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Abstract

The ability to create realistic digital aggregates is the first step to computationally optimise civil engineering materials such as concrete, asphalt, or ballast, which are based on aggregates. A method to generate aggregates with realistic shapes has been created in a physics engine. The approach uses morphological properties of the aggregates as input parameters, such as the Perimeter, Area, and Weibull parameters of Minor Feret and Aspect Ratio, and consists of three major stages: (i) extraction of morphological information from real aggregates samples through digital image analysis; (ii) computational generation of 3D aggregates; and (iii) computational optimization of the aggregates via Differential Evolution methods. The efficiency of the method has been tested and validated by reproducing thousands of stones of 16 different types. The results indicate that the method can simulate aggregates, and a preliminary application indicates that these can be packed to obtain stone skeletons with realistic features.

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... This can be done by using imaging techniques, which capture the projection of aggregates to measure their shapes (Czajkowska et al. 2015). After, virtual geometries with shapes equivalent to rocks must be created (Garcia et al. 2020. Then, the rocks need to be compacted; see and the results compared to experiments, such as values from X-Ray Computed Tomography Scans (Yin et al. 2015, Yang et al. 2016. ...
... The diameter of one circle (x area ) which has the same area of that measured aggregate was also introduced to help describe aggregate's height (H v ). More details can be found in Garcia et al. 2020. ...
... Then, the prisms are deformed until their perimeter and area match those measured experimentally. The creation process is described clearly in (Garcia et al. 2020). Figure 1 shows an example of virtual granite aggre gates with a size of 14 mm. ...
... The minor Feret and aspect ratio are enough to characterise the dimensions of each particle projection [18]. The algorithm described in the previous section produces angular particles which minor Ferets and aspect ratios do not fit those of the actual aggregates. ...
... As it will be shown in the Results section, the aspect ratio and minor Feret of each aggregate type have been characterised using the Weibull distribution function, as it was done in [18]. This distribution is defined by two parameters, one of shape, k , and another one of scale, , which have been measured experimentally, see also Table 2. ...
... The minor Feret and Aspect Ratio data obtained from ImageJ have been analysed using the Anderson-Darling adjustment, which indicates the goodness-of-fit to a distribution curve; the closer the result is to zero, the better the fit of the curve to the data points [21]. Based on [18], a twoparameter Weibull distribution functions has been used to fit the minor Feret and Aspect Ratio. An example can be seen in Fig. 5, which shows the cumulative probabilities for the minor Feret of G1 aggregates. ...
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An algorithm to re-create virtual aggregates with realistic shapes is presented in this paper. The algorithm has been implemented in the Unity 3D platform. The idea is to re-create realistically the virtual coarse and crushed aggregates that are normally used as a material for the construction of roads. This method consists of two major procedures: (i) to combine a spherical density function with a noise matrix based on the Perlin noise to obtain shapes of appropriate angularity and, (ii) deform the shapes until their minor ferret, aspect ratio and, thickness are equivalent to those wanted. The efficiency of the algorithm has been tested by reproducing nine types of aggregates from different sources. The results obtained indicate that the method proposed can be used to realistically re-create in 3D coarse aggregates. Graphic abstract
... Several pieces of research have addressed this in the past. For example, [14,15] used a spherical harmonic function to create real-shaped aggregates based on reconstructed Computed Tomography (CT) scan images [16] assembled spheres to create realistic particles [17] used revolution solids to create particles [18] adjust the geometry of 2D projections obtained from CT scans until they matched aggregate distributions [19] adjust the geometry of a prism using a Perlin noise to produce realistic aggregate distributions. ...
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Aggregate skeleton in asphalt concrete mixtures plays a significant role in the pavement performance. However, the mechanical roles for different-sized particles in the aggregate skeleton have not been fully revealed due to the limitations of physical techniques. This study utilizes a numerical simulation approach to evaluate aggregate structure characteristics and their resistance to deformation. Using the discrete element method (DEM), a three-dimensional (3D) aggregate blend was generated with due consideration of the gradation. The blend was employed to simulate the penetration test of aggregate blends with different friction coefficients of 0.1, 0.2, 0.3, 0.4 and 0.5, respectively. The determination of the friction coefficient and the validation of DEM model were further conducted by laboratory experiments. Using the validated DEM model, penetration tests of five uniform blends and nine graded blends were simulated. External applied force (i.e., penetration force), penetration displacement, contact force, contact number and force taken by aggregate particles of different sizes were calculated using the DEM simulation to explore the mechanical characteristics of aggregate particle. This study demonstrated that the aggregate size plays an important role on the mechanical performance of aggregate skeleton. The results of this research can be applied to optimize the mix design of asphalt concrete and to further improve the aggregate gradation design.
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This paper presents a study of the micromechanical behaviour of crushable soils. For a single grain loaded diametrically between flat platens, data are presented for the tensile strengths of particles of different size and mineralogy. These data are shown to be consistent with Weibull statistics of brittle fracture. Triaxial tests on different soils of equal relative density show that the dilatational component of internal angle of friction reduces logarithmically with mean effective stress normalized by grain tensile strength. The tensile strength of grains is also shown to govern normal compression. For a sample of uniform grains under uniaxial compression, the yield stress is related to the average grain tensile strength. If particles fracture such that the smallest particles are in geometrically self-similar configurations under increasing macroscopic stress, with a constant probability of fracture, a fractal geometry evolves with the successive fracture of the smallest grains, in agreement with the available data. A new work equation predicts that the evolution of a fractal geometry gives rise to a linear compression line when voids ratio is plotted against the logarithm of macroscopic stress, in agreement with published data.
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In current practice of mixture design, volumetric properties such as voids and binder content along with mechanical properties such as modulus or rutting resistance are used as the main quality indicators. Visualisation is an important tool that has not been widely used in asphalt mixtures. As part of the Reunion Internationale des Laboratoires et Experts des Materiaux activities, the aggregate structure has been identified as a possible important mixture characteristic in need of measuring and quantifying. This paper is a report on part of this effort. Software for processing and analysing two-dimensional images of asphalt concrete mixtures to provide information about the aggregate structure within a mix was developed. Images with accompanying volumetrics and gradation information can be processed with the software and a virtual sieve analysis of aggregates within the image is performed to verify a match with known measured gradations. Once images were successfully processed, analysis is performed to determine the number of contact points between aggregates as well as radial distribution and orientation of each aggregate. Segregation of aggregates within each specimen was also determined. Mixtures with a broad range of variables were compacted in the laboratory, using a number of compaction methods of various countries. In addition, mixtures with various nominal maximum aggregate sizes, aggregate type (limestone or gravel) and design ESALs (E-3 or E-10) were compacted in the US gyratory compactor, using two pressures (600 and 300 kPa) and two temperature levels (120°C and 60°C). Results indicate that the aggregate structure is affected by compaction methods and conditions although volumetrics are very similar. The results show that a fresh look at evaluating the aggregate structure within mixtures is required.
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The microfabric discrete element modeling (MDEM) approach is used herein to predict the asphalt mixture complex modulus in extension/compression across a range of test temperatures and load frequencies. The method allows various constitutive models to be employed to describe particle and interface properties, such as normal and shear stiffness and strength. An uncalibrated two-dimensional (2-D) model was developed, and complex modulus predictions were compared to theoretical bounds on moduli. As expected, the uncalibrated 2-D model underestimates the significant stiffening effects of the coarse aggregate skeletal structure and predictions are found to be near the lower theoretical bounds, well below experimentally determined moduli. A technique was developed to calibrate the MDEM model to experimental results by dilating aggregates to create additional aggregate contact, which is believed to be more representative of the actual three-dimensional behavior. This method is shown to provide better modulus estimates across a range of test temperatures and load frequencies compared to more traditional calibration methods. As future modeling efforts are extended to three dimensions, the degree of model calibration required should be greatly reduced.
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Granular materials occur almost everywhere in nature, and are actively studied in many fields of research, from food industry to planetary science. One approach to the study of granular media, the continuum approach, attempts to find a constitutive law that determines the material's flow, or strain, under applied stress. The main difficulty with this approach is that granular systems exhibit different behavior under different conditions, behaving at times as an elastic solid (e.g. pile of sand), at times as a viscous fluid (e.g. when poured), or even as a gas (e.g. when shaken). Even if all these physics are accounted for, numerical implementation is made difficult by the wide and often discontinuous ranges in continuum density and sound speed. A different approach is Discrete Element Modeling (DEM). Here the goal is to directly model every grain in the system as a rigid body subject to various body and surface forces. The advantage of this method is that it treats all of the above regimes in the same way, and can easily deal with a system moving back and forth between regimes. But as a granular system typically contains a multitude of individual grains, the direct integration of the system can be very computationally expensive. For this reason most DEM codes are limited to spherical grains of uniform size. However, spherical grains often cannot replicate the behavior of real world granular systems. A simple pile of spherical grains, for example, relies on static friction alone to keep its shape, while in reality a pile of irregular grains can maintain a much steeper angle by interlocking force chains. In the present study we employ a commercial DEM, nVidia's PhysX Engine, originally designed for the game and animation industry, to simulate complex granular flows with irregular, non-spherical grains. This engine runs as a multi threaded process and can be GPU accelerated. We demonstrate the code's ability to physically model granular materials in the three regimes mentioned above: (1) a static and steep granular pile; (2) granular flow with a complex velocity field; and (3) an agitated granular pile resulting in size based segregation. We compare our simulations to laboratory experiments in the first and third regimes, and to a known empirical constitutive law (Jop et al. 2006) in the second. We discuss application of this code in studies of several planetary systems, including analysis of the tensile strength of comets from evidence of tidal disruption, and bulking and banding on rubble-pile asteroids, as an indication of their seismic history.
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An effective computer generation method is presented in this paper to more perfectly and rapidly generate the random distribution domains with large numbers of grains (pores). At first, the geometries of heterogeneous grains and the stationary random distribution model with large numbers of grains are defined. Second, the effective computer generation method, including compactness algorithm and selection algorithm, is described in detail. Then the effectiveness of the generation method and the comparison with the take-and-place method are given, and some examples with different geometries of grains in 2- and 3-dimension cases are illustrated. The computer generation method in this paper has been applied to the computation of effective heat transfer behavior for the composites of the random distribution with large numbers of grains, and some numerical results are demonstrated. The generation method in this paper is able to make the generated samples hold better stochastic property, and it is also suitable to generating samples subjected to non-uniform probability model.
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The properties of composites made by placing inclusions in a matrix are often controlled by the shape and size of the particles used. Mathematically, characterizing the shape of particles in three dimensions is not a particularly easy task, especially when the particle, for whatever reason, cannot be readily visualized. But, even when particles can be visualized, as in the case of aggregates used in concrete, three-dimensional (3-D) randomness of the particles can make mathematical characterization difficult. This paper describes a mathematical procedure using spherical harmonic functions that can completely characterize concrete aggregate particles and other particles of the same nature. The original 3-D particle images are acquired via X-ray tomography. Three main consequences of the availability of this procedure are mathematical classification of the shape of aggregates from different sources, comparison of composite performance properties to precise morphological aspects of particles, and incorporation of random particles into many-particle computational models.
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Porous materials due to their complex geometry are difficult to be examined by FEM-based approaches and usually are simulated by simplified geometrical models. In the present paper a novel procedure for describing the solid geometry of open-cell foams is introduced, facilitating the establishment of a corresponding FEM model for simulating the material behavior in micro-tension. Open-cell Al-foams were fabricated using the polymer impregnating method. A serial sectioning image-based process is described to capture, reproduce and visualize the exact three-dimensional (3D) microstructure of the examined foam. The generated 3D geometry of the Al-foam, derived from the synthesis of digital cross sectional images of the foam, was appropriately adjusted to build a FE model simulating the deformation conditions of the Al-foam under micro-tension loads. The obtained results render possible the visualisation of the stress fields in the Al-foam, allowing for a full investigation of its mechanical behavior.
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Physical particle packing is becoming a hot topic in concrete technology as more and more types of granular materials are used in concrete either for ecological or for engineering purposes. Although various analytical methods have been developed for optimum mixture design, comprehensive information on particle packing properties is still missing, e.g. on the impact of the packing method on such properties. Computer simulation therefore provides a promising perspective for particle packing simulation. However, developing flexible algorithms for simulation of arbitrary shaped particle packing still remains a challenge for concrete researches. This study aim offers a solution for these problems. The strategy of simulating particles of arbitrary shape is based on an experimental approach to this problem. The simulation strategies are thereupon implemented into a DEM-based dynamic concurrent algorithm-based simulation (CAS) approach for particle packing. Finally, influences of particle shape, particle size and packing method on packing density are evaluated and discussed. This methodology renders possible producing virtual concrete on meso-level. In combination with FEM, the influence of particle packing on mechanical properties of concrete has been assessed in this way. In the same way the simulation of cement particle packing can be realized on micro-level. Upon simulation of hydration, the capacity of self-healing of cracks due to unhydrated cement is assessed by a DEM-based simulation system for different cement types and packing densities.
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