Question $2$:

A square footing was placed at a depth of $1\mathrm{.}5m$ below the ground surface in a sand deposit as shown in Fig. $2.$ The unit weight of the soil ${}_d=17\mathrm{.}5k\frac{N}{m^3}$ and ${}_{\text{s}\text{a}\text{t}}=19k\frac{N}{m^3}.$ The ground water table is at a depth of $1m$ below the ground level. The standard penetration test $($SPT$)$ results performed in the sand deposit are shown in Table $1.$ Answer the following questions:

$($a$)$ What is the expected type of failure $($i$.$e$.,$ GSF$,$ LSF or PSF$)$ for this scenario? Provide your reasons.

$($b$)$ It is proposed to carry the load from a $5-$story structure on an area of $600m^2$ in sand using $50$ square footings. Determine the size of square footing to carry gross allowable load based on Terzaghi's bearing capacity theory $(1943),$ assuming a factor of safety is $3.($Hint: Assume a load of $10$kPa per story.$)$

$($c$)$

Table $1$: SPT$-$N values

$\backslash$table$[[$Table $1$: SPT$-$N values$],[$Depth $($m$),N_{60}$