# Deep Foundation

 Question 1
A circular pile of diameter $0.6 \mathrm{~m}$ and length $8 \mathrm{~m}$ was constructed in a cohesive soil stratum having the following properties: bulk unit weight $=$ $19 \mathrm{kN} / \mathrm{m}^{3}$; angle of internal friction $=0^{\circ}$ and cohesion $=25 \mathrm{kPa}$.
The allowable load the pile can carry with a factor of safety of 3 is ____ $\mathrm{kN}$ (round off to one decimal place).
[Adopt: Adhesion factor, $\alpha=1.0$ and Bearing capacity factor, $\left.\mathrm{N}_{\mathrm{C}}=9.0\right]$
 A 112.5 B 321.5 C 125.6 D 146.9
GATE CE 2023 SET-2   Geotechnical Engineering
Question 1 Explanation:
End bearing capacity
$\mathrm{Q}_{\mathrm{pu}}=\mathrm{C}_{\mathrm{u}} \mathrm{N}_{\mathrm{c}} \mathrm{A}_{\mathrm{b}}$
where, $\quad C_{u}=25 \mathrm{kPa}$
$N_{c}=9$
$A_{b}=\frac{\pi}{4} \times 0.6^{2}=0.283 \mathrm{~m}^{2}$
$\therefore \quad \mathrm{Q}_{\mathrm{Pu}}=25 \times 9 \times 0.283$ $=63.62 \mathrm{kN}$

Skin friction capacity
$\mathrm{Q}_{\mathrm{s}}=\alpha \mathrm{C}_{\mathrm{u}} \mathrm{A}_{\mathrm{s}}$
Where,
\begin{aligned} \alpha & =1.0 \\ \mathrm{C}_{\mathrm{u}} & =25 \mathrm{kPa} \\ \mathrm{A}_{\mathrm{s}} & =\pi \mathrm{DL}=\pi \times 0.6 \times 8 \\ & =15.08 \mathrm{~m}^{2} \\ \therefore \quad Q_{\mathrm{s}} & =1 \times 25 \times 15.08=377 \mathrm{kN} \end{aligned}
$\therefore$ Ultimate pile capacity $=63.62+377$ $=440.62 \mathrm{kN}$
Allowable load $=\frac{440.62}{3}=146.87 \mathrm{kN}$
 Question 2
A group of 9 friction piles are arranged in a square grid maintaining equal spacing in all directions. Each pile is of diameter $300 \mathrm{~mm}$ and length $7 \mathrm{~m}$. Assume that the soil is cohesionless with effective friction angle $\phi^{\prime}=32^{\circ}$. What is the center-to-center spacing of the piles (in $\mathrm{m}$ ) for the pile group efficiency of $60 \%$ ?
 A 0.582 B 0.486 C 0.391 D 0.677
GATE CE 2023 SET-1   Geotechnical Engineering
Question 2 Explanation: $\mathrm{n}=9$
Dia. of pile $=300 \mathrm{~mm}$
Length of pile $(\mathrm{L})=7 \mathrm{~m}$
Using the Converse Labarre formula.
$m=3, \quad n=3$
$n_{g}=1-\frac{\theta}{90} \frac{[m(n-1)+n(m-1)]}{m n}$
\begin{aligned} 0.6 & =1-\frac{\theta}{90} \times \frac{3 \times 2+3 \times 2}{3 \times 3} \\ \frac{\theta}{90} \times \frac{12}{9} & =0.4 \\ \theta & =\frac{0.9 \times 9 \times 90}{12} \\ \tan \theta & =\tan \left(\frac{0.4 \times 9 \times 90}{12}\right) \\ \frac{d}{s} & =\tan \theta \\ \frac{0.3 \mathrm{~m}}{\mathrm{~s}} & =0.5095 \Rightarrow \mathrm{S}=0.588 \mathrm{~m} \end{aligned}

 Question 3
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
$\eta _g=1-\frac{\theta }{90}\left [ \frac{(n-1)m+(m-1)n}{mn} \right ]$
where m and n are number of rows and columns in the plan grid of pile arrangement, and $\theta =\tan ^{-1}\left ( \frac{d}{s} \right )$.
The design value of the pile group capacity (in kN) in the vertical downward direction is __________________. (round off to the nearest integer)
 A 14520 B 23521 C 11085 D 25120
GATE CE 2022 SET-2   Geotechnical Engineering
Question 3 Explanation:
\begin{aligned} \eta _g&=1-\frac{\theta }{90}\left \{ \frac{m(n-1)+n(m-1)}{mn} \right \} \\ \theta &=\tan ^{-1}\left ( \frac{d}{s} \right )=\tan ^{-1}\left ( \frac{1}{3} \right )=18.43^{\circ}\\ \eta _g&=\frac{Q_{ug}}{nQ_{up}}\\ Q_{ug}&=\left [ 1-\frac{18.43}{90}\left \{ \frac{4(4-1)+4(4-1)}{4 \times 4} \right \} \right ](16 \times 1000)\\ &=11085kN \end{aligned}
 Question 4
A timber pile of length 8 m and diameter 0.2 m is driven with a 20 kN drop hammer, falling freely from a height of 1.5 m. The total penetration of the pile in the last 5 blows is 40 mm. Use the Engineering News Record expression. Assumea factor of safety of 6 and empirical factor (allowing reduction in the theoretical set, due to energy losses) of 2.5cm. The safe load carrying capacity of the pile (in kN, round off to 2 decimal places) is _______
 A 80.24 B 151.51 C 182.54 D 224.32
GATE CE 2019 SET-2   Geotechnical Engineering
Question 4 Explanation:
L = 8 m; d = 0.2 m, 20 kN = W ( drop hammer)
H = 1.5 m
Penetration in 5 blows = 40 mm
\begin{aligned} \therefore \; \text{in 1 blow}&=\frac{40}{5}=8mm=0.8cm\\ Q_{safe}&=\left ( \frac{WH}{s+c} \right )\times \frac{1}{FOS}\\ &=\frac{1}{6}\left [ \frac{20kN \times (1.5 \times 100)}{0.8cm+2.5cm} \right ]\\ Q_{safe}&=151.51kN \end{aligned}
 Question 5
A reinforced concrete circular pile of 12 m length and 0.6 m diameter is embedded in stiff clay which has an undrained unit cohesion of 110 $kN/m^2$. The adhesion factor is 0.5. The Net Ultimate Pullout (uplift) Load for the pile (in kN, round off to 1 decimal place) is _______
 A 1244.1 B 1110.5 C 560.8 D 1820.4
GATE CE 2019 SET-1   Geotechnical Engineering
Question 5 Explanation: \begin{aligned} &\text{Net Ultimate pullout} \\ &=\alpha CA_s =0.5 \times 110(\pi dL) \\ &=0.5 \times 110(\pi \times 0.6 \times 12)\\&=1244.1kN \end{aligned}

There are 5 questions to complete.

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