$($c$)$ A rectangular footing $(5m2m)$ is founded at a depth of $1\mathrm{.}25m$ in a clay soil having the following properties $c^{\text{'}}=17\mathrm{.}5$kPa,${}^{\text{'}}=27$ and $Y=18\mathrm{.}7k\frac{N}{m^3}.$ Assume ${}_w$ to be $9\mathrm{.}81k\frac{N}{m^3}.$

Determine the ultimate bearing capacity of the footing

i$.$ When the water table is well below the base;

$[5$ Marks$]$

ii$.$ When the water table is at the foundation level;

$[3$ Marks$]$

iii. When the water table is at the ground surface;

$[3$ Marks$]$

iv$.$ When the water table is at the ground surface, and there is

$[3$ Marks$]$ upward seepage with a hydraulic gradient $i=0\mathrm{.}7.$