In this paper, modelling of the superposition of stress-induced and inherent anisotropy of soil small strain stiffness is presented in the framework of hyperelasticity. A simple hyperelastic model, capable of reproducing variable stress-induced anisotropy of stiffness, is extended by replacement of the stress invariant with mixed stress–microstructure invariant to introduce constant inherent cross-anisotropic component. A convenient feature of the new model is low number of material constants directly related to the parameters commonly used in the literature. The proposed description can be incorporated as a small strain elastic core in the development of some more sophisticated hyperelastic-plastic models of overconsolidated soils. It can also be used as an independent model in analyses involving small strain problems, such as dynamic simulations of the elastic wave propagation. Various options and features of the proposed anisotropic hyperelastic model are investigated. The directional model response is compared with experimental data available in the literature.

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AbstractTime dependence of soft soils has already been thoroughly investigated. The knowledge on creep and relaxation phenomena is generally available in the literature. However, it is still rarely applied in practice. Regarding the organic soils, geotechnical engineers mostly base their calculations on the simple assumptions. Yet, as presented within this article, the rate-dependent behaviour of soft soils is a very special and important feature. It influences both the strength and the stiffness of a soil depending on time. It is, thus, significant to account for time dependence in the geotechnical design when considering the soft soils. This can result in a more robust and economic design of geotechnical structures. Hence, the up-to-date possibilities of regarding creep in practice, which are provided by the existing theories, are reviewed herein.In this article, we first justify the importance of creep effects in practical applications. Next, we present the fundamental theories explaining the time-dependent behaviour of organic soils. Finally, the revision of the existing constitutive models that can be used in numerical simulations involving soft soils is introduced. Both the models that are implemented in the commercial geotechnical software and some more advanced models that take into account further aspects of soft soils behaviour are revised. The assumptions, the basic equations along with the advantages and the drawbacks of the considered models are described.

The pure cross-anisotropy is understood as a special scaling of strain (or stress). The scaled tensor is used as an argument in the elastic stiffness (or compliance). Such anisotropy can be overlaid on the top of any elastic stiffness, in particular on one obtained from an elastic potential with its own stress-induced anisotropy. This superposition does not violate the Second Law. The method can be also applied to other functions like plastic potentials or yield surfaces, wherever some cross-anisotropy is desired. The pure cross-anisotropy is described by the sedimentation vector and at most two constants. Scaling with more than two purely anisotropic constants is shown impossible. The formulation was compared with experiments and alternative approaches. Static and dynamic calibration of the pure anisotropy is also discussed. Graphic representation of stiffness with the popular response envelopes requires some enhancement for anisotropy. Several examples are presented. All derivations and examples were accomplished using the algebra program Mathematica.