Lateral Earth Pressures
Duration: 18 min
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SIVA
Contents
• Geotechnical applications
• K0, active & passive states
• Rankine’s earth pressure theory
A 2-minute break
• Design of retaining walls
• A Mini Quiz
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Lateral Support
In geotechnical engineering, it is often necessary to
prevent lateral soil movements.
Tie rod
Anchor
Sheet pile
Cantilever
retaining wall
Braced excavation
Anchored sheet pile
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Lateral Support
We have to estimate the lateral soil pressures acting on
these structures, to be able to design them.
Gravity Retaining
wall
Soil nailing
Reinforced 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 walls are increasingly becoming popular.
geosynthetics
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Lateral Support
Crib walls have been used in Queensland.
filled with
soil
Good drainage & allow plant growth.
Looks good.
Interlocking
stretchers
and headers
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Earth Pressure at Rest
In a homogeneous natural soil deposit,
GL
v’
h’
X
the ratio h’/v’ is a constant known as coefficient
of earth pressure at rest (K0).
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,
K0 

1
Poisson’s
ratio
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Active/Passive Earth Pressures
- in granular soils
Wall moves
away from soil
A
Wall moves
towards soil
B
smooth wall
Let’s look at the soil elements A and B during the
wall movement.
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Active Earth Pressure
- in granular soils
v’ = z
v’ z
h’
A
Initially, there is no lateral movement.
h’ = K0 v’ = K0 z
As the wall moves away from the soil,
v’ remains the same; and
h’ decreases till failure occurs.
Active state
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Active Earth Pressure
- in granular soils
As the wall moves away from the soil,

Initially (K0 state)
Failure (Active state)
v ’
active earth
pressure

decreasing h’
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Active Earth Pressure
- in granular soils

WJM Rankine
(1820-1872)

[h’]active
v’

[ h ' ]active  K A v '
1  sin 
KA 
 tan 2 (45   / 2)
1  sin 
Rankine’s coefficient of
active earth pressure
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Active Earth Pressure
- in granular soils

Failure plane is at
45 + /2 to horizontal
v’
h’
45 + /2

A
90+
[h’]active
v’

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Active Earth Pressure
- in granular soils
As the wall moves away from the soil,
h’ decreases till failure occurs.
v’ z
h’
A
h’
K0 state
Active
state
wall movement
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Active Earth Pressure
- in cohesive soils
Follow the same steps as
for granular soils. Only
difference is that c  0.
[ h ' ]active  K A v '2c K A
Everything else the same
as for granular soils.
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Passive Earth Pressure
- in granular soils
Initially, soil is in K0 state.
As the wall moves towards the soil,
v’
h’
B
v’ remains the same, and
h’ increases till failure occurs.
Passive state
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Passive Earth Pressure
- in granular soils
As the wall moves towards the soil,

Initially (K0 state)
Failure (Active state)
passive earth
pressure
v ’
increasing h’

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Passive Earth Pressure
- in granular soils


v’
[h’]passive

[ h ' ] passive  K P v '
1  sin 
KP 
 tan 2 (45   / 2)
1  sin 
Rankine’s coefficient of
passive earth pressure
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Passive Earth Pressure
- in granular soils

Failure plane is at
45 - /2 to horizontal
v’
h’
45 - /2

A
90+
v’
[h’]passive

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Passive Earth Pressure
- in granular soils
As the wall moves towards the soil,
h’ increases till failure occurs.
v’
h’
h’
Passive state
B
K0 state
wall movement
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Passive Earth Pressure
- in cohesive soils
Follow the same steps as
for granular soils. Only
difference is that c  0.
[ h ' ] passive  K P v '2c K P
Everything else the same
as for granular soils.
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Earth Pressure Distribution
- in granular soils
[h’]active
PA and PP are the
resultant active and
passive thrusts on
the wall
[h’]passive
H
PA=0.5 KAH2
h
PP=0.5 KPh2
KPh
KAH
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h’
Passive state
Active state
K0 state
Wall movement
(not to scale)
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Rankine’s Earth Pressure Theory
[ h ' ]active  K A v '2c K A
[ h ' ] passive  K P v '2c K P
 Assumes smooth wall
 Applicable only on vertical walls
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Retaining Walls - Applications
Road
Train
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Retaining Walls - Applications
highway
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Retaining Walls - Applications
High-rise building
basement wall
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Gravity Retaining Walls
cement mortar
plain concrete or
stone masonry
cobbles
They rely on their self weight to
support the backfill
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Cantilever Retaining Walls
Reinforced;
smaller section
than gravity
walls
They act like vertical cantilever,
fixed to the ground
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Design of Retaining Wall
- in granular soils
2
Block no.
2
3
3
1
1
toe
toe
Wi = weight of block i
Analyse the stability of this rigid body with
xi = horizontal distance of centroid of block i from toe
vertical walls (Rankine theory valid)
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Safety against sliding along the base
Fsliding 
PP  {Wi }. tan 
soil-concrete friction
angle  0.5 – 0.7 
PA
to be greater
than 1.5
2
2
PA
H
3
3
PA
1
PP
S
toe
h PP
1
S
R
toe
y
R
y
PP= 0.5 KPh2
PA= 0.5 KAH2
Safety against overturning about toe
Foverturning 
PP h / 3  {Wi xi }
PA H/3
to be greater
than 2.0
2
2
PA
H
3
3
1
PP
S
toe
h PP
R
y
1
S
toe
R
y
PA
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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)?
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