Slope volume calculation

Hello everyone,

I have a quick question about volume calculation. I'm a bit stuck right now.

A slope is to be set back by 2.50 m on the top and bottom edge over a length of 35 m. The slope inclination should remain the same as it is now. The slope is 1:1.5. The length from bottom edge to top edge is about 5.50 m.
If this area is excavated as described, how many cubic meters or tons of earth will then be removed?

Do you need any further information for the calculation?
I am grateful for any help.

Thanks!
Best regards

The cross-section of the slope is a right-angled triangle. The hypotenuse (the part of the slope visible from the outside) is 5.5 m long. We also know that the lengths of the legs have the ratio 1:1.5 (this is how I interpret your statement). 1.) a² + b² = c² with c = 5.5 m 2.) a : b = 1 : 1.5 Two equations, two unknowns. The result is a = 3.48 m, b = 4.26 m, if I am not mistaken.

The slope volume follows from the triangle area and the length of 35 m to 259.4 m³.

Set back by 2.5 m means additionally moving the earth behind the slope, thus 35 m * 2.5 m * 3.48 m = 304.5 m³ (assuming the height of the slope is 3.48 m, depending on the definition of your ratio).

Without guarantee.

Since the slope should be present again at the end, I would use a parallelogram for the calculation.

If the slope has a ratio of 1:1.5 (a to b), 3.48 and 4.26 are incorrect, as that would be a ratio of 1:1.22.

I arrive at a slope height of ~3m.
The whole thing should be offset 2.5m to the back.

This results in a cross-section of 7.5m².

Over a length of 35m, it would then be a volume of 262.5m³.

You are of course right! I apparently forgot the square in the calculation with 1.5. The height of 3.05 m is correct with a ratio of 1:1.5. The depth of the slope is then 4.58 m.

The 7.5 m² are apparently the product of height and 2.5 m. Hmm, but not only this rectangular section has to be moved, but also the slope itself.

The above method (slope + hinterland, rectangular) yields with the corrected numbers 244.5 m³ + 266.9 m³ = 511.4 m³. It is correct that the slope must be calculated twice: 511.4 + 244.5 = 755.9 m³.

The parallelogram (good idea) has a cross-section of 21.6 m² (slope depth of 4.6 m + 2.5 m offset) and thus a volume of 756 m³.

You probably want to dispose of this soil as well? Then add about a factor of 1.3 to the calculated volume, since the soil is no longer compacted.

And depending on the weather, add a bit more before the excavations.

: True, I overlooked the embankment and only considered the rectangular part. So your 755.9 m³ is correct.