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)

Vv

Vt

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)

Vv

Vt

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)

Vv

Vt

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)

Vv

Vt

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)

Vv

Vt

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)

Vv

Vt

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)

Vv

Vt

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)

Vv

Vt

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)

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 (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)

Vv

Vt

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)

Vv

Vt

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)

Vv

Vt

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)

Vv

Vt

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

Vv

Vt

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)

Vv

Vt

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)

Vv

Vt

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)

Vv

Vt

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