GATE Civil Engineering
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A clay layer of thickness $\text{H}$ 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  $p_{0}< p_{c}< \left ( p_{0} +\Delta p\right )$, then the correct expression to estimate the consolidation settlement $(S_{c})$ of the clay layer is

  1. $s_{c}=\frac{H}{I+e_{0}}\left [ C_{c} \log\frac{p_{c}}{p_{0}}+C_{s}\log \frac{p_{0}+\Delta p}{p_{c}} \right ]$
  1. $s_{c}=\frac{H}{I+e_{0}}\left [ C_{s} \log\frac{p_{c}}{p_{0}}+C_{c}\log \frac{p_{0}+\Delta p}{p_{c}} \right ]$
  1. $s_{c}=\frac{H}{I+e_{0}}\left [ C_{c} \log\frac{p_{0}}{p_{c}}+C_{s}\log \frac{p_{0}+\Delta p}{p_{c}} \right ]$
  1. $s_{c}=\frac{H}{I+e_{0}}\left [ C_{s} \log\frac{p_{0}}{p_{c}}+C_{c}\log \frac{p_{0}+\Delta p}{p_{c}} \right ]$
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