1. Lateral Earth Pressure and Retaining Walls

2. Vertical or near-vertical slopes of soil are supported by retaining walls, cantilever sheet-pile walls, bulkheads sheet-piles, braced cuts and other similar structures.

3. Lateral Earth Pressures

5. Lateral Support
In geotechnical engineering, it is often necessary to prevent lateral soil movements.
Tie rod
Sheet pile
Anchor
Braced excavation
Cantilever retaining wall
Anchored sheet pile
dr. isam jardaneh / foundation engineering / 2010

6. 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
dr. isam jardaneh / foundation engineering / 2010

8. dr. isam jardaneh / foundation engineering 61303 / 2010

9. Sheet Pile Sheet pile wall
dr. isam jardaneh / foundation engineering / 2010

10. Soil Nailing
dr. isam jardaneh / foundation engineering / 2010

14. Lateral Support
Reinforced earth walls are increasingly becoming popular.
dr. isam jardaneh / foundation engineering / 2010

16. dr. isam jardaneh / foundation engineering 61303 / 2010

19. dr. isam jardaneh / foundation engineering 61303 / 2010

20. dr. isam jardaneh / foundation engineering 61303 / 2010

21. dr. isam jardaneh / foundation engineering 61303 / 2010

22. dr. isam jardaneh / foundation engineering 61303 / 2010

23. dr. isam jardaneh / foundation engineering 61303 / 2010

24. Lateral earth pressure is a function of several factors, such as:
The proper design of those structures requires an estimation of lateral earth pressure.
Lateral earth pressure is a function of several factors, such as:
The type and amount of wall movement
The shear strength parameters of the soil
The unit weight of the soil
The drainage conditions in the backfill
dr. isam jardaneh / foundation engineering / 2010

25. Nature of Lateral Earth Pressure
dr. isam jardaneh / foundation engineering / 2010

26. Passive
At Rest
Active
dr. isam jardaneh / foundation engineering / 2010

27. Lateral Earth Pressure
Lateral earth pressure is a function of effective vertical stress
dr. isam jardaneh / foundation engineering / 2010

28. Ơh= f (Ơv)

29. K=coefficient of lateral earth pressure
Ơh=kƠv
K=coefficient of lateral earth pressure

30. Lateral Earth Pressure at Rest
Lateral earth pressure is a function of effective vertical stress
dr. isam jardaneh / foundation engineering / 2010

31. dr. isam jardaneh / foundation engineering 61303 / 2010

32. Water Table
dr. isam jardaneh / foundation engineering / 2010

33. q γ1 K0
γ1H1 H1 γ2 H2
γwH2
γ1H1 q
γ2H2 K0 K0 K0

34. Ko = 0.4 + 0.007 (PI) for 0 > PI > 40
Ko = 1 - sinφ for NCC
Ko = sinφ for NCC
Ko = (PI) for 0 > PI > 40
Ko = (PI) for 40 > PI > 80
Ko = log(PI)

35. Active Lateral Earth Pressure
Wall moves away from the soil

36. William John Macquorn Rankine 1820 – 1872
Scottish civil engineer, physicist and mathematician.
He was a founding contributor to the science of thermodynamics, particularly focusing on the first of the three thermodynamic laws.
Rankine developed a complete theory of the steam engine and indeed of all heat engines.
He was an enthusiastic amateur singer, pianist and cellist who composed his own humorous songs. He was born in Edinburgh and died in Glasgow, a bachelor.
Rankine's theory, developed in 1857

37. Assumptions
No friction between the backfill soil and retaining wall. Angle of friction(δ) = 0
Retaining wall is vertical
Surface of backfill is horizontal

38. Rankine Active Earth Pressure

39. σ`a = Rankine Active earth pressure
σ`0 = Effective vertical stress
C = Cohesion
Φ = Angle of internal friction
Ka = Rankine active pressure coefficient
Ka =(1 – sin φ)/(1+sinφ) =

40. dr. isam jardaneh / foundation engineering 61303 / 2010

41. Zc = depth at which pressure = zero Zc = depth of tensile cracks
dr. isam jardaneh / foundation engineering / 2010

42. dr. isam jardaneh / foundation engineering 61303 / 2010

43. Example

44. Example
dr. isam jardaneh / foundation engineering / 2010

45. dr. isam jardaneh / foundation engineering 61303 / 2010

46. dr. isam jardaneh / foundation engineering 61303 / 2010

47. dr. isam jardaneh / foundation engineering 61303 / 2010

48. Use this
dr. isam jardaneh / foundation engineering / 2010

49. dr. isam jardaneh / foundation engineering 61303 / 2010

50. dr. isam jardaneh / foundation engineering 61303 / 2010

51. dr. isam jardaneh / foundation engineering 61303 / 2010

52. dr. isam jardaneh / foundation engineering 61303 / 2010

53. Example
dr. isam jardaneh / foundation engineering / 2010

54. Charles Augustin de Coulomb
Born in France.
His studies included philosophy, language and literature. He also received a good education in mathematics, astronomy, chemistry and botany.
He was involved in structural engineering , soil mechanics, as well as other fields of engineering.
He discovered an inverse relationship of the force between electric charges and the square of its distance, later named after him as Coulomb's law.
Coulomb leaves a legacy as a pioneer in the field of geotechnical engineering for his contribution to retaining wall design. His name is one of the 72 names inscribed on the Eiffel Tower.

55. Coulomb Active Earth Pressure

56. Comments: Coulomb considered friction δ
Due to friction, the failure surface is NOT PLANE
He considered it PLANE for easy solution
No big difference in results
When δ increases, the error in calculating Pp increases and the situation may be UNSAFE
The REAL failure surface is LOGSPIRAL as shown

57. 45+Ф/2
45+Ф/2
ACTIVE δ
H/3 Pa
45 - Ф/2
45 - Ф/2 Pp
PASSIVE δ
H/3

58. dr. isam jardaneh / foundation engineering 61303 / 2010

59. dr. isam jardaneh / foundation engineering 61303 / 2010

60. dr. isam jardaneh / foundation engineering 61303 / 2010

61. Example
dr. isam jardaneh / foundation engineering / 2010

62. Passive Lateral Earth Pressure
Wall moves towards the soil

63. Rankine Passive Earth Pressure

64. Use this
dr. isam jardaneh / foundation engineering / 2010

65. dr. isam jardaneh / foundation engineering 61303 / 2010

66. dr. isam jardaneh / foundation engineering 61303 / 2010

67. Passive Pressure Passive Force where
dr. isam jardaneh / foundation engineering / 2010

68. dr. isam jardaneh / foundation engineering 61303 / 2010

69. Solve this problem for passive case
Example
Solve this problem for passive case

70. Coulomb Passive Earth Pressure

71. * Passive means the wall moves into the backfill soil.
* Coulomb assumes that there is friction between RW and backfill materials
* Passive means the wall moves into the backfill soil.
dr. isam jardaneh / foundation engineering / 2010

72. dr. isam jardaneh / foundation engineering 61303 / 2010

73. dr. isam jardaneh / foundation engineering 61303 / 2010

74. dr. isam jardaneh / foundation engineering 61303 / 2010

75. Problem # 1
dr. isam jardaneh / foundation engineering / 2010

76. Problem # 2
Refer to problem # 1 above. For the retaining wall, determine the Rankine active force per unit length of the wall and the location of the line of action of the resultant.
dr. isam jardaneh / foundation engineering / 2010

77. Problem # 3
dr. isam jardaneh / foundation engineering / 2010

78. Problem # 4
dr. isam jardaneh / foundation engineering / 2010