**% Students Correctly Answered:**

**17.2%**

Solution

**Answer: D) 6.8 inch**

Long-term settlement is caused by the clay layer.

Calculate the original pressure in the middle of the clay layer:

\[p_0= \gamma _1 h_1+ \gamma _2 h_2+( \gamma '_3h_3)/2=80 \times 10+120 \times 15 + ((105-62.4) \times 20)/10=2685\ PSF\]

Additional Pressure caused by the building is given in the middle of the clay layer:

\[\triangle p =1200\ PSF\]

Final Pressure at Middle of Clay Layer:

\[p_f=p_0+∆p=2685+1200 =3885\ PSF\]

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:**

**\[S = \frac{H C_{c} Log_{10} (p_{f} /p_{0}) }{(1+ e_{0}) } =\frac{(20\times0.36 \times Log(3885/2685)}{(1+1.04)} =\ 0.566\ ft=6.8\ inch\]**