This document discusses the concepts of total stress, effective stress, and pore water pressure in soils. It defines total stress as the vertical stress applied by overlying loads divided by the cross-sectional area. Effective stress is defined as the total stress minus the pore water pressure. The document provides examples of calculating total stress, pore water pressure, and effective stress for different soil layers based on the soil properties, stratigraphy, and water table level.

1. Effective Stress

2. W
W
Soil loaded by an
applied weight W
Soil loaded by water
weighing W

3. W
W
Soil loaded by an
applied weight W
Soil loaded by water
weighing W
Compression No deformation

4.  v Vertical Stress
Vertical Force
Cross Sectional Area
  (1)
Definition of Total and Effective Stress

5.  v Vertical Stress
Vertical Force
Cross Sectional Area
 
 
v v w
u
'  
(1)
(2)
Definition of Total and Effective Stress
Effective vertical stress

6.  v Vertical Stress
Vertical Force
Cross Sectional Area
 
 
v v w
u
'  
(1)
(2)
Definition of Total and Effective Stress
Effective vertical stress
  v  u w   v ´
C a se (a ) W
A
0 W
A

7.  v Vertical Stress
Vertical Force
Cross Sectional Area
 
 
v v w
u
'  
(1)
(2)
Definition of Total and Effective Stress
Effective vertical stress
  v  u w   v ´
C a se (a ) W
A
0 W
A
C a se (b ) W
A
W
A
0

8. Layer 1
Layer 2
Layer 3
d1
d2
d3
 
bulk  1
 
bulk  2
 
bulk  3
Fig 3 Soil Profile
Surcharge q
v
z
Calculation of Effective Stress

9. d1
d2
q
 v
z
A
Plan
Elevation
Calculation of Total Vertical Stress
z
Force on base = Force on top + Weight of soil

10. d1
d2
q
 v
z
A
Plan
Elevation
Calculation of Total Vertical Stress
z
Force on base = Force on top + Weight of soil
A v = A q + A 1 d1 + A 2 d2 +
A 3 ( z - d1 - d2 )

11. d1
d2
q
 v
z
A
Plan
Elevation
(4)
Calculation of Total Vertical Stress
z
Force on base = Force on top + Weight of soil
A v = A q + A 1 d1 + A 2 d2 +
A 3 ( z - d1 - d2 )
v = q + 1 d1 + 2 d2 +3 ( z - d1 - d2 )

12. Fig 4 Soil with a static water table
Water table
H
P u P H
w w
( )   (5)
Calculation of pore water pressure

13. Fig 4 Soil with a static water table
Water table
H
P u P H
w w
( )   (5)
• The water table is the level of the water surface in a borehole.
Calculation of pore water pressure

14. Fig 4 Soil with a static water table
Water table
H
P u P H
w w
( )   (5)
• The water table is the level of the water surface in a borehole.
• It is the level at which the pore water pressure uw = 0
Calculation of pore water pressure

15. Dry
Saturated
2 m
3m
Fig 5 Soil Stratigraphy
 
bulk dry

 
bulk sat

Step 1: Draw ground profile showing soil stratigraphy
and water table
Example: determining the effective stress

16. Distribution by
Volume
Solid
Voids
Vv=e Vs
= 0.7m3
Vs= 1m3
Step 2: Calculation of relevant bulk unit weights
Example

17. Distribution by
Volume
Solid
Voids
Vv=e Vs
= 0.7m3
Distribution by weight
for the dry soil
Vs= 1m3
W V G
kN
kN
s s s w
  
  


1 27 98
2646
. .
.
W= 0
Step 2: Calculation of relevant bulk unit weights
Example

18. Distribution by
Volume
Solid
Voids
Vv=e Vs
= 0.7m3
Distribution by weight
for the dry soil
Distribution by weight
for the saturated soil
Vs= 1m3
W V kN
kN
kN
w v w
 
 


07 98
686
. .
.
W V G
kN
kN
s s s w
  
  


1 27 98
2646
. .
.
W V G
kN
kN
s s s w
  
  


1 2 7 98
2646
. .
.
W= 0
Step 2: Calculation of relevant bulk unit weights
Example

19. Distribution by
Volume
Solid
Voids
Vv=e Vs
= 0.7m3
Distribution by weight
for the dry soil
Distribution by weight
for the saturated soil
Vs= 1m3
W V kN
kN
kN
w v w
 
 


07 98
686
. .
.
W V G
kN
kN
s s s w
  
  


1 27 98
2646
. .
.
W V G
kN
kN
s s s w
  
  


1 2 7 98
2646
. .
.
Ww=0
Step 2: Calculation of relevant bulk unit weights
Example


dry
s w
kN
m
kN m
G
e
  
+
2646
170
1556
1
3
3
.
.
. /

20. Distribution by
Volume
Solid
Voids
Vv=e Vs
= 0.7m3
Distribution by weight
for the dry soil
Distribution by weight
for the saturated soil
Vs= 1m3
W V kN
kN
kN
w v w
 
 


07 98
686
. .
.
W V G
kN
kN
s s s w
  
  


1 27 98
2646
. .
.
W V G
kN
kN
s s s w
  
  


1 2 7 98
2646
. .
.
Ww=0




dry
s w
sat
w s
kN
m
kN m
G
e
kN
m
kN m
G e
e
  
+

+
 
+
+
26 46
170
1556
1
26 46 686
170
19 60
1
3
3
3
3
.
.
. /
( . . )
.
. /
( )
Step 2: Calculation of relevant bulk unit weights
Example

21. 2 m
3m
v kPa kN m
  +  
1556 2 19 60 3 89 92 2
. . . ( / )
Step 3 Calculate total stress
Example

22. 2 m
3m
v kPa kN m
  +  
1556 2 19 60 3 89 92 2
. . . ( / )
Step 3 Calculate total stress
Example
u kPa
w   
3 9 8 29 40
. .
Step 4 Calculate pore water pressure

23. 2 m
3m
v kPa kN m
  +  
1556 2 19 60 3 89 92 2
. . . ( / )
Step 3 Calculate total stress
Example
u kPa
w   
3 9 8 29 40
. .
Step 4 Calculate pore water pressure
Step 5 Calculate effective stress
     
 
v v w
u kPa
89 92 29 40 6052
. . .

24. 0 50 100 150
0m
2m
4m
6m
8m
kPa
pore water
pressure Effective
stress
Total
Stress (5m)
Depth
Vertical stress and pore pressure variation