Slip Line Analysis

Slip-Line Analysis

Either for a full solution or to aid in the trial-and-error approach to upper-bound limit analysis, further knowledge of the shape of preferred mechanisms is crucial. Nature will select the type and location of slip surface that requires the least amount of energy (or force) to bring it about. In previews pages, this minimization was demonstrated without knowledge of the correct “type” of mechanism and, by the upper-bound theorem, values obtained for the col-lapse load must necessarily be incorrect on the high side (unconservative).

The question then is: how sensitive is the collapse load to the choice of failure mechanism or, put differently, how close must we estimate the shape and the position of the slip surface to get good approximations?

To address this question and better understand the physics of collapse, the geometric characteristics of correct slip mechanisms must be investigated and “exact” solutions found for some basic problems to compare to the more easily obtained approximate answers. This can be done by looking at the basic differential field equations of equilibrium coupled with the yield condition. In this chapter we will do this not only for an ideal EPS material but also for the more general MohrCoulomb (M-C) material.