# Question about how volumes are calculated in Cross-Sections

Good Afternoon,

I have a long, linear, alignment based project that we are tracking monthly volumes by producing cross-sections that have a volume of material calculated on them. I am beginning to question the method the volumes are calculated because I am noticing large differences based on if I just sum the volumes from the cross-sections or if I run a surface to surface comparison.

For example: the last cross-sections produced totaled 86,000 CY of import. The surface to surface calcs show only 67,000. I have verified that the material used does not have a shrinkage factor applied and there is no factor applied in the surface to surface calculation either. I canâ€™t seem to see why there would be such a large discrepancy. Any ideas?

Cross Section volumes use the end area method to determine the quantities. The accuracy of the computed volumes is very much dependent on two factors

1. The station Interval that you use for the computations
2. What happens in the surfaces between the sections computed

If you use a small interval between the sections, then the volumes calculations should closely approximate to the volumes of a surface to surface calculation.

If you use a large interval between the sections then the volumes can wildly differ

So what constitutes an OK interval for corridor end section volumes depends very much on what the cross sections are doing between the stations used. If you use an interval of e.g. 5.0â€™ then it is unlikely that a significant different section will exist between stations, whereas if you use an interval of say 100.0â€™ it is highly likely that the section at one used station is very different to the next station used.

Remember that end section method uses the computation as follows

1. Take the sectional area of the volume you are interested in at Station 1 and Station 2 e.g. Cut Qty or Fill Qty
2. Add the Area from Station 1 to the same material Area in Station 2 and divide it by 2 to get the average area over that station range (This is where the variation of the sections between the stations come in - if it varies a lot, this method will miss the volume in that area depending what is found at Station 1 and Station 2)
3. Multiply the Average Area from 2 by the distance between the stations e.g. 25â€™ or 50â€™ or 100â€™ etc. to compute the volume of that material over that station range.
4. Add up all of the End Section Areas volumes along the length of the job for each material over each station range to compute the total volumes for each material.

This method is for sure not as accurate as a surface to surface volume unless you use short station ranges to make sure you capture the most accurate assessment of the volume. The method was developed to handle a) Complex Cross Sections with multiple material areas and b) was defined to increase the speed of computations of volumes for linear projects at a time when computational power was not available and c) was defined yo work the way that â€ścontractors and estimators workâ€ť i.e. using cross sections and cross sectional areas to check and validate corridors and corridor quantities.

It is a good method when used in the right way, but it is 100% dependent on the station interval being chosen that is suited to the project variations that you are working with.

Try running the calcs with a 5â€™ interval and a 10â€™ interval and a 20â€™ interval and a 50â€™ interval - you should find that as the interval gets smaller you will approximate to the volumes computed using surface to surface.

Instead of using triangles, you may want to try using the grid volumes method (Takeoff Method) in Volumes Manager or grid volumes by boundary command. The time to compute volumes even with a grid of 1â€™ is way faster than the equivalent computation using triangles, and you will typically find that the volumes calcs are almost identical. Again in the same was as end sections, if you use a 50â€™ grid the volumes will be not be the same as those computed with a 1â€™ grid, and a 1â€™ grid will be very close to the TIN volumes computed using surface to surface calculations.

Alan

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