Multiscale numerical modelling of internal erosion

SP Pirnia

In the proceedings of: GeoVancouver 2016: 69th Canadian Geotechnical Conference

Session: FUNDAMENTALS - VII Soil & Rock Mechanics

ABSTRACT: Continuum models, the most common type of numerical model for porous media in geotechnical engineering, tend to perform poorly when modelling phenomena that are essentially dependent on behaviour at the particle scale, such as internal erosion and filtration. The discrete nature of granular materials can be modelled through the Discrete Element Method (DEM). However, the number of particles that can be included in a DEM simulation is limited, thus restricting the volume of soil that can be modelled. The development of multiscale models combining continuum analyses and discrete elements is a promising research avenue to combine the advantages associated with both modelling scales. In this project, an interface between two codes was programmed to allow multiscale modelling. Through a JAVA class, the interface combines DEM modelling at the particle scale (open-source code YADE), with large scale modelling with the finite element method (commercial software package COMSOL). The interface between the two codes was validated with a simple example . A comparison of results for the coupled model and the analytical solution shows that the interface and its algorithm work properly. The paper also presents practical applications for the interface.

RÉSUMÉ: Les modèles numériques de type milieu continu, le type de modèle le plus commun pour les milieux poreux en géotechnique, sont peu efficaces pour la modélisation de phénomènes qui dépendent essentiellement du comportement , comme l'érosion interne et la filtration. La nature discrète des matériaux granulaire peut être modélisée Toutefois, le nombre de particules dans ce type de modèle est limité, tout comme le volume de sol qui est simulé. Le développement de modèles numériques multi-échelles qui combinent la modélisation par milieu continu et les éléments discrets est une avenue de recherche prometteuse qui permettrait de combiner les avantages associés aux deux échelles de modélisation. Dans ce projet, une interface entre deux codes a été programmée afin de permettre une modélisation multi-échelles. combine la modélisation à particules utilisant la méthode des éléments discrets (logiciel code source ouvert YADE), avec la modélisation échelle du milieu continu utilisant la méthode des éléments finis (logiciel commercial COMSOL). est validée avec un exemple simple basé sur la loi de Stokes. Une comparaison des résultats du modèle couplé et de la solution analytifonctionnent adéquatement. erface. INTRODUCTION Flow through granular materials, like the body of an earth dam, have conventionally been analysed within a continuum framework. Continuum models have had particular success in capturing some important aspects of porous media behaviour, such as seepage and stress-strain behaviour. Nevertheless, some phenomena, like internal erosion, derive from complex microstructural mechanisms at the particle level, and are difficult to model with continuum models. The discrete nature of soils is not taken into account explicitly in continuum models. To understand phenomena like internal erosion, the modelling should be done at the particle scale (Guo et al. 2014). The Discrete Element Method (DEM) is becoming increasingly common in geotechnical engineering (DEM is a numerical method for computing the motion and interaction of a large number of small particles. This approach considers explicitly each particle in a granular material hence it can simulate finite displacements and rotations of particles (Cundall et al. 1993). Besides the capability of DEM to simulate complex phenomena in granular materials, the main advantage of DEM compared with other methods is simplicity of governing equations and computational cycle. It has had outstanding success in reproducing the mechanical response of dry granular material at both the particle and continuum scales (e.g., O'Sullivan et al. (2008)). However, for most soil mechanic applications, it is not feasible to model large scale structures, like an earth dam, solely with DEM. The current practical limit on the number of particles in a model is around 100 000. For fine sand (d = 0.10 mm), this translates to a maximum model volume on the order of 70 mm3 for hexagonal close packing. As a consequence, to be included in the modelling of large scale applications, DEM must be coupled with continuum models in a multiscale analysis where small scale DEM simulations are conducted for selected nodes in the model. This type of multiscale hybrid model remains in development and has not seen widespread use in geotechnical practice. Meier et al. (2008, 2009) developed a coupled FEM-DEM model based on the assumption of restricted particle displacements at the microscale. This assumption leads to a mechanical behaviour that is stiffer and less dissipative. A coupled model aimed at monitoring strain localization problems based on the assumption of a

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