A column of a building carries a load of 1000 kips. The load is transferred to sub soil through a square footing of size 16 x 16 ft founded at a depth of 6.5 ft below ground level. The soil below the footing is fine sand up to a depth of 16.5 ft and below this is a soft compressible clay of

Question

A column of a building carries a load of 1000 kips. The load is transferred to sub soil through a square footing of size 16 x 16 ft founded at a depth of 6.5 ft below ground level. The soil below the footing is fine sand up to a depth of 16.5 ft and below this is a soft compressible clay of thickness 16 ft. The water table is found at a depth of 6.5 ft below the base of the footing. The specific gravities of the solid particles of sand and clay are 2.64 and 2.72 and their natural moisture contents are 25 and 40 percent respectively. The sand above the water table may be assumed to remain saturated. If the plastic limit and the plasticity index of the clay are 30 and 40 percent respectively, estimate the probable settlement of the footing

Accepted Answer

1. Required [latex]\Delta p[/latex] at the middle of the clay layer using the Boussinesq equation

[latex]\frac{z}{B}=\frac{24.5}{16}=1.53<3.0[/latex]

Divide the footing into 4 equal parts so that ZIB > 3

The concentrated load at the center of each part = 250 kips

Radial distance, r = 5.66 ft

By the Boussinesq equation the excess pressure [latex]\Delta p[/latex] at depth 24.5 ft is [latex]\left(I_{B}=0.41 ight)[/latex]

[latex]\Delta p=4 imes \frac{Q}{z^{2}} I_{B}=\frac{4 imes 250}{24.5^{2}} imes 0.41=0.683 \mathrm{k} / \mathrm{ft}^{2}[/latex]

2. Void ratio and unit weights

Per the procedure explained in Ex. 7.3

For sand [latex]\gamma_{t}=124 \mathrm{lb} / \mathrm{ft}^{3} \quad \gamma_{b}=61.6 \mathrm{lb} / \mathrm{ft}^{3}[/latex]

For clay [latex]\gamma_{b}=51.4 \mathrm{lb} / \mathrm{ft}^{3} \quad e_{0}=1.09[/latex]

3. Overburden pressure [latex]p_{0}[/latex]

[latex]p_{0}=8 imes 51.4+10 imes 62+13 imes 124=26391 \mathrm{~b} / \mathrm{ft}^{2}[/latex]

4. Compression index

[latex]w_{l}=I_{p}+w_{p}=40+30=70 \%, \quad C_{c}=0.009(70-10)=0.54[/latex]

Settlement [latex]S_{t}=\frac{0.54}{1+1.09} imes 16 imes \log \frac{2639+683}{2639}=0.413 \mathrm{ft}=4.96 \mathrm{in}[/latex] .

Question 7.4: A column of a building carries a load of 1000 kips. The load...

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