To solve this problem, we need to understand the concept of quicksand and how it relates to the groundwater table. Quicksand is a condition where water saturates the soil in such a way that it loses its ability to support weight. In this case, the quicksand condition occurs at a depth of 4.2 m of excavation, meaning that the water table is at this depth.

We are given that the submerged density of the fine sand is 11 kN/m3 and the density of water is 10 kN/m3. We need to find the depth of lowering of the groundwater table required for making an excavation 5 m deep.

Let's solve this problem step by step:

1. Determine the unit weight of the fine sand:
The unit weight of the fine sand is given as 11 kN/m3.

2. Determine the unit weight of water:
The unit weight of water is given as 10 kN/m3.

3. Calculate the effective stress at the quicksand depth:
Effective stress is the difference between the total stress and the pore water pressure. In this case, the total stress is the unit weight of the fine sand multiplied by the depth of excavation (6 m). The pore water pressure is the unit weight of water multiplied by the depth of the quicksand condition (4.2 m).

Total stress = 11 kN/m3 * 6 m = 66 kN/m2
Pore water pressure = 10 kN/m3 * 4.2 m = 42 kN/m2

Effective stress = Total stress - Pore water pressure
Effective stress = 66 kN/m2 - 42 kN/m2 = 24 kN/m2

4. Determine the depth of lowering of the groundwater table:
To find the depth of lowering of the groundwater table, we need to calculate the effective stress at the desired excavation depth of 5 m. The total stress remains the same, but the pore water pressure will change.

Total stress = 11 kN/m3 * 6 m = 66 kN/m2
Pore water pressure = 10 kN/m3 * (4.2 m + x) [where x is the depth of lowering of the groundwater table]

Effective stress = Total stress - Pore water pressure
Effective stress = 66 kN/m2 - 10 kN/m3 * (4.2 m + x)

We want the effective stress to be greater than zero to avoid quicksand conditions. Therefore, we can set up the equation:

66 kN/m2 - 10 kN/m3 * (4.2 m + x) > 0

Solving this equation will give us the value of x, which represents the depth of lowering of the groundwater table:

66 kN/m2 - 10 kN/m3 * (4.2 m + x) > 0
66 kN/m2 - 42 kN/m2 - 10 kN/m3 * x > 0
24 kN/m2 - 10 kN/m3 * x > 0
10 kN/m3 * x < 24="" />
x < 2.4="" />

Therefore, the depth of lowering of the groundwater table required for making an excavation 5 m deep is less than 2.4 m. The closest option to this value is 1.68 m

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