Recent developments in soil yield criteria and numerical applications

Abstract

INTRODUCTION RECENT achievements in critical state soil mechanics advanced by Roscoe and his coworkers [1, 2] and redocumented recently by Kurtay and Reece [3] have stimulated many other investigators searching for practical applications. Initial attempts at numerical applications have been made by Smith and Kay [4], Zienkiewicz [5], Chung and Lee [6], and Chung, Costes, and Lee [7] in the context of finite element techniques. The present study is an extension of [6, 7] with some significant modifications with reference to interpretation of the yield criteria of Roscoe and Burland [l]. In the previous works [6, 7], the authors considered the strain-hardening parameter to be controlled by the constant yield stress, an independent material parameter, in addition to the basic material properties (M, ~., K) proposed by Roscoe and Burland [1]. However, in view of the fact that the equation of the yield surface and subsequently the equation of the yield locus as defined in [1] are based on the normality requirements of the plastic strain vector [8] with strain-hardening phenomena incorporated in the plastic potential function, additional imposition of strain-hardening through a constant yield stress is unnecessary. Because the terms included in the plastic potential function [6, 7] consist of deviatoric stress invariant and the basic soil mechanics material properties (M, L, K) associated with the mean pressure the later contributions in the plastic potential function must provide strain-hardening behaviour in the sense of the classical incremental theory of plasticity. This argument leads to the standard manner of handling the plastic potential function in that the variation of this function depends on the second deviatoric stress invariant and the strain-hardening parameter. If the differential of such a function is equal to zero we have a neutral loading, and the positive and negative values would indicate loading and unloading, respectively. The positive change of this potential function, therefore, shifts the yield locus in the deviatoric-mean stress space whose projection back to the void ratio-mean stress space lies entirely on the yield surface at all times. The constitutive relationships and the finite element equations are derived as demonstrated earlier [6, 7]. The plastic tangent stiffness matrix is updated for small increments of loading. The repetitive solution of the equilibrium equations continues until the total load is reached. Numerical examples for the plate-bearing and conepenetrometer are presented to evaluate correctness of the procedure. Comparisons with test results indicate close agreement.