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# Earth pressure 14 2-2012

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### Earth pressure 14 2-2012

1. 1. Prof. S.P.PARMAR DEPARTMENT OF CIVIL ENGINEERING DHARMASINH DESAI UNIVERSITY, NADIAD Mail: samirddu@gmail.com 1
2. 2. WHERE EARTH PRESSURE?  Calculating lateral earth pressure is necessary in order to design structures such as:  Retaining Walls  Bridge Abutments  Bulkheads  Temporary Earth Support Systems  Basement Walls 2
3. 3. TYPES OF RETAINING WALLS: 3
4. 4. USE OF RETAINING WALLS 4
5. 5. USE OF RETAINING WALLS 5
6. 6. IN GEOTECHNICAL ENGINEERING, IT IS OFTEN NECESSARY TO PREVENT LATERAL SOIL MOVEMENTS Cantilever retaining wall Braced excavation Anchored sheet pile 6
7. 7. DEFINITION OF KEY TERMS  Active earth pressure coefficient (Ka): It is the ratio of horizontal and vertical principal effective stresses when a retaining wall moves away (by a small amount) from the retained soil.  Passive earth pressure coefficient (Kp): It is the ratio of horizontal and vertical principal effective stresses when a retaining wall is forced against a soil mass.  Coefficient of earth pressure at rest (Ko): It is the ratio of horizontal and vertical principal effective stresses when the retaining wall does not move at all, i.e. it is “at rest”. 7
8. 8. LATERAL EARTH PRESSURE – BASIC CONCEPTS  We will consider the lateral pressure on a vertical wall that retains soil on one side.  First, we will consider a drained case, i.e. The shear strength of the soil is governed by its angle of friction φ.  In addition, we will make the following assumptions: – The interface between the wall and the soil is frictionless. – The soil surface is horizontal and there are no shear stresses on horizontal and vertical planes, i.e. The horizontal and vertical stresses are principal stresses. – The wall is rigid and extends to an infinite depth in a dry, homogenous, isotropic soil mass. – The soil is loose and initially in an at-rest state. 8
9. 9. LATERAL EARTH PRESSURE THEORY  There are two classical earth pressure theories. They are  1. Coulomb's earth pressure theory.  2. Rankine's earth pressure theory. 9
10. 10. THE RANKINE THEORY ASSUMES:  There is no adhesion or friction between the wall and soil  Lateral pressure is limited to vertical walls  Failure (in the backfill) occurs as a sliding wedge along an assumed failure plane defined by φ.  Lateral pressure varies linearly with depth and the resultant pressure is located one-third of the height (H) above the base of the wall.  The resultant force is parallel to the backfill surface. 10
11. 11. THE COULOMB THEORY IS SIMILAR TO RANKINE EXCEPT THAT:  There is friction between the wall and soil and takes this into account by using a soil-wall friction angle of δ.  Note that δ ranges from φ/2 to 2φ/3 and δ = 2φ/3 is commonly used.  Lateral pressure is not limited to vertical walls  The resultant force is not necessarily parallel to the backfill surface because of the soil-wall friction value δ. 11
12. 12. LATERAL EARTH PRESSURE FOR AT REST CONDITION  If the wall is rigid and does not move with the pressure exerted on the wall, the soil behind the wall will be in a state of elastic equilibrium. 12
13. 13. LATERAL EARTH PRESSURE FOR AT REST CONDITION Element E is subjected to the following pressures. E 13
14. 14. LATERAL EARTH PRESSURE FOR AT REST CONDITION  If we consider the backfill is homogeneous then v and h both increase linearly with depth z.  In such a case, the ratio of h to v remains constant with respect to depth, that is Where, Ko is called the coefficient of earth pressure for the at rest condition or at rest earth pressure Coefficient. The lateral earth pressure h acting on the wall at any depth z may be expressed as 14
15. 15. LATERAL EARTH PRESSURE FOR AT REST CONDITION 15
16. 16. COEFFICIENTS OF EARTH PRESSURE FOR AT REST CONDITION : KO Type of soil Ip Ko Loose sand, saturated 0.46 Dense sand, saturated 0.36 Dense sand, dry (e = 0.6) 0.49 Loose sand, dry (e = 0.8) 0.64 Compacted clay 9 0.42 Compacted clay 31 0.60 Organic silty clay, undisturbed (w{ = 74%) 45 0.57 16
17. 17. FACTORS AFFECTING KO  The value of Ko depends upon the relative density of the sand and the process by which the deposit was formed.  If this process does not involve artificial tamping the value of Ko ranges from about 0.40 for loose sand to 0.6 for dense sand.  Tamping the layers may increase it to 0.8. 17
18. 18. DEVELOPMENT OF ACTIVE AND PASSIVE EARTH PRESSURES 18
19. 19. HORIZONTAL STRESS AS A FUNCTION OF THE DISPLACEMENT 19
20. 20. DEVELOPMENT OF EARTH PRESSURES Active Pressures ◦ Overburden (σ1) Driving Passive Pressures ◦ Wall (σ3) Driving 20
21. 21. ACTIVE EARTH PRESSURE  ‐ Wall moves away from soil 21
22. 22. ACTIVE EARTH PRESSURE 22
23. 23. PASSIVE EARTH PRESSURE 23
24. 24. PASSIVE EARTH PRESSURE 24
25. 25. MOVEMENT REQUIRED TO DEVELOP ACTIVE EARTH PRESSURE Soil Type & Condition H Required Sands , Granular soil Dense 0.001 H to 0.002H loose 0.002 H to 0.004 H Clays Stiff/Hard 0.01H to 0.02 H Soft material 0.02 H to 0.05H H H 25
26. 26. RANKINE'S EARTH PRESSURE THEORIES 26
27. 27. RANKINE'S CONDITION FOR ACTIVE AND PASSIVE FAILURES IN A SEMI-INFINITE MASS OF COHESIONLESS SOIL 27
28. 28. 28
29. 29. RANKINE’S THEORY: ACTIVE EARTH PRESSURE 29
30. 30. SMOOTH VERTICAL WALL WITH COHESIONLESS BACKFILL  Backfill Horizontal-Active Earth Pressure 30
31. 31.  Backfill Horizontal-Passive Earth Pressure 31
32. 32. RANKINE’S THEORY: PASSIVE EARTH PRESSURE 32
33. 33.  Relationship between Kp and KA 33
34. 34. RANKINE’S THEORY: ACTIVE EARTH PRESSURE 34
35. 35. TENSION CRACK IN SOIL 35
36. 36. RANKINE'S ACTIVE PRESSURE UNDER SUBMERGED CONDITION IN COHESION LESS SOIL 36
37. 37. RANKINE'S ACTIVE PRESSURE IN COHESIONLESS BACKFILL UNDER PARTLY SUBMERGED CONDITION WITH SURCHARGE LOAD 37
38. 38. RANKINE'S ACTIVE PRESSURE FOR A SLOPING COHESIONLESS BACKFILL 38
39. 39. MOHR DIAGRAM 39
40. 40. RANKINE'S PASSIVE PRESSURE IN SLOPING COHESIONLESS BACKFILL 40
41. 41. RANKINE'S ACTIVE EARTH RESSURE WITH COHESIVE BACKFILL 41
42. 42. RANKINE'S ACTIVE EARTH RESSURE WITH COHESIVE BACKFILL 42
43. 43. ACTIVE EARTH PRESSURE ON VERTICAL SECTIONS IN COHESIVE SOILS 43
44. 44. EFFECT OF WATER TABLE ON LATERAL EARTH PRESSURE NΦ = tan2 (45+Φ/2) 44
45. 45. RANKINE’S THEORY: SPECIAL CASES σh = K aσv ′ + u σv‘= σv-u u= pore water pressureSubmergence: Inclined Backfill: Inclined but Smooth Back face of wall: 45
46. 46. COULOMB'S EARTH PRESSURE THEORY 46
47. 47. 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 47
48. 48. CONDITIONS FOR FAILURE UNDER ACTIVE CONDITIONS 48
49. 49. PROCEDURE TO DRAW  ABC 1. AB is the pressure face 2. The backfill surface BE is a plane inclined at an angle  with the horizontal 3.  is the angle made by the pressure face AB with the horizontal 4. H is the height of the wall 5. AC is the assumed rupture plane surface, and 6.  is the angle made by the surface AC with the horizontal 7. W = yA, where A = area of wedge ABC 49
50. 50. ACTIVE EARTH PRESSURE 50
51. 51. COULOMB'S EARTH PRESSURE THEORY FOR SAND FOR PASSIVE STATE 51
52. 52. COULOMB’S THEORY: PASSIVE EARTH PRESSURE ( GRAPHICAL METHOD) Wall Friction: Coulomb’s theory overestimates Passive EP 52
53. 53. COULOMB’S THEORY: ACTIVE EARTH PRESSURE ( GRAPHICAL METHOD) Wall Friction: Coulomb’s theory underestimates Active EP 53
54. 54. COULOMB’S THEORY: SOLUTIONS 54
55. 55. CULMANN’S GRAPHICAL METHOD: ACTIVE EP 55
56. 56. CULMANN’S GRAPHICAL METHOD: PASSIVE EP 56
57. 57. PRESSURE DISTRIBUTION FOR STRATIFIED SOILS 57
58. 58. THE LOCATION OF STRUTS AFFECTS THE VALUES AND DISTRIBUTIONS OF LATERAL EARTH PRESSURES 58
59. 59. MODES OF GEOTECHNICAL FAILURES Sliding Overturning Bearing Overall Stability Settlement 59
60. 60. LATERAL SUPPORT Gravity Retaining wall Soil nailing Reinforced earth wall 60
61. 61. SOIL NAILING 61
62. 62. 62 SHEET PILE
63. 63. THE MAGNITUDE OF LATERAL EARTH PRESSURE DEPENDS ON:  Shear strength characteristics of soil  2. Lateral strain condition  3. Pore water pressure  4. State of Equilibrium of soil  5. Wall and ground surface shape Previous conditions depends mainly on: a) Drainage conditions b) Interaction between soil and wall 63
64. 64. 64
65. 65. WALL DRAINAGE Accumulation of rain water in the back fill results in its saturation, and thus a considerable increase in the earth pressure acting on the wall. This may eventually lead to unstable conditions. Two of the options to take care of this problem are the following: 􀂅 Provision of weep holes w/o geo-textile on the back-face of wall 􀂅 Perforated pipe draining system with filter 65
66. 66. WALL DRAINAGE Weep Holes: They should have a minimum diameter of 10 cm and be adequately spaced depending on the backfill material. Geotextile material or a thin layer of some other filter may be used on the back face of wall for the full height in order to avoid the back fill material entering the weep holes and eventually clogging them. 66
67. 67. GABION RETAINING WALL 67
68. 68. REFERANCES: 1. Soil Mecahnics & Foundation Engg. - Arora. 2. Soil Mechanics – V.N.S.Murthy 3. www.wikipedia.com 68
69. 69. 69