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8/15/2019 001 Earth Pressure_Part 1
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Earth Pressures
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Analysis and Design
of Earth Retaining Structures
• Distribution of vertical and lateral earth
pressures must be estimated
• Magnitude of earth pressure depends on
state of strain in the soil behind the
structure
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Earth Pressure Theory
• The following 3 states are defined:
- At rest state: elastic equilibrium with no lateral
strain
- Active state: plastic equilibrium with lateral
expansion
- Passive state: plastic equilibrium with lateral
compression
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At-rest State
• Lateral effective stress, sh' = Ko sv'
• sv' = sv – u• Ko = coefficient of earth pressure at rest
sh’
sv’
Groundlevel
z
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Value of Ko
• For normally consolidated soils,
Ko = 1 – sinf'
• For overconsolidated soils,
Ko = (1 – sinf' ) (OCR)0.5
• From elastic theory,
Ko =
1
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Rankine’s Earth Pressure Theory
• In Rankine’s method, it is assumed that there is no
friction or adhesion between soil and the back of the
retaining structure. Therefore, the normal stress acting
on the retaining structure will be a principal stress. If the
back of the retaining structure is vertical and the soilsurface horizontal, the vertical and horizontal stresses
throughout the retained soil mass will be principal
stresses.
• The horizontal stress can be calculated from the Mohr-
Coulomb failure criterion.
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Active Earth Pressure: Granular Soil
sv’
sh’
z
A
B
• Initially, no movement of boundary AB
At-rest state
sv’ = z, assuming u = 0
sh’ = Ko sv
’ = Ko z
• Boundary AB moves away from element,
No change in sv’
Decrease in sh’ until it reaches a
minimum value, sha’ , at failure
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Active Earth Pressure: Rankine’s Theory
Granular Soil (c' = 0)
s'
Decreasing h’
At-rest state
Active state
sha’
'σK 'σ vaha
)2/'45(tan
'sin1
'sin1 pressureearthactiveof tcoefficienK 2a f
f
f
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Passive Earth Pressure: Granular Soil
sv’
sh’
z
A
B
• Boundary AB moves towards element,
No change in sv’
Increase in sh’ until it reaches amaximum value, shp’ , at failure
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Passive Earth Pressure: Rankine’s Theory
Granular Soil
s’sv’
increasing sh’
shp’
c' = 0
At-rest statePassive state
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Passive Earth Pressure: Rankine’s Theory
Granular Soil (c' = 0)
'σK 'σ v php
)2/'45(tan'sin1
'sin1
pressureearth passiveof tcoefficienK 2
p f f
f
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Earth Pressure Theory:
Orientation of Failure Plane
• In the active case, the
failure plane is inclined at an
angle of (45o + f'/2) to the
horizontal.
• In the passive case, the
failure plane is inclined at an
angle of (45o - f'/2) to the
horizontal.
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Earth Pressure Theory:
Orientation of Failure Plane
• In the active case, the failure plane is inclined at an angle of (45o +
f'/2) to the horizontal.
• In the passive case, the failure plane is inclined at an angle of (45o -
f'/2) to the horizontal.
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Mobilisation of Earth Pressure with Movement
• Significantly higher movement is required to mobilise full passive pressure
than to mobilise active pressure
Towards
soil
Away
from soil
Kp
Ko
Ka
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Earth Pressure: c' – f' soil
Rankine-Bell Equations
• Active case:
• Passive case: pv php K 2c''σK 'σ
c' s' tan f'
avaha K 2c''σK 'σ
sv'sha' shp' s'
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Earth Pressure: c' – f' soil
Rankine-Bell Equations
• Active case
– When c‘ is greater than zero, sha'
is zero at a specific depth, zo.
– Within a depth zo, active earth
pressure is negative.
aK 2c'
ava K 2c''σK
zo
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Earth Pressure Distribution
• Effect of
– Groundwater level
– Surcharge
– Stratified soil
– Sloping ground
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Influence of Sloping Ground
'cos-coscos
'cos-cos-cosK
22
22
a
f
f
'cos-coscos
'cos-coscosK 22
22
p
f
f
H H
3
H
Active pressure, pa = Ka sv' cos
Where sv' = Hcos
Active force, F A = Ka H2 cos
Passive pressure, pp = Kp sv' cos
Passive force, FP = Kp H2 cos
21
2
1
F A