- Effective stress is the stress borne by the soil skeleton and is equal to the total stress minus the pore water pressure. - Effective stress increases as the groundwater table lowers or under surcharge loading. It increases under downward seepage and decreases under upward seepage. - In saturated soils, effective stress depends on the depth of soil and fluctuations in groundwater table. In unsaturated soils above the water table, pore water pressure is negative and effective stress is higher due to tension in the soil.

1. Topic: Effective Stress Principle
By
Dr. S. Dutta

2. Saturated Soil Mass
Let us consider cross sectional area of the soil prism = A
Total weight of the soil prism = vertical force (P)
h
A
)
Ah
(
)
(
stress
Total sat
sat





)
Ah
(
P sat


Pore water pressure (u) is the pressure due to water filling the voids of the soil.
h
)
u
(
pressure
water
Pore w


)
u
(
pressure
water
pore
)
(
stress
total
)
,
or
'
(
stress
Effective 





3. u
' 



h
h
h
' sub
w
sat 






When the ground water table is at ground surface,
 Pore water pressure is also termed as neutral stress.
 Effective stress is also termed as intergranular stress.
 
u
'
u
A
N
A
A
uA
N
A
uA
N
A
U
N
)
P
(
force
vertical
Total
w
w

















 N = intergranular force
U = force taken by pore water
- Effective stress is dependent on the
intergranular force, but not same as contact
stress. It can not be directly measured in
laboratory. It is estimated as the numerical
difference between total stress and pore water
pressure.

4.  Effect of water table fluctuations on effective stress
At section XX at a depth of H, while
the GWT is at depth H1,
2
sat
1 H
H
)
(
stress
Total 




2
wH
)
u
(
pressure
water
Pore 

2
sub
1
2
w
sat
1
2
w
2
sat
1
H
H
'
H
)
(
H
'
H
)
H
H
(
'
u
)
'
(
stress
Effective


























 As the ground water table lowers down, the effective stress increases.

5.  Effective stress in a soil mass under hydrostatic
condition
At level AA,
H
)
(
stress
Total w



H
u w

 0
u
' 




At level BB,
  1
1
sat
w H
H 




 
1
w H
H
u 


   
  1
1
sub
1
w
1
1
sat
w
H
'
H
H
H
H
'
u
'


















6. At level CC,
    2
2
sat
1
1
sat
w H
H
H 






 
2
1
w H
H
H
u 



     
    2
2
sub
1
1
sub
2
1
w
2
2
sat
1
1
sat
w
H
H
'
H
H
H
H
H
H
'
u
'























7.  Increase in effective stress due to surcharge
At level AA,
q
)
(
stress
Total 

0
u  q
u
' 




At level BB,
1
1H
q 


 0
u 
1
1H
q
u
' 






At level CC,
  2
2
sat
1
1 H
H
q 




 2
wH
u 

 
  2
2
sub
1
1
2
w
2
2
sat
1
1
H
H
q
'
H
H
H
q
'
u
'





















8.  Effective stress in soils saturated by capillary action
If the soil above the water table is saturated by capillary action,
 the pore water pressure above the water table is negative. Above
water table, the soil comes under tension due to negative pore water
pressure and effective stress increases.
 at water table, pore water pressure is zero.
 below water table pore water pressure is positive.
Capillary
fringe
-
PWP Diagram
At point E,
h
u w



Capillary rise in a glass tube

9. At level AA,
0
)
(
stress
Total 

0
u  0
u
' 




At level DD,
1
'
H


 "
H
u 1
w



"
H
'
H
'
)
"
H
(
'
H
'
u
'
1
w
1
1
w
1

















- Due to capillary rise of water, at section DD effective stress increased by an
amount of γwH1"
At level BB,
1
sat
1 "
H
'
H 



 0
u 
1
sat
1
1
sat
1 "
H
'
H
0
"
H
'
H
'
u
'















Capillary
fringe
γ

10. 2
wH
u 

At level CC,
2
sub
1
sat
1
2
w
2
sat
1
sat
1
H
"
H
'
H
'
H
H
"
H
'
H
'
u
'






















Capillary
fringe
2
sat
1
sat
1 H
"
H
'
H 






- Due to capillary rise of water, at section BB and CC, effective stress
increased due to increase in unit weight of soil in the capillary fringe.

11.  Effective stress under steady seepage conditions
(a) Downward seepage/ flow of water
At level AA,
w
wH
)
(
stress
Total 


w
wH
u 
 0
u
' 




At level BB,
  1
1
sat
w
w H
H 




1
w
wH
u 

 
 
   
1
w
w
1
w
1
1
sub
1
w
w
w
w
1
w
1
1
sub
1
w
w
1
1
sat
w
w
H
H
H
H
'
H
H
H
H
'
H
H
H
'
u
'






























   
  1
w
1
1
sub
1
1
1
w
w
1
w
1
1
sub
H
i
H
'
H
H
H
H
H
H
'















12. At level CC,
    2
2
sat
1
1
sat
w
w H
H
H 






0
u 
   
   
     
w
2
1
w
2
2
sub
1
1
sub
w
w
2
w
1
w
2
2
sub
1
1
sub
2
2
sat
1
1
sat
w
w
H
H
H
H
H
'
H
H
H
H
H
'
0
H
H
H
'
u
'



































   
 
 
     
2
1
w
2
2
sub
1
1
sub
2
1
2
1
w
2
2
sub
1
1
sub
H
H
i
H
H
'
H
H
H
H
h
H
H
'


















 L
i
)
p
(
pressure
Seepage
w
s


L = length of soil sample in
the direction of flow

13. L
i
)
p
(
pressure
Seepage w
s 

hA
LA
L
h
J
LA
i
A
p
)
J
(
force
Seepage
w
w
w
s








w
w
i
LA
hA
LA
J
j
V
J
)
j
(
volume
unit
per
force
Seepage







Unit = kN/m2
Unit = kN
Unit = kN/m3

14. (b) Upward seepage/ flow of water
At level AA,
w
wH
)
(
stress
Total 


w
wH
u 
 0
u
' 




At level BB,
  1
1
sat
w
w H
H 




1
w
wH
u 

 
 
   
)
H
H
(
H
H
'
H
H
H
H
'
H
H
H
'
u
'
w
1
1
w
w
1
1
sub
1
w
w
w
w
1
w
1
1
sub
1
w
w
1
1
sat
w
w






























   
 
  1
w
1
1
sub
1
1
w
1
1
w
w
1
1
sub
H
i
H
'
H
H
H
H
H
H
'















15. At level CC,
    2
2
sat
1
1
sat
w
w H
H
H 






2
w
wH
u 

   
   
     
 
    h
H
H
'
H
H
H
H
H
H
'
H
H
H
H
H
H
'
H
H
H
H
'
u
'
w
2
2
sub
1
1
sub
w
2
1
2
w
w
2
2
sub
1
1
sub
w
w
2
w
1
w
2
w
w
2
2
sub
1
1
sub
2
w
w
2
2
sat
1
1
sat
w
w















































   
 
 
     
2
1
w
2
2
sub
1
1
sub
2
1
2
1
w
2
2
sub
1
1
sub
H
H
i
H
H
'
H
H
H
H
h
H
H
'


















 L
i
)
p
(
pressure
Seepage
w
s


L = length of soil sample in
the direction of flow

16.  For downward seepage of water through soil, the
effective stress increases as compared to the hydrostatic
condition. The amount of increase in effective stress is
equal to seepage pressure.
 For upward seepage of water through soil, the effective
stress decreases as compared to the hydrostatic
condition. The amount of decrease in effective stress is
equal to seepage pressure.

17.  Quick sand condition
The effective stress gets reduced due to upward flow of water. When the
head causing flow is increased, a stage is reached when the effective
stress reduces to zero. The condition so developed in coarse grained soils
is known as quick sand condition.
Upward seepage of water
At level CC,
L
sat



1
w
wH
u 

 
L
i
L
'
h
L
'
L
H
L
'
H
L
L
'
H
L
'
u
'
w
sub
w
sub
1
w
w
sub
1
w
w
w
sub
1
w
w
sat





































w
sub
c
w
c
sub
i
0
L
i
L
,
0
'
if










ic is termed as critical
hydraulic gradient.

18.  The effective stress is zero at critical hydraulic gradient.
 Shear strength (s) of soil is expressed as, '
tan
'
'
c
s n 



c' = cohesion, ф' = angle of internal friction, σn' = effective normal stress
 When effective stress reduces to zero at critical hydraulic gradient,
- for cohesionless soil, shear strength (s) = 0
- for cohesive soil, shear strength (s) = c
 The cohesionless soil looses its shear strength entirely at critical
hydraulic gradient. This condition is called as quick sand condition.
 If the critical gradient is exceeded, the soil particles move upward
and the soil surface appears to be boiling. The quick condition is also
known as boiling condition. During this stage, a violent and visible
agitation of particles occurs.

19.  The discharge suddenly increases due to an increase in the coefficient of
permeability occurred in the process. Reaching quick sand condition, the
soil behaves as a liquid slurry having no shear strength. If a weight is
placed on the soil surface, it sinks down.
 The cohesive soil does not become quick at zero effective stress,
as it still possesses some shear strength equal to the cohesion
intercept.
 A quick sand condition is most likely to occur in silt and fine sand.
The discharge required to maintain a quick sand condition increases as the
permeability of the soil increases. For gravel, quick sand condition is
generally not developed as it requires very high discharge that may not be
available.
 The quick sand is not a special type of soil. It is a hydraulic
condition.

20. Topic: Seepage Analysis
By
Dr. S. Dutta

21. - Seepage is the flow of water under gravitational force in a
permeable medium. Flow of water takes place from a point of high
head to a point of low head.
- The flow is generally laminar.
- The path taken by a water particle is represented by a flow line.
Although an infinite number of flow lines can be drawn, for
convenience, only a few are drawn.
- At certain points on different flow lines, the total head will be the
same. The lines connecting points of equal total head can be
drawn. These lines are known as equipotential lines.
- The equipotential lines cross the flow lines at right angles. The
flow lines and equipotential lines together form a flow net. The flow
net gives a pictorial representation of the path taken by water
particles and the head variation along that path.

24. Flow net for field condition for a sheet pile wall storing water
Graphical method (Flow net construction):

26.  Characteristics of flow net
(1)The equipotential lines should be orthogonal to the
flow lines. They should intersect at right angle.
(2)The discharge between any two adjacent flow lines is
constant. It means that the discharge through all the
flow channels is same.
(3) The drop of head between two adjacent equipotential
lines is constant.
(4)The ratio of the length and width of each field is
constant. The ratio is generally taken as unity for
convenience. In other words, the flow net consists of
approximate squares.

27. Fig. 9.20 (From Arora)

31. e
1
1
G
e
1
1
G
i
i
w
w
c
w
sub
c













32. Flow net for a dam
 Flow net construction for a concrete dam

34. Failure may occur in downstream slope due to seepage through the earthen
embankment, if no filter is provided at the downstream side.
 Flow through earthen embankment

35.  Derivation of Laplace’s equation