Eg:
Calculate the volume of earthwork for the embankment 75m. long having 4m. width at the top. Depth of embankment at every 15m. interval is 1.45m., 1.70m., 1.95m., 2.25m., 2.55m., &2.80m. The side slope on both sides is 1:2.
To find:
We have to calculate the total volume of earthwork in the embankment by using the mean area method.
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Procedure:
Consider an embankment section having 15m. length = L1 as shown in the above drawing.
1. First, you have to calculate the sectional area A1 for the initial depth d1.
The formula for calculating A1 = [ bd1 + d1²S]
Before proceeding further, Go through the article 👇
👀. How to calculate the sectional area of an embankment?
To understand the formula derivation & clear concept of calculation.
2. Similarly, the sectional area A2 should be calculated for the given depth d2 after a 15m. interval.
The volume of earthwork for an embankment for the 1st. 15m. length
= V15 = [ Am ✖ L1]
Where the mean area
Am = [(A1 +A2) ➗ 2]
3. In a similar way, the volume of earthwork for every 15m. embankment section should be calculated.
4. The total volume of earthwork for embankment
V = [V15 + V30 +V45 + V60 + V75]
Calculation:
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1. Volume V15:
A1 = [ bd1 + d1²S]
= [ (4m. ✖ 1.45m.) + (1.45² ✖ 2)]
= [5.8m² + 4.205m²]
A1 = 10.005m².
A2 = [ bd2 + d2²S]
= [ (4m. ✖ 1.70m.) + (1.70² ✖ 2)]
= [6.8m² + 5.78m²]
A2 = 12.58m².
V15 = [{(A1 +A2) ➗ 2} ✖ L1]
= [{(10.005 + 12.58) ➗ 2} ✖ 15]
V15 = 169.39m³.
2. Volume V30:
A3 = [ bd3 + d3²S]
= [ (4m. ✖ 1.95m.) + (1.95² ✖ 2)]
= [7.8m² + 7.605m²]
A3 = 15.405m².
V30 = [{(A2 +A3) ➗ 2} ✖ L2]
= [{(12.58 + 15.405) ➗ 2} ✖ 15]
V30 = 209.88m³.
NOTE: Area A2 becomes the surface sectional area for the next 15m. length of the embankment.
3. Volume V45:
A4 = [ bd4 + d4²S]
= [ (4m. ✖ 2.25m.) + (2.25² ✖ 2)]
= [9.0m² + 10.125m²]
A4 = 19.125m².
V45 = [{(A3 +A4) ➗ 2} ✖ L3]
= [{(15.405 + 19.125) ➗ 2} ✖ 15]
V45 = 258.975m³.
4. Volume V60:
A5 = [ bd5 + d5²S]
= [ (4m. ✖ 2.55m.) + (2.55² ✖ 2)]
= [10.20m² + 13.005m²]
A5 = 23.205m².
V60 = [{(A4 +A5) ➗ 2} ✖ L4]
= [{(19.125 + 23.205) ➗ 2} ✖ 15]
V60 = 317.475m³.
5. Volume V75:
A6 = [ bd6 + d6²S]
= [ (4m. ✖ 2.80m.) + (2.80² ✖ 2)]
= [11.20m² + 15.68m²]
A6 = 26.88m².
V75 = [{(A5 +A6) ➗ 2} ✖ L4]
= [{(23.205 + 26.88) ➗ 2} ✖ 15]
V75 = 375.637m³.
The total volume of earthwork for embankment
V = [V15 + V30 +V45 + V60 + V75]
= [169.39m³ + 209.88m³ + 258.975m³ + 317.475m³ + 375.637m³]
= 1331.357m³
Note:
The calculation is done in an elaborate way to understand the concept clearly. Once known, the calculation should be done in a table format as shown below.
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Thank you for going through these calculation steps❤. Have a good day 😄.
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