ARTICLE IN PRESS

International Journal of Rock Mechanics & Mining Sciences 44 (2007) 860–870

www.elsevier.com/locate/ijrmms

A study of isolated draw zones in block caving mines by means

of a large 3D physical model
R. Castro,1, R. Trueman, A. Halim
Julius Kruttschnitt Mineral Research Centre, University of Queensland, Australia
Received 25 April 2006; received in revised form 5 December 2006; accepted 5 January 2007
Available online 10 April 2007

Abstract

Block caving methods rely on gravity to break and transport large amounts of ore and waste. Despite the importance of gravity flow,
there is debate within the literature about the influence that the height of draw, particle size and particle size distribution has on the
geometry of extraction and movement zones. This paper presents the results of an experimental programme conducted in the largest
three-dimensional (3D) physical model to investigate the mechanisms of flow of cohesionless materials when drawing from a single
drawpoint. Experimental results showed that isolated draw zones are mainly influenced by mass drawn and height of draw. Particle size
was found to have a slight effect on extraction zones and no significant effect on movement zone width. Particle size composition (wide or
narrow distributions) and drawpoint width were found not to have a major role on drawzone geometry. Those conclusions were based on
statistical analysis of experimental data to define the controlling parameters in isolated draw. Model theory principles were used to
investigate within the physical modelling framework the possibility of directly scaling the geometry of the extraction zones, which
indicated that flow zones could be scaled in cohesionless materials under a set of assumptions. A mechanistic model of isolated draw is
also postulated from experimental data from observations of stresses and the IMZ’s geometry.
r 2007 Elsevier Ltd. All rights reserved.

Keywords: Isolated draw; Gravity flow mechanisms; Cohesionless granular materials; Block caving; Scaling rules; Dimensional analysis

1. Introduction The caving process transforms the initially in situ solid rock
into a broken rock mass, which flows towards the
Block caving refers to mass mining methods in which the drawpoints as it is extracted by mechanised equipment at
ore body caves naturally after undercutting and the caved drawpoints located in the production level [2].
ore is recovered through drawpoints. These include block Due to the high initial capital investment of a block cave
caving, panel caving and its variations. These methods and its lack of flexibility, it is critical for the success of
currently have the lowest operational costs and highest caving mines to achieve an economically acceptable level of
productivity in underground mining [1]. ore recovery and dilution content when in operation. Ore
The cost effectiveness of a block caving operation relies recovery and dilution in a block caving operation are
strongly on the use of gravity to both cave and transport strongly determined by the design and performance of the
large amounts of broken rock from its in situ location. In production level and the flow characteristics of the ore and
block caving methods, the ore and the waste caves under waste material [3].
the influence of gravity and the redistributed in situ stresses Research on gravity flow has mainly focused on under-
after the undercutting of the orebody base. As material is standing the mechanisms involved and their impact on the
extracted, the cave front propagates upwards until the design and operation of the mine’s production level.
overlying rock also caves and surface subsidence occurs. Despite its importance and the substantial research work,
gravity flow mechanisms of the caved ore are still not well
Corresponding author. Tel.: +61 7 33655954; fax: +61 7 33655999. understood [4]. This paper attempts to address some of the
E-mail address: raul.castro@uq.edu.au (R. Castro). questions raised in the literature by using a Large three-
1
On secondment from the University of Chile, Santiago, Chile. dimensional (3D) Physical Model built at The University

1365-1609/$ - see front matter r 2007 Elsevier Ltd. All rights reserved.
doi:10.1016/j.ijrmms.2007.01.001
 ARTICLE IN PRESS
R. Castro et al. / International Journal of Rock Mechanics & Mining Sciences 44 (2007) 860–870 861

of Queensland as part of the International Caving Study, under those conditions. As a first step towards that
an international collaborative project funded by several objective, a study of similitude between the large physical
major mining houses. model set up and the prototype (mine) was carried out.

2. Previous work
3. Analysis of similitude
The flow characteristics of the caved rock in block caving
The gravity flow of caved rock in block caving is a very
have been studied through physical and numerical models
complex process. The rock mass that is initially in a solid
and full-scale trials [5–17]. There is consensus in the
state becomes a fragmented mass by the action of stresses
literature that the gravity flow of a granular medium
due to the caving process, that is, the primary fragmenta-
generates two definite zones: the extraction zone formed by
tion process. Afterwards, the caved rock is removed
the removed material and the movement zone formed by
through drawpoints. As materials flows, secondary frag-
the material under flow [9,10]. The majority of researchers
mentation of the rock through point loading and abrasion
have concluded that the shape of extraction and movement
mechanisms takes place. Additionally, factors such as
zones is ellipsoidal and called the zones accordingly [9–16].
water intrusion, high level of fine fragmented rock and
Others have observed that the extraction zone geometry
large stresses could potentially have a strong effect on
follows other shapes [4,6]. In this paper, in order to avoid
material strength behaviour and therefore on its gravity
reference to a particular shape of the flow zones when a
flow characteristics. In order to physically model the flow
point of draw is worked in isolation, we use the term
of caved rock, a simplified version of the process was
isolated extraction zone (IEZ) to refer to the extracted
established which incorporates the following simplifica-
zone; and isolated movement zone (IMZ), to refer to the
tions and assumptions: (a) gravity flow in caving mines
volume that defines the flowing material.
involves the study of non-cohesive, coarse fragments,
To date most of the current understanding of the
moving slowly under the action of gravity. (b) The granular
mechanics of isolated draw has been gained through
mass is heterogenous but isotropic. (c) The granular flow
physical modelling due to the practical difficulties in
occurs in a 3D environment without any special weak
directly observing the caved rock flow in situ. Despite a
boundaries. (d) Rock breakage mechanisms, primary and
considerable research effort, there is still debate in the
secondary breakage, are not considered.
literature about the controlling parameters on isolated
For the stipulated assumptions, an analysis of similitude
draw in block caving. For example, McCormick [13]
showed that the gravity flow patterns observed in two
observed in small sand models that the IMZ followed a
different geometrical scaled models will be similar if the
cylindrical shape and reached a constant width with
following conditions hold. (1) There is geometrical
extraction. He concluded that particle size and drawpoint
similitude for the whole block geometry. That includes
width had a minimal effect on the maximum IMZ’s width.
block dimensions (height and area of draw), drawpoint
Marano [12] and others [14,15] later conducted tests on
dimensions, particle size distribution and particle shape. (2)
large 3D sand models and concluded that the IMZ has a
Gravity and bulk density in the model and prototype are
cylindrical shape and reached a maximum width soon after
the same: lr ¼ lg ¼ 1. (3) The scale of times is related to
the start of draw. Marano’s tests were used by Laubscher
that of the length by lt ¼ l1/2l . (4) The scale of stresses is
[2,3] to propose a guideline for the design of production
related to that of lengths by lo ¼ lr ¼ ll. (5) The residual
levels in block caves based on the geometry of the IMZ.
friction angles are the same: lfr ¼ 1. (6) Wall friction angle
Experiments measuring IEZs using gravel as the model
are similar to the internal friction angle: fw ¼ f, where l is
media have been carried out in order to understand the
the scale factor for each of the variables under study.
flow of coarse caved rock [6,16]. Peters [7] concluded that
During this study, the above hypothesis of scaling was
particle size had a small effect on the IEZ width and
tested by carrying out experiments at two different
indicated that the drawpoint width dimensions have a
geometrical scales.
major role in determining its geometry. Peters observed
that the extraction zones in gravel were not elliptical as
described by Kvapil, but were elongated in the centre; he 4. Experimental description
observed that the IEZ reached a maximum width with
extraction. Power [16] who conducted 3D modelling using The large physical model was designed to run simula-
gravel, found that the height of draw and particle size had a tions of flow for block caving under both isolated draw and
strong effect on IEZ’s geometry. interactive draw conditions. Variations of design para-
In this paper, the authors present a study of the meters such as drawpoint dimensions were also incorpo-
controlling parameters in isolated draw for the flow of rated in the design. The physical model main assembly is
coarse caved rock from the results of experiments in the 3.5 m wide, 2.5 m long, and 3.3 m high. It holds approxi-
largest 3D physical model ever constructed to study gravity mately 55 tonnes of aggregate. This represents the largest
flow in caving mines. Statistical analyses on the data were 3D physical model ever constructed to study flow in block
carried out to help delineate the controlling parameters caving using gravel as the model media (see Fig. 1).
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862 R. Castro et al. / International Journal of Rock Mechanics & Mining Sciences 44 (2007) 860–870

the markers located at full height arrived at the drawpoint,

which occurred after recycling gravel on the model’s top.

4.1. Model media

The tests described in this paper were conducted using

crushed phyllite gravel purchased from a local quarry. The
gravel was air dried prior to being used in the experiments.
This had the objective of avoiding cohesion due to capillary
effects on the material’s fine fraction. During the experi-
mental phase, two different media were tested, one using a
narrow distribution (8 mm-ND) and another using a wide
size distribution (18 mm-WD) of particle sizes. Additional
to those tests, experiments on IEZs for a 20 mm narrow
distribution media conducted by Power [16] were incorpo-
rated in the analysis. The cumulative size distribution for
the different particle sizes is presented in Fig. 2.
The shear strength characteristics of the different media
tested were determined using a large 300 mm diameter
shear box. Samples were subjected to different normal
forces ranging from 32 to 240 kPa, and results are
presented in Fig. 3. Repeats of the shear strength tests
showed that the error in the estimate of the friction angle
was 1.51. The results suggest that friction angle slightly
increased with particle size.
Other properties of the media under study were
measured and are summarised in Table 1. In this, the
uniformity index of the distribution Cu is defined as
Fig. 1. Large three-dimensional JKMRC physical model.
p60
Cu ¼ , (1)
p10
The physical model was configured to represent modern
where p10 is the size corresponding to the 10% passing and
block cave geometries using two different geometrical
the p60 is the 60% passing size. The rock shape factor is
scales 1:30 and 1:100. The dimensions in the model were
calculated by [19]
determined after conducting a benchmark of current mine
design practise [18]. At these scales the physical model 6V
attempted to represent the flow of coarse fragmented caved rv ¼ , (2)
pd 3
rock having a mean size of 0.7 m and a height of draw of
100–330 m. The model height was 3300 mm and draw point where V is the mean volume of a particle and d is the mean
dimensions were 120 mm wide  100 mm high and particle diameter calculated from the arithmetic mean of
36  30 mm accordingly. For the isolated draw experi- width, length and depth of a particle.
ments, drawpoints were located in the centre of the model’s
base so the flow zones did not intersect the model’s walls. 100
20mm_ND
Material was extracted using a vibrational loader so that 90
8mm_ND
it was not in contact with the model, preventing vibrations 80
Cumulative passing (%)

18mm_WD
from affecting the flow. This system allowed material to be 70
drawn remotely from beneath the model and fed onto a 60
series of conveyors which transported it to a weigh point. 50
The vibrational loader was designed and comparisons 40
were made between extracting material using a model 30
bucket and the vibrational loader with no difference being 20
noted. 10
Refilling of the model was performed after the IMZ had 0
reached the surface. This had the objective of preventing 1 10 100
Size (mm)
material riling towards the crater and of maintaining a
constant level of vertical stresses. Thus, the maximum Fig. 2. Size distribution of material for different particle size distributions
height of the IEZ referred to in this paper is that at which under study.
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300
8 mm-ND 20 mm-ND 18 mm-WD
Linear (8 mm-ND) Linear (18 mm-WD) Linear (20 mm-WD)
250

Shear Strength (kPa)

200

150

100

50

0
0 30 60 90 120 150 180 210 240 270 300
Normal Stress (kPa)

Fig. 3. Maximum shear strength for different particle sizes.

Table 1
Summary of model media characteristics used during experiments

Material p50, mm Cu f Solid/bulk density, Ton/m3 Size fraction, mm Aspect ratio (w:l:d), mm Shape factor rv

WD-18 mm 16.8 2.33 45 2.7/1.9 19 32:24:14 0.78 (70.17)

9.5 13:9:3 0.75 (70.13)
3.5 7:5:3 0.82 (70.28)
ND-8 mm 8.3 1.53 41 2.70/1.55 13:9:6 0.81 (70.14)
ND-20 mm 20 1.21 46 2.71/1.5 32:20:13 0.84 (70.47)

4.2. Measurement devices sensors was significantly less that the number of markers
used to determine the IEZ.
Because of the 3D configuration of the physical model,
material was surrounded on all sides and thus modelling
5. Experimental results
was, in effect, blind. In order to determine the extraction
zone, painted numbered markers were positioned inside the
Experiments were carried out to investigate the effect
model and recovered at the drawpoint (Fig. 4a).
that the height of draw, particle size, particle size
However, only the geometry of the extraction zone for
distribution and drawpoint dimensions have on flow zone
a given mass drawn could be deduced from the system
dimensions. Table 2 presents a summary of the database
of markers. For that reason, sensors were developed in
used to investigate the controlling parameters on isolated
order to determine the movement zone. The movement
draw.
probes are of an extensometer configuration (Fig. 4b).
A length of piano wire slides inside a length of brass tube,
propelled by the internal spring of a microswitch. The 5.1. Effect of height of draw
frictional force between the sliding wire and tube is just low
enough for the microswitch to move the piano wire Figs. 5 and 6 show typical results of the isolated
forward when the assembly is horizontal. Adjustment is extraction and movement zones for different accumulated
provided so that the piano wire can be set relative to the mass drawn. This figure corresponds to a vertical section
end of the tube when held back by a particle. The passing through the middle of the drawpoint of the
movement probes are designed to detect the beginning respective 3D flow geometry. It is observed that the
of movement of the particle directly in front of the probe geometry of the width of extraction and movement zones
tip. Prior to installation, the sensors were tested in a 2D increases with the height of IEZ and IMZ, respectively.
model from where the flow contour could be observed and The IMZ reaches the surface of the model well before the
calibrated. IEZ; and it is always wider and higher than the IEZ for a
Sensors were positioned within the model at five given mass drawn. The IEZs and IMZs could be reason-
different levels to determine the evolution of the IMZ with ably well fitted by an ellipsoid contour. The smoothness of
mass drawn. The spacing of sensors in the horizontal was the IEZ profile is different to that of the movement zone
50 mm for the fine and 100 mm for the coarser fragmented due to the larger number of labelled markers compared to
material. In order to avoid flow interference, the number of movement sensors.
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864 R. Castro et al. / International Journal of Rock Mechanics & Mining Sciences 44 (2007) 860–870

5.2. Effect of particle size

kg drawn
3300
Fig. 7 presents the extraction zone widths for different 3000 1600
particle sizes as a function of the height of draw. In this
graph, we plotted the 95% confidence interval for the 2700
1400
estimate of the width of the IEZ’s for the 20 mm-ND 2400
media. Within that range, the widths of the IEZ for all 1200
2100

Height (mm)
1800 1000

1500 800

1200
600

900
400
600

300 200

0
–400 –300 –200 –100 0 100 200 300 400
E–W axis (mm)

kg drawn

2000
3000
1800

2500 1600

1400
2000
Height (mm)

1200

1500 1000

800

1000
600

400
500

200

0
–500 –400 –300 –200 –100 0 100 200 300 400
E–W axis (mm)

Fig. 5. Vertical view of extraction zone for the (a) 8 mm-ND; (b) 18 mm-
Fig. 4. (a) Example of marker used to determine extraction zone; Marker WD particle size distributions.
is 20 mm passing size; (b) modified extensometer used to detect the
movement envelope.

Table 2
Summary of experimental set up

Experiment Model media Drawpoint dimensions Geometrical Height filled hf, mm dpw/p50 hf/p50
(mm) dpw  dph, mm scale lL

T1 ND-20 120  100 1:30 3300 6 165

T2 ND-20 120  100 1:30 3300 6 165
T3 ND-8 36  30 1:100 3300 4.5 413
T4 ND-8 36  30 1:100 3300 4.5 413
T5 ND-8 36  30 1:100 3300 4.5 413
T6 ND-8 120  100 1:30 3300 15 423
T7 WD-18 120  100 1:30 3300 6.7 183
T8 WD-18 120  100 1:30 3300 6.7 183
T9 WD-18 120  100 1:30 3300 6.7 183
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1200
kg drawn
T120mm_ND
250
T220mm_ND
3000 1000
T38mm_ND

2500 200 T48mm_ND

800
T58mm_ND

Width of IEZ (mm)

Height (mm)

2000 T718mm_WD
150
600
1500
100
400
1000

50
500 200

0
–400 –300 –200 –100 0 100 200 300 400 500
0
0 500 1000 1500 2000 2500 3000 3500
N–S axis (mm)
Height of IEZ (mm)

kg drawn Fig. 7. IEZ’s width measured at different height and particle sizes. The
95% confidence bound for the width of the 20 mm-ND had been included.
3000 600

800
2500 500 18mm_WD 8mm_ND 18mm_WD all data
700
Height (mm)

2000 400 600

Width of IMZ (mm)

500
1500 300
400

1000 200
300

200
500 100
100

0 0
–400 –300 –200 –100 0 100 200 300 400 500 0 500 1000 1500 2000 2500 3000 3500
N–S axis (mm) Height of IMZ (mm)

Fig. 6. Movement zone for 8 mm-ND model media before and after the Fig. 8. IMZ’s width as a function of IMZ’s height for different particle
IMZ reached the surface. size distributions. The mean and error band at 95% confidence interval
had been included.

media size were similar for heights of draw below 3000 mm. 5.3. Effect of drawpoint dimensions
At 3000 mm, that is, close to the end of the experiment, the
8 mm-WD and the 18 mm-WD media were slightly The effect of drawpoint width on draw geometry was
narrower (100 mm) than the IEZ’s width of the 20 mm- investigated using two different drawpoint geometries.
ND media. Given the size of the experimental set up here described,
The average IMZ’s width for two different media is it was not feasible to carry out repeat tests on
presented in Fig. 8. The calculated IMZ’s width standard 120 mm  100 mm drawpoint dimensions. However it was
deviations were 53 and 23 mm for the 18 mm-WD and possible to statistically test if the drawpoint dimensions
8 mm-ND media, respectively. The large data dispersion affected the flow zones using the experimental errors
for the wide distribution was expected given the larger calculated from previous tests. Tables 3 and 4 show the
spacing (100 versus 50 mm in the horizontal plane) that had results of the extracted area and the width of IMZ
to be used to determine the movement envelope in the measured at different heights (hi). In this analysis we
coarser material. The analysis shown in Fig. 8 indicated included the mean values and standard deviation (in
that there was no statistical evidence to conclude that the brackets) corresponding to three tests using a 36  30 mm
width of the IMZ between the two media differed drawpoint dimension and a single test using a
significantly. 120  100 mm drawpoint. Given the experimental errors,
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866 R. Castro et al. / International Journal of Rock Mechanics & Mining Sciences 44 (2007) 860–870

Table 3
Effect of drawpoint width on the IEZ’s geometry

IEZ height, mm hi, mm IEZ area (dpw ¼ 36 mm), IEZ area Difference mm2
mm2 (dpw ¼ 120 mm), mm2

3300 2400 397,400 (21,779) 382,000 15,400

1600 493,400 (8202) 487,600 5800
800 307,600 (3960) 310,400 2800
2000 1500 238,800 (8485) 244,800 6000
1000 281,000 (1414) 282,000 1000
500 129,200 (2263) 127,600 1600
1000 750 79,600 (8445) 73,600 6000
500 74,600 (4283) 71,600 3000
250 37,800 (283) 37,600 200

Table 4
Effect of drawpoint width on IMZ’s geometry

IMZ height, mm hi, mm IMZ’s width wIMZ IMZ’s width wIMZ wIMZ (dpw ¼ 36 mm) wIMZ
(dpw ¼ 36 mm), mm (dpw ¼ 120 mm), mm (dpw ¼ 120 mm), mm

3300 2400 577 (731) 540 37

1600 627 (721) 600 27
800 557 (721) 500 57
2000 1500 467 (715) 380 87
1000 480 (730) 390 90
500 367 (723) 350 17

1000 750 247 (721) 230 17

500 257 (735) 260 3
250 187 (715) 220 33

it was concluded that there is no significant difference in would be determined by the following dimensionless
both extracted area and the IMZ width for the range of parameters:
drawpoint dimensions under study. hIEZ wIEZ dp
p1 ¼ ; p2 ¼ ; p3 ¼ w , (3)
dp dp dp
5.4. Effect of model scale
where dp is a characteristic particle size and hIEZ, wIEZ are
One of the most difficult questions that physical the height and width of the IEZ and dpw is the drawpoint’s
modellers face after they have carried out experiments at width. The characteristic particle size p50 was used as
reduced scale is the meaning and transfer of quantitative experiments conducted in [16] and those presented here
results to industrial applications. This is more crucial in showed no particular change in IEZ or IMZ width.
block caving given the lack of quantitative full-scale data In our experiments the drawpoint dimensions and the
from which it could be possible to compare scaled values. particle size were varied according to two different
A way of addressing this problem is through the applica- geometrical scale models, 1:100 and 1:30. By reducing
tion of model theory. Model theory states that a simultaneously the size of the particles and the drawpoint
quantitative result would be scalable as long as the dimensions, the dimensionless p3 ¼ dpw/d506 was con-
governing phenomena equations are the same between stant between the two scales. This meant that, the small-
the scaled model and the prototype [20]. In other words, particle-drawpoint-width dimensions experiments were a
input and output dimensionless quantities between model scaled model (1:3) of the large-fragment-size-drawpoint-
and prototype are kept constant. width experiment. As noted in the value of p3, the particle
The isolated draw tests carried out using a range of size used, represents a relatively coarse fragmentation when
drawpoint dimensions and particle sizes enabled us to compared to the drawpoint width dimensions, which
study the effect of scale on the IEZ geometries. If there is resulted in intermittent mechanical hang ups at the
distortion or it is not possible to scale the geometry of the drawpoint.
IEZ between different scaled models, a reduction in the Fig. 9 shows the dimensionless width p2 as a function of
geometrical scale factors would result in significant the dimensionless extracted heights p1 measured in the two-
differences between dimensionless IEZ geometries. We scaled models. It is noted that p2 is a linear function of p2
postulate that in the flow of cohesionless materials, under for the range of heights under study. The analysis of error
the set of assumptions stated in Section 3, gravity flow as shown in Fig. 6 concluded that the change in geometrical
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R. Castro et al. / International Journal of Rock Mechanics & Mining Sciences 44 (2007) 860–870 867

scale did not change the dimensionless extraction width. decreases during extraction and reached a constant value.
This indicated that for cohesionless materials, the geometry The relationship between the IMZ height (hIMZ) and the
of the IEZ was comparable between different geometrical accumulated mass drawn (m) was fitted by an equation of
scales, at least for the ranges studied. the form
hIMZ ðmÞ ¼ h0 ð1  em=mh Þ þ cm; (4)
6. Granular flow mechanisms
where ho and mh represents the height and mass at which
The controlling mechanisms of isolated draw were the IMZ’s height increases exponentially with mass; and c
studied by observing the change in the geometry of the is the final rate of growth when the height grows linearly
IMZ at different stages of draw together with direct stress with the mass drawn.
measurements. Previous research conducted with numer- The IMZ is by definition a zone within the granular
ical models [5] has postulated that the IMZ was controlled material that has undergone an increase in porosity.
by two different mechanisms: collapse of an arch and Measurements of stresses showed that immediately above
erosion at the sides, as material is drawn. In this part of the the IMZ’s height there is a zone of high horizontal stresses.
paper we investigated the isolated draw mechanisms based It is postulated that this higher horizontal stressed zone
on experimental observations. identifies a stress arch that separates the lower (final) and
As it is shown in Figs. 10 and 11, the overall geometry of higher (initial) porosity zones. Eq. (4) shows that the rate
the IMZ and IEZ is mainly controlled by the mass drawn. of collapse of this arch grew rapidly at the initiation of
We noticed that the geometry of the IMZ did not change if draw and reached a constant collapse rate c when m0 kg
material was not being drawn. It was observed that the rate had been drawn. The values of the fitted coefficients and
of growth of the IMZ’s height as a function of mass drawn the correlation coefficient of the non-linear model are
shown in Table 5. These values were obtained using the
60 non-linear Levenberg–Marquardt regression method. It is
1:100 (p50=8 mm) 1:30 (p50=20 mm) (Power,2004) interesting to note that although the IEZ could not strictly
50 be used to understand mechanisms; the IEZ’s width could
be fitted using Eq. (4). However, as shown in Table 5 the
40 fitted coefficients for the IEZ are an order of magnitude
larger than those of the IMZ.
wIEZ/p50

30 In Fig. 11, the change on the IMZ and IEZ’s width with
mass drawn is plotted. The analysis showed that the width
20 of both zones increased with the mass drawn. The rate of
expansion of the IMZ’s width decreased with accumulated
10 mass drawn. We observed that the horizontal expansion of
the IMZ with the mass drawn occurred in two separate
0 stages. The first stage occurred when the IMZ was fully
0 20 40 60 80 100 120 140 160 180 200
hIEZ/p50
contained within the boundaries of the model and the
second stage occurred after the IMZ broke through to the
Fig. 9. Dimensionless IEZ’s width as a function of the dimensionless surface. The relationship between the width of the IMZ
IEZ’s height. and the mass drawn was shown to be non-linear and be

3600
T3 T4 T5 T6 EQ. 3
3300
3000
Maximum height of IMZ (mm)

2700
2400
2100
1800
1500
1200
900
600
300
0
0 50 100 150 200 250 300
Mass drawn (Kg)

Fig. 10. IMZ’s height as a function of the accumulated mass draw for the 8 mm-ND media.
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1000
T3 T4 T5 T3-IEZ T4-IEZ T5-IEZ
900

800

Maximum width of IMZ/IEZ (mm)

700

600

500

400

300

200

100

0
0 200 400 600 800 1000 1200 1400 1600 1800 2000
Accumulated mass drawn (Kg)

Fig. 11. Maximum width of IMZ and IEZ as a function of the mass drawn for the 8 mm-ND for dpw ¼ 36 mm.

Table 5
Eq. (4) parameters for material under study

Media Flow zone h0, mm mh, Kg c, mm/Kg R2

8 mm-ND IMZ 1225 (7164) 20.8 (77) 9.2 (71.04) 0.96

18 mm-WD IMZ 2087 (71020) 65.8 (721.4) 3.73 (71.59) 0.97
8 mm-ND IEZ 1424 (770) 140 (721) 0.98 (70.06) 0.99
18 mm-WD IEZ 1480 (763) 159 (720) 0.87 (70.04) 0.99
20 mm-WD IEZ 1578 (752) 194 (718) 0.68 (70.03) 0.99

Table 6
Eq. (5) parameters for material under study

Media Flow zone w0, mm m1, Kg m2,Kg b R2

8 mm-ND IMZ 1004 (716) 40 (73.8) 775 (774) 0.47 (70.01) 0.97
18 mm-WD IMZ 1216 (7154) 54.2 (714) 1285 (7443) 0.31 (70.02) 0.94
8 mm-ND IEZ 770 (710) 17.2 (73.4) 584 (725) 0.26 (70.01) 0.99
18 mm-WD IEZ 779 (747) 86.2 (758) 887 (7243) 0.24 (70.08) 0.98
20 mm-WD IEZ 1183 (7382) 138 (775) 2263 (71987) 0.29 (70.04) 0.94

well fitted by a relation of the type to the width in terms of the height is given by the following
expression:
wIMZ ðmÞ ¼ w0 ð1  bem=m1  ð1  bÞem=m2 Þ, (5)  
b 1 þ eaðhIMZ h0 Þ
where w0 is the maximum width after the IMZ reached the wIMZ ðhIMZ Þ ¼ ahIMZ  , (6)
a 1 þ eah0
surface, b is an adjusting constant (dimensionless) and m1,
m2 are the masses identifying the two stages on the IMZ’s where a and b are positive dimensionless constants, a is in
width expansion. The values of the fitted constants and the mm1 and h0 is the inflexion point in terms of height which
statistical analysis of the fitted parameters are presented in the rate of horizontal expansion decreases. There are two
Table 6. As with the previous relationship, the IEZ’s width terms in Eq. (6); a linear and an exponential decay that
could be fitted with a similar function. could be used as a means of interpreting the overall
The change in the width of the movement zones with geometry change during draw. In the initial stage of draw,
height is shown in Fig. 12. In this case we have included the the width increases at a rate of (a+b) mm per each mm in
derivative (dwIMZ/dhIMZ) to show the change in the rate of height. After the IMZ had reached a critical height h0 there
expansion of the IMZ’s width with height. This shows that is a decrease in the rate of expansion. The parameter a is an
wIMZ increases with hIMZ irrespective of particle size. adjustment parameter that defines the rate in which the
However, the rate at which the width increases with height final stage is reached. The fitted coefficients for the data
decreases as the IMZ moves towards the surface. A good fit obtained are presented in Table 7.
 ARTICLE IN PRESS
R. Castro et al. / International Journal of Rock Mechanics & Mining Sciences 44 (2007) 860–870 869

700 0.3
T3 T4 T5 Eq. 5 dw/dh
600
0.25
500

dwIMZ/dhIMZ
0.2

wIMZ (mm)
400

300 0.15

200
0.1
100

0 0.05
0 400 800 1200 1600 2000 2400 2800 3200
hIMZ (mm)

Fig. 12. IMZ’s width as a function of the IMZ’s height.

Table 7
Eq. (6) parameters for different media

Media a b a (mm1)  102 h0, mm R2

8 mm-ND 0.08 (70.03) 0.18 (70.05) 4.37 (70.36) 2054 (7224) 0.98
18 mm-WD 0.13 (70.02) 0.06 (70.042) 9.9 (712000) 1564 (7866) 0.89

7. Conclusions to model scale, results describing no significant distortions

between scales are encouraging and may open the
There is debate within the literature about the effect that possibility to extrapolate results from model scale to full
particle size and height of draw has on the isolated scale.
extraction and movement zone geometries. Experiments
were carried out in a Large Physical Model in order to
Acknowledgements
investigate the influence of those variables on the gravity
flow of cohesionless materials. The results suggest that the
This paper describes a component of work carried out
main variables that affect the geometry of flow zones are
within the International Caving Study (ICS II) run through
the mass drawn and the height of draw. Within the
the University of Queensland’s Julius Kruttschnitt Mineral
precision and range of particle sizes of our experiments, it Research Centre, in Brisbane Australia. Sponsors of the
was observed that particle size only had a small effect upon
ICS II include: CODELCO, DeBeers, LKAB, Newcrest
extraction and movement zone widths. More experiments
Mining, Northparkes Mines, Rio Tinto, WMC Resources
at small fraction sizes where the friction angle and particle
and Sandvik Tamrock. Their support and recommenda-
shape are constant, would be beneficial in order to
tions for the direction taken in the ICS II Gravity Flow
determine the values at which particle size may have a
research are appreciated. The authors are also grateful to
significant effect on flow geometries. The drawpoint width
Gideon Chitombo, and Geoffrey Just of the University of
and the size composition (wide or narrow distribution of
Queensland for useful comments throughout the research
sizes) were found to have a negligible effect on draw zone and to Italo Onederra and Libby Hill for proof reading the
geometries.
manuscript.
These experiments allow a better understanding of the
mechanism involved in isolated draw. It was experimen-
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