Multi Yield-Loci Theories of Soil Deformation

The form of constitutive equations for soils that use multi yield loci are stated. The stability of the material is examined in the light of Drucker’s criterion which postulates that a material is stable if in an incremental loading process the increment of incremental plastic work is positive semidefinite. It is shown that while if a single family of yield surfaces is used then the so-called normality condition (the coincidence of the plastic potential surface and the yield surface) must hold. On the other hand the normality condition is not necessarily satisfied, even if Drucker’s criterion is, if a multitude of families of yield loci are employed. As an example it is shown that the model proposed by Poorooshasb and Yong (1982) to describe clay deformation does satisfy the stability condition, nevertheless one family of the yield loci and the corresponding plastic potential surfaces are not coinciding.