Hello everyone~!
The main question is information regarding to plane failure of the stereographic projection.
According to book(rock slope engineering, hoek and bray 1981), it clearly says “The plane on which sliding occurs must strike parallel or nearly parallel (whining approximately ±20°) to the slope face.”
I would like to know why “approximately ±20°”, Or reference ?
To see the answer I sugest to draw the great circles for some slope and failure plane to see the effect on the drawing. For example, try to plot the following planes: slope plane with dip amount of 90/60 and failure plane with dip amount 90/30. Then if you do a variation of slope planes in a range of 110/60 or 70/60you will see the effect because slope and failure planes are not any more "parallel". So, if you have wider range than +_20 degres and some combination with other joint set then the other mode of failure (wedge failure) is more posinle than the plane failure.
To see the answer I sugest to draw the great circles for some slope and failure plane to see the effect on the drawing. For example, try to plot the following planes: slope plane with dip amount of 90/60 and failure plane with dip amount 90/30. Then if you do a variation of slope planes in a range of 110/60 or 70/60you will see the effect because slope and failure planes are not any more "parallel". So, if you have wider range than +_20 degres and some combination with other joint set then the other mode of failure (wedge failure) is more posinle than the plane failure.
Here is a nice learning tool with explanations that might help you:
http://www.dipanalyst.com/Kinematic%20Analysis/Kinematic%20Analysis.html
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