The Use of Particle Flow Code in Gravity Ore Flow Studies

G.J. VAN HOUT, De Beers Corporate Headquarters, Johannesburg, South-Africa ABSTRACT: Very few numerical modelling codes are capable of modelling gravity flow. Despite cave mining methods being used extensively in the industry, the mechanisms behind the flow process are not fully understood. The Particle Flow Code is used to investigate granular flow and more recently, modelling studies are in progress to analyse cave mining principles in depth. It is anticipated that numerical modelling will assist in a better comprehension of the caving processes and will be complementary to the empirical guidelines used when designing a cave production lay out. This paper discusses some of the work carried out at De Beers using the Particle Flow Code and references to some historical numerical and physical models.

1 INTRODUCTION It is anticipated that numerical modelling of gravity flow in general and caving processes in particular will result in a better insight into the material flow mechanisms. Early gravity flow studies by means of visual observations of laboratory scale physical models, simulating the drain of hoppers and bins, are the foundation of the fundamentals for bulk flow (Kvapil 1965). However, the material used in these models was granular and not irregularly shaped as in cave mining conditions. Non spherical particles obviously complicate the flow process. It is difficult to quantify angularity and even more strenuous to determine/describe its effect on the flow mechanisms. Numerical modelling is an excellent tool to get a better understanding on this complex topic. The application of the early gravity flow principles in the mining industry is also limited by an important, often overseen bias: the conclusions were derived for material flow from a single draw point. Experimental work done at Shabani Mine, using a three dimensional model under dynamic conditions, revealed that the principles derived from working single draw points are not valid when simultaneously drawing multiple draw points with spacings kept below a minimum critical distance. (Marano 1980). This distance depends on the physical characteristics of the material and has the utmost importance in cave mining layout since it determines the drawbell spacings. Again, numerical modelling can be the key towards a more comprehensive approach to gravity flow mechanisms. Despite the shortcomings of the granular single drawpoint models, the concept of the draw ellipsoid is still the most widely used approach to study ore gravity flow (Janelid & Kvapil 1966). Powerful numerical models only became available to the mining industry in the last two decades and cave mine design was based almost purely on practical experience of trial-and-error methods. The empirical design guidelines in the form of classification tables and stability charts developed by D.H. Laubscher (1994) are still the only reliable and practical set of rules widely used and well accepted in the industry. It must be emphasised that numerical packages appropriate for gravity flow simulations, based on the Distinct Element Method (Cundall & Strack 1979) can, at present, not be utilised to build huge models and draw conclusions solely based on a single model to design an optimal mine production layout. Initially, numerical modelling should be employed as an instrument to verify and confirm the empirical design rules. The next step would be a sensitivity analysis of these rules, improving the current knowledge. This can only be achieved by investigating, in smaller representative models, all the distinctive parameters in

the empirical rules. This “modular” approach of breaking up the large complicated model in smaller and easier to study models is the preferred way to assess the effect of each parameter. In addition to this approach, an “adaptive modelling” process (Starfield & Cundall 1988) should be practised where one progresses slowly and painfully from the simplest model, adding complexity once it is fully understood and the results are confirmed by experimental or field data. From the simple models, one should understand and be able to develop equations based on the mechanisms revealed by these models. In the case of gravity flow models these equations should be equivalent to or confirm the empirical guidelines established by D.H. Laubscher. This paper describes the use of a numerical code in some of the work carried out to better understand the gravity flow of non-granular material.

2 THE PARTICLE FLOW CODE (PFC) The Particle Flow Code (ITASCA 1995) is a discrete element code used as an efficient tool to perform research into the behaviour of granular material, gravity flow applications, caving mechanisms, fracture studies, etc. PFC may operate in either two or three-dimensions. There are three important features in PFC, which make the code different from other widespread numerical programs. Firstly, it allows displacements and rotations of discrete bodies, with virtually no limit to the magnitude of these changes. Secondly, new contact detection between circular elements is simpler than contact detection between angular particles, thus making the code more efficient and thirdly, it is possible to construct blocks capable of breaking. The two fundamental components making up a PFC model are an assembly of balls and a set of walls. The particle assembly parameters consist of the locations and size distribution of particles. The number of balls is only limited by the RAM of the computer on which the model is run (30,000 balls typically require +/- 16 MB RAM in 2D). Complex fragment shapes can be simulated by combining several balls, bonded at their contact points. These fragments then can act as autonomous entities and depending on the bond strengths can split up into smaller, fragments depending on the mechanical loading.

The contact behaviour and associated material properties dictate the type of response the model will display upon disturbance. In order to run a realistic simulation with PFC, after particle generation and property declaration, boundary and initial conditions must be specified to define the in situ state. The planar walls or a string of boundary balls can be used to achieve the model specific initial and boundary conditions. PFC thus simulates the mechanical behaviour of a system comprised of a collection of circular or arbitrarily shaped particles. All that is needed to build even the most complex model is a set of circular balls; some walls and bond properties. The specification of the model geometry, element properties and solution conditions is not straightforward in PFC. It is a thinking process to identify ball and bond properties so that the simulated solid matches with a real solid tested in the laboratory. Setting the initial and boundary conditions is more complicated than for continuum models and the modeller has to rely on guidelines to assist him in setting up realistic models.

3 GRANULAR FLOW MODELS Because the mechanisms driving gravity flow operations are not well understood, in the past effort has been directed towards empirical methods to optimise mining methods. With increasing computer power facilities, significant improvement in the design process can be made through accurate computational PFC modelling of gravity flow situations. Before trying to model the flow of blocky fragments, granular flow models were investigated. These tests permitted recognition of the important parameters influencing the flow behaviour as well as establishing their effect on the flow. Extrapolation of the derived principles could then be verified with the more complex irregular material models. It is anticipated that the obtained postulations for the non-granular flow won’t be similar to the ones derived for the granular materials. Several modelling exercises using PFC to simulate physical sand models did not achieve “calibration” of the numerical model satisfactorily (Lorig et al. 1995). However, this was mainly due to the two dimensional approach of the problem, which turned out to be a wrong assumption/approximation. The conclusions based on physical granular flow analyses cannot be extrapolated to cave mining conditions (primordial to the current investigations). This is confirmed by different authors: • Experimental work done at Shabani Mine, using a three

dimensional model under dynamic conditions, revealed that the principles derived from working single draw points are not valid when drawing simultaneously multiple draw points with spacings kept below a minimum critical distance.

• Large-scale test results do not indicate that the behaviour of granular sand flow could be extrapolated to larger actual laboratory conditions (McNearny 1991).

• Yenge (1980) concluded that the flow of caved ore cannot be described satisfactorily by theories developed for the flow of sand. In the mining environment, particle sizes, particle shapes, flow rates and boundary conditions are not similar to those applying in the bins and bunkers.

4 NON GRANULAR FLOW MODELS The two dimensional version of PFC was used successfully to simulate a physical model of a block-caving mining method (McNearny & Barker 1998). The physical model was constrained to display blocky behaviour, common to block cave environments, rather than the granular flow behaviour seen in the sandbox models. This was achieved by closely packed layers of concrete bricks, hammered into position with a rubber mallet. The use of bricks permits a closer representation of a block cave environment than the sand models. The sand particle sizes are much smaller by comparison to the discharge opening holes in the physical models than the rock fragment sizes by comparison to the cave drawpoint dimensions. The brick model represents a more realistic particle to opening size ratio. In the PFC model, the bricks were created as two cylindrical particles bonded together. Figure 1 shows the PFC model at an intermediate stage in the flow process. The drawdown patterns and the rate of draw developed during numerical modelling closely simulated the physical models. The good match between physical and numerical models looks promising for the success of future numerical modelling.

Figure 1. PFC flow model of brick material. (After McNearny & Barker)

5 CAVE MINING MODELS STRATEGY The ultimate goal of achieving a close similarity between large cave mining layouts and 3D computer models is not for the immediate future. It is not feasible yet to set up a 3D model, which simulates accurately an extensive orebody incorporating all the known geological features, the stress regime, the tunnels, drawbells and other excavations. A more realistic way to analyse cave behaviour and to design optimal layouts is to break the entire process up into separate components. These components can be studied better by using smaller models, concentrating on one specific aspect of the whole cave. The “modular” approach permits the designer to use other programs when and where these are more appropriate than PFC. A suggested scheme of separation into smaller models is shown in figure 2.

Figure 2: Modular approach to cave mining modelling. 5.1 Primary fragmentation size model An initial model incorporating the rock mass properties such as the joint geometry, rock mass ratings, groundwater characteristics and stress levels should produce a primary fragmentation distribution for that orebody to be mined by means of caving. The Block Cave Fragmentation (BCF) program (Esterhuizen, 1994) is a reliable program to give an accurate prediction of the primary fragmentation. This BCF program is based on expert knowledge of cave behaviour, rock mass structural data and operating experience within block caving operations. Another

advantage of BCF is that it evaluates a situation much faster and modelling is straightforward. A major disadvantage of the BCF is that the block creation does not take place within a well-defined volume in space. The output information from BCF, block sizes and block shapes, does not include the relative position of these blocks in real space. It is therefore not possible to construct within the finite orebody boundaries a numerical rock mass model, comprised of blocks with the shapes and sizes, determined in BCF. Nevertheless, BCF can still be used to calibrate the PFC models that have the same input as fed into BCF. The most important of this data is the joint set geometry data: angle, spacing and persistence statistics. In PFC the facilities exist to determine fragmentation size distributions in an easy way. The calibration would be successful once there is a close match between the fragmentation distribution curves obtained from BCF and the ones determined in PFC. The primary fragmentation size distribution of a specific orebody is essential input data for two independent numerical models: undercut models (5.2) and communition models (5.3). 5.2 Undercut layout model In addition to the primary fragmentation size distribution, accurate stress values and appropriate material properties are the most important input data required setting up a numerical model investigating undercut layouts. PFC is the preferred code to perform these investigations as it can easily handle distribution curves as an input, but also, simulate excavation sequences and investigate the rock mass response in one and the same model. Initially, the study should concentrate on the cavability of the orebody so as to quantify the required hydraulic radius to induce caving. Thereafter, different undercut techniques and undercut sequences should be modelled to investigate the cave propagation potential for each of the undercut layouts considered. An example of a comparative study between two types of undercut techniques is discussed in section 6. An important aspect of undercutting operations is the existence of abutment stresses. The magnitude and orientation of these stresses are dependent on the virgin stresses and the undercut direction. The investigation of these stresses could be done more efficiently with the aid of other numerical codes as the abutment stresses mainly affect the stability of the rock below and ahead of the undercut, thus, outside the region of interest where gravity flow occurs. Continuum codes are better suited to model the stresses and their important effects on the stability of the major/minor apex, and tunnels at extraction or undercut level. 5.3 Communition model The fragment size distribution of the ore drawn from a drawpoint is a function of the age of a drawpoint. When a drawpoint comes in production, the ore flowing out of the drawpoint is coarse and is classified as the primary fragmentation stage. The virgin stress state and geological features such as joint sets mainly determine the primary fragmentation distribution. As the drawpoint ages, the material reporting to the drawpoint has travelled a substantial distance towards the drawpoint. During the draw down, the fragments are broken up by communition in the cave, resulting in a smaller fragment size distribution. This process is called the secondary fragmentation and is influenced by the stress state in the cave, material properties (strength), the path the primary fragments travelled and the production rate of the drawpoint.

Joint geometry and statistics

Rock mass ratings Stress levels

Groundwater characteristics …

Primary fragmentation distribution models (5.1)

Undercut simulations (5.2) Communition simulations (5.3)

Hangup simulations (5.4)

secondary fragmentation distributions drawbell geometry

Drawbell interaction simulations (5.5)

Hydraulic radius Optimal undercut sequence

Drawbell spacing Hangup statistics Secondary blasting requirements

Draw rates

With a primary fragmentation size distribution as an input (derivation described in 5.1), numerical models can be set up to investigate communition processes in the cave. PFC is extremely well suited to do this type of modelling: PFC is one of the very few codes that can model the interaction between realistic shaped blocks including the communition of these blocks as they move towards a drawpoint. High mechanical forces at the contact points between these blocks cause destruction of bonds between some balls making up the block, simulating thus fragmentation. The model should be kept as simple as possible by only investigation the ore flow to only one drawbell. The studies investigating the interaction of several drawbells is described in 5.5. The primary output of a PFC model is a series of fragmentation size distributions, as a function of drawpoint age or of remaining column height. The PFC models can give additional information such as the evolution of the draw ellipsoid boundaries, stress distribution within the cave, velocity profiles, etc. BFC can also be used to investigate communition in caving conditions. The BCF simulation does not model the physical block fragmentation as in PFC, but the communition process is controlled by empirical rules. These rules are based on practical experience and field data and require the height of the column that a block has to travel before it arrives at the drawpoint. The BCF output is again a fragmentation size distribution with a description of the block sizes and shapes. The BCF models should be used to calibrate PFC as the BCF model relies on real field data. Once PFC simulations produce adequate fragmentation size distributions as predicted by the BCF program, studies investigating drawbell geometry can start. These studies should concentrate on the influence of the drawbell geometrical parameters (width, height, and length) on the flow process, more specifically on the draw ellipsoid shape and the communition process in terms of fragmentation size distributions. 5.4 Hangup models In competent orebodies with coarse fragmentation large rocks often form hangups above the drawpoints, particularly at the initial stage of production. A poor draw layout that shows little or no interaction between drawbells also results in an increasing number of hangups. To avoid low draw rates hangups are removed by blasting or breaking the fragments forming the hangup. This secondary blasting or breakage is an expensive and labour intensive operation and can also damage the drawbell, the brow and drawpoint support. Therefore, for planning purposes it is useful to have a prediction of the percentage distribution of the hangups. This enables the designer to plan for extra drilling machines and secondary blasting requirements needed to remove the hangups. It would also be beneficial to know if the incidence of hangups is temporary, at the early stages of a drawpoint only, or if it is expected to occur all. Because the draw rate is affected by the number of hangups in a drawpoint, a mine plan should have the provision for more drawpoints when many hangups are predicted. Hangup studies in PFC are easy once the communition models (see 5.3) are calibrated. The communition models are appended with an extra algorithm that not only detects and removes the hangups but also classifies each hangup together with information of the blocks forming the hangup. The classification is based on the position of the hangup (high or low) and the type of hangup (cluster of blocks or single block). The algorithm is also appropriate for the multiple drawbell simulations (see5.5).

BCF can also be used to do hangup investigations with simulation times many orders of magnitudes smaller than those of the PFC models. But the advantage of the PFC simulations is that the models demonstrate the physical process of hangup development. The PFC models give more information than just hangup statistics. The models show the conditions under which hangups are formed, what the effects are on draw rate, stress state and other cave characteristics. Furthermore, it is possible to investigate the effect of the drawbell geometry on the hangup statistics. 5.5 Drawbell interaction models It should be emphasised that all the PFC models described up to this section involve only the action of one single drawbell. Once the behaviour of a single drawbell is fully understood, studies can be done to investigate the more complex interaction between the drawbells. At this stage, there is no other program than PFC available to the geotechnical engineers to carry these multiple drawbell ore flow studies. The model can be used to investigate the most important parameters in a cave layout, the height of interaction and the drawpoint spacing. These critical parameters are shown in figure 3. Figure 3. Important geometrical parameters. Good flow into the drawbell can only be achieved by correct drawbell geometry combined with effective interaction occurring between the drawpoints. Interaction between drawpoints can be achieved by adequate drawpoint spacing. The drawpoint spacing should be chosen so that the isolated draw zones from the drawpoint overlap. The isolated draw zones have conical shapes that, at a certain distance above the extraction level, can be approximated by a cylindrical volume. The drawpoints should be spaced on a pattern so that these cylinders at least are touching to ensure drawpoint interaction. This means that there is a direct relationship between the isolated draw zone diameter and the drawpoint spacing. The isolated draw zone diameter depends on the ore fragmentation characteristics. An increase in drawpoint spacing has several advantages: • Improvement of the strength of the extraction level. • Provision for larger and longer drawpoints. • Potential for larger size LHD. • Reduction of development requirements.

height of interaction

zone

isolated draw

drawpoint spacing

drawzone diameter interaction

However, possible disadvantages are: • Too little interaction between drawpoints. • Insufficient number of drawpoints. • Unacceptable dilution entry. The current design parameters are based on three dimensional sand model tests, ore fragmentation, marker experiments and empirical data from underground observations (Laubscher, 1999). PFC models should be used initially to confirm the accuracy of these empirical guidelines. After this “calibration” stage, sensitivity studies on the drawpoint spacing, draw profiles, etc. should provide sound design principles. More complex geological situations with zones of different fragmentation characteristics will be a challenge to model. These studies will provide a better insight of how the cave will propagate preferentially, the optimal draw control layout to manage different geological zones where the fragmentation differences play an important role. Draw control studies should also result in strategies to minimise dilution entries. The ultimate objective of PFC in block cave simulations: is to come up with accurate design graphs for every possible orebody mined by caving methods.

6 UNDERCUT SIMULATIONS Care must be taken that there is no stacking of large blocks on the major apex as this could prevent cave propagation. A rule of thumb introduced years ago was that the top of the undercut had to be 45° from the edge of the major apex above the brow. PFC can be used to investigate the performance of different undercut layouts and an optimal strategy can be derived from these studies. Undercutting is the initial and important operation before full production can start. A good undercut sequence is essential to the caving process, as the undercut has to destabilise the overlying orebody by creating a void underneath the ore column. Pillars are not allowed to form in the undercut horizon, as these pillars will transmit the high stresses down to the production level where the tunnels can be damaged under high stress environment. The void created by the undercut fills up by bulking of the material as ore fragments detach from the roof. Stacks of large blocks on the major apex should be avoided since it prevents cave propagation. A series of PFC models was set up to study a flat undercut in comparison with an inclined undercut. The simulations suggested that at the initial stages of the cave, when the extent of bulked material (failing zone) grows upwards, the inclined undercut layout is the preferred option. This confirms the rule of thumb, introduced years ago, that the top of the undercut had to be 45° from the edge of the major apex above the brow.

Figure 4. Model geometry used for undercut simulations. Figure 4 shows the model geometry with two 8m wide drawbells, spaced at a distance of 30 m in this instance. Further parametric studies, not discussed in this paper looked at varying the drawbell spacing. Figure 5 shows the flat two metres high undercut layout and the extraction sequence. Initially, a six metres wide undercut was excavated above the drawbells and in the centre on the pillar between the two drawbells. The model was then run for some calculation cycles before excavating the second cut which mined the rest of the undercut. The undercut was not modelled as an entire excavation of the rock within the zone of the undercut height. As shown in figure 5, the original intact material was replaced at the bottom 75 % of the undercut height by loosened material and the top 25 % was left as void. This was done to adjust the two dimensional model representing the three dimensional reality. The undercut height in the models described in this paper was set to 2 m but parametric studies looked at variable heights. Figure 5. Flat undercut sequence.

First cut

Second cut

75%

void

loose material

(2 m)

60 m

8 m

(60 m)

8 m

(30 m)

The second layout represented an undercut flat above the drawbells but inclined at the sides, towards the centre of the pillar between them. This is shown in figure 6. Figure 6. Inclined undercut sequence. The generic model consists of two joint sets with a specific joint spacing, angle and persistency for both joint sets. This is shown in figure 7 where both joints were modelled as through going (hundred percent persistency). The initial models have one horizontal and one vertical joint set considered. The fragments formed by these continuous joints were three metres by three metres rectangular blocks, modelled as indestructible. This was justified since the purpose of this exercise was only to determine to what vertical extent both undercuts could destabilise the rock. During this initial loosening process, there is almost no communition or breakage taken place in the rock. Figure 7. Two joint sets in rock mass in two dimensional model. After running both models for a same number of calculation cycles, a comparison between the two layouts was made. Figures 8 and 9 show the material after the undercut has taken place. It is clear from these plots that the inclined undercut has loosened more material than the flat undercut. This is confirmed by figure 10 showing for both models, the accumulated tons passed through the draw bells as a function of calculation cycles. The inclined undercut layout shows a substantial larger amount of tons. PFC simulations also revealed that the zone of mobilised material in the inclined undercut layout also extends further outwards in the lateral direction. This can be seen in figure 9 where the zone of immobile material, above the centre of the pillar, is smaller than in figure 8. A very important practical implication is that modelling indicates that for the same width of

the undercut the inclined layout mobilises a larger area of rock positioned above the minor or major apex of the drawbells. In the flat undercut layout, the material above the apex tends to form stacks of blocks filling up the void created by the undercut. This would prevent the cave to propagate upwards. In the inclined undercut layout the formation of a stable pile of fragments on the apex is prevented as the material can slide down the inclined walls.

Figure 8: resulting profile in flat undercut case. The vertical dotted lines mark the zone of immobile material and the curves above the drawbells outline the zone of loosening.

Figure 9. Resulting profile in inclined undercut case The vertical dotted lines mark the zone of immobile material and the curves above the drawbells outline the zone of loosening. Note the vertical displacement at the top right of the model.

draw down tons in time

0

50,000

100,000

150,000

200,000

250,000

300,000

350,000

400,000

450,000

500,000

0 1 2 3 4 5 6 7 8 9 10loop number after u-cut

tonsdrawn

Figure 10. Tons drawn as function of time for both layouts.

First cut

Second cut

S2

α2

S1

α1

JJOOIINNTTEEDD RROOCCKKMMAASSSS::

SS11,,SS22:: jjooiinntt ssppaacciinngg α1,, α1:: jjooiinntt aannggllee

inclined undercut

flat undercut

7 ORE FRAGMENT FLOW SIMULATIONS Large-scale models were constructed to investigate the flow of irregular shaped ore fragments in a “bin” geometry (figure 11).

Figure 11. A multiple drawpoint large scale PFC geometry. The objective was to keep the models generic enough to investigate a wide range of possible applications. Initially, only two-dimensional modelling was done only to keep the simulation time within acceptable limits during the stage when the datafiles were written. The datafiles contain the command lines to build the whole PFC model and is rather a difficult task. It is not a straightforward process to immediately achieve a correct set up. The datafiles are very similar for the two dimensional models and the three dimensional models. Since the two dimensional models require much less computer time than the three dimensional models, debugging and checking the validity of the datafiles was done with PFC2D. This does not mean that further studies would use the conclusions from the two dimensional models for establishing design graphs. Modification of the input files for three dimensional modelling is very simple and should be run once computers become powerful enough to handle large three dimensional models in an acceptable time period. However, the two dimensional did show some interesting phenomenons expected to be confirmed and quantified in the three dimensional models. The following points were investigated in detail. • The first input of the model was the construction of the bin

geometry with five drawpoints, a straightforward process. • The creation of non-spherical fragments in a simple way

was a second, more complicated, step. • After fragment generation, the integration of a draw control

practice was written to cater for all possible combinations of opening and closing off the drawpoints.

• Hangups at the drawpoints can be identified and removed. • Size distribution data is monitored during the whole draw

process. The use of a programming language, embedded in PFC, is essential to create generic models. The model geometry was constructed by walls spaced at variable distances and angles.

A front-end program is used to create Voronoi polygons filling up the bin. The PFC model consists of balls, all bonded together and packed in a regular pattern as shown in figure 12. The polygon outlines are used in PFC to delete bonds or balls at both sides of a polygon boundary line. This process of deleting balls or bonds is repeated for all polygons, resulting in the formation of Voronoi shaped particles. The front-end program requires several parameters such as the bin geometry plus Voronoi shape and size variables, making it a very generic application tool.

Figure 12. Creation of Voronoi fragments in bin flow models. After creating the Voronoi polygons, the model is brought to equilibrium. Figure 13 shows the model after opening all drawpoints and running the model for a few time steps. Each polygon is thus a set of balls, bonded together. The bond strengths were considered to be weak enough to allow breakage when the mechanical forces acting upon the balls are high enough to initiate failure. The ability of PFC to cater for this communition process is of utmost importance to the realistic simulation of ore flowing towards the drawpoints. Fragments in the model did brake up, especially at the two bottom corners of the bin where. At these locations high stresses are present and the material cannot move to the drawpoints. The high stress state and the material immobilisation induce failure.

Figure 13. Bin filled with non-spherical fragments.

Figure 14 shows the same model after which approximately fifty percent of the ore were pulled through all the open drawpoints. The crushing of material in the model corners and close to the drawpoint boundaries can also be observed.

Figure 14. Fragments left in bin after 50 % of material drawn out. The dotted lines delineate the “crushed” zones. The integration of a generic draw control layout was useful to investigate and compare different draw practices. A few models were run, each with a different opening and closing sequence of the drawpoints. The first model ran a layout in which all drawpoints were continuously open. The second model was set up so that from the left to the right drawpoint, the opening times were 0%, 25%, 50%, 75%, 100%. A third model only had the middle drawpoint pulling ore while the other drawpoints remained closed. A useful tool to compare the different layouts was the use of “markers” in the model for which the trajectories were monitored during the whole draw down process. Tracking the position of markers within the cave gives an insight to the cave behaviour whilst being drawn. Figures 15, 16 and 17 show the trajectories of the markers during the extraction process for the three models. The plots show that the ore fragments can travel a substantial distance in the horizontal direction if a differential draw profile is applied.

Figure 15. All drawpoints open all the time.

Figure 16. Drawpoints to the right longer opening time (gradually from 0 % at left to 100 % at right)

Figure 17. Only middle drawpoint open. In these simulations, block hangups at drawpoints can be detected and eliminated in an easy way. A hangup is detected when no more ore has flown through that drawpoint over a given period. The fragments forming the hangup are then automatically “blasted” out, allowing the drawpoint to continue working. A typical occurrence of a hangup in the models is shown in figure 18. The bars in the figure represent contact forces between the fragments. The width of the bar is equivalent to the magnitude of the force. In this instance, a high hangup in the drawpoint is formed by arching of several smaller ore fragments.

Figure 18. A typical hangup occurring at a drawpoint. After the study of the three different models, concepts were developed to keep track of the fragment size distributions of the material flowing out of each drawpoint. This could be very useful to investigate the secondary fragmentation process as the size of the fragments reporting at the drawpoints indicate how much communition has taken place during the stay in the cave.

8 CONCLUSIONS The application of PFC modelling shows great potential in assisting to understand gravity flow of non-granular material. This knowledge can be translated in principles to be used when designing a cave mining operation, in conjunction with the presently available empirical guidelines.

9 ACKNOWLEDGEMENTS The permission of the Director, Operations and the Consulting Geotechnical Engineer, De Beers Consolidated Mines Limited, to present this paper is gratefully acknowledged.

10 REFERENCES Kvapil, R. 1965. Gravity flow of granular materials in hoppers

and bins, Int. J. Rock Mech. Min. Sci. Vol. 2, pp. 35-41. Marano, G. 1980. The interaction between adjoining draw points

in free flowing materials and its application to mining. Chamber of Mines Journal.

Janelid, I & Kvapil, R 1966. Sublevel Caving. Int. J Rock Mech. Min. Sci, Vol. 3, pp 129-153.

Laubscher, D.H. 1994. Cave mining, the state of the art. Journal of the South African Institute of Mining and Metallurgy.

Cundall, P. & Strack, O. 1979. A discrete numerical model for granular assemblies. Geotechnique, Vol. 29, pp. 47-65.

Starfield, A & Cundall, P 1988.Towards a methodology for rock mechanics modelling. Int. J. Rock Mech. Min. Sci., Vol. 25, pp 99-106.

ITASCA Consulting Group, 1995. PFC2D User’s Manual, Version 1.1.

Lorig, L. et al. 1995. Gravity flow simulations with the particle flow code (PFC). Int. J. Rock Mech. Min. Sci., Vol. 3, pp 18-24.

McNearny, R. 1991. Large Scale Two Dimensional Block Caving Model Test. Thesis for the Degree of PhD, Colorado School of Mines Golden U.S.A.

Yeng, L. 1980. Analysis of bulk flow of materials under gravity caving process. Part 1.Sublevel caving in relation to flow in bins and bunkers. Colo. School of Mines 75 (4), 1-45

McNearny, R. & Barker, K. 1998. Numerical modeling of large-scale block cave physical models using PFC2D. Mining Engineering, Vol. 50, No 2.

Esterhuizen, G. 1994. A program to predict block cave fragmentation-Technical reference and user’s guide, report to Rio Tinto South Africa

Laubscher, D. 1999. CaveBase Manual (Unpublished).