1. Stress Distribution and all of its mysteries

2. I. The Bulb of Pressure Force

3. I. The Bulb of Pressure “what are the stresses at this point?” Force

4. II. The Boussinesq Equation A. Goal: to determine the vertical and horizontal stresses under a point load in a homogeneous, isotropic medium. “Allows us to determine vertical and horizontal stresses at any point in space” (boo-sinn-esk)

5. II. The Boussinesq Equation B. The Equation:

6. Where v = Poisson’s Ratio (0.48)

12. 6.71

13. If Poisson’s ratio is ~0.5, equations simplify to: σx = 3Px 2 z 2π R 5 σy = 3Py 2 z 2π R 5

14. Your turn: Vertical load of 2500 lb/ft2 Determine horizontal and vertical stresses at X= 5, Y= 2, Z = 6

15. Borrow & Fill Computations

16. Cut and Fill Slopes FHWA, 2004

17. Proper OM & MD at time of compaction???

18. Photo: Rick Wooten ………………..Progressive Slope Failures

26. Vol (ft 3 )Wt. (lbs/ft 3 ) VaAirWa VwWaterWw VsSoilWs Borrow Data: Wet density in situ = 106 lbs/ft3 Specific gravity = 2.70 Moisture Content = 15% Proctor Results: OM = 9% MD = 117 lbs/ft3 (dry) Vv Vt

27. Vol (ft 3 )Wt. (lbs/ft 3 ) VaAirWa VwWaterWw VsSoilWs Ws = Dry Density (lbs/ft3) = Wet Density (lbs/ft3) 1 + moisture content (decimal form) Borrow Data: Wet density in situ = 106 lbs/ft3 Specific gravity = 2.70 Moisture Content = 15% Proctor Results: OM = 9% MD = 117 lbs/ft3 (dry)

28. Vol (ft 3 )Wt. (lbs/ft 3 ) VaAirWa VwWaterWw VsSoilWs Ws = Dry Density (lbs/ft3) = Wet Density (lbs/ft3) 1 + moisture content (decimal form) Ws = Dry Density (lbs/ft3) = 106 lbs/ft 3 1 + 0.15 Borrow Data: Wet density in situ = 106 lbs/ft3 Specific gravity = 2.70 Moisture Content = 15% Proctor Results: OM = 9% MD = 117 lbs/ft3 (dry)

29. Vol (ft 3 )Wt. (lbs/ft 3 ) VaAirWa VwWaterWw VsSoil Ws 92 Ws = Dry Density (lbs/ft3) = Wet Density (lbs/ft3) 1 + moisture content (decimal form) Ws = Dry Density (lbs/ft3) = 106 lbs/ft 3 1 + 0.15 Ws = 92 lbs/ft 3 Borrow Data: Wet density in situ = 106 lbs/ft3 Specific gravity = 2.70 Moisture Content = 15% Proctor Results: OM = 9% MD = 117 lbs/ft3 (dry)

30. Vol (ft 3 )Wt. (lbs/ft 3 ) VaAirWa VwWaterWw VsSoil Ws 92 Moisture Content = weight of water *100 weight of soil Ws = Dry Density (lbs/ft3) = Wet Density (lbs/ft3) 1 + moisture content (decimal form) Ws = Dry Density (lbs/ft3) = 106 lbs/ft 3 1 + 0.15 Ws = 92 lbs/ft 3 Borrow Data: Wet density in situ = 106 lbs/ft3 Specific gravity = 2.70 Moisture Content = 15% Proctor Results: OM = 9% MD = 117 lbs/ft3 (dry)

31. Vol (ft 3 )Wt. (lbs/ft 3 ) VaAirWa VwWaterWw VsSoil Ws 92 Moisture Content = weight of water *100 weight of dry soil 15 = Ww *100 92 lbs/ft 3 Ws = Dry Density (lbs/ft3) = Wet Density (lbs/ft3) 1 + moisture content (decimal form) Ws = Dry Density (lbs/ft3) = 106 lbs/ft 3 1 + 0.15 Ws = 92 lbs/ft 3 Borrow Data: Wet density in situ = 106 lbs/ft3 Specific gravity = 2.70 Moisture Content = 15% Proctor Results: OM = 9% MD = 117 lbs/ft3 (dry)

32. Vol (ft 3 )Wt. (lbs/ft 3 ) VaAirWa VwWater Ww 14 VsSoil Ws 92 Moisture Content = weight of water *100 weight of soil 15 = Ww *100 92 lbs/ft 3 Ww = 14 lbs/ft3 Ws = Dry Density (lbs/ft3) = Wet Density (lbs/ft3) 1 + moisture content (decimal form) Ws = Dry Density (lbs/ft3) = 106 lbs/ft 3 1 + 0.15 Ws = 92 lbs/ft 3 Borrow Data: Wet density in situ = 106 lbs/ft3 Specific gravity = 2.70 Moisture Content = 15% Proctor Results: OM = 9% MD = 117 lbs/ft3 (dry)

33. Vol (ft 3 )Wt. (lbs/ft 3 ) VaAir Wa 0 VwWater Ww 14 VsSoil Ws 92 Specific Gravity (Gs) = 2.70 (unitless) Unit Weight water (γ w ) = 62.4 lbs per ft 3

34. Vol (ft 3 )Wt. (lbs/ft 3 ) VaAir Wa 0 VwWater Ww 14 VsSoil Ws 92 Specific Gravity (Gs) = 2.70 (unitless) Unit Weight water (γ w ) = 62.4 lbs per ft 3 Vol Soil (Vs) = Ws Gs * γw

35. Vol (ft 3 )Wt. (lbs/ft 3 ) VaAir Wa 0 VwWater Ww 14 Vs 0.55 Soil Ws 92 Specific Gravity (Gs) = 2.70 (unitless) Unit Weight water (γ w ) = 62.4 lbs per ft 3 Vol Soil (Vs) = Ws= 92 lbs/ft3 Gs * γw (2.70)*(62.4 lbs)

36. Vol (ft 3 )Wt. (lbs/ft 3 ) VaAir Wa 0 VwWater Ww 14 Vs 0.55 Soil Ws 92 Specific Gravity (Gs) = 2.70 (unitless) Unit Weight water (γ w ) = 62.4 lbs per ft 3 Vol Soil (Vs) = Ws= 92 lbs/ft3 Gs * γw (2.70)*(62.4 lbs) Vs = 0.55 ft3

37. Vol (ft 3 )Wt. (lbs/ft 3 ) VaAir Wa 0 VwWater Ww 14 Vs 0.55 Soil Ws 92 Specific Gravity (Gs) = 2.70 (unitless) Unit Weight water (γ w ) = 62.4 lbs per ft 3 Vol Soil (Vs) = Ws= 92 lbs/ft3 Gs * γw (2.70)*(62.4 lbs) Vs = 0.55 ft3 Vol Voids (Vv) = Vt - Vs

38. Vol (ft 3 )Wt. (lbs/ft 3 ) VaAir Wa 0 VwWater Ww 14 Vs 0.55 Soil Ws 92 Specific Gravity (Gs) = 2.70 (unitless) Unit Weight water (γ w ) = 62.4 lbs per ft 3 Vol Soil (Vs) = Ws= 92 lbs/ft3 Gs * γw (2.70)*(62.4 lbs) Vs = 0.55 ft3 Vol Voids (Vv) = Vt - Vs Vv = 1 – 0.55 Vv = 0.45 ft3 (we will use this value later…)

39. Vol (ft 3 )Wt. (lbs/ft 3 ) VaAir Wa 0 VwWater Ww 14 Vs 0.55 Soil Ws 92 Specific Gravity (Gs) = 2.70 (unitless) Unit Weight water (γ w ) = 62.4 lbs per ft 3 Vv = 0.45 ft3 Vw = Ww = 14 lbs/ft3 γ w 62.4 lbs

40. Vol (ft 3 )Wt. (lbs/ft 3 ) VaAir Wa 0 Vw 0.22 Water Ww 14 Vs 0.55 Soil Ws 92 Specific Gravity (Gs) = 2.70 (unitless) Unit Weight water (γ w ) = 62.4 lbs per ft 3 Vw = Ww = 14 lbs/ft3 γ w 62.4 lbs Vw = 0.22 ft3

41. Vol (ft 3 )Wt. (lbs/ft 3 ) VaAir Wa 0 Vw 0.22 Water Ww 14 Vs 0.55 Soil Ws 92 Specific Gravity (Gs) = 2.70 (unitless) Unit Weight water (γ w ) = 62.4 lbs per ft 3 Vv = 0.45 ft3 Vol Air = Va = Vv – Vw

42. Vol (ft 3 )Wt. (lbs/ft 3 ) VaAir Wa 0 Vw 0.22 Water Ww 14 Vs 0.55 Soil Ws 92 Specific Gravity (Gs) = 2.70 (unitless) Unit Weight water (γ w ) = 62.4 lbs per ft 3 Vv = 0.45 ft3 Vol Air = Va = Vv – Vw Va = 0.45 – 0.22

43. Vol (ft 3 )Wt. (lbs/ft 3 ) Va 0.23 Air Wa 0 Vw 0.22 Water Ww 14 Vs 0.55 Soil Ws 92 Specific Gravity (Gs) = 2.70 (unitless) Unit Weight water (γ w ) = 62.4 lbs per ft 3 Vol Air = Va = Vv – Vw Va = 0.45 – 0.22 Va = 0.23 ft3

44. Vol (ft 3 )Wt. (lbs/ft 3 ) Va 0.23 Air Wa 0 Vw 0.22 Water Ww 14 Vs 0.55 Soil Ws 92 Specific Gravity (Gs) = 2.70 (unitless) Unit Weight water (γ w ) = 62.4 lbs per ft 3 Vv = 0.45 ft3 Void Ratio (e) = Vv Vs

45. Vol (ft 3 )Wt. (lbs/ft 3 ) Va 0.23 Air Wa 0 Vw 0.22 Water Ww 14 Vs 0.55 Soil Ws 92 Specific Gravity (Gs) = 2.70 (unitless) Unit Weight water (γ w ) = 62.4 lbs per ft 3 Void Ratio (e) = Vv Vs = 0.45 0.55

46. Vol (ft 3 )Wt. (lbs/ft 3 ) Va 0.23 Air Wa 0 Vw 0.22 Water Ww 14 Vs 0.55 Soil Ws 92 Specific Gravity (Gs) = 2.70 (unitless) Unit Weight water (γ w ) = 62.4 lbs per ft 3 Void Ratio (e) = Vv Vs = 0.45 0.55 e = 0.82

47. Vol (ft 3 )Wt. (lbs/ft 3 ) VaAirWa VwWaterWw VsSoilWs Fill Data: Wet density in situ = 106 lbs/ft3 Specific gravity = 2.70 Moisture Content = 15% Specific Gravity = 2.7 Proctor Results: OM = 9% MD = 117 lbs/ft3 (dry) Vv Vt

48. Vol (ft 3 )Wt. (lbs/ft 3 ) VaAirWa VwWaterWw VsSoilWs Fill Data: Wet density in situ = 106 lbs/ft3 Specific gravity = 2.70 Moisture Content = 15% Specific Gravity = 2.7 Proctor Results: OM = 9% MD = 117 lbs/ft3 (dry) Vv Vt Moisture Content = weight of water *100 weight of soil

49. Vol (ft 3 )Wt. (lbs/ft 3 ) VaAirWa VwWaterWw VsSoilWs Fill Data: Wet density in situ = 106 lbs/ft3 Specific gravity = 2.70 Moisture Content = 15% Specific Gravity = 2.7 Proctor Results: OM = 9% MD = 117 lbs/ft3 (dry) Vv Vt Moisture Content = weight of water *100 weight of soil 9 = Ww *100 117 lbs/ft3

50. Vol (ft 3 )Wt. (lbs/ft 3 ) VaAirWa VwWater Ww 10.5 VsSoilWs Fill Data: Wet density in situ = 106 lbs/ft3 Specific gravity = 2.70 Moisture Content = 15% Specific Gravity = 2.7 Proctor Results: OM = 9% MD = 117 lbs/ft3 (dry) Vv Vt Moisture Content = weight of water *100 weight of soil 9 = Ww *100 117 lbs/ft3 Ww = 10.5 lbs/ft3

51. Vol (ft 3 )Wt. (lbs/ft 3 ) VaAirWa VwWater Ww 10.5 VsSoil Ws 117 Fill Data: Wet density in situ = 106 lbs/ft3 Specific gravity = 2.70 Moisture Content = 15% Specific Gravity = 2.7 Proctor Results: OM = 9% MD = 117 lbs/ft3 (dry) Vv Vt Ws = Dry Density (lbs/ft3) = MD = 117 lbs/ft3

52. Vol (ft 3 )Wt. (lbs/ft 3 ) VaAir Wa 0 VwWater Ww 10.5 VsSoil Ws 117 Fill Data: Wet density in situ = 106 lbs/ft3 Specific gravity = 2.70 Moisture Content = 15% Specific Gravity = 2.7 Proctor Results: OM = 9% MD = 117 lbs/ft3 (dry) Vv Vt Ws = Dry Density (lbs/ft3) = MD = 117 lbs/ft3

53. Fill Data: Wet density in situ = 106 lbs/ft3 Specific gravity = 2.70 Moisture Content = 15% Specific Gravity = 2.7 Proctor Results: OM = 9% MD = 117 lbs/ft3 (dry) Vv Vt Vol Soil (Vs) = Ws= 117 lbs/ft3 Gs * γw (2.70)*(62.4 lbs) Vol (ft 3 )Wt. (lbs/ft 3 ) VaAir Wa 0 VwWater Ww 10.5 VsSoil Ws 117

54. Fill Data: Wet density in situ = 106 lbs/ft3 Specific gravity = 2.70 Moisture Content = 15% Specific Gravity = 2.7 Proctor Results: OM = 9% MD = 117 lbs/ft3 (dry) Vv Vt Vol Soil (Vs) = Ws= 117 lbs/ft3 Gs * γw (2.70)*(62.4 lbs) Vs = 0.69 ft3 (compared to 0.55 from the borrow source) Vol (ft 3 )Wt. (lbs/ft 3 ) VaAir Wa 0 VwWater Ww 10.5 Vs 0.69 Soil Ws 117

55. Fill Data: Wet density in situ = 106 lbs/ft3 Specific gravity = 2.70 Moisture Content = 15% Specific Gravity = 2.7 Proctor Results: OM = 9% MD = 117 lbs/ft3 (dry) Vv Vt Vol (ft 3 )Wt. (lbs/ft 3 ) VaAir Wa 0 VwWater Ww 10.5 Vs 0.69 Soil Ws 117 Vol Voids (Vv) = Vt - Vs

56. Fill Data: Wet density in situ = 106 lbs/ft3 Specific gravity = 2.70 Moisture Content = 15% Specific Gravity = 2.7 Proctor Results: OM = 9% MD = 117 lbs/ft3 (dry) Vv Vt Vol (ft 3 )Wt. (lbs/ft 3 ) VaAir Wa 0 VwWater Ww 10.5 Vs 0.69 Soil Ws 117 Vol Voids (Vv) = Vt - Vs Vv = 1 – 0.69 Vv = 0.31 ft3

57. Fill Data: Wet density in situ = 106 lbs/ft3 Specific gravity = 2.70 Moisture Content = 15% Specific Gravity = 2.7 Proctor Results: OM = 9% MD = 117 lbs/ft3 (dry) Vv Vt Vol (ft 3 )Wt. (lbs/ft 3 ) VaAir Wa 0 VwWater Ww 10.5 Vs 0.69 Soil Ws 117 Vw = Ww = 10.5 lbs/ft3 γ w 62.4 lbs

58. Fill Data: Wet density in situ = 106 lbs/ft3 Specific gravity = 2.70 Moisture Content = 15% Specific Gravity = 2.7 Proctor Results: OM = 9% MD = 117 lbs/ft3 (dry) Vv Vt Vol (ft 3 )Wt. (lbs/ft 3 ) VaAir Wa 0 Vw 0.17 Water Ww 10.5 Vs 0.69 Soil Ws 117 Vw = Ww = 10.5 lbs/ft3 γ w 62.4 lbs Vw = 0.17

59. Fill Data: Wet density in situ = 106 lbs/ft3 Specific gravity = 2.70 Moisture Content = 15% Specific Gravity = 2.7 Proctor Results: OM = 9% MD = 117 lbs/ft3 (dry) Volume of voids = 0.31 Vv Vt Vol (ft 3 )Wt. (lbs/ft 3 ) VaAir Wa 0 Vw 0.17 Water Ww 10.5 Vs 0.69 Soil Ws 117 Vol Air = Va = Vv – Vw Va = 0.31 – 0.17

60. Fill Data: Wet density in situ = 106 lbs/ft3 Specific gravity = 2.70 Moisture Content = 15% Specific Gravity = 2.7 Proctor Results: OM = 9% MD = 117 lbs/ft3 (dry) Vv Vt Vol (ft 3 )Wt. (lbs/ft 3 ) Va 0.14 Air Wa 0 Vw 0.17 Water Ww 10.5 Vs 0.69 Soil Ws 117 Vol Air = Va = Vv – Vw Va = 0.31 – 0.17 Va = 0.14 ft3

61. Fill Data: Wet density in situ = 106 lbs/ft3 Specific gravity = 2.70 Moisture Content = 15% Specific Gravity = 2.7 Proctor Results: OM = 9% MD = 117 lbs/ft3 (dry) Vv Vt Vol (ft 3 )Wt. (lbs/ft 3 ) Va 0.14 Air Wa 0 Vw 0.17 Water Ww 10.5 Vs 0.69 Soil Ws 117 Void Ratio (e) = Vv Vs

62. Fill Data: Wet density in situ = 106 lbs/ft3 Specific gravity = 2.70 Moisture Content = 15% Specific Gravity = 2.7 Proctor Results: OM = 9% MD = 117 lbs/ft3 (dry) Vv Vt Vol (ft 3 )Wt. (lbs/ft 3 ) Va 0.14 Air Wa 0 Vw 0.17 Water Ww 10.5 Vs 0.69 Soil Ws 117 Void Ratio (e) = Vv Vs = 0.31 0.69 e = 0.45

63. Vol (ft 3 )Wt. (lbs/ft 3 ) Va 0.14 Air Wa 0 Vw 0.17 Water Ww 10.5 Vs 0.69 Soil Ws 117 Vol (ft 3 )Wt. (lbs/ft 3 ) Va 0.23 Air Wa 0 Vw 0.22 Water Ww 14 Vs 0.55 Soil Ws 92 BORROW DATA FILL DATA

64. The Answer: How much borrow material is needed?

65. The Answer: Volume of Borrow = 1 + e borrow Volume of Fill 1 + e fill

66. The Answer: Volume of Borrow = 1 + e borrow Volume of Fill 1 + e fill Volume of Borrow = 1 + 0.82 50,000 yd 3 1 + 0.45

67. The Answer: Volume of Borrow = 1 + e borrow Volume of Fill 1 + e fill Volume of Borrow = 1 + 0.82 50,000 yd 3 1 + 0.45 Volume of Borrow = 62,759 yd 3