As shown in the figure, we are tasked with designing a shallow foundation for a three$-$floor villa.

The initial trial dimensions for the foundation are $2m4m,$ with the foundation depth set at $D_f=1$

m $.$ The foundation will be placed on soft, saturated clay with a unit weight of $=20k\frac{N}{m^3}.$

Laboratory tests, including undrained $($UU$)$ and consolidated undrained $($CU$)$ triaxial tests, have

been performed on the soil, yielding the following parameters:

$C_u=24$kPa,${}^{\text{'}}=25,c^{\text{'}}=0$

a$)$ Assess whether the ultimate bearing capacity is more critical $($i$)$ immediately after

construction or $($ii$)$ after several years?

b$)$ Determine whether the allowable bearing capacity is sufficient for the applied load,

assuming a factor of safety $($FS$)$ of $3.$