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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.

ndthl
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  • 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 Jul 30 '13 at 13:57
  • When the bund is pushed into the pit, there will be an angle of between the original ground surface (horizontal) and the material pushed in as it slopes down to the base of the pit. This angle should not exceed 30 degrees. Yes, the pits will have sloping walls and this slope should not exceed 30 degrees. I thought a way to do this would be to make a 1m incremental series of buffers of the line of the intersection between the original land surface and the topo surface. These buffers would describe lines across the pit base that I could use sample the topo surface elevation. – ndthl Aug 01 '13 at 09:44
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    A method to create a specified slope is described in my answer at http://gis.stackexchange.com/questions/17793/how-to-build-an-artificial-dam-across-a-river/17805#17805; it will work here, too. – whuber Aug 01 '13 at 12:27
  • Hi again, not sure if this will appear in your inbox but we'll see. I am going to try this exercise today, it will be my first attempt at map algebra. I discussed your proposal with a colleague who said that your method is fine for straight lines but on an irregular pentagon shaped bund around a pit it may not work. What will happen at the corners? Anyway, we'll see what happens. I guess I could just turn it into a simplified series of five lines representating the sides if worst comes to worst. – ndthl Aug 22 '13 at 08:45
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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 http://gis.stackexchange.com/a/18079 clarifies the situation. – whuber Aug 22 '13 at 11:53
  • Hi, yes I had found that item already and it was useful to have the extra guidance. I think it's more that the colleague I spoke to had never done this before so did not understand how it would work. I shouldn't have listened to their doubts perhaps. Anyway, I'm yet to actually try it, as usual other tasks have gotten in the way. I'm excited by the promise of a solution though, it's seems better than having to iterate through a series of negative buffers of a fill polygon to see which produces a 30 degree slope. It's surprising there isn't a tool that just constructs a slope for me anyway. – ndthl Aug 22 '13 at 13:01
  • Hi @whuber I have now begun to work through your suggestion. I created a euclidean distance grid (EDG) for polyline z feature class of the line representing the edge of the fill polygon from a cut/fill analysis of the pit. Then I multiplied it by -.577 to get a 30 degree slope into the pit. I looked at it in ArcScene and the ridge in the resulting raster was not at the same elevation as the source polyline z. To me this means further raster calcs to combine the topo surface with the proposed 30 degree slope surface will not be correct. – ndthl Aug 25 '13 at 06:00
  • Now I understand that the EDG*-.577 (30 degree slope) raster is just something to subtract from the elevation of the top of the feature. It does not need to represent topography itself. This elevation changes around the entire perimeter. I'll see what I can do following the instructions for this in your other post regarding calculating a euclidean allocation grid. It was pleasing at least to be able to produce a 30 degree slope inward from the fill edge polygon. – ndthl Aug 25 '13 at 07:16
  • Ok. I finally got there. I had to actually add the slope raster to the raster produced from the euclidean allocation tool described in your other post. Only problem is that the resolution of this is significantly less than that of the topographic surface, I think because of the need to convert it to integer raster for the allocation tool. Anyway, it's satisfying to see a slope that I have constructed cresting above the topo surface in places where the slope classification tool has identified a topo slope of greater than 30 degrees. – ndthl Aug 25 '13 at 09:40
  • Last of all, the pit where I am doing this calculation does not have a flat base. There are many instances within the pit of slopes >30°. To satisfy the contract we have to at least get rid of all such slopes. Of course the easiest thing is to refill the pit but it is too large for this. Hence I will have to construct a new slope raster starting at the top of each of these I am guessing, since the one for the perimeter is just essentially a cone extending at 30° inward. Where these slopes are higher than the topo surface I can get the volume between to see if we have enough soil for the work. – ndthl Aug 25 '13 at 10:14
  • In my answer at http://gis.stackexchange.com/questions/18077/how-to-create-a-field-with-a-specified-slope-projecting-from-a-3d-polygon/18079#18079 I explain that you can overcome the resolution difficulties by rounding to fractions of an integer rather than integers. – whuber Aug 25 '13 at 15:44
  • Hi @whuber, thanks again for your efforts to educate me. I followed all of your instructions including rounding to the nearest hundredth. The problem remains, however, that this is an integer raster which is not going to have the same elevations around the top of the slope as the TIN that I have made of the topography. I guess I could just use an integer raster of the topography for the purposes of this calc but to me this is losing too much accuracy given we have a very high accuracy DEM from a LIDAR total station. – ndthl Aug 27 '13 at 11:09
  • Ultimately I want to submit the constructed surface to the 'Surface difference' or 'cut/fill' tool in ArcGIS along with my high accuracy DEM and calculate precisely how much extra material will need to be deposited on the internal bund slopes to remove gradients of more than 30 degrees. The most satisfying way for me to go about this would be to apply the euclidean distance grid to a TIN (or at least non integer) version of the euclidean allocation grid. Is there a TIN approach to solving this, easier than my idea using iterations of a negative buffer described in the original post? – ndthl Aug 27 '13 at 11:14
  • I'm sorry, but I am not aware of any earth-moving equipment that can work to millimeter accuracy (or even centimeter accuracy for that matter), regardless of how accurate the LIDAR might be. Because such precision is available in a grid, your complaints about loss of accuracy seem misdirected here. – whuber Aug 27 '13 at 13:17
  • You're right. I'll suck it up. I'm not sure what you mean though about precision since it's an integer raster that the euclidean allocation tool outputs. Whilst the discretisation effect will have been reduced in some cases it will still be out by half a metre. Anyway again thanks so much for the help you have provided, I really have learned a lot. – ndthl Aug 27 '13 at 13:35
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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 Aug 27 '13 at 15:07
  • Thanks. For rounding to nearest 100th I found http://forums.arcgis.com/threads/86162-Round-to-nearest-100th. Raster calculator, however, only has round down or round up. A formula like Int(Round("Raster",2)) does not work (error "Round is undefined"). Hence I used Int("Raster"+0.5) and this at least rounded all values up or down rather than simply truncating the decimal. I thought I had figured out a way to round to the nearest 100th using raster calculator but it is not working today so perhaps I have forgotten. Do you have any advice about this? – ndthl Aug 28 '13 at 09:25
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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 Aug 28 '13 at 13:41

1 Answers1

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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

DA53
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