Design Miniproject $.$A $1\mathrm{.}0-m$ square, $0\mathrm{.}5-m$ deep footing carries a downward load of $200$ kN $.$ It is underlain by an over consolidated clay $($ OC case I $)$ with the following engineering properties: $C_c=0\mathrm{.}20,C_r=0\mathrm{.}05,e=0\mathrm{.}7,$ and $=15k\frac{N}{m^3}$ above the groundwater table and $16k\frac{N}{m^3}$ below. The ground water table is at a depth of $1$ m below the ground surface.

a$)$ Using the classical method, determine the total settlement of this footing.

b$)$ Design the required footing width to obtain a total settlement of no more than $25$ mm $.$ Select a width that is a multiple of $100$ mm $.$ Would it be practical to build such a footing considering the constraints?