Thursday, 28 July 2011

Earthwork Volume using Simpson's Rule

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)=21.65

Total = 76.6

    Total earth filling volume = 373.83 x (d/3)

                                               =373.83 x (5/3) = 623 M3


  1. Best example to understand the method. this can be modified by implementing the formula to the individual heights to calculate the area of whole section at respective grids.

  2. 2 x (3.575+3.875) <> 21.65

    The 2x calculated numbers in the pink column are all wrong. The formula is correct though and the answer should be 569m3