Lower bound collapse theorem and lack of normality of strain rate to yield surface for soils

In soil mechanics practice there is a need for a lower bound collapse theorem, which permits an analysis with a result on the safe side. The usual analysis of slip surfaces may give unsafe results for a purelyl cohesive soil, since it is based upon a kinematically admissable collapse system and therefore constitutes an upper bound. It is therefore necessary to investigate a great number of slip surfaces and the smallest load is an approximation to the actual load which will produce collapse, but it is never known how much the computed load exceeds the actual one.