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

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.

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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

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.

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

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

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

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.