Civil Engineering GATE 2023 Set-1 Questions with Answer

Ques 27 General Aptitude

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Let a = 30! b = 50! and c = 100! Consider the following numbers:
log_ca, log_ac, log_ba, log_ab.
Which one of the following inequalities is CORRECT?

A

log_ca < log_ba < log_ab < log_ac

B

log_ca < log_ab < log_ba < log_bc

C

log_ca < log_ba < log_ac < log_ab

D

log_ba < log_ca < log_ab < log_ac

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Ques 28 General Aptitude

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A square of side length 4 cm is given. The boundary of the shaded region is defined by one semi-circle on the top and two circular arcs at the bottom, each of radius 2 cm, as shown. The area of the shaded region is _______ cm².

A

8

B

4

C

12

D

10

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Ques 29 Geotechnical Engineering

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The specific gravity of a soil is 2.60. The soil is at 50% degree of saturation with a water content of 15%. The void ratio of the soil is _______.

A

0.35

B

0.78

C

0.87

D

1.28

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Ques 30 Geotechnical Engineering

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A group of 9 friction piles are arranged in a square grid maintaining equal spacing in all directions. Each pile is of diameter 300 mm and length 7 m. Assume that the soil is cohesionless with effective friction angle $phi'=32$^o. What is the center-to-center spacing of the piles (in m) for the pile group efficiency of 60%?

A

0.582

B

0.486

C

0.391

D

0.677

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Ques 31 Geotechnical Engineering

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A possible slope failure is shown in the figure. Three soil samples are taken from different locations (I, II and III) of the potential failure plane. Which is the most appropriate shear strength test for each of the sample to identify the failure mechanism? Identify the correct combination from the following options:
P: Triaxial compression test
Q: Triaxial extension test
R: Direct shear or shear box test
S: Vane shear test

A

I-Q, II-R, III-P

B

I-R, II-P, III-Q

C

I-S, II-Q, III-R

D

I-P, II-R, III-Q

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Ques 32 Geotechnical Engineering

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A drained direct shear test was carried out on a sandy soil. Under a normal stress of 50 kPa, the test specimen failed at a shear stress of 35 kPa. The angle of internal friction of the sample is _______ degree (round off to the nearest integer).

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Ques 33 Geotechnical Engineering

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With reference to the compaction test conducted on soils, which of the following is INCORRECT?

A

Peak point of the compaction curve gives the maximum dry unit weight and optimum moisture content

B

With increase in the compaction effort, the maximum dry unit weight increases

C

With increase in the compaction effort, the optimum moisture content decreases

D

Compaction curve crosses the zero-air-voids curve

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Ques 34 Geotechnical Engineering

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Consider that a force P is acting on the surface of a half-space (Boussinesq's problem). The expression for the vertical stress ($\sigma_{z}$) at any point (r, z), within the half-space is given as,

where, r is the radial distance, and z is the depth with downward direction taken as positive. At any given r, there is a variation of $\sigma_{z}$ along z, and at a specific z, the value of $\sigma_{z}$ will be maximum. What is the locus of the maximum $\sigma_{z}$?

(A) $z^{2}=\frac{3}{2}r^{2}$
(B) $z^{3}=\frac{3}{2}r^{2}$
(C) $z^{2}=\frac{5}{2}r^{2}$
(D) $z^{3}=\frac{5}{2}r^{2}$

A

$z^{2}=\frac{3}{2}r^{2}$

B

$z^{3}=\frac{3}{2}r^{2}$

C

$z^{2}=\frac{5}{2}r^{2}$

D

$z^{3}=\frac{5}{2}r^{2}$

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Ques 35 Geotechnical Engineering

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A square footing of size 2.5 $m \times$ 2.5 m is placed 1.0 m below the ground surface on a cohesionless homogeneous soil stratum. Considering that the groundwater table is located at the base of the footing, the unit weights of soil above and below the groundwater table are 18 $kN/m^{3}$ and 20 $kN/m^{3}$, respectively, and the bearing capacity factor $N_{q}$ is 58, the net ultimate bearing capacity of the soil is estimated as 1706 kPa (unit weight of water = 10 $kN/m^{3}$).
Earlier, a plate load test was carried out with a circular plate of 30 cm diameter in the same foundation pit during a dry season, when the water table was located beyond the plate influence zone. Using Terzaghi's bearing capacity formulation, what is the ultimate bearing capacity (in kPa) of the plate?

(A) 110.16
(B) 61.20
(C) 204.00
(D) 163.20

A

110.16

B

61.20

C

204.00

D

163.20

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Ques 36 Geotechnical Engineering

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A soil having the average properties, bulk unit weight = 19 kN/m³; angle of internal friction = 25° and cohesion = 15 kPa, is being formed on a rock slope existing at an inclination of 35° with the horizontal. The critical height (in m) of the soil formation up to which it would be stable without any failure is _______ (round off to one decimal place).
[Assume the soil is being formed parallel to the rock bedding plane and there is no groundwater effect.]

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Ques 37 Geotechnical Engineering

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A smooth vertical retaining wall supporting layered soils is shown in the figure. According to Rankine's earth pressure theory, the lateral active earth pressure acting at the base of the wall is _______ kPa (round off to one decimal place).

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Ques 38 Geotechnical Engineering

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A vertical trench is excavated in a clayey soil deposit having a surcharge load of 30 kPa. A fluid of unit weight 12 kN/m³ is poured in the trench to prevent collapse as the excavation proceeds. Assume that the fluid is not seeping through the soil deposit. If the undrained cohesion of the clay deposit is 20 kPa and saturated unit weight is 18 kN/m³, what is the maximum depth of unsupported excavation (in m, rounded off to two decimal places)?

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Ques 39 Hydrology

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When a supercritical stream enters a mild-sloped (M) channel section, the type of flow profile would become _______.

A

M₁

B

M₂

C

M₃

D

M₁ and M₂

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