Question $3(20\%)$ : A $5m$ wide and $10m$ long footing will be built $3m$ below ground surface, in a loose sand layer with a frietion angle of $30.$ Groundwater is also at the foundation level $({}_w=10k\frac{N}{m^3}).$ Formulas and charts you may need are given on the next two pages, after the question.

$($a$)$ Calculate the ultimate bearing capacity, considering local shear is likely to occur in this loose sand.

Formulise:

see below for $N_4{N}_7+N_4$

Terzaghi & Peck shape factors: $S_s=1+0\mathrm{.}2\frac{B}{L}$

$S_y=1-0\mathrm{.}2\frac{B}{L}$

$S_4=1$

Figure $4\mathrm{.}3$ Bearing capacity factors

$($b$)$ Find the net safe bearing capacity a factor of safety of $2\mathrm{.}5$