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On the Shape Simulation of Aggregate and Cement Particles in a DEM System Hindawi Publishing Corporation Advances in Materials Science and Engineering Volume 2015, Article ID 692768, 7 pages http://dx.doi.org/10.1155/2015/692768 Research Article On the Shape Simulation of Aggregate and Cement Particles in a DEM System Huan He,1,2 Piet Stroeven,2 Eric Pirard,3 and Luc Courard3 1 College of Architecture and Civil Engineering, Beijing University of Technology, Beijing 100122, China 2Faculty of Civil Engineering and Geosciences, Delft University of Technology, Stevinweg 1, 2628 CN Delft, Netherlands 3GeMMe (Minerals Engineering, Materials and Environment), University of Liege,` Chemin des Chevreuils 1, 4000 Liege,` Belgium Correspondence should be addressed to Huan He; [email protected] Received 30 April 2015; Revised 6 July 2015; Accepted 7 July 2015 Academic Editor: Ana S. Guimaraes˜ Copyright © 2015 Huan He et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Aggregate occupies at least three-quarters of the volume of concrete, so its impact on concrete’s properties is significant. Both size and shape of aggregate influence workability, mechanical properties, and durability of concrete. On the other hand, the shape of cement particles plays also an important role in the hydration process due to surface dissolution in the hardening process. Additionally, grain dispersion, shape, and size govern the pore percolation process that is of crucial importance for concrete durability. Discrete element modeling (DEM) is commonly employed for simulation of concrete structure. To be able to do so, the assessed grain shape should be implemented. The approaches for aggregate and cement structure simulation by a concurrent algorithm-based DEM system are discussed in this paper. Both aggregate and cement grains were experimentally analyzed by X-ray tomography method recently. The results provide a real experimental database, for example, surface area versus volume distribution, for simulation of particles in concrete technology. Optimum solutions are obtained by different simplified shapes proposed for aggregate and cement, respectively. In this way, more reliable concepts for aggregate structure and fresh cement paste can be simulated by a DEM system. 1. Introduction The shape of cement particles plays also an important role in the hydration process due to surface dissolution in A particle is defined as the smallest discrete unit of a powder the hardening process. Additionally, grain dispersion, shape, mass that cannot be easily subdivided [1]. The shapes of real and size govern the pore percolation process that is of crucial particles are irregular from coarse aggregate to a mineral importance for concrete durability [2]. Cement hydration admixture in concrete. Aggregate occupies at least three- in a DEM approach renders the possibility of investigating quarters of the volume of concrete, so its impact on concrete’s microstructure development and resulting properties of con- properties is significant. The sieve curve traditionally defines crete. A digital image-based model [3]aswellascontinuum the aggregate size range. Another essential property is grain models [4–6] has been developed for this purpose. Apart shape. Both size and shape influence compactability and from the digital image-based model, particle shape is gener- workability in the fresh state and the mechanical and durabil- allyassumedtobespherical,becauseofinherentsimplifica- ity properties of the hardened concrete. The definition of the tion in algorithm formulation, however, at the cost of biases actual grain shape as well as the representation in a discrete in the simulation results. Recently, some reference cement element modeling (DEM) system is complicated, however. and aggregate materials were analyzed by microtomography Furthermore, the real shape of aggregate or binder particles (CT) and X-ray tomography (CT), respectively [7, 8]. The can vary widely. The sphere is therefore generally adopted results provide real experimental databases of aggregate and in conventional simulation systems in concrete technology cement grains, providing valuable parameters for the DEM that are mostly of random sequential addition (RSA) nature, simulation. This is even more so, since traditional shape despite imposing serious limitations and biases. analysis methods, for example, manual measurement or 2 Advances in Materials Science and Engineering Gravel Ellipsoids Aggregate Crushed rock Polyhedra Figure 1: Simulation strategy of arbitrary shaped aggregate: (top) differently shaped ellipsoids represent river gravel; (bottom) differently shaped polyhedrons represent crushed rock. experimental techniques in building codes such as ASTM generation of the particles and interparticle computational D-3398-97, cannot provide sufficient information for particle requirement [10]. reconstruction in the DEM systems. The involved experimen- As a practical example, a series of regular polyhedrons tal difficulties would be even greater for very fine particles with 4 to 8 facetted surfaces were employed to represent such as cement grains. Simulation of concrete by a DEM crushed rock aggregate as used in railroad beds [11]. This system requires a large number of particles with different greatly simplifies the simulation, since only the two param- sizes to guarantee the RVE demand. They will inevitably also eters should be specified, that is, the sieve size and the have different shapes. However, giving all particles individual maximum size of the surface element. Figure 2 presents the shapes in DEM would be too expensive and (computer) meshed particles of the regular polyhedrons employed in this time-consuming for solving practical engineering problems study. The volume fraction of each type of polyhedron is taken [9]. Therefore, a practical strategy is to select a single shape similartothatfoundinthefieldstudyofGuo[11]. parameter, or eventually a limited number of typical shapes Recently, in a study of Erdogan et al. [8], the shapes of four to represent a particles mixture. different types of aggregate, denoted by GR, LS, IN, andAZ, In this paper, simulation strategies are presented for the wereinvestigatedbytheCTmethodandreconstructedbythe representation of real aggregate and cement grains in con- spherical harmonic (SH) technique [8]. The most interesting crete technology. This simulation approach is incorporated in information coming from this shape analysis is the global a physical concurrent algorithm-based DEM system, that is, surface area ()tovolume() curve of each type of aggregate. HADES. The system is developed for making more realistic Afunction= was used to represent the versus curve packing simulations by using nonspherical particles. It is for each type of aggregate [8]. The coefficients and were based on a contact mechanism that evaluates the interaction assessed for all cases and are listed in Table 1 [8]. The variances forces exerted between segmented surfaces of neighboring of the regression approximations were exceeding 0.98 in all particles. It can provide packing densities up to the dense cases. 2/3 random packing state relevant for the present purposes. More The regression function = was employed to detailed information about the system can be found in [10]. fit the different types of aggregate. Next, is determined 3 A practical shape analysis study is conducted on the basis of (volume < 4000 mm ) with a variation lower than 5% for each CT and CT results available in the international literature type of aggregate, as given in Table 1.Acommonshapeindex [7, 8]. Specific simulation strategies could be proposed for like sphericity is finally determined for each type of aggregate both aggregate and cement particle simulation. by 2/3 ( / ) −1 2. Shape Simulation of Aggregate Grains = eq.sphere = 4 3 4 = . () Sphericity 2/3 4 836 (1) particle Aggregate in concrete can be divided into two groups, that is, gravel of fluvial origin and crushed rock, representing in which is the coefficient in the above-mentioned relation- 2/3 rounded and angular-shaped particles, respectively, as shown ship of versus . Sphericity is defined as the surface area in Figure 1. The ellipsoid was selected to represent the ratio of the equivalent sphere and the real particle, so both river gravel particles, whereas the polyhedron was used for having equal volume. The sphericity values are also listed in simulation of crushed rock grains. The surface of these model Table 1.Obviously,thecrushedrocktypesGRandLScannot particles is tessellated by a mesh positioned on the grains’ be distinguished by means of sphericity. The natural river surfaces. The mesh should be fine enough for a proper gravel types IN and AZ have a relatively larger sphericity, as Advances in Materials Science and Engineering 3 III I II Tetrahedron Pentahedron Hexahedron II I II I Heptahedron Octahedron Figure 2: Nine regular polyhedra with facet numbers 4∼8. Table 1: - correlation coefficients found by Erdogan et al. [8] for four types of aggregate: and are from =, while coefficient is 2/3 from = . Sphericity is calculated by (1). 2 Aggregate type Coefficient Coefficient Variance Coefficient Sphericity GR 8.1 0.63 0.99 6.13 0.79 LS 7.5 0.64 0.997 6.12 0.79 IN 8.6 0.62 0.99 6.06 0.80 AZ 9.1 0.61 0.98 5.95 0.81 Table 2: Shape indices of the regular polyhedra, appropriate proportions according to Guo [11], and revised proportions for better overall simulation results. Shapes Facet number Sphericity Proportion by Guo [11] Revised proportion Tetrahedron 4 0.67 7.21 10.0% 5% Pentahedron I 5 0.70 6.95 12.5% 5% Pentahedron II 5 0.72 6.71 12.5% 5% Hexahedron I (cube) 6 0.81 6.00 17.5% 10% Hexahedron II 6 0.76 6.39 17.5% 10% Heptahedron I 7 0.83 5.83 10.0% 15.5% Heptahedron II 7 0.80 6.06 10.0% 15.5% Octahedron I 8 0.85 5.72 5.0% 17% Octahedron II 8 0.78 6.24 5.0% 17% Sphere ∞ 1.00 4.84 — — could be expected. But sphericity seems not very effective in in Figure 3. Generally speaking, Guo’s proposal fits the data of distinguishing between actual shapes.
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