A deformação dos solos é, atualmente, objeto de intensas pesquisas em todo o mundo movidas pelas necessidades da engenharia geotécnica. Este trabalho, que aborda o tema nos aspectos teórico e experimental, inicia-se revendo as relações constitutivas elasto-plásticas e o modelo Cam-Clay, cuja formulação matemática é apresentada de um modo diferente do usual. O modelo é construído de forma sistêmica a partir das equações elasto-plásticas gerais. Na parte experimental investiga-se o comportamento de um solo siltoso remoldado, quando submetido a ensaios triaxiais com diferentes trajetórias de tensão após adensamento isotrópico. Por fim comparam-se resultados experimentais e teóricos. Conclui-se que o modelo comporta-se melhor nas trajetórias de tensão em que não há diminuição da tensão octaédrica, embora preveja deformações volumétricas exageradas. Por sua vez, nas trajetórias em que há diminuição da tensão octaédrica, a diferença entre o comportamento previsto e o observado é grande, revelando que o modelo não deve ser aplicado nesses casos. / Soil deformation is today a subject of intense research all over the world motivated by the necessities of the geotechnical engineering. This work, which approaches the theme in both theoretical and experimental aspects, reviews the elastoplastic constitutive relations and the Cam-Clay model, and examines the behavior of a remoulded silty soil when subjected to different stress paths. Following a brief exposition of some basic Continuum Mechanics concepts, the elastic and elastoplastic constitutive equations are presented in a general form, which serve as a basis for several soil models. After a discussion about soil behavior and its representation by models, the Cam-Clay mathematical formulation is presented in an unusual form: it begins with the general elastoplastic constitutive equations, the elastic stress-strain relation, the yield function and the hardening law being given. The plastic stress-strain relation in deduced. In the experimental part the behavior of a remoulded silty soil from the Escola Politécnica Foundation Experimental Field is investigated. Oedometric, isotropic and triaxial compression tests (that were performed as part of the research) are described and analysed. Among them the triaxial tests with different stress paths after isotropic consolidation constitute the principal subject of analysis. Finally the Cam-Clay equations are integrated along the tests stress paths and the experimental e theoretical results are confronted. The conclusions is that the model behaves better in stress paths where there is no octabedral stress reduction, although even then it predicts exaggerated volumetric strains. In its turn, in stress paths where there is an octahedral stress reduction the difference between predicted and observed behavior is large, revealing that the model should not be applied in such cases.

A deformação dos solos é, atualmente, objeto de intensas pesquisas em todo o mundo movidas pelas necessidades da engenharia geotécnica. Este trabalho, que aborda o tema nos aspectos teórico e experimental, inicia-se revendo as relações constitutivas elasto-plásticas e o modelo Cam-Clay, cuja formulação matemática é apresentada de um modo diferente do usual. O modelo é construído de forma sistêmica a partir das equações elasto-plásticas gerais. Na parte experimental investiga-se o comportamento de um solo siltoso remoldado, quando submetido a ensaios triaxiais com diferentes trajetórias de tensão após adensamento isotrópico. Por fim comparam-se resultados experimentais e teóricos. Conclui-se que o modelo comporta-se melhor nas trajetórias de tensão em que não há diminuição da tensão octaédrica, embora preveja deformações volumétricas exageradas. Por sua vez, nas trajetórias em que há diminuição da tensão octaédrica, a diferença entre o comportamento previsto e o observado é grande, revelando que o modelo não deve ser aplicado nesses casos. / Soil deformation is today a subject of intense research all over the world motivated by the necessities of the geotechnical engineering. This work, which approaches the theme in both theoretical and experimental aspects, reviews the elastoplastic constitutive relations and the Cam-Clay model, and examines the behavior of a remoulded silty soil when subjected to different stress paths. Following a brief exposition of some basic Continuum Mechanics concepts, the elastic and elastoplastic constitutive equations are presented in a general form, which serve as a basis for several soil models. After a discussion about soil behavior and its representation by models, the Cam-Clay mathematical formulation is presented in an unusual form: it begins with the general elastoplastic constitutive equations, the elastic stress-strain relation, the yield function and the hardening law being given. The plastic stress-strain relation in deduced. In the experimental part the behavior of a remoulded silty soil from the Escola Politécnica Foundation Experimental Field is investigated. Oedometric, isotropic and triaxial compression tests (that were performed as part of the research) are described and analysed. Among them the triaxial tests with different stress paths after isotropic consolidation constitute the principal subject of analysis. Finally the Cam-Clay equations are integrated along the tests stress paths and the experimental e theoretical results are confronted. The conclusions is that the model behaves better in stress paths where there is no octabedral stress reduction, although even then it predicts exaggerated volumetric strains. In its turn, in stress paths where there is an octahedral stress reduction the difference between predicted and observed behavior is large, revealing that the model should not be applied in such cases.

The mechanical behaviour of geomaterials (e.g. soils, rocks and concrete) under plastic deformation is highly complex due to that fact that they are granular materials consisting of discrete non-uniform particles. Failure of geomaterials is often related to localisation of deformation (strain-localisation) with excessive shearing inside the localised zones. The microstructure of the material then dominates the material behaviour in the localised zones. The formation of the localised zone (shear band) during plastic deformation decreases the material strength (softening) significantly and initiates the failure of the material. There are two main approaches to the numerical modelling of localisation of deformation in geomaterials; discrete and continuum. The discrete approach can provide a more realistic material description. However, in the discrete approach, the modelling of all particles is complicated and computationally very expensive for a large number of particles. On the other hand, the continuum approach is more flexible, avoids modelling the interaction of individual particles and is computationally much cheaper. However, classical continuum plasticity models fail to predict the localisation of deformation accurately due to loss of ellipticity of the governing equations, and spurious mesh-dependent results are obtained in the plastic regime. Generalised plasticity models are proposed to overcome the difficulties encountered by classical plasticity models, by relaxing the local assumptions and taking into account the microstructure-related length scale into the models. Among generalised plasticity models, Cosserat (micropolar) and stain-gradient models have shown significant usefulness in modelling localisation of deformation in granular materials in the last few decades. Currently, several elastoplastic models are proposed based on Cosserat and strain-gradient theories in the literature. The individual formulation of the models has been examined almost always in isolation and are paired with specific materials in a mostly arbitrary fashion. Therefore, there is a lack of comparative studies between these models both at the theory level and in their numerical behaviour, which hinders the use of these models in practical applications. This research aims to enable broader adoption of generalised plasticity models in practical applications by providing both the necessary theoretical basis and appropriate numerical tools. A detailed comparison of some Cosserat and strain-gradient plasticity models is provided by highlighting their similarities and differences at the theory level. Two new Cosserat elastoplastic models are proposed based on von Mises and Drucker- Prager type yield function. The finite element formulations of Cosserat and strain-gradient models are presented and compared to better understand their advantages and disadvantages regarding numerical implementation and computational cost. The finite elements and material models are implemented into the finite element program ABAQUS using the user element subroutine (UEL) and an embedded user material subroutine (UMAT) respectively. Cosserat finite elements are implemented with different Cosserat elastoplastic models. The numerical results show how the Cosserat elements behaviour in the plastic regime depends on the models, interpolation of displacement and rotation and the integration scheme. The effect of Cosserat parameters and specific formulations on the numerical results based on the biaxial test is discussed. Two new mixed-type finite elements as well as existing ones (C1, mixed-type and penalty formulation), are implemented with different strain-gradient plasticity models to determine the numerical behaviour of the elements in the plastic regime. A detailed comparison of the numerical results of Cosserat and strain-gradient elastoplastic models is provided considering specific strain-localisation problems. Finally, some example problems are simulated with both the Cosserat and strain-gradient models to identify their applicability.