A stratum of normally consolidated clay 7 m thick is located at a depth 12m below ground level. The natural moisture content of the clay is 40.5 per cent and its liquid limit is 48 per cent. The specific gravity of the solid particles is 2.76. The water table is located at a depth 5 m below ground

Question

A stratum of normally consolidated clay 7 m thick is located at a depth 12m below ground level. The natural moisture content of the clay is 40.5 per cent and its liquid limit is 48 per cent. The specific gravity of the solid particles is 2.76. The water table is located at a depth 5 m below ground surface. The soil is sand above the clay stratum. The submerged unit weight of the sand is [latex]11 \mathrm{kN} / \mathrm{m}^{3}[/latex] and the same weighs[latex]18 \mathrm{kN} / \mathrm{m}^{3}[/latex] above the water table. The average increase in pressure at the center of the clay stratum is[latex]120 \mathrm{kN} / \mathrm{m}^{2}[/latex] due to the weight of a building that will be constructed on the sand above the clay stratum. Estimate the expected settlement of the structure

Accepted Answer

1 . Determination of e and [latex]\gamma_{b}[/latex] for the clay

[latex]\frac{W_{w}}{W_{s}}=w_{n}, W_{s}=V_{s} G_{s} \gamma_{w}=1 imes 2.76 imes 1=2.76 \mathrm{~g}[/latex]

[latex]W_{w}=\frac{40.5}{100} imes 2.76=1.118 \mathrm{~g}[/latex]

[latex]V_{w}=\frac{W_{w}}{\gamma_{w}}=\frac{1.118}{1}=1.118 \mathrm{~cm}^{3}[/latex]

[latex]e_{0}=\frac{V_{w}}{V}=\frac{1.118}{1}=1.118[/latex]

[latex]W=W_{w}+W_{s}=1.118+2.76=3.878 \mathrm{~g}[/latex]

[latex]\gamma_{t}=\frac{W}{1+e_{0}}=\frac{3.88}{2.118}=1.83 \mathrm{~g} / \mathrm{cm}^{3}[/latex]

[latex]\gamma_{b}=(1.83-1)=0.83 \mathrm{~g} / \mathrm{cm}^{3}[/latex]

2. Determination of overburden pressure [latex]p_{0}[/latex]

[latex]p_{0}=\gamma_{1} h_{1}+\gamma_{2} h_{2}+\gamma_{3} h_{3} ext { or }[/latex]

[latex]p_{0}=0.83 imes 9.81 imes 3.5+11 imes 7+18 imes 5=195.5 \mathrm{kN} / \mathrm{m}^{2}[/latex]

Compression index [latex]\overline{P_{a}}=P_{a}+P_{w}=\frac{1}{2} \gamma_{b} H^{2} K_{A}+\frac{1}{2} \gamma_{w} H^{2}[/latex] (11.17)

[latex]C_{c}=0.009\left(w_{l}-10 ight)=0.009 imes(48-10)=0.34[/latex]

4. Excess pressure

[latex]\Delta p=120 \mathrm{kN} / \mathrm{m}^{2}[/latex]

5. Total Settlement

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

[latex]=\frac{0.34}{2118} imes 700 \log \frac{195.5+120}{1055}=23.3 \mathrm{~cm}[/latex]

Estimated settlement = 23.3 cm.

Question 7.3: A stratum of normally consolidated clay 7 m thick is located...

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