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Solution
Answer: C) 6 inch
Long-term settlement is caused by the clay layer.
Calculate the original pressure in the middle of the clay layer:
\[p_0= \gamma _1 h_1+ \gamma _2 h_2+( \gamma '_3h_3)/2=80 \times 10+120 \times 15 + ((105-62.4) \times 20)/2=3,026\ PSF\]
Additional Pressure caused by the building is given in the middle of the clay layer:
\[\triangle p =1,200\ PSF\]
Final Pressure at Middle of Clay Layer:
\[p_f=p_0+∆p=3026+1200 =4226\ PSF\]Original void content in clay, where w is clay water content:
\[e_0≈w(SG)=0.40 \times 2.6=1.04\]
Compression index:
\[C_c = 0.009(LL-10) = 0.009 \times (50-10) =0.36\]
Long-term settlement in clay layer Long-term settlement in the clay layer:
\[S = \frac{H C_{c} Log_{10} (p_{f} /p_{0}) }{(1+ e_{0}) } =\frac{(20\times0.36 \times Log(4226/3026)}{(1+1.04)} =\ 0.51\ ft=6.1\ inch\]
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