Question

In an oedometer apparatus a specimen of fully saturated clay has been consolidated under a vertical pressure of 100 kPa and is at equilibrium state. Immediately on increasing the vertical pressure to 150 kPa, the effective stress \( \sigma' \) and excess pore water pressure \( \Delta u \) will be

• A. \( \sigma' = 50 \, {kPa}, \, \Delta u = 100 \, {kPa} \)
• B. \( \sigma' = 100 \, {kPa}, \, \Delta u = 50 \, {kPa} \)
• C. \( \sigma' = 150 \, {kPa}, \, \Delta u = 50 \, {kPa} \)
• D. \( \sigma' = 100 \, {kPa}, \, \Delta u = 150 \, {kPa} \)

Hint:

In consolidation problems, the effective stress \( \sigma' \) is the difference between the total vertical stress and the pore water pressure. The change in pore water pressure is equal to the change in the applied vertical pressure in an instant.

Answer 1

The Correct Option is B

In an oedometer test, when a fully saturated specimen of clay is consolidated under a vertical pressure, the effective stress \( \sigma' \) is given by:

\[ \sigma' = \sigma - u \]

where:

• \( \sigma \) = total vertical stress
• \( u \) = pore water pressure

Initially:

• The specimen is under a vertical pressure of **100 kPa**.
• At equilibrium, the effective stress \( \sigma' \) will also be **100 kPa**.

When the vertical pressure is increased to **150 kPa**, an excess pore water pressure \( \Delta u \) is generated due to the sudden increase in applied load.

The excess pore water pressure is calculated as:

\[ \Delta u = 150 \, \text{kPa} - 100 \, \text{kPa} = 50 \, \text{kPa} \]

Thus, the effective stress remains 100 kPa, and the excess pore water pressure is 50 kPa.

Hence, the correct answer is option (B).