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In this paper the basic features of a constitutive model for normally and lightly overconsolidated soils, based on the multilaminate framework, are discussed. Multilaminate models simulate the stress-strain behaviour of a material by considering the response on so-called integration or sampling planes. Yield and plastic potential functions are expressed in terms of normal and shear stresses on these integration planes, and thus the mathematical formulations remain relatively simple even for complex strain-hardening/softening models. The model includes a deviatoric yield surface with a non-associated flow rule and a volumetric yield surface with an associated flow rule. Induced anisotropy and the effect of rotation of principal stress axes are intrinsically taken into account in multilaminate models without requiring additional material parameters. Inherent anisotropy can be modelled by introducing a structural tensor. A slight disadvantage of the multilaminate approach is that no function for a yield surface in three-dimensional stress space exists, and therefore comparison with other constitutive models is difficult on a visual basis. However, it is shown that the model produces approximately a MohrCoulomb failure surface in the deviatoric plane, which can be easily modified to incorporate anisotropic behaviour with respect to strength, providing a significant extension of the model. The influence of the integration rule on the obtained failure surface is discussed. Comparison with experimental data from a comprehensive series of stress-path-controlled triaxial tests on Poko clay shows the capability of the approach for modelling the mechanical behaviour of soft clays. The significant importance of the formulation of the flow rule on the model's performance for undrained triaxial stress paths is discussed by comparison with experimental data. Finally some results from a slope stability analysis are presented.

Funding informationThe Netherlands Organisation for Scientific Research (NWO); Deltares; Royal Boskalis Westminster N. V.; Van Oord Dredging and Marine Contractors; Rijkswaterstaat; Stichting FloodControl IJkdijk SummaryWithin the standard material point method (MPM), the spatial errors are partially caused by the direct mapping of material-point data to the background grid. In order to reduce these errors, we introduced a novel technique that combines the least squares method with the Taylor basis functions, called the Taylor least squares (TLS), to reconstruct functions from scattered data while preserving their integrals. The TLS technique locally approximates quantities of interest such as stress and density, and when used with a suitable quadrature rule, it conserves the total mass and linear momentum after transferring the material-point information to the grid. The integration of the technique into MPM, dual domain MPM, and B-spline MPM significantly improves the results of these methods. For the considered examples, the TLS function reconstruction technique resembles the approximation properties of highly accurate spline reconstruction while preserving the physical properties of the standard algorithm.

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