A cut slope is made in a silty clay soil for a new road project, as shown in the figure. The locations of ground water table (GWT) and potential failure surface are shown in the figure. After the cut is made, the excess pore water pressure is fully dissipated, and the shear stress at the point A is $60 \mathrm{kN} / \mathrm{m}^2$. The factor of safety at the point A for longterm stability is __________ (rounded off to 2 decimal places).

Note:

Shear strength properties of silty clay: $c^{\prime}=15 \mathrm{kN} / \mathrm{m}^2, \phi^{\prime}=15^{\circ}$, and $c_u=75 \mathrm{kN} / \mathrm{m}^2$ Unit weight of soil above the GWT $(\gamma)=19 \mathrm{kN} / \mathrm{m}^3$

Unit weight of soil below the GWT $\left(\gamma_{\text {sat }}\right)=20 \mathrm{kN} / \mathrm{m}^3$

Unit weight of water $\left(\gamma_w\right)=9.81 \mathrm{kN} / \mathrm{m}^3$

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).