Question

When effective stress on a normally consolidated clay is increased from 25 kN/m\(^2\) to 50 kN/m\(^2\), settlement becomes 5mm. If the stress is increased to 175 kN/m\(^2\), settlement will increase to (assuming coefficient of volume-decrease to be constant):

• A. 25 mm
• B. 30 mm
• C. 35 mm
• D. 40 mm

Hint:

Settlement increases in proportion to the increase in effective stress, assuming the coefficient of volume-decrease remains constant.

Answer 1

The Correct Option is C

The settlement is directly proportional to the increase in effective stress in normally consolidated clay. Hence, we use the formula: \[ \frac{\Delta S_1}{\Delta S_2} = \frac{\Delta \sigma_1}{\Delta \sigma_2} \] Where: - \( \Delta S_1 \) = settlement for the first increase in stress = 5 mm - \( \Delta S_2 \) = settlement for the second increase in stress - \( \Delta \sigma_1 = 50 - 25 = 25 \, \text{kN/m}^2 \) - \( \Delta \sigma_2 = 175 - 50 = 125 \, \text{kN/m}^2 \) Substitute the values into the equation: \[ \frac{5}{\Delta S_2} = \frac{25}{125} \] \[ \Delta S_2 = \frac{5 \cdot 125}{25} = 25 \, \text{mm} \]
Step 2: Conclusion.
The total settlement will be: \[ 5 \, \text{mm} + 25 \, \text{mm} = 35 \, \text{mm} \]
Final Answer: \[ \boxed{35 \, \text{mm}} \]