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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
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1 3
Granular Matter (2021) 23:41
The spherical primitive andperlin noise method torecreate realistic
aggregate shapes
S.Michot‑Roberto1· A.Garcia‑Hernández1 · S.Dopazo‑Hilario2· A.Dawson1
Received: 4 October 2020 / Accepted: 24 February 2021 / Published online: 1 April 2021
© The Author(s) 2021
An algorithm to re-create virtual aggregates with realistic shapes is presented in this paper. The algorithm has been imple-
mented 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.
Keywords Aggregates· 3D virtual modelling· Morphological properties· Physics engines· Concavities
1 Introduction
In order to design civil engineering materials, such as
asphalt, with optimised workability, durability and mechani-
cal properties, it is of the foremost importance to understand
how size distribution and shape of aggregates influence their
porosity, stone interlock and amounts of asphalt binder or
mortar required for an effective binding action [1, 2].
In order achieve a proper design of aggregate-based
materials, the specifications allow ranges of gradations
and shapes of the particles. There is no standard to deter-
mine how particle changes influence the overall material
behaviour [3]. This is because laboratory studies of material
behaviour are expensive and time consuming. On the other
hand, most of the computer simulations of granular materials
at the scale levels, still have drawbacks such as generating
realistic randomized 3D particles, which are difficult to gen-
erate [46] and the computational cost involved in quantify-
ing the interaction between numerous particles [7, 8].
The first step to create computer simulations of aggregate-
based materials is to reproduce realistic aggregates virtually.
For example, [9] employed a spherical harmonic function to
reproduce over ten thousand of real-shaped aggregates based
on the reconstructed aggregate data by X-ray CT technology,
and further quantified their shape and size [10, 11]. [13]
created realistic particles by assembling spheres, which is
could be very costly computationally. [14] created angular
particles which, although appear realistic do not have mor-
phological properties, such as angularity or sphericity con-
trolled. [15] simulated aggregates using revolution solids.
[16] deformed aggregate projections obtained from a CT
Scan gradually, untilmatching with a target distribution.
Garcia etal. similarly, [13, 14, 17] were able to generate
aggregates with concavities by creating the particles based
on surface coordinates generated by a spherical harmonic
After the virtual aggregates are available, these need to be
packed. A very extended methodology to pack virtual aggre-
gates is the Discrete Element Modelling (DEM) method,
which considers a granular material’s discrete nature, has
limitations when it comes to incorporating particles with
realistic shapes. The reason is because it is computation-
ally expensive, since a granular assemblage is composed of
a multitude of particles interacting [5]. Many studies have
modelled packings of aggregates with realistic shapes, using
different Discrete Element Methods [1921]. However, the
* A. Garcia-Hernández
1 Nottingham Transportation Engineering Centre, Department
ofCivil Engineering, University ofNottingham,
NottinghamNG72RD, UK
2 XR-Project, Carrer Josep Vilaseca, 23. Cardedeu,
08440Barcelona, Spain
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S.Michot-Roberto et al.
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41 Page 2 of 11
computational cost of DEM is also very high. For that rea-
son, these authors propose to develop new techniques that
allow a realistic modelling of particle size and morphology,
for a better and deeper study on how they influence different
materials behaviour.
An alternative to DEM methods are Physics Engines,
which are mainly used in the videogame and animation
industry. These serve to perform simulations based on real
physics parameters. Examples of previous related works are
those from Peng Cao etal., who modelled convex polyhe-
drons as coarse aggregates [6] and created their convex hull
using the Quickhull algorithm [7]. Aggregate conglomerates
were created by importing the particles to the Physic Engine
SWIG-Bullet multi-body, based on the Monte Carlo method
[8]. Izadi etal. simulate pluviation phenomenon using the
Bullet physics engine as well [22]. The gravel was repre-
sented through randomly shaped polyhedrons, created with
the Voronoi’s tessellation [23]. Thus, it can be concluded
that a physics engine can be employed as a geotechnical
engineering simulation tool. In addition, Garboczi etal. [12]
and Zhu etal. [13] developed algorithms that work similarly
to those in a physics motor to realise random pacing of real-
istically shaped aggregates. From these papers, the sections
about the overlapping between particles will be relevant for
the adoption of Physical Engines to pack virtual aggregates.
Finally, [16, 24] have also used statistically-based methods
to generate packs of particles from planar 2D surfaces.
The objective of this paper is to show a novel algorithm
for the creation of virtual realistic 3D aggregates. The
algorithm uses inputs from 2D aggregates to define the
3D geometries. Previous research has shown thatthere are
linear correlations between 3 and 2D size descriptors [28].
The algorithm consists of a spherical density function and
a Perlin noise to deform the spherical density function. By
combining both density functions, a scalar field is created,
which generates a cloud of points that re-creates the shape
of the aggregates in a realistic way. Then, the points are tri-
angulated by using the Marching Cube algorithm [2527].
Finally, the particles are deformed until they match the
aspect ratio and minor Feret of the aggregates that we want
to deform. The model proposed also offers the possibility
of changing the particle sizes and shapes by considering the
statistical parameters of real aggregate samples.
2 Materials andmethods
2.1 Experimental measurement ofaggregates’
morphological properties
Nine types of coarse aggregates from different sources and
with different shape characteristics have been used in this
study, namely glass spheres, crushed glass, round gravel,
limestone of maximum size 14, 10, and 6mm and two types
of granite of 14mm. Each type of stone had its morphologi-
cal information extracted in order to implement the proba-
bilistic parameters in the virtual aggregates model. The
shape factors used to measure the aggregates are described
in Table1.
Pictures have been obtained from the aggregates rest-
ing over their most stable position and, the analysis of their
geometries has been carried out by the digital image pro-
cessing software ImageJ, see examples of the aggregates in
Fig.1. The image analysis included (i) establishing the scale,
(ii) highlighting the borders of the particles and correcting
the shading following the procedure mentioned in [32] and,
(iii) measuring and calculation the properties from Table1,
using the BioVoxel plugin and its functions for extended
particle analysis [33]. The distribution of the properties from
Table1 has been analysed in the Minitab software using the
Weibull distribution, which is a commonly accepted one to
create aggregate distributions. The morphological informa-
tion of the aggregate types has been quantified in terms of
the 50th percentile, P50.
Finally, the height of the aggregates has also to be
adjusted to that of the aggregates. It has been defined by a
new parameter,
, which we will call thickness from now
on, and is the ratio between the minor Feret and the average
height of 50 stones, measured with a calliper. The height has
been measured when the stone is lying in the most stable
position, in the direction perpendicular to the surface.
Table 1 Morphological
parameters to characterize
Parameters Formula Reference Equation
Major and Minor Feret diameter Meassured with ImageJ [29]
Aspect ratio, AR
ISO9276-6, [30] (1)
Sphericity/Cox’s circularity,
Roundness/Pentland’s circularity,
2[31] (3)
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The spherical primitive andperlin noise method torecreate realistic aggregate shapes
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2.2 Physics engine: Unity 3D
The platform chosen to do this research is Unity3D, which
utilises NVIDIA´s PhysX physics engine, and C# as the
development language. PhysX is a multi-threaded physics
simulation, which supports real-time simulation of rigid and
soft bodies, fluids and springs, with a focus on application to
the gaming industry [34]. This physics engine is well docu-
mented and allows to detect collisions between objects with
complex shape thanks to its built-in collision detection and
response algorithms and mesh collide [35].
2.3 Create complex virtual particles withdents
similar tothatofaggregates
In order to re-create dented virtual aggregates, this sec-
tion presents the spherical primitive + Perlin noise method,
will deforms a spherical primitive using a Perlin noise
matrix, until its angularity and circularity, their denting
level, becomes like that of an aggregate. The Perlin noise is
widely used in the animation and movies industry in order
to simulate natural-looking landscapes. In general terms,
it consists of a generator of pseudo-random numbers,
which are softened by a weighted average of the points
[36]. Figure2 summarises the process to produce a virtual
Firstly, a spherical primitive with radius r, is inscribed
in a grid of N x N x N voxels, see Fig.2a, where N is the
number of voxels and d, the distance between the nodes
of the voxels. The radius of the sphere is defined by the
following equation:
An increase in the number of voxels, N, implies an
improvement of the resolution of the 3D model but has
the inconvenience of a higher computational cost. In
this paper, a grid of 7 × 7 × 7 voxels with 1 unit distance
between them has been chosen by trial and error, since it
has been found that this permits a good resolution while
avoiding large memory requirements [37].
Then, a 3D density function
that determines
which lattice nodes, with coordinates,
, are inside
or outside the sphere is defined. In this case, the nodes
outside the sphere are positive, the nodes inside the sphere
are negative and, the nodes at the surface have a value
of 0. The formula that defines the weights in the density
function is (5). In addition, a weight parameter (
), has
been added that increases the density values of the spheri-
cal functions. This factor is used to control the influence
of the spherical density function in the final shape of the
aggregates. In other words, it controls the sphericity of
the virtual aggregates. As the numbers of voxels is 7, and
the distance between them 1, the radius, from the centre
of the voxel, is 3 and the density function values inside the
sphere range between 0 and 3.
Fig. 1 Examples of the aggre-
gates analysed
Granite 1, 14 mm (G1) Granite 2, 14mm (G2) Round Gravel, 20 mm (RG)
Limestone, 14 mm (L1) Limestone, 10 mm (L2) Limestone, 6 mm (L3)
Glass Sphere, 15 mm (GS) Crushed Glass, 6 mm, (CG) Slag, 6 mm (S)
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S.Michot-Roberto et al.
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is the distance from the voxel’s centre to the
centre of the sphere.
In order to introduce dents in the particles that are like
those in crushed aggregates, a second grid with 7 × 7 × 7
voxels is generated and combined with the spherical one,
see Fig.2b. The node values, with coordinates
), of the second grid are obtained from a
Perlin noise generator, which values may range between
0 and a maximum value of 4, depending on the degree
of deformation desired, we have called the highest value
of the Perlin’s noise range, f. The advantage of using a
Perlin noise is that it produces a gradient, natural looking
surfaces [39]. If the value is 0, there is no deformation. If
the value is 4, the deformation is the highest. This value
has been determined by the trial and error method and, a
higher value could produce unrealistic shapes (see Fig.3),
with holes. Each aggregate has a different matrix. To con-
trol the angularity of the aggregates,
can be multiplied
by a factor that we have named Intensity of deformation,
, which weights
Finally, the density function of the aggregates,
is created by multiplying the spherical density function
and the noise density function as follows, see also Fig.2c:
Finally, a Marching Cube algorithm is used in order to
triangulate the shape of the virtual saggregate. The points
in the voxels’ edges that cross the density values equal to
0 are identified by the Marching Cube and triangles are
generated that transverse them and form the shape of the
virtual aggregate.
In occasions, the method presented above may produce
virtual aggregates with topological inconsistencies, such
as holes in the mesh, see Fig.3 as an example. In this
research, it could happen for two reasons: (i) due to the
intrinsic nature of the Marching Cube algorithm, which
in occasions may interpret that some faces correspond
to holes [17] and (ii) the random density matrix which
can deform the particles excessively. These ambiguities
occur when there is more than one possible way to trian-
gulate the points at the voxels’ corners and these can be
interpreted as holes. A solution for this could simply be
to increase the number of voxels in the matrix, N; other
researchers have also identified this problem and proposed
solutions that minimise but, they do not correct it com-
pletely [38].
Such virtual stones are discarded by a particle control
routine that uses an operation from Unity that “sends a
virtual laser ray” that can detect surfaces. In this way the
surface of aggregates is mapped and aggregates with holes
are detected, depending on whether some rays go through
the stone, and when any are found, the stone is discarded.
def ]
(a) Spherical density matrix (b) Perlin noise matrix (c) Particle with complex shape
Fig. 2 Process to create a dented particle
Un-realistic aggregate
(excessive irregularity) Realistic aggregate
Fig. 3 Example of un-realistic and realistic virtual aggregates
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The spherical primitive andperlin noise method torecreate realistic aggregate shapes
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2.4 Deform theparticles toadjust their minor Feret
andaspect ratio inthemost stable position
tothatofaggregate projections
The minor Feret and aspect ratio are enough to characterise
the dimensions of each particle projection [18]. The algo-
rithm described in the previous section produces angular
particles which minor Ferets and aspect ratios do not fit
those of the actual aggregates. For that reason, a method has
been created that rescales the angular particles, to achieve
the desired minor Feret and aspect ratio.
As it will be shown in the Results section, the aspect ratio
and minor Feret of each aggregate type have been character-
ised using the Weibull distribution function, as it was done
in [18]. This distribution is defined by two parameters, one
of shape,
, and another one of scale,
, which have been
measured experimentally, see also Table2.
To select the aspect ratio and minor Feret of each parti-
cle, a pseudorandom function, with range between 0.05 and
0.95 generates numbers, which are imputed as probabilities
in Weibull distribution functions of aspect ratio and minor
Feret that uses as scale and shape factors measured experi-
mentally. The results are values of minor Feret an aspect
ratio which fall within the same distribution of aggregates
measured experimentally.
A virtual laser is used to scan every virtual particle and
select the different views of the particle, see Fig.4, based
on the position of the points on the particle’s surface “hit”
by the ray. Then, an array with the coordinates of the out-
line plan view is created, which enables definition of the
perimeter. From this array, the minor Feret and the major
Feret are identified and measured, see Fig.4d. The area is
measured based on the triangular division formed by the
segments between the perimeter array and the centre of
the particle’s projection, Fig.4d, following the procedure
described in [40]. Note that these particles are still approxi-
mately spherical.
Finally, one of the views is selected and, the virtual aggre-
gates are rescaled so that their planar projections have the
minor Feret and aspect ratios within the Weibull probability
range measured experimentally. In addition, the thickness
of the aggregates is adjusted so that their thickness fits that
determined experimentally.
2.5 Select input parameters thatdefine thesize
andshape ofvirtual aggregates
A summary of all the input parameters required to reproduce
the aggregates can be found in Table2. In order to calculate
automatically the input combinations, we have used a DE
algorithm [41]. The outputs that the algorithm has used are
, which is the median value of the perimeter and
, the
median value of the area.
2.6 Explanation oftheuse ofvirtual aggregates
G2 materials were used to prepare an aggregate packing
to explain the use of the virtual aggregates. The packing
weighted approximately 500 ± 5g. The aggregates were
placed in a cylindrical container to compact the aggre-
gates, whose dimensions are 9.4cm in diameter and 8cm
in height. The compaction test was conducted using a
vibratory table with flexible springs and an engine speed
of 3600rpm, making the table vibrated in a horizontal
sine wave. The frequency was 60Hz, and the three axes
displacement ranged between 0 and 1.58mm. The stones
were firstly vibrated for 2min and secondly, a metal
cylinder, with weight 2.7kg and 8cm of diameter was
dropped from a 5cm height above the aggregates and, the
Table 2 Input parameters to control size and shape of virtual aggre-
gates in the model
Input parameters
Angularity and sphericity Controls sphericity,
Intensity of deformation,
Perlin’s noise range, f
Size and shape Minor Feret, shape factor,
Minor Feret, scale factor,
Aspect ratio, shape factor,
Aspect ratio, scale factor,
Thickness Β
Minor Feret
(c) Plan view of a
virtual stone
Side view of a
virtual stone
(b) Front view of a
virtual stone
(d) Shape factors
Fig. 4 Orthogonal views of virtual aggregates and shape factors
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S.Michot-Roberto et al.
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41 Page 6 of 11
vibration continued for five additional minutes. Finally,
the pack of G2 aggregates was CT scanned as described in
[42], and the images were treated with the image process-
ing software ImageJ following the procedure described
in [43].
An equivalent mass of G2 virtual aggregates was
compacted in the Physics Engine by pouring them in a
cylindrical container with the same dimensions as the
real one. The total number of particles in the simulation
was defined by the total mass of the sample and the den-
sity, as Unity 3D measures each particle’s volume. The
vibrations over the virtual cylinder mimicked those of the
experiment and, compaction was stopped when the height
of the virtual specimen reached that of the experiment.
Parameters used in the simulation were concave collider,
default contact onset 0.0001m, bounciness 0.315, static
friction 0, 30 iterations per frame and a fixed timestep
of 0.002.
3 Results anddiscussion
3.1 Experimental values oftheaggregates studied
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 distri-
bution curve; the closer the result is to zero, the better the
fit of the curve to the data points [21]. Based on [18], a two-
parameter 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. The Anderson–Darling test
statistic value, A2, is 0.479.
Table3 shows the values that characterise the aggregates
studied. See for example the glass spheres, which show
aspect ratio approximately equal to 1, minor Feret approxi-
mately 15mm, and area and perimeter like those of the cir-
cle with equivalent diameter.
The aggregates with the largest shape parameter values
are RG and GS, whereas the aggregates with the smallest
shape parameter values are S and L3. The aggregates with
a more uniform size distribution are L1 and G1, with shape
values greater than 10; followed by S, CG and G2, with
shape values between 5 and 10. In addition, the aggregates
with highest AR are GS, RG, and L2, while the aggregates
with lowest AR are CG, L3 and S. Those are also the aggre-
gates with higher and lower angularity and circularity. Fur-
thermore, the thicker aggregates, with β greater than 0.5
are RG, G2 and L1, whilst the thinner aggregates are L3,
S, and CG.
Finally, Fig.6 shows the aggregate classification based
on their circularity and sphericity, using the Krumbein chart
Fig. 5 Weibull plot of Minor Feret
Table 3 Experimentally
measured shape factors that
characterise the aggregates
Min Feret50
is the median value of minor feret,
is the median value of aspect ratio,
Max Feret50
is is
the median value of major feret,
is the median value of the perimeter,
is the median value of the
is the median value of the radius,
is the median value of circularity
G1 G2 RG L1 L2 L3 GS CG S
12.57 5.69 4.45 13.84 3.76 3.66 379 5.12 8.54
(mm) 15.07 13.27 19.18 15.22 7.86 5.23 14.9 8.7 5.34
(mm) 14.62 12.36 16.82 14.68 7.19 4.76 15.12 8.04 4.92
7.15 7.9 7.82 9.59 6.73 6.59 385 7.84 6.63
0.75 0.73 0.8 0.79 0.71 0.67 0.99 0.66 0.68
0.71 0.69 0.76 0.78 0.68 0.65 0.99 0.64 0.66
(mm) 20.42 17.57 23.25 19.19 10.61 7.14 15.26 11.2 7.43
(cm) 6.03 5.5 6.72 5.81 3.15 2.13 4.79 3.25 2.11
(cm2) 2.08 1.56 2.73 2.02 0.52 0.24 1.83 0.64 0.25
0.65 0.7 0.71 0.69 0.61 0.61 1.00 0.65 0.61
0.71 0.67 0.73 0.78 0.67 0.68 1.00 0.70 0.68
0.52 0.6 0.53 0.54 0.44 0.39 1.00 0.49 0.42
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The spherical primitive andperlin noise method torecreate realistic aggregate shapes
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used for visual evaluation of aggregates [44]. From results
from Table3, it can be concluded that
are lin-
early related:
In addition, a linear trend can be also observed between
these two parameters,
, which implies that, for the
aggregates used in construction materials such as asphalt or
concrete, its value does not need to be measured:
does not show any clear relationship with
3.2 Input parameters togenerate theaggregates
The input parameters that control the scalar density func-
tions are
, f. Varying these parameters controls the
degree of particle deformation and contributes to achieve
various levels of angularity and sphericity. Their combi-
nation has been found by trial and error through a visual
inspection using Krumbein’s chart classification, which can
be found in [44]. Figure7 shows the input values used to
find a wide range of morphologies that corresponds to those
commonly found in the aggregates used in civil engineering.
Figure8, shows the virtual aggregates in a Krumbein
chart, based on the circularity and sphericity of the aggre-
gates. This Figure has been prepared to give the reader an
idea of the general shape of the virtual aggregates and the
parameters used to create them. The objective is to show that
the methodology shown in this paper can be used to re-create
any aggregate from those commonly used in civil engineer-
ing. It is remarkable that this methodology has allowed to
precisely control the angularity and circularity of the virtual
To compare the real vs virtual aggregates, these have been
simply represented one versus the other. Figure9 shows the
distribution of Minor Feret of G2 aggregates as an example.
In general, it was found that the main difference corresponds
to the extremes of the distribution. This can induce errors
in the representations of aggregates, such as aggregates that
are too elongated, or bigger than normal. If these aggregates
would be used to make virtual asphalt mixtures or other
types of aggregate-based materials, the most extreme virtual
aggregates should be eliminated in order to produce correct
mixtures. Obviously, the simulation shows a high level of
similarity because the virtual aggregates have been made to
fit the experimental data.
The algorithm has been validated by comparing the real
and virtual morphological information of each type of aggre-
gate. The validation has been done by a correlation parame-
ter named reliability index, which compare the median of the
virtual stone´s samples to the experimental results, in order
to know the quality of fit of the virtual aggregate model with
the real data; see Eq.(9). A reliability index value equal to
one indicates a perfect adjustment.
The reliability indexes are shown in Table 4. As the
Weibull’s distribution parameters are inputs imposed by the
user, those generated by the algorithms are identical or very
close to them.
It is worth mentioning that the perimeter, area, circu-
larity and roundness show the lowest accuracy. This is
due to (i) errors induced from the selection of the high
number of variables involved in the creation of parti-
cles, which were chosen by the trial and error method;
Reliability index = P50 virtual
50 real
Fig. 6 Aggregate chart classifi-
cation of the aggregates studied
> 0.85
> 0.80
– 0.85
< 0.70
L2 L3
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S.Michot-Roberto et al.
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41 Page 8 of 11
for example, f,
, and
and, (ii) the measurements of
area and perimeter by ImageJ, which may be influenced
by shadowing and thresholding. In the future, an optimi-
sation algorithm can be used to identify the aggregates
more precisely.
3.3 Comparison ofasimulated aggregate packing
In order to give an idea of the capabilities of using Phys-
ics Engines to produce aggregate packings, Fig.10 shows
a comparison between a simulation and a packing of
S= 1
S= 0.8
S= 0.70
Very Angular Sub-AngularSub-Rounded Rounded
Idef 0.015
Idef 0.020
Idef 0.030
Idef 0.090
Idef 1.000
Idef 0.02
Idef 0.045
Idef 0.055
Idef 1.000
Idef 1.200
Idef 0.015
Idef 0.020
Idef 0.030
Idef 0.070
Idef 1.400
Fig. 7 Aggregate chart classification of the aggregates studied
Fig. 8 Aggregate chart classifi-
cation of the virtual aggregates
> 0.85
> 0.80
< 0.70
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The spherical primitive andperlin noise method torecreate realistic aggregate shapes
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aggregates G2, obtained through X-ray CT scans. The
goodness of fit of the vertical distribution of pores has
been found via the Kolmogorov–Smirnov Test [45], using
the critical value for a confidence level at 95% (
are the population size of the samples.
= 0.028; if
is smaller than the maximum
absolute distance between the expected and observed distri-
bution functions (
), we can conclude that the values from
the experiments and simulations are equivalent. In this case
, hence, we can confirm that the virtual aggre-
gate’s packing has a very close AV distribution function than
the experimental one. Finally note that for the same equiva-
lent mass, the experiment comprised 104 particles, while the
simulation 110 particles.
4 Conclusions
This article has shown a novel methodology to re-create
commonly used aggregates in civil engineering. It is based
on a spherical primitive that is deformed by means of a
Perlin noise. Then, the shape and size of the virtual aggre-
gates is adjusted by deforming the shapes until they fall
crit,0.05 =1.36
Cumulative frequency (%)
Minor Feret (mm)
Unity 3D
Fig. 9 Distribution of Minor Ferets for G2 aggregates, calculated
from simulations and experiments
Table 4 Reliability indexes
resultant from comparing the
simulations with experiments
G1 G2 RG L1 L2 L3 L4 L5 GS CG S
0.997 0.989 0.964 0.978 1.037 1.017 1.024 0.969 0.999 0.969 1.027
0.997 0.989 0.964 0.978 1.037 1.017 1.024 0.969 0.999 0.969 1.027
1.017 0.999 0.924 1.062 0.907 1.024 0.998 0.938 1.007 1.103 0.934
0.831 0.879 0.895 0.854 1.165 0.830 0.854 0.845 0.976 0.809 0.806
0.887 0.860 0.971 1.155 1.194 1.113 1.194 1.205 1.036 1.235 1.245
1.120 1.008 1.033 1.199 1.146 1.183 1.156 1.161 0.975 1.132 1.161
1.051 1.043 1.035 0.929 0.949 0.954 0.957 1.008 0.983 1.095 1.143
Fig. 10 Vertical distribution
of air voids in a simulated
and experimental packs of G2
Height (%)
Air Vo id Content (%)
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S.Michot-Roberto et al.
1 3
41 Page 10 of 11
in the same statistical range of the real aggregates. The
algorithm has been implemented in the NVIDIA PhysX
physical engine, with the objective of being able to use
these aggregates in future research that will involve creat-
ing virtual aggregate gradations.
The following conclusions have been obtained:
This methodology allows to re-create the morphologies
of aggregates virtually. Based on the experience of the
researchers, hundreds of aggregates were generated in
a few seconds.
This algorithm has allowed to re-create realistic virtual
aggregate shapes that include concavities. The authors
are convinced that the precision of these virtual aggre-
gates will be enough to analyse the influence of the
aggregate shapes on the packing of aggregates.
The angularity and sphericity of the particles are con-
trolled by three inputs that weight the spherical primi-
tive and Perlin noise. In the current research, these
inputs have been adjusted by trial and error, until
the shape of the virtual shapes was found. In future
research, this will be updated by using an optimisation
algorithm, which will allow the creation of aggregates
in a fast and efficient way.
The comparison between the virtual and the real geo-
metrical properties’ data indicates that the algorithm to
create virtual aggregates can achieve minor and major
Ferets like those measured in real aggregate samples.
In addition, this methodology allows to create virtual
particles with area, perimeter, sphericity, and angular-
ity similar to those of the real materials.
In occasions, the methodology proposed in this article
produced aggregates that presented unnatural shapes,
including holes and bottlenecks. The reasons for this
are still unsolved. The unnatural particles appeared
very seldomly. However, if hundreds of particles are
produced to create an aggregate packing and some
unnatural particles appear results could be affected. For
this reason, the authors have developed a new method-
ology to produce virtual aggregates that is presented in
It has been found that the methodology allows to re-
create full gradations by using the Weibull distribu-
tion to decide the minor Feret of the virtual aggregates.
However, in future research the extreme aggregates
need to be eliminated, to allow re-creating unrealistic
Acknowledgements The authors want to acknowledge the sponsorship
of Tarmac Ltd, which is the UK’s leading sustainable building materi-
als & construction solutions businesses. Specifically, the contribution
of Ms Kerry Nadel measuring the shape of the aggregates is very much
Conflict of interest The authors declare that they have no conflict of
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... The first step to manufacture virtual particulate materials is to create virtual aggregates. To do so, the shape of particles can be recorded, which can be done by using different acquisition systems as 3D laser scanner, X-ray Computed Tomography, or image acquisition systems, as can be seen in [11] and [12] and [13] respectively. Then, we need to recreate these shapes computationally. ...
... Eleven types of coarse aggregates from different sources and different shape characteristics have been used in this study. These aggregates had been characterised in detail in reference [13], where they have been also classified based on their circularity and sphericity, using the Krumbein chart used for visual evaluation of aggregates. The particles are glass spheres (GS); crushed glass (CG); round gravel (RG); slag (S); five types of Limestone: L1, L2, L3, L4 and L5, with maximum size 20 mm, 6 mm, 10 mm, 14 mm and 20 mm respectively, and two types of granite, G1 and G2, with size 14 mm and 6 mm, respectively. ...
... 1) The median of the: area (A 50 ), perimeter (P 50 ), minor feret (MinFeret 50 ), major feret (MaxFeret 50 ), aspect ratio (AR 50 ), circularity (C 50 ), roundness (R 50 ). A deeper explanation of these concepts can be found in reference [13]. ...
In this paper, an impulse-based Discrete Element numerical Method (iDEM) included in a physics toolbox, has been used to compact virtual aggregates. Firstly, geometrical properties, such as area, aspect ratio, perimeter, minor and major feret, circularity and roundness, of eleven types of coarse aggregates were measured. Then, a mass of each of these aggregates was compacted under vibration. The aggregate packings’ properties, such as aggregate segregation and orientation, porosity, pore -diameter, -tortuosity, -connectivity, -aspect ratio, -circularity, and -vertical distribution, were measured from Computed Tomography scans. Secondly, the aggregates were simulated using a Perlin noise in spherical primitives, which adjusted their geometry until they achieved realistic morphologies and gradations. iDEM detects contacts between complex shapes, including concavities, and computes the interaction between large amounts of complex objects. Results show that the properties from the packing experiments and simulations are highly comparable. This paper demonstrates the capacity of the physics toolbox to simulate granular materials effectively.
Full-text available
Morphological parameters may lead to the understanding of important characteristics relating to sedimentary particles such as those involved in its transport, its residence time in the sedimentary cycle and the distance of sediment source areas. For too long the sedimentologists dedicated to the description of characteristics related to the particle shape through different mathematical formulations, leading them to the development of different concepts and terminology such as roundness, circularity and sphericity. However, there has never been consensus on the use of these parameters sometimes difficult to apply or highly subjective. More recently, the development of digital photomicrography coupled with image processing software, gave new impetus to the morphological studies of sedimentary particles. They also become subject to other sciences such as geotechnical and civil engineering. In this research it was carried out a review of methods for the quantitative morphological description of particles and evaluated the ability of some parameters used by the software ImageJ in differentiating coastal environments of deposition. The survey was carried out in nine different coastal depositional environments in insular and continental sites of Santa Catarina state (rivers, beaches and dunes). The parameters used to describe quartz-grain morphometric features were roundness of Cox (1927), the circularity of Pentland (1927), the sphericity of Landini (2006) and aspectratio. The first three descriptors allowed a statistically significant difference between the samples and the environments of deposition, particularly between the rivers and dunes. The aspectratio did not lead to satisfactory results. The use of specialized digital imaging software packages is presented as promising tool , since they allow acquire several metrics that may be complementary to traditional sedimentological analyses and provide a performance up to recognize depositional environments in ancient sediments.
Full-text available
Macroscopic mechanical properties of granular materials are closely related to particle morphology. For practical reasons, the morphological features are commonly examined from projected two-dimensional (2D) images of the three-dimensional (3D) particles. This brings forward the need for quantifying the correlations between the 2D and 3D particle descriptors. This paper addresses these correlations for irregular granular particles. Three-dimensional images of sand particles were acquired through microfocus X-ray computed tomography, based on which 3D surfaces of the particles were reconstructed using spherical harmonic analyses. The 3D particle size and shape descriptors were subsequently evaluated. All-around projection and random projection of the particles onto 2D planes were undertaken numerically to obtain the projected 2D images and thus the corresponding 2D size and shape descriptors. The results indicate that there are close correlations between 3D and 2D size descriptors averaged from the all-around projections. 2D and 3D shape descriptors can be approximately fitted with a linear relationship. The mean value of 2D descriptors of the tested sands obtained from a series of independent random-projection tests is essentially identical to that from the all-around projections; except that the data from the random-projection tests show a larger scatter. In light of the relationships among the descriptors, a novel and promising approach to predict the cumulative distribution of 3D descriptors from that of 2D descriptors evaluated from a random-projection test is proposed.
Full-text available
Based on the Aggregate Imaging Measurement System (AIMS) and the Particle Flow Code in Two Dimensions (PFC2D), an algorithm for modeling two-dimensional virtual aggregates was proposed in this study. To develop the virtual particles precisely, the realistic shapes of the aggregates were captured by the AIMS firstly. The shape images were then processed, and the morphological characteristics of aggregates were quantified by the angularity index. By dividing the particle irregular shape into many triangle areas and adjusting the positions of the generated balls via coordinate systems’ conversion within PFC2D, the virtual particles could be reconstructed accurately. By calculating the mapping area, the gradations in two-dimensions could be determined. Controlled by two variables (μ_1 and μ_2), which were drawn from the uniform distribution (0, 1), the virtual particles forming the specimens could be developed with random sizes and angular shapes. In the end, the rebuilt model of the SMA-13 aggregate skeleton was verified by the virtual penetration tests. The results indicated that the proposed algorithm can not only model the realistic particle shape and gradations precisely, but also predict its mechanical behavior well.
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.
The mechanical properties of concrete composites mainly depend on its ingredients and meso-structure, especially the shape, distribution, and grading of aggregates. Therefore, it is very important to establish realistic meso-scale models for concrete composites performance prediction and structural optimization design. However, there is only a few methods to generate models with high volume fraction in current studies. In this paper, a novel idea for numerical modeling, namely the aggregate expansion method, is used to establish more realistic 3D models with different volume fractions of convex and concave aggregates. The shrunken aggregates are first placed in an empty container, and then these aggregates are expanded to the predetermined sizes to obtain a numerical model. Using this approach can efficiently obtain a high volume fraction model with randomly distributed aggregates. In addition, realistic aggregates are generated according to the statistical data of actual aggregates shapes. A series of statistical data show that the randomness of aggregates in the space before and after expansion is still maintained. At last, the simulation results of 3D numerical models with different volume fractions under uniaxial tension are calculated. The consistency between the simulation results and experimental data verifies the good accuracy of the models.
This paper investigates the effects of air void topology on hydraulic conductivity in asphalt mixtures with porosity in the range 14%–31%. Virtual asphalt pore networks were generated using the Intersected Stacked Air voids (ISA) method, with its parameters being automatically adjusted by the means of a differential evolution optimisation algorithm, and then 3D printed using transparent resin. Permeability tests were conducted on the resin samples to understand the effects of pore topology on hydraulic conductivity. Moreover, the pore networks generated virtually were compared to real asphalt pore networks captured via X-ray Computed Tomography (CT) scans. The optimised ISA method was able to generate realistic 3D pore networks corresponding to those seen in asphalt mixtures in term of visual, topological, statistical and air void shape properties. It was found that, in the range of porous asphalt materials investigated in this research, the high dispersion in hydraulic conductivity at constant air void content is a function of the average air void diameter. Finally, the relationship between average void diameter and the maximum aggregate size and gradation in porous asphalt materials was investigated.
We present a voxel-based rendering pipeline for large 3D line sets that employs GPU ray-casting to achieve scalable rendering including transparency and global illumination effects that cannot be achieved with GPU rasterization. Even for opaque lines we demonstrate superior rendering performance compared to GPU rasterization of lines, and when transparency is used we can interactively render large amounts of lines that are infeasible to be rendered via rasterization. To achieve this, we propose a direction-preserving encoding of lines into a regular voxel grid, along with the quantization of directions using face-to-face connectivity in this grid. On the regular grid structure, parallel GPU ray-casting is used to determine visible fragments in correct visibility order. To enable interactive rendering of global illumination effects like low-frequency shadows and ambient occlusions, illumination simulation is performed during ray-casting on a level-of-detail (LoD) line representation that considers the number of lines and their lengths per voxel. In this way we can render effects which are very difficult to render via GPU rasterization. A detailed performance and quality evaluation compares our approach to rasterization-based rendering of lines.
Particle angularity significantly affects the macroscopic mechanical behavior of aggregate assemblages. However, most of the current approaches used for quantifying particle angularity are only applicable to star-like particles. This study presents a new approach allowing the quantification of angularity of general-shape particles. The method first reconstructs the particle morphology by applying Fourier series analysis to the two-dimensional image of the particle. The gradient-based angularity index (AIg) is then evaluated from the reconstructed morphology through numerical integration. AIg is zero for images of any circularly shaped particles, including circles and ellipses, and it increases with increasing particle angularity. Images included in commonly used standard charts are evaluated for their AIgs. The results show a consistent pattern in regard to the qualitative angularity ranking of the particles. Based on the findings, a simple-to-use criterion is suggested for the quantitative classification of particle angularity.