Representação Matemática do Comportamento Mecânico Cíclico de Solos Saturados e não Saturados / Mathematical Representation of the Cyclic Mechanical Behaviour of Saturated and Unsaturated Soils

AUTOR(ES)
DATA DE PUBLICAÇÃO

2006

RESUMO

Granular materials, such as soils, exhibit a relatively complex mechanical behaviour. Usually, the mechanical behaviour of soils is studied with the aid of the Continuum Mechanics. Materials under cyclic loadings exhibit a dierent mechanical behaviour, with respect to monotonic loadings. The mathematical theory of elastoplasticity has been employed to the numerical simulation of the behaviour of soils. For cyclic loadings, the concept of subloading is a useful tool to represent the elastic-plastic transition. The concept of internal variables is essential to the elaboration of laws which memorize the internal features of the material. The resulting equations form a Dierential Algebraic System (DAS) which may be solved by the Runge-Kutta method. Four schemes are analysed: a) the explicit rst order Forward-Euler (FE); b) the implicit rst order Backward-Euler (BE); c) the explicit second order Modied-Euler (ME); and c) the explicit fth order Runge-Kuta-Dormand-Prince (RKDP). The embedded Runge-Kutta schemes, like ME and RKDP, are useful to the elaboration of algorithms which automatically determine the substep size. These substeps are necessary to increase the accuracy and, in the case of BE scheme, to assure the convergence. Failure criteria are considered by constitutive models. For soils, the Mohr-Coulomb, Lade-Duncan and Matsuoka-Nakai are commonly adopted. The Matsuoka-Nakai criterion may be considered by means of an equation presented by Sheng et al. (2000) and which has roots in a work of Argyris et al. (1974). Two new criteria are presented: one for isotropic materials, with similar characteristics to that of Lade-Duncan criterion, and other for materials with inherent and/or induced anisotropy. The Evolutionary Genetic Algorithm (EGA) is employed to the determination of constitutive parameters. For that, the parameters are grouped into individuals by means of representation functions. The evolution of individuals leads to the best parameters for a set of experimental results. Islands of individuals help to keep the diversity of individuals. The subloading tij model (Subtij) of Nakai &Hinokio (2004) is reviewed and its equations are deduced under the framework of elastoplasticity. Therefore, the solution of the corresponding DAS may be done with Runge-Kutta schemes. A new model for saturated soils subjected to cyclic loadings is introduced. This model, named Subloading Cam-clay (SubCam), was originated with some ideas of the Subtij model and considering the subloading concept. The SubCam model can represent the cyclic behaviour of soils. Two models for unsaturated soils are presented. The rst one, named Extended Barcelona (BarcelonaX) is a simple extension to Barcelona model (BBM) of Alonso et al. (1990), which has the same characteristics of BBM, with the exception of the shear strength representation. This considers the inuence of Lode angle, similarly to Matsuoka-Nakai criterion. The second model, named Subloading Barcelona (SubBar), is an extension to the BarcelonaX model which adds the concept of subloading, therefore, this model is able to represent the cyclic behaviour. BarcelonaX model adds a new parameter to control the unique surface in the stress/suction space and SubBar model adds two new parameters to control the decrease of exibility due to suction and/or stress cycles. viii

ASSUNTO(S)

geociencias carregamentos cíclicos solos não saturados modelagem constitutiva integração numérica

ACESSO AO ARTIGO

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