Q$1$: A square footing $2m$ by $2m(BL)$ on plan is located at a depth of $1m$ in a sand with

angle of friction ${}^{\text{'}}=30$degree and $c^{\text{'}}=0$kPa. The unit weight of the sand above the water

table is $16k\frac{N}{m^3}$ and the saturated unit weight is $18k\frac{N}{m^3}.$ Unit weight of water is $9\mathrm{.}81$

$k\frac{N}{m^3}.$ The water table is shown in Figure $1\mathrm{.}1$ and there is seepage vertically downward

under a hydraulic gradient of $0\mathrm{.}15.(14$ marks$)$

$($a$)$ Determine the ultimate bearing capacity using Terzaghi's bearing capacity theory, under

the assumption of general shear failure mode. $(4$ marks$)$

$($b$)$ Following $($a$),$ what is the ultimate bearing capacity using Terzaghi's bearing capacity

theory, under the assumption of local shear failure mode. $(4$ marks$)$

$($c$)$ If the footing is subjected to the following loading condition $($see Figure $1\mathrm{.}2)$: $Q=300kN$

and $M=60kNm$ per meter long. Please determine the factor of safety against shear failure

using the gross method, assume water table is raised to the ground level due to a heavy

rainfall and hydraulic gradient increased to $0\mathrm{.}25,$ assume local shear failure mode. $(6$

marks$)$

Figure $1\mathrm{.}1$