3}$ and $20k\frac{N}{m^3}$ respectively. The unit weight of the clay below water table is $19k\frac{N}{m^3}.$ The footing will impose an increase in vertical effective stress at the middle of the clay layer by $55k\frac{N}{m^2}.$ Other design parameters are:

Compression index of the clay, $c_c=0\mathrm{.}65$

Re$-$compression index of the clay, $c_r=0\mathrm{.}30$

Initial void ratio of the clay, $e_0=0\mathrm{.}70$

$($i$)$ Assume the soil to be normally consolidated, estimate the ultimate primary consolidation settlement due to the foundation,

$(4$ marks$)$

$($ii$)$ Estimate the ultimate primary consolidation settlement of the foundation again assuming that the soil is over$-$consolidated and has a pre$-$consolidation pressure of $200k\frac{N}{m^2}.$

$(4$ marks$)$

Figure Q$5($a$)$