1. Borrow & Fill Computations

2. Cut and Fill Slopes FHWA, 2004

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

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

12. 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

13. 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)

14. 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)

15. 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)

16. 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)

17. 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)

18. 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)

19. 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

20. 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

21. 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)

22. 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

23. 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

24. 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…)

25. 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

26. 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

27. 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

28. 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

29. 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

30. 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

31. 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

32. 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

33. 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

34. 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

35. 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

36. 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

37. 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

38. 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

39. 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

40. 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

41. 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

42. 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

43. 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

44. 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

45. 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

46. 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 (compared to 0.23 from the borrow source)

47. 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

48. 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 Compared to e = 0.82 from the Borrow Source

49. 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

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

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

52. 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

53. 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