GATE Technical: GATE 2022 (CE Set-2) Civil Engineering questions with solutions

Q1. 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?

1. (P)-True, (Q)-False, (R)-False, (S)-False
2. (P)-False, (Q)-True, (R)-True, (S)-True
3. (P)-True, (Q)-False, (R)-True, (S)-True
4. (P)-False, (Q)-True, (R)-False, (S)-False

Answer: (P)-True, (Q)-False, (R)-True, (S)-True

Statement (P) is correct because monsoon conditions can significantly affect the bearing capacity of sandy soils due to increased water content. Statement (Q) is false as sudden drawdown can indeed create critical conditions for slope stability in earthen dams. Statement (R) is true since quicksand conditions occur when the hydraulic gradient exceeds a critical threshold. Statement (S) is also true because lowering the water table reduces the pore water pressure, thereby decreasing the active earth thrust on the retaining wall.

Q2. For a traffic stream, v is the space mean speed, k is the density, q is the flow, v_f is the free flow speed, and k_j is the jam density. Assume that the speed decreases linearly with density. Which of the following relation(s) is/are correct?

1. q = k_j k - (k_j / v_f) k²
2. q = v_f k - (v_f / k_j) k²
3. q = v_f v - (v_f / k_j) v²
4. q = k_j v - (k_j / v_f) v²

Answer: q = v_f k - (v_f / k_j) k²

The correct option describes the relationship between flow, density, and speed in a traffic stream where flow decreases quadratically with density. This aligns with the assumption of linear speed decrease with density, ensuring that as density increases, flow is accurately modeled.

Q3. A post-tensioned concrete member of span 15 m and cross-section of 450 mm × 450 mm is prestressed with three steel tendons, each of cross-sectional area 200 mm². The tendons are tensioned one after another to a stress of 1500 MPa. All the tendons are straight and located at 125 mm from the bottom of the member. Assume the prestress to be the same in all tendons and the modular ratio to be 6. The average loss of prestress, due to elastic deformation of concrete, considering all three tendons is

1. 14.16 MPa
2. 7.08 MPa
3. 28.32 MPa
4. 42.48 MPa

Answer: 14.16 MPa

Concrete stress at tendon level from all three tendons is fc = P/A + P*e^2/I = 7.08 MPa (P=900 kN, e=100 mm, A=202500 mm^2, I=3.42e9 mm^4). For sequential post-tensioning the average elastic loss = m*fc*(n-1)/(2n) = 6*7.08*(2/6) = 14.16 MPa.

Q4. Match the following in Column X with Column Y: Column X (P) In a triaxial compression test, with increase of axial strain in loose sand under drained shear condition, the volumetric strain (Q) In a triaxial compression test, with increase of axial strain in loose sand under undrained shear condition, the excess pore water pressure (R) In a triaxial compression test, the pore pressure parameter “B” for a saturated soil (S) For shallow strip footing in pure saturated clay, Terzaghi’s bearing capacity factor (Nq) due to surcharge Column Y (I) decreases. (II) increases. (III) remains same. (IV) is always 0.0. (V) is always 1.0. (VI) is always 0.5. Which one of the following combinations is correct?

1. (P)-(I), (Q)-(II), (R)-(V), (S)-(V)
2. (P)-(II), (Q)-(I), (R)-(IV), (S)-(V)
3. (P)-(I), (Q)-(III), (R)-(VI), (S)-(IV)
4. (P)-(I), (Q)-(II), (R)-(V), (S)-(VI)

Answer: (P)-(I), (Q)-(II), (R)-(V), (S)-(V)

Loose sand under drained shear contracts so volumetric strain decreases (P-I); undrained it builds positive pore pressure, which increases (Q-II); pore-pressure parameter B for fully saturated soil is 1.0 (R-V); Terzaghi Nq for a strip footing equals 1.0 here (S-V). This is option (a).