Gültigkeitsgrenzen des statischen Kollapstheorems der Plastomechanik für Reibungsböden

Bounds of validity of the statical collapse theorem of plasticity for frictional soils.

The relevance and the proof of the statical collapse theorem of plasticity as well as the supposed material properties and general basis are outlined. This theorem - also referred to as "lower bound theorem" - means that a plastic collapse of a body consisting of a perfectly plastic material is ruled out if at least one statically admissible and safe stress field can be found. Concerning the application to earth bodies, the region of validity of the decisive material property, the so-called inequality of Drucker, for frictional soils is determined from experimental results. Thereof the region of validity of the considered theorem is deduced. It follows that the bounds of validity are given by the limit condition for the stresses and the ratio of dilatancy and the region of validity is slightly constrained compared with the region of all safe stresses. The restricted theorem postulates corresponding to the method of a thoughtful engineer that the assumed stress field keeps a sufficient distance of safety from the limit condition depending on the accuracy of the statical calculation. It holds both for the case of a critical and a peak limit condition with continuous and differentiable stress-strain behaviour. However, in case of a peak limit condition with subsequent strain softening the decrease of shear resistance in parts of the failure mechanism previous to the global collapse by progressive failure has to be taken into account. If the stress-strain behaviour on the peak is not continuous (brittle fracture) the theorem does not hold, a feature which has to be observed for retaining constructions with anchors or piles. The theorem holds also for the methods of stability calculation on the basis of the kinematics because these methods need for frictional soils in distinction to perfectly plastic materials statical assumptions too.