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In the 1399 Road Construction Cost-Estimate book, a formula for calculating volume based on a Truncated Pyramid is provided.
As shown in the figure below, since the publication of this cost-estimate book, this formula has been included in the "Sections Analysis" dialog box, allowing the user to use this formula as the basis for volume calculations.
Here, the above formula and the method of calculating volume as a Truncated Pyramid are reviewed.
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- The approved formulas for calculating the volumes of cross-sections in road construction are presented in the figure below.
- In calculating cross-section volumes, the prism model is considered as a Truncated Wedge.
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- This is because the model used to calculate cross-section volumes as a Truncated Wedge is more accurate. The Truncated Pyramid model is not used because it always gives a lower volume than the actual volume.
- In a Truncated Pyramid, the zero-level surface is a single point, whereas in a Truncated Wedge, the zero-level surface is a rectangle with the road width and zero height.
- When cross-sections have retaining walls on both sides, the Truncated Pyramid volume formula always produces smaller values than the actual volume, which is the result of the Truncated Wedge method.
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- Regardless of the above explanations, when calculating the volumes of separate embankment layers or excavation volumes based on different soil classifications, using the Truncated Pyramid formula for volume calculation results in discrepancies between the separate volumes and the total volume. An example of this situation is shown in the figure opposite.
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- In the table above, the volume results calculated using the Truncated Pyramid formula are presented as both total and separate volumes. The discrepancy between the two volumes, 845.55 and 833.00, is clearly evident.
- In the table below, the Truncated Wedge formula is used, and the consistency between the separate volumes and the total volume is clearly evident.
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