image based modelling of rock fragmentation

Image based modeling of rock fragmentation
Nenad Djordjevic ⇑
JKMRC, SMI, University of Queensland, 40 Isles Road, Indooroopilly, Qld 4068, Australia
a r t i c l e i n f o
Article history:
Received 15 November 2012
Accepted 7 March 2013
Available online 2 May 2013
Keywords:
Image
Rock fragmentation
Modeling
Ore
Liberation
Fracture
a b s t r a c t
In the mineral extraction industry, comminution modeling is not only interested in maximum rock
strength, but also, or much more, in the energy required to induce rock fracture and, most significantly,
into the effect of energy application on the produced rock fragments size distribution. An additional
aspect of rock breakage, specific to the mineral extraction industry, is the modeling of liberation of par-
ticular mineral grains from the host rock matrix. These aspects of rock behavior make comminution mod-
eling a unique field of rock mechanics.
From a traditional engineering point of view (mining and civil), rock samples are considered to be
homogenous. Although the mechanical properties of individual minerals can vary significantly, the prop-
erties of the minerals and of the mineral boundaries interact randomly enough to assume that in the size
of rock samples mechanical properties can be considered homogenous. However, from a comminution
point of view, heterogeneity caused by a difference in the properties of minerals are crucial and therefore
rock material, even in the scale of a few centimeters, should be considered as heterogeneous. The com-
minution response of such rock will be influenced by the textural parameters of the rock as well as
mechanical properties of constitutive mineral grains.
Image based numerical modeling is a useful tool for investigation of the pattern and dynamics of the
rock breakage process. Its usefulness rests on the fact that a difficult step of building a faithful model
of rock texture and composition, as a pre-requisite for modeling of rock breakage, is removed. Numerical
modeling based on the use of classified digital image of the rock surface, could be particularly effective in
the mineral extraction industry, where one of the key objectives is liberation of specific minerals, by pro-
viding inside view of mechanisms that are responsible for liberation of valuable minerals embedded into
specific ore matrix.
Ó 2013 Elsevier Ltd. All rights reserved.
1. Introduction
One way to investigate the effect of different textural classes is
to perform numerical modeling of the effect of certain textural
types on rock fragmentation and mineral liberation. Textural clas-
ses can be the product of mathematical modeling or can be a digital
image of a typical rock texture of a certain rock type. Regardless of
how a particular ore texture is generated it is of interest to inves-
tigate the spatial and temporal pattern of the rock fragmentation.
Recent developments in computing power have created the
opportunity for more rock specific modeling of rock fragmentation.
This is based on the application of object-oriented finite element
modeling of the rock deformation and breakage. In this context,
the object represents a specific type of mineral or structural fea-
tures. This modeling has been performed using the OOF (Object
Oriented Finite) element code, (Langer et al., 2001). The proposed
approach is particularly attractive, due to the nature of its input,
which is a digital image of the rock surface.
The objective is to establish a cause-effect relationship between
the presence of certain mineral grains and their pattern of distribu-
tion on the propensity for liberation of another mineral type, i.e., a
mineral which is of economic interest. One of the most significant
objectives is to establish the maximum size of the rock fragments
required for the full or partial liberation of the mineral of interest.
Obviously, critical fragment size is dependent on the textural fea-
tures of the rock, mechanical properties of individual minerals,
and the nature of the stress field to which a rock sample is exposed.
2. Modeling methodology
Before we continue, we should remind ourselves what rock tex-
ture is. According to Encyclopedia Britannica, the texture of a rock
is the size, shape, and arrangement of the grains (for sedimentary
rocks) or crystals (for igneous and metamorphic rocks). Therefore,
the definition of texture is essentially geometric and pictorial, in
nature. The classical definitions of texture do not include informa-
tion about the mechanical/physical properties of grains or crystals.
However, from the point of view of rock comminution in the
0892-6875/$ - see front matter Ó 2013 Elsevier Ltd. All rights reserved.
http://dx.doi.org/10.1016/j.mineng.2013.03.002
⇑ Tel.: +61 7 3365 5888; fax: +61 7 3365 5999.
E-mail address: n.djordjevic@uq.edu.au
Minerals Engineering 46–47 (2013) 68–75
Contents lists available at SciVerse ScienceDirect
Minerals Engineering
journal homepage: www.elsevier.com/locate/mineng

context of the recovery of particular minerals, the mechanical
properties of minerals are of great importance. Another parameter
which is not explicitly considered in traditional definitions of tex-
ture is the presence and nature of voids (pores and microcracks).
The modeling methodology of rock mass behavior is strongly
influenced by the nature of the rock mass. In the case of rocks as
natural geologic materials, physical and mechanical properties
need to be determined rather than selected through a manufactur-
ing process. In the case of man-made materials, the common pur-
pose of routine mechanical testing is not to gain new knowledge,
but to provide quality control and verification.
Rock mass in situ is characterized by unknown structural prop-
erties, the unknown state of stress and unknown details of the
mechanical properties. From a practical point of view, all these
properties are not just unknown in detail but they are frequently
practically unknowable. To a lesser extent, the same is applicable
for the modeling rock matrix (in the scale of rock samples). This
lack of precise information indicates that the approach to rock
modeling should be different from one used for the modeling
behavior of known materials (man-made), whose properties are
generally known.
3. Determinations of the mechanical properties of the minerals
Input parameters for OOF modeling are mechanical parameters
of the minerals identified in the image. Among them are Young’s
module of elasticity, Poisson’s ratio, and compressive and tensile
strength. These parameters are determined either from the avail-
able published information or they are measured through nano-
(micro) indentation testing. In terms of the published information,
they tend to be restricted to the modulus of elasticity and Poisson’s
ratio. The strength properties of minerals are rarely available.
Strength properties as well as elastic properties are determined
through instrumented, computer controlled, nano-indentation
testing. Indentation or hardness testing has been used for a long
time for material characterization. Traditional hardness testing
consists of the application of a single static force for a specified
time. Depending on the shape and tip material of the indenter,
the dimensions of the impression created will be in order of milli-
meters. The output of the traditional hardness tester is typically a
single indentation hardness value that is a measure of the relative
penetration depth.
In contrast to traditional hardness testing, instrumented inden-
tation testing allows the application of a specified force or dis-
placement history. Force and displacement are measured
continuously over a complete loading cycle. For the purpose of
instrumented nano-indentation we used the UMIS nano-indenta-
tion instrument from the CSIRO. UMIS measures elastic, plastic,
strain hardness, creep, fracture and other mechanical properties
of a material surface. The UMIS offers in situ observation of the
indentation process, and specimen positioning to within 0.1 lm.
Testing has been performed using a Berkowich diamond tip in-
denter, with constant force (5–10 tests per mineral sample). In the
case of homogenous minerals, testing produced an indent of highly
reproducible size and shape, Figs. 1 and 2. From the unloading part
of the load-deformation curve, the instrument calculates the elas-
tic modulus of the indented surface.
Elastic modulus is calculated with the assumption that Poisson
ratio is equal to the mean value published in the literature for a
particular mineral. This assumption introduces error. However,
the magnitude of the error in most cases is not high. Due to the
high elastic modulus of the diamond tip used for indentation,
and the nature of the testing method, the calculated values of the
elastic modulus of the minerals are within the range of ±3% of
the value if the exact value of the Poisson ratio of the mineral is
known. For instance, an error of 20% in the assumed value of the
Poisson ratio of the mineral results in an error of 3% in the calcu-
lated value of the elastic modulus, Fig. 3.
Elastic properties of the same mineral vary from mine to mine,
and probably within the same mine, depending on the specific his-
tory of mineralization. This is illustrated in the case of sphalerite, in
which Young’s modulus varies substantially between Rosebury
and Broken Hill mines (Australia). Therefore, using the properties
of Rosebury sphalerite to model behavior of Broken Hill ore may
produce incorrect results, (see Fig. 4) Fig. 9.
However, within the same mineralization the mechanical prop-
erties of a particular mineral, tend to vary in a relatively narrow
Fig. 1. Nano-indentation testing of sphalerite (Rosebury).
Fig. 2. Nano-indentation testing of sphalerite (Broken Hill).
Fig. 3. Normalised (non-dimensional), value of the elastic modulus as a function of
the assumed Poisson’s ratio, using for normalization value of elastic modules that
correspond to the Poisson ratio of 0.25.
N. Djordjevic / Minerals Engineering 46–47 (2013) 68–75 69

range. This is illustrated in the case of chalcopyrite from Mt. Isa
Mine, Fig. 5.
4. Modeling the influence of texture on rock strength
One of the key properties of rock as a natural material is its het-
erogeneity. The onset of crack initiation and crack propagation is
heavily influenced by the heterogeneity of the rock material.
There is a significant body of experimental results which shows
that the texture of rock will have an effect on rock strength. For in-
stance, Everitt and Lajtai (2004) investigated the contribution of
rock fabric on excavation damage development in the granite of
the Lac du Bonnet Batholith. Data collected in their study demon-
strated the highly heterogeneous internal structure characteristic
of apparently homogenous batholiths, and the influence of this
heterogeneity on rock mass response. Grain size had a clear impact
on the strength. With an increase in the grain size of main minerals
types (quartz, feldspars), rock strength decreased.
Different techniques were used to introduce rock heterogeneity
into the numerical models. Garboczi and Day (1995) used mesh
with a random geometry, but equal properties for the elements.
The authors developed an algorithm based on FEM applied to dig-
ital images for computing the linear elastic properties of heteroge-
neous materials. Schlangen and Garboczi (1997) applied an
approach where the generated microstructure is projected to reg-
ular elements to which different properties are assigned according
to their position.
Blair and Cook (1998a,b) developed a non-linear rule-based
model for the fracture in compression of heterogeneous brittle
materials such as rock, and used it to study crack nucleation and
propagation at the grain scale. The authors used the model to sim-
ulate uniaxial compression tests of rock samples. The results
underscored the importance of crack interaction in tensile cracking
of rock in compression even at low crack densities. The model pro-
duces non-linear stress–strain behavior similar to that observed in
laboratory tests. They performed a parameter-sensitivity analysis
to evaluate the relative importance of different types of grain-scale
heterogeneity on fracture processes and the compressive strength
in simulated compression tests. The results presented indicate that
heterogeneity in a local stress field (due to grain shape and load-
ing) has a first-order effect on macroscopic properties and is much
more important than heterogeneity initial strength (i.e. strengths
of mineral grains).
Tang et al. (2000) developed RFPA2D a
finite element code (Rock
Failure Process Analysis). The code was developed by considering
the deformation of an elastic material containing an initial random
distribution of micro-features. By introducing the heterogeneity of
rock properties into the model, the RFPA code can simulate non-
linear deformation of a quasi-brittle behavior with an ideal brittle
constitutive law for the local material elements.
Langer et al. (2001) developed Object Oriented Finite element
code (OOF) for modeling macroscopic properties from images of
real or simulated microstructures. OOF takes a non-reductionist,
brute force approach in a user-friendly way. The user starts with
a digitized image of the rock texture and builds a data structure
on top of it. Tools are provided to allow the user to graphically se-
lect features in the microstructural image of the rock and specify
their properties. For OOF, the microstructure is a data structure
composed of image and property data.
The mechanical properties of mineral grains or mineral phases
which are required for modeling, depend on the intended type of
modeling. In cases of modeling the elastic properties of rock and
the stress distribution within a rock, resulting from the application
of an external force, the only parameters required are Young’s
modulus of elasticity and Poisson’s ratio. If anisotropy coefficients
of individual minerals are known, the coefficient of anisotropy can
also be used.
In cases when modeling is concerned with some form of rock
fracturing or rock damage, then parameters which describe min-
eral strength (compressive and tensile) need to be introduced. Be-
sides strength limits, it is also necessary to introduce parameters
which control post-peak strength behavior of the particular min-
eral. Fragment size distribution which comes as a result of OOF
modeling is determined using the Image Tools code. Considering
that OOF modeling is in 2D domain, the calculated fragment distri-
bution is relative to the initial area of the sample (i.e., due to con-
fining effect of 3rd dimension, real fragmentation will be to some
extent coarser).
5. Influence of the mechanical properties of minerals on the
fragmentation model
It is of interest to know how different a mechanical property
needs to be to cause a visible difference in the output of the frag-
mentation model. In the case of samples from Ernest Henry Mine
(Queensland, Australia), we noticed that the presence of magnetite
is of critical significance for fragmentation. The influence of mag-
netite appears to be particularly strong in comparison with pyrite.
This would seem surprising considering that pyrite has a higher va-
lue of elastic modulus than magnetite and will, therefore, absorb
higher stresses. The high stress focusing abilities of pyrite, should
result in efficient debonding of pyrite from the host matrix, due
to yielding of relatively soft Feldspar, which dominates the matrix.
In terms of mechanical properties, the main difference between
magnetite and pyrite is in the value of the Poisson ratio. Magnetite
has a much higher value of the Poisson ratio than pyrite (0.25 vs.
0.17), which indicates that the ability of magnetite to deform and
transfer stress into the neighboring mineral grains will be higher.
We investigated the effect of Poisson ratio on the patterns of frag-
mentation of the sample, while all other properties of minerals are
kept constant.
Fig. 4. Elastic modulus of sphalerite from Rosebury and Broken Hill mine.
Fig. 5. Elastic modulus of chalcopyrite from Mt. Isa Mine.
70 N. Djordjevic / Minerals Engineering 46–47 (2013) 68–75

Of particular relevance to texture, is the effect of the shape of
the grains and their distribution, on the fracture initiation and
propagation. Previous research (Blair and Cook, 1998a,b) has indi-
cated that stress amplification associated with the shape of the
minerals is a more significant factor than the mechanical proper-
ties of minerals (particularly of presence of relatively corners/tips,
which acts as stress amplification points).
In the first phase, we modeled the mechanical response of the
rock texture, which was composed from the grains extracted from
the images of real rock texture. The intention was to develop
clearly different textural types and to investigate sensitivity of
the methodology. For this purpose we used texture from Ernest
Henry mine, which was then simplified to the level that textural
model was composed from 1 to 3 mineral types. Models were com-
posed from three common minerals, K-spar, chalcopyrite and mag-
netite. Elastic properties of minerals are accepted based on the
published values. Strength properties are determined based on
the published value for elastic modulus of elasticity and approxi-
mate relationship that compressive strength of materials tends to
be approximately 1/400th of the elastic modulus, and that tensile
strength is 10% of the compressive strength, Table 1.
From the point of view of the influence of texture, two cases are
of particular interest: first when chalcopyrite and magnetite are
uniformly distributed within the host matrix composed from K-
spar, and a second case where magnetite and chalcopyrite are clus-
tered into separate clusters, Figs. 6 and 7. Properties of gangue
minerals are kept same.
The application of a vertical load, modeling resulted in fragmen-
tation patterns which are clearly different, as shown in Figs. 8 and
9.
From the modeled fragmentation pattern, the fragment size dis-
tribution is calculated. Fragment size distribution shows that the
clustered magnetite will produce finer fragmentation, Figs. 10
and 11.
However, from the point of view of liberation of chalcopyrite it
is clear that liberation of chalcopyrite will be stronger, in the mod-
eled case of texture where chalcopyrite and magnetite were mixed
together. This is indicated based on the improved ability for gener-
ation of relatively small fragments, in the second case. Improved
ability for generation of small fragments comes as result of interac-
tion between relatively hard magnetite grains and relatively soft
chalcopyrite grains. In the modeled case, difference in pattern of
liberation of chalcopyrite is also affected by the clustering’s of chal-
copyrite and position of the cluster. However, in any case results
shows that, depending on the textural features of rock, good rock
fragmentation and good liberation of valuable minerals may not
occur simultaneously.
6. Influence of grain boundaries
At present all of the digital images which were used as input for
numerical modeling using OOF code, came as classified images of
mineral phases present in the polished section of the ore. In many
cases, some minerals such as K-spar are not represented as distinc-
tive singular mineral grains, but as a continuous area, composed
from many mineral grains of K-spar. On the other hand, minerals
such as magnetite tend to present themselves in the polished sec-
tion as the singular grains. Another, potentially significant aspect
of modeling, is that interfaces between different minerals are con-
sidered to be continuous, and there is no special weakening of the
materials as the result of discontinuity in the type of materials
Table 1
Mechanical properties of minerals used in modeling.
Mineral Elastic
modulus
(GPa)
Poisson’s
ratio
Compressive
strength (MPa)
Tensile
strength
(MPa)
K-spar 39.7 0.33 99 9.9
Chalcopyrite 84.6 0.28 210 21
Magnetite 230.6 0.25 570 57
Pyrite 292 0.17 720 72
Fig. 6. Case of uniformly distributed magnetite (black) and chalcopyrite (red)
within K-spar matrix (sample 1). (For interpretation of the references to color in this
figure legend, the reader is referred to the web version of this article.)
Fig. 7. Case where magnetite and chalcopyrite and separated into distinctive
clusters (sample 2).

(from one mineral grain to another). Or in other words, even for the
case of mono-minerals, multi-grain material, mineral boundaries
are not considered to be weaker than the main body of the mineral.
However, it is commonly believed that the interface between
two mineral grains is characterized with lower strength than the
mineral grain itself. This is confirmed with modeling. Results pre-
sented by Tromans and Meech (2002) show that, on average, grain
boundary fracture toughness is lower than trans-granular fracture
toughness. By fitting numerical values presented by these authors,
we concluded that grain boundary fracture toughness is lower on
average by about 9% than trans-granular fracture toughness,
Fig. 12.
The implications of ignoring systematic reduction in strength,
associated with grain boundaries, are investigated by modeling
mechanical response and fragmentation for two cases of synthetic
texture. In one case a model is built with minerals without reduc-
tion in mechanical proprieties along the grain boundaries, while in
the other case strength of the material along a relatively thick grain
boundary region is reduced by 10%, relative to the strength of min-
eral (K-spar) which comprised the dominant mineral phase in the
model, Fig. 13.
Fig. 8. Fragmentation pattern for the case of homogenous distribution of magnetite
and chalcopyrite (sample 1) with black regions indicates fractures.
Fig. 9. Fragmentation pattern for the case of clustered distribution of magnetite
and chalcopyrite (sample 2) with black regions indicates fractures.
Fig. 10. Fragment size distributions of modeled compression tests (based of
fragment area).
Fig. 11. Fragment size distributions of modeled compression tests, based on
fragment volume.
Fig. 12. Relationship between grain boundary fracture toughness and transgranular
fracture toughness for a range of minerals (modified after Tromans and Meech,
2002).

The same modeling is repeated, without specific grain bound-
aries. The results obtained demonstrate that in the case where
the second phase is a mineral which is very different (harder) than
the host minerals, the effect of grain boundaries appears to be
insignificant, Figs. 14 and 15.
In the case where textures are composed from the minerals in
which the mechanical properties are similar, assuming that shape
of grains is the same or similar, it is reasonable to expect that
reduction in strength associated with grain boundaries will be of
greater consequence. Considering, the random nature of the orien-
tation of the load and the orientation of the grain boundaries, it is
not surprising that in such cases liberation of any particulate min-
erals will appear as a random process.
This is common for waste rock where minerals tend to be of
similar mechanical properties. In the case of ore, where frequently
valuable minerals are of strikingly different mechanical properties
from associated gangue minerals, randomness associated with ori-
entation of grains in relation to the direction of pressure applica-
tion, is reduced. In such cases we can argue that preferential
liberation of minerals will occur more frequently.
7. Influence of texture vs. mechanical properties of minerals on
the rock fragmentation pattern
To further investigate the sensitivity of fragmentation modeling
on the variation in mechanical properties of minerals, we modeled
a case where rock is composed from matrix and one type of min-
eral in which properties were varied. In both cases matrix is repre-
sented with K-spar, while the second phase was either magnetite,
pyrite or chalcopyrite. Mechanical properties of matrix were kept
constant, while properties of 2nd mineral phase were selected as
per Table 1. Samples were loaded along vertical axis in compres-
sion on a fixed base. In the case of pyrite vs. magnetite, the final
pattern of fracturing is almost identical, Figs. 16 and 17.
The results show that differences in elastic properties between
pyrite and magnetite are not sufficient to produce a noticeable
difference in fragmentation pattern where the host matrix is K-
spar.
In the case where the second phase is chalcopyrite, the pattern
of fragmentation at the same level of strain, differs significantly
from the one observed in the case of pyrite and magnetite, Fig. 18.
Fig. 13. Synthetic texture used to investigate effect of grain boundaries (black) for
model composed from K-spar (gray) and magnetite (blue). (For interpretation of the
references to color in this figure legend, the reader is referred to the web version of
this article.)
Fig. 14. Fragmentation pattern for the case with grain boundaries, with black
regions indicates fractures.
Fig. 15. Fragmentation pattern for the case without grain boundaries, black regions
indicate fractured rock.
Fig. 16. Fragmentation for the case of pyrite as second phase, black indicates
fractures.

The difference in properties between pyrite and chalcopyrite
become significant, in terms of level of damage that can be induced
in the rock, for a given amount of introduced energy. For the same
amount of strain, pyrite as the second phase will cause substantial
weakening of K-spar matrix while, in the case of chalcopyrite, only
minor debonding will occur, Figs. 19 and 20.
It is quite informative to compare the final pattern of fragmen-
tation, in the case of two radically different textures, but with the
same second phase mineral (magnetite), Figs. 17 and 21.
Although fraction of the second phase minerals was not identi-
cal, differences in pattern of fragmentation for the same amount of
strain are large. This is clearly visible in the fragment size distribu-
tions, Fig. 22.
These results indicate that the difference in texture may be
more significant for the final pattern of fragmentation, than small
or even moderate differences in the mechanical properties of min-
erals. The case where second phase mineral is widely distributed
within a relatively soft matrix (of identical properties in both
cases), is conducive for fine fragmentation, while the opposite is
the case where second phase, where relatively hard mineral, is
present in the form of a few relatively large grains. The implica-
tions are that any third mineral phase homogenously distributed
Fig. 17. Fragmentation for the case of magnetite as second phase, black indicates
fractures.
Fig. 18. Fragmentation for the case of chalcopyrite as second phase, black indicates
fractures.
Fig. 19. Pattern of fracturing for the case of pyrite as second phase minerals, black
indicates fractures.
Fig. 20. Pattern of fracturing for the case of chalcopyrite as the second phase
mineral, under same loading conditions, black indicates fractures.
Fig. 21. Case of large grains, largely of regular shape (EH2), black indicates
fractures.

within matrix, which may be of economical interest, is much more
likely to be liberated when hard mineral phase is also relatively
widely distributed within matrix. This indicates that liberation of
the 3rd phase (chalcopyrite) as result of proximity to harder min-
erals (pyrite, magnetite) is strong function of distance between
those grains. More even distribution of hard grains will be more
conducive to liberation of chalcopyrite grains dispersed in their
vicinity.
8. Conclusions
Image based numerical modeling is a useful tool for investiga-
tion of the pattern and dynamics of the rock breakage process.
Its usefulness rests on the fact that a difficult step of building a
faithful model of rock texture and composition, as a pre-requisite
for modeling of rock breakage, is removed. Images based numerical
modeling could be particularly effective in the mineral extraction
industry, where the key objective of crushing and grinding is the
full or partial liberation of specific minerals.
One of the stumbling blocks in the implementation of the method
is the determination of the necessary input parameters, such as
Young’s modulus of elasticity and the strengths of minerals. In cases
where reliable information cannot be found in the literature, this
obstacle can be removed by micro-indentation testing of the polished
samples of rock. Micro-indentation testing is a fast and sufficiently
accurate method for the determination of the key mechanical param-
eters of minerals required for numerical modeling.
In cases where matrix is of significantly lower elasticity and
strength than the included minerals, modeling results indicate that
even moderate variation in the mechanical properties of valuable
minerals will not change the final pattern of fragmentation. Tex-
tural parameters of the rock, such as size, shape and distribution
of minerals are more important than their mechanical properties
within the range investigated. This may not be the case when min-
erals are of similar mechanical properties to the properties of
matrix.
The modeling approach used so far, mimics slow compression
loading. In real crushing and grinding environments, the rate of
loading is faster; therefore there is a possibility that some selectiv-
ity, in terms of breakage and liberation, seen in this modeling, may
not be present in cases of more dynamic modeling. To investigate
cases of the dynamic breakage of rock, it is necessary to use differ-
ent types of FE codes. This may be possible by transferring rock im-
age based, structured FE mesh from the OOF code into compatible
dynamic FE codes.
Acknowledgments
This research was part of collaborative geometallurgical project
being undertaken at CODES (University of Tasmania) and JKMRC
(SMI, University of Queensland). The author would like to acknowl-
edge help of Dr. Steven Walters who created images of synthetic
rock texture and Dr. Luke Keeney who performed micro-indenta-
tion testing. Thanks are due to Dr. Rob Morrison for insightful com-
ments and Mrs. K. Holtham for editing help. The author
acknowledges financial support and permission to publish from
industry sponsors of the AMIRA International GEM Project.
References
Blair, S.C., Cook, N.G.W., 1998a. Analysis of compressive fracture in rock using
statistical techniques: Part I. A non-linear rule-based model. International
Journal of Rock Mechanics and Mining Sciences 35 (7), 837–848.
Blair, S.C., Cook, N.G.W., 1998b. Analysis of compressive fracture in rock using
statistical techniques: Part II. Effect of microscale heterogeneity on macroscopic
deformation. International Journal of Rock Mechanics and Mining Sciences 35
(7), 849–861.
Everitt, R.A., Lajtai, E.Z., 2004. The influence of rock fabric on excavation damage in
the Lac du Bonnett granite. International Journal of Rock Mechanics and Mining
Sciences 41(8). Rock Mechanics Results from the Underground Research
Laboratory, Canada, December 2004, pp. 1277–1303.
Garboczi, E.J., Day, A.R., 1995. An algorithm for computing the effective linear elastic
properties of heterogeneous materials: three-dimensional results for
composites with equal phase Poisson’s ratios. Journal of the Mechanics and
Physics of Solids 43 (9), 1349–1362.
Langer, S.A., Fuller Jr., E.R., Carter, W.C., 2001. OOF: an image-based finite-element
analysis of material microstructures. Computing in Science & Engineering 3 (3),
15–23.
Schlangen, E., Garboczi, E.J., 1997. Fracture simulations of concrete using lattice
models: computational aspects. Engineering Fracture Mechanics 57 (2–3), 319–
332.
Tang, C.A., Liu, H., Lee, P.K.K., Tsui, Y., Tham, L.G., 2000. Numerical studies of the
influence of microstructure on rock failure in uniaxial compression – Part I:
Effect of heterogeneity. International Journal of Rock Mechanics and Mining
Sciences 37 (4), 555–569.
Tromans, D., Meech, J.A., 2002. Fracture toughness and surface energies of minerals:
theoretical estimates for oxides, sulphides, silicates and halides. Minerals
Engineering 15 (12), 1027–1041.
Fig. 22. Fragment size distribution curve for two radically different textures (with
same properties of the second phase mineral under identical loading conditions).

image based modelling of rock fragmentation

Recommended

Recommended

More Related Content

What's hot

What's hot (19)

Viewers also liked

Viewers also liked (15)

Similar to image based modelling of rock fragmentation

Similar to image based modelling of rock fragmentation (20)

image based modelling of rock fragmentation