Borrow & Fill Computations. Cut and Fill Slopes FHWA, 2004.

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Presentation transcript:

Borrow & Fill Computations

Cut and Fill Slopes FHWA, 2004

Proper OM & MD at time of compaction???

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

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

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)

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 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)

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 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)

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 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)

Vol (ft 3 )Wt. (lbs/ft 3 ) VaAirWa VwWaterWw VsSoil Ws 92 Moisture Content = weight of water *100 weight of dry soil 15 = Ww * 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 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)

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 * 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 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)

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 (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

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)

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 (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

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…)

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

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

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

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

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

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

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 =

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 = e = 0.82

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

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

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 * lbs/ft3

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 * lbs/ft3 Ww = 10.5 lbs/ft3

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

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

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

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

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

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

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

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

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

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)

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

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 = e = 0.45 Compared to e = 0.82 from the Borrow Source

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

The Answer: How much borrow material is needed?

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

The Answer: Volume of Borrow = 1 + e borrow Volume of Fill 1 + e fill Volume of Borrow = ,000 yd

The Answer: Volume of Borrow = 1 + e borrow Volume of Fill 1 + e fill Volume of Borrow = ,000 yd Volume of Borrow = 62,759 yd 3