HOMEWORK SOLUTION

HW #6

GEOTECHNICAL ENGINEERING I

(Question no. 6.1a, 6.6a, 6.13, 6.21b, & 6.24b ..Al-Khafaji textbook) 6.1a     Determine the normal and the shear stress on a plane inclined at an angle of 30o (use analytical procedure). Solution:       45 psi

6.6a     Determine the magnitude and direction of the principle stresses for the soil shown below (use the analytical procedure) Solution:  25 psi   sy = 45 psi

sx = 25 psi            from the x axis (counter clockwise)

from A-A axis = 67.5o + (55o-90o)

= 32.5o (counter clockwise)

6.13          Plot the total overburden pressure (s), pore water pressure (u) and effective overburden pressure for the soil profile below.

Solution:

 50’

 50’  sand  clay  0 – 50’    50’ – 100’    Result in the following table and plotted in the graph

 Depth s u s effective = s - u 0 0 -3120 3120 10 1173 -2496 3669 20 2346 -1872 4218 30 3519 -1248 4767 40 4692 -624 5316 50 5865 0 5865 60 7044 624 6420 70 8223 1248 6975 80 9402 1872 7530 90 10581 2496 8085 100 11760 3120 8640 6.21b   Calculate then plot the vertical stress increment under 6000 kN load (5 ft depth increment) and x=2 m

Solution:

 Q2 6000 kN

 Q1 4000 kN

 2 m     Depth 25 m z = depth

Q= Point load

Ipz from graph / figure 6.11

then tabled and plotted as follow:

 z r1/z Ipz1 r2/z Ipz2 Dsz1 Dsz2 Dsztotal 0 ~ 0 0 0.4775 0 ~ ~ 5 0.4 0.329622 0 0.4775 52.73957 114.6 167.3396 10 0.2 0.43309 0 0.4775 17.3236 28.65 45.9736 15 0.133333 0.457119 0 0.4775 8.126559 12.73333 20.85989 20 0.1 0.46597 0 0.4775 4.659702 7.1625 11.8222 25 0.08 0.470148 0 0.4775 3.00895 4.584 7.59295 6.24b  Calculate then plot the vertical stress increment under point midway between the 500 kN/m and the 800 kN/m line loads, (the increment=5 ft) and x=2 m.

Solution:

 Q2 800 kN/m

 Q1 500 kN/m

 1 m

 1 m    Depth 25 m   z = depth

Q= line load

Ilz from graph / figure 6.13a

or, Ilz= then tabled and plotted as follow:

 z x1/z ILz1 x2/z ILz2 Dsz1 Dsz2 Dsztotal 0 ~ 0 ~ 0 0 0 0 5 0.2 0.612445 0.2 0.612445 61.24449 97.99118 159.2357 10 0.1 0.630636 0.1 0.630636 31.53182 50.4509 81.98272 15 0.066667 0.634124 0.066667 0.634124 21.13748 33.81997 54.95744 20 0.05 0.635354 0.05 0.635354 15.88386 25.41417 41.29803 25 0.04 0.635925 0.04 0.635925 12.7185 20.34961 33.06811 