**Given Data:**
- Settlement of a normally consolidated clay layer = 25 mm
- Increase in effective stress from 15 to 30 kPa

**To Find:**
Additional settlement when the effective stress is increased from 30 to 60 kPa.

**Explanation:**

1. Settlement of a normally consolidated clay layer is the amount of compression or decrease in volume that occurs when a load is applied to the soil.
2. Settlement is directly related to the increase in effective stress applied to the soil.
3. The settlement of the clay layer can be determined using the relationship between settlement and effective stress known as the compression index (Cc).
4. The compression index is defined as the slope of the settlement curve on a log scale.
5. The settlement can be calculated using the formula:

Settlement = Cc * log10((σ1 + Δσ)/σ1) * H

Where,
- Settlement is the total settlement (mm)
- Cc is the compression index
- σ1 is the initial effective stress (kPa)
- Δσ is the increase in effective stress (kPa)
- H is the height of the clay layer (mm)

6. Given that the settlement is 25 mm when the effective stress increases from 15 to 30 kPa, we can use this information to calculate the compression index (Cc).
7. Rearranging the settlement formula, we get:

Cc = Settlement / (log10((σ1 + Δσ)/σ1) * H)

Plugging in the values, we get:

Cc = 25 / (log10((15 + 15)/15) * H)

Cc = 25 / (log10(2) * H)

Cc = 25 / (0.3010 * H)

Cc ≈ 82.724 / H

8. Now, we need to calculate the additional settlement when the effective stress is increased from 30 to 60 kPa.
9. Using the settlement formula, we have:

Additional Settlement = Cc * log10((σ1 + Δσ)/σ1) * H

Plugging in the values, we get:

Additional Settlement = (82.724 / H) * log10((30 + 30)/30) * H

Additional Settlement = 82.724 * log10(2)

Additional Settlement ≈ 82.724 * 0.3010

Additional Settlement ≈ 24.879 mm

The additional settlement is approximately 24.879 mm, which can be rounded to 25 mm (option B).

Hence, the correct answer is option B) 50 mm.

A