Geotechnical Engineering

Question 1
A saturated compressible clay layer of thickness h is sandwiched between two sand layers, as shown in the figure. Initially, the total vertical stress and pore water pressure at point P, which is located at the mid-depth of the clay layer, were 150 kPa and 25 kPa, respectively. Construction of a building caused an additional total vertical stress of 100 kPa at P. When the vertical effective stress at P is 175 kPa, the percentage of consolidation in the clay layer at P is _____________. (in integer)

A
25
B
30
C
50
D
80
GATE CE 2022 SET-2      Consolidation of Soils
Question 1 Explanation: 
Initial effective stress at P
\sigma _{P_1}'=150-25=125kPa
After construction,
\sigma _{P_2}'=125+100=225kPa
100% consolidation will occur when effective stress at P reaches 225 kPa.
Percentage of consolidation when vertical effective stress is at P is 175 kPa.
=\frac{175-125}{225-125} \times 100=\frac{50}{100} \times 100=50
Question 2
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      Deep Foundation
Question 2 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 3
A soil sample is underlying a water column of height h_1, as shown in the figure. The vertical effective stresses at points A, B, and C are \sigma '_A, \sigma '_B, and \sigma '_C respectively. Let \gamma _{sat} and \gamma ' be the saturated and submerged unit weights of the soil sample, respectively, and \gamma _{w} be the unit weight of water. Which one of the following expressions correctly represents the sum (\sigma '_A+ \sigma '_B+\sigma '_C )?

A
(2h_2+h_3 )\gamma \;'
B
(h_1+h_2+h_3 )\gamma \;'
C
(h_2+h_3 )(\gamma _{sat}-\gamma _w )
D
(h_1+h_2+h_3 )\gamma _{sat}
GATE CE 2022 SET-2      Effective Stress and Permeability
Question 3 Explanation: 

\begin{aligned} \sigma _A'&=0\\ \sigma _B'&=h_2\gamma '\\ \sigma _C'&=(h_2+h_3)\gamma '\\ \sigma _A'+\sigma _B'+\sigma _C'&=(2h_2+h_3)\gamma '\\ \end{aligned}
Question 4
Match the following in Column X with Column Y:
\begin{array}{|l|l|}\hline \text{Column X}&\text{Column Y} \\ \hline \text{(P) In a triaxial compression test, with increase of axial }\\ \text{ strain in loose sand under drained shear condition,}\\ \text{ the volumetric strain} & \text{((I) decreases.} \\ \hline \text{(Q) In a triaxial compression test, with increase of axial}\\ \text{ strain in loose sand under undrained shear condition,}\\ \text{ the excess pore water pressure} & \text{(II) increases.}\\ \hline \text{(R) In a triaxial compression test, the pore pressure}\\ \text{ parameter "B" for a saturated soil}& \text{(III) remains same.}\\ \hline \text{(S) For shallow strip footing in pure saturated clay,}\\ \text{ Terzaghi's bearing capacity factor }\\ (N_q) \text{ due to surcharge}& \text{(IV) is always 0.0.}\\ \hline & \text{(V) is always 1.0.}\\ \hline &\text{is always 0.5.} \end{array}
Which one of the following combinations is correct?
A
(P)-(I), (Q)-(II), (R)-(V), (S)-(V)
B
(P)-(II), (Q)-(I), (R)-(IV), (S)-(V)
C
(P)-(I), (Q)-(III), (R)-(VI), (S)-(IV)
D
(P)-(I), (Q)-(II), (R)-(V), (S)-(VI)
GATE CE 2022 SET-2      Shear Strength of Soil
Question 4 Explanation: 
In a triaxial compression test, with increase of axial strain in loose sand under drained shear condition, the volumetric strain decreases. As the sample is compressing. Hence, volume is decreasing.
In a triaxial compression test, with increase of axial strain in loose sand under undrained shear condition, the excess pore water pressure increases.
(R) In a triaxial compression test, the pore pressure parameter ?B? for a saturated soil is 1.
(S) For shallow strip footing in pure saturated clay, Terzaghi's bearing capacity factor (Nq) due to surcharge is 1.
Question 5
In a triaxial unconsolidated undrained (UU) test on a saturated clay sample, the cell pressure was 100 kPa. If the deviatoric stress at failure was 150 kPa, then the undrained shear strength of the soil is _________ kPa. (in integer)
A
25
B
50
C
75
D
85
GATE CE 2022 SET-2      Consolidation of Soils
Question 5 Explanation: 
\sigma _3=\sigma _c=100kPa , \sigma _d=\sigma _1-\sigma _3=150kPa
For UU test

Undrained shear strenth
C_{uu}=\tau _f=\frac{\sigma _1-\sigma _3}{2}=\frac{150}{2}=75KPa
Question 6
A concentrically loaded isolated square footing of size 2 m x 2 m carries a concentrated vertical load of 1000 kN. Considering Boussinesq's theory of stress distribution, the maximum depth (in m) of the pressure bulb corresponding to 10% of the vertical load intensity will be ________. (round off to two decimal places)
A
1.25
B
4.35
C
5.36
D
6.25
GATE CE 2022 SET-2      Stress Distribution in the Soil
Question 6 Explanation: 
Considering Boussinesq's theory of stress distribution
\sigma _x=\frac{3Q}{2\pi z^2}\left [ \frac{1}{1+\left ( \frac{r}{z} \right )^2} \right ]^{5/2}
For r=0, \sigma _z=\frac{3Q}{2\pi z^2}
\sigma _z=0.1q=0.1 \times \frac{Q}{B^2}=\frac{0.1}{2^2}Q
\frac{1}{40}Q=\frac{3Q}{2 \pi z^2}
z^2=\frac{3 \times 40}{2 \pi}\Rightarrow z=4.37m
Question 7
The inside diameter of a sampler tube is 50 mm. The inside diameter of the cutting edge is kept such that the Inside Clearance Ratio (ICR) is 1.0% to minimize the friction on the sample as the sampler tube enters into the soil.
The inside diameter (in mm) of the cutting edge is ________. (round off to two decimal places)
A
49.52
B
25.36
C
42.25
D
36.32
GATE CE 2022 SET-2      Soil Stabilization and Soil Exploration
Question 7 Explanation: 


Moisture content
\begin{aligned} C_i&=\frac{D_3-D-1}{D_1} \times 100\\ 1&=\frac{50-D_1}{D_1} \times 100\\ D_1&=49.50mm \end{aligned}
Question 8
Read the following statements:

(P) While designing a shallow footing in sandy soil, monsoon season is considered for critical design in terms of bearing capacity.
(Q) For slope stability of an earthen dam, sudden drawdown is never a critical condition.
(R) In a sandy sea beach, quicksand condition can arise only if the critical hydraulic gradient exceeds the existing hydraulic gradient.
(S) The active earth thrust on a rigid retaining wall supporting homogeneous cohesionless backfill will reduce with the lowering of water table in the backfill.

Which one of the following combinations is correct?
A
(P)-True, (Q)-False, (R)-False, (S)-False
B
(P)-False, (Q)-True, (R)-True, (S)-True
C
(P)-True, (Q)-False, (R)-True, (S)-True
D
(P)-False, (Q)-True, (R)-False, (S)-False
GATE CE 2022 SET-2      Shallow Foundation and Bearing Capacity
Question 8 Explanation: 
In monsoon season sand will be fully saturated hence this will be critical condition in designing of shallow foundation.
In case of sudden drawdown flow direction reverses hence for slope stability, it will be critical condition.
In sandy sea beach, quicksand condition can arise only if existing hydraulic gradient exceeds the critical hydraulic gradient.
Question 9
A raft foundation of 30 m x 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)
A
3525
B
1254
C
1736
D
2463
GATE CE 2022 SET-1      Consolidation of Soils
Question 9 Explanation: 


\begin{aligned} (T_v)_{50}&=C_v\frac{t}{d^2} \;\;\; (\text{from lab})\\ \frac{\pi}{4}(0.5)^2&=C_v \times \frac{10 min}{\left ( \frac{25}{2} \times 10^{-3} \right )^2}\\ (T_v)_{25}&=C_v\frac{t}{d^2} \;\;\; (\text{from field})\\ \frac{\pi}{4}(0.25)^2&=C_v \frac{t}{(12.5)^2}\\ \end{aligned}
Since the soil is same -> C_v same
\begin{aligned} \frac{\pi}{4}(0.25)^2&= \frac{\frac{\pi}{4}(0.5)^2 \times (12.5 \times 10^{-3})^2}{10} \times \frac{t}{(12.5)^2}\\ t&=1736 \;days \end{aligned}
Question 10
A square concrete pile of 10 m length is driven into a deep layer of uniform homogeneous 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 N_c 9; adhesion factor \alpha =0.7 )
A
400
B
124
C
105
D
600
GATE CE 2022 SET-1      Shallow Foundation and Bearing Capacity
Question 10 Explanation: 
\begin{aligned} Q_{up}&=q_bA_b+q_sA_s\\ C_u&=\frac{q_u}{2}=\frac{100}{2}=50kN/m^2\\ &=9 \times CB^2+\alpha \bar{C}(4BL)\\ 632kN&=9 \times 50 \times B^2 +0.7 \times 50(4B \times 10)\\ B&=0.4m\\ B&=400mm \end{aligned}


There are 10 questions to complete.

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