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Physical Modelling as an Engineering Tool for Mining: Theory and
Practice Castro, R Orellana, L Pineda, M Laboratorio de Block
Caving (BCL) Advanced Mining Technology Centre Universidad de Chile
Abstract Mining is one of the disciplines that require more
engineering resources given the important decisions that may cost
several millions of dollars to develop. Engineering tools for this
purpose include numerical, scaled models, and full scale tests.
From all thee, the ones that have gained more attention in the past
years are numerical models and full scale trials. Physical
modeling, despite being the lowest cost approach, seems to have
lost credibility in the last years due to the over expectation of
being reality (not a model).To clarify this, in this paper the
fundamentals and related applications for the use of physical
scaled models for block caving applications is presented.
Applications include the study of the caved rock flow in caving
mines and the equipment performance for the design of novel draw
systems. The results of the scaled models are compared to mine data
which allowed the role of physical modeling to be quantified. They
indicate that for engineering purposes physical modeling is a tool
that could be confidently used for decisions making purposes in
caving engineering.
1 Introduction This paper attempts to formally re-introduce
scaled physical modeling into the mining engineering community.
This approach has been successfully used for several years in other
engineering disciplines including mining, but seems to have been
abandoned in recent years. Physical modeling continues to be used
in other disciplines (especially in civil engineering) that have
use it for design purposes for several years to solve very complex
problems (Langhaar, 1959). When analyzing the research that is
taking place around the world there seem to be a tendency to focus
on the use of numerical modeling for problem solving in mining
engineering. There may be reasons for this, one is that the old
generations went to the process of physical modeling in some areas
(e.g. in geomechanics) without plenty of success. The other reason
is that in the curriculum of mining engineers there is a lack of
understanding of the fundamentals of physical modeling. In this
paper the theory as well as practical examples of the use of
physical modeling in mining engineering is presented. The scope of
physical modeling is also described not only qualitatively but with
clear examples to justify the use of this approach, and why there
should be allowance for this technique in mining engineering
programs.
2 Similitude analysis Physical modeling follows the following
steps:
a) Similitude analysis. b) Construction of the physical model
and the extraction system. c) Diagnosis and calibration of the
model d) Conduction of Experiments e) Comparisons to full scale
trials f) Proposals for further studies and design. The theory
behind the use of scaled models is similitude analysis to
understand the physics of the system, and can be found in several
text books (e.g. Langhaar, 1959). In summary, when a
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system is reduced the basic idea is to preserve the geometry,
velocities and the acting forces in the scaled system (model) so
that it is realistic with respect to the system under study
(prototype). Of course when scaling down systems there are
distortions that are likely to occur due to the presence of
spurious forces that may affect the scaled system. The modeler
should then determine the conditions that are more realistic. This
is determined by defining first the ratio of the main forces acting
in the prototype to define the constants. Theoretical analysis of
the forces that may be due to the scaled effect is then conducted.
Table 1 shows the main variable scales to be considered when
gravity is the main acting force.
Table 1. Similitude analysis variables scaling parameters
Variable Scale Factor Length !! Area !!!
Volume !!! Velocity !!!/!
Time !!!/! Weight !!!
Stresses and material strength !! FrictionAngle 1
3 Case Study 1: Design of a new materials handling system A
novel material handling system has been developed by the Institute
of Mining and Metallurgy Innovation (IM2) and CODELCO with the
objective of increasing the production rate of massive underground
mining methods (Encina, Geister, Baez, & Steinberg, 2008). The
system is based on stationary plate feeders installed at the
drawpoints. In this way, more than one drawpoint could work at the
same time, producing a significant increase in the rate of
extraction. In 2006 full scale trials were conducted at El Salvador
Mine to evaluate the feasibility of the system. The Block Caving
Laboratory (BCL) was asked by IM2 to develop an experimental plan
to understand the fundamentals of gravity theory for design
purposes for this new material handling system.
3.1 Experimental Set Up The experiments at scale were conducted
in two stages in order to gain confidence in the physical modeling
work. It should be emphasized that this was required as both the
geometry and the equipment were scaled, and results were also
available for the tests on the mine to compare the physical
modeling results and therefore adjust the parameters including the
material strength characteristics. The first model built was a 2D
representation across the gallery (Error! Reference source not
found.). The geometric scale was 1:50, so the model represents a 50
[m] extraction column of broken material (Alvarez, 2010; Orellana,
2011). The production gallery dimensions were 4 x 4 [m x m] and the
material size distribution was characterized by crushed stone with
D50 equal to 1.8 [cm] (!!"= 0.9 [m] mine scale) at laboratory
scale.
Rachel Stephan 12-5-17 11:06 AMDeleted: Figure 1
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Figure 1. Experimental set up for the 2D (left) and 3D model of
flow (right).
The second stage was the construction of a 3D model of a
drawpoint. The experimental plan considered the evaluation of the
system in a new mine (Orellana & Castro, 2011). The methodology
was similar to the 2D model including measurement of horizontal
stresses to further investigate the arching effect. The geometric
scale was 1:50 so the model represents a 50 [m] extraction column
of broken material. The experimental plan for both models aimed to
characterize the flow behavior of the new system in comparison to
the LHD draw system. This was done by conducting a series of tests
varying different parameters that include the geometry of the
drawbell and drawpoint, the fragment size distribution (narrow,
wide distribution and fragment size), the strength of the material
and the plate feeder configuration (speed and geometry). The
variables under analysis included the productivity (tons/cycle),
hang ups (frequency and type), stresses at the boundaries, the
forces requirement to move the plate feeder and the
interferences.
3.2 Methodology The methodology for the measurement of the
variables included the flow geometry, interference and equipment
productivity. To establish a mechanistic model for flow, a number
of experiments were conducted considering the parameters indicated
in Table 2.
Table 2. Parameters under study Number Parameter Nomenclature
Range of experiment
(scaled values) 1 Width of drawpoint Hg 4 m 2 Height of
drawpoint Hh 3-4 m 3 Angle of the drawbell a 53-58
4 Roughness of the drawbell w 0 and 45 6 Distance between brow
and drift 2.1-3.1 m 5 Material point load strength index
resistance (gravel to gypsum) I50 0.21-21.62 MPa
6 Material density (in-situ) 2.5 2.84 ton/m3 7 Height of draw Hc
50 m 9 Characteristic fragment size D50 0.9 m
10 Size distribution (coefficient of uniformity)
Cu=D60/D10 2.23 2.75
11 Width of the plate feeder Wpf 1.85 m
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12 Angle of the plate feeder 90 and 62
3.3 Results The results obtained during the experiments could be
divided into three. Those that correspond to the flow geometry (due
to the influence on recovery), operational interferences (hang ups)
and another set to the equipment performance during the tests
(productivity per cycle). In terms of flow the use of markers
allowed the extraction zone to be determined. As noted in Figure 2,
the flow develops in the middle of the drawbell and grows as an
ellipse as indicated in the results when using granular materials.
In terms of the hang up prediction, the hang ups were classified
according the geometry in four types shown in the following
figure.
Hangups, material supported at the top of drawbell
Hangups, material supported at the bottom of drawbell
Hangups, material forming an arch between the bottom of drawbell
and production gallery
Hangups, material over the plate feeder forming a stable
structure
Figure 2. Hang up types noted during the experiments.
In terms of the equipment one of the reasons to conduct these
experiments was to understand the way that the plate feeder
produced the flow. It was noted that the flow is through pushing of
the material at the base of the feeder (Figure 3, area 2). In this
case the flow occurs in mass (zone1) under the drawpoint, using
more of the area below the drawbell. In this system there is a no
flow zone near the back of the feeder (zone 4). This is different
than in a LHD system where the draw occurs only near the brow.
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Figure 3. Flow mechanisms for a plate feeder configuration
The quantitative results of the tests are summarized in Table 3.
It is worth noting that in general, the cinematic similitude was
achieved and that the dynamic similitude (forces required by the
plate feeder) could be achieved by changing the strength of the
material.
Table 3. Summary of results of measured variables
Parameter Productivity (tons/cycle)
Hang up frequency # hang up/1000 ton
(scaled) Stresses
Force in the plate feeder
kN (scaled to mine)
Gravity flow pattern
(width of draw)
Fragment size
The smaller the fragment size the smaller (-50%) the smaller the
tons per cycle (-49%).
Coarser fragments
tend to arch over the drawpoint.
Does not influence.
Does not influence. System
works at 11000 [kN].
The larger the fragment size the
larger the flow zone
Fragment distribution
Narrow size distribution materials (dm = 1 cm; 0.5 [m]) produced
more tons per cycle when compared to a wide distribution (dm = 1.8
cm;0.9 m).
Coarse particle distribution increase the hang ups rate
Does not influence.
Does not influence. System works kt 11000
[kN].
Coarse particle distributions
increase the flow zone width.
Material strength
For the range of materials analyzed there is an influence of
around 40% on tons/cycle.
Different material tests show the same type of hang-ups but with
different proportion of occurrence.
Different
weights of extraction
column
The system required 3500 to 7000 [kN].
Different
materials affects geometry the
flow zone
Angle of drawbell Does not influence Does not influence
It was observed that vertical stress was modified.
Does not influence. System
works at 11000 [kN].
Does not influence
Drawpoint geometry
A decrease in the section
area (-27%) meant a reduction on production
rate (-71%).
The result shows that hang-ups rate increase 4 times.
Does not influence
Does not influence. System works at 11000 [KN].
Does not influence
Width of the feeder
An increase on a 27 % in area the production per
cycle in 29% Does not influence Does not influence
Does not influence. System
works at 11000 [kN].
Does not influence
Angle of feeder Does not influence Does not influence
Does not influence.
The experimental test show that its possible to reduce the
energy required to 9000 Kk (18 % of
Does not influence
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cycles).
4 Case Study 2: Design of a new production level al Goldex
Goldex Mine is exploited by a novel mining method that combines the
efficiency of sublevel stoping drilling and blasting and an
extraction similar to a block cave with one extraction level
located at the base of the stope (Frennete, 2010). At the request
of the Agnico-Eagle Mines Limited Goldex Project management, the
BCL was asked to provide physical modeling in order to understand
the flow mechanism governing muck flow at the Eastern Primary Stope
to improve ore recovery and minimize dilution. The principal
concerns lied in the fact that the footprint is smaller than the
projection of the ore body, generating concerns about the mobility
of the ore located at the footwall of the stope. In addition theres
no notion of the predominant phenomena governing the flow, and the
mixing profile due to extraction. Section 609 was chosen to be
analyzed as a function of the amount of reserves located in the
footwall wedge. A limit equilibrium analysis was also conducted for
the different sections of the ore body.
4.1 Experimental Set Up The model consists of four dismountable
plexiglass walls that delineate the final geometry of the stope for
the Section 609 block of the mine. The dimensions of the model are
1.6 m height x 1 m length x 0.25 m width. The base of the assembly
incorporates the extraction system (11 drawpoints and the drawbell
geometry where each one has a shovel installed). These shovels are
linked to a servomechanism that gives an electrical impulse that is
controlled by an in-house built software that allows varying the
rate of extraction.
Figure 4. (Right) Physical Model. (Left) Drawpoints Level 76 and
apex through section 609.
In this model 5 experiments were run(Table 4).
Table 4. Experiments for Goldex flow study Experiment Draw
strategy Objective
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1 Uniform draw To determine the potential failure of the broken
rock located at the FW of the main stope and to quantify primary
ore recovery when
drawing from level 76.
2 Isolated raw To determine isolated flow zone diameter for
design of the new extraction level.
3 Uniform draw To determine the potential failure of the broken
rock located at the FW of the main stope and to quantify primary
ore recovery when
drawing from level 76 and from the proposed new level 73.
4 Uniform draw This experiment is a duplicate from experiment 3,
in order to quantify the experimental error and results
accuracy.
5 Uniform draw This experiment simulates continuous dilution
entry at the top of
the stope. The aim is to quantify potential dilution entry
mechanism and ore recovery
Figure 5. Experimental plan scheme
4.2 Results The experimental plan and the obtained results can
be classified as 4 main cases, due to the observed governing
mechanism of the caved rock flow. The cases are listed below and
presented in Figure 8:
Case 1: The extraction is performed by drawing only from the
main extraction level (Level 76). This case doesnt include
dilution.When drawing from the main extraction level it was
observed that the flow developed upwards towards the hanging wall
as this represents a lower strength path for the movement to
develop. Since the drawpoints are sufficiently close together,
there is an evident interaction between them and it results in a
vertical massive flow as wide as the footprint width of the
extraction level. The vertical massive flow doesnt mobilize the
footwall in these conditions. Nevertheless, the ore located at the
footwalls surface is able to flow by the rilling mechanism from the
FW to the HW direction.
Case 2: The extraction is performed by drawing from the main
extraction level (Level 76) and then drawing from level 76 and
level 73 (proposed new level as a result of the IDZ experiment)
simultaneously. This case doesnt include dilution. When drawing
both from level 76 and level 73, a fraction of the material located
at the FW is mobilized. Still there is a passive zone located at
the FW that is not mobilized by drawing from level 73 and that will
be able to flow by rilling.
Case 3: The extraction performed by drawing from the main
extraction level (Level 76). Once the subsidence is achieved, the
refill starts simulating entry dilution at the stope. When the
Rachel Stephan 12-5-17 11:06 AMDeleted: 7
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uniform extraction from level 76 begins the flow stream quickly
propagates vertically up to the stope surface as observed in the
previous experiments. As soon as the flow breakthrough the surface
the dilution is mobilized. As seen from the experiments without
dilution, the extraction from level 76 results in a vertical
massive flow as wide as the footprint of the extraction level. This
vertical flow shows preferential movement towards the HW. The
vertical massive flow doesnt mobilize the footwall in these
conditions. Dilution entry for the drawpoints is mainly influenced
by the cave profile during the first part of the extraction. Since
this cave profile develops faster towards the HW, dilution entry
for the drawpoints located near the HW is reported earlier.
Case 4: The extraction performed by drawing from the main
extraction level (Level 76) and then drawing from level 76 and
level 73 simultaneously. Once the flow breaks through to surface,
the refill starts simulating entry dilution at the stope.
Continuing extraction from level 76 and starting draw from level
73, the flow mechanism due to extraction from level 73 generates
lateral movement of the broken rock. The mobilized zone due to the
extraction from level 73 generates an early connection with the low
density zone due to extraction from level 76 causing lateral
dilution entry at level 73 starting from the HW towards the FW.
Lateral dilution is therefore the phenomenon that will determine
the closure of the extraction for the drawpoints located at level
73.
Figure 6. Conceptual scheme of the experimental results for the
studied cases
Using the information obtained from the labeled markers, it can
be obtained the final ore recovery for the studied cases. These
results are listed in Table 5 which was used to define the
requirement of a new level for the mine.
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Rachel Stephan 12-5-17 11:06 AMDeleted: Table 5
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Table 5. Summary of results for the experimental plan
Experiment Case Extraction With dilution Estimated Ore
Recovery
Experiment 1 and 3 1 Level 76 No 100%
Experiment 3 and 4 2 Level 76 and 73 No 100%
Experiment 5 3 Level 76 Yes 54% (100% dilution)
Experiment 5 4 Level 76 and 73 Yes 68% (100% dilution)
Experiment 6 Level 76 73 and 65 Yes 85% (100% dilution)
5 Conclusions Physical modeling is an old technique that has
been used for several years in other engineering disciplines. In
this paper the theory and practical examples of the technique are
presented. The results so far have indicated that physical modeling
is an effective tool for engineering design at least in the cases
studied. As more knowledge is gained, the more it would advance the
mining engineering discipline.
6 Acknowledgements The authors would like to thank Codelco and
Agnico Mine for providing funding for the research. This research
has been conducted as part of the Conicyt project through the
Advanced Mining Technology Center at the University of Chile.
7 References Castro, R. Pineda, M. (2012). Draw control at
Goldex mine. Internal report to Agnico-Eagle, Laboratorio de Block
Caving, Universidad de Chile.
Frennete , P. (2010) The Goldex mine mining method. Proceeding
of Caving 2010 Conference, Perth, 20-22 April pp. 253-266.
Langhaar, H. (1959). Dimensional analysis and theory of models.
John Wiley Sons (Eds)
Alvarez, P., (2010). Modelamiento fsico de la minera continua.
Engineering Thesis, Universidad de Chile
Orellana, M. (2011). Numerical modelling of the continuos mining
system. Master in Mining Eng. Thesis , University of Chile,
Santiago, Chile.
Orellana, L., & Castro, R., (2011). Modelamiento fsico de la
minera continua fase II. Internal Report to IM2.
Encina,V., Geister, F., Baez, F., & Steinberg, (2008).
Mechanised continuous drawing system: a technical answer to
increase production capacity for large block caves mines in
proceeding of MassMin2010, p. 553-562.