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Question 7.6: A soil sample has a compression index of 0.3. If the void ra...

A soil sample has a compression index of 0.3. If the void ratio e at a stress of 2940 \mathrm{lb} / \mathrm{ft}^{2} is 0.5,compute (i) the void ratio if the stress is increased to4200 \mathrm{lb} / \mathrm{ft}^{2}, and (ii) the settlement of a soil stratum 13 ft thick.

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Given:  C_{c}=0.3, e_{1}=0.50, p_{1}=2940 \mathrm{lb} / \mathrm{ft}^{2}, p_{2}=4200 \mathrm{lb} / \mathrm{ft}^{2}

 

(i)  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)

 

C_{c}=\frac{e_{1}-e_{2}}{\log p_{2}-\log p_{1}}=\frac{e_{1}-e_{2}}{\log p_{2} / p_{1}}

 

or e_{2}=e_{j}-C_{\mathrm{c}} \log p_{2} / p_{1}

 

substituting the known values, we have,

 

e_{2}=0.5-0.3 \log \frac{4200}{2940}=0.454

 

(ii) The settlement per  S_{t}=\frac{C_{c}}{1+e_{0}} H \log \frac{p_{0}+\Delta p}{p_{0}} (7.10) is

 

S=\frac{C_{c}}{1+e_{1}} H \log \frac{p_{2}}{p_{1}}=\frac{0.3 \times 13 \times 12}{1.5} \log \frac{4200}{2940}=4.83 \mathrm{in}

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