Two points on a curve for a normally consolidated clay have the following coordinates.
Point 1: e_{1}=0.7, \quad p_{1}=2089 \mathrm{lb} / \mathrm{ft}^{2}
Point 2: e_{2}=0.6, \quad p_{2}=6266 \mathrm{lb} / \mathrm{ft}^{2}
If the average overburden pressure on a 20 ft thick clay layer is 3133 \mathrm{lb} / \mathrm{ft}^{2}, how much settlement will the clay layer experience due to an induced stress of 3340 \mathrm{lb} / \mathrm{ft}^{2} at its middepth.
C_{c}=\frac{e_{0}-e}{\log p-\log p_{0}}=\frac{e_{0}-e}{\log p / p_{0}}=\frac{\Delta e}{\log p / p_{0}} (7.4) we have
C_{c}=\frac{e_{1}-e_{2}}{\log p_{2} / p_{1}}=\frac{0.7-0.6}{\log (6266 / 2089)}=0.21
We need the initial void ratio e_{0} at an overburden pressure of 3133 \mathrm{lb} / \mathrm{ft}^{2} .
C_{c}=\frac{e_{0}-e_{2}}{\log p_{2} / p_{0}}=0.21
or \left(e_{0}-0.6\right)=0.21 \log (6266 / 3133)=0.063
or e_{0}=0.6+0.063=0.663
Settlement, S=\frac{C_{c}}{1+e_{0}} H \log \frac{p_{0}+\Delta p}{p_{0}}
Substituting the known values, with \Delta p=3340 \mathrm{lb} / \mathrm{ft}^{2}
S=\frac{0.21 \times 20 \times 12}{1663} \log \frac{3133+3340}{3133}=9.55 in