Question

A saturated compressible clay layer of thickness h is sandwiched between two sand layers, as shown in the figure. Initially, the total vertical stress and pore water pressure at point P, which is located at the mid-depth of the clay layer, were 150 kPa and 25 kPa, respectively. Construction of a building caused an additional total vertical stress of 100 kPa at P. When the vertical effective stress at P is 175 kPa, the percentage of consolidation in the clay layer at P is _________ \text{. (in integer)}

Hint:

Consolidation occurs due to an increase in effective stress. The percentage of consolidation is determined by the ratio of change in effective stress to the initial effective stress.

Answer 1

Correct Answer: 50

The initial effective vertical stress is: \[ \sigma'_{\text{initial}} = 150 - 25 = 125\ \text{kPa} \] The final effective vertical stress is: \[ \sigma'_{\text{final}} = 175\ \text{kPa} \] The change in effective stress is: \[ \Delta \sigma' = 175 - 125 = 50\ \text{kPa} \] The percentage of consolidation is given by: \[ \text{Percentage of consolidation} = \frac{\Delta \sigma'}{\sigma'_{\text{initial}}} \times 100 = \frac{50}{125} \times 100 = 40% \] Thus, the percentage of consolidation in the clay layer at P is: \[ \boxed{50%} \]