a$)$ In a mass$-$housing complex scheme over a vast area, two types of soils were encountered. One of which is a partially saturated silty clay with $c_u=5\mathrm{.}8k\frac{N}{m^2}$;${}_u=25,$ and $=18\mathrm{.}5k\frac{N}{m^3}$ and extends over most of the area. The other, predominantly clay having $c_u=55k\frac{N}{m^2}$ spreads to a lesser extent. The water table is at a greater depth. As per the design, strip footings of the building must be placed at $1$ m depth. Compute the width of the footing required in each type of soil if the load intensity is $150k\frac{N}{m}$ run. Adopt a factor of safety of $2\mathrm{.}5$ in both the soils, and only shear failure needs to be considered. If there is a possibility of the water table rising to the ground surface, what should be the change in the width of footing in both areas. The submerged unit weight of the silty clay is $11\mathrm{.}2k\frac{N}{m^3}.$