Volume Calculation for Areas found using Section Method
Once the section wise area calculation is done using section method, either of the 3 Volume calculation methods can be used for Volume Calculation
- Average End Area Method
- Prismoidal Rule
- Simpsons 1/3rd Rule
Average End Area Volume Calculation (Trapezoidal Method)
The formula for calculation of volume by average end area:
Volume = L x 1/2 (A1 + A2) cubic meter
L – Distance in meters
A1 and A2 – area in Square meters
The average end area calculation is used to calculate volume between two cross sections i.e., two cross sectional areas are averaged and multiplied by the length (distance) between two cross sections to get the volume.
If there are a series of areas A1, A2, A3,….An at regular interval L,
V=L/2[(A1+An)+2A2+A3+…..+An-1)]
Prismoidal Formula
Prismoidal formula is accurate in finding the volume of prisms, pyramids, wedges, and prismoids having irregular end sections. The estimation of earthwork gives nearly an accurate volume.
The formula given is
V=d/3[Sum of areas of end two sections+ 4(sum of the even sections) +2(sum of the remaining sections)]
Example 7:
In this example, we have found out the area of cutting and filling for all the 6 Sections using Trapezoidal Method at formation level 20.
The area calculation details are as below:
| Sl. No. | Section No. | Cutting Area | Filling Area |
|
1 |
729 |
1.85 |
2.45 |
|
2 |
732 |
17.10 |
|
|
3 |
735 |
78.90 |
|
|
4 |
738 |
20.85 |
|
|
5 |
741 |
72.00 |
|
|
6 |
744 |
14.70 |
|
|
Total |
1.85 |
206.00 |
Section – SummaryVolume Calculation – Average Earthwork Method