Barodesy is a constitutive model based on proportional paths and the asymptotic behaviour of soil. It was originally developed for sand in 2009 by Kolymbas, and a version for clay was introduced in 2012. A shortcoming of former barodetic models was that tensile stresses can occur for certain dilative deformations. In this article, an improved version of barodesy for clay and a simplified calibration procedure are proposed. Basic features are shown, and simulations of element tests are compared with experimental data of several clay types.

Asymptotic behaviour of soil deserves particular attention: If soil is deformed with a proportional strain path, the resulting stress path approaches asymptotically a proportional stress path. In this arcticle, we review existing experimental evidence on this phenomenon and discuss it in the frame of barodesy. Here, the presented relation is a modification of a barodetic expression and includes Jáky's relation, inhibits tensile stress and is able to predict asymptotic stress ratios based on experimental findings. The proposed relation is compared with experimental data as well as with the so-called stress-dilatancy relations and other constitutive relations proposed so far.

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Summary The intergranular strain concept was originally developed to capture the small‐strain behaviour of the soil with hypoplastic models. A change of the deformation direction leads to an increase of the material stiffness. To obtain elastic behaviour for smallstrains, only the elastic part of the material stiffness matrix is used. Two different approaches for an application of this concept to nonhypoplastic models are presented in this article. These approaches differ in the determination of the elastic stress response, which is used for reversible deformations. The first approach determines an elastic response from the original material model, and the second one uses an additional elastic model. Both approaches are applied on barodesy. The simulations are compared with experimental results and with simulations using hypoplastic models with the original intergranular strain concept.

SUMMARYThis article is an attempt at providing an insight into the development of hypoplasticity (including barodesy, which is a recent development of hypoplasticity) as a theory elaborated since 1977, when the first version was published by the first author, until present. The multiplicity of the many versions published since then is hard to overlook. This article presents a review and insight into the evolution of a theory and the struggle to formulate a satisfactory constitutive law. Among the many proposed versions, we focus on those ones that can be seen as changes of paradigm. Copyright © 2016 John Wiley & Sons, Ltd. ON THE DIVERSITY OF CONSTITUTIVE MODELSA constitutive law (or 'constitutive relation' or 'constitutive model') is a theory that describes the mechanical behaviour of a material or class of materials, in our case, soil (and other granular materials). Some scientific communities use the alternative term 'closure equation', as a constitutive equation provides the missing link that is needed next to the balance laws of physics to solve a boundary value problem. Being a theory, a constitutive law is virtually an assumption that can be used as long as it has not been disproved. It is, however, not so straightforward to judge upon falsification of a theory. In the realm of physics, mechanics and, in our case, soil mechanics, theories have always a limited range of validity. Thus, the question whether a particular experimental outcome discredits a theory or not can also be considered as the question whether this outcome falls within the range of validity of the considered theory. Moreover, there is always a deviation between theoretical predictions and experimental outcomes. It is often a subjective judgement whether a deviation is considered as small or large. For these reasons, a constitutive law cannot be simply rated as 'right' or 'wrong', there are many nuances between these attributes. In case a constitutive law provides a prediction judged as non-satisfactory, the question arises whether the shortage can be removed by a modification or it is due to an inherent conceptual failure of the underlying theory. Thus, theories can be either modified or abandoned and replaced by completely new ones.The emergence of a new version not only signifies an improvement but also blames the precedent version for inadequacy. It underlines thus the feeling that a constitutive relation does not mirror a permanent truth. Similar mixed feelings are evoked whenever a new operational system is launched for our computer: the expectation of improved performance is counterbalanced by the displeasure for the necessary rearrangements. In the end, we should realize that perfection is achievable neither for operational systems nor for constitutive relations. The possibility of modifications proves, however, that a given system or theory can still be useful.It should be mentioned that we have refrained from assessing each version by mentioning its advantages and disadvantages, as this would render the paper overly long and is ...

Barodesy is a new hypoplastic frame for constitutive models to describe granular materials. It has already been introduced for sand, and this article adjusts barodesy for clay. Common concepts of soil mechanics, such as critical states, barotropy (i.e. the dependence of stiffness and strength on the stress level), pyknotropy (i.e. the dependence of stiffness and strength on density) and a stressdilatancy relation can easily be included in the presented model. Despite its mathematical simplicity, barodesy is able to describe many aspects of clay behaviour. Only four material constants are required, which can be determined by means of a single consolidated undrained triaxial test.

Die Wahl eines passenden Materialmodells, das in der Lage ist, das Bodenverhalten bei FE‐Berechnungen realistisch darzustellen, hat einen maßgeblichen Einfluss auf die dabei erhaltenen Berechnungsergebnisse. Anhand von Vergleichsrechnungen mit mehreren Materialmodellen sollen die Gemeinsamkeiten und Unterschiede bei den Ergebnissen verdeutlicht werden. Hierfür wird ein Baugrubenaushub simuliert und sowohl die auftretenden Verformungen als auch die mittels Parameterreduktion ermittelte Standsicherheit betrachtet. Dabei wird neben den bekannteren Modellen Hardening Soil und der Hypoplastizität die Barodesie als Modell für FE‐Berechnungen vorgestellt. Während sich bei allen Modellen vergleichbare Verformungen einstellen, werden bei der berechneten Standsicherheit deutliche Unterschiede festgestellt.

With constant stretching of soil, the memory is gradually swept out and the so-called asymptotic states are reached: asymptotic states are proportional stress paths as well as particular curves in the void ratio against the mean stress plane. The so-called asymptotic state boundary surface (ASBS) serves as a graphical representation for asymptotic states. In contrast to asymptotic states, peak states of drained triaxial tests are states with vanishing stiffness. In this paper, an explicit formulation of the ASBS and peak state envelope of barodesy are introduced. Different clay types are compared with barodesy as well as with predictions by hypoplasticity. The peak states of the experiments confirm the results obtained with barodesy and hypoplasticity. It is shown that different to elastoplastic models, the ASBS does not include peak states in barodesy and hypoplasticity. In addition to standard axisymmetric simulations, investigations are also carried out in the deviatoric plane with the focus on plane strain failure.