Lectures of Earth Retaining Structures as a Compulsory Course for M. Engg Program at NEDUET, Karachi. Author: Engr. Shoaib Yaqub Asssitant Professor Department of Urban & Infrastructure Engineering NEDUET, Karachi. Note: Lectures have no copyrights and shared here as the gestures to share knowledge among the students and Engineering fraternity.

1. EARTH RETAINING STRUCTURES
C V - 5 4 0
Engr. Shoaib Yaqub
B.S (Civil), M.Engg (Geotech.)
Assistant Professor
N E D U n i v e r s i t y o f E n g i n e e r i n g & T e c h n o l o g y , K a r a c h i .
L e c t u r e – 0 3 & 0 4

2. IN THIS LECTURE YOU WILL FIND;
• Lateral Earth Pressure Theories
1. Hydrostatic Pressure
2. Pressure at Rest
3. Active Earth Pressure
4. Passive Earth Pressure
Brooker & Irelands (1965)
Rankine (1857)
&
Coulombs (1776)

3. Types of Retaining Structures
LATERAL EARTH PRESSURE

4. Lateral Earth Pressure
• Retaining structures are built to support Earth, water or both.
• The lateral forces acting on Retaining Structures built Pressure
on these structures termed as “Lateral earth Pressure.
• There are Four possible conditions of Pressure on Retaining
Structure i.e. Wall.

5. Lateral Earth Pressure
• There are Four possible conditions of Pressure on Retaining
Structure i.e. Wall.
1. Hydrostatic Pressure
2. Pressure at Rest
3. Active Earth Pressure
4. Passive Earth Pressure
Brooker & Irelans (1965)
Rankine (1857)
&
Coulombs ()

6. Lateral Earth Pressure
1. Hydrostatic Pressure

7. Lateral Earth Pressure
2. Earth Pressure at REST. (No movement in Wall)

8. Lateral Earth Pressure
2. Earth Pressure at REST. (No movement in Wall)

9. Introduction
2. Earth Pressure at REST. (No movement in Wall)

10. Introduction
Type of Soil Ko
Loose Sand 0.45 – 0.6
Dense Sand 0.3 – 0.5
Normal Consolidated Clay 0.5 – 0.7
Over Consolidated Clay 1 – 4
Compacted Clay 0.7 - 2
2. Earth Pressure at REST. (No movement in Wall)

11. Lateral Earth Pressure
• There are Four possible conditions of Pressure on Retaining
Structure i.e. Wall.
1. Hydrostatic Pressure
2. Pressure at Rest
3. Active Earth Pressure
4. Passive Earth Pressure
Brooker & Irelands (1965)
Rankine (1857)
&
Coulombs ()

12. Types of Retaining Structures
Rankine’s Theory

13. Rankine’s Theory for Lateral Earth Pressure
3. Active Earth Pressure
4. Passive Earth Pressure
Rankine (1857)
&
Coulombs (1776)
ASSUMPTIONS
• Soil is Homogeneous
• The wall surface is Perpendicular to Plane.
• The wall is Frictionless.

14. Rankine’s Theory for Lateral Earth Pressure
3. Active Earth Pressure. (Wall moves Away from the Soil)
Earth pressure at rest
z
σ
v
σh
A
B
Unit weight of soil = γ
 tancf 
Rankine’s theory (1857) considers the state of
stress in a soil mass when the condition of plastic
equilibrium has been Reached, i.e. when shear
failure is on the point of occurring throughout the
mass.
If wall AB is allowed to move away from the soil
mass gradually, horizontal stress will decrease. This
is represented by Mohr’s circle in the subsequent
slide.

15. Rankine’s Theory for Lateral Earth Pressure
3. Active Earth Pressure. (Wall moves Away from the Soil)

16. Rankine’s Theory for Lateral Earth Pressure
3. Active Earth Pressure. (Wall moves Away from the Soil)
aa K2c-Kz
z
zo
aK2c-aK2c-
Kz a

17. Rankine’s Theory for Lateral Earth Pressure
3. Active Earth Pressure. (Wall moves Away from the Soil)
OR

18. Rankine’s Theory for Lateral Earth Pressure
3. Active Earth Pressure. (Wall moves Away from the Soil)
aa K2c-Kz
z
zo
aK2c-aK2c-
Kz a
= depth of tension crack
a
o
K
c
z

2

For pure cohesive soil, i.e. when  = 0 :

c
zo
2


19. Rankine’s Theory for Lateral Earth Pressure
3. Active Earth Pressure. (Wall moves Away from the Soil)

20. aa K2c-Kz
z
zo
aK2c-aK2c-
Kz a
Rankine’s Theory for Lateral Earth Pressure
3. Active Earth Pressure. (Wall moves Away from the Soil)
COHESSIONLESS SOIL

21. aa K2c-Kz
z
zo
aK2c-aK2c-
Kz a
Rankine’s Theory for Lateral Earth Pressure
3. Active Earth Pressure. (Wall moves Away from the Soil)
COHESSIONLESS SOIL

22. For cohesionless soil, c = 0
aava KzK  
z
Kz a
Rankine’s Theory for Lateral Earth Pressure
3. Active Earth Pressure. (Wall moves Away from the Soil)
COHESSIONLESS SOIL

23. Rankine’s Theory for Lateral Earth Pressure
3. Active Earth Pressure. (Wall moves Away from the Soil)
• For INCLINED BACKFILL

24. Rankine’s Theory for Lateral Earth Pressure
4. Passive Earth Pressure. (Wall moves Towards the Soil)
Shear
stress
Normal
stress
 tancf 
C
D
D
’
OA σ
p
Ko
σv
b
a
σ
v


c
Mohr’s circle representing Rankine’s passive state.

25. aa K2cKz 
z
zo
aK2caK2c
Kz a
Rankine’s Theory for Lateral Earth Pressure
4. Passive Earth Pressure. (Wall moves Towards the Soil)

26. Rankine’s Theory for Lateral Earth Pressure
4. Passive Earth Pressure. (Wall moves Towards the Soil)
Shear
stress
Normal
stress
 tancf 
C
D
D
’
OA σ
p
Ko
σv
b
a
σ
v


c
Mohr’s circle representing Rankine’s passive state.
OR

27. Rankine’s Theory for Lateral Earth Pressure
• For INCLINED BACKFILL
4. Passive Earth Pressure. (Wall moves Towards the Soil)

28. Types of Earth Retaining Structures

29. Types of Earth Retaining Structures

30. Types of Retaining Structures
Coulomb’s Theory

31. Coulomb’s Theory for Lateral Earth Pressure
3. Active Earth Pressure
4. Passive Earth Pressure
Rankine (1857)
&
Coulombs (1776)
Mainly for;
• The wall surface is inclined to Plane.
• When Friction is considered. ( )

32. Coulomb’s Theory for Lateral Earth Pressure
Due to wall friction the shape of
the failure surface is curved near
the bottom of the wall in both the
active and passive cases, as
indicated in Figure, but in the
Coulomb theory the failure
surfaces are assumed to be plane
in each case.
If = 0 the results shall be
identical to Rankine’s.
3. Active Earth Pressure. (Wall moves Away from the Soil)

33. Coulomb’s Theory for Lateral Earth Pressure
3. Active Earth Pressure. (Wall moves Away from the Soil)

34. Coulomb’s Theory for Lateral Earth Pressure
3. Active Earth Pressure. (Wall moves Away from the Soil)

35. Coulomb’s Theory for Lateral Earth Pressure
3. Passive Earth Pressure. (Wall moves Towards the Soil)

36. Coulomb’s Theory for Lateral Earth Pressure

37. Coulomb’s Theory for Lateral Earth Pressure

38. Coulomb’s Theory for Lateral Earth Pressure