Earth pressure( soil mechanics)

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1. Vishvakarma Government Engineering College, Chandkheda Name –Darshil Vekaria Branch –Civil Engineering Topic - Earth Pressure (Soil Mechanics)

2. W HERE E ARTH P RESSURE ?  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. U SE OF RETAINING WALLS 4

4. I N GEOTECHNICAL ENGINEERING , IT IS OFTEN NECESSARY TO PREVENT LATERAL SOIL MOVEMENTS Cantilever retaining wall Braced excavation Anchored sheet pile 6

5. D EFINITION OF K EY T ERMS  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

6. L ATERAL E ARTH P RESSURE - B ASIC C ONCEPTS  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

7. 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

8. T HE R ANKINE T HEORY 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

9. T HE C OULOMB T HEORY IS SIMILAR TO R ANKINE 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

10. 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

11. L ATERAL EARTH PRESSURE FOR AT REST CONDITION Element E is subjected to the following pressures. E 13

12. L ATERAL 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

13. L ATERAL EARTH PRESSURE FOR AT REST CONDITION 15

14. C OEFFICIENTS OF EARTH PRESSURE FOR AT REST CONDITION : K O 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, 45 0.57 undisturbed (w{ = 74%) 16

15. F ACTORS AFFECTING K O  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

16. D EVELOPMENT OF ACTIVE AND PASSIVE EARTH PRESSURES 18

17. H ORIZONTAL STRESS AS A FUNCTION OF THE DISPLACEMENT 19

18. D EVELOPMENT OF E ARTH P RESSURES Active Pressures ◦ Overburden (σ1) Driving Passive Pressures ◦ Wall (σ3) Driving 20

19. A CTIVE E ARTH P RESSURE  - Wall moves away from soil 21

20. A CTIVE E ARTH P RESSURE 22

21. P ASSIVE E ARTH P RESSURE 23

22. P ASSIVE E ARTH P RESSURE 24

23. M OVEMENT REQUIRED TO DEVELOP A CTIVE E ARTH P RESSURE Soil Type & Condition  H Required  H Sands , Granular soil Dense 0.001 H to 0.002H H 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 25

24. RANKINE'S EARTH PRESSURE THEORIES 26

25. R ANKINE ' S CONDITION FOR ACTIVE AND PASSIVE FAILURES IN A SEMI - INFINITE MASS OF C OHESIONLESS SOIL 27

26. 28

27. R ANKINE ’ S T HEORY : A CTIVE E ARTH P RESSURE 29

28. SMOOTH VERTICAL WALL WITH COHESIONLESS BACKFILL  Backfill Horizontal-Active Earth Pressure 30

29.  Backfill Horizontal-Passive Earth Pressure 31

30. R ANKINE ’ S T HEORY : P ASSIVE E ARTH P RESSURE 32

31.  Relationship between Kp and KA 33

32. R ANKINE ’ S T HEORY : A CTIVE E ARTH P RESSURE 34

33. R ANKINE ' S ACTIVE PRESSURE UNDER SUBMERGED CONDITION IN COHESION LESS SOIL 36

34. R ANKINE ' S ACTIVE PRESSURE IN COHESIONLESS BACKFILL UNDER PARTLY SUBMERGED CONDITION WITH SURCHARGE LOAD 37

35. R ANKINE ' S ACTIVE PRESSURE FOR A SLOPING COHESIONLESS BACKFILL 38

36. R ANKINE ' S PASSIVE PRESSURE IN SLOPING COHESIONLESS BACKFILL 40

37. RANKINE'S ACTIVE EARTH RESSURE WITH COHESIVE BACKFILL 41

38. RANKINE'S ACTIVE EARTH RESSURE WITH COHESIVE BACKFILL 42

39. A CTIVE EARTH PRESSURE ON VERTICAL SECTIONS IN COHESIVE SOILS 43

40. E FFECT OF WATER TABLE ON LATERAL EARTH PRESSURE NΦ = tan2 (45+Φ/2) 44

41. R ANKINE ’ S T HEORY : S PECIAL C ASES σ v ‘= σ v -u Submergence: Inclined Backfill: σ h = K a σ v ′ + u u= pore water pressure Inclined but Smooth Back face of wall: 45

42. COULOMB'S EARTH PRESSURE THEORY 46

43. 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

44. C ONDITIONS FOR FAILURE UNDER ACTIVE CONDITIONS 48

45. P ROCEDURE 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

46. A CTIVE E ARTH P RESSURE 50

47. COULOMB'S EARTH PRESSURE THEORY FOR SAND FOR PASSIVE STATE 51

48. C OULOMB ’ S T HEORY : P ASSIVE E ARTH P RESSURE ( G RAPHICAL M ETHOD ) Wall Friction: Coulomb’s theory overestimates Passive EP 52

49. C OULOMB ’ S T HEORY : A CTIVE E ARTH P RESSURE ( G RAPHICAL M ETHOD ) Wall Friction: Coulomb’s theory underestimates Active EP 53

50. C OULOMB ’ S T HEORY : S OLUTIONS 54

51. C ULMANN ’ S G RAPHICAL M ETHOD : A CTIVE EP 55

52. C ULMANN ’ S G RAPHICAL M ETHOD : P ASSIVE EP 56

53. P RESSURE D ISTRIBUTION FOR S TRATIFIED S OILS 57

54. M ODES OF G EOTECHNICAL F AILURES Bearing Sliding Overturning 59 Overall Stability Settlement