A $6 \mathrm{~m} \times 6 \mathrm{~m}$ square footing constructed in clay is subjected to a vertical load of 2500 kN at its centre. The base of the footing is 2 m below the ground surface, as shown in the figure. The footing is made of 2 m thick concrete. The ground water table is at a great depth. Considering Terzaghi's bearing capacity theory, the factor of safety of footing against the bearing capacity failure is _________ (rounded off to 2 decimal places). Note:

Unit of concrete $=24 \mathrm{kN} / \mathrm{m}^3$

Properties of clay: $c=50 \mathrm{kN} / \mathrm{m}^3, \phi=0^{\circ}$, and $\gamma=19 \mathrm{kN} / \mathrm{m}^3$

For $\phi=0^{\circ}: N_c=5.7, N_q=1, N_\gamma=0$

A clayey soil has a moisture content of $18 \%$, a specific gravity of soil solids of 2.74 , and a degree of saturation of $65 \%$. The soil soaks up water during a rain event, and the degree of saturation increases to $85.2 \%$. The change of the volume during the soaking is negligible. The new moisture content (in \%) of the soil will be _________ (rounded off to 2 decimal places).

A single pile with 450 mm diameter has been driven into a homogeneous clay layer, which has an undrained cohesion ( $\mathrm{c}_{\mathrm{u}}$ ) of 20 kPa and unit weight of $18 \mathrm{kN} / \mathrm{m}^3$. The ground water table is found to be at the surface of the clay layer. The adhesion factor ( $\alpha$ ) of the soil is 0.95 and bearing capacity factor $\left(N_c\right)$ is 9 . The pile is supporting a column load of 144 kN with a factor of safety of 3.0 against ultimate axial pile capacity in compression.

The required embedment depth of the pile (in m ) is _________ (rounded off to the nearest integer).

Two soils of permeabilities $\mathrm{k}_1$ and $\mathrm{k}_2$ are placed in a horizontal flow apparatus, as shown in the figure. For Soil 1, $L_1=50 \mathrm{~cm}$, and $k_1=0.055 \mathrm{~cm} / \mathrm{s}$; for Soil 2, $L_2=30 \mathrm{~cm}$, and $\mathrm{k}_2=0.035 \mathrm{~cm} / \mathrm{s}$. The cross sectional area of the horizontal pipe is $100 \mathrm{~cm}^2$, and the head difference ( $\Delta \mathrm{h}$ ) is 150 cm . The discharge (in $\mathrm{cm}^3 / \mathrm{s}$ ) through the soils is ________ (rounded off to 2 decimal places).