Question

The net stress increase due to a building at the middle of a 6 ft normally consolidated clay layer is 400 psf. The compression index of the soil is 0.6 and its void ratio is 1.3. If the primary consolidation settlement is 2.34 inch, the initial effective consolidation stress (psf) is most nearly equal to

a) 1400 b) 1200 c) 1000 d) 1600

Please show all steps

Answer 1

Let the initial effective stress at middle of clay = q'

Increase in effective stress at middle of clay = 400 psf

Final effective stress at middle of clay = q'_f = q' + 400

Height of clay layer = 6 ft

Void ratio = e = 1.3

Compression index = C_c = 0.6

Primary Consolidation settlement = S = 2.34 in

= 2.34/12 ft

Settlement for a normally consolidated clay is given by

Putting values

2.34/12 = (0.6x6)/(1+1.3)xlog(q' + 400/q')

0.12458 = log(q' + 400/q')

10^0.12458 = q'+400/q'

1.332 xq' = q' + 400

0.332q' = 400

q' = 1204.82 psf

= 1200 psf