How do I convert points to a line at a specific distance; based on the elevation values of the points?

[GauravDewan]

Hi,

I am working on creating an elevation model for a quarry showing how the quarry would look post closure. One of the key requirements is that the slopes along the benches should be 30 degrees, for rehabilitation. For that purpose, I was thinking about extracting the elevation points along a particular boundary and exporting the attributes table to Excel. Then, based on the assumed base elevation and the elevation of each of the points along the boundary, I was wondering if I could create a new layer of points which would be the base of the slope. The points would be at a distance from the boundary such that the slope would be equal to 30 degrees theoretically; when viewed from an aspect angle of 90 degrees, relative to the quarry boundary.

Is there a general equation to calculate the XY coordinates of the points at the base, based on the coordinates of the elevation points on the boundary? For instance, let us consider a point on the boundary and a point to be placed at the base of the slope. The XY coordinates of the point at the boundary is known and the elevation values for both the point on the boundary and the point at the base are known. To obtain a 30 degree slope, is it able to obtain the XY coordinates of the base point using a general equation? Like a python code or could it be worked out in Excel?

Thanks for your suggestions.

Gaurav Dewan

[DarrenWiens2]

You mention that the elevation values at both boundary and base are known, so I assume there is some constant elevation drop for the bench...? I'll assume 10m drop, just for illustration.

Since you know the drop and the angle, you can figure out the horizontal distance of the bench using:

tan(theta) = O/A
O = 10
theta  = 30
A = 10/tan(30)

So, if the bench drops 10m, it must extend 17.3m to fit a 30 degree angle. So, buffer the boundary by -17.3m to get your base boundary. From there, you can convert the buffer to line, convert line to raster, and use Con() to extract elevations at the base of the slope.

[GauravDewan]

Hi,

Thanks for your suggestion. Yes the elevation values are known, at both the boundary and at the base, it has been assumed to ensure that maximum amount of rock can be extracted till closure of the pit. However, the elevations along the boundary are not constant and there are significant undulations. So I was wondering if there is a way to get the elevation points at the base of the slope, based on the elevation points along the boundary such that when viewing at an aspect of 90 degrees with respect to the boundary, the slopes are 30 degrees.

After I get the elevation points at the base of the slope, I can use Topo to Raster tool to convert the points to raster. Will you be able to tell me how to get the points at the base of the slope? Based on the elevation values along the boundary. For instance, along a particular boundary, the elevation varies from 200m to 215m. Assuming a base elevation of 170m, how can I generate the points at the base of the slope such that the slope angle is 30degrees? When viewing at an angle of 90 degrees, relative to the boundary.

[GauravDewan]

I have been able to generate the points at the base of the slope using Excel. However I run into a problem on using Topo to Raster tool. The points at the base of the slope are located at a distance such that if a line is drawn from a point at the base of the slope to the corresponding point on the boundary, the slope should be 30 degrees. However on interpolating the points using Topo to Raster tool, I get a slope range of 29-39 along the slope plane.

How can I refine this?