Question Bank • QB_SWCE_EXP_012 NAT • 2 Marks

Section 4: Soil and Water Conservation Engineering

Soil Mechanics

Subtopic: Terzaghi's one dimensional soil consolidation theory

Question Statement:

A normally consolidated clay layer of thickness $3.0\text{ m}$ has an initial void ratio $e_0 = 0.85$ and compression index $C_c = 0.28$. The initial effective overburden stress is $100\text{ kPa}$. Due to an embankment construction, the stress increases by $50\text{ kPa}$. The primary consolidation settlement of the clay layer in centimeters is ________ (round off to 2 decimal places).

Answer Key:

7.99

Step-by-Step Solution & Explanation

Consolidation settlement $\Delta H$ is given by Terzaghi's 1D formula: $\Delta H = \frac{C_c H_0}{1 + e_0} \log_{10} \left(\frac{\sigma_0' + \Delta \sigma'}{\sigma_0'}\right)$ Given: • $H_0 = 3.0\text{ m} = 300\text{ cm}$ • $e_0 = 0.85$ • $C_c = 0.28$ • $\sigma_0' = 100\text{ kPa}$ • $\Delta \sigma' = 50\text{ kPa} \implies \sigma_0' + \Delta \sigma' = 150\text{ kPa}$ $\frac{\sigma_0' + \Delta \sigma'}{\sigma_0'} = \frac{150}{100} = 1.5$ $\log_{10}(1.5) \approx 0.17609$ $\Delta H = \frac{0.28 \times 300}{1 + 0.85} \times 0.17609 = \frac{84}{1.85} \times 0.17609 = 45.405 \times 0.17609 \approx 7.995\text{ cm} \approx 7.99\text{ cm}$
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