GATE Technical: Civil Engineering (CE) questions with solutions

Q1. The Surface Overflow Rate (SOR) in a rectangular sedimentation tank is 45 m³/m²/d. Minimum diameters of spherical inorganic and organic particles expected to be completely removed in this tank are calculated. A sum that Stokes’s law is applicable. Specific gravity of inorganic particles = 2.65 Specific gravity of organic particles = 1.20 Acceleration due to gravity (g) = 9.81 m/s² Kinematic viscosity (ν) = 1 × 10⁻⁶ m²/s Which of the following options is/are correct:

1. Minimum diameter of inorganic particles is 24 μm
2. Minimum diameter of organic particles is 69 μm
3. Minimum diameter of inorganic particles is 15 μm
4. Minimum diameter of organic particles is 55 μm

Answer: Minimum diameter of inorganic particles is 24 μm

The correct option states that the minimum diameter of inorganic particles is 24 μm, which is derived from applying Stokes's law to the sedimentation conditions in the tank. This calculation takes into account the specific gravity of the particles, the kinematic viscosity of the fluid, and the surface overflow rate, leading to the conclusion that particles of this size can be effectively removed.

Q2. In an oedometer apparatus a specimen of fully saturated clay has been consolidated under a vertical pressure of 100 kPa and is at equilibrium state. Immediately on increasing the vertical pressure to 150 kPa, the effective stress σ' and excess pore water pressure Δu will be

1. σ' = 50 kPa, Δu = 100 kPa
2. σ' = 100 kPa, Δu = 50 kPa
3. σ' = 150 kPa, Δu = 50 kPa
4. σ' = 100 kPa, Δu = 150 kPa

Answer: σ' = 100 kPa, Δu = 50 kPa

When the vertical pressure is increased from 100 kPa to 150 kPa, the total stress increases by 50 kPa. Since the clay is fully saturated, this increase in total stress results in an equivalent increase in pore water pressure, leading to an excess pore water pressure of 50 kPa. The effective stress is then calculated as the total stress minus the pore water pressure, resulting in an effective stress of 100 kPa.