This is a cut/fill problem.

We have pits that have been dug in the ground, usually rectangular. They have a bund wall around them. They are being rehabilitated by pushing the bund back into the pit. Usually the bund is not enough to refill the pit. We need to achieve a maximum 30 degree slope between the original land surface outside the feature and the backfilled material pushed in from the bund. We need to know if we have enough material in the bunds to achieve this angle of slope.

We know the bund volume from topographic survey (interpolated the original land surface under the bund from elevation points outside the feature in the topographic data). From this interpolated surface we know the location and height from which the 30 degree slope will start and go down into the pit. Is there a tool in any GIS or CAD program that will take this line (as a polyline or polygon for example), take the angle (in this case 30 degrees) and output a new line or polygon showing where the topographic surface will be intersected, right the way around the pit? With this new line, a TIN could be created of the elevations along it at the bottom of the proposed slope and the elevations of the intersection at the top of the slope between the original land surface and the topographic surface. The topographic surface could then be subtracted from this new TIN to get the volume and see whether it is the same or less than the volume in the bund.

If there is a tool to automate this, it would make life much easier. Otherwise we could calculate a few points around the pit manually for a coarser estimate.

  • It is unclear what you mean by a "maximum 30 degree slope between the original land surface ... and the backfilled material." Does this mean that the slope of the backfilled material within the pits cannot exceed 30 degrees or might it mean that the exterior angle made at the edge of the pits cannot exceed 30 degrees? Either way, would it be correct to conceive of your plan as ending up with pits that have sloping walls instead of vertical walls?
    – whuber
    Commented Jul 30, 2013 at 13:57
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    A method to create a specified slope is described in my answer at gis.stackexchange.com/questions/17793/…; it will work here, too.
    – whuber
    Commented Aug 1, 2013 at 12:27
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    Could you please elaborate on how such a solution would not "work" for concave polygons? (There is no problem in the calculation at the corners or anywhere else--try it!) That will help us understand what your question really is. Maybe you will find the analysis at gis.stackexchange.com/a/18079 clarifies the situation.
    – whuber
    Commented Aug 22, 2013 at 11:53
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    Sure, needing integer raster is a problem: so change the elevation units to millimeters (by multiplying a floating point DEM with meter elevations by 1000 and rounding) and voila, you have millimeter precision. It's that easy.
    – whuber
    Commented Aug 27, 2013 at 15:07
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    Int("Raster" * 100 + 0.5) works just fine. Yes, all numbers are 100 times greater than they were before: but that only means you interpret the elevations as centimeters instead of meters (and change back to your favorite units at the end of your analysis).
    – whuber
    Commented Aug 28, 2013 at 13:41

1 Answer 1


If you have 3D-model of your pit (as xyz point or mesh surface),then you can use 3D BLENDER to draw and find volume of required backfill at any slope angle

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