Volume Calculation – Contour Method
Volume can be measured by a contour map, but the volume calculated by this method is approximate. It cannot be compared with the volume calculated by the cross-section method. As the full ground irregularities are not predicted by contours, and also as the contour intervals are not small, volume calculated from contours is likely to be an approximate one. To calculate volume by this method, general recommendations of contour interval is a maximum of 2 meters for a regular ground surface, and 0.5 meter for an irregular topography. This method is used mainly to find the capacity of a reservoir. To find out the capacity of a contour, two methods can be adopted.
- Average area method (Known as trapezoidal method)
- Prismoidal formula
By average end-area (trapezoidal) method
Volume = L x 1/2 (A1 + A2) cubic meter
By Prismoidal formula
V= L (A + Square Root (A*B) + B) / 3
For the following Example,
Volume Calculation Using Average Method
Contour |
Area |
Previous Area |
Average Area |
Contour Interval |
Area between Contours |
Cumulative Volume (Cubic Meters) |
|
2 |
0.52 |
0 |
2 |
2 |
0 |
0 |
|
4 |
3.068 |
0.52 |
1.794 |
2 |
3.588 |
3.588 |
|
6 |
7.74 |
3.068 |
5.404 |
2 |
10.808 |
14.396 |
|
8 |
14.534 |
7.74 |
11.137 |
2 |
22.274 |
36.67 |
|
10 |
23.824 |
14.534 |
19.179 |
2 |
38.358 |
75.028 |
|
12 |
37.008 |
23.824 |
30.416 |
2 |
60.832 |
135.86 |
|
14 |
55.65 |
37.008 |
46.329 |
2 |
92.658 |
228.518 |
|
16 |
78.886 |
55.65 |
67.268 |
2 |
134.536 |
363.054 |
|
18 |
114.916 |
78.886 |
96.901 |
2 |
193.802 |
556.856 |
|
20 |
262.949 |
114.916 |
188.9325 |
2 |
377.865 |
934.721 |
Volume Calculation Using Prismoidal Method
Contour |
Area |
Previous Area |
Area(A + Square Root (A*B) + B) / 3 |
Contour Interval |
Area between Contours |
Cumulative Volume (Cubic Meters) |
|
2 |
0.52 |
0.00 |
0.00 |
2.00 |
0.00 |
0.00 |
|
4 |
3.07 |
0.52 |
1.62 |
2.00 |
3.23 |
3.23 |
|
6 |
7.74 |
3.07 |
5.23 |
2.00 |
10.45 |
13.69 |
|
8 |
14.53 |
7.74 |
10.96 |
2.00 |
21.92 |
35.61 |
|
10 |
23.82 |
14.53 |
18.99 |
2.00 |
37.98 |
73.59 |
|
12 |
37.01 |
23.82 |
30.18 |
2.00 |
60.35 |
133.94 |
|
14 |
55.65 |
37.01 |
46.01 |
2.00 |
92.03 |
225.96 |
|
16 |
78.89 |
55.65 |
66.93 |
2.00 |
133.86 |
359.82 |
|
18 |
114.92 |
78.89 |
96.34 |
2.00 |
192.68 |
552.50 |
|
20 |
262.95 |
114.92 |
183.90 |
2.00 |
367.80 |
920.30 |
Division of Square method Earthwork Area & Volume Calculation Summary