Question $4$:

$($Value: $25$ marks$)$

The following results were obtained from an oedometer test $($i$.$e$.,$ consolidation test$)$ on a specimen of saturated clay:

$\backslash$table$[[$Pressure $(k\frac{N}{m^2}),27,54,107,214,429,214,107,54],[$Void ratio,$1\mathrm{.}243,1\mathrm{.}217,1\mathrm{.}144,1\mathrm{.}068,0\mathrm{.}994,1\mathrm{.}001,1\mathrm{.}012,1\mathrm{.}024]]$

A layer of this clay $8m$ thick lies below a $4m$ depth of sand, the water table being at the surface. The saturated unit weight for both soils is $19k\frac{N}{m^3}.$ A $4m$ depth of fill of unit weight $20k\frac{N}{m^3}$ is placed on the sand over an extensive area.

a$.$ Determine the settlement due to consolidation of the clay.

b$.$ If the fill was removed some time after the completion of consolidation, calculate the heave or consolidation that would eventually take place due to swelling of the clay?