The correct answer is: A. directly proportional to the voids ratio.
The voids ratio is a measure of the amount of empty space in a soil. The higher the voids ratio, the more empty space there is in the soil. When a soil is consolidated, the empty space is reduced and the soil particles come closer together. The amount of consolidation settlement is directly proportional to the initial voids ratio. This means that the more empty space there is in the soil, the more the soil will settle when it is consolidated.
The compression index is a measure of how much a soil will compress when it is subjected to a load. The higher the compression index, the more the soil will compress. However, the compression index does not affect the ultimate consolidation settlement. This is because the ultimate consolidation settlement is reached when the soil has reached its maximum density. The compression index only affects the rate at which the soil consolidates, not the amount of consolidation settlement.
The following is a brief explanation of each option:
- Option A: The ultimate consolidation settlement of a soil is directly proportional to the voids ratio. This means that the more empty space there is in the soil, the more the soil will settle when it is consolidated.
- Option B: The ultimate consolidation settlement of a soil is directly proportional to the compression index. This is not correct because the compression index only affects the rate at which the soil consolidates, not the amount of consolidation settlement.
- Option C: The ultimate consolidation settlement of a soil is inversely proportional to the compression index. This is not correct because the compression index does not affect the ultimate consolidation settlement.
- Option D: None of the above. This is the correct answer because the ultimate consolidation settlement of a soil is directly proportional to the voids ratio.