Plastic deformation of compressible ground

Abstract

To solve the problem of plastic flow of ground we usually enlist the associated f r law [i], i.e., it is assumed that the plastic potential exactly coincides with the cot • tlon of plasticity. The associated flow law enables us to solve a wlde range of problems, but In certain cases the theoretical results conflict with the actual data. For example, from thls law it follows that any deformation of a material Is accompanied by Its expansion. Depending on its initial density, ground may either undergo expansion or compaction during deformation [2].To eliminate this discrepancy between theory and experiment, some investigators [3,4] postulate expressions for the plastic potential which differ from the plasticity conditions and contain the experimentally determined coefficient of dilatancy.In thls case, however, the characteristics for the stresses and rates of deformation do not coincide, and therefore neither do the regions of the solutions for the stresses and deformations.Other methods for taking account of the compressibility of ground have been suggested [5,6], but in these too the characteristics for the stresses and rates of deformation do not coincide.We have developed a somewhat modified version of the method proposed by Ivlev and Martynova [7] for taking account of the compressibility of ground. We have obtained equ ations representing plane deformation of compressible ground, and have examined equations for fracture; an example illustrating the qualitative side of deformation of such ground is given.I. It will be assume that the following plasticity condition holds true for the ground: where 6ij is the Kronecker delta, and ~j the rates of deformation deviator components.From Eq. (2) we haveEquations (i), (3), and (4) show that e ~ 0 only when Ell # 0. If we put o = o, = ~,-a,-0, then Ia = Is = O, whence Ell = 0 and therefore e = 0. Thus the compressibility determined by Eq. (3) depends markedly on the distortion, and material for which Eq. (2) holds true cannot be compressed by hydrostatic pressure. Thls is observed only for overdense or completely waterlogged (outflow precluded) ground.All-Unlon Sclentlflc-Research Mlne Surveying Institute, Leningrad.