Effective Stress

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Effective Stress
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Soil loaded by an applied weight W
Soil loaded by water weighing W
W
W
3
Soil loaded by an applied weight W
Soil loaded by water weighing W
W
W
Compression
No deformation
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Definition of Total and Effective Stress
(1)
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Definition of Total and Effective Stress
(1)
Effective vertical stress
(2)
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Definition of Total and Effective Stress
(1)
Effective vertical stress
(2)
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Definition of Total and Effective Stress
(1)
Effective vertical stress
(2)
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Effective Stress
Fig 2 Two Pieces of Rock in Contact
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Effective Stress
Effective Force
(3a)
U uw ( A - Ac )
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Effective Stress
Effective Force
(3a)
U uw ( A - Ac )
Frictional Failure
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Effective Stress
Effective Force
(3a)
U uw ( A - Ac )
Frictional Failure
Failure in terms of stress
(3b)
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Calculation of Effective Stress
Surcharge q
d1
Layer 1
Layer 2
d2
z
Layer 3
d3
Fig 3 Soil Profile
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Calculation of Total Vertical Stress
Elevation
q
Force on base Force on top Weight of soil

d1
d2
z
Plan
A
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Calculation of Total Vertical Stress
Elevation
q
Force on base Force on top Weight of soil
A ?v A q A ?1 d1 A ?2 d2
A ?3 ( z - d1 - d2 )

d1
d2
z
Plan
A
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Calculation of Total Vertical Stress
Elevation
q
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 )
d1
d2
z
(4)
Plan
A
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Calculation of pore water pressure
Water table
H
(5)
P
Fig 4 Soil with a static water table
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Calculation of pore water pressure
Water table
H
(5)
P
Fig 4 Soil with a static water table

• The water table is the level of the water
  surface in a borehole.

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Calculation of pore water pressure
Water table
H
(5)
P
Fig 4 Soil with a static water table

• 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

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Example determining the effective stress
Step 1 Draw ground profile showing soil
stratigraphy and water table
Dry
2 m
3m
Saturated
Fig 5 Soil Stratigraphy
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Example
Step 2 Calculation of relevant bulk unit
weights
Vve Vs 0.7m3
Voids
Vs 1m3
Solid
Distribution by Volume
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Example
Step 2 Calculation of relevant bulk unit
weights
Vve Vs 0.7m3
W 0
Voids
Vs 1m3
Solid
Distribution by weight for the dry soil
Distribution by Volume
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Example
Step 2 Calculation of relevant bulk unit
weights
Vve Vs 0.7m3
W 0
Voids
Vs 1m3
Solid
Distribution by weight for the dry soil
Distribution by Volume
Distribution by weight for the saturated soil
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Example
Step 2 Calculation of relevant bulk unit
weights
Vve Vs 0.7m3
Ww0
Voids
Vs 1m3
Solid
Distribution by weight for the dry soil
Distribution by Volume
Distribution by weight for the saturated soil
?
kN
G
26
46
.
3
s
w
?
kN
m
?
?
?
15
56
.
/
dry
3
m
e
?
1
70
1
.
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Example
Step 2 Calculation of relevant bulk unit
weights
Vve Vs 0.7m3
Ww0
Voids
Vs 1m3
Solid
Distribution by weight for the dry soil
Distribution by Volume
Distribution by weight for the saturated soil
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Example
Step 3 Calculate total stress
2 m
3m
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Example
Step 3 Calculate total stress
2 m
Step 4 Calculate pore water pressure
3m
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Example
Step 3 Calculate total stress
2 m
Step 4 Calculate pore water pressure
3m
Step 5 Calculate effective stress
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Vertical stress and pore pressure variation
0
50
100
150
kPa
0m
2m
4m
Total Stress
(5m)
pore water pressure
6m
Effective stress
Depth
8m
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Stresses acting on a soil element
z
z
y
x
x
Fig 7 Definition of Stress Components
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Principle of Effective Stress
Effective stress relations for general stress
states
(10)
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Example
1 m
Initial GWL
3 m
Lowered GWL
z
Clay
Rock aquifer
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Example
1 m
Initial GWL
3 m
Lowered GWL
z
Clay
Rock aquifer
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Example

• Effective stress increases - soil compresses -
  ground surface settles
• Effective stress decreases- soil swells - ground
  surface heaves. The following problems may then
  occur
• surface flooding
• flooding of basements built when GWL lowered
• uplift of buildings
• failure of retaining structures
• failures due to reductions in bearing capacity

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