A 3D semi-digital model for the placing of granular materials

Abstract

A 3D semi-digital model has been developed in order to simulate the gravitational placing of granular mixtures composed of spherical particles of different sizes allowing the optimization of mixtures proportions. The aim is to control concrete placing in formworks particularly in the presence of reinforcement bars. In this case, the representation of a large number of particles is necessary and segregation or wall effects have to be taken into account. Moreover, an easy representation of complex geometries and obstacles of arbitrary shapes should be possible. In order to respect these conditions, the used 3D semi-digital model is based on the digitization of a calculation volume and on the representation of spherical particles with real numbers. The model takes into account only steric repulsion between particles and simulates their collisions during placing by random displacements. The simplicity of the model allows the simulation of up to 2 million spherical particles without spending too much computational time. The model can therefore be used for the simulation of granular materials having a spread granulometry-like concrete. The packing density of binary mixtures of spherical particles with different size ratios and varying proportions of small and big particles is first studied. The results are compared successfully with theoretical packing density of binary mixtures without interactions. It is therefore demonstrated that the semi-digital model can be used for the simulation of binary mixtures having low size ratios (0.1), which corresponds approximately to the size ratio of fine and coarse aggregates in concrete. Secondly, digitized cylindrical obstacles are added in the systems with the aim to represent reinforcement bars in a formwork. The influence of small and big particles proportioning on the local packing density and the homogeneity of the mixture is studied. The results show that in the presence of obstacles, the optimum placing is obtained when the proportion of small particles in the mixture is higher than that without obstacles. This is due principally to the looser packing of big particles around obstacles.