A kinematic hardening constitutive model for sands: the multiaxial formulation

Abstract

This paper explores the possibility of using well-accepted concepts*Mohr-Coulomb-like strength criterion, critical state, existence of a small strain elastic region, hyperbolic relationship for representing global plastic stress}strain behaviour, dependence of strength on state parameter and #ow rules derived from the Cam-Clay Model*to represent the general multiaxial stress}strain behaviour of granular materials over the full range of void ratios and stress level (neglecting grain crushing). The result is a simple model based on bounding surface and kinematic hardening plasticity, which is based on a single set of constitutive parameters, namely two for the elastic behaviour plus eight for the plastic behaviour, which all have a clear and easily understandable physical meaning.In order to assist the convenience of the numerical implementation, the model is de"ned in a &normalized' stress space in which the stress}strain behaviour does not undergo any strain softening and so certain potential numerical di$culties are avoided.In the "rst part the multiaxial formulation of the model is described in detail, using appropriate mixed invariants, which rationally combine stress history and stress. The model simulations are compared with some experimental results for tests on granular soils along stress paths lying outside the triaxial plane over a wide range of densities and mean stresses, using constitutive parameters calibrated using triaxial tests. Furthermore, the study is extended to the analysis of the e!ects induced by the di!erent shapes of the yield and bounding surfaces, revealing the di!erent role played by the size and the curvature of the bounding surface on the simulated behaviour of completely stress-and partly strain-driven tests. Figure 1. Sections through strength surface, critical state surface and yield surface in p : q planeaxes, simple shear tests and circular stress paths in the deviatoric plane performed in a multiaxial apparatus. The model is formulated in terms of e!ective stresses and therefore the use of the usual to distinguish such stresses from total stresses will be omitted. Moreover, following continuum mechanics tradition, stresses are assumed positive in tension and compressive volumetric strain is assumed negative. However, in order to make easier the comprehension of the "gures and the comparison with experimental "ndings, the results have been plotted according to the usual geomechanics convention namely, compressive stresses and strains are assumed positive. The primary emphasis here is on deviatoric response * so, as formulated here, the model will be most applicable on paths where deviatoric e!ects dominate. It would be straightforward to add a volumetric cap as a second plastic mechanism to improve the performance of the model for paths where increases of mean stress are clearly important.Models which describe anisotropic e!ects need to be de"ned in terms of mixed invariants which incorporate the memory of the soil for its history. In the present model the axis of the kinematica...

On generalization of constitutive models from two dimensions to three dimensions

“…Constitutive models for three dimensional stress and strain states are also predominately formulated based on the von Mises method or modified Mises method. A small percentage of models are formulated based on the generalized shear stress ratio derived from failure criterions at critical state for geomaterials (e.g., Lade, 1977;Gajo and Muir Wood, 1999;Matsuoka et al, 1999).…”

“…The use of the generalized shear stress ratio, other than those described previously under von Mises criterion, is discussed here. The method has been used for extending both constitutive models and constitutive equations (e.g., Lagioia et al, 1996;Gajo and Muir Wood, 1999;Liu and Carter 2004). The generalized stress ratio is normally worked out from a criterion for failure at critical state such as those proposed by Lade (1977), Matsuoka and Nakai (1982) and Liu and Carter (2004).…”

“…Several approaches have been proposed in the literature. Among the notable contributions include the work of Lagioia et al (1996), Gajo and Muir Wood (1999), Liu and Carter (2002), Wheeler et al (2003), Dafalias et al (2006), among others. However, most of these approaches have been based on certain simplifying assumptions and their applicability and effectiveness have yet to be examined in detail.…”

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