Solution

**Answer: A) 0.64 in**

Calculate the effective stress at the mid-depth of the soil layer:

$$ {\sigma\prime}_v=\left(125\ pcf-62.4\ pcf\right)\ast\frac{15\ ft}{2}\ \ =\ 469.5\ psf $$

Calculate past pressure based on overconsolidation ratio of existing soil:

$$ OCR\ =\ \frac{{\sigma^\prime}_p}{{\sigma^\prime}_v} $$

$$ {\sigma^\prime}_p=\ OCR\ast{\sigma^\prime}_v=3\ast469.5\ psf=1408.5\ psf\ $$

Using 2V:1H stress distribution, calculate the stress increase at mid-depth of the layer:

$$ \Delta\sigma=\frac{300\ kip\ \ast\ 1000\ lb/kip}{\left(6\ ft\ +7.5\ ft\right)\ast(40\ ft+7.5\ ft)}=467.84\ psf $$

$$ {\sigma\prime}_v+\Delta\sigma=469.5\ psf+467.84\ psf=937.34\ psf<{\sigma^\prime}_p(1408.5\ psf) $$

Calculate OCR after the footing is applied and loaded:

$$ OCR=\frac{{\sigma^\prime}_p}{{\sigma\prime}_v+\Delta\sigma}=1.5>1 $$

$$ \therefore Soil\ is\ overconsolidated $$

Calculate the primary consolidation based on an overconsolidated clay:

$$ s=\ \frac{C_r}{1+e_0}H{log}_{10}\frac{{\sigma\prime}_v+\Delta\sigma}{{\sigma\prime}_v} $$

$$ s=\ \frac{0.02}{1+0.7}\ast15\ ft\ast12\frac{in}{ft}\ast{log}_{10}\frac{469.5\ psf+467.84\ psf}{469.5\ psf}=0.64\ in $$