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In a normally consolidated clay of LL=65.65% and 5m thickness, the overburden pressure is increased from 210kN/m$^{2}$ by 120kN/m$^{2}$. Estimate the settlement that takes place.

Assume saturated water content and specific gravity of solid are 45% and 2.7 respectively.

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Estimate compression index $, C_{c}, p_{0}, \Delta p$ and $e_{0}$ $$ \begin{array}{l} C_{c}=0.009(\text { L.L. }-10)=0.009 \times 55.5=0.50 \\ p_{0}=250 \mathrm{kN} / \mathrm{m}^{2} ; \Delta_{p}=120 \mathrm{kN} / \mathrm{m}^{2} ; p_{0}+\Delta p=370 \mathrm{kN} / \mathrm{m}^{2} \\ \text { given } w=45 \% \\ e_{0}=w G ; \text { assuming } G=2.7 \\ e_{0}=0.45 \times 2.7=1.215 \end{array} $$ Estimate consolidation settlement $(\Delta H)$ $$ \Delta H=\frac{C_{c} H}{\left(1+e_{0}\right)} \log _{10}\left(\frac{p_{0}+\Delta p}{p_{0}}\right) $$ given $H=5 \mathrm{~m}=5000 \mathrm{~mm}$ $$ \Delta=\left(\frac{0.5 \times 5000}{2.215}\right) \log _{10}\left(\frac{370}{250}\right)=192 \mathrm{~mm} $$

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