HOMEWORK SOLUTION

HW #9

GEOTECHNICAL ENGINEERING I

(Question no. 7.16, 7.18, 7.22, ..Al-Khafaji textbook)

 10’

 60’

 10’

 10’

7.16

Question:

Determine the ultimate consolidation settlement caused by the placement of 5 ft of fill on top of the above profile. (assume sm fill = 110.4 pcf)

Solution:

due to the fill = 110.4 x 5 = 552 psf

7.18

e=1.00

e=0.9

t50 = 12 min              (two way drainage)

d1  = 25.2 mm

d2  = 24.3 min                       T50 = 0.197

Question:

Determine the coefficient of permeability (k) and the compression Index (Cc) for the clay.

Solution:

7.22                  footing(rectangular)=2.4m x 1.8m

(L/B=2.4/1.8=1.33<10)

Question:

Settlement after 1 year.

Solution:

Iz (0) = 0.1

Iz (2B) = 0       2B=2x1.8=3.6m

Iz (B/2) = 0.5+0.1

= 0.5+0.1

svp (B/2) = 14.9x(0.9) = 13.41

 Depth (m) qc Es=2.5xqc (MN/m2) sm (kN/m3) 0.6-1.2 2.85 7.125 14.9 1.2-1.8 3.14 7.85 14.9 1.8-2.1 5.6 14 16.5 2.1-2.4 8.33 20.825 16.5 2.4-3.0 5 12.5 16.5 3.0-3.6 7.37 18.425 18.9 3.6-4.2 12.5 31.25 18.9

 Dz (m) Iz E (MN/m2) (Iz/E)xDz (m3/MN) 0.6 0.38 7.125 0.032 0.6 0.93 7.85 0.071 0.3 0.774 14 0.017 0.3 0.67 20.825 0.0097 0.6 0.516 12.5 0.0248 0.6 0.31 18.425 0.01 0.6 0.1 31.25 0.0019

Total    =          0.1661 m3/MN

=          1.661x10-4 m3/kN

t=1 year

=   1.2

Settlement (r)=

= 0.98 x 1.2 x 254.6 x 0.0001661

= 49.73 x 10-3 m

= 49.73 mm      ~     5 cm