A theoretical investigation is given of quasi-static axially symmetric plastic deformations in soils.The mechanical behaviour of a natural soil is approximated by that of an ideal soil which obeys Coulomb’s yield criterion and associated flow rule, with restriction to rigid, perfectly plastic deformations. There are considerable variations in the structure of the associated stress and velocity field equations for the various plastic regimes, but it is noteworthy that real families of characteristics occur in all non-trivial cases. Attention is focused on those plastic régimes agreeing with the heuristic hypothesis of Haar & von Kármán as being seemingly of application to certain classes of problems, in particular to those of indentation. The stress and velocity fields are then hyperbolic with identical families of characteristics, and the stress field is statically determinate under appropriate boundary conditions. In applications of the theoretical analysis, attention is confined to situations involving only the Haar & von Kármán plastic regimes. First, possible velocity fields are obtained for the incipient plastic flow of a right circular cylindrical sample of soil subjected to uni-axial compressive stress parallel to its axis. Secondly, a complete solution is obtained for the incipient plastic flow in a semi-infinite region of soil, bounded by a plane surface, due to load applied through a flat-ended,smooth, rigid, circular cylinder; numerical results obtained for this problem include the variation of yield-point load with angle of internal friction of the ideal soil. These applications relate to problems of the mechanical testing of soil samples and of load-bearing capacity in foundation engineering.
Analysis of spatial stress and velocity fields in plastic flow processes
