GATE Technical: CE (Set No 3) Stage 2 questions with solutions

Q1. An earthen dam of height H is made of cohesive soil whose cohesion and unit weight are c and γ, respectively. If the factor of safety against cohesion is F_c, the Taylor’s stability number (Sₙ) is

1. γH/(cF_c)
2. cF_c/(γH)
3. c/(F_cγH)
4. F_cγH/c

Answer: c/(F_cγH)

Taylor's stability number is Sn = c_mobilized/(gamma H) with mobilized cohesion c/Fc, giving Sn = c/(Fc x gamma x H). That is option index 2, not the stored cFc/(gamma H).

Q2. The notation “SC” as per Indian Standard Soil Classification System refers to

1. Sandy clay
2. Silty clay
3. Clayey silt
4. Clayey sand

Answer: Clayey sand

The notation "SC" in the Indian Standard Soil Classification System specifically denotes clayey sand, which is a soil type that contains a significant amount of sand mixed with clay, affecting its engineering properties.

Q3. An anisotropic soil deposit has coefficient of permeability in vertical and horizontal directions as k_z and kₓ, respectively. For constructing a flow net, the horizontal dimension of the problem’s geometry is transformed by a multiplying factor of

1. √(k_z/kₓ)
2. √(kₓ/k_z)
3. kₓ/k_z
4. k_z/kₓ

Answer: √(k_z/kₓ)

To draw an isotropic flow net for anisotropic soil, the horizontal dimensions are scaled by the factor sqrt(k_z/k_x) (transformed x = x*sqrt(k_z/k_x)). The stored answer sqrt(kx/kz) is the reciprocal; the correct multiplying factor is sqrt(k_z/k_x).

Q4. The value of the function f(x) is given at n distinct values of x and its value is to be interpolated at the point x*, using all the n points. The estimate is obtained first by the Lagrange polynomial, denoted by I_L, and then by the Newton polynomial, denoted by I_N. Which one of the following statements is correct?

1. I_L is always greater than I_N
2. I_L and I_N are always equal
3. I_L is always less than I_N
4. No definite relation exists between I_L and I_N

Answer: I_L and I_N are always equal

Both the Lagrange polynomial and the Newton polynomial are methods of polynomial interpolation that yield the same interpolating polynomial when given the same set of data points. Therefore, their estimates at any point x* will be equal.

Q5. The speed-density relationship in a mid-block section of a highway follows the Greenshield’s model. If the free flow speed is v_f and the jam density is k_j, the maximum flow observed on this section is

1. v_f k_j
2. v_f k_j / 2
3. v_f k_j / 4
4. v_f k_j / 8

Answer: v_f k_j / 4

The maximum flow in the Greenshield's model occurs at half the free flow speed and half the jam density, leading to the formula for maximum flow being v_f k_j / 4, which represents the optimal balance between speed and density.

Q6. Chlorine is used as the disinfectant in a municipal water treatment plant. It achieves 50 percent of disinfection efficiency measured in terms of killing the indicator microorganisms (E-Coli) in 3 minutes. The minimum time required to achieve 99 percent disinfection efficiency would be

1. 9.93 minutes
2. 11.93 minutes
3. 19.93 minutes
4. 21.93 minutes

Answer: 19.93 minutes

The relationship between disinfection efficiency and time is often logarithmic, meaning that each additional log reduction in microorganisms requires a significantly longer time. Since achieving 50% disinfection takes 3 minutes, reaching 99% disinfection (which is a 2-log reduction) typically requires about 6 times that initial time, leading to approximately 19.93 minutes.

Q7. A camera with a focal length of 20 cm fitted in an aircraft is used for taking vertical aerial photographs of a terrain. The average elevation of the terrain is 1200 m above mean sea level (MSL). What is the height above MSL at which an aircraft must fly in order to get the aerial photographs at a scale of 1:8000?

1. 2600 m
2. 2800 m
3. 3000 m
4. 3200 m

Answer: 2800 m

To achieve a scale of 1:8000, the height at which the aircraft flies must be calculated based on the focal length of the camera and the elevation of the terrain. The correct height of 2800 m ensures that the scale is maintained, allowing for accurate aerial photographs of the terrain.

Q8. A flexible pavement has the following class of loads during a particular hour of the day: i. 80 buses with 2-axles (each axle load of 40 kN) ii. 160 trucks with 2-axles (front and rear axle loads of 40 kN and 80 kN, respectively) The equivalent standard axle load repetitions for this vehicle combination as per IRC:37-2012 would be

1. 180
2. 240
3. 250
4. 320

Answer: 180

Standard axle = 80 kN, VDF = (P/80)^4. Buses: 80 x 2 axles of 40 kN = 160 x 0.0625 = 10. Trucks: 160 x [(40/80)^4 + (80/80)^4] = 160 x 1.0625 = 170. Total ESAL = 10 + 170 = 180.