1. RETAINING WALL

2. UNIT V RETAINING WALLS
Plastic equilibrium in soils – active and passive states – Rankine‟s theory – cohesionless and cohesive soil – Coulomb‟s wedge theory – Condition for critical failure plane – Earth pressure on retaining walls of simple configurations – Culmann Graphical method – pressure on the wall due to line load – Stability analysis of retaining walls.

3. 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 Pile
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. Lateral Earth Pressure
There are 3 states of lateral earth pressure
Ko = At Rest
Ka = Active Earth Pressure (wall moves away from soil)
Kp = Passive Earth Pressure (wall moves into soil)
Passive is more like a resistance σv z H σh

12. 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.

13. 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

14. 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.

15. Active Earth Pressure
Active earth pressure occurs when the wall tilts away from the soil
(a typical free standing retaining wall)

16. Active Earth Pressure
Active earth pressure occurs when the wall tilts away from the soil
(a typical free standing retaining wall)

17. Active Earth Pressure
Active earth pressure occurs when the wall tilts away from the soil
(a typical free standing retaining wall)

18. 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

19. Active Earth Pressure
Active earth pressure occurs when the wall tilts away from the soil
(a typical free standing retaining wall)
Ka can be calculated as follows:
Ka = tan2 (45 – φ/2)
thus: σa‘ = Ka σv’ – 2 c (Ka)1/2
Soil sliding down pushing the wall
Failure wedge H
45 + φ/2

20. 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

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

22. 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’

23. 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

24. 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.

25. 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

26. Passive Earth Pressure
Passive earth pressure occurs when the wall is pushed into the soil
(typically a seismic load pushing the wall into the soil or a foundation pushing into the soil)
Kp can be calculated as follows:
Kp = tan2 (45 + φ/2)
thus: σp‘ = Kp σv’ + 2 c (Kp)1/2
Soil being pushed up the slope H
Failure wedge
45 - φ/2

27. 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’

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

29. 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’

30. 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

31. 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.

32. 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

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

36. Active Stress Distribution (c = 0)γ
c = 0 Φ
dry soil H
Pa = ?
? - What is this value
σa‘ = Ka σv’ – 2 c (Ka)1/2
σa‘ = Ka σv’
σa‘ is the stress distribution
Pa is the force on the wall (per foot of wall)
How is Pa found?

37. Passive Stress Distribution (c = 0)γ
c = 0 Φ
dry soil H
Pp = ?
? - What is this value
σp‘ = Kp σv’ – 2 c (Kp)1/2
σp‘ = Kp σv’
σp‘ is the stress distribution
Pp is the force on the wall (per foot of wall)
How is Pp found?

38. Stress Distribution - Water Table (c = 0)H1
Effective Stress
Pore Water Pressure
Ka γ H1 H2 Pa
Ka γ H1
Ka γ’ H2
γw H2 or
Ka (γ H1 + γ’ H 2)
Pa = Σ areas = ½ Ka γH12 + Ka γH1H2 + ½ Ka γ’H22 + 1/2γwH22

39. Stress Distribution With Water Table
Why is the water pressure considered separately? (K) H1
Effective Stress
Pore Water Pressure
Ka γ H1 H2 Pa
Ka γ H1
Ka γ’ H2
γw H2 or
Ka (γ H1 + γ’ H 2)

40. Active Stress Distribution (c ≠ 0)zo γ
c ≠ 0 Φ
dry soil H _ - =
Ka γH
2 c (Ka)1/2
Ka γH – 2 c (Ka)1/2
Find zo:
Ka γzo – 2 c (Ka)1/2 = 0
Zo = 2c / γ (Ka)1/2
Pa = ?

41. Passive Stress Distribution (c ≠ 0)γ
c ≠ 0 Φ
dry soil H + - =
Kp γH
2 c (Kp)1/2
Kp γH + 2 c (Kp)1/2
Pp = ?

44. COULOMB'S EARTH PRESSURE THEORY FOR SAND FOR ACTIVE STATE
Coulomb made the following assumptions in the development of his theory:
1. The soil is isotropic and homogeneous
2. The rupture surface is a plane surface
3. The failure wedge is a rigid body
4. The pressure surface is a plane surface
5. There is wall friction on the pressure surface
6. Failure is two-dimensional and
7. The soil is cohesionless

50. Importance of Drainage for Retaining Walls
Drains, Filters & Weep holes
Granular zone or
geofabric drain
Weep holes

56. Kind of loads Soil a) Rest b) Active c) Passive Surcharge Water
Static
Finite
Infinite
Dynamic
Water
Dynamics

57. Design of Retaining Wall
1- External Stability
2- Internal Stability

58. External Stability External Stability 1- Sliding 2- Overturning
3- Bearing Capacity
4- Overall Failure

59. Sliding
FR = Pp + Friction & Cohesion
FD = Pa

60. Overturning MR = Pp.yp + W1 a1 + W2 a2 +W3 a3 +W4 a4 MD = Pa . ya
Moment About o

61. Bearing Capacity

62. Bearing Capacity

63. Bearing Capacity

64. Overall Failure

65. Check for Overturning

66. Check for Overturning

67. Check for Overturning

68. Check for Sliding

69. Check for Sliding

70. Internal Stability

71. Internal Stability

72. Internal Stability