Cut and Fill Calculations Calculation of the cut-and-fill volumes is an essential component to any site development project Topographic data is required to estimate ...

CIVL 1112

Cut-and-Fill - Part 1

Cut and Fill Calculations Calculation of the cut-and-fill volumes is an essential component to any site development project

Cut and Fill Calculations Topographic data is required to estimate cutand-fill volumes

Cut and Fill Calculations Topographic data is required to estimate cutand-fill volumes

Cut and Fill Calculations Topographic data is required to estimate cutand-fill volumes

Cut and Fill Calculations Topographic data is required to estimate cutand-fill volumes

Cut and Fill Calculations Topographic data is required to estimate cutand-fill volumes

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CIVL 1112

Cut-and-Fill - Part 1

Cut and Fill Calculations

Cut and Fill Calculations

From the topographic data of the site, different alternative site plans can be evaluated The basic calculation is the difference between the desired elevation and the original elevations Original Elevations

2/5

Traditionally, elevations for a topographic survey are collected using some type of regular grid system Using the elevation data and the grid system, a threedimensional model of the cut-and-fill volumes can be constructed 105 ft.

102 ft.

Proposed Elevations 102 ft.

50 ft.

105 ft.

50 ft.

100 ft. 98 ft.

100 ft.

Fill Areas

Cut Areas

98 ft.

3-D view of grid cell

Cut and Fill Calculations

Cut and Fill Calculations

The volume of material in this grid cell may be estimated as the volume of the quadrilateral cell

Consider a cell in the grid system with the following elevations

Volume equals the average of the cell height times the area of the cell

Development at this site requires that this area be at an elevation of 101 feet

Cell Area (50 ft.)(50 ft.) 2,500 ft.2

105 ft.

102 ft.

Cut Areas

98 100 102 105 2 Volume ft. (2,500 ft. ) 4

100 ft.

Volume 253,125 ft.

3

100 ft. 98 ft.

9,375 yd.

3

98 ft.

Fill Areas 3-D view of grid cell

Cut and Fill Calculations To estimate the cut-and-fill required in this cell, first compute the change in volume V = original elevations - proposed elevations 105 ft.

102 ft.

101 ft.

3-D view of grid cell

Cut and Fill Calculations The volume of cut-and-fill in this grid cell may be estimated as the volume of the quadrilateral cell Volume equals the average of the cell height times the area of the cell Cell Area (50 ft.)(50 ft.) 2,500 ft.2 3 1 1 4 2 Volume ft. (2,500 ft. ) 4

100 ft. 98 ft.

105 ft.

102 ft. 101 ft.

minus

Volume 625 ft.3 23.15 yd.3

Original elevations

Proposed elevations

The total cut-and-fill can be estimated by summing the cutand-fill from each cell for the entire grid system

CIVL 1112

Cut-and-Fill - Part 1

Cut and Fill Calculations

Cut and Fill Calculations

Compute the total cut-and-fill for the following site The original elevations are:

1 2 3 4 5

1 105 104 103 103 101

2 104 104 103 102 100

3 104 103 102 101 99

4 103 102 101 100 98

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5 102 101 100 99 97

Below is an Excel plot of the original elevations and the proposed elevations 105

105 104

104 103

103

102

102

101

101 1

100

The size of each cell is 25 ft. by 25 ft.

99

Cut and Fill Calculations

2 3.00 3.00 2.00 1.00 -1.00

3 3.00 2.00 1.00 0.00 -2.00

4 2.00 1.00 0.00 -1.00 -3.00

5 1.00 0.00 -1.00 -2.00 -4.00

Positive values indicate cut and negative values indicate fill.

Cut and Fill Calculations

1 4.00 3.00 2.00 2.00 0.00

2 3.00 3.00 2.00 1.00 -1.00

3 3.00 2.00 1.00 0.00 -2.00

4 2.00 1.00 0.00 -1.00 -3.00

5 1.00 0.00 -1.00 -2.00 -4.00

For the cell above, the volume of cut-and-fill is:

3 3 3 2 ft. (625 ft.2 ) Volume 4

5 1

2

5

3

4

5

Compute the volume of cut-and-fill for each grid cell Average the elevations for each grid cell times the cell area

1 2 3 4 5

1 4.00 3.00 2.00 2.00 0.00

2 3.00 3.00 2.00 1.00 -1.00

3 3.00 2.00 1.00 0.00 -2.00

4 2.00 1.00 0.00 -1.00 -3.00

5 1.00 0.00 -1.00 -2.00 -4.00

For the cell above, the volume of cut-and-fill is: Volume

4 3 3 3 ft. (625 ft.2 ) 4

3 2,031.3 ft.3 75.23 yd.

Cut and Fill Calculations

For the cell to the right, compute the volume of cut-and-fill

1 2 3 4 5

4

Cut and Fill Calculations

To compute the cut-and-fill compute the change in elevations (original elevations minus proposed elevations gives). 1 4.00 3.00 2.00 2.00 0.00

3

4

97

5 2

3

98

4

97 1

1 2 3 4 5

2

99

3

98

The proposed site is at an elevation of 101 ft.

1

100

2

3 1,718.8 ft.3 63.66 yd.

For the cell to the right, compute the volume of cut-and-fill

1 2 3 4 5

1 4.00 3.00 2.00 2.00 0.00

2 3.00 3.00 2.00 1.00 -1.00

3 3.00 2.00 1.00 0.00 -2.00

4 2.00 1.00 0.00 -1.00 -3.00

5 1.00 0.00 -1.00 -2.00 -4.00

For the cell above, the volume of cut-and-fill is: Volume

3 2 2 1 ft. (625 ft.2 ) 4

3 1,250 ft.3 46.30 yd.

CIVL 1112

Cut-and-Fill - Part 1

Cut and Fill Calculations The resulting cut-and-fill volumes (yd.3) for each cell in the entire grid system is:

4/5

Cut and Fill Calculations The total cut-and-fill for this site may be estimated by summing the cut-and-fill volumes for each cell

1

1 75.23

2 63.66

3 46.30

4 23.15

1

1 75.23

2 63.66

3 46.30

4 23.15

2 3 4

57.87 40.51 11.57

46.30 23.15 -11.57

23.15 0.00 -34.72

0.00 -23.15 -57.87

2 3 4

57.87 40.51 11.57

46.30 23.15 -11.57

23.15 0.00 -34.72

0.00 -23.15 -57.87

A sited model with a 5 x 5 grid system contains 4 x 4 cells

Cut and Fill Calculations The total cut this site may be estimated by summing the positive (+) cut-and-fill volumes for each cell

For this example the total is: 284 yd.3

Cut and Fill Calculations The total fill this site may be estimated by summing the negative (-) cut-and-fill volumes for each cell

1

1 75.23

2 63.66

3 46.30

4 23.15

1

1 75.23

2 63.66

3 46.30

4 23.15

2 3 4

57.87 40.51 11.57

46.30 23.15 -11.57

23.15 0.00 -34.72

0.00 -23.15 -57.87

2 3 4

57.87 40.51 11.57

46.30 23.15 -11.57

23.15 0.00 -34.72

0.00 -23.15 -57.87

For this example the total is: 411 yd.3

For this example the total is: -127 yd.3

Use Excel function: =sumif(A1:D4,”>0”)

Use Excel function: =sumif(A1:D4,”<0”)

Cut and Fill Calculations

Cut and Fill Calculations

An estimate of the cost of cut-and-fill for the entire site can be made by considering:

An estimate of the cost of cut-and-fill for the entire site can be made by considering:

On-site cost ($2.50/yd.3) for total cut-and-fill volume:

Off-site cost: $5/yd.3 for fill and $3/yd.3 for cut)

$2.50 $2.50 Onsite cut fill 411 ( 127) yd.3 3 3 yd. yd.

cos t cos t Off site cut fill 411 127 yd.3 3 3 yd. yd.

On site $1,345

$3 Off site 284 yd.3 $852 3 yd.

Note: since fill volume is always (-) negative, therefore to compute the total earthwork volume use (cut – fill)

TotalCost $1,345 $852

$2,197

CIVL 1112

Cut-and-Fill - Part 1

End of Cut-and-Fill 1

Any Questions?

5/5

Cut-and-Fill - Part 1

Cut and Fill Calculations Calculation of the cut-and-fill volumes is an essential component to any site development project

Cut and Fill Calculations Topographic data is required to estimate cutand-fill volumes

Cut and Fill Calculations Topographic data is required to estimate cutand-fill volumes

Cut and Fill Calculations Topographic data is required to estimate cutand-fill volumes

Cut and Fill Calculations Topographic data is required to estimate cutand-fill volumes

Cut and Fill Calculations Topographic data is required to estimate cutand-fill volumes

1/5

CIVL 1112

Cut-and-Fill - Part 1

Cut and Fill Calculations

Cut and Fill Calculations

From the topographic data of the site, different alternative site plans can be evaluated The basic calculation is the difference between the desired elevation and the original elevations Original Elevations

2/5

Traditionally, elevations for a topographic survey are collected using some type of regular grid system Using the elevation data and the grid system, a threedimensional model of the cut-and-fill volumes can be constructed 105 ft.

102 ft.

Proposed Elevations 102 ft.

50 ft.

105 ft.

50 ft.

100 ft. 98 ft.

100 ft.

Fill Areas

Cut Areas

98 ft.

3-D view of grid cell

Cut and Fill Calculations

Cut and Fill Calculations

The volume of material in this grid cell may be estimated as the volume of the quadrilateral cell

Consider a cell in the grid system with the following elevations

Volume equals the average of the cell height times the area of the cell

Development at this site requires that this area be at an elevation of 101 feet

Cell Area (50 ft.)(50 ft.) 2,500 ft.2

105 ft.

102 ft.

Cut Areas

98 100 102 105 2 Volume ft. (2,500 ft. ) 4

100 ft.

Volume 253,125 ft.

3

100 ft. 98 ft.

9,375 yd.

3

98 ft.

Fill Areas 3-D view of grid cell

Cut and Fill Calculations To estimate the cut-and-fill required in this cell, first compute the change in volume V = original elevations - proposed elevations 105 ft.

102 ft.

101 ft.

3-D view of grid cell

Cut and Fill Calculations The volume of cut-and-fill in this grid cell may be estimated as the volume of the quadrilateral cell Volume equals the average of the cell height times the area of the cell Cell Area (50 ft.)(50 ft.) 2,500 ft.2 3 1 1 4 2 Volume ft. (2,500 ft. ) 4

100 ft. 98 ft.

105 ft.

102 ft. 101 ft.

minus

Volume 625 ft.3 23.15 yd.3

Original elevations

Proposed elevations

The total cut-and-fill can be estimated by summing the cutand-fill from each cell for the entire grid system

CIVL 1112

Cut-and-Fill - Part 1

Cut and Fill Calculations

Cut and Fill Calculations

Compute the total cut-and-fill for the following site The original elevations are:

1 2 3 4 5

1 105 104 103 103 101

2 104 104 103 102 100

3 104 103 102 101 99

4 103 102 101 100 98

3/5

5 102 101 100 99 97

Below is an Excel plot of the original elevations and the proposed elevations 105

105 104

104 103

103

102

102

101

101 1

100

The size of each cell is 25 ft. by 25 ft.

99

Cut and Fill Calculations

2 3.00 3.00 2.00 1.00 -1.00

3 3.00 2.00 1.00 0.00 -2.00

4 2.00 1.00 0.00 -1.00 -3.00

5 1.00 0.00 -1.00 -2.00 -4.00

Positive values indicate cut and negative values indicate fill.

Cut and Fill Calculations

1 4.00 3.00 2.00 2.00 0.00

2 3.00 3.00 2.00 1.00 -1.00

3 3.00 2.00 1.00 0.00 -2.00

4 2.00 1.00 0.00 -1.00 -3.00

5 1.00 0.00 -1.00 -2.00 -4.00

For the cell above, the volume of cut-and-fill is:

3 3 3 2 ft. (625 ft.2 ) Volume 4

5 1

2

5

3

4

5

Compute the volume of cut-and-fill for each grid cell Average the elevations for each grid cell times the cell area

1 2 3 4 5

1 4.00 3.00 2.00 2.00 0.00

2 3.00 3.00 2.00 1.00 -1.00

3 3.00 2.00 1.00 0.00 -2.00

4 2.00 1.00 0.00 -1.00 -3.00

5 1.00 0.00 -1.00 -2.00 -4.00

For the cell above, the volume of cut-and-fill is: Volume

4 3 3 3 ft. (625 ft.2 ) 4

3 2,031.3 ft.3 75.23 yd.

Cut and Fill Calculations

For the cell to the right, compute the volume of cut-and-fill

1 2 3 4 5

4

Cut and Fill Calculations

To compute the cut-and-fill compute the change in elevations (original elevations minus proposed elevations gives). 1 4.00 3.00 2.00 2.00 0.00

3

4

97

5 2

3

98

4

97 1

1 2 3 4 5

2

99

3

98

The proposed site is at an elevation of 101 ft.

1

100

2

3 1,718.8 ft.3 63.66 yd.

For the cell to the right, compute the volume of cut-and-fill

1 2 3 4 5

1 4.00 3.00 2.00 2.00 0.00

2 3.00 3.00 2.00 1.00 -1.00

3 3.00 2.00 1.00 0.00 -2.00

4 2.00 1.00 0.00 -1.00 -3.00

5 1.00 0.00 -1.00 -2.00 -4.00

For the cell above, the volume of cut-and-fill is: Volume

3 2 2 1 ft. (625 ft.2 ) 4

3 1,250 ft.3 46.30 yd.

CIVL 1112

Cut-and-Fill - Part 1

Cut and Fill Calculations The resulting cut-and-fill volumes (yd.3) for each cell in the entire grid system is:

4/5

Cut and Fill Calculations The total cut-and-fill for this site may be estimated by summing the cut-and-fill volumes for each cell

1

1 75.23

2 63.66

3 46.30

4 23.15

1

1 75.23

2 63.66

3 46.30

4 23.15

2 3 4

57.87 40.51 11.57

46.30 23.15 -11.57

23.15 0.00 -34.72

0.00 -23.15 -57.87

2 3 4

57.87 40.51 11.57

46.30 23.15 -11.57

23.15 0.00 -34.72

0.00 -23.15 -57.87

A sited model with a 5 x 5 grid system contains 4 x 4 cells

Cut and Fill Calculations The total cut this site may be estimated by summing the positive (+) cut-and-fill volumes for each cell

For this example the total is: 284 yd.3

Cut and Fill Calculations The total fill this site may be estimated by summing the negative (-) cut-and-fill volumes for each cell

1

1 75.23

2 63.66

3 46.30

4 23.15

1

1 75.23

2 63.66

3 46.30

4 23.15

2 3 4

57.87 40.51 11.57

46.30 23.15 -11.57

23.15 0.00 -34.72

0.00 -23.15 -57.87

2 3 4

57.87 40.51 11.57

46.30 23.15 -11.57

23.15 0.00 -34.72

0.00 -23.15 -57.87

For this example the total is: 411 yd.3

For this example the total is: -127 yd.3

Use Excel function: =sumif(A1:D4,”>0”)

Use Excel function: =sumif(A1:D4,”<0”)

Cut and Fill Calculations

Cut and Fill Calculations

An estimate of the cost of cut-and-fill for the entire site can be made by considering:

An estimate of the cost of cut-and-fill for the entire site can be made by considering:

On-site cost ($2.50/yd.3) for total cut-and-fill volume:

Off-site cost: $5/yd.3 for fill and $3/yd.3 for cut)

$2.50 $2.50 Onsite cut fill 411 ( 127) yd.3 3 3 yd. yd.

cos t cos t Off site cut fill 411 127 yd.3 3 3 yd. yd.

On site $1,345

$3 Off site 284 yd.3 $852 3 yd.

Note: since fill volume is always (-) negative, therefore to compute the total earthwork volume use (cut – fill)

TotalCost $1,345 $852

$2,197

CIVL 1112

Cut-and-Fill - Part 1

End of Cut-and-Fill 1

Any Questions?

5/5