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.

Yielding Characteristic and Non-Coaxiality of Toyoura Sand on p′-Constant Shear Stress Plane

“…Then it is considered that deformation behavior is elastic under the yield point stress level and plastic over the yield point stress level. Studies on yielding of sand started from Poorooshasb et al (1966Poorooshasb et al ( , 1967, Scoˆeld and Wroth (1968) and Barden et al (1969) in earnest. Subsequently, Nishi and Esashi (1978) and Vermeer (1978) proposed a model considering yielding behavior accompanied by consolidation, and then Tatsuoka and Molenkamp (1983) discussed about yield surface considering coupling eŠect of consolidation and shear deformation.…”

Generalized Phenomenological Cyclic Stress-Strain-Strength Characterization of Granular Media.

“…The ratios of the components of the increments of inelastic strain remain fairly constant along each radial or proportional (q/p = constant) loading path in stress space. Data presented by Poorooshasb et al (1966), Figure 3.8, and Tatsuoka (1972) substantiate this contention. Implicit in this premise is the existence of a radial, path-independent zero dilation line, and experimental studies by Kirkpatrick (1962) and Habib and Luong (1978) have confirmed the existence of such a line.…”

“…At a given stress point, the ratios of the components of the inelastic strain increments are the same for all outward loading paths through the point (Poorooshasb et al, 1966) …”

“…it must also be parrellel to the hydrostatic axis at the zero dilation line. Figure 3.13 shows plots of smooth yield surfaces back-fitted from the trajectory of plastic strain increments observed from a series of axial compression tests on Ottawa sand (Poorooshasb et al, 1966). Guided by these pictures, the meridional section of the yield surface below the zero dilation line ( 2 /Ii ( N) was chosen to be an ellipse…”

Monotonic Behaviour of Sand Under Torsional Loading With Different Confine Stress

“…First, the conventional triaxial apparatus was largely used by Poorooshasb, et al [10], Poorooshasb, et al [11], Tatsuoka and Ishihara [12], Ishihara and Okada [13] and Vaid, et al [14], among others, used to investigate the effects of stress-induced anisotropy on the subsequent drained and undrained behaviour of dense sand. One of the objectives was to recognize the yield surface within the light of the elastoplasticity framework.…”