Numerical validation of a population balance model describing cement paste rheology

Rheology control is essential during the period in which cement and concrete pastes are encountered in the fresh state, due to the fact that it directly affects workability, initial placement and the structural performance of the hardened material. Optimizations of clinker formulations and reductions in cement-to-water ratios induced by economic and environmental considerations have a significant effect in rheology, which invokes the need for mechanistic models capable of describing the effect of multiple relevant phenomena on the observed paste flow. In this work, the population balance framework was implemented to develop a model able to relate the transient microstructural evolution of cement pastes under typical experimental conditions with its macroscopic rheological responses. Numerical details and performance are assessed and discussed. It was found that the model is capable of reproducing experimentally observed flow curves by using measured cluster size distribution information. It is also able to predict the complex rheological characteristics typically found in cement pastes. Furthermore, a spatially resolved scheme was proposed to investigate the nature of flow inside a parallel-plates rheometer geometry with the objective of assessing the ability of the model of qualitatively predicting experimentally observed behavior and to gain insight into the effect of possible secondary flows

Finite volume approach for fragmentation equation and its mathematical analysis

peer-reviewedThis work is focused on developing a finite volume scheme for approximating a fragmentation equation. The mathematical analysis is discussed in detail by examining thoroughly the consistency and convergence of the numerical scheme. The idea of the proposed scheme is based on conserving the total mass and preserving the total number of particles in the system. The proposed scheme is free from the trait that the particles are concentrated at the representative of the cells. The verification of the scheme is done against the analytical solutions for several combinations of standard fragmentation kernel and selection functions. The numerical testing shows that the proposed scheme is highly accurate in predicting the number distribution function and various moments. The scheme has the tendency to capture the higher order moments even though no measure has been taken for their accuracy. It is also shown that the scheme is second-order convergent on both uniform and nonuniform grids. Experimental order of convergence is used to validate the theoretical observations of convergence

A comparative study of numerical approximations for solving the Smoluchowski coagulation equation

In this work, numerical approximations for solving the one dimensional Smoluchowski coagulation equation on non-uniform meshes has been analyzed. Among the various available numerical methods, finite volume and sectional methods have explicit advantage such as mass conservation and an accurate prediction of different order moments. Here, a recently developed efficient finite volume scheme (Singh et al., 2015) and the cell average technique (Kumar et al., 2006) are compared. The numerical comparison is established for both analytically tractable as well as physically relevant kernels. It is concluded that the finite volume scheme predicts both number density as well as different order moments with higher accuracy than the cell average technique. Moreover, the finite volume scheme is computationally less expensive than the cell average technique

Grading evolution and critical state in a discrete numerical model of Fontainebleau sand

Granular materials reach critical states upon shearing. The position and shape of a critical state line (CSL) in the compression plane are important for constitutive models, interpretation of in situ tests and liquefaction analyses. It is not fully clear how grain crushing may affect the identification and uniqueness of the CSL in granular soils. Discrete-element simulations are used here to establish the relation between breakage-induced grading evolution and the CSL position in the compression plane. An efficient model of particle breakage is applied to perform a large number of tests, in which grading evolution is continuously tracked using a grading index. Using both previous and new experimental results, the discrete-element model is calibrated and validated to represent Fontainebleau sand, a quartz sand. The results obtained show that, when breakage is present, the inclusion of a grading index in the description of critical states is advantageous. This can be simply done using the critical state plane (CSP) concept. A CSP is obtained for Fontainebleau sand.Peer ReviewedPostprint (author's final draft

Discrete modelling of capillary mechanisms in multi-phase granular media

A numerical study of multi-phase granular materials based upon micro-mechanical modelling is proposed. Discrete element simulations are used to investigate capillary induced effects on the friction properties of a granular assembly in the pendular regime. Capillary forces are described at the local scale through the Young-Laplace equation and are superimposed to the standard dry particle interaction usually well simulated through an elastic-plastic relationship. Both effects of the pressure difference between liquid and gas phases and of the surface tension at the interface are integrated into the interaction model. Hydraulic hysteresis is accounted for based on the possible mechanism of formation and breakage of capillary menisci at contacts. In order to upscale the interparticular model, triaxial loading paths are simulated on a granular assembly and the results interpreted through the Mohr-Coulomb criterion. The micro-mechanical approach is validated with a capillary cohesion induced at the macroscopic scale. It is shown that interparticular menisci contribute to the soil resistance by increasing normal forces at contacts. In addition, more than the capillary pressure level or the degree of saturation, our findings highlight the importance of the density number of liquid bonds on the overall behaviour of the material

Packing Characteristics of Different Shaped Proppants for use with Hydrofracing - A Numerical Investigation using 3D FEMDEM

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