Yielding and Flow of Sand in Triaxial Compression: Part I

Abstract

A theoretical and experimental study of the nature of deformation of a sand sample when tested in the triaxial apparatus is presented. The medium is shown to be elastic-strain hardening plastic but does not conform to certain rules usually adopted in the classical theory of plasticity. Experimental verification of an earlier suggestion by Poorooshasb (1961) leads to a proof of the existence of a potential function, known as the plastic potential, of the form Ψ(σ, e) the parameters σ representing the stress and e the voids ratio. The plastic potential curves defined by Ψ = constant, e = constant, trace a family of geometrically similar curves when plotted in a stress space. The yield loci, on the other hand, are found to be independent of voids ratio and are only functions of the ratio of the second invariant of the stress deviation tensor to the first invariant of the stress tensor. It is noted, therefore, that the plastic potential and yield surface are not coincidental. This defies the normality condition and in this respect the medium's behaviour appears to deviate from that of a classical plastic body. Although the scope of the study is limited, being applicable only to stress conditions provided in a triaxial compression test, extensions are made to incorporate stress and strain in their more general form. This is done to stimulate further research on the subject, although a fair amount of evidence is available to support, qualitatively at least, the validity of the propositions made. The paper is concluded by presenting the flow rule for the medium and discussing the application of the theory presented to the solution of equilibrium and eigenvalue problems involving stress and deformation.