1. Lateral Earth Pressures
N. Sivakugan
Duration: 18 min

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

3. Lateral Support
In geotechnical engineering, it is often necessary to prevent lateral soil movements.
Tie rod
Sheet pile
Anchor
Cantilever retaining wall
Braced excavation
Anchored sheet pile

4. Lateral Support
We have to estimate the lateral soil pressures acting on these structures, to be able to design them.
Soil nailing
Gravity Retaining wall
Reinforced earth wall

5. Soil Nailing

6. Sheet piles marked for driving

7. Sheet Pile
Sheet pile wall

8. Sheet Pile
Sheet pile wall
During installation

9. Lateral Support
Reinforced earth walls are increasingly becoming popular.
geosynthetics

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

11. Earth Pressure at Rest In a homogeneous natural soil deposit, v’ h’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.

12. 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,
Poisson’s ratio

13. Active/Passive Earth Pressures
- in granular soils
Wall moves away from soil
Wall moves towards soil A B
smooth wall
Let’s look at the soil elements A and B during the wall movement.

14. Active Earth Pressure - in granular soils v’ = z
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

15. Active Earth Pressure - in granular soils
As the wall moves away from the soil,  
failure envelope
Initially (K0 state)
Failure (Active state)
v’
decreasing h’
active earth pressure

16. Rankine’s coefficient of active earth pressure
- in granular soils  
failure envelope 
WJM Rankine
( )
[h’]active
v’
Rankine’s coefficient of active earth pressure

17. Active Earth Pressure - in granular soils    A v’ h’ [h’]active
failure envelope 
Failure plane is at
45 + /2 to horizontal A
v’
h’
45 + /2
90+
[h’]active
v’

18. Active Earth Pressure - in granular soils
As the wall moves away from the soil,
h’ decreases till failure occurs.
wall movement
h’
K0 state A
v’
h’ z
Active state

19. Active Earth Pressure - in cohesive soils
Follow the same steps as for granular soils. Only difference is that c  0.
Everything else the same as for granular soils.

20. Passive Earth Pressure
- in granular soils
Initially, soil is in K0 state.
As the wall moves towards the soil,
v’ remains the same, and B
v’
h’
h’ increases till failure occurs.
Passive state

21. Passive Earth Pressure
- in granular soils
As the wall moves towards the soil,  
failure envelope
Initially (K0 state)
Failure (Active state)
passive earth pressure
v’
increasing h’

22. Passive Earth Pressure
- in granular soils  
failure envelope 
v’
[h’]passive
Rankine’s coefficient of passive earth pressure

23. Passive Earth Pressure
- in granular soils  
failure envelope 
Failure plane is at
45 - /2 to horizontal A
v’
h’
45 - /2
90+
[h’]passive
v’

24. Passive Earth Pressure
- in granular soils
As the wall moves towards the soil,
h’ increases till failure occurs.
wall movement
h’
Passive state B
v’
h’
K0 state

25. Passive Earth Pressure
- in cohesive soils
Follow the same steps as for granular soils. Only difference is that c  0.
Everything else the same as for granular soils.

26. Earth Pressure Distribution
- in granular soils
[h’]active
PA and PP are the resultant active and passive thrusts on the wall H
[h’]passive
PA=0.5 KAH2 h
PP=0.5 KPh2
KPh
KAH

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

28. Rankine’s Earth Pressure Theory
Assumes smooth wall
Applicable only on vertical walls

29. Retaining Walls - Applications
Road
Train

30. Retaining Walls - Applications
highway

31. Retaining Walls - Applications
High-rise building
basement wall

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

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

34. Design of Retaining Wall
- in granular soils 1 2 3
Block no.
toe
Wi = weight of block i
Analyse the stability of this rigid body with vertical walls (Rankine theory valid)
xi = horizontal distance of centroid of block i from toe

35. Safety against sliding along the base
soil-concrete friction angle  0.5 – 0.7 
to be greater than 1.5 H 1 2 3 PA PP h S
toe R y
PP= 0.5 KPh2
PA= 0.5 KAH2

36. Safety against overturning about toe
to be greater than 1.5 H 1 2 3 PA PP h S
toe R y

37. 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)?