Question

A layer of normally consolidated, saturated silty clay of 1 m thickness is subjected to one dimensional consolidation under a pressure increment of 20 kPa. The properties of the soil are: specific gravity = 2.7, natural moisture content = 45%, compression index = 0.45, and recompression index = 0.05. The initial average effective stress within the layer is 100 kPa. Assuming Terzaghi’s theory to be applicable, the primary consolidation settlement (rounded off to the nearest mm) is 
1. 2 mm
2. 9 mm
3. 14 mm
4. 16 mm
5.

Answer 1

Correct Answer - Option 4 : 16 mm

Concept:

The final consolidation settlement is given by,

\({\rm{Δ H}} = \left( {\frac{{{C_c}\; × \;{H_0}}}{{1\; + \;{e_0}}}} \right) \;× \;{\log _{10}}\frac{{{σ _0}' \;+\; {\rm{Δ }}σ }}{{{σ _0}'}}\)

ΔH - ultimate consolidation settlement

C_c - Compression index, H₀ - Initial thickness of soil layer

σ₀^' - Initial effective stress, Δσ^'  - Increase in effective stress

Calculation:

Given:

σ0' = 100 kN/m², Δσ^' = 20 kN/m²

H₀ = `1 m, G = 2.7, W = 45%, C_c =0.45, C_r = 0.05

The relationship between w, G, S, and e is given by

w × G = S × e

0.45 × 2.7 = 1 × e

e = 1.215

\({\rm{Δ H}} = \left( {\frac{{{C_c} \;× \;{H_0}}}{{1\; + \;{e_0}}}} \right) × {\log _{10}}\frac{{{σ _0}'\; + \;{\rm{Δ }}σ }}{{{σ _0}'}}\)

 \({\rm{Δ H}} = \left( {\frac{{0.45\; \times \;1}}{{1 \;+ \;1.215}}} \right) \times {\log _{10}}\frac{{100 \;+\; 20}}{{100}}\)

Δ H = 0.016 m = 16 mm.