WES Theoretical Manual, Part XI: Slip on Circular Failure Surface (Hansen’s Method)

This part covers slip on a circular failure surface, using Hansen's method. A circular surface forms between the tips of the outboard and inboard walls, the part of the cell above it rotates as a rigid body about the center of the circle, and sliding occurs between the fill and the walls and between some of the sheets in the crosswall.

Hansen proposed two versions, an equilibrium method and a simpler extreme method that gives essentially the same results. The extreme method approximates the circle with a logarithmic spiral, so that the resultant force on the failure surface passes through the pole of the spiral and drops out of the moment equation.

The manual is candid about the limits. The method rests on circular failure surfaces seen only in very small models, with rigid walls that probably carried more of the load than real sheeting would. It is conservative, since it ignores friction between wall and fill. And it is complicated enough, particularly on soil foundations, that it is not recommended for everyday use.