Create slope and generate contours for pit face

[NealaGriffin]

I am working on the post development plans for a quarry.  The pit will be mined out to an elevation of 98m.  I need to create a slope of 30 degrees from the edge of the quarry boundary (to the pit floor elevation of 98m).  Then, within this sloped area, I need to generate contours.

I have attached an image of an old plan that shows what I am trying to accomplish (AE_Post_CP.jpg) and an image of the new contours I am working with.  The new contours came from survey points that are much more accurate then the contours on the old plan. 

The second image  (post_working.jpg) shows the old sloped area, quarry boundary and new contours.  Any suggestions for creating the new 30 degree sloped area and contours within this area would be greatly appreciated!

I am working in 9.3.1 and have all extensions.

Neala

[DanPatterson_Retired]

Is this a spatial analyst or 3D analyst issue?  perhaps a redirect to the appropriate forum would be advised, this is the General forum

[Anonymous User]

Original User: mstead

Create two lines at your toe at the base elevation and beyond the crest (use your 30% slope to figure out an elevation at some distance beyond the crest. Make this into a tin and convert to a grid. Convert your contours into a DEM with toporaster. Mosiac your two rasters using the minimum value setting. oh....and then make contours from that grid

[NealaGriffin]

Is this a spatial analyst or 3D analyst issue?  perhaps a redirect to the appropriate forum would be advised, this is the General forum

Yes, it is a spatial analyst issue...my mistake for posting in the general forum.  Do you know how it can be moved?

[Anonymous User]

Original User: nealacg

"use your 30% slope to figure out an elevation at some distance beyond the crest."

This is the part I don't know how to do....can you provide me the actual steps in Arc to complete this?  Thanks!

[Anonymous User]

Original User: whuber

A good approach is to start with a DEM, not contours.  You don't need a DEM of the whole area; you really only need elevations at grid cells through which the quarry boundary passes.  If you don't have this DEM, there are straightforward ways to prepare one from the contour layer.

This problem begs us to characterize constant slopes in the following way.  First, a slope of t degrees has a rise:run ratio of tan(t).  (When t = 30 degrees, tan(t) = 1/Sqrt(3) = 0.57735.)  Let x be any location within the finished quarry and let z(x) be its elevation.  Assume z(x) is above 98 m so that the slope criterion applies.  Consider an arbitrary point y on the quarry's boundary and let d = |y - x| be the Euclidean distance between x and y.  Moving from x to y at the maximum allowable slope would increase one's elevation from z(x) to z(x) + d*tan(t).  If this is less than z(y), then x is too deep.  We can re-express this necessary criterion as follows:
[INDENT]z(x) >= z(y) - |y - x| tan(t) for all boundary points y.
[/INDENT]You want to dig out as much as possible from the quarry, so you will dig until there exists at least one boundary point y for which the inequality is actually an equality.  There is the formula we need:
[INDENT]z(x) = Min{z(y) - |y - x| tan(t), y on the boundary}.
[/INDENT]Carrying out this calculation is complicated because it looks like you need to compute the Euclidean distance grid x --> |y - x| for every cell y on the boundary.  However, the calculation for all points y at any given altitude can be carried out at once.  This algorithmic improvement makes the whole thing feasible.  Detailed steps are given in the old forums at http://forums.esri.com/Thread.asp?c=93&f=40&t=246814&g=1#754330 .  Once you have computed the result, take the maximum of it and a constant 98 m grid to determine the floor.  Spatial Analyst will easily contour that.

[MichaelStead]

If the furthest part of your crest is ~150 metres you could make your plane 200 m total. To figure out the elevation of this line just use slope = rise/run  (0.3 = rise/200; rise =0.3*200; rise =  60 so the elevation of the line would be 60 + 98 = 158 m)

If you can follow William Hubers methodology he is bloody amazing and it is almost certainly a better solution in some way, but I have done variations on this this before and it should give you what you want. The only possible pitfalls are if you end up with 0 value cells getting counted in the mosiac "min" function (if there is black around your slope plane after you convert from TIN to DEM run a copy raster with the remove null value toggle), and the possibility of "ravines" remaining in the plane face if the original topography is lower than the new plane surface.

[Anonymous User]

Original User: nealacg

If you can follow William Hubers methodology he is bloody amazing and it is almost certainly a better solution in some way

Thank you both for your responses.  William's methodology does look amazing...however my math skills are not!  I understand how to get the distance of the pit face that will be equal to 30 degrees, but I am not following how the toe of the slope will be generated automatically.  I have been testing some things manually, but know this is NOT the way to do it...unless I want to end up in a mental institution!  Perhaps a break from this for a few hours will help 🙂

[WilliamHuber]

The toe of the slope is obtained in the final step, Neala, where you create a floor of 98 m.

Geometrically, you are creating a collection of similar cones: their tips are pointed upwards and located at all the boundary points.  The boundary of the union of all these cones includes the sides of the quarry that would be created if you could dig as deep as possible subject to the 30 degree slope limitation.  Imagine doing this but then re-filling the quarry (with water, say) up to a constant elevation of 98 m.  The resulting shoreline is the toe of the slopes.  The filling is done with the maximum function.

[Anonymous User]

Original User: nealacg

Thanks, I was able to figure some of this out and in the end came up with what I needed.  Do either of you use any third party software add ons for geology work in ArcGIS?  I might look into investing in some software that is geared towards drilling, profiling etc and wondered if you might have any suggestions.

Cheers,
Neala