The correct answer is D. None of the above.
The settlement of a clay is a function of the effective stress, the initial void ratio, and the compressibility of the clay. The effective stress is the difference between the total stress and the pore water pressure. The initial void ratio is the ratio of the void volume to the total volume of the clay. The compressibility of the clay is a measure of how much the clay will compress when the effective stress is increased.
In this case, the effective stress is increased from 100 kN/m2 to 200 kN/m2, and the settlement is 10 mm. This means that the compressibility of the clay is 10 mm/(200 kN/m2) = 0.05 mm/kN/m2.
If the effective stress is further increased from 200 kN/m2 to 400 kN/m2, the settlement will be 40 mm. However, this is only an estimate, and the actual settlement may be different depending on the initial void ratio and the compressibility of the clay.
The following are the explanations of each option:
- Option A: 10 mm. This is the settlement that occurred when the effective stress was increased from 100 kN/m2 to 200 kN/m2. However, this is only an estimate, and the actual settlement may be different depending on the initial void ratio and the compressibility of the clay.
- Option B: 20 mm. This is twice the settlement that occurred when the effective stress was increased from 100 kN/m2 to 200 kN/m2. However, there is no reason to expect that the settlement will be proportional to the increase in effective stress.
- Option C: 40 mm. This is the settlement that would occur if the clay were perfectly incompressible. However, no clay is perfectly incompressible, so the actual settlement will be less than 40 mm.
- Option D: None of the above. This is the correct answer, as explained above.