The soil profile at a road construction site is as shown in figure (not to scale). A large embankment is to be constructed at the site. The ground water table (GWT) is located at the surface of the clay layer, and the capillary rise in the sandy soil is negligible. The effective stress at the middle of the clay layer after the application of the embankment loading is 180 kN/m\(^2\). Take unit weight of water, \( \gamma_w = 9.81 \, \text{kN/m}^3 \).
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The primary consolidation settlement is calculated using the compression index, the change in effective stress, the thickness of the layer, and the initial void ratio.
The primary consolidation settlement (\( \Delta H \)) of the clay layer due to the embankment loading can be calculated using the following formula:
\[
\Delta H = \frac{C_c \times \Delta \sigma' \times H}{1 + e_0},
\]
where:
- \( C_c = 0.25 \) is the compression index,
- \( \Delta \sigma' = 180 \, \text{kN/m}^2 \) is the effective stress applied by the embankment,
- \( H = 6 \, \text{m} \) is the thickness of the clay layer,
- \( e_0 \) is the initial void ratio, which is determined using the specific gravity of the soil and the water content.
The void ratio \( e_0 \) is calculated as:
\[
e_0 = \frac{G_s \times w}{1 - w},
\]
where:
- \( G_s = 2.65 \) is the specific gravity,
- \( w = 0.45 \) is the water content.
Substituting the values:
\[
e_0 = \frac{2.65 \times 0.45}{1 - 0.45} = 0.48.
\]
Now, calculate the primary consolidation settlement:
\[
\Delta H = \frac{0.25 \times 180 \times 6}{1 + 0.48} = 0.32 \, \text{m}.
\]
Thus, the primary consolidation settlement is \( \boxed{0.32} \, \text{m} \).
