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 30^o (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

s_y = 45 psi

s_x = 25 psi

from the x axis (counter clockwise)

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

= 32.5^o (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

I_pz 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

I_lz from graph / figure 6.13a

or, I_lz=

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