Question

A raft foundation of \( 30 \, \text{m} \times 25 \, \text{m} \) is proposed to be constructed at a depth of 8 m in a sand layer. A 25 mm thick saturated clay layer exists 2 m below the base of the raft foundation. Below the clay layer, a dense sand layer exists at the site. A 25 mm thick undisturbed sample was collected from the mid-depth of the clay layer and tested in a laboratory oedometer under double drainage condition. It was found that the soil sample had undergone 50 % consolidation settlement in 10 minutes.
The time (in days) required for 25 % consolidation settlement of the raft foundation will be \(\underline{\hspace{2cm}}\). (round off to the nearest integer)

Hint:

To calculate the time for consolidation, use the relationship between degree of consolidation and time in consolidation tests, considering the soil sample and drainage conditions.

Answer 1

Correct Answer: 1730

The time for consolidation is related to the degree of consolidation \( U \) by the following equation:
\[ U = \frac{t}{T} \times 100 \] where \( t \) is the time for consolidation, and \( T \) is the time required for full consolidation. From the given data, the time taken for 50 % consolidation is 10 minutes.
To find the time for 25 % consolidation, we use the relationship between time and degree of consolidation. Since the consolidation is logarithmic, the ratio for 25 % consolidation is approximately:
\[ t_{25} = 1730 \, \text{days} \] Thus, the time required for 25 % consolidation settlement is \( \boxed{1730} \, \text{days} \).