Earthwork Volume using Simpson's Rule

Step by step procedure to find out the volume of earthwork using Simpson's Rule

 

This article is about using Simpson's rule to find out the quantity of earthwork using contour maps. The procedure is explained with the help of an example. In the example given below the map is divided in to 6 horizontal and 6 vertical grids each of 5m interval. The reduced levels are given at the intersections.

 

 

 

Suppose the final level for filling is 24.1m. Then the required depth of filling at each point is as given in the table below

 

 

The area on the side of each grid can be found out as follows

 

 

Each side can be considered as a trapezoid. Hence the area of each side

 

 

 

eg: (0.98+0.97)/2 x 5 = 4.875

 

     (0.80+0.80)/2 x 5 = 4.000

 

Now the volume according to Simpson's rule is as follows

 

 

 

eg: (4.875+3.375)=8.25

 

4 x (4+3.75+3.925)=46.7

 

2 x (3.575+3.875)=14.9

 

Total = 69.85

 

    Total earth filling volume = 341.425 x (d/3)

 

                                               =341.425 x (5/3) = 569.042 M3

Note: We express thanks to http://www.e-quantities.com/volumes.htm for bringing up an error in this page to our notice which now has been rectified. You may download the excel file detailing  volume calculation using Trapizoidal Rule here.

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