Marks 1
A square concrete pile of 10 m length is driven into a deep layer of uniform homogenous clay. Average unconfined compressive strength of the clay, determined through laboratory tests on undisturbed samples extracted from the clay layer, is 100 kPa. If the ultimate compressive load capacity of the driven pile is 632 kN, the required width of the pile is __________ mm. (in integer)
Bearing capacity factor Nc = 9; adhesion factor $$\alpha$$ = 0.7)
A raft foundation of 30 m $$\times$$ 25 m is proposed to be constructed at a depth of 8 m in a sand layer. A 25 m thick saturated clay layer exists 2 m below the base of the raft foundation. Below the clay layer, a dense sand layer exists at the site. A 25 mm thick undisturbed sample was collected from the mid-depth of the clay layer and tested in a laboratory oedometer under double drainage condition. It was found that the soil sample had undergone 50% consolidation settlement in 10 minutes. The time (in days) required for 25% consolidation settlement of the raft foundation will be ___________. (round off to the nearest integer)
Marks 2
A $4 \times 4$ group pile, with each pile 20 m long and 500 mm in diameter, is installed in a square pattern in a clayey soil, as shown in the figure. The average unconfined compressive strength of the soil is $100 \mathrm{kN} / \mathrm{m}^2$, and the adhesion factor is 0.8 . Neglect the bearing at the tip of the piles. For a group efficiency factor of 1.0 , the centre to centre spacing (s) of the piles (in m ) would be ________ (round off to two 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).
A group of total 16 piles are arranged in a square grid format. The center-to-center spacing (s) between adjacent piles is 3 m. The diameter (d) and length of embedment of each pile are 1 m and 20 m, respectively. The design capacity of each pile is 1000 kN in the vertical downward direction. The pile group efficiency $${\eta _g}$$ is given by
$${\eta _g} = 1 - {\theta \over {90}}\left[ {{{(n - 1)m + (m - 1)n} \over {mn}}} \right]$$
where m and n are number of rows and columns in the plan grid of pile arrangement and $$\theta = {\tan ^{ - 1}}\left( {{d \over s}} \right)$$.
The design value of the pile group capacity (in kN) in the vertical downward direction is _________. (round off to the nearest integer)