Incipient failure of a circular cylinder under gravity

What is the final shape of a viscoplastic slump?

“…One also needs an analogue of the expansion fan to begin the slipline construction, and suitable velocity boundary conditions on the free surface. One method which has been used to overcome some of these issues is the so-called Haar-Karman hypothesis [19,20], which assumes that the intermediate principal stress is equal to one of the other two principal stresses. Thus, one can eliminate one of the stress components from the stress equations, which then decouple from the velocity equations.…”

“…Later, Nye [8] also reported the first-order correction term to (20), although it was derived through a more heuristic argument. As we see in (20), Nye's correction is actually accurate to order 3 .…”