Keywords: soil specimen, triaxial compression and extension, localisation of deformation, finite element analysis, constitutive models, Cam-clay.

Elastoplastic constitutive models for geomaterials, such as Mohr-Coulomb model, Drucker-Prager model and Cam-clay model are generally represented in principal stress space. The characteristics of the yield surface are, in general, described by the shape of its projection on the meridian plane and its cross-sectional shape on the deviatoric stress plane. The cross-sectional shapes of these models on the deviatoric stress plane, excepting Mohr-Coulomb model, are concentric circles, the centre of which is the hydrostatic stress axis. But these models are usually said to be not sufficient to predict an important property of geomaterials that the failure strength in compression is higher than that in tension. This typical property in geomaterials can be captured by introducing the third invariant of the stress into the yield function.

In experiments for geomaterials such as triaxial tests, specimen should retain the uniformity during the deformation to obtain pure material properties. When we conduct such material tests, there exist, however, many influential factors, such as inhomogeneity of soils, very small geometric distortion of specimens, and friction between the specimen and testing apparatus. Bifurcation phenomena, which may induce localisation of deformation or shear bands, are recognised as one of the most important and unavoidable factors [1]. It is thus very difficult in fact to realise ideal experiments under uniform deformation. Material properties obtained from test results under such situation thus seem to be greatly affected by these factors.

We investigate in this paper the influence of non-uniformity of deformation on test results through numerical analyses. A series of three-dimensional analyses is conducted for triaxial compression and extension. Deformation and failure behaviour of the specimens are computed by nonlinear finite element analyses, and 'macroscopic' state variables at the failure are evaluated from the numerical results.

First, we compute pure mechanical responses of constitutive model under triaxial compression and extension to estimate the results of ideal experiments under uniform deformation. Modified Cam-clay model [2,3,4] are employed as an model example. We here refer to these results as 'constitutive responses.' In the principal stress space, the critical state of this model is represented by a cone whose axis of rotational symmetry coincides with the hydrostatic stress axis. The shape of the projection of the cone on the - plane is reduced to a straight line, and the cross-sectional shape on the deviatoric stress plane is a circle. This model thus cannot express the different responses for triaxial compression and extension. The critical stress ratio predicted by this model is the same value even for triaxial compression and extension.

Next, we conduct a series of three-dimensional nonlinear finite element analyses for triaxial compression and extension to compute 'macroscopic' responses of the specimens. The same constitutive model as used in the analysis of 'constitutive responses', namely, the modified Cam-clay model, are employed as a local material property. We consider two types of the shapes of the specimens to examine shape effects: (1) rectangular brick specimens and (2) circular cylindrical specimens. Frictional boundary conditions at top and bottom ends of the specimens are assumed to model actual testing conditions. Through these numerical analyses, stress paths traced by the specimens are obtained under several different values of confining pressures, and 'macroscopic' state variable, namely, the critical stress ratio, at failure of the specimens are evaluated for triaxial compression and extension, respectively. Comparison between the response for triaxial compression and the one for triaxial extension shows that the 'macroscopic' critical stress ratio in extension is about 10 percent smaller than that in compression. This result implies that the 'macroscopic' responses of the specimens show the different behaviour under triaxial compression and extension, even for the use of simple material model which cannot express the different responses for triaxial compression and extension,

The results of this paper suggest the significance of the influence of non-uniform or localised deformation in soil specimens, and provide an aspect of the rational interpretation for the relation between experimental results and constitutive models.

1

K. Ikeda, Y. Yamakawa, S. Tsutsumi: "Simulation and interpretation of diffuse mode bifurcation of elastoplastic solids", Journal of the Mechanics and Physics of Solids, Vol. 51, pp. 1649-1673, 2003. doi:10.1016/S0022-5096(03)00073-5

2

R. I. Borja, C. Tamagnini: "Cam-clay plasticity Part III: Extension of the infinitesimal model to include finite strains", Computer Methods in Applied Mechanics and Engineering, Vol. 155, pp. 73-95, 1998. doi:10.1016/S0045-7825(97)00141-2

3

G. Meschke, W. N. Liu: "A re-formulation of the exponential algorithm for finite strain plasticity in terms of cauchy stresses", Computer Methods in Applied Mechanics and Engineering, Vol. 173, pp. 167-187, 1999. doi:10.1016/S0045-7825(98)00267-9

4

K. Hashiguchi: "On the linear relations of V-ln p and v-ln p for isotropic consolidation of soils", International Journal of Numerical and Analytical Methods in Geomechanics, Vol. 19, pp. 367-376, 1995. doi:10.1002/nag.1610190505

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