# Deep Foundation

 Question 1
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 1 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 2
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 2 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 3
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 3 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}
 Question 4
A group of nine piles in a 3 x 3 square pattern is embedded in a soil strata comprising dense sand underlying recently filled clay layer, as shown in the figure. The perimeter of an individual pile is 126 cm. The size of pile group is 240 cm x 240 cm. The recently filled clay has undrained shear strength of 15 kPa and unit weight of $16 kN/m^{3}$

The negative frictional load (in kN, up to two decimal places) acting on the pile group is______
 A 258.38 B 479.67 C 369.45 D 472.32
GATE CE 2018 SET-2   Geotechnical Engineering
Question 4 Explanation:
$3 \times 3$ pile group
Negative skin friction for group.
$=\alpha \bar{c}(4 B L)+$ weight of soil in
negative zone.
\begin{aligned} =& \alpha \bar{c}(4 B L)+\gamma(\text { Area } \times \text { length }] \\ =& 1 \times 15[4 \times 2.4 \times 2]+16\left[2.4^{2} \times 2\right] \\ &=472.32 \mathrm{kN} / \mathrm{m}^{2} \end{aligned}
Negative skin friction in individual action.
$\begin{array}{l} =n[\alpha \bar{c} \text { (perimeter } \times l] \\ =9[0.5 \times 15 \times 1.26 \times 2] \\ \text { [Assume } \alpha=0.5] \\ =170.1 \mathrm{kN} / \mathrm{m}^{2} \end{array}$
Negative skin friction is maximum of above
(two)
$Q_{n t}=472.32 \mathrm{kN} / \mathrm{m}^{2}$
 Question 5
A 0.5 m x 0.5 m square concrete pile is to be driven in a homogeneous clayey soil having undrained shear strength, $c_{u}$= 50 kPa and unit weight, $\gamma = 18.0 kN/m^{3}$. The design capacity of the pile is 500 kN. The adhesion factor $\alpha$ is given as 0.75. The length of the pile required for the above design load with a factor of safety of 2.0 is
 A 5.2 m B 5.8 m C 11.8 m D 12.5 m
GATE CE 2018 SET-1   Geotechnical Engineering
Question 5 Explanation:
\begin{aligned} C_{u}=& 50 \mathrm{kPa}, \gamma=18 \mathrm{kN} / \mathrm{m}^{3}, \mathrm{FOS}=2 \\ Q_{\text {up}}=& 9 \mathrm{C} \times B^{2}+\alpha \bar{C}(4 \mathrm{BL})=1000 \mathrm{kN} \\ 1000=& 9 \times 50 \times 0.5 \times 0.5+0.75 \\ & \times 50(4 \times 0.5 \mathrm{L}) \\ L=& 11.83 \mathrm{m} \end{aligned}
 Question 6
Two identical concrete piles having the plan dimensions 50 cm x 50 cm are driven into a homogeneous sandy layer as shown in the figures. Consider the bearing capacity factor $N_{q}$, for $\phi =30^{\circ}$ as 24

If $Q_{P1}$ and $Q_{P2}$ represent the ultimate point bearing resistance of the piles under dry and submerged conditions, respectively, which one of the following statements is correct?
 A $Q_{P1} \gt Q_{P2}$ By about 100% B $Q_{P1} \lt Q_{P2}$ By about 100% C $Q_{P1} \gt Q_{P2}$ By about 5% D $Q_{P1} \lt Q_{P2}$ By about 5%
GATE CE 2017 SET-2   Geotechnical Engineering
Question 6 Explanation:
The point bearing resistance of piles in sandy soils
$Q_P=A_b cdot \sigma '_v \cdot N_q$
As the area at base $(A_b)$ and $N_q$ are same for both the piles given, $Q_P \propto \sigma '_v$
For dry sand condition, $\sigma '_v=\sigma _v=20 \times \gamma$
For submerged condition, $\sigma '_v=20 \times \gamma '$
\begin{aligned} \text{Since, } \gamma '&= \frac{1}{2} \gamma \\ \therefore \;\; QP_2&\approx \frac{1}{2} QP_1\\ QP_1& \approx QP_2 \end{aligned}
Therefore, $QP_1 \gt QP_2$ by about 100%.
 Question 7
It is proposed to drive H-piles up to a depth of 7 m at a construction site. The average surfacearea of the H-pile is 3 $m^{2}$ per meter length. The soil at the site is homogeneous sand, havingan effective friction angle of 32$^{\circ}$. The ground water table (GWT) is at a depth of 2 m below the ground surface. The unit weights of the soil above and below the GWT are 16 $kN/m^{3}$ and 19 $kN/m^{3}$ respectively. Assume the earth pressure coefficient, K= 1.0, and the angle of wall friction $\delta =23^{\circ}$, The total axial frictional resistance (in kN, up to one decimal place) mobilized on the pile against the driving is _____
 A 350.7 B 40.7 C 390.8 D 309.2
GATE CE 2017 SET-1   Geotechnical Engineering
Question 7 Explanation:

\begin{aligned} Q_{s t} &=\frac{1}{2} k \gamma L_{1} \tan \delta A_{s_{1}}+\frac{1}{2} K\left[\gamma L_{1}+\gamma^{\prime} L_{2}\right] \tan \delta A_{s_{2}} \\ &=\frac{1}{2} \times 1 \times 16 \times 2 \tan 23^{\circ}(3 \times 2) \\ &+\frac{1}{2} \times 1[16 \times 2+77.95] \times \tan 23^{\circ}(5 \times 3) \\ &=390.8 \mathrm{kN} \end{aligned}
 Question 8
A pile of diameter 0.4 m is fully embedded in a clay stratum having 5 layers, each 5 m thick as shown in the figure below. Assume a constant unit weight of soil as 18 kN/$m^{3}$ for all the layers. Using $\lambda$-method ($\lambda$=0.15 for 25 m embedment length) and neglecting the end bearing component, the ultimate pile capacity (in kN) is ________.
 A 1060.2 B 1100.5 C 1010.4 D 1625.7
GATE CE 2015 SET-2   Geotechnical Engineering
Question 8 Explanation:
Ultimate bearing capacity
\begin{aligned} &=\lambda\left(\sigma_{\mathrm{v} a v}+2 C_{u}\right) A_{s} \\ &=0.15\left[18 \times 12.5+2 C_{u}\right] \times(\pi \times 0.4 \times 25) \\ \end{aligned}
$C_{u}$ is the average value of all layers i.e., 60 kPa.
\begin{aligned} &=0.15[18 \times 12.5+2 \times 60] \times(\pi \times 0.4 \times 25) \\ &=1625.77 \mathrm{kN} \end{aligned}
 Question 9
A single vertical friction pile of diameter 500 mm and length 20 m is subjected to a vertical compressive load. The pile is embedded in a homogeneous sandy stratum where: angle of internal friction is $\phi=30^{\circ}$, dry unit weight $(\gamma _{d})=20 kN/m^{3}$ and angle of wall friction is $\delta =2\varphi /3$. Considering the coefficient of lateral earth pressure (K)=2.7 and the bearing capacity factor ($N_q$)=25, the ultimate bearing capacity of the pile (in kN) is________
 A 196.56 B 1965.6 C 617.5 D 6174.5
GATE CE 2014 SET-2   Geotechnical Engineering
Question 9 Explanation:

Homogeneous sandy stratum
\begin{aligned} \phi &=30^{\circ} \\ \gamma_{d} &=20 \mathrm{kN} / \mathrm{m}^{3} \end{aligned}
Wall friction angle.
$\delta=\frac{2}{3} \phi=\frac{2}{3} \times 30=20^{\circ}$
Lateral earth pressure coefficient,
$K=2.7$
Bearing capacity factor,
$N_{q}=25$
$Q_{u}=?$
Vertical effective stress at 20m.
$\overline{\sigma_{v}}=20 \times 20=400 \mathrm{kN} / \mathrm{m}^{2}$
From 0 to 20m, unit point bearing
resistance and skin friction resistance remain
constant at
$\overline{\sigma_{\mathrm{v}}}=400 \mathrm{kN} / \mathrm{m}^{2}$
The ultimate load capacity is given by
\begin{aligned} Q_{u}&=q_{\mathrm{up}} \cdot A_{p}+q_{\mathrm{s}} \cdot A_{s}\\ &=f_{s}\left(Q_{u p}=0\right. for friction pile) \\ \text{where}\quad q_{s}&=\frac{1}{2} \cdot \overline{\sigma_{v}} \cdot K \cdot \tan \delta\\ &=\frac{1}{2} \times 400 \times 2.7 \tan 20^{\circ} \\ &=196.54 \mathrm{kN} / \mathrm{m}^{2} \end{aligned}
Skin friction resistance,
\begin{aligned} Q_{u}=f_{s} &=196.54 \times \pi \times 0.5 \times 20 \\ &=6174.49 \mathrm{kN} \end{aligned}
 Question 10
The action of negative skin friction on the pile is to
 A increase the ultimate load on the pile B reduce the allowable load on the pile C maintain the working load on the pile D reduce the settlement of the pile
GATE CE 2014 SET-1   Geotechnical Engineering
There are 10 questions to complete.