With advancement of Technology there is a lot of progress in the way we take Ground reading. Earlier only Auto Levels were used, whereas now Total Station, GPS, LIDAR are being used to take ground reading. Previously Earthwork Calculations were simply done on paper followed by some simple computer applications. Now, however, either Spread Sheets likes Excel are used or advanced software products which are specifically designed for earthwork calculation are used. But volumetric calculations done by software still have to presented in understandable manner even while getting different results from different software products.

There are three different methods popularly used for doing Earthwork Calculation for Cutting/Filling Projects. Before discussing these in detail let us try to understand Some Basic definition of Terms related to Earthwork Calculation.

Earthworks

Earthworks are engineering works created through the moving and/or processing of massive quantities of soil or unformed rock. Earthwork is done to reconfigure the topography of a site to achieve the design levels. Earthwork involves cutting and filling to achieve the required topography.

Cutting

Cutting is the process of excavating earth material from a work location to achieve the desired topography.

Filling

Filling is the process of moving the excavated material or additional earth material to a work location to achieve the desired topography.

Let us take 2 Simple Examples for our Study

In the Example below the plot is 30 X 30 Meters and all the Grid levels measured at Grid level of 10M
Example 1 (Only Cutting)
Ground Level
Section 0 10 20 30
30 192.51 193.71 193.21 193.47
20 193.04 193.14 192.92 193.01
10 192.61 192.56 192.63 192.67
0 192.56 192.68 192.67 192.57
Formation Level
191.9 193.1 192.6 192.87
192.43 192.53 192.31 192.4
192.01 191.96 192.03 192.06
191.95 192.07 192.07 191.97
Example 2 (Both Cutting and Filling)
Ground Level
       
192.51 193.71 193.21 193.47
193.04 193.14 192.92 193.01
192.61 192.56 192.63 192.67
192.56 192.68 192.67 192.57
Formation Level
193.4 193.5 193.3 193.2
193.5 193.3 193.2 193.4
193.4 193.6 193.4 193.4
193.1 193.4 193.5 193.3

Average method:

In this method Levels at each grid point is found out. Difference between the Average of Two Sets of Levels multiplied by Area gives the Result. This is a very simple and straight forward method. But this can be used only when there is cutting or filling. When Leveling of surface includes both cutting and filling, Average method gives wrong result as cutting and filling values nullify each other while averaging.

Example 1(Only Cutting)
Filling
0 0 0 0  
0 0 0 0  
0 0 0 0  
0 0 0 0  
    Average 0 0
Cutting
0.61 0.61 0.61 0.6  
0.61 0.61 0.61 0.61  
0.6 0.6 0.6 0.61  
0.61 0.61 0.6 0.6  
    Average 0.606 545.62
Example 2 (Both Cutting and Filling)
Filling
0 0.21 0 0.27  
0 0 0 0  
0 0 0 0  
0 0 0 0  
    Average 0.03 27
Cutting
0.89 0 0.09 0  
0.46 0.16 0.28 0.39  
0.79 1.04 0.77 0.73  
0.54 0.72 0.83 0.73  
    Average 0.526 473.625

Volume = Average * 900 = 0.606 * 900 = 545.62

Block Method (Division of Square Method):

In this method, volume of cutting or filling is found out for each block and added together to get the final volume. This is mathematically simpler then Section Method, but more accurate than Average method. The problem of nullification is also encountered here when in the same block there is both cutting and filling. But here the margin of error is very small when compared to Average method for whole area.

Example 1(Only Cutting):

Difference in Average for Each 10 X 10 Block
       
  0.61 0.61 0.6075
  0.605 0.605 0.6075
  0.605 0.6025 0.6025

Volume = Sum * 100 (Area of Each block) = 5.455 * 100 = 545.5 (Cutting)

Note: Value 0.61 = Average (192.51, 193.71, 193.04, 193.14) – Average (191.9, 193.1, 192.43, 192.53) [Values taken from first 2 rows and 2 columns of ground and formation level)

Example 2 (Both Cutting and Filling) :

Difference in Average for Each 10 X 10 Block
       
  0.325 0.08 0.1225
  0.6125 0.5625 0.5425
  0.7725 0.84 0.765

Volume = Sum * 100 (Area of Each block) = 4.6225 * 100 = 462.25 (Filling).

Note: Although in this example there is some cutting, because of nullification of value in same block we are not getting any value in Cutting.

Section Method:

In this method Sections are drawn for Each Line of Value. Area of Cutting and Filling is found out for each Section with Trapezoidal Method or Nett Area Calculation Method. Then volume is determined by multiplying Average Area with Distance between Sections. This method is more accurate, but for larger area, finding the area becomes difficult as we need to find intersection of points where lines representing Surfaces meet.

Example 1(Only Cutting):

Sl.
No.
Section Cutting Volume Filling Volume
Area
Sq. Mtrs
Previous
Area
Average
Sq. Mtrs
Volume
Cu Meters
Area
Sq. Mtrs
Previous
Area
Average
Sq. Mtrs
Volume
Cu Meters
1 0.000 18.150 0.000 9.075 0.000 0.000 0.000 0.000 0.000
2 10.000 18.050 18.150 18.100 181.000 0.000 0.000 0.000 0.000
3 20.000 18.300 18.050 18.175 181.750 0.000 0.000 0.000 0.000
4 30.000 18.250 18.300 18.275 182.750 0.000 0.000 0.000 0.000
    Total     545.500       0.000

Sections Related to Example 2 (Both Cutting and Filling) :

Earthwork

Example 2 (Both Cutting and Filling) :

Sl.
No.
Section Cutting Volume Filling Volume
Area
Sq. Mtrs
Previous
Area
Average
Sq. Mtrs
Volume
Cu Meters
Area
Sq. Mtrs
Previous
Area
Average
Sq. Mtrs
Volume
Cu Meters
1 0.000 0.000 0.000 0.000 0.000 21.850 0.000 10.925 0.000
2 10.000 0.000 0.000 0.000 0.000 25.700 21.850 23.775 237.750
3 20.000 0.000 0.000 0.000 0.000 8.650 25.700 17.175 171.750
4 30.000 1.948 0.000 0.974 9.740 3.848 8.650 6.249 62.490
    Total     9.740       471.990

Summary of Results
Sl. Method Example 1 Example 2
    Cutting Filling Cutting Filling
1 Average Method 545.62 0 27.000 473.625
2 Block method 545.5 0 0.000 462.25
3 Section Method 545.500 0 9.740 471.990

Summary of Various Methods
Methods Methods / Formula Advantages Disadvantages Applicability
Average Method Volume=Depth of cutting/filling* area Easiest Method for calculation
  • Approximate,
  • cannot be applied when both cutting and filling are there
Used for very small projects
Block Method Volume=Sum of (Depth of cutting/filling* area of each block) It Is very easy to calculate the area Box method will nullify volume when both cutting and filling are there in the same block Commonly used to find volume for leveling projects before the construction of a building
Section Method Area to be found out using
  • Trapezoidal Method
  • Nett area Method
Volume = Lx1/2(A1+ A2)
Mathematically, very good and hence adopted in majority of infrastructure projects Involves a lot of calculations Used in most of the infrastructure Projects including
Roads, Irrigation Projects, Rail Road Projects, etc.

Conclusion

From the above examples, we can conclude that Section Method is complex compared to any other method but gives accurate results. Also if the Average method or Block Method is used for calculation then it is likely that Volume will be little lesser and the contractor will get lesser quantity and hence less payment for his work.
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