A proposed office building will include an $8-$ft $6-$in square, $3-$ft deep spread

footing that will support a vertical downward service load of $160$ k $.$ The soil

below this footing is an overconsolidated clay $($OC case I$)$ with the

following engineering properties: $C_d(1+e_0)=0\mathrm{.}10,\frac{C_{}}{1+e_0}=0\mathrm{.}022,$

and $=113l\frac{b}{f}{t}^3.$ This soil strata extends to a great depth and the

groundwater table is at a depth of $50$ ft below the ground surface.

Determine the total settlement of this footing.