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Borrow & Fill Computations. Cut and Fill Slopes. FHWA, 2004. FHWA, 2004. Proper OM & MD at time of compaction???. ………………..Progressive Slope Failures. Photo: Rick Wooten. Borrow Data:. Wet density in situ = 106 lbs/ft3 Specific gravity = 2.70 Moisture Content = 15% Proctor Results: - PowerPoint PPT Presentation
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Borrow & FillComputations
Cut and Fill Slopes
FHWA, 2004
FHWA, 2004
Proper OM & MD at time of compaction???
Photo: Rick Wooten
………………..Progressive Slope Failures
Vol (ft3) Wt. (lbs/ft3)
Va Air Wa
Vw Water Ww
Vs Soil Ws
Borrow Data:Wet density in situ = 106 lbs/ft3Specific gravity = 2.70Moisture Content = 15%Proctor Results: OM = 9% MD = 117 lbs/ft3 (dry)
VvVt
Vol (ft3) Wt. (lbs/ft3)
Va Air Wa
Vw Water Ww
Vs Soil Ws
Ws = Dry Density (lbs/ft3) = Wet Density (lbs/ft3) 1 + moisture content (decimal form)
Borrow Data:Wet density in situ = 106 lbs/ft3Specific gravity = 2.70Moisture Content = 15%Proctor Results: OM = 9% MD = 117 lbs/ft3 (dry)
Vol (ft3) Wt. (lbs/ft3)
Va Air Wa
Vw Water Ww
Vs Soil Ws
Ws = Dry Density (lbs/ft3) = Wet Density (lbs/ft3) 1 + moisture content (decimal form)
Ws = Dry Density (lbs/ft3) = 106 lbs/ft3 1 + 0.15
Borrow Data:Wet density in situ = 106 lbs/ft3Specific gravity = 2.70Moisture Content = 15%Proctor Results: OM = 9% MD = 117 lbs/ft3 (dry)
Vol (ft3) Wt. (lbs/ft3)
Va Air Wa
Vw Water Ww
Vs Soil Ws 92
Ws = Dry Density (lbs/ft3) = Wet Density (lbs/ft3) 1 + moisture content (decimal form)
Ws = Dry Density (lbs/ft3) = 106 lbs/ft3 1 + 0.15
Ws = 92 lbs/ft3
Borrow Data:Wet density in situ = 106 lbs/ft3Specific gravity = 2.70Moisture Content = 15%Proctor Results: OM = 9% MD = 117 lbs/ft3 (dry)
Vol (ft3) Wt. (lbs/ft3)
Va Air Wa
Vw Water Ww
Vs Soil 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/ft3 1 + 0.15
Ws = 92 lbs/ft3
Borrow Data:Wet density in situ = 106 lbs/ft3Specific gravity = 2.70Moisture Content = 15%Proctor Results: OM = 9% MD = 117 lbs/ft3 (dry)
Vol (ft3) Wt. (lbs/ft3)
Va Air Wa
Vw Water Ww
Vs Soil Ws 92
Moisture Content = weight of water *100 weight of dry soil
15 = Ww *100 92 lbs/ft3
Ws = Dry Density (lbs/ft3) = Wet Density (lbs/ft3) 1 + moisture content (decimal form)
Ws = Dry Density (lbs/ft3) = 106 lbs/ft3 1 + 0.15
Ws = 92 lbs/ft3
Borrow Data:Wet density in situ = 106 lbs/ft3Specific gravity = 2.70Moisture Content = 15%Proctor Results: OM = 9% MD = 117 lbs/ft3 (dry)
Vol (ft3) Wt. (lbs/ft3)
Va Air Wa
Vw Water Ww 14
Vs Soil Ws 92
Moisture Content = weight of water *100 weight of soil
15 = Ww *100 92 lbs/ft3
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/ft3 1 + 0.15
Ws = 92 lbs/ft3
Borrow Data:Wet density in situ = 106 lbs/ft3Specific gravity = 2.70Moisture Content = 15%Proctor Results: OM = 9% MD = 117 lbs/ft3 (dry)
Vol (ft3) Wt. (lbs/ft3)
Va Air Wa 0
Vw Water Ww 14
Vs Soil Ws 92
Specific Gravity (Gs) = 2.70 (unitless)Unit Weight water (γw) = 62.4 lbs per ft3
Vol (ft3) Wt. (lbs/ft3)
Va Air Wa 0
Vw Water Ww 14
Vs Soil Ws 92
Specific Gravity (Gs) = 2.70 (unitless)Unit Weight water (γw) = 62.4 lbs per ft3
Vol Soil (Vs) = Ws Gs * γw
Vol (ft3) Wt. (lbs/ft3)
Va Air Wa 0
Vw Water Ww 14
Vs 0.55 Soil Ws 92
Specific Gravity (Gs) = 2.70 (unitless)Unit Weight water (γw) = 62.4 lbs per ft3
Vol Soil (Vs) = Ws = 92 lbs/ft3 Gs * γw (2.70)*(62.4 lbs)
Vol (ft3) Wt. (lbs/ft3)
Va Air Wa 0
Vw Water Ww 14
Vs 0.55 Soil Ws 92
Specific Gravity (Gs) = 2.70 (unitless)Unit Weight water (γw) = 62.4 lbs per ft3
Vol Soil (Vs) = Ws = 92 lbs/ft3 Gs * γw (2.70)*(62.4 lbs)
Vs = 0.55 ft3
Vol (ft3) Wt. (lbs/ft3)
Va Air Wa 0
Vw Water Ww 14
Vs 0.55 Soil Ws 92
Specific Gravity (Gs) = 2.70 (unitless)Unit Weight water (γw) = 62.4 lbs per ft3
Vol Soil (Vs) = Ws = 92 lbs/ft3 Gs * γw (2.70)*(62.4 lbs)
Vs = 0.55 ft3
Vol Voids (Vv) = Vt - Vs
Vol (ft3) Wt. (lbs/ft3)
Va Air Wa 0
Vw Water Ww 14
Vs 0.55 Soil Ws 92
Specific Gravity (Gs) = 2.70 (unitless)Unit Weight water (γw) = 62.4 lbs per ft3
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 (ft3) Wt. (lbs/ft3)
Va Air Wa 0
Vw Water Ww 14
Vs 0.55 Soil Ws 92
Specific Gravity (Gs) = 2.70 (unitless)Unit Weight water (γw) = 62.4 lbs per ft3
Vv = 0.45 ft3
Vw = Ww = 14 lbs/ft3 γw 62.4 lbs
Vol (ft3) Wt. (lbs/ft3)
Va Air Wa 0
Vw 0.22Water Ww 14
Vs 0.55 Soil Ws 92
Specific Gravity (Gs) = 2.70 (unitless)Unit Weight water (γw) = 62.4 lbs per ft3
Vw = Ww = 14 lbs/ft3 γw 62.4 lbs
Vw = 0.22 ft3
Vol (ft3) Wt. (lbs/ft3)
Va Air Wa 0
Vw 0.22Water Ww 14
Vs 0.55 Soil Ws 92
Specific Gravity (Gs) = 2.70 (unitless)Unit Weight water (γw) = 62.4 lbs per ft3
Vv = 0.45 ft3
Vol Air = Va = Vv – Vw
Vol (ft3) Wt. (lbs/ft3)
Va Air Wa 0
Vw 0.22Water Ww 14
Vs 0.55 Soil Ws 92
Specific Gravity (Gs) = 2.70 (unitless)Unit Weight water (γw) = 62.4 lbs per ft3
Vv = 0.45 ft3
Vol Air = Va = Vv – Vw Va = 0.45 – 0.22
Vol (ft3) Wt. (lbs/ft3)
Va 0.23 Air Wa 0
Vw 0.22Water Ww 14
Vs 0.55 Soil Ws 92
Specific Gravity (Gs) = 2.70 (unitless)Unit Weight water (γw) = 62.4 lbs per ft3
Vol Air = Va = Vv – Vw Va = 0.45 – 0.22
Va = 0.23 ft3
Vol (ft3) Wt. (lbs/ft3)
Va 0.23 Air Wa 0
Vw 0.22Water Ww 14
Vs 0.55 Soil Ws 92
Specific Gravity (Gs) = 2.70 (unitless)Unit Weight water (γw) = 62.4 lbs per ft3
Vv = 0.45 ft3
Void Ratio (e) = Vv Vs
Vol (ft3) Wt. (lbs/ft3)
Va 0.23 Air Wa 0
Vw 0.22Water Ww 14
Vs 0.55 Soil Ws 92
Specific Gravity (Gs) = 2.70 (unitless)Unit Weight water (γw) = 62.4 lbs per ft3
Void Ratio (e) = Vv Vs
= 0.45 0.55
Vol (ft3) Wt. (lbs/ft3)
Va 0.23 Air Wa 0
Vw 0.22Water Ww 14
Vs 0.55 Soil Ws 92
Specific Gravity (Gs) = 2.70 (unitless)Unit Weight water (γw) = 62.4 lbs per ft3
Void Ratio (e) = Vv Vs
= 0.45 0.55
e = 0.82
Vol (ft3) Wt. (lbs/ft3)
Va Air Wa
Vw Water Ww
Vs Soil Ws
Fill Data:Wet density in situ = 106 lbs/ft3Specific gravity = 2.70Moisture Content = 15%Specific Gravity = 2.7 Proctor Results: OM = 9% MD = 117 lbs/ft3 (dry)
VvVt
Vol (ft3) Wt. (lbs/ft3)
Va Air Wa
Vw Water Ww
Vs Soil Ws
Fill Data:Wet density in situ = 106 lbs/ft3Specific gravity = 2.70Moisture Content = 15%Specific Gravity = 2.7 Proctor Results: OM = 9% MD = 117 lbs/ft3 (dry)
VvVt
Moisture Content = weight of water *100 weight of soil
Vol (ft3) Wt. (lbs/ft3)
Va Air Wa
Vw Water Ww
Vs Soil Ws
Fill Data:Wet density in situ = 106 lbs/ft3Specific gravity = 2.70Moisture Content = 15%Specific Gravity = 2.7 Proctor Results: OM = 9% MD = 117 lbs/ft3 (dry)
VvVt
Moisture Content = weight of water *100 weight of soil
9 = Ww *100 117 lbs/ft3
Vol (ft3) Wt. (lbs/ft3)
Va Air Wa
Vw Water Ww 10.5
Vs Soil Ws
Fill Data:Wet density in situ = 106 lbs/ft3Specific gravity = 2.70Moisture Content = 15%Specific Gravity = 2.7 Proctor Results: OM = 9% MD = 117 lbs/ft3 (dry)
VvVt
Moisture Content = weight of water *100 weight of soil
9 = Ww *100 117 lbs/ft3
Ww = 10.5 lbs/ft3
Vol (ft3) Wt. (lbs/ft3)
Va Air Wa
Vw Water Ww 10.5
Vs Soil Ws 117
Fill Data:Wet density in situ = 106 lbs/ft3Specific gravity = 2.70Moisture Content = 15%Specific Gravity = 2.7 Proctor Results: OM = 9% MD = 117 lbs/ft3 (dry)
VvVt
Ws = Dry Density (lbs/ft3) = MD = 117 lbs/ft3
Vol (ft3) Wt. (lbs/ft3)
Va Air Wa 0
Vw Water Ww 10.5
Vs Soil Ws 117
Fill Data:Wet density in situ = 106 lbs/ft3Specific gravity = 2.70Moisture Content = 15%Specific Gravity = 2.7 Proctor Results: OM = 9% MD = 117 lbs/ft3 (dry)
VvVt
Ws = Dry Density (lbs/ft3) = MD = 117 lbs/ft3
Fill Data:Wet density in situ = 106 lbs/ft3Specific gravity = 2.70Moisture Content = 15%Specific Gravity = 2.7 Proctor Results: OM = 9% MD = 117 lbs/ft3 (dry)
VvVt
Vol Soil (Vs) = Ws = 117 lbs/ft3 Gs * γw (2.70)*(62.4 lbs)
Vol (ft3) Wt. (lbs/ft3)
Va Air Wa 0
Vw Water Ww 10.5
Vs Soil Ws 117
Fill Data:Wet density in situ = 106 lbs/ft3Specific gravity = 2.70Moisture Content = 15%Specific Gravity = 2.7 Proctor Results: OM = 9% MD = 117 lbs/ft3 (dry)
VvVt
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 (ft3) Wt. (lbs/ft3)
Va Air Wa 0
Vw Water Ww 10.5
Vs 0.69 Soil Ws 117
Fill Data:Wet density in situ = 106 lbs/ft3Specific gravity = 2.70Moisture Content = 15%Specific Gravity = 2.7 Proctor Results: OM = 9% MD = 117 lbs/ft3 (dry)
VvVt
Vol (ft3) Wt. (lbs/ft3)
Va Air Wa 0
Vw Water Ww 10.5
Vs 0.69 Soil Ws 117
Vol Voids (Vv) = Vt - Vs
Fill Data:Wet density in situ = 106 lbs/ft3Specific gravity = 2.70Moisture Content = 15%Specific Gravity = 2.7 Proctor Results: OM = 9% MD = 117 lbs/ft3 (dry)
VvVt
Vol (ft3) Wt. (lbs/ft3)
Va Air Wa 0
Vw Water 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/ft3Specific gravity = 2.70Moisture Content = 15%Specific Gravity = 2.7 Proctor Results: OM = 9% MD = 117 lbs/ft3 (dry)
VvVt
Vol (ft3) Wt. (lbs/ft3)
Va Air Wa 0
Vw Water Ww 10.5
Vs 0.69 Soil Ws 117
Vw = Ww = 10.5 lbs/ft3 γw 62.4 lbs
Fill Data:Wet density in situ = 106 lbs/ft3Specific gravity = 2.70Moisture Content = 15%Specific Gravity = 2.7 Proctor Results: OM = 9% MD = 117 lbs/ft3 (dry)
VvVt
Vol (ft3) Wt. (lbs/ft3)
Va Air Wa 0
Vw 0.17 Water Ww 10.5
Vs 0.69 Soil Ws 117
Vw = Ww = 10.5 lbs/ft3 γw 62.4 lbs
Vw = 0.17
Fill Data:Wet density in situ = 106 lbs/ft3Specific gravity = 2.70Moisture Content = 15%Specific Gravity = 2.7 Proctor Results: OM = 9% MD = 117 lbs/ft3 (dry)
Volume of voids = 0.31
VvVt
Vol (ft3) Wt. (lbs/ft3)
Va 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
Fill Data:Wet density in situ = 106 lbs/ft3Specific gravity = 2.70Moisture Content = 15%Specific Gravity = 2.7 Proctor Results: OM = 9% MD = 117 lbs/ft3 (dry)
VvVt
Vol (ft3) Wt. (lbs/ft3)
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/ft3Specific gravity = 2.70Moisture Content = 15%Specific Gravity = 2.7 Proctor Results: OM = 9% MD = 117 lbs/ft3 (dry)
VvVt
Vol (ft3) Wt. (lbs/ft3)
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/ft3Specific gravity = 2.70Moisture Content = 15%Specific Gravity = 2.7 Proctor Results: OM = 9% MD = 117 lbs/ft3 (dry)
VvVt
Vol (ft3) Wt. (lbs/ft3)
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
Vol (ft3) Wt. (lbs/ft3)
Va 0.14 Air Wa 0
Vw 0.17 Water Ww 10.5
Vs 0.69 Soil Ws 117
Vol (ft3) Wt. (lbs/ft3)
Va 0.23 Air Wa 0
Vw 0.22Water 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 + eborrow
Volume of Fill 1 + efill
The Answer:Volume of Borrow = 1 + eborrow
Volume of Fill 1 + efill
Volume of Borrow = 1 + 0.8250,000 yd3 1 + 0.45
The Answer:Volume of Borrow = 1 + eborrow
Volume of Fill 1 + efill
Volume of Borrow = 1 + 0.8250,000 yd3 1 + 0.45
Volume of Borrow = 62,759 yd3
