Estimating Cut and Fill Volumes

This article explains how to estimate cut and fill volumes for earthworks projects using the grid method. It provides step-by-step instructions on how to calculate cut and fill depth, volume, and area. The article also includes a table summarizing the cut and fill volumes for each grid.

Running head: ESTIMATING CUT AND FILL VOLUMES
ESTIMATING CUT AND FILL VOLUMES
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ESTIMATING CUT AND FILL VOLUMES 2
Estimating Cut and Fill Volumes
It is assumed that an average of 250 mm of topsoil will be removed before any
construction can start. This means that there will be a cut depth of 250 mm for each grid
irrespective of whether the grid has cut or fill. The cut and fill volumes are calculated using grid
method. The first step is to find cross-sectional area of the grid and multiply it by the depth of cut
or fill to find the volume of soil to be cut or filled. The cut or fill depth is obtained by subtracting
average proposed elevation from the average existing elevation. The grid is cut when the
resultant depth is positive and fill when the resultant depth is negative (Woods, 2017). The grid’s
averaged depth is obtained by adding the four depths of the grid and dividing the answer by four
(Duffy, 2018). Total cut volume is obtained by adding the cut volume for each grid, and the fill
volume is determined by adding fill volume for each grid.
The proposed elevation of each corner was taken as the nearest topographical elevation to that
particular corner of the grid
EE = existing elevation
PE = proposed elevation
F = fill
C = cut
Area of one grid = 40 m x 40 m = 1,600 m2. It is assumed that all the grids are squares measuring
40 m by 40 m.
Grid Ordinates Area Average Ht. Volume
Cut Fill

ESTIMATING CUT AND FILL VOLUMES 3
Grid 1
Corner 1:
EE = 91.673; PE = 91.77
EE – PE = 91.673 – 91.77 = -0.097 m (F)
Corner 2:
EE = 91.633; PE = 91.81
EE – PE = 91.633 – 91.81 = -0.177 m (F)
Corner 3:
EE = 91.687; PE = 91.83
EE – PE = 91.687 – 91.83 = -0.143 m (F)
Corner 4:
EE = 91.721; PE = 91.87
EE – PE = 91.721 – 91.87 = -0.149 m (F)
Avg . Fill= 0.097+ ( 0.177 ) + ( 0.143 ) + ( 0.149 )
4
= 0.1415 m
Avg. Cut = 0.25m
F: 1,600 m2
C: 1,600 m2
F: 0.1415 m
C: 0.25 m 400 m3
226.4 m3
Grid 2
Corner 1:
EE = 91.633; PE = 91.81
EE – PE = 91.633 – 91.81 = -0.177 m (F)
Corner 2:
EE = 91.662; PE = 91.85
EE – PE = 91.662 – 91.85 = -0.188 m (F)
Corner 3:
EE = 91.721; PE = 91.87
EE – PE = 91.721 – 91.87 = -0.149 m (F)
Corner 4:
EE = 91.790; PE = 91.91
EE – PE = 91.790 – 91.91 = -0.12 m (F)
Avg . Fill= 0.177+ ( 0.188 ) + ( 0.149 ) + ( 0.12 )
4
= 0.1585 m
F: 1,600 m2
C: 1,600 m2 F: 0.1585 m
C: 0.25 m 400 m3
253.6 m3

ESTIMATING CUT AND FILL VOLUMES 4
Avg. Cut = 0.25m
Grid 3
Corner 1:
EE = 91.662; PE = 91.85
EE – PE = 91.662 – 91.85 = -0.188 m (F)
Corner 2:
EE = 91.828; PE = 91.89
EE – PE = 91.828 – 91.89 = -0.062 m (F)
Corner 3:
EE = 91.79; PE = 91.91
EE – PE = 91.79 – 91.91 = -0.12 m (F)
Corner 4:
EE = 91.787; PE = 91.95
EE – PE = 91.787 – 91.95 = -0.163 m (F)
Avg . Fill= 0.188+ ( 0.062 ) + ( 0.12 ) + ( 0.163 )
4
= 0.13325 m
Avg. Cut = 0.25m
F: 1,600 m2
C: 1,600 m2 F: 0.13325 m
C: 0.25 m 400 m3
213.2 m3
Grid 4
Corner 1:
EE = 91.673; PE = 91.70
EE – PE = 91.673 – 91.70 = -0.027 m (F)
Corner 2:
EE = 91.621; PE = 91.75
EE – PE = 91.621 – 91.75 = -0.129 m (F)
Corner 3:
EE = 91.597; PE = 91.77
EE – PE = 91.597 – 91.77 = -0.173 m (F)
Corner 4:
EE = 91.633; PE = 91.81
EE – PE = 91.633 – 91.81 = -0.177 m (F)
Avg . Fill= 0.027+ ( 0.129 ) + ( 0.173 ) + ( 0.177 )
4
= 0.1265 m
F: 1,600 m2
C: 1,600 m2 F: 0.1265 m
C: 0.25 m 400 m3
202.4 m3

ESTIMATING CUT AND FILL VOLUMES 5
Avg. Cut = 0.25 m
The total cut and fill volume are provided in the table below
Grid Area Average height Volume
Cut Fill Cut Fill Cut Fill
Grid 1 1,600 m2 1,600 m2 0.25 m 0.1415 m 400 m3 226.4 m3
Grid 2 1,600 m2 1,600 m2 0.25 m 0.1585 m 400 m3 253.6 m3
Grid 3 1,600 m2 1,600 m2 0.25 m 0.13325 m 400 m3 213.2 m3
Grid 4 1,600 m2 1,600 m2 0.25 m 0.1265 m 400 m3 202.4 m3
Total 1,600 m3 895.6 m3
The calculations above show that there will be fill in each grid because existing level is
lower than the proposed level in every grid. Nevertheless, there is a condition or assumption that
an average of 0.25 m of topsoil must be removed before any construction. This means that there
will be a cut depth of 0.25 m in each grid.
Works Cited
Duffy, D. (2018, July 23). Estimating Earthwork Volumes. Retrieved from Forester Network:
https://foresternetwork.com/weekly/grading-excavation-contractor-weekly/construction-
software/measuring-earthwork-volume/
Woods, L. (2017, September 6). How to Calculate Cut and Fill for Earthworks Projects. Retrieved from
Kubla: https://www.kublasoftware.com/how-to-calculate-cut-and-fill/