Problem $1$: At a constructions site with expansive soil, the water content variation with depth is shown in the following table. Suction data indicated that the active zone is $22$ ft $.$ deep. The swell$-$index for the soil was determined to be $0\mathrm{.}056.$ Assume that, following construction the soil becomes saturated over the entire active zone. Determine the heave of the soil under the following conditions.

a$.$ Slab with negligible load constructed on surface

b$.{60}^{\text{'}}{40}^{\text{'}}$ mat with $3\mathrm{.}5$ ksf load placed on surface

c$.{60}^{\text{'}}{40}^{\text{'}}$ mat with $3\mathrm{.}5$ ksf load placed at $8$ ft depth

$\backslash$table$[[$Depth ft$.,\backslash$table$[[$Corrected Swell$],[$Pressure $($psf$)]],\backslash$table$[[$Soil unit weight$],[($pcf$)]],$Void ratio,$\backslash$table$[[$Water content$],[(\%)$