This document is a series of lecture slides from Assistant Professor Khalid R. Mahmood at the University of Anbar in Iraq-Ramadi on the topic of effective stress concepts in soil mechanics. It introduces key concepts such as effective stress, total stress, pore water pressure, and their relationships. It also discusses effective stress in saturated soil with and without seepage, seepage forces, filter requirements, capillary rise in soil, and two example problems calculating stresses with depth.

1. University of Anbar
College of Engineering
Civil Engineering Department
Iraq-Ramadi
Asst. Prof. Khalid R. Mahmood (PhD.)
215
Effective Stress Concept
Topics
Effective Stress Concept
Effective Stress in Saturated Soil with
no Seepage
Effective Stress in Saturated Soil with
Seepage
Seepage Force
Filter Requirements and Selection of Filter Material
Capillary Rise in Soil
Effective Stress in Capillary Zone
Water
Water Table (W.T.)
Ground Surface (G.S.) Air
Voids
Solid

2. University of Anbar
College of Engineering
Civil Engineering Department
Iraq-Ramadi
Asst. Prof. Khalid R. Mahmood (PhD.)
216
Effective Stress Concept
•Soil is a multi phase system
•To perform any kind of analysis - we must understand stress
distribution
•The concept of effective stress:
• The soil is “loaded” (footing for example)
• The resulting stress is transmitted to the soil mass
• The soil mass supports those stresses at the point to point
contacts of the individual soil grains

3. University of Anbar
College of Engineering
Civil Engineering Department
Iraq-Ramadi
Asst. Prof. Khalid R. Mahmood (PhD.)
217
The total stress at A is calculated from:
The weight of the soil above A
The weight of the water above A
= H w + (HA - H) sat
= Total Stress at A
w = Unit Weight of Water
sat = Saturated Unit Weight
HA = Height of A to Top of water
H = Height of water

4. University of Anbar
College of Engineering
Civil Engineering Department
Iraq-Ramadi
Asst. Prof. Khalid R. Mahmood (PhD.)
218
• is the stress applied to the soil by its own weight
• As you go deeper in the soil mass, the stress increases
• The soil carries the stress in 2 ways:
• A portion is carried by the water (acts equally in all
directions)
• A portion is carried by the soil solids at their point of
contact.

5. University of Anbar
College of Engineering
Civil Engineering Department
Iraq-Ramadi
Asst. Prof. Khalid R. Mahmood (PhD.)
219
/
= (P1v+P2v+P3v .....+Pnv) / A
If as = a1 + a2 + a3 +...an
Then the space occupied by water = A - as
Assume u = HA w HA = Height of water
= /
+ u(A - as) / A

6. University of Anbar
College of Engineering
Civil Engineering Department
Iraq-Ramadi
Asst. Prof. Khalid R. Mahmood (PhD.)
220
Since as is very small, assume = 0
= /
+ u
Recall the following equation:
= H w + (HA - H) sat
Now, /
= - u
Substituting: /
= [H w + (HA - H) sat] - HA w
Rearranging: /
= (HA - H)( sat - w) = Hsoil
/
Effective Stress is independent of height of water
In the equation: = /
+ u
/
is the soil skeleton stress
u is the stress in the water, or pore water pressure

7. University of Anbar
College of Engineering
Civil Engineering Department
Iraq-Ramadi
Asst. Prof. Khalid R. Mahmood (PhD.)
221
Effective Stress in Saturated Soil with no Seepage

8. University of Anbar
College of Engineering
Civil Engineering Department
Iraq-Ramadi
Asst. Prof. Khalid R. Mahmood (PhD.)
222
Effective Stress in Saturated Soil with Seepage
Upward flow

9. University of Anbar
College of Engineering
Civil Engineering Department
Iraq-Ramadi
Asst. Prof. Khalid R. Mahmood (PhD.)
223
Note that the h/H2 is the hydraulic gradient that caused flow
therefore,
wc izz
And limiting conditions may occur when 0wc izz which
lead to
icr = critical hydraulic gradient
w
cri
for most soils 0.9-1.1 ith average value of 1

10. University of Anbar
College of Engineering
Civil Engineering Department
Iraq-Ramadi
Asst. Prof. Khalid R. Mahmood (PhD.)
224
Downward flow

11. University of Anbar
College of Engineering
Civil Engineering Department
Iraq-Ramadi
Asst. Prof. Khalid R. Mahmood (PhD.)
225
Seepage Force
Azp1
Aizforceseepage
forceseepagepAizzp
w
w 12 )(
Aizforceseepage
forceseepagepAizzp
w
w 33 )(

12. University of Anbar
College of Engineering
Civil Engineering Department
Iraq-Ramadi
Asst. Prof. Khalid R. Mahmood (PhD.)
226
The volume of the soil contributing to the effective stress force
equals zA, so the seepage force per unit volume of the soil is
w
w
i
zA
Aiz
in the direction of seepage (see the fig.)
Therefore, in isotropic soil and in any direction, the force acts in
the same direction as the direction of flow. Thus, the flow nets
can be used to find the hydraulic gradient at any point to find
seepage force at that point. This concept is useful to estimate F.S
against heave

13. University of Anbar
College of Engineering
Civil Engineering Department
Iraq-Ramadi
Asst. Prof. Khalid R. Mahmood (PhD.)
227
Factor of Safety against heave at the downstream of hydraulic structures
Terzaghi (1922)
H1
H2
Sheet pile
Impermeable layer
Permeable layer
D
D/2
D
D/2
W
U
Heave zone

14. University of Anbar
College of Engineering
Civil Engineering Department
Iraq-Ramadi
Asst. Prof. Khalid R. Mahmood (PhD.)
228
wav
wav
wav
wsat
i
iD
D
ixvolumesoil
DD
U
W
seepagebycausedforceUplift
weightSubmerged
SF
2
2
2
1
2
1
)(
))(2/(
.

15. University of Anbar
College of Engineering
Civil Engineering Department
Iraq-Ramadi
Asst. Prof. Khalid R. Mahmood (PhD.)
229
Estimation of iav
a b c
e
d
nd = 10
Drivinghead
a b c

16. University of Anbar
College of Engineering
Civil Engineering Department
Iraq-Ramadi
Asst. Prof. Khalid R. Mahmood (PhD.)
230
point driving
head
a
H
10
4
b H
10
7.6
c H
10
5.2
D
h
i
hhh
h
av
av
bca
av
2
2/)(

17. University of Anbar
College of Engineering
Civil Engineering Department
Iraq-Ramadi
Asst. Prof. Khalid R. Mahmood (PhD.)
231
Filter Requirements and Selection of Filter Material
In practice, for the safe of the hydraulic structure, a minimum
value of 4 to 5 for F.S against heaving is used, because of the
uncertainty in the analysis. One way to increase the F.S is using
filter.
Filter:- is a granular material with opening small enough to
prevent the movement of the soil particles upon which is
placed and, at the same time, is previous enough to offer little
resistance to seepage through it.

18. University of Anbar
College of Engineering
Civil Engineering Department
Iraq-Ramadi
Asst. Prof. Khalid R. Mahmood (PhD.)
232
a b c
e
d
nd = 10
D
D/2
W
W
U
D1

19. University of Anbar
College of Engineering
Civil Engineering Department
Iraq-Ramadi
Asst. Prof. Khalid R. Mahmood (PhD.)
233
wav
F
wav
F
F
i
D
D
iD
DDD
U
WW
SF
1
2
1
2
2
1
2
1
2
1
.

20. University of Anbar
College of Engineering
Civil Engineering Department
Iraq-Ramadi
Asst. Prof. Khalid R. Mahmood (PhD.)
234
Selection of Filter Material
Capillary R

21. University of Anbar
College of Engineering
Civil Engineering Department
Iraq-Ramadi
Asst. Prof. Khalid R. Mahmood (PhD.)
235
Capillarity rise in Soil

22. University of Anbar
College of Engineering
Civil Engineering Department
Iraq-Ramadi
Asst. Prof. Khalid R. Mahmood (PhD.)
236
For pure water and clean glass = 0
w
c
d
T
h
4
For water T = 72 m.N/m
d
hc
1
the smaller the capillarity tube, the larger capillary rise

23. University of Anbar
College of Engineering
Civil Engineering Department
Iraq-Ramadi
Asst. Prof. Khalid R. Mahmood (PhD.)
237
For soils, the capillary tubes formed because of the continuity of
voids have variable cross sections. The results of the
nonuniformity on capillary can be demonstrated as shown in the
fig.
Variation of S in the soil

24. University of Anbar
College of Engineering
Civil Engineering Department
Iraq-Ramadi
Asst. Prof. Khalid R. Mahmood (PhD.)
238
Hazen (1930) give a formula to estimate the height of capillary
10
)(
eD
C
mmh c

25. University of Anbar
College of Engineering
Civil Engineering Department
Iraq-Ramadi
Asst. Prof. Khalid R. Mahmood (PhD.)
239
Effective Stress in Capillary Zone
The general relationship of effective stress is
u
For soil fully saturated by capillary wchu
For soil partially saturated by capillary wch
S
u
100

26. University of Anbar
College of Engineering
Civil Engineering Department
Iraq-Ramadi
Asst. Prof. Khalid R. Mahmood (PhD.)
240
Examples
EXAMPLE1. Plot the variation of total and effective vertical
stresses, and pore water pressure with depth for the soil profile
shown below in Fig.

27. University of Anbar
College of Engineering
Civil Engineering Department
Iraq-Ramadi
Asst. Prof. Khalid R. Mahmood (PhD.)
241

28. University of Anbar
College of Engineering
Civil Engineering Department
Iraq-Ramadi
Asst. Prof. Khalid R. Mahmood (PhD.)
242

29. University of Anbar
College of Engineering
Civil Engineering Department
Iraq-Ramadi
Asst. Prof. Khalid R. Mahmood (PhD.)
243
The values of v, u and /
v computed above are summarized in
Table 1.
Table 6.1 Values of v, u and /
v in Ex. 1

30. University of Anbar
College of Engineering
Civil Engineering Department
Iraq-Ramadi
Asst. Prof. Khalid R. Mahmood (PhD.)
244
EXAMPLE2. Plot the variation of total and effective vertical
stresses, and pore water pressure with depth for the soil profile
shown below in Fig.
Dry Sand
Gs = 2.66
Moist Sand Zone of capillary rise
Gs = 2.66
Saturated Clay
= 42%
A
H1 = 2 m
B
H2 = 1.8
m
C
H3 = 3.2
m
G.W.
Rock

31. University of Anbar
College of Engineering
Civil Engineering Department
Iraq-Ramadi
Asst. Prof. Khalid R. Mahmood (PhD.)
245
Dry sand 84.1681.9
55.01
66.2
e1
G
w
s
d kN/m3
Moist sand 58.1881.9
55.01
55.0*5.066.2
e1
SeG
w
s
t kN/m3
Saturated Clay
138.1
1
42.0*71.2
S
G
e s
66.1781.9
138.11
138.166.2
e1
eG
w
s
sat kN/m3

32. University of Anbar
College of Engineering
Civil Engineering Department
Iraq-Ramadi
Asst. Prof. Khalid R. Mahmood (PhD.)
246
Point v kN/m2
u kN/m2 /
v kN/m2
A 0 0 0
0 33.68
B 2*16.84=33.68 - S w H2 = - 0.5*9.81*1.8 =
- 8.83
33.68-(-8.83) =
42.51
C 2*16.84+1.8*18.58 = 67.117 0 67.117
D 2*16.84+1.8*18.58+3.2*17.66 =123.68 3.2*9.81=31.39
123.68-31.39 =
92.24

33. University of Anbar
College of Engineering
Civil Engineering Department
Iraq-Ramadi
Asst. Prof. Khalid R. Mahmood (PhD.)
247
The plot is shown below in Fig.
Variation of v, u and /
v with depth
0
1
2
3
4
5
6
7
8
-20 -10 0 10 20 30 40 50 60 70 80 90 100 110 120 130 140
Stress, kN/m2
depth,(m)
Total stress
Pore water pressure
Effective stress