Let us calculate the sectional area of the embankment as shown below.
Given data:
Breadth of embankment = b = 8m.
Depth of embankment at the given section = d = 3.5m.
Embankment slope = S = 1:2
Calculation:
The sectional area of the embankment is calculated by the formula
A = [bd + d²S]
= [ (8m. x 3.5m.) + ( 3.5² x 2)]
= [28m². + 24.5m²]
= 52.50 m²
Now, the question that comes to your mind is,
How is the formula [bd + d²S] derived?
Let us observe the drawing as shown below.
To calculate the sectional area of the embankment, we have divided it into 2 triangles ABC & DEF on either side & a rectangle BCED at the center.
As you know,
The slope 1: S means for every 1 unit rise, the value of the run will be S units.
Therefore, if the height of the triangle is d, then the length of the base of the triangle will be d x S.
If you have any doubt regarding the run, rise, gradient, or slope calculations, Go through the article 👇
👀. How to calculate gradient, run & rise in civil construction?
Now,
The sectional area
A = [ (area of rectangle) + (2nos. x area of triangles)]
= [(breadth x height) + ( 2nos. x 1/2 x base x height )]
= [( b x d) + ( 2 x 1/2 x d x S x d )]
= [ bd + d²S] ✅
Usually, the slope of 1:2 is provided for the embankments. In some cases, slopes of 1:1.5, and 1:1 are taken in earthworks.
Whatever might be the value of slope S, you will get the correct sectional area by using the formula.
Thank you for going through these calculation steps❤. Have a good day 😄.
