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Lateral Earth Pressures

1. Lateral Earth Pressures

Duration: 18 min
N. Sivakugan

2. Contents

Copyright©2001
SIVA
Contents
• Geotechnical applications
• K0, active & passive states
• Rankine’s earth pressure theory
A 2-minute break
• Design of retaining walls
• A Mini Quiz
2

3. Lateral Support

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SIVA
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
3

4. Lateral Support

Copyright©2001
SIVA
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 4

5. Soil Nailing

6. Sheet Pile

7. Sheet Pile

8. Sheet Pile

9. Lateral Support

10. Lateral Support

Copyright©2001
SIVA
Lateral Support
Crib walls have been used in Queensland.
filled with
soil
Good drainage & allow plant growth.
Looks good.
Interlocking
stretchers
and headers
10

11. Earth Pressure at Rest

Copyright©2001
SIVA
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.
11

12. Estimating K0

Copyright©2001
SIVA
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
12

13. Active/Passive Earth Pressures

Copyright©2001
SIVA
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.
13

14. Active Earth Pressure

Copyright©2001
SIVA
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
14

15. Active Earth Pressure

16. Active Earth Pressure

Copyright©2001
SIVA
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
16

17. Active Earth Pressure

18. Active Earth Pressure

19. Active Earth Pressure

Copyright©2001
SIVA
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.
19

20. Passive Earth Pressure

Copyright©2001
SIVA
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
20

21. Passive Earth Pressure

22. Passive Earth Pressure

23. Passive Earth Pressure

24. Passive Earth Pressure

25. Passive Earth Pressure

Copyright©2001
SIVA
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.
25

26. Earth Pressure Distribution

SIVA
Copyright©2001
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
26

27.

h’
Passive state
Active state
K0 state
Wall movement
(not to scale)

28. Rankine’s Earth Pressure Theory

29. Retaining Walls - Applications

30. Retaining Walls - Applications

31. Retaining Walls - Applications

SIVA
Copyright©2001
Retaining Walls - Applications
High-rise building
basement wall
31

32. Gravity Retaining Walls

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SIVA
Gravity Retaining Walls
cement mortar
plain concrete or
stone masonry
cobbles
They rely on their self weight to
support the backfill
32

33. Cantilever Retaining Walls

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SIVA
Cantilever Retaining Walls
Reinforced;
smaller section
than gravity
walls
They act like vertical cantilever,
fixed to the ground
33

34. Design of Retaining Wall

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SIVA
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)
34

35.

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

36.

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

37. Points to Ponder

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SIVA
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)?
37

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