Given data:

Settlement of normally consolidated clay layer = 25 mm

Increase in effective stress from 15 kPa to 30 kPa

To find:

Additional settlement when effective stress is increased from 30 kPa to 60 kPa

Solution:

We can use the concept of Terzaghi's one-dimensional consolidation theory to solve this problem.

Terzaghi's theory states that the settlement of a clay layer under a constant load can be calculated using the following equation:

s = Cv * H * log10((t+T)/T)

where

s = settlement

Cv = coefficient of consolidation

H = thickness of clay layer

t = time

T = time factor = (Cv * H^2) / (4 * k)

k = coefficient of permeability

From the given data, we can assume that the clay layer is homogeneous and the coefficient of permeability is constant.

When the effective stress is increased from 15 kPa to 30 kPa, the settlement can be calculated as:

s1 = Cv * H * log10((t+T1)/T1)

where

T1 = (Cv * H^2) / (4 * k1)

k1 = coefficient of permeability at an effective stress of 15 kPa

Similarly, when the effective stress is increased from 30 kPa to 60 kPa, the settlement can be calculated as:

s2 = Cv * H * log10((t+T2)/T2)

where

T2 = (Cv * H^2) / (4 * k2)

k2 = coefficient of permeability at an effective stress of 30 kPa

The additional settlement between the two effective stresses can be calculated as:

s2 - s1 = Cv * H * (log10((t+T2)/T2) - log10((t+T1)/T1))

s2 - s1 = Cv * H * log10(((t+T2)/T2) / ((t+T1)/T1))

Taking antilogarithm on both sides, we get:

((t+T2)/T2) / ((t+T1)/T1) = 10^((s2 - s1)/(Cv * H))

((t+T2)/T2) = ((t+T1)/T1) * 10^((s2 - s1)/(Cv * H))

t = (T2 / (10^((s2 - s1)/(Cv * H))) - T1)

Substituting the given values in the equation, we get:

t = (T2 / (10^(25/(Cv * H)))) - T1

Since the thickness of the clay layer and the coefficient of permeability are assumed to be constant, the time factor T1 and T2 are proportional to the effective stress.

Therefore, the additional settlement between the effective stress of 30 kPa and 60 kPa is the same as the settlement between the effective stress of 15 kPa and 30 kPa, which is 25 mm.

Hence, the correct option is (A) 25 mm.