Question

A clay layer of thickness \( H \) has a preconsolidation pressure \( p_c \) and an initial void ratio \( e_0 \). The initial effective overburden stress at the mid-height of the layer is \( p_0 \). At the same location, the increment in effective stress due to applied external load is \( \Delta p \). The compression and swelling indices of the clay are \( C_c \) and \( C_s \), respectively. If \( p_0 < p_c < (p_0 + \Delta p) \), then the correct expression to estimate the consolidation settlement \( s_c \) of the clay layer is

• A. \( s_c = \frac{H}{1 + e_0} \left[ C_c \log \frac{p_c}{p_0} + C_s \log \frac{p_0 + \Delta p}{p_c} \right] \)
• B. \( s_c = \frac{H}{1 + e_0} \left[ C_s \log \frac{p_c}{p_0} + C_c \log \frac{p_0 + \Delta p}{p_c} \right] \)
• C. \( s_c = \frac{H}{1 + e_0} \left[ C_c \log \frac{p_c}{p_0} + C_s \log \frac{p_0 + \Delta p}{p_c} \right] \)
• D. \( s_c = \frac{H}{1 + e_0} \left[ C_s \log \frac{p_0}{p_c} + C_c \log \frac{p_0 + \Delta p}{p_c} \right] \)

Hint:

The formula for consolidation settlement incorporates the compression and swelling indices along with the stress changes in the soil.

Answer 1

The Correct Option is B

The consolidation settlement \( s_c \) of a clay layer is determined by the change in effective stress and the corresponding change in void ratio. The expression for \( s_c \) when the preconsolidation pressure \( p_c \) and the increment in stress \( \Delta p \) are known is given by the formula: \[ s_c = \frac{H}{1 + e_0} \left[ C_s \log \frac{p_c}{p_0} + C_c \log \frac{p_0 + \Delta p}{p_c} \right]. \] This formula accounts for both compression and swelling of the soil layer, with \( C_s \) and \( C_c \) being the swelling and compression indices, respectively. Therefore, the correct answer is (B). Final Answer: \( s_c = \frac{H}{1 + e_0} \left[ C_s \log \frac{p_c}{p_0} + C_c \log \frac{p_0 + \Delta p}{p_c} \right] \)