# Calculate maximal slope angle of tarrain above a retaining wall

I want to build a retaining wall in my garden with stones like that

(I don't know the english word for it, in German it is called "Pflanzsstein").

I.e. something like this:

My problem is that all manufacturers I found so far, assume in their standard cases that the terrain above the wall is flat without slope, for example like this:

Taking this image as example (70 degree angle of the wall), the maximal height with flat terrain above the wall would be 2 meters.

Suppose my wall has only 1,5 meters and the terrain above it has a slope angle beta. How can I determine the maximal slope angle beta that works for this example?

Is there any free software which does the calculations for me in this and similar cases?

• Depends on the soil type, annual rainfall, presence or absence of trees tell us more – kevinsky Jul 8 '18 at 14:34
• It might be easier to separate the problem into: 1) dedicated retaining wall for slope above and 2) manufacturer calculation for garden wall. That way you separate concerns and maximize safety. That garden wall of loose cinder blocks would not hold back a landslide. – OyaMist Jul 8 '18 at 15:14
• "Angle of repose" should be a useful search term. It's the angle a pile of material will naturally take after being shaken around some. If your slope exceeds that for your material, trouble is often the result. Those odd stones will of course affect the angle of repose in they area they cover, but not the slope above. – Wayfaring Stranger Jul 8 '18 at 18:22
• Hi Sarah! If you don't receive an answer in the following days, try to ask on SE Mathematics. If you do that, don't delete the question here because it's still useful to our community. – Alina Jul 8 '18 at 19:16