Packing Density Of Binary Mixtures Research Articles

Effect of surface texture, size ratio and large particle volume fraction on packing density of binary spherical mixtures

Packing density is a key factor in governing the properties of materials such as concrete, asphalt, ceramic etc. Therefore, determination of packing density of a particulate mixture accurately, is of great importance. However, involvement of many external and internal factors such as surface texture, shape, method of packing etc. has made it very complicated and tedious to determine the packing density. The study investigated the combined effect of particle surface texture, size ratio and large particle volume fraction on packing density and developed a descriptive model to predict the packing density. Further, design graphs were also developed for the convenience. The study revealed that the British pendulum number value of the surface texture linearly varies with the packing density. The rougher the surface, the lower the packing density. The interparticle friction hinders the particle rearrangement. Hence, the ability to achieve a higher packing state is reduced. Further, irregularities in the surface boundary create void spaces, increasing the total voids in the mix. Thus, the packing density reduces. The increase of the size ratio decreases the packing density linearly. The packing density variation with a large particle volume fraction follows a 3rd order polynomial curve. The trend analysis was conducted to develop the descriptive model and design graphs to predict the packing density of binary mixtures.

A new framework for understanding aggregate structure in asphalt mixtures

ABSTRACT Aggregate size distribution is an important parameter in asphalt mixture design and performance. The main objective of this study is to develop a framework to define the aggregate structure of asphalt mixtures when fine and coarse aggregate stockpiles are blended. To develop this framework, an analytical model for binary mixtures is proposed. The model considers the effect of size ratio and air volume between the particles on the aggregate structure and packing density of binary mixtures. Based on this model, three aggregate structures, namely coarse pack (CP), dense pack (DP) and fine pack (FP), are defined. The model is validated using a series of 3D discrete element simulation. Furthermore, the simulation of multi-sized aggregate blends using two representative sizes for fine and coarse stockpiles was carried out to apply the proposed analytical model to actual aggregate blends. In order to assess how well the model applies to asphalt mixtures, compaction parameters including compaction slope (CS), initial density (N ini), locking point and compaction energy index (CEI) were analyzed. The numerical simulations verify the proposed analytical model can satisfactorily determine the particle structure of binary and multi-sized asphalt mixture gradations and can be used to better design asphalt mixtures for improved performance.

A Theoretical Packing Density Model (TPDM) for ordered and disordered packings

In previous papers, the 4-parameter Compressible Packing Model (CPM) was theoretically developed and validated for the packing density of binary mixtures of spheres and crushed aggregate particles. The 4-parameter CPM is now called the Theoretical Packing Density Model (TPDM). The TPDM is a self-consistent packing density model which is now validated for both disordered and ordered packings. Thanks to the compaction index K which is representative of the packing process efficiency and thanks to the critical cavity size ratio from which the loosening effect appears, the TPDM is successfully applied to densest binary crystalline structures (K = 100) and to disordered ternary mixtures of spherical, round aggregate and crushed aggregate particles (from K = 4.7 to K = 15). The critical cavity size ratio can be selected in the range between 0 for irregular particles with strong surface roughness and 0.2 for frictionless spherical particles. The TPDM predictions are excellent for the peak packing density obtained for each of the densest binary crystalline structures identified. The TPDM also proves its efficiency for disordered ternary mixtures from the analysis of 408 results published in the literature when compared with the PAL (Prior, Almeida, Loureiro) model and with the 3-parameter Particle Packing Model (3PPM, Kwan et al.). The question of optimization of ternary mixtures is finally addressed. A simplified model is proposed for the purpose of building the densest ternary mixture. The analytical expressions for the highest packing density and for the corresponding volume fractions of each granular class are established. Thanks to its theoretical wall effect and loosening effect functions, the TPDM appears to be a useful tool for optimizing the granular skeleton in all circumstances: whatever its packing process (simple pouring or highly sophisticated packing process) and whatever the material (crushed aggregate particles with strong surface roughness or frictionless spherical particles).

Effect of the particle size ratio on the structural properties of granular mixtures with discrete particle size distribution

In this study, the discrete element method was used to examine the structural properties and geometric anisotropy of polydisperse granular packings with discrete uniform particle size distributions. Confined uniaxial compression was applied to granular mixtures with different particle size fractions. The particle size fraction (class) was defined as the fraction of the sample composed of particles with a certain size. The threshold value of number of particle size fractions (i.e., the value above which structural properties of assemblies remain constant) was determined. The effect of heterogeneity in particle size on the critical value of number of particle size fractions was investigated for packings with different ratios between diameters of the largest and smallest grains. The threshold number of particle size classes decreased from five to three as the diameter ratio between the largest and smallest grains increased. Regardless of the diameter ratio, the critical number of particle size fractions (above which the packing density and coordination number of the granular mixtures remained constant) was determined to be five. The study has also shown an increase in packing density of binary mixtures with particle size ratio increasing up to 2.5, which was followed by decrease in density of mixtures with larger particle size ratios, which has not so far been reported in the literature.

The 4-parameter Compressible Packing Model (CPM) for crushed aggregate particles

The 4-parameter Compressible Packing Model (CPM) has been developed to predict the packing density of binary mixtures of spherical particles. The four parameters are: the loosening effect parameter a, the wall effect parameter b, the compaction index K and a critical cavity size ratio x0. The two geometrical interactions have been studied theoretically on the basis of a spherical cell centered on a secondary class bead. For the loosening effect, the critical cavity size ratio x0, below which a fine particle can be inserted into a small cavity created by touching coarser particles, is introduced. This is the only parameter which requires adaptation to extend the model to crushed aggregate particles. The 4-parameter CPM proves its efficiency from the analysis of 334 results published in the literature: correlation coefficient is 96.6% and mean absolute deviation is 0.009. By comparison with the original CPM (with a, b, K incorporated) and the 3-parameter model (with a, b and wedging effect parameter c), it is the most accurate and widely applicable. It opens industrial perspectives in high performance concrete, roller-compacted concrete for dams and road construction layers.

The 4-parameter Compressible Packing Model (CPM) including a new theory about wall effect and loosening effect for spheres

A new version of the Compressible Packing Model (CPM) (de Larrard et al.), the 4-parameter CPM, is introduced to predict the packing density of maximally dense disordered packings of bidisperse spherical particles. Based on the assumption of a dominant granular class, it takes into account the packing process efficiency and two geometrical interactions objects of a new theory: the wall effect and the loosening effect. For the latter, a critical cavity size ratio, below which a fine bead can be inserted into a small cavity created by touching coarser particles, is introduced. When the packing process is perfect, the packing density reaches a maximum virtual density defined as the maximum packing density attainable for a given mixture. In this reference frame, the theory for wall effect and loosening effect is based on a specific treatment of configurations of one secondary class particle surrounded by dominant class neighbours. The four parameters are: the wall effect and the loosening effect coefficients, the compaction index and the critical cavity size ratio which can be adjusted for aggregates, but whose value is 0.2 for spheres, in harmony with the tetrahedral cavern theory. The 4-parameter CPM demonstrates its efficiency to predict packing density of binary mixtures from the analysis of 320 results. Correlation coefficients are 99% for glass beads (300 values) and 98.7% for numerically simulated spherical particles (20 values).

Shape and size effects on the packing density of binary spherocylinders

The shape and size of particles are the main factors which influence the packing density of binary mixtures. However, investigations of the single effect of size and shape on the binary mixtures of non-spherical particles are much absent. A systematic computational investigation on the binary packing of spherocylinders considering the single effect of shape and size respectively is carried out with the sphere assembly models and relaxation algorithm. Random packings of binary spherocylinders with the same volume, aspect ratio and diameter are simulated numerically to investigate the single effect of shape, size and their combination respectively. The shape effect is observed to present a linear relationship between the packing density and the volume fraction, while the size effect shows a trend of convex. The combined effect, as the case of the same diameter, can be considered as a linear superposition of the shape and size effect, since we find the particle size and shape determine the mixture density independently with no coupling terms. Accordingly, we propose an explicit empirical formula for evaluating the mixture density of binary spherocylinders, and the predicted densities agree well with the simulation results and previous empirical formula in all the cases of the same volume, aspect ratio and diameter, as well as some general cases. For verification, the monophasic packings of spherocylinders are simulated and the results coincide with previous works.

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

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.