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8/9/2019 3-Lateral Earth Pressures
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Lateral Earth Pressures
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Contents
Geotechnical applications
K0, active & passive states
Rankines earth pressure theory
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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 pressuresacting 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 wallsare increasingly becoming popular.
geosynthetics
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Lateral Support
Crib wallshave been used in Queensland.
Interlocking
stretchersand 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 (K0).
Importantly, at K0state, there are no lateral strains.
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Estimating K0
For normally consolidated clays and granular soils,
K0= 1sin
For overconsolidated clays,K0,overconsolidated= K0,normally consolidatedOCR
0.5
From elastic analysis,
1
0KPoissons
ratio
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Active/Passive Earth Pressures- in granularsoils
smooth wall
Wall moves
away from soil
Wall moves
towards soil
A
B
Lets look at the soil elements A and B during the
wall movement.
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Active Earth Pressure- in granularsoils
A
v
h
z
As the wall moves away from the soil,
Initially, there is no lateral movement.
v= z
h= K
0
v= K
0z
vremains the same; and
hdecreases till failure occurs.
Active state
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Active Earth Pressure- in granularsoils
v
decreasing h
Initially (K0state)
Failure (Active state)
As the wall moves away from the soil,
active earth
pressure
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Active Earth Pressure- in granularsoils
v[h]active
']'[ vAactiveh K
)2/45(tan
sin1
sin1 2
AK
Rankines coefficient of
active earth pressure
WJM Rankine
(1820-1872)
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Active Earth Pressure- in granularsoils
v[h]active
A
v
h45 + /2
90+
Failure plane is at
45 + /2 to horizontal
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Active Earth Pressure- in granularsoils
A
v
h
z
As the wall moves away from the soil,
hdecreases till failure occurs.
wall movement
h
Active
state
K0state
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Active Earth Pressure- in cohesivesoils
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 granularsoils
B
v
h
Initially, soil is in K0 state.
As the wall moves towards the soil,
vremains the same, and
hincreases till failure occurs.
Passive state
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Passive Earth Pressure- in granularsoils
v
Initially (K0state)
Failure (Active state)
As the wall moves towards the soil,
increasing h
passive earth
pressure
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Passive Earth Pressure- in granularsoils
v [h]passive
']'[ vPpassiveh K
)2/45(tansin1
sin1 2
PK
Rankines coefficient of
passive earth pressure
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Passive Earth Pressure- in granularsoils
v
[h]passive
A
v
h
90+
Failure plane is at
45 - /2 to horizontal
45 - /2
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Passive Earth Pressure- in granularsoils
B
v
h
As the wall moves towards the soil,
hincreases till failure occurs.
wall movement
h
K0state
Passive state
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Passive Earth Pressure- in cohesivesoils
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 granularsoils
[h]passive
[h]active
H
h
KAHKPh
PA=0.5 KAH2
PP=0.5 KPh2
PAand PPare the
resultant active and
passive thrusts on
the wall
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Wall movement
(not to scale)
h
Passive state
Active state
K0state
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Rankines 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
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Cantilever Retaining Walls
They act like vertical cantilever,
fixed to the ground
Reinforced;
smaller section
than gravity
walls
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Design of Retaining Wall
1
1
2 2
3 3
toe
toe
Wi= weight of block i
xi= horizontal distance of centroid of block i from toe
Block no.
- in granularsoils
Analyse the stability of this rigid body with
vertical walls (Rankine theory valid)
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1
1
2 2
3 3
PA
PA
PPP
P
S
Stoe
toeR
Ryy
Safety against sliding along the base
tan}.{
A
iP
sliding
P
WPF
H
h
soil-concrete friction
angle 0.5 0.7
to be greater
than 1.5
PP= 0.5 KPh2 PA= 0.5 KAH
2
S f i i
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1
1
2 2
3 3
PA
PA
PPP
P
S
Stoe
toeR
Ryy
Safety against overturning about toe
H/3
}{3/
A
iiP
goverturnin
P
xWhPF
H
h
to be greater
than 2.0
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Points to Ponder
How does the key help in improving the stability
against sliding?
Shouldnt we design retaining walls to resist at-rest
(than active) earth pressures since the thrust on the
wall is greater in K0state (K0> KA)?