For a partially saturated soil deposit at a construction site, water content $(w)$ is $15 \%$, degree of saturation ( S ) is $67 \%$, void ratio ( e ) is 0.6 and specific gravity of solids in the soil $\left(G_s\right)$ is 2.67 . Consider unit weight of water as $9.81 \mathrm{kN} / \mathrm{m}^3$.

To fully saturate $5 \mathrm{~m}^3$ of this soil, the required weight of water (in kN ) will be __________ (round off to the nearest integer).

In the context of shear strength of soil, which of the following statements is/are CORRECT?

The bank of a canal has the profile shown in the figure. The material is a homogeneous clay with a bulk unit weight of $20 \mathrm{kN} / \mathrm{m}^3$, undrained cohesion of 30 kPa and it is fully saturated ( $\phi_u=0$ ). For the trial slip circle shown, the area ABCDEA is $150 \mathrm{~m}^2$ and the centroid is at P. A tension crack (DE) of 2.5 m deep was also observed. Assume unit weight of water is $9.81 \mathrm{kN} / \mathrm{m}^3$ and consider 1 m run of the bank for the analysis.

Considering the canal is empty and tension crack is completely filled with water, the factor of safety against slope failure of the bank is __________ (round off to two decimal places).

A designer used plate load test to obtain the value of the bearing capacity factor $\mathrm{N}_\gamma$. A circular plate of 1 m diameter was placed on the surface of a dry sand layer extending very deep beneath the ground. The unit weight of the sand is $16.66 \mathrm{kN} / \mathrm{m}^3$. The plate is loaded to failure at a pressure of 1500 kPa .

Considering Terzaghi's bearing capacity theory, the bearing capacity factor $\mathrm{N}_\gamma$ is________ (round off to the nearest integer).