n. sivakugan duration: 18 min siva copyright©2001 2 geotechnical applications k 0, active &...
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Lateral Earth PressuresLateral Earth PressuresLateral Earth PressuresLateral Earth Pressures
N. SivakuganDuration: 18 min
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ContentsContents
• Geotechnical applications
• K0, active & passive states
• Rankine’s earth pressure theory
• Design of retaining walls• A Mini Quiz
A 2-minute breakA 2-minute break
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Lateral Support
In geotechnical engineering, it is often necessary to prevent lateral soil movements.
Cantilever retaining wall
Braced excavation Anchored sheet pile
Tie rod
Sheet pile
Anchor
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Lateral Support
We have to estimate the lateral soil pressureslateral soil pressures acting on these structures, to be able to design them.
Gravity Retaining wall
Soil nailingReinforced earth wall
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Soil Nailing
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Sheet Pile
Sheet piles marked for driving
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Sheet Pile
Sheet pile wall
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Sheet Pile
During installation Sheet pile wall
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Lateral Support
Reinforced earth wallsReinforced earth walls are increasingly becoming popular.
geosynthetics
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Lateral Support
Crib wallsCrib walls have been used in Queensland.
Interlocking stretchers
and headers
filled with soil
Good drainage & allow plant growth.
Looks good.
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Earth Pressure at Rest
GL
In a homogeneous natural soil deposit,
Xh’
v’
the ratio h’/v’ is a constant known as coefficient of earth pressure at rest (Kcoefficient of earth pressure at rest (K00).).
Importantly, at K0 state, there are no lateral strains.
Importantly, at K0 state, there are no lateral strains.
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Estimating K0
For normally consolidated clays and granular soils,
K0 = 1 – sin ’
For overconsolidated clays,
K0,overconsolidated = K0,normally consolidated OCR0.5
From elastic analysis,
10K
Poisson’s ratio
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Active/Passive Earth Pressures- in granular soils
smooth wall
Wall moves away from soil
Wall moves towards soil
A
B
Let’s look at the soil elements A and B during the wall movement.
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Active Earth Pressure- in granular soils
A
v’
h’z
As the wall moves away from the soil,
Initially, there is no lateral movement.
v’ = z
h’ = K0 v’ = K0 z
v’ remains the same; and
h’ decreases till failure occurs.
Active stateActive state
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Active Earth Pressure- in granular soils
failure envelope
v’
decreasing h’
Initially (K0 state)
Failure (Active state)
As the wall moves away from the soil,
active earth pressure
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Active Earth Pressure- in granular soils
v’[h’]active
failure envelope
']'[ vAactiveh K
)2/45(tansin1
sin1 2
AK
Rankine’s coefficient of active earth pressure
WJM Rankine(1820-1872)
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Active Earth Pressure- in granular soils
v’[h’]activ
e
failure envelope
A
v’
h’45 + /2
90+
Failure plane is at 45 + /2 to horizontal
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Active Earth Pressure- in granular soils
A
v’
h’z
As the wall moves away from the soil,
h’ decreases till failure occurs.
wall movement
h’
Active state
K0 state
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Active Earth Pressure- in cohesive soils
Follow the same steps as for granular soils. Only difference is that c 0.
AvAactiveh KcK 2']'[
Everything else the same as for granular soils.
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Passive Earth Pressure- in granular soils
B
v’
h’
Initially, soil is in K0 state.
As the wall moves towards the soil,
v’ remains the same, and
h’ increases till failure occurs.
Passive state
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Passive Earth Pressure- in granular soils
failure envelope
v’
Initially (K0 state)
Failure (Active state)
As the wall moves towards the soil,
increasing h’
passive earth pressure
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Passive Earth Pressure- in granular soils
v’ [h’]passive
failure envelope
']'[ vPpassiveh K
)2/45(tansin1
sin1 2
PK
Rankine’s coefficient of passive earth pressure
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Passive Earth Pressure- in granular soils
v’ [h’]passive
failure envelope
A
v’
h’
90+
Failure plane is at 45 - /2 to horizontal
45 - /2
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Passive Earth Pressure- in granular soils
B
v’
h’
As the wall moves towards the soil,
h’ increases till failure occurs.
wall movement
h’
K0 state
Passive state
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Passive Earth Pressure- in cohesive soils
Follow the same steps as for granular soils. Only difference is that c 0.
PvPpassiveh KcK 2']'[
Everything else the same as for granular soils.
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Earth Pressure Distribution- in granular soils
[h’]passive
[h’]active
H
h
KAHKPh
PA=0.5 KAH2
PP=0.5 KPh2
PA and PP are the resultant active and passive thrusts on
the wall
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Wall movement (not to scale)
h’
Passive state
Active stateK0 state
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Rankine’s Earth Pressure Theory
Assumes smooth wall
Applicable only on vertical walls
PvPpassiveh KcK 2']'[
AvAactiveh KcK 2']'[
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Retaining Walls - Applications
Road
Train
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Retaining Walls - Applications
highway
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Retaining Walls - Applications
basement wall
High-rise building
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Gravity Retaining Walls
cobbles
cement mortarplain concrete or stone masonry
They rely on their self weight to support the backfill
They rely on their self weight to support the backfill
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Cantilever Retaining Walls
They act like vertical cantilever, fixed to the ground
They act like vertical cantilever, fixed to the ground
Reinforced; smaller section
than gravity walls
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Design of Retaining Wall
11
2 2
3 3
toe
toe
Wi = weight of block i
xi = horizontal distance of centroid of block i from toe
Block no.
- in granular soils
Analyse the stability of this rigid body with vertical walls (Rankine theory valid)
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2 2
3 3
PA
PA
PP
PPS
Stoe
toeR
Ryy
Safety against sliding along the base
tan }.{
A
iPsliding P
WPF
H
h
soil-concrete friction angle 0.5 – 0.7
to be greater than 1.5
to be greater than 1.5
PP= 0.5 KPh2PP= 0.5 KPh2 PA= 0.5 KAH2PA= 0.5 KAH2
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2 2
3 3
PA
PA
PP
PPS
Stoe
toeR
Ryy
Safety against overturning about toe
H/3
}{3/
A
iiPgoverturnin P
xWhPF
H
h
to be greater than 1.5
to be greater than 1.5
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Points to Ponder
How does the key help in improving the stability against sliding?
Shouldn’t we design retaining walls to resist at-rest (than active) earth pressures since the thrust on the wall is greater in K0 state (K0 > KA)?