Report 2010:P1 ISSN 1653-5006
Swedish Blasting Research CentreMejerivägen 1, SE-117 43 Stockholm
Luleå University of TechnologySE-971 87 Luleå www.ltu.se
Gravity flow of broken rock in sublevel caving (SLC) – State-of-the-art
Gravitationsflöde hos sprängda bergmassor i skivrasbrytning – dagens teknik läge
Matthias Wimmer, Swebrec
Universitetstryckeriet, L
uleå
Swebrec Report 2010:P1
Gravity flow of broken rock in sublevel caving (SLC) – State-of-the art
Gravitationsflöde hos sprängda bergmassor i skivrasbrytning – dagens teknik läge
Matthias Wimmer, Swebrec
Luleå November 2010, revised December 8, 2010
Swebrec - Swedish Blasting Research Centre
Luleå University of Technology
Department of Civil and Environmental Engineering • Division of Rock Engineering
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SUMMARY
This report surveys the state-of-the art of gravity flow in sublevel caving (SLC). The principles of
SLC operations are firstly explained as well as factors influencing gravity flow behavior of blasted
and caved rock.
Thereafter, flow of broken rock is highlighted from a modeling perspective. The traditional
ellipsoid approach and its later modifications are firstly reviewed. Common modern modeling
approaches are surveyed. Small- and full-scale experimental studies are presented in detail with
respect to their actual performance and outcomes.
The difficulties in simulating SLC relate to the physical scale as well as the broad range of time-
scales involved: this results in a vast number of unknowns and uncertainties. It is commonly
accepted that blasting greatly influences the subsequent flow phase. Various attempts have been
made to increase understanding of gravity flow even though the initial situation after blasting is
somewhat obscure. Interest is great as ore recovery, dilution, and flow disturbance are direct
consequences of flow behavior.
Several conceptual flow models have, therefore, been developed based on small- and full-scale
experiments. Of these, the disturbed flow models, and in particular the phenomenon of shallow
draw is the subject of special attention since observations of it recently have been made in large-
scale, modern SLC geometries.
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SAMMANFATTNING
Denna rapport ger en översikt över kunskapsläget inom gravitationsflöden inom skivrasbrytning.
Till att börja med gås grundförutsättningarna för skivrasbrytningen och möjliga påverkansfaktorer
igenom.
Sedan belyses flödet eller rörelsen av den sprängda malmen från modelleringssynpunkt, med
början i den traditionella ellipsoidmodellen och dess successiva förbättringar fram till modernare
modelleringsansatser. Modell- och fullskaleförsök presenteras med fokus på hur de fungerat och
vilka resultat de gett.
Svårigheterna med att simulera rasflöden har dels med skalan att göra, dels med de olika tidsskalor
som är inblandade. Dessa ger i sin tur ett stort antal okända parametrar och förhållanden.
Det antas vanligen att sprängningen kraftigt påverkar rasflödet. Även om förhållandena direkt efter
sprängning är höljda i dunkel, så har olika försök att öka kunskapen om rasflöden gjorts. Den
praktiska drivkraften bakom detta är att såväl malmutbytet som gråbergsinblandningen är en följd
av hur rasflödet fungerar.
Därför har flera olika s.k. konceptuella modeller förslagits med grund i sådana modell- och
fullskaleförsök. Av dessa bör modeller med ojämnt flöde och särskilt den med grund drag
(”shallow draw” phenomenon) uppmärksammas då observationer av detta fenomen nyligen gjorts i
storskaliga, moderna skivrasgruvor.
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CONTENTS
1 SUBLEVEL CAVING (SLC) .................................................................................... 1
1.1 Basic considerations ................................................................................................................ 1
1.2 Factors influencing flow behavior ........................................................................................... 2
2 GRAVITY FLOW OF BROKEN ROCK ................................................................... 4
2.1 Modeling gravity flow ............................................................................................................. 4
2.1.1 Ellipsoid Theories.................................................................................................................... 4
2.1.2 Newer modeling approaches ................................................................................................... 9
2.2 Experimental work ................................................................................................................ 12
2.2.1 Small-scale experiments ........................................................................................................ 12
2.2.2 Full-scale experiments ........................................................................................................... 16
2.3 Conceptual flow models ........................................................................................................ 25
3 CONCLUDING REMARKS ....................................................................................33
4 REFERENCES .......................................................................................................34
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FIGURES
Figure 1. Sublevel caving at the Kiruna LKAB iron ore mine. ............................................................... 1
Figure 2. Fragmentation in the context of sublevel caving. .................................................................... 3
Figure 3. Mechanisms of gravity flow (Kvapil, 1998). ........................................................................... 5
Figure 4. Shape and eccentricity as a function of material mobility (Kvapil, 1998). .............................. 6
Figure 5. Successive phases of extraction (Kvapil, 1982). ...................................................................... 6
Figure 6. Velocity distribution in the ellipsoid of loosening (Kvapil, 1998). ......................................... 7
Figure 7. Ellipsoid where all particles along the contour of the ellipsoid would move with the same
velocity (Kvapil, 1998). ...................................................................................................... 7
Figure 8. Gravitational (F1) and resisting forces (F2) acting on a rock particle (Kuchta, 2002). ........... 8
Figure 9. Draw body constructed using the Berg-mark-Roos equation with s1 = 10 m and αG = 70°
(Kuchta, 2002). ................................................................................................................... 8
Figure 10. Results of three-dimensional SLC models using the numerical modeling code PFC3D
(DeGagné & McKinnon, 2006). ....................................................................................... 11
Figure 11. Single boulder blockage in model-scale experiment (Stazhevskii, 1996). .......................... 13
Figure 12. Influence of a blast created slot on waste rock ingress (Stazhevskii 1996). ........................ 14
Figure 13. Geometry of the SLC blast model and order of initiation (Rustan, 1970). .......................... 15
Figure 14. Model after blasting (Rustan, 1970). ................................................................................... 15
Figure 15. Full-scale versus model-scale results (Janelid, 1973). ......................................................... 18
Figure 16. Draw bodies at Longtan iron ore mine (Rustan, 2000). ....................................................... 19
Figure 17. Marker recovery from different zones, total of 24 rings (Larsson, 1998). ........................... 20
Figure 18. North-South section showing different ring layouts at levels 849, 878 and 907 m. ............ 21
Figure 19. Typical result from marker trials (left ║ and right ┴ ring planes), Ridgeway mine, double
ring interactive draw in 5 m drifts, cross-cuts X0 & X2 with ring 51 & 52 at the 5250
mine level (Power, 2004a). ............................................................................................... 23
Figure 20. Extraction zone shapes noted by Power (2005) on the basis of marker trials at Ridgeway
mine. ................................................................................................................................. 23
Figure 21. Typical result from marker trials, Perseverance mine, cross section looking west and long
section looking north (Hollins & Tucker, 2004). .............................................................. 24
Figure 22. Development of waste inflow with percentage extraction (modified after Quinteiro et al.,
2004) ................................................................................................................................. 25
Figure 23. Waste rock inflow from backbreak of previous ring (Gustafsson, 1998). ........................... 28
Figure 24. Draw bodies of ring no 5 and 6, drift 9, level 335 m (Janelid, 1973). ................................. 29
Figure 25. Palm-and-finger draw body shape (Gustafsson, 1998). ....................................................... 29
Figure 26. Explanation of the pulsation seen in large scale sublevel caving (Larsson, 1996 cited by
Hustrulid, 2000). ............................................................................................................... 30
Figure 27. Sequences of cavity formation and failure (after Gustafsson, 1998). .................................. 30
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Figure 28. Shallow draw phenomenon. ................................................................................................. 31
Figure 29. Formation of a compacted interface due to blasting (Kvapil, 2008). ................................... 31
Figure 30. Location of observation drift at Ridge-way mine (Power, 2004b). ..................................... 32
Figure 31. Photographs taken from observation drift, width of opening about 1.5 m (Power, 2004b). 32
Figure 32. Vertical cross section showing section along drift axis and incompletely blasted rings. Long
arrow indicates camera viewing direction (Selldén & Pierce, 2004). ............................... 32
Figure 33. Open gap between blasthole plane and a combination of confined ore and compacted waste
in previous gaps. The damaged brow is the brighter material in the far left of the picture.
(Selldén & Pierce, 2004). .................................................................................................. 32
TABLES
Table 1. Conceptual models of gravity flow mechanisms in sublevel caving. ..................................... 26
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1 SUBLEVEL CAVING (SLC)
1.1 Basic considerations
Sublevel caving is a mass mining method based upon the utilization of gravity flow of blasted ore
and caved waste rock (Kvapil, 1998). It relies on the principle that ore is fragmented by blasting
while the overlying host rock fractures and caves under the action of mine induced stresses and
gravity. Thereby the caved waste originating from the overlying rock mass fills the temporary void
created by ore extraction. The method itself has been initially applied in the early 1900s to extract
soft iron ores found in Minnesota and Michigan (Cokayne, 1982). At that time heavily timbered
drift support was sequentially removed at the end of a drift initiating the ore to cave and then was
being slushed out. As dilution became excessive the next set of timbers was removed and so on.
Today many uncertainties of fragmentation and ore cavability are eliminated since each tonne of
ore is drilled and blasted from the sublevels. Breaking the ore by blasting removes the dependency
on “natural” fragmentation as the mechanism for ore breakage shared by most other methods of
caving. For this reason SLC is strictly speaking not considered a caving method any longer as far as
the ore is concerned, but SLC does rely on the walls caving and thus the name is retained. As
practiced today the method should probably be given another name, such as sublevel retreat
stoping, continuous underhand sublevel stoping or something similar that better reflects the process
(Hustrulid, 2000). SLC is nowadays usually applied in hard, strong ore materials in which the
hanging wall progressively caves, keeping pace with the retreating rings.
Key layout and design considerations are to achieve high recovery with an acceptable amount of
dilution. Current SLC geometries (Figure 1) consist of a series of sublevels created at intervals of
between 20 and 30 m beginning at the top and working downward.
Figure 1. Sublevel caving at the Kiruna LKAB iron ore mine.
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A number of parallel drifts are excavated on each sublevel with drifts being offset between the
individual sublevels. From each sublevel vertical or near vertical fans of holes are drilled upward to
the overlying sublevels. The burden between the blast rings is about 2 - 3 m. Beginning typically at
the hanging wall the rings are blasted one by one against the material lying in front consisting of
ore from overlying slices and caved waste. The extraction of ore from the blasted slice continues
until a total dilution or some other determining measure reaches a prescribed level. Thereupon the
next slice is blasted and the process continued. Depending on the thickness of the orebody the
technique may be applied using traverse or longitudinal retreat.
1.2 Factors influencing flow behavior
The major disadvantage of SLC is the relatively high dilution of the ore by waste which is based on
the flow characteristics of both materials. Fragmentation of the ore slice itself can be regarded as a
core element for successful SLC (see Figure 2). The general tendency is that more finely
fragmented ore has greater mobility in the stope area. Thorough fragmentation allows drawing of
the ore from over the entire width of the extraction drift and from deep in the muck pile. Both of
these factors allow for a uniform gravity flow and this promotes a higher recovery of ore and hence
overall effective use of the SLC method. In this respect blasting has been throughout the literature
identified as the initial, but also the major impact upon primary fragmentation and later material
flow characteristics (Janelid, 1968; Cullum, 1974; Marklund, 1976; Kvapil, 1982; Stazhevskii,
1996; Bull & Page, 2000; Hustrulid, 2000; Rustan, 2000; Power, 2004a-b; Selldén & Pierce, 2004;
Minchinton & Dare-Bryan, 2005; Zhang, 2005 & 2008; DeGagné & McKinnon, 2005).
In SLC, blasting takes place in a semi-confined situation, where the blasted material is allowed to
swell due to the compaction of the caved material and to a minor extent swell into the void volume
of the production drift. Even though several analytical and empirical models have been developed
in the past the interaction of semi-confined blasting conditions, SLC blast design and rock mass
characteristics on blast performance are not well understood. Layout criteria for ring blasting
concerning overall geometry (ring inclination, shoulder hole angles, design powder factor),
burden/spacing ratios, explosive properties and timing are commonly based on site experience.
With the general trend towards larger blast layouts over the past years and considering the
fundamental importance of blasting to the success of a SLC mining operation it is remarkable that
only a limited number of well documented experiments have been undertaken to quantify the
impact of altered blast design parameters on the resulting material flow characteristics (Rustan,
1970; Kosowan, 1999; Quinteiro et al., 2001; Zhang, 2004; Power, 2004a-b; Clout, 2004;
Quinteiro, 2004; Zhang, 2005; Brunton et al., 2010). The impact of measured blast performance
such as vibration records, VOD measurements, and backbreak studies should be of particular
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interest when gravity flow is studied (Rustan, 1993; Hedström, 2000; Fjellborg, 2002; Zhang,
2005; Brunton, 2009; Wimmer et al., 2009).
Figure 2. Fragmentation in the context of sublevel caving.
In practice the quantification of the physical and mechanical properties of blasted or caved rock is
difficult. Rustan (2000) stated that the most important parameters influencing flow width are
fragment size distribution, shape factor of particles, surface friction of fragments, attrition, density,
shear strength, cohesion of the bulk material and moisture content. The rock material properties
internal angle of friction, limit border angle and angle of repose at dumping or loading have been
assessed. The properties swelling, packing and porosity vary though in space and time and it has
not been possible to assess them or assign a value to them.
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2 GRAVITY FLOW OF BROKEN ROCK
Flow behavior of broken rock has been investigated through small-scale experimental studies
aimed at understanding fundamental mechanisms and factors influencing material flow behavior in
storage bins. Experiments of this type are well suited to construct general applicable mathematical
models.
Mine-based experimental models have been set up to model specific situations. The literature
outlines that the development of efficient design and the operation of SLC mines relied upon
results obtained from experiments that directly modeled specific situations in small- or full-scale
tests.
Generally, the latter focuses on quantifying the impact of various mine design parameters based
upon a specific geometry of the mine and its orebody on material flow behavior and subsequent ore
recovery as well as dilution. They also serve to validate and further improve numerical models. The
following summarizes the current understanding of SLC material flow behavior.
2.1 Modeling gravity flow
2.1.1 Ellipsoid Theories
The theory proposed by Kvapil (1965) was one of the first attempts to fit general mathematical
models using physical models to the flow of granular material. Although it has been developed
using small-scale 2D models aiming at modeling flow in storage bunkers is has become highly
significant for caving methods and was extensively used as a design tool for these methods before
other modern modeling approaches became accepted.
The results obtained by Kvapil are based on studies of free discharge of granulated material
through an outlet at the bottom of a hopper. Central to this theory is the progressive expansion of a
flow ellipsoid which progresses upwards as material is discharged. Meanwhile the geometry of
granular flow is described as the concept of “ellipsoids of motion”. It also outlines dependencies of
the ellipsoid of motion on particle sizes and how the design of a hopper could be determined given
this knowledge.
In subsequent years the flow ellipsoid has been divided into two ellipsoids, each with distinct
boundaries (see Figure 3). These are named the ellipsoid of extraction and the ellipsoid of
loosening (Janelid & Kvapil, 1966). The ellipsoid of extraction is stated as the limiting boundary,
which defines the original location of material that has been extracted from the outlet whereas the
ellipsoid of loosening defines the boundary between stationary material and material that has
moved from its original location at any given point in time material is discharged.
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Shapes defining the ellipsoid of extraction and loosening have been referred to in a number of
different ways in the literature (Trueman, 2004). Beyond the loosening ellipsoid all particles
remain stationary in a region known as the passive zone. As drawing proceeds, the material within
the extraction ellipsoid is removed and replaced by surrounding particles. However, it is only the
material within the loosening ellipsoid that has the opportunity to enter the extraction ellipsoid. The
size and eccentricity of both ellipsoids gradually develop as material is removed.
Figure 3. Mechanisms of gravity flow (Kvapil, 1998).
By placing markers in a certain pattern within the granular material in a 3D model the validity of
the existence of both zones has been demonstrated. Markers extracted defined the ellipsoid of
extraction and those that just moved to the draw point the ellipsoid of loosening.
The shape of a given ellipsoid is described by its eccentricity related to the major and minor semi-
axes of the ellipsoid. As a rule, the volume of loosening ellipsoid is about 15 times larger than the
volume discharged: expressed in terms of heights this yields a 2.5 times larger loosening ellipsoid.
It is well known that particle size directly influences eccentricity as, for instance, smaller particles
will generate thinner ellipsoids with a proportionally higher eccentricity. Also the eccentricity of
the ellipsoid of extraction and loosening increases with the height of the ellipsoid. This effect,
which is relatively small in SLC, has a much greater importance in block caving due to the very
large block heights. Moreover, eccentricity depends on a number of other factors (Kvapil, 1998),
such as shape (spherical, irregular), surface roughness of the particles (smooth, rough) material
properties (density, strength, moisture content), extraction rate (high, low and continuous versus
interrupted).
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Consideration of all these factors, results in a certain flow behavior which might be expressed in
terms of the mobility of granular or coarse material. A greater mobility results in easier flow and a
higher eccentricity of the ellipsoids as shown qualitatively in Figure 4.
Figure 4. Shape and eccentricity as a function of material mobility (Kvapil, 1998).
Considering models with horizontally layered white and black granulated material and studying
deflections of the layers indicated the active zone and also that the drawdown of the material itself
occurs in the form of an inverted cone (see Figure 5). This indicates that the vector velocity in the
center of the draw is highest and is reduced proportionally on either side of the draw cone axis until
a particle velocity of zero is achieved at the boundary.
Figure 5. Successive phases of extraction (Kvapil, 1982).
The velocity distribution is shown in Figure 6, which represents the velocity distribution through
sections E-E` to A-A`. The boundaries of the loosening ellipsoid have an instantaneous velocity of
zero and the central flow axis vectors indicate the progression of relative values such that v4 > v3 >
v2 > v1. For better visualization the velocity vectors are constructed perpendicular to the axial
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section of the ellipsoid. From the previous figure one can derive zones of the same particle velocity
v1 defined on the boundary shown in Figure 7. A line connecting the particles of the same velocity
forms an elliptic looking figure in 2D and an ellipsoid of same velocity in 3D. Evidently, the shape
of the gravity zones is controlled by a specific distribution of the velocity of motion, resulting in
ellipsoids of the same velocity. Therefore, not only does the zone of loosening have the shape of an
ellipsoid, but so also does the zone from which the discharged material was extracted (ellipsoid of
extraction).
Figure 6. Velocity distribution in the ellipsoid of loosening (Kvapil, 1998).
Figure 7. Ellipsoid where all particles along the contour of the ellipsoid would move with the
same velocity (Kvapil, 1998).
Cox (1969) made model experiments and also underground studies at Mufulira mine in the
Zambian copper belt, initially without the knowledge of theory of ellipsoid flow (Kvapil & Janelid,
1966), but his findings were in close agreement with the theory. Further validation of the theory
and a relatively close fit have been shown by full-scale tests from the Grängesberg SLC operation
(Janelid, 1973), see chapter 2.2.2. A reflection of the general level of acceptance of this theory is
that even today, many general mining textbooks with sections on granular flow, use the ellipsoid
model as their basic flow theory (Kvapil, 1998; Hustrulid, 2000; Brady & Brown, 2004).
During the period in which ellipsoid theory was gaining acceptance other workers have added
valuable contributions to gravity flow theory. Worth mentioning is experimental work by Gardner
(1966) on flow in bins and hoppers in a 2D model. There a mathematical model was presented that
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predicted the shape of the dead zones at the bottom of a bin as a function of the internal angle of
friction of the model media.
The ellipsoid theory presented has since then been further refined, taking into consideration a near
elliptical form of the extraction draw body but with a maximum width occurring above the upper
half of the draw body; the so-called “drop hypothesis”. The model assumes that a particle moves in
a straight line from its resting point to the opening and that rock is removed continuously.
Consideration of a decomposition of forces acting on a rock particle in opposite directions (see
Figure 1), namely one component of the gravitational force and a resisting force from surrounding
particles, yields the so-called Bergmark-Roos equation (Bergmark, 1975; Hedén, 1976):
s(α) = s1 * [(sinα – sin αG) / (1 – sin αG)]
s…travel distance
α...travel angle
αG..maximum angle at which the broken rock does not flow
s1…height of the extraction draw body
By use of the Bergmark-Roos equation the shape of the extraction draw body can be constructed
(see Figure 2).
Figure 8. Gravitational (F1) and resisting forces (F2) acting on a rock particle (Kuchta, 2002).
Figure 9. Draw body constructed using the Berg-mark-Roos equation with s1 = 10 m and αG = 70°
(Kuchta, 2002).
One of the shortcomings of this equation is that the width of the draw body continues to increase
with increasing extraction heights due to the assumption that rock particles travel in a straight-line
path towards the opening. On the other hand research has shown that in rock, the width of the draw
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body will reach a maximum value at very great extraction heights and does not continue to increase
with increasing extraction heights (Rustan, 2000). Indeed, at low or moderate extraction heights, an
approximate shape of the draw body may be derived.
Kuchta (2002) presented a revised version of the Bergmark-Roos equation accounting for a non-
zero opening width. This version includes equations derived for the area, volume and maximum
width of the draw body for a given extraction height.
2.1.2 Newer modeling approaches
The problem of analyzing the progressive flow of rock through an enclosed stope could not be seen
as wholly analogous to theories developed for the flow of granular materials (Yenge, 1980). This is
due to the discrepancies in particle size, the relative sizes between the containers and particles and
boundary conditions. Three distinct differences exist between the flow of materials in bins and in
an SLC environment and they can be summarized as follows:
The friction between broken rock and the solid face of the unbroken ring affects the flow
pattern of the blasted rock, i.e. in a bin the material is surrounded by four solid walls
whereas the rock in SLC is surrounded on three sides by broken rock and on the fourth side
by the in-situ rock of the next slice to be blasted,
Blasting the ore column creates density variations within the ore and between ore and
waste,
SLC exists under substantially higher overburden pressures than are usually found in bin
flow.
There are also appreciable differences between the slower discharge rates, the large increases in
void volume and the delayed ground caving response in SLC as compared to granular solid models.
A number of problems that appear when describing SLC flow by idealized ellipsoid theory have
long been recognized, both when doing small and full-scale experiments (Fröström, 1970; Just &
Free, 1971; Cullum, 1974; Janelid, 1975; Just, 1981; Yenge, 1981; Kvapil, 1982; Peters, 1984;
Gustafsson, 1998; Rustan, 2000; Clout, 2004; Hollins & Tucker, 2004; Power, 2004a-b).
Consequently more advanced model and full-scale experiments have been set up. Subsequent
research has been directed towards mathematical methods to address phenomena observed in the
experiments and to improve model performance such as:
Stochastic methods (Chen, 1997; Gustafsson 1998) assume that gravity flow is a stochastic process,
i.e. they include the probabilities of downwards propagation of a particle or upwards propagation of
voids (void diffusion). Another conceivable way of creating voids would be a differential flow of
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particles but is actually not considered in these models. It is important to understand that the
physics of granular flow are almost completely ignored with these methods.
Plasticity theory (Pariseau & Pfleider, 1968; Nedderman 1992) is the commonest coarse grained
approach for the prediction of velocity distribution in granular materials. In these models, the stress
distribution in the static material is first calculated and from this the velocity distribution is
obtained. Although little progress has been achieved for the prediction of velocity fields in specific
cases, plasticity theory provides more realistic predictions for granular flows in hoppers since it
only applies when particles are small and the material may be considered to act as an equivalent
continuum. There is, however, difficulty in determining a range of the required material properties.
Cellular automata, CA (Sharrock et al., 2004; Alfaro & Saavedra, 2004; Castro et al., 2009) divide
the volume of material into a large number of cells that interact according to differential equations,
describing the physics of the system. In this approach, cells contain discrete objects that are
categorized by individual state parameters that evolve dynamically according to the partial
differential equations.
An example of cellular automata model is, for example, e.g. FlowSim (Castro et al., 2009) which
uses local rules that simulate the gravity flow from discrete elements that change their state through
local rules. The movement of grains is simulated through two mechanisms, one incorporating the
increase in porosity and another rule incorporating the movement of particles driven by gravity.
Both local rules are summarized by two adjusting parameters which require calibration through
experimental data. A distinct difference with discrete element methods (Cundall & Strack, 1979) is
that in FlowSim particle shape or forces are not explicitly calculated. These simplifications were
intentionally made so that FlowSim could computationally be faster than other methods based on
discrete elements. This does not necessarily mean a loss in the rigorousness of the model, as the
aim of a mathematical flow model for block caving applications is to help in defining the design or
draw control practices for a large number of draw points and elements.
Another example of cellular automata, CA, is CAVE-SIM. However, both of these examples aim to
develop an engineering tool to determine the dilution entry point, mixing of grades and recovery in
a large, actual, production block cave scenario.
Discrete element method, DEM (Hustrulid, 1997; Selldén & Pierce, 2004; Minchinton & Dare-
Bryan, 2005; DeGagné & McKinnon, 2005 & 2006) involves computing the contact forces and
resulting Newtonian dynamics of individual particles in an assembly. As a result, the values of
shear and normal forces, rotation, velocity and displacement are determined for each particle.
Figure 10 demonstrates a possible modeling outcome using PFC3D.
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Gravity flow of broken rock in SLC Swebrec Report 2010:P1
Figure 10. Results of three-dimensional SLC models using the numerical modeling code PFC3D (DeGagné & McKinnon, 2006).
A further development to this is the modeling software REBOP (Rapid Emulator Based on PFC3D;
Lorig & Cundall, 2000) which incorporates rules based on mechanisms observed and determined in
PFC3D simulations, confirmed by physical model tests performed at the JKMRC (Power, 2004a)
and calibrated at various mine sites such as Henderson, Northparkes, Palabora and Cullinan
(Pierce, 2004). It embodies the incremental evolution of IMZ (Isolated Movement Zone) and IEZ
(Isolated Extraction Zone) for each draw point, those volumes being equivalent to the ellipsoid of
loosening and ellipsoid of extraction in the conceptual model derived by Kvapil (1998). In contrast
to gravity flow simulation packages using fixed draw cone shapes, REBOP does not make
assumptions about the geometry of the IMZs and IEZs. The shape of these three dimensional
volumes evolves continuously as an iteration of quite simple micro rules applied in a time step
fashion that mimics production from the draw points on a daily basis. The equations of these micro
rules govern the material flow from one horizontal layer to the underlying layer by mechanisms
such as collapsing arches at the top of an IMZ and erosion of material in the vertical walls between
adjacent IMZs. The overall objective of the REBOP simulation modeling is to be a practical tool
for engineers for mining design and production control mainly in a larger context e.g. in block
caving operations. REBOP allows predictions of extracted ore grade or other caved rock properties
in caving operations and offers visualization of the movement and distribution of material above
the draw points in three dimensions.
Other, DEM codes are FASTDISC and FLOW3D. Because of the accuracy of DEM, it is well
suited for detailed gravity flow analysis on factors affecting complex flow phenomena in sublevel
or block caving mines. However, its application has several limitations associated with numerical
stability and computation time.
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The key motivation for development of these models was to simulate the effects of different
geometries and draw strategies on the economic performance of SLC operations. Furthermore, the
development of theories and models is important for the ongoing success and economic viability of
the mining method. A much more detailed summary of numerical models used to emulate the
gravity flow of fragmented rock is given by Castro et al. (2009).
Attempts to simulate sublevel caving are hindered by the physical scale of the operation. In
addition, blasting takes place rapidly while the draw of material may last several days for an
individual SLC ring. Incorporating flow from other higher or adjacent levels extends the process to
months. Incorporating the period of draw of rock form other higher or adjacent levels extends the
process to months or even years.
Validation of small and full-scale experimental results is critical for all numerical models. It is
therefore of great value that a number of experiments have been conducted which allowed this
validation to be undertaken (Brown, 2003; Power, 2004a-b; Selldén & Pierce, 2004; Brunton &
Chitombo, 2009).
2.2 Experimental work
2.2.1 Small-scale experiments
Physical modeling was carried out for the optimization of block caving mines in the US from 1916
onwards, and later was carried out in Africa (Lehman, 1916; Bucky et al., 1943; McNicholas et al.,
1946; Airey, 1965). The objectives of these models have been the identification of the parameters
of the process, the extent to which these parameters influence material flow, and whether the
results could be applicable to full-scale production. Model complexity evolved continually from
early bin models to models incorporating mine geometry as well as material flow properties of
blasted material.
In the late 1950s SLC became increasingly used. This called for more efficient and rational design
techniques, and small-scale testing considering different SLC layouts commenced. In these
experiments the interaction of parameters such as sublevel height, drift spacing and shape, ring
burden and inclination, fragment size and excavation techniques on material flow behavior have
been extensively studied (Sjöstrand, 1957; Koppanyi, 1960; Finkel & Skalare, 1963; Redaelli,
1963; Airey, 1965; Janelid & Kavpil, 1966; Free, 1970; Janelid, 1972; Tessem & Wennberg, 1981).
Most of these experiments have been of two-dimensional character as extraction and movement
zones have been studied through plexiglass side windows. They confirmed the ellipsoid theories as
discussed in detail in chapter 2.1.1.
13
Gravity flow of broken rock in SLC Swebrec Report 2010:P1
By contrast McCormick (1968) observed in laboratory tests with sand that the flow above a draw
point expands vertically upwards in a funnel shape during which a flow channel with parallel walls
develops. Furthermore he recognized two main mechanisms, namely collapses of hang-formations,
and normal draw-down flow. He suggests that flow cones develop because sand breaks down
continuously from the sides of arches. Once the cone becomes so wide that temporarily stable
arches could no longer develop and finally collapse, normal flow arises and a channel with parallel
wall develops.
A major limitation of all these early works was the difference between material properties produced
by SLC blasting and those selected for the model experiments. These material properties include
fragmentation distribution, bulk density or degree of compaction of the ore and waste material,
friction, cohesion properties and stress distribution within the material. A number of small-scale
experiments were conducted which took account of previous uncertainties (Panczakiewicz, 1977;
Yenge, 1981; Stazhevskii, 1996; Kosowan 1999). Of particular importance is the work by
Panczakiewicz (1977) and Stazhevskii (1996) which attempted to incorporate complex material
properties encountered in full-scale SLC rings in small-scale experiments.
Panczakiewicz (1977) constructed both 2D and 3D models to investigate various SLC geometries
for the Mount Isa Mine in Australia and the impact of fragmentation distribution and material bulk
density on flow behavior. In these studies fragmentation was divided into uniform and well-graded
distributions. Bulk density contrasts between ore and waste rock were realized by three different
categories of compaction: uncompacted, light and heavy. Arching was observed for compacted
materials which led to significant changes in flow behavior, or, in extreme cases, to a complete
blockage. Stazhevskii (1996) summarizes another attempt to model the inhomogeneous nature of
blasted rock material in model-scale by investigating the influence of material bulk density,
fragmentation distribution and oversize, by which is meant boulders, on flow behavior, see Figure
11.
Figure 11. Single boulder blockage in model-scale experiment (Stazhevskii, 1996).
14
Gravity flow of broken rock in SLC Swebrec Report 2010:P1
Figure 12. Influence of a blast created slot on waste rock ingress (Stazhevskii 1996).
However, a major drawback in the Stazhevskii (1996) study is that a discussion of model geometry
or testing procedure is lacking. From this study it is shown that both the material bulk density and
the presence of boulders have a significant influence on material flow behavior and hence on the
ingress of waste material into the extraction zone. It was concluded that a strictly symmetric flow
pattern in mining conditions would be rather exceptional.
The modeling of a slot or void created during the blasting process is also of note. The theory in the
study which originates from Markenzon (1967) suggests that a slot is formed as the burden moves
forward and compresses the caved material during the blasting process (see Figure 12). Based upon
modeling (Stazhevskii, 1996) concludes that the material above the blasted burden could then
access the newly formed slot resulting in a layer of broken material that is inhomogeneous in
composition and density with indeterminate thickness and boundaries. Such a layer would be likely
to cause waste dilution at an early stage of excavation, but also pulsating phenomena of alternating
ore and waste rock inflow observed at SLC operations.
Model-scale experiments incorporating confined blasting in the study of gravity flow have seldom
been carried out. Rustan (1970) simulated blasting and loading of SLC rounds and benches in
models on a scale of 1:75, see Figure 13 and Figure 14. The blasting was carried in a container
filled with limestone. The development of a material for the model that would give a scaled
fragmentation of full-scale fragmentation was important. To achieve this, it was necessary to insert
artificial weakness planes in the model material, because, without weakness planes, the middle size
fractions were lacking (Rustan, 1990). With a mixture of two-thirds of coarse magnetite and one-
third of fine magnetite an artificial orebody with high density could be created. Finally, the
magnetite was mixed with cement, water, and crushed microscope glass plates that would act as
natural weakness planes.
15
Gravity flow of broken rock in SLC Swebrec Report 2010:P1
Figure 13. Geometry of the SLC blast model and order of initiation (Rustan, 1970).
Figure 14. Model after blasting (Rustan, 1970).
After blasting the loaded material has been separated in terms of magnetite and waste rock
(limestone) by means of a magnet. Many of the phenomena observed at full-scale also could be
recognized in the model such as overbreak effects at the breakage surface, and variations in waste
rock content during the extraction process.
The influence of specific charge, timing, compressive strength as well as joint frequency of the
model material and confining pressure on the fragment size distribution has been studied in great
detail.
With the aim of studying flow in more detail, additional, holes have been drilled within the burden
to position markers inside some of the blasts. Several markers could be found on the muck pile
directly after blasting. The extraction showed that more markers were found to originate from the
mid-part and closest to the blasted ring plane of the entire ring. Additionally, some waste rock
fragments were found on the muck pile directly after blasting. It was explained that the dynamic
movement of the burden towards the waste rock likely opens up a slot between the burden and the
front in which waste rock can fall down from the top of the blasted ore (Stazhevskii, 1996).
Carefully excavating the model stepwise also allowed an investigation of swelling and bulking of
the blasted round by means of the markers. Correlations with timing, compressive strength and
confinement stresses have been made.
Moreover, burden kinematics in a confined state, such as swelling, velocity, acceleration and
retardation have been studied on bench blasts by using a high-speed camera (4100 fps).
16
Gravity flow of broken rock in SLC Swebrec Report 2010:P1
Zhang (2004) conducted gravity flow experiments based on SLC blasting models made of concrete
at a scale of 1:50. After blasting, the covering material of the models was manually excavated and
separated from the blasted material, which was colored a priori representing different heights. The
experiments demonstrated that the draw body is of complex shape with a volume much smaller
than the actual blasted volume. With respect to fragment sizes a tendency for coarser particles with
increasing height and remnants at the toe region has been observed. Further it is pointed out that in
order to solve the ore dilution problem associated with the discharge process, the blast and ore
discharge processes need to be treated together.
In summary, small-scale experiments have evolved from simplistic bin models to relatively
complex models incorporating SLC geometry and inhomogeneous material parameters. Numerous
limitations associated with small-scale experiments have been discussed in the literature relating to
issues of similitude (Free, 1970; Sandström, 1972; Alford, 1978; Gustafsson, 1998; Power, 2004a),
model design and properties of ore and waste (Sandström, 1972; Cullum, 1974; Janelid, 1975;
Panczakiewicz, 1977; Alford, 1978; Yenge, 1981; Stazhevskii, 1996; Gustafsson, 1998; Kosowan,
1999; Hustrulid, 2000). Despite these limitations it has at the same time been concluded that small-
scale experimental work has provided quantitative and qualitative results usable for the design and
operation of SLC mines. Further, due to the importance of material properties on flow behavior
future direction of SLC small-scale flow modeling needs to incorporate blasting (Rustan, 2000).
2.2.2 Full-scale experiments
Results from full-scale experiments investigating material flow behavior are crucial for further
development, assessment and validation of numerical and small-scale models.
Monitoring SLC material flow is generally done by means of markers (metal or plastic objects with
unique identification numbers stamped upon them) installed and grouted in drill holes located
inside the burden to be blasted. Recovery is usually done visually at the draw-point or by magnetic
separation during the later material handling process, for example at the primary crusher. A number
of limitations are associated with both types of markers. This has initiated an effort to develop an
electronic marker system based on existing RFID technique. This would allow for real time
detection of markers at the draw-point (Brunton, 2009). Details about the development and final
shape of the extraction zone are obtainable based upon the recovered markers. On the other hand,
studying the progression of the movement zone is a much more complex matter, but the following
developments are noteworthy. There is ongoing research (Baiden et al., 2008) in which synthetic
instrumented rock pieces are deployed to sense rock flow and transmit their actual positions via
VLF communication methods in real time. There are, however, no actual test results from a mine.
There is also an earlier parallel development of instrumented boulders (Hanisch et al., 2003) to
study the dynamics of debris flow on mountain slopes. The authors claim that the configuration and
17
Gravity flow of broken rock in SLC Swebrec Report 2010:P1
the redundant layout of the built-in 3D accelerometers and the differentiation and combination of
translational and rotational movements could be computed with reasonably stable long-time
behavior. There are no field data to support these claims though.
Geophysical methods could also be used to study gravity flow in-situ. Passive seismic tomography,
for example, applied in block caving to obtain information around and within the cave; for example
cave propagation, stress conditions, fragmentation and compaction zones (Glazer & Lurka, 2007;
Lynch & Lötter, 2007). Furthermore gravity measurements are carried out to estimate cave back
positions in block caving (Gaete et al., 2007). However, the study of gravity flow of individual ring
blasts would require methods that have much finer resolution. A recent attempt to pinpoint
magnetite ore residues within caving debris by means of various geophysical borehole probes
(GPR, magnetometer and susceptibility measurement) has given some promising results, but also
shown clear limitations related to the inhomogeneous nature of the material studied (Wimmer &
Ouchterlony, 2008).
Visual observations, which allow a sporadic insight into the caving flow (Selldén & Pierce, 2004;
Power, 2004a-b) are very important. The acquisition of geo-referenced 3D images from inside
cavities and behind rings in the LKAB Kiruna mine in the case of openings of a new draw point or
in hang-up situations is a promising direct approach (Wimmer et al., 2009).
It is worth noting that only a few full-scale SLC draw marker trials have been carried out in the
past due to the complexity and costs involved in such tests. The following surveys the most
important ones.
a) Grängesberg mine (Sweden)
Between 1969 and 1970 full-scale marker trials were carried out at different sublevels in the
Timmergruvan mine (Janelid, 1973). At this location the magnetite orebody has a dip of 60 - 70
degrees and varying width of 20 - 25 m. The sublevel height was either 13 or 7 m with drifts 3.3 m
wide and 3.2 m in height. The SLC ring inclination was vertical in all cases. Most blasts were
either fired individually (23 tests, each 500 tonnes), but sometimes two rings were shot
simultaneously (8 tests, each 1000 tonnes). A total of 12628 plastic markers have been inserted in
holes drilled downwards from higher sublevels and about 70 % of these have been recovered
visually at the draw points. Marker density can be regarded as very high (five rings with installed
markers inside a 1.5 m burden) but were restricted to the upper part of the expected draw body.
Besides the recording of marker identities, the additional parameters measured included the
fragment size distribution (Fröström & Lamperud, 1973), the hang-up frequency, visual estimates
of the percentage of waste rock, and wagon weights.
18
Gravity flow of broken rock in SLC Swebrec Report 2010:P1
Figure 15. Full-scale versus model-scale results (Janelid, 1973).
In these tests clear correlations were observed between the shape of the body of extraction and
disturbances, which were observed in the field such as hang-ups, boulders and unsymmetrical
draw. The apex of motion was found to be situated at a distance of around 0.5 m from the mining
front, both with single and double ring blasts. Maximum width and depth of the draw body was
found to be at the same height above the sublevel. A comparison of extraction zones from full-scale
tests and those of previous small-scale tests yielded similar results, but the small-scale results were
more repeatable, see Figure 15. The small-scale tests gave a slightly higher and narrower extraction
zone, which was attributed to a lower compaction degree of the caving debris. It has also been
observed that the draw body in full-scale tests could take the shape of an inverted drop at 60 - 70
percent of the extraction.
b) Longtan mine (China)
In China a series of full-scale experiments have been undertaken at various mine sites from 1975 to
1985 (Gustafsson, 1998). Examples are the trials undertaken at the Longtan SLC iron ore mine
from 1976 to 1977 (Chen & Boshkow, 1981; Gustafsson, 1998; Rustan, 2000). The ore was a low
grade magnetite (3800 kg/m3) with an orebody 30 – 50 m thick dipping at 80 - 90 degrees. Both the
geometry and blasting conditions for this operation were unique insofar as the blasted ring height
amounted to 50 m at a burden of approx. 1 m. Eight vertically drilled rings with a total burden of
8.4 m were blasted simultaneously yielding 32000 tonnes of ore. A total of 3520 markers (wood
filled plastic tubes or ventilation pipes) were placed in 177 marker holes. Marker rings consisted of
9 to 12 holes drilled from the lower level and 18 - 19 holes from the higher sublevel. Recovery of
markers was done by visual means; no waste rock percentage during loading was reported. The raw
19
Gravity flow of broken rock in SLC Swebrec Report 2010:P1
data itself indicated that the extraction zone was not ellipsoid but rather had the shape of a drop, see
Figure 16.
Referring to vertical sections drawn, the final depths, widths and heights of the draw body were
about 7 m, 12 m and 54 m respectively.
Figure 16. Draw bodies at Longtan iron ore mine (Rustan, 2000).
c) Kiruna mine (Sweden)
The first full-scale field trials were undertaken in Kiruna between 1966 and 1967 (Haglund, 1968).
Totally 184 rings were monitored with a wide range of design parameters. Modified design
parameters included sublevel heights (9 - 13.5 m), ring inclination (70 - 90 degrees), ring burden
(1.2 - 2.4 m), and the number of blastholes (12 - 14). No details of the number or type of markers
are provided (if they were used at all). The results from these trials indicated best recovery values
for a ring inclination of 80 degrees, 1.8 m burden and 12 blastholes.
In the project “SLC 2000” the impact of SLC geometry, blast design, draw control procedures on
ore recovery, waste rock dilution and flow behavior has been studied in more detail (Quinteiro et
al., 2001). As part of this work, gravity flow behavior has been investigated during the years 1995-
97 by installing 908 markers halfway inside the burden in 24 rings (Larsson, 1998). Markers
consisted of 1 m long electric cable pieces, each with identification. A video system has been
installed on-site to facilitate locating markers at the front and to gather qualitative observations of
the outflow into the drift during the mucking operation. Totally 32 % of the markers have been
20
Gravity flow of broken rock in SLC Swebrec Report 2010:P1
recovered and of these only a very small number originated from the sides of the ring, see Figure
17. On the other hand a large number of markers were recovered from the central part of the ring,
indicating predominant ore flow in the centre. It was concluded that this type of flow will result in
early waste rock dilution. Insufficient marker recovery made attempts to define extraction zones
difficult if not impossible (Gustafsson, 1998).
Figure 17. Marker recovery from different zones, total of 24 rings (Larsson, 1998).
Instead, the analysis was based upon ore recovery and waste rock content measured by weighing
the loaded bucket during mucking. The results indicated that an increase in ring burden (3 - 3.5 m)
resulted in a 32 % reduction in ore recovery and a 10 % increase in dilution. An increase in
production drift width (7 - 11 m) has shown both a 7 % improvement in ore recovery and dilution.
A significant reduction in dilution was observed by changing firing delays for blasting the 10 holes
of a ring, i.e. first blasting the four middle holes using short electronic delay intervals and after a
longer delay of 300 ms blasting the other holes in a ring. A delay of 100 ms was used between each
of the outer holes.
An important finding of the marker trials is that the layout designed with shorter and flatter side
holes to initiate interactive draw zones does not work. Flow rather occurs inside a relatively thin
vertical zone and this has caused some basic changes in the SLC ring layout, see Figure 18. The
present layout has, with a transition level in between, been changed to a silo-shaped layout.
21
Gravity flow of broken rock in SLC Swebrec Report 2010:P1
Figure 18. North-South section showing different ring layouts at levels 849, 878 and 907 m.
Furthermore, a project was conducted at LKAB during 2003 - 2004 with the overall objective to
carry out research to achieve higher ore recovery and controlled dilution through improved
fragmentation of the blasted rings. The main outcome can be summarized as follows. Observations
made in the test area when measuring VOD is that top initiation can be an alternative layout since it
has shown promising results regarding ore recovery and waste content. Fragmentation analysis of
nine blasted rings using electronic detonators has shown no substantial differences in the average
fragmentation size when compared with a standard layout or a top initiation layout. Moreover,
about 18 % of the electronic detonators did not respond to logging just before blasting, indicating a
system malfunction probably induced probably by blasting nearby rings (shock problem,
communication problem and/or shear off problem of wires). Interestingly, image analysis
measurements indicate that fragmentation with a lower value of xc (characteristic size, 63.2 %
passing value) and higher value of n (Rosin Rammler uniformity index) gives better ore recovery
and lower dilution.
d) Stobie mine (Canada)
A series of full-scale experiments were conducted in 1996 (Kosowan, 1999) to assess ore recovery
for sublevel heights of 21 m (9 tests) and 31 m (8 tests). The percent of ore recovered for each trial
was estimated from visual grade control techniques (no markers used). A number of factors were
considered including drilling practices, blast design and implementation, excavation technique and
draw point width. Fragmentation for each trial ring was measured as well by means of image
analysis. In summary, fragmentation for the increased sublevel height was poor, which resulted in
an unacceptable level of ore dilution and recovery. The major problems identified were blast design
and initiation performance, with a high percentage of holes not detonating.
22
Gravity flow of broken rock in SLC Swebrec Report 2010:P1
e) Ridgeway mine (Australia)
The most detailed full-scale experiments to date have been conducted at Ridgeway with over 70
individual trials conducted from 2002 -2006 (Power, 2004a-b; Brunton, 2009; Brunton et al.,
2010). The aim of the experimental program was to determine the geometry of the extraction zone,
investigate the hypothesis of interactive draw, gather information on flow mechanisms, determine
recovery and dilution factors and develop strategies for increasing metal recovery and/or reducing
costs. Markers adjusted to the approx. mean fragment size (steel pipes filled with concrete, Ø 42 x
250 mm) were grouted into place in either two or three marker ring planes inside a 2.6 m burden.
Initially marker recovery was undertaken with a combination of visual recovery and magnetic
separation during the handling process (Power, 2004a-b) and was changed due to low marker
recovery rates to magnetic separation exclusively (Brunton, 2009).
The results (Power, 2004a-b) indicated that the extraction zone was not of ellipsoid shape and that
the width and depth of the extraction zone was respectively narrower and shallower than the
blasted ring geometry, see Figure 19. At first the extraction zone develops along the mining front
(ring face) and then deepens. No evidence of interactive flow between adjacent extraction zones
could be seen. It turned out that the nature of the flow was episodic with flow proceeding in stages
from different parts of the ring. Furthermore dilution entry of waste could be identified to originate
from above the actual blasted ring at relatively low draw rates. Primary and combined recovery
(recovery at the current and next level) was determined to be on average 59 % and 75 %
respectively.
Based upon the marker trials a summary of the observed extraction zones was made (Power, 2005).
As a part of the experimental program a number of blast design parameters, i.e. number of
blastholes per ring, toe hole spacing, explosive density and initiation timing, were modified in
order to evaluate the impact on flow behavior.
Summarized, the draw point width at the brow and the depth of draw has an impact on the primary
recovery. Further, Clout (2004) concluded that blast powder factor, explosive sleep time and
number of blastholes had no major influence on primary recovery. However, Brunton (2009)
suggested, based on an additional independent analysis, a trend between blast powder factor and
primary ring recovery.
23
Gravity flow of broken rock in SLC Swebrec Report 2010:P1
Figure 19. Typical result from marker trials (left ║ and right ┴ ring planes), Ridgeway mine, double ring interactive draw in 5 m drifts, cross-cuts X0 & X2 with ring 51 & 52 at the 5250 mine level (Power,
2004a).
Figure 20. Extraction zone shapes noted by Power (2005) on the basis of marker trials at Ridgeway
mine.
24
Gravity flow of broken rock in SLC Swebrec Report 2010:P1
f) Perseverance mine (Australia)
Several full-scale trials were undertaken from 2002 - 2004 (Hollins & Tucker, 2004). The trials
were conducted in five production drifts on three different sublevels. The centre-to-centre crosscut
spacing was reduced from 17.5 - 14.5 m with the intention to cause interactive draw (Bull & Page,
2000). Essentially, this concept contains a uniform draw of the caved material, reducing early
dilution ingress and hence improved material recovery. A total of 1762 markers (steel pipes filled
with concrete, Ø 45 x 250 mm) were installed in the 3 m burden and at one meter intervals within
the marker ring. Markers have been recovered through a combination of visual identification (53
%) at the draw point and later magnetic separation (additional 20 %). The major conclusion of
these trials was that interactive draw between draw points does not occur, see Figure 21. The
maximum width of draw was on average 11.5 m which indicated that a zone of material located
between production drifts and the toes of the blastholes did not reach the draw points at all.
Figure 21. Typical result from marker trials, Perseverance mine, cross section looking west and long section looking north (Hollins & Tucker, 2004).
Concluding, all recent full-scale experiments conducted exhibited irregular and asymmetrical
shapes of the extraction zones of large-scale, modern SLC geometries. These results differ from
early full-scale tests: This discrepancy might be explained by the actual draw height and
consequently the stress regime having changed tremendously during these years. However, the fact
that the extraction rate was considered to be relatively uniform and shaped like a tear drop with an
effective ring height of 50 m, like in the Longtan mine, remains to be explained. An explanation of
this discrepancy might be the difference in blast design. It would be expected that multiple blast
rings with burdens of just 1 m instead of 2 - 3 m would provide a high explosive distribution and
well fragmented ore throughout the rings. This could have provided ideal flow conditions for a
uniform extraction zone to develop in the Longtan mine.
25
Gravity flow of broken rock in SLC Swebrec Report 2010:P1
2.3 Conceptual flow models
Previous discussions (see chapter 2.2.2) have pointed towards irregular and asymmetrical shape of
the draw body for large-scale, modern SLC geometries. It follows that waste rock ingress, which is
measured by weighing buckets during the mucking procedure, exhibits a typically episodic
character, see Figure 22. To equalize fluctuations a simple moving average of 15 samples is
calculated.
For the ring in this figure, which was blasted using standard practice, waste first appeared when the
percentage of extraction was about 60 %. Afterwards the waste content increased with the
extraction percentage and the ring was abandoned when the extraction percentage reached 116 %.
At this point the average waste content of the last 25 % of the extraction exceeded 40 %. However,
the details of such curves usually vary considerably from ring to ring, and even between adjacent
rings.
Figure 22. Development of waste inflow with percentage extraction (modified after Quinteiro et al., 2004)
Simulations made so far have shown that quite different approaches could yield the same response,
such as with regard to pulsation effects in dilution entry curves. Thus response curves by
themselves are not uniquely related to the conditions imposed and hence are insufficient to validate
these conditions. Reduction of such ambiguities can only be made by in-situ observations which
aim to understand the relevant flow mechanisms. To summarize, the information acquired in the
research of gravity flow in SLC is still so limited that a generally accepted conceptual model
cannot yet be constructed.
26
Gravity flow of broken rock in SLC Swebrec Report 2010:P1
Table 1 surveys the existing relevant conceptual models. This survey shows that characteristics
could greatly differ. Conceptual models, considering issues of disturbed flow (highlighted in Table
1) are examined in more detail in the following discussion.
Table 1. Conceptual models of gravity flow mechanisms in sublevel caving.
Conceptual model Dilution Ore losses Observation References
Extraction- and
loosening ellipsoid ideally none
zones outside
extraction
ellipsoid
shape & eccentricity of
both ellipsoids
Janelid & Kvapil, 1966;
Janelid, 1972
Drop hypothesis ideally none
zones beyond
drop draw
body
shape of draw body
Fröström, 1970; Janelid,
1972; Chen & Boshkow,
1981. Bergmark-Roos
equation (Bergmark,
1975; Hedén, 1976;
Kuchta, 2002)
Geological variations in-situ in-situ variations of in-situ ore
grades
Gustafsson, 1998
Boulder blockage lateral above
size, location of ore
boulders within caving
flow
Stazhevskii, 1996;
Gustafsson, 1998
Blast heave
explanation above above
waste rock from upper
level trapped within ore
during blasting process
Markenzon, 1967;
Stazhevskii, 1996;
Gustafsson, 1998
Backbreak lateral above
backbreak between
boreholes within a caving
round
Janelid, 1972; Gustafsson,
1998; Hollins & Tucker,
2004; Brunton, 2009
Palm- and finger
draw body above/lateral
immobilized
material
within the
round
extended "mass flow
channels" from a main
draw body
Gustafsson, 1998;
Brunton, 2009
Cavity formation lateral above compacted ore in the upper
zones
Gustafsson, 1998;
Hustrulid, 2000
Shallow draw
phenomen above
frozen ore
band and
penetrated ore
within the
caved material
well-graded interfaces
(banding effect); possible
gap between the blasthole
plane at the brow and the
compacted material
Selldén & Pierce, 2004;
Power, 2004a-b; Brunton,
2009; Kvapil, 2008
27
Gravity flow of broken rock in SLC Swebrec Report 2010:P1
a) Geological variations
In this model (Gustafsson, 1998), it is assumed that flow fields are time-independent and reflect
cyclic variations in the in-situ ore grade. By assuming that the ore grade varies spatially in a cyclic
way, a simple flow model would lead to varying waste rock content at the brow. Consideration of
the homogenous character of the ore bodies usually mined by SLC makes this assumption rather
unrealistic. With respect to the mine in Kiruna, waste rock inflow at the draw-point might occur
periodically close to the footwall as the lower part of a SLC ring is drilled within waste rock. Waste
lenses also exist in some rings and these lenses then will arrive at the draw point during loading,
but in general this is a rare phenomenon given the large size of the waste lens needed to distort the
waste rock curve.
b) Boulder blockage
Boulders and larger rock particles are here assumed to be the cause of waste rock content peaks.
Stazhevskii (1996) observed in model experiments that a single boulder could get stuck between
the mining front and the flowing rock, see chapter 2.2.1, Figure 11. This causes the ore above the
boulder to stop flowing and waste from previous blasted rings in front to flow in, causing a waste
rock peak in the extraction process. When flow under the boulder has gone on for a while, the
cavity which appears under it grows and the boulder finally becomes insufficiently supported. The
boulder then drops and ore flow from the ring could resume.
The proposed theory could also be extended to blockage by several large boulders. At the
beginning of the draw, finer size classes will flow faster, and flow between the larger particles. If
there are several larger boulders they may move until they come into contact with each other and
cause a blockage by interlocking with each other. When such a blockage is formed in the blasted
ring, coarser ore pieces from regions above with lower specific charge will be hindered in their
flow. Meanwhile, lateral waste fines will flow through the blockage and cause waste rock inflow to
the muck pile. When a significant amount of waste has flowed through the blockage the flow will
stop and the rock level below the blockage will sink. Stresses now occasioned solely by the
blockage will gradually increase until they are sufficient to break down the blockage, which ends
the waste rock peak.
The main flaw in this theory is that waste rock inflow in reality might also be present even when
very few boulders are actually observed during mucking. However, data show that there is a
correlation between many boulders in the beginning of a ring and an early beginning of waste rock
peaks (Gustafsson, 1998). This might also explain why several waste rock peaks usually are
observed. This explanation supposes that the excess waste rock in the waste rock peaks passes
through larger blocks which might be regarded as a “sieving effect”. It can be deduced that this
28
Gravity flow of broken rock in SLC Swebrec Report 2010:P1
explanation predicts a size distribution of waste rock with a lower upper size limit than that before
or after the waste rock peak.
c) Blast heave explanation
According to this theory (Markenzon, 1967), the blast would cause the ore to penetrate into the
caved masses and thereby open a slot between the blasted rock and the remaining mining front
(ring face). Waste rock from above the ring would then have the chance to enter the draw body and
become trapped when the gas pressure decreases so that the blasted ring is pushed back into its
original position, see chapter 2.2.1, Figure 10.
There are several reasons why this explanation is physically incorrect. If it were true it is very
difficult to understand why in reality a series of waste rock inflows with intermittent ore inflows
reaches the draw point. Gustafsson (1998) has also employed a simplistic calculation that the
opening time is at a maximum in the range of a few tenths of a second. This would give the broken
rock from above far too little time to fall down far enough for it to appear early on the waste rock
curve. This explanation also implicitly supposes that the gas pressure during the blast is sufficient
to force about several thousand tonnes of ore into the caved masses, but that at the same time it
would not affect the free fall of broken rock into the slot from above.
d) Backbreak
Another possible explanation of waste rock inflow is backbreak from one ring to another. Evidence
that draw bodies could diverge to the location of backbreak, provided by markers, was given by
Gustafsson (1998) and Janelid (1973), see Figure 23 and Figure 24. However, both observed that
the hypothesis of waste inflow due to backbreak only was confirmed in a few individual ring blasts.
Further observations of backbreak influencing material flow were made by Hollins & Tucker
(2004) and Brunton (2009).
Figure 23. Waste rock inflow from backbreak of previous ring (Gustafsson, 1998).
29
Gravity flow of broken rock in SLC Swebrec Report 2010:P1
Figure 24. Draw bodies of ring no 5 and 6, drift 9, level 335 m (Janelid, 1973).
e) Palm- and finger draw body
The general shape of the marker plots from Kiruna data (see chapter 2.2.2) indicate that the draw
bodies are much more complex than those of model experiments or conventional explanatory
hypotheses. Interpreting the results has indicated that the draw bodies of the experiments typically
consist of a lower compact part and several long structures above, termed as palm-and-finger draw
body shapes by Gustafsson (1998), see Figure 25. This complex shape of a draw body is thought to
be caused by spatial variations (e.g. related to blastholes) in the mobility of broken rock before
mucking. As a consequence fingers extending into the waste rock would cause the observed peaks
of waste rock.
Figure 25. Palm-and-finger draw body shape (Gustafsson, 1998).
30
Gravity flow of broken rock in SLC Swebrec Report 2010:P1
f) Cavity formation
Another explanation of pulsation effects of waste rock inflow reflects the relative mobility of the
ore in the upper parts of the ring and the caved rock, see Figure 26 and Figure 27. This is one
interpretation of observations made at LKAB Kiruna mine.
Figure 26. Explanation of the pulsation seen in large scale sublevel caving (Larsson, 1996 cited by
Hustrulid, 2000).
Figure 27. Sequences of cavity formation and failure (after Gustafsson, 1998).
The assumption is that broken rock will flow much more easily in the lower ring parts than in the
upper parts. Consequently, the material of the lower part will start to flow at the start of mucking
whereas the upper part will remain in its post blasting position, gradually forming a gap. Regions of
31
Gravity flow of broken rock in SLC Swebrec Report 2010:P1
material from the previous rings will ultimately start to bulge, their stability decrease and thereupon
they collapse and flow out into the gap until they reach their angle of repose. The sudden stress
change will also cause the upper part of the material to fill in the part of the gap which has not been
filled by waste rock so far. As mucking continues the granular material flows predominately along
the in-situ rock (ring face) rather than along the broken rock. This will create another air gap in the
ring and the process repeats is repeated.
Validating the cavity formation explanation is a difficult matter. The best chances actually would
be if one could observe the establishment and later breakdown of cavities, but this is impossible
with the observation techniques presently available, see chapter 2.2.2.
g) Shallow draw phenomenon
Field observations made at the Ridgeway mine (Power, 2004a-b) and at the Kiruna mine (Selldén
& Pierce, 2004) led to a model termed the “shallow draw phenomenon”, see Figure 28.
Figure 28. Shallow draw phenomenon. Figure 29. Formation of a compacted interface due to blasting (Kvapil, 2008).
Inadequate space for swelling of blasted ore means that only the material closest to the blast plane
is sufficiently broken to be mobilized, and the material further away is heavily confined and is not
mobile. Therefore, draw predominantly occurs closest to the blast front and progresses upwards,
which would make dilution entry from above possible once the top of the blasted ring is extracted.
The proposed theory has similarities with the hypothesis by Hustrulid (2000). The only difference
is that the shallow draw implies dilution entry from above. Interestingly, Kvapil (2008) has also
adopted a theory of draw bodies in SLC which says that ore fragments would penetrate into the
32
Gravity flow of broken rock in SLC Swebrec Report 2010:P1
coarser cave rock, allowing for a preferential shallow, vertical and upwards orientated flow, see
Figure 29.
An observation drift above the actual draw level at the Ridgeway mine facilitated observations of
the mechanisms of a shallow draw which did not involve marker results, see Figure 30 and Figure
31. The width of the opening (= 1.5 m) is similar to the depth of many draw envelopes measured in
the marker trials. The compact and well-graded interface of the rock mass on the right side, and
also the arch, a remnant of the initial rock mass structure, are of note.
There is one documented observation of a hang-up formation at the Kiruna mine. This indicated
that there was an occurrence of shallow draw. A gap between the blast plane at the brow and the in-
situ ore can be identified in Figure 32 and Figure 33. The ore appears to be highly compacted if not
solid, but is believed to become rather well-fragmented rock if brought into motion again.
Figure 30. Location of observation drift at Ridge-way mine (Power, 2004b).
Figure 31. Photographs taken from observation drift, width of opening about 1.5 m (Power, 2004b).
Waste
Ore
Figure 32. Vertical cross section showing section along drift axis and incompletely
blasted rings. Long arrow indicates camera viewing direction (Selldén & Pierce, 2004).
Figure 33. Open gap between blasthole plane and a combination of confined ore and compacted waste in previous gaps. The damaged brow is the brighter
material in the far left of the picture. (Selldén & Pierce, 2004).
33
Gravity flow of broken rock in SLC Swebrec Report 2010:P1
3 CONCLUDING REMARKS
Attempts to simulate sublevel caving are hindered by the physical scale of the operation. In
addition, blasting takes place rapidly while the draw of material may last several days for an
individual SLC ring. Incorporating the period of draw of rock from other higher or adjacent levels
extends the process to months or even years.
Information on gravity flow behavior in sublevel caving (SLC) mines can be regarded as sparse.
This is a result of there being several unknowns and uncertainties with respect to the actual effects
of confined blasting in caving rounds. Subjects under continuing discussion are, for example:
Quantification of the physical and mechanical properties of blasted ore and caved rock
Remnant pillars, completed breakage and overbreak to subsequent rings
Mobilization of blasted ore with influence on the
o growth rate of the extraction and movement zone
o formation and failure of semi-stable arches, so-called hang-ups
Interaction effects between
o rings (interactive draw, i.e. material from adjacent rings enter the same draw point)
o blasted ore and pillar
o blasted ore and caving masses
Position variance within the
o blasted round (height, width, burden)
o deposit (longitudinal, transverse, depth)
Additional influences, e.g.
o drilling and charging procedure
o rock mass characteristics
o different confining pressure of caved masses, etc.
o temporal factor (sleep time of explosives, duration between blasting-loading, etc.).
Blasting exerts a great influence on the subsequent flow phase. Although blasting is of great
interest it is a neglected area of study. The probable reason for this neglect is that experimental
work in the SLC environment is a challenge. Various attempts have been made to increase
knowledge regarding gravity flow especially as the initial situation after blasting is rather obscure.
This is important because ore recovery, dilution as well as flow disturbances are the direct
consequences of flow behavior.
Because of this several conceptual flow models have been developed based upon small- and full-
scale experiments. Of these the phenomenon of “shallow draw” might well be paid special
attention since several studies of this recently have been made in large-scale, modern SLC
geometries.
34
Gravity flow of broken rock in SLC Swebrec Report 2010:P1
4 REFERENCES
Airey, L.D. (1965). The introduction of mechanized mining methods at Mufulira Copper Mines
Ltd. In J.M. Dew & R.T. Modigan (Eds.), 8th Commonwealth Mining and Metallurgical Congress
(pp. 16-26). Dunedin, New Zealand: University of Otaga.
Alfaro, M. & Saavedra, J. (2004). Predictive models for gravitational flow. In A. Karzulovic &
M.A. Alafaro (Eds.), 4th International Conference and Exhibition on Mass Mining (pp. 179-184).
Santiago, Chile: Instituto de Ingenieros de Chile.
Alford, C.G. (1978). Computer simulation models for the gravity flow of ore in sublevel caving
(Master thesis). University of Melbourne, Melbourne, Australia.
Baiden, G.R., Bissiri, Y. & Saari, A.V. (2008). Real time sensing of rock flow in a block cave
mine. In H. Schunnesson & E. Nordlund (Eds.), 5th International Conference and Exhibition on
Mass Mining (pp. 993-1002). Luleå, Sweden: Luleå University of Technology.
Bergmark, J.E. (1975). Beräkning av ortavstånd och försättning vid skivrasbrytning [Calculation of
drift spacing and ring burden for sublevel caving] (Note RU 75-16). Malmberget, Sweden: LKAB.
Brady, B.H.G. & Brown, E.T. (2004). Rock mechanics for underground mining (3rd
ed.). Dortrecht,
Netherlands: Kluwer Academic Publishers.
Brown, E.T. (2003). Block caving geomechanic. The international caving study, stage I 1997-2000.
Indooroopilly, Australia: Julius Kruttschnitt Mineral Research Centre.
Brunton, I.A. (2009). The impact of blasting on sublevel caving flow behaviour and recovery
(Doctoral thesis). University of Queensland, Brisbane, Australia.
Brunton, I. & Chitombo, G.P. (2009). Modeling the impact of SLC blast design & performance on
material recovery. In J.A. Sanchidrián (Ed.), 9th International Symposium on Rock Fragmentation
by Blasting (pp. 353-362). London, England: CRC Press.
Brunton, I., Fraser, S.J., Hodgkinson, J.H. & Stewart, P.C. (2010). Parameters influencing full scale
sublevel caving material recovery at the Ridgeway gold mine. International Journal of Rock
Mechanics and Mining Sciences, 47(6), 647-656.
Bucky, P.B, Stewart, J.W. & Boshkov, S. (1943). What is the proper drawpoint spacing for block
caving? Engineering and Mining Journal 144(6), 70-75.
35
Gravity flow of broken rock in SLC Swebrec Report 2010:P1
Bull, G. & Page, C.H. (2000). Sublevel caving – today`s dependable low cost ore factory. In G.
Chitombo (Ed.), 3rd
International Conference and Exhibition on Mass Mining (pp. 537-556).
Melbourne, Australia: Australasian Institute of Mining and Metallurgy.
Castro, R.L., Gonzalez, F. & Arancibia, E. (2009). Development of a gravity flow numerical model
for the evaluation of draw point spacing for block/panel caving. Journal of The Southern African
Institute of Mining and Metallurgy, 109(7), 393-400.
Chen, G. (1997). Stochastic modeling of rock fragment under gravity. International Journal of
Rock Mechanics and Mining Sciences, 34(2), 323-331.
Chen, J.Y. & Boshkow, S. (1981). Recent developments and applications of bulk mining methods
in the Peoples Republic of China. In D.R. Stewart (Ed.), Design and operation of caving and
sublevel stoping mines (pp. 393-423). New York, USA: Society of Mining Engineers of the
American Institute of Mining, Metallurgical, and Petroleum Engineers.
Clout, J. (2004). The continuation of full scale sublevel caving experiments – Cadia Valley
operation – underground (Ridgeway gold mine). (Unpublished report, ENGG 7240, Engineering
project 4A). Brisbane, Australia: University of Queensland.
Cokayne, E.W. (1982). Sublevel Caving. In W.A. Hustrulid, Underground mining methods
handbook (pp. 872-879). New York, USA: Society of Mining Engineers of the American Institute
of Mining, Metallurgical, and Petroleum Engineers.
Cox, J.A. (1969). Sub-level caving methods at Mufulira Copper Mines. Mining Magazine 20(5),
31-36.
Cullum, A.J. (1974). The effects of confined blasting on rock fragmentation and flow
characteristics in sublevel caving (Master thesis). University of Queensland, Brisbane, Australia.
Cundall, P.A. & Strack, O.D.L. (1979). A discrete numerical model for granular assemblies.
Géotechnique, 29(1), 47-65.
DeGagné, D.O & McKinnon, S.D. (2005). The influence of blasting fragmentation on ore recovery
in sublevel cave mines. In G. Chen et al. (Eds.), 40th U.S. Rock Mechanics Symposium (Alaska
Rocks 2005) (Paper No. ARMA/USRMS 05-811). Alexandria, USA: American Rock Mechanics
Association.
DeGagné, D.O. & McKinnon, S.D. (2006). The influence of cave mass properties on discrete
sublevel cave models. In S. Yale et al. (Eds.), 41st U.S. Rock Mechanics Symposium (Golden Rocks
36
Gravity flow of broken rock in SLC Swebrec Report 2010:P1
2006 – 50 Years of Rock Mechanics) (Paper No. 06-1148). Alexandria, USA: American Rock
Mechanics Association.
Finkel, M. & Skalare, H. (1963). Skivrasbrytning – delrapport över hållutningens inverkan vid
modellförsök [Sublevel caving – interim report concerning the influence of hole inclination for
model-scale tests] (Report series C, no. 7). Stockholm, Sweden: Svenska Gruvföreningen,
Stiftelsen Gruvforskningen.
Fjellborg, S. (2002). The value of measuring VOD in large scale sublevel caving. In X. Wang
(Ed.), 7th International Symposium on Rock Fragmentation by Blasting (pp. 717-724). Bejing,
China: Metallurgical Industry Press.
Free, G.D. (1970). Mathematical and model studies of the flow of material in the sublevel caving
mining method (Master thesis). University of Queensland, Brisbane, Australia.
Fröstrom, J. (1970). Undersökning av ekvivalenta modellmaterial för utveckling och projektering
av skivrasbrytning [Examination of equivalent model material for development and design of
sublevel caving] (Master thesis). Royal Institute of Technology, Stockholm, Sweden.
Fröström, J. & Lamperud, B. (1973). Bestämning av styckefall vid fullskaleförsöket i Grängesberg
[Determination of fragment size distribution in a full-scale test in Grängesberg]. In I. Janelid (Ed.),
Rasbrytning [Cave mining]. Stockholm, Sweden: BeFo, Swedish Rock Engineering Research
Foundation.
Gaete, S., Dunlop, R., Parraguez, R., Parra, J.C. & Rodriguez, F. (2007). Estimation of cave back
using gravity measurements at the El Teniente Mine. In T.R. Stacey (Ed.), 1st International
Symposium on Block and Sub-Level Caving (pp. 389-396). Johannesburg, South Africa: The
Southern African Institute of Mining and Metallurgy.
Gardner, G.C. (1966). The region of flow when discharging granular materials from bin-hopper
systems. Chemical Engineering Science, 21(3), 261-271.
Glazer, S.N. & Lurka, A. (2007). Application of passive seismic tomography to cave mining
operations based on experience at Palabora Mining Company, South Africa. In T.R. Stacey (Ed.),
1st International Symposium on Block and Sub-Level Caving (pp. 369-388). Johannesburg, South
Africa: The Southern African Institute of Mining and Metallurgy.
Gustafsson, P. (1998). Waste rock content variations during gravity flow in sublevel caving
(Doctoral thesis). Luleå University of Technology, Luleå, Sweden.
37
Gravity flow of broken rock in SLC Swebrec Report 2010:P1
Haglund, M, (1968). Skivrasbrytnings Konferens i Malmberget [Sublevel caving conference]
(Protocol G68-94). Malmberget, Sweden: LKAB.
Hanisch, J., Ergenzinger, P. & Bonte, M. (2003). Dumpling – an “intelligent” boulder for studying
internal processes of debris flows. In D. Rickenmann & C. Chen (Eds.), 3rd
International
Conference on Debris-Flow Hazards Mitigation: Mechanics, Prediction and Assessment (pp. 843-
849). Rotterdam, Netherlands: Millpress.
Hedén, H. (1976). Fysikalisk modell för beskrivning av gravitationsflödet [Physical model for the
description of gravity flow]. In H. Hedén (Ed.), Kompendium från Rasbrytningseminarium
[Proceedings of cave mining seminar] (pp. I1 - I7). Kiruna, Sweden: LKAB.
Hedström, O. (2000). Funktionskontroll av produktionssalvor i Kiirunavaara [Function control of
production blasts at the Kiruna mine] (Master thesis). Luleå University of Technology, Luleå,
Sweden.
Hollins, B. & Tucker, J. (2004). Draw point analysis using a marker trial at the Perseverance
Nickel Mine, Leinster, Western Australia. In A. Karzulovic & M.A. Alafaro (Eds.), 4th
International Conference and Exhibition on Mass Mining (pp. 498-502). Santiago, Chile: Instituto
de Ingenieros de Chile.
Hustrulid, A.I. (1997). A computational methodology for modeling large scale sublevel caving with
a three-dimensional discrete element method (Doctoral thesis). Colorado School of Mines, Golden,
USA.
Hustrulid, W.A. (2000). Method selection for large scale underground mining. In G. Chitombo
(Ed.), 3rd
International Conference and Exhibition on Mass Mining (pp. 29-56). Melbourne,
Australia: Australasian Institute of Mining and Metallurgy.
Janelid, I. (1968). Sublevel caving: how to use it; what are advantages, problems. World Mining,
21(9), 76-78.
Janelid, I. (1972). Study of the gravity flow process in sublevel caving. International sublevel
caving symposium (pp. 1-23). Stockholm, Sweden: Atlas Copco.
Janelid, I. (1973). Rasbrytning [Cave mining] (Report). Stockholm, Sweden: BeFo, Swedish Rock
Engineering Research Foundation.
Janelid, I., (1975). Sublevel Caving. In Separate Preprints, Annual Meeting of the Society of
Mining Engineers (Preprint 75-AU-15).
38
Gravity flow of broken rock in SLC Swebrec Report 2010:P1
Janelid, I. & Kvapil, R. (1966). Sublevel caving. International Journal of Rock Mechanics and
Mining Sciences, 3(2), 129-153.
Just, G.D: & Free, G.D. (1971). The gravity flow of material in the sub-level caving mining
system. In 1st Australia – New Zealand Conference on Geomechanics (pp. 88-97). Sydney,
Australia: The Secretary of the Institution of Engineers.
Just, G.D. (1981). The significance of material flow in mine design and production. In D.R. Stewart
(Ed.), Design and Operation of Caving and Sublevel Stoping Mines (pp. 715-728). New York,
USA: Society of Mining Engineers of the American Institute of Mining, Metallurgical, and
Petroleum Engineers.
Koppanyi, F. (1960). Optimering av skivrasbrytning med modellförsök [Optimization of sublevel
caving with model-scale tests] (Master thesis). Royal Institute of Technology, Stockholm, Sweden.
Kosowan, M.I. (1999). Design and operational issues for increasing sublevel cave intervals at
Stobie Mine (Master thesis). Laurentian University, Greater Sudbury, Canada.
Kuchta, M.E. (2002). A revised form of the Bergmark-Roos equation for describing the gravity
flow of broken rock. Mineral Resources Engineering, 11(4), 349-360.
Kvapil, R. (1965). Gravity flow of granular material in hoppers and bins. International Journal of
Rock Mechanics and Mining Sciences, 2(1), 25-41 & 2(3), 277-304.
Kvapil, R. (1982). The mechanics and design of sublevel caving systems. In W.A. Hustrulid (Ed.),
Underground mining methods handbook (pp. 880-897). Littleton, USA: Society of Mining
Engineers of the American Institute of Mining, Metallurgical, and Petroleum Engineers.
Kvapil, R. (1998). The mechanics and design of sublevel caving systems. In R.E. Gertsch & R.L.
Bullock, Techniques in underground mining. Selections from underground mining methods
handbook (pp. 621-653). Littleton, USA: Society for Mining. Metallurgy, and Exploration, Inc.
Kvapil, R. (2008). Gravity flow in sublevel and panel caving – a common sense approach. Luleå,
Sweden: Luleå University of Technology.
Larsson, L. (1998). Slutrapport “Projekt Skivras 2000” [Final report ”project sublevel caving
2000”] (Unpublished report 98-765). Kiruna, Sweden: LKAB.
Lehman, G.R. (1916). Ore-drawing tests and the resulting mining method of Inspiration
Consolidated Copper Company. Transactions of the American Institute of Mining, Metallurgical,
and Petroleum Engineers, 55, 218-231.
39
Gravity flow of broken rock in SLC Swebrec Report 2010:P1
Lorig, L.J. & Cundall, P.A. (2000). A rapid gravity flow simulator. In E.T. Brown, The
International Caving Study I (Unpublished final report). Brisbane, Australia: JKMRC and Itasca
Consulting Group, Inc.
Lynch, R.A. & Lötter E.C. (2007). Estimation of cave geometry using constrained velocity model
inversion with passive seismic data. In T.R. Stacey (Ed.), 1st International Symposium on Block
and Sub-Level Caving (pp. 355-368). Johannesburg, South Africa: The Southern African Institute
of Mining and Metallurgy.
Markenzon, E.I. (1967). Mechanism of blasting without a compensation space. Journal of Mining
Science, 3(1), 45 - 47.
Marklund, I. (1976). Sprängningens inverkan på rasförloppet [Influence of blasting on gravity
flow]. In H. Hedén (Ed.), Kompendium från Rasbrytningseminarium [Proceedings of cave mining
seminar] (pp. L1 – L9). Kiruna, Sweden: LKAB.
McCormick, R.J. (1968). How wide does a draw point draw? Engineering and Mining Journal,
169(6), 106-116.
McNicholas, F.S., Roberts, V.C. & Walker, M.S. (1946). An experimental study of caving and
drawing large orebodies. Transactions of the American Institute of Mining, Metallurgical, and
Petroleum Engineers, 163, 156-197.
Minchinton, A. & Dare-Bryan, P. (2005). The application of computer modeling for blasting and
flow in sublevel caving operations. In 9th AusIMM Underground Operators` Conference, (pp. 65-
73). Melbourne, Australia: AusIMM, The Australasian Institute of Mining and Metallurgy.
Nedderman R.M. (1992). Statics and kinematics of granular materials. Cambridge, England:
Cambridge University Press.
Panczakiewicz, T. (1977). Optimization of the sublevel caving mining method investigated by
physical models (Master thesis). University of Melbourne, Melbourne, Australia.
Pariseau, W.G. & Pfleider, E.P. (1968). Soil plasticity and the movement of materials in ore passes.
Transactions Society of Mining Engineers of the American Institute of Mining, Metallurgical, and
Petroleum Engineers, 241(1), 42-56.
Peters, D.C. (1984). Physical modelling of the draw behaviour of broken rock in caving. Colorado
School of Mines Quarterly, 79(1), 1-60.
40
Gravity flow of broken rock in SLC Swebrec Report 2010:P1
Pierce, M. (2004). Development of REBOP as a practical tool for draw prediction in caving mines.
In E.T. Brown, The International Caving Study I (Unpublished final report). Brisbane, Australia:
JKMRC and Itasca Consulting Group, Inc.
Power, G. (2004a). Modeling granular flow in caving mines: large scale physical modeling and full
scale experiments. (Doctoral thesis). University of Queensland, Brisbane, Australia.
Power, G. (2004b). Full scale SLC draw trials at Ridgeway Gold Mine. In A. Karzulovic & M.A.
Alafaro (Eds.), 4th International Conference and Exhibition on Mass Mining (pp. 225-230).
Santiago, Chile: Instituto de Ingenieros de Chile.
Power, G. (2005). SLC marker trials project (3.2.1) (Unpublished presentation). MMT meeting in
Sudbury, Canada, October 2005.
Quinteiro, C., Larsson, L. & Hustrulid, W.A. (2001). Theory and practice of very large scale
sublevel caving. In W.A. Hustrulid & R.L. Bullock (Eds.), Underground mining methods –
engineering fundamentals and international case studies (pp. 381-384). Littleton, USA: Society for
Mining, Metallurgy, and Exploration, Inc.
Quinteiro, C. (2004). Final report: Orica-fragmentation project (Unpublished report 05-722).
Kiruna, Sweden: LKAB.
Redaelli, L.L. (1963). Sub-level caving at Koskullskulle. Mine and Quarry Engineering, 29(6),
261-264.
Rustan, A. (1970). Volymviktmetodens teoretiska grunder för bestämning av malmhalt hos en
blandning av sprängd malm och gråberg. Kinematik, svällning, uppluckring, och styckefall i
försättningen vid sprängning mot löst berg i pall- och skivrasmodeller. [Theoretical basics of the
volume-weight-method for the determination of the ore content of a mixture of blasted ore and
waste rock. Kinematics, swelling, loosening and fragment size in the burden for confined blasting
in model-scale.] (Licentiate thesis). Royal Institute of Technology, Stockholm, Sweden.
Rustan, A. (1990). The importance of using joints to achieve scaled fragmentation in magnetite
concrete used for sublevel caving blast models. Engineering Fracture Mechanics, 35(1-3), 425-
438.
Rustan, A. (1993). Minimum distance between charged boreholes for safe detonation. In H.P.
Rossmanith (Ed.), 4th International Symposium on Rock Fragmentation by Blasting (pp. 127-135).
Rotterdam, Netherlands: Balkema.
41
Gravity flow of broken rock in SLC Swebrec Report 2010:P1
Rustan, A. (2000). Gravity flow of broken rock – what is known and unknown. In G. Chitombo
(Ed.), 3rd
International Conference and Exhibition on Mass Mining (pp. 557-567). Melbourne,
Australia: Australasian Institute of Mining and Metallurgy.
Sandström, P.O. (1972). Application and optimization of sublevel caving techniques. Engineering
and Mining Journal, 173(6), 112 – 125.
Selldén, H. & Pierce, M. (2004). PFC3D modeling of flow behaviour in sublevel caving. In A.
Karzulovic & M.A. Alafaro (Eds.), 4th International Conference and Exhibition on Mass Mining
(pp. 201-214). Santiago, Chile: Instituto de Ingenieros de Chile.
Sharrock, G., Beck, D., Booth, G. & Sandy, M. (2004). Simulating gravity flow in sub-level caving
with cellular automata. In A. Karzulovic & M.A. Alafaro (Eds.), 4th International Conference and
Exhibition on Mass Mining (pp. 189-194). Santiago, Chile: Instituto de Ingenieros de Chile.
Sjöstrand, W. (1957). Skivrasbrytning i Kiirunavaara med modellförsök [Sublevel caving in the
Kiirunavaara mine with model-scale tests] (Master thesis). Royal Institute of Technology,
Stockholm, Sweden.
Stazhevskii, S.B. (1996). Features of flow of broken rock in extraction of ores with sublevel
caving. Journal of Mining Science, 32(5), 403-416.
Tessem, S. & Wennberg, S. (1981). Longitudinal sublevel caving at Fosdalens Bergverks-
Aktieselskab, Norway. In D.R. Stewart (Ed.), Design and operation of caving and sublevel stoping
mines (pp. 365-371-423). New York, USA: Society of Mining Engineers of the American Institute
of Mining, Metallurgical, and Petroleum Engineers.
Wimmer, M. & Ouchterlony, F. (2008). Application of borehole geophysics to identify variations in
sublevel caving debris – Field tests in drifts filled with ore and waste (Swebrec Report 2008:P4).
Luleå, Sweden: Luleå University of Technology.
Wimmer, M., Ouchterlony, F., Moser, P., Nordqvist, A. & Lenz, G. (2009). Referenced 3D images
from inside cavities and behind rings in sublevel caving. In J.A. Sanchidrián (Ed.), 9th International
Symposium on Rock Fragmentation by Blasting (pp. 91-100). London, England: CRC Press.
Yenge, L.I. (1980). Analysis of bulk flow of materials under gravity caving process – Part 1:
Sublevel caving in relation to flow in bins and bunkers. Colorado School of Mines Quarterly,
75(4), 1-45.
42
Gravity flow of broken rock in SLC Swebrec Report 2010:P1
Yenge, L.I. (1981). Analysis of bulk flow of materials under gravity caving process – Part 2:
Theoretical and physical modelling of gravity flow of broken rock. Colorado School of Mines
Quarterly, 76(3), 1-67.
Zhang, G. (2004). Behaviour of caved ore mass in sublevel caving and its effect on ore dilution. In
A. Karzulovic & M.A. Alafaro (Eds.), 4th International Conference and Exhibition on Mass Mining
(pp. 238-242). Santiago, Chile: Instituto de Ingenieros de Chile.
Zhang, Z.X. (2005). Increasing ore extraction by changing detonator positions in LKAB
Malmberget mine. Fragblast – International Journal of Blasting and Fragmentation, 9(1), 9-46.
Zhang, Z.X. (2008). Impact of rock blasting on mining engineering. In H. Schunnesson & E.
Nordlund (Eds.), 5th International Conference and Exhibition on Mass Mining (pp. 671-680).
Luleå, Sweden: Luleå University of Technology.
Report 2007:1 ISSN 1653-5006
Swedish Blasting Research CentreMejerivägen 1, SE-117 43 Stockholm
Luleå University of TechnologySE-971 87 Luleå www.ltu.se
An experimental investigation of blastability
Experimentell bestämning av sprängbarhet
Matthias Wimmer, Swebrec
Universitetstryckeriet, L
uleå