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.

Question

Two points on a curve for a normally consolidated clay have the following coordinates.

Point 1: [latex]e_{1}=0.7, \quad p_{1}=2089 \mathrm{lb} / \mathrm{ft}^{2}[/latex]

Point 2: [latex]e_{2}=0.6, \quad p_{2}=6266 \mathrm{lb} / \mathrm{ft}^{2}[/latex]

If the average overburden pressure on a 20 ft thick clay layer is [latex]3133 \mathrm{lb} / \mathrm{ft}^{2}[/latex], how much settlement will the clay layer experience due to an induced stress of [latex]3340 \mathrm{lb} / \mathrm{ft}^{2}[/latex] at its middepth.

Accepted Answer

[latex] 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}} [/latex] (7.4) we have

[latex]C_{c}=\frac{e_{1}-e_{2}}{\log p_{2} / p_{1}}=\frac{0.7-0.6}{\log (6266 / 2089)}=0.21[/latex]

We need the initial void ratio [latex]e_{0}[/latex] at an overburden pressure of 3133 [latex]\mathrm{lb} / \mathrm{ft}^{2}[/latex] .

[latex]C_{c}=\frac{e_{0}-e_{2}}{\log p_{2} / p_{0}}=0.21[/latex]

or [latex]\left(e_{0}-0.6 ight)=0.21 \log (6266 / 3133)=0.063[/latex]

or [latex]e_{0}=0.6+0.063=0.663[/latex]

Settlement, [latex]S=\frac{C_{c}}{1+e_{0}} H \log \frac{p_{0}+\Delta p}{p_{0}}[/latex]

Substituting the known values, with [latex]\Delta p=3340 \mathrm{lb} / \mathrm{ft}^{2}[/latex]

[latex]S=\frac{0.21 imes 20 imes 12}{1663} \log \frac{3133+3340}{3133}=9.55[/latex] in

Question 7.7: Two points on a curve for a normally consolidated clay have ...

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