The Stability Graph Method for Qpen-Stope Design (1)

C H A P T E R 59

The Stability Graph Method for Qpen-Stope Design Yves Potvirt* and John Hadjigeorgioist

60*1

INTRODUCTION!

from time to time, been the source of confusion amongst people not familiar with open-stope mining. There are multiple and interrelated factors that potentially contribute to the instability of excavations. For convenience, they can be divided into two groups: the ones related to the in-situ conditions prevailing before mining, and the factors related to the disturbance of these conditions induced by mining. The premining conditions can be characterised by rock-mass classification schemes and supplemented with structural geology data and an estimation of the in-situ stress field. The major factors related to mining are the size, shape, and orientation of excavations as well as the ground support used (including backfill). Blast damage and the effect of time in highly convergent rock may also affect the stability of excavations.

In the late 1970s to early 1980s, the underground metal-mining industry shifted its extraction strategy from highly selective "entry" methods, such as cut-and-fill, to "non-entry" methods such as open stoping. A review of Canadian practice has shown that 90% of the total production of underground metal mines, based on reported tonnage, rely on open-stope mining methods (Poulin et al. 1995). The popularity of open-stope operations can be attributed to the higher productions levels achieved by employing larger excavations and using mechanised equipment. Considering the high cost of developing each stope, there is a significant incentive to produce a smaller number of large open stopes. The consequences, however, of exceeding the maximum critical stable dimensions of a stope can be disastrous. Instability around open stopes may require large remedial costs for ground rehabilitation, production delays, mining equipment loss, ore reserves loss, and, at the extreme, injuries or fatalities to mine workers. Pakalnis (1986) reports that in a survey of 15 Canadian mines, almost half (47%) of the open-stope mines had more than 20% dilution with one fifth suffering excessive dilution of over 35%. Based on field data from 34 Canadian mines, Potvin (1988) demonstrated that open-stope design was based on past experience of mine operators in similar mining conditions and on trial and error. Consequently, it can be argued that the reported high dilution rates in the early 1980s could be attributed to the absence of comprehensive engineering design tools. It follows that there are significant economic gains to be made by improving open-stope stability.

S0a3 D E S C R I P T I O N O F T H E STABS L I T Y m A P U ¡1ETO0O The stability-graph method is an empirical method for open-stope design (non-entry excavations). It aims to account for and quantify the major factors influencing the stability of open stopes. A stability index for each stope surface is subsequently traced against its dimensions. A series of empirically derived guidelines allow for predictions on the overall stability of a stope. Since its introduction (Mathews et al. 1981), it has gained wide acceptance and is used worldwide as a design tool. There are documented case studies of the method being used in Africa, Europe, and the United States, and extensive databases of case studies in Canada and Australia. In practice, the stability graph can be employed during three distinct mining stages. Its primary use is during the feasibility stage but it has also been found useful during individual stope planning. Finally, through the use of back analysis, it provides an index of stope performance and allows the mine operation to develop remedial strategies where warranted. The method traces its origin to the recognition that traditional rock-mass classification and design tools were based on tunnelling case studies. A review of some case studies and engineering judgement resulted in the first version of the method, whereby a stability number (N) was traced against the hydraulic radius of a stope surface. The stability-graph method uses the NGI tunnelling index Q (Barton, Lien, and Lunde 1974) as a basis for estimating rockmass quality.

@Qd2 EXCAVATION STABILITY Evaluating the stability of a non-entry excavation such as a stope can be subjective. Unlike entry excavations in which mine workers have access, isolated rock falls in stopes are generally of no consequence, providing that they can be handled by mucking units. Therefore, a stope can be considered to be stable if it yields low dilution (less than 5%) and if there are no ground-fallrelated operational problems. It has been argued (Pakalnis, Poulin, and Hadjigeorgiou 1995) that there is a unique acceptable dilution rate for every mine operation. This is defined as a function of ore grade, costs, grade of dilution material, and metal prices. Consequently, provided the operation remains safe and economical, it is possible to tolerate a level of dilution and a degree of instability for every stope. Open stopes that display excessive dilution and/or unmanageable stability problems are often referred to as caved. In this context, the term "caved" indicates major stability problems and should not be confused with the cave mining interpretation where it refers to orebody failure (cavings) after undercutting. This overlap of terminology has,

where: Q = NGI tunnelling index with RQD = rock quality designation

* Australian Center for Geomechanics, Nedlands, WA, Australia, t Laval University, Quebec City, Quebec, Canada.

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FIG URE SO 1

Stability graph, after Mathews et al. (1981)

15

Hydraulic radius (m)

Hydraulic radios (m) FIGURE 60.2

J'r = joint roughness number

Stability graph after Potvin (1998)

1.0

Jw = joint water reduction number Jn = joint set number Ja = joint alteration number SRF = stress reduction factor Using SRF equal to 1 is a departure from the original system (Barton, Lien, and Lunde 1974). This modified tunnelling index, Q, is further adjusted to account for stress, rock defect orientation, and design-surface orientation factors to arrive at a stability number N. The stability number was plotted against the hydraulic radius (surface area/perimeter) of the studied surface of an excavation (Mathews et al. 1981). Three zones of potentially stable, unstable, and caving were proposed with reference to the predicted stability of an excavation (see Figure 60.1). In its early days, a major shortcoming of the method was that it was backed by limited field data—26 case studies from three mines. Once the database was expanded to 175 cases from 34 mines and the stability graph modified (Potvin 1988), the method rapidly gained wide acceptance in the Canadian mining industry. The transition zone from stable to unstable was reduced significantly, thus removing some of the subjectivity in using the design chart (see Figure 60.2). It should be noted that in the Potvin database, the adjustment factors were different than those proposed by Mathews et al. (1981). This resulted in what is commonly referred to as the modified stability-graph method using a stability index AT. N' =

Q'xAxBxC

where: AT = stability number Q' = modified tunnelling quality index (NGI) A = stress factor B = joint orientation factor C = gravity factor A-Factor. The A-factor is used to account for the resulting induced stress in the investigated stope surface. A series of charts that provided preliminary estimates of induced stresses for

i i 42 iW

0.8 0.6 0.4 0.2 0.1 0

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Relative difference in dip between the critical Joint and slope surface FIGURE 60A (1988)

i

Determination of the Orientation Factor, after Potvin

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Inclination of critical joint FIGURE 60 6 Influence of gravity for sliding mode of failure, after Hadjigeorgiou Leclair and Potvin (1995)

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inclination of : FIGURE 60.5 of failure

©0=4

Influence of gravity for slabbing and gravity fall modes

DISCUSSION OF THE INPUT FACTORS

As a result of wide dissemination in a number of textbooks (Hoek, Kaiser, and Bawden 1995, Hutchinson and Diederichs 1996) the input factors for the calculation of N' described above have now gained broad acceptance from practitioners and researchers. The applicability of the input methodology on a case-by-case analysis was reviewed and, with the exception of the minor modifications to the C factor shown in Figure 60.6, were found to be appropriate (Hadjigeorgiou, Leclair, and Potvin 1995). On the other hand, some authors (Stewart and Forsyth 1995; Trueman et al. 2000) have indicated their preference for the formulation of the input factors as originally proposed (Mathews et al. 1981).

Several other modifications to the stability graph have been proposed during the last decade. The following offers a brief historical review. It should be noted that most of these proposals have not yet been extensively tested by case studies nor are they widely employed by practitioners. Scoble and Moss (1994) suggested that there was merit in adding two further adjustment factors, D for blasting and E for sublevel interval rating with some tentative factors proposed. A fault factor was been developed that can be incorporated into the stability factor (Suorineni, Tannant, and Kaiser 1999). This fault factor accounts for the angles between fault and stope surface and the position where the fault intersects the stope surface. The fault factor was derived based on modelling and demonstrated that it could be critical for a series of documented case studies in Canada and Africa. At the Golden Giant Mine in Ontario, Canada, it was shown that under high-stress environments the introduction of a stress-damage factor merited attention (Sprott et al. 1999). Based on 3-D numerical modelling, they used the "extra stress deviator," the uniaxial resistance of the rock, and the hydraulic radius to define a stress-damage factor. It has been argued that the stability predictions of the stability-graph method may prove inaccurate due to the influence of rock-mass degradation and relaxation (Kaiser et al. 1997). It was recommended that stope sequencing be used as a tool to minimise stress-induced rock-mass degradation and to minimise stress relaxation. In their work, they defined rock-mass relaxation as stress reduction parallel to the excavation wall—not to stress reductions in the radial or a reduction in confinement. Rock-mass degradation was quantified as loss of rock-mass strength. S0oS

HYDRAULIC RADIUS

The term "hydraulic radius" has been used in the past to characterise the size and shape of stope surfaces (Laubscher 1977). This is the area over the perimeter of a given stope surface. It has also been demonstrated that, despite the advantages of hydraulic radius over span, it still has important limitations (Milne, Pakalnis, and Felderer 1996). In particular, when applied to irregularly shaped stope surfaces, it is possible to arrive at the

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FIGURE 60.7 (1996)

Determination of the radius factor, after Milne et at.

same hydraulic radius. It has been put forward that a better way to describe the geometry of an irregularly shaped excavation is the radius factor (see Figure 60.7). This is determined by identifying the centre of any excavation and by taking distance measurements to abutments at small regular increments: RF =

FIGURE 60.8

Stability graph, after Nickson (1992)

°-5 I y n = i i n^Q r0

where re = distance from the surface centre to the abutments at angle q n = number of rays measured to the surface edge In principle, the radius factor can be determined at any point on a surface. If the centre cannot be determined, a series of calculations are possible with the maximum value assumed to be the radius factor. Despite its somewhat cumbersome definition, the radius factor can easily be calculated by a routine integrated into a computerised design package. 8©oS

BEBim

charts

In reviewing the proposed chart, Figure 60.1 (Mathews et al. 1981), it can be seen that the developed guidelines were somewhat vague for design purposes. This was because there was insufficient data to provide more accurate zone definition. As more case studies became available, a narrower transition zone and a "support requirement zone" were defined (Potvin 1988). This has allowed for a calibrated and more versatile design tool (Figure 60.2). A more comprehensive statistical analysis further modified the support zones by introducing lines indicating where cable bolting could be used (see Figure 60.8) (Nickson 1992). A review of a larger database (Hadjigeorgiou, Leclair and Potvin 1995) confirmed the general validity of previous work (Potvin 1988, Nickson 1992) within statistical limits. It should be noted that the work of Hadjigeorgiou et al. (1995) demonstrated that, for larger stopes with a hydraulic radius greater than 15, the design curve was in fact flatter (see Figure 60.9). More recent work in the United Kingdom by Pascoe et al. (1998) and in Australia by Trueman et al. (2000) has confirmed the same trends. A series of design guidelines were proposed (Stewart and Forsyth 1995) that allowed for a finer definition of the types of

FIGURE 60.9 Stability graph design lines as developed by Hadjigeorgious et al. (1995)

stope failure, distinguishing between potentially unstable, potentially major, and caving failure separated by transition zones (see Figure 60.10). In their experience, the boundary between stable and unstable is clear cut, while the transition between unstable and major failure is not as well defined. It is of interest that the transition between a "potentially stable zone" and a "potentially unstable zone" is identical to Potvin's transition zone. In practice, it could be argued that, for open-stope design purposes, it is somewhat irrelevant to subdivide the area defining stope failure into three zones as the objective is to design stable stopes. Cavity monitoring laser surveys have been employed to backanalyse the resulting volumetric measurements of overbreak/

The Stability Graph Method for ©pesi-Stope Design

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FIGURE 60=10

Stability graph after Stew rt & Forsyth (1993)

s?

s* j.

y

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I .

Cross-Sections Gì Generated from IMS Survey

l/\ \ Equivalent Linear Overbreak/Slough (Expressed in Meters

E l Slough from Stope Wails

I Equivalent linear overbreak/Slough

FIGURE 60.11 Schematic definition of the ELOS parameter, after Clark and Pakalnis 1997

slough and underbreak, and a new index has been proposed (Clark and Pakalnis 1997) (see Figure 60.11): ELOS

equivalent linear overbreak slough volume of slough from stope surface stope height x wall strike length

In Figure 60.12, ELOS has been integrated in the stability graph, providing a series of design zones (Clark and Pakalnis 1997). Although this data presentation does not account for the influence of support, it provides a useful back-analysis tool for hanging walls and footwalls in a low- or relaxed-stress state and with parallel geological structure being present. All of the above graphs rely on arbitrarily drawn design curves. The first comprehensive statistical analysis of the thenavailable field data (Nickson 1992) clearly demonstrated the applicability of the modified stability graph (Potvin 1988) and laid the foundations for further statistical work (Hadjigeorgiou,

15

Hydraulic radius (m)

(m)

Stope „ Width

Length

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Hyaraulic r diu

FIGURE 60.12 Estimation of overbreak/slough for nonsupported hangingwalls and footwalls, after Clark and Pakalnis 1997

Leclair, and Potvin 1995, Pascoe et al. 1998, and Suorineni 1998). Successful applications of the stability graph recognise that the method remains subjective. Despite using quantifiable values, the precise degree of inherent conservatism is not known. It reflects "current and past practice," which may have been influenced by legislation, local practices, or geological peculiarities, and does not necessarily constitute an optimum design methodology. 80.7

¡RISK A N A L Y S I S

It has been argued that the design of non-entry excavations lends itself to risk analysis much more than the design of access ways where worker safety is the major concern (Pine et al. 1996, Pascoe et al. 1998, Diederichs and Kaiser 1996). There are two basic elements in risk analysis. The first one deals with input variability and the second deals with calibration uncertainty. For practical purposes, the major challenge lies in defining how much risk is acceptable for design purposes. Using risk probability procedures for fine-tuning or calibrating site-specific design guidelines, while attractive, is hindered in that site-specific calibrated guidelines will be validated only towards the end of mine life. At that time, their impact will be limited to providing a better understanding of particular field conditions, but it may be too late to implement major design changes. 60.8

S U P P O R T RECOIVIIVSENDATSONS

Potvin (1988) first addressed the influence of support on the stability of open stopes. The area of the graph that could successfully be supported by cable bolts was refined, and a series of design recommendations made on cable-bolting patterns (Nickson 1992). The basic concept is that there is a zone where support cannot be effectively used to stabilise the excavation. It has been shown (Hadjigeorgiou, Leclair, and Potvin 1995) that the actual supportable zone was smaller than predicted (Nickson 1992). A design chart is available to select a suitable cable-bolt density as a function of relative block size (RQD/Jn) and the hydraulic radius (Potvin and Milne 1992). This graph, slightly modified in Figure 60.13, is most appropriate for stope backs. It has also been employed for hanging-wall reinforcement design, provided a systematic and regular cable-bolt pattern is used.

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(RQD/Jn) Hydraulic radius FIGURE 60.13

Determination of cable bolt density

At the time when the design curves for cable reinforcement were developed, support often consisted of single plain-strand cables. Recent years have seen a shift towards double-strand and modified-geometry cables as they provide higher support capacity. This is achieved in the presence of sufficiently high ground deformation whereby the strength of the steel is being mobilized. In other words, pattern reinforcement is designed to help the rock support itself and not necessarily to support the dead weight of the rock. A series of semi-empirical design charts to determine the design spacing for both single- and doublestrand cable bolts has been proposed (Diederichs, Hutchinson, and Kaiser 1999). It should be noted, however, that there are no documented case studies confirming their application. SQ3 L I M I T A T I O N S ©F TiHE S T A B I L I T Y QiRAPU All empirical methods are limited in their application to cases that are similar to the one used in the developmental database. Therefore, the stability graph is inappropriate in severe rockbursting conditions, in highly deformable (creeping) rock mass, and for entry methods. Since its introduction, the stability graph method has been the subject of extensive efforts to expand its applicability to better account for the presence of faults, blast damage, and stress damage. Unfortunately, some of the proposed modifications are not supported by field data. Furthermore, when merging databases from diverse sources, it is necessary to verify the quality of collected data. In particular, the practice of using empirical correlations to convert from one rock-mass classification system to another should only be used as a last resort and even then with great caution. For all practical purposes, the stability graph can be used during the feasibility stage, during individual stope planning, and for stope reconciliation or back analyses. e®D10 DESDGN C O N S I D E R A T I O N S T H E FEASIBILITY STA©E The determination of adequate stope dimension is one of the most critical decisions to be made at the feasibility study stage of a mine. The profitability of an operation is directly linked to productivity, which in turn, is influenced by stope dimensions. Validation of stope-design methodology can begin once the first stope is extracted. By this time, however, the mine infrastructure is already in place, allowing for no or only minor modifications to

design stope dimensions. This emphasizes the importance of developing a reliable stope-design methodology at the earliest possible stage. Many practitioners have reported on the reliability of the stability-graph method during the last 12 years (Reschke and Romanowski 1993, Bawden 1993, Pascoe et al. 1998, Dunne et al. 1996, and Goel and Wezenberg 1999). When properly used, the method provides a good "ball park" estimate of stable stope dimensions under different conditions. The major limitation at the feasibility study stage is the availability of quality geotechnical data. This is a concern for all design methods. Consequently, it is essential to optimise all available data while being fully aware of any limitations. The following guidelines can facilitate the estimation of realistic stability numbers during the feasibility stage. An integral part of the stability method is the quantification of rock-mass quality based on the Q system. At the "green field" stage, the majority of geomechanical data are derived from boreholes. Consequently, it is possible to develop a comprehensive database of RQD readings, which can easily be integrated into geological models easily accessed by both planning and rock mechanics. It is strongly suggested that the number of joint sets be determined by using oriented diamond-drill cores in the orebody. There are several case studies where core data were used to derive representative Q readings for underground mines (Milne, Germain and Potvin 1992, Germain, Hadjigeorgiou, and Lessard 1996). This has included a simplified approach to determine joint alteration, Ja. If the joint cannot be scratched with a knife, Ja is assumed to be equal to 0.75, and if it is possible to scratch, it varies from 1.0 to 1.5. When a joint feels slippery to touch and can scratched with a fingernail, Ja is equal to 2; and when it is possible to indent with a fingernail, Ja is equal to 4. The joint roughness parameter (J r ) is more difficult to assess on a small exposed surface of a core. However, in most cases, it is possible to estimate whether the surface is smooth or rough. In the absence of reliable data, joints are assumed to be planar. This allows for Jr values of 0.5 for slickenslide planar, 1.0 for smooth planar, and 1.5 for rough planar joints. Factor A can generally be assumed to be equal to 1 for all stope walls, unless mining is to proceed very deep (say 1,000 m and deeper). As a first-pass estimation, the stress induced in stope backs could be assumed to be around 1.5 times the premining horizontal stress for transversal mining (mining across the strike of the orebody). In longitudinal mining (mining along strike), a rough estimate of the induced stress in the back can be obtained by doubling the premining horizontal stress perpendicular to the orebody strike. The premining stress can be measured if underground access is available or otherwise based on regional data. The uniaxial compressive strength of rock is easily obtained by standard laboratory tests on cored rock. A larger database of UCS values can also be gathered at low cost using a standard point load test. When at least some oriented core is available, Factor B can be estimated. In the absence of joint orientation data, a minimum value of 0.2 is assumed. The estimation of factor C is independent of ground conditions and is, therefore, straightforward to determine, even at the feasibility stage. A good methodology for the construction of a geomechanical model and the application of the stability graph method for mine feasibility assessment exists (Nickson et al. 1995). Stability numbers are calculated for back and walls and displayed on mine sections. For each stability number (N), a hydraulic radius (S) is determined from the stability graph in Figure 60.14, using the upper section of the transition zone. The option of increasing stope dimensions exists if a systematic pattern of cable-bolt support is to be used. This can be assessed using Figure 60.8. Unless the ground conditions are consistent throughout the orebody, a number of stable hydraulic radii will be produced, which can be grouped into domains and displayed on a longitudinal section. Because most mines employ systematic layouts, a

The Stability Graph Method for ©pesi-Stope Design

@©„1± D E S I G N C O N S I D E R A T I O N S F O R INDIVIDUAL STOPE PLANNING

z o Q

3CQQ EL HW Q : = 10 A=1 B = 0.3 C = 3.5 N'= 10.5 3=6

S li

El a

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ROD >= 0% > = 20% > = 40% > = 60% > = 75%

It is good engineering practice to employ the stability graph at the planning stage to evaluate the stability of each stope. At this stage of development, there is usually underground access that allows for a revaluation of the rock-mass data collected during the feasibility study. Direct underground mapping can provide more reliable information than diamond-drill hole data. Another advantage of underground observations is that it can reveal early signs of stress. This can be complemented by stress measurements allowing for a better assessment of stress influence on the stopes. At this point, it is possible to integrate numerical modelling to investigate optimum sequencing. Access to more quality data can allow for greater confidence in stope stability estimates than allowed during the feasibility study. Consequently, it is possible to consider modifications or fine-tuning to the ground support and extraction strategies. At this stage, it is also important to assess the influence on stope stability of some of the factors not well accounted-for in the stability-graph method. These can include faulting, shear zones, or areas susceptible to rock bursts. One of the great benefits of using such a method at the planning stage is that it brings geomechanical considerations into stope design and increases the awareness of mine planners to ground-control issues. Modern stope designs require the close cooperation of geology, mine planning, and rock mechanics.

60 12

FIGURE 60.14 A case study during the feasibility stage, after Nickson et ai. 1995 unique stope dimension is usually determined for each mine domain. Engineering judgement must be used in selecting the appropriate hydraulic radius. Selecting the smallest hydraulic radius would ensure that all stopes would be stable, but would not likely be the most economical option. Notwithstanding the value of ore, the impact of dilution, acceptable risks, and the operating philosophy, a good starting point for selecting a mean hydraulic radius for an entire domain would be to ensure that approximately 80% of the stopes are stable. The remaining 20% or so can then be dealt with individually using specific ground support or different extraction strategies. The stope height, length, and width within each domain can be determined from the mean hydraulic radii (roof and walls). The orebody geometry obviously has an important influence on the determination of the stope geometry. In many cases, there will be an economic advantage to maximising the stope height as it has a major influence on the sublevel interval, and therefore, on the mine infrastructure cost. As more and more operations integrate backfill in the extraction process, its impact on stope stability must be accounted for. The main function of mine backfill is to limit the exposure of stope surfaces during extraction by filling adjacent mined-out stopes. Provided a good quality-control program is followed, it can reasonably be assumed that backfill provides adequate support of adjacent mined out stopes. Consequently, the stability-graph method treats backfill as a rock material when calculating stope-wall dimensions. In practice, however, it is rare that a tight fill can be established against a stope back. As a result, in stope-back analysis, the influence of backfill is assumed to be minimal and ignored.

STOPE RECONCILIATION

Using the stability graph to assess and document stope performance is useful to build site-specific empirical knowledge that can be used in future design. Once a sufficient number of case histories have been collected, it may even be possible to refine the stability graph for a given site or extend its predictive capability to dilution (Pakalnis, Poulin, and Hadjigeorgiou 1995) or to quantify the probability of failure (Diederichs and Kaiser 1996). A major aid in stope reconciliation has been the introduction of cavity-monitoring systems. These refinements are interesting and contribute to a better understanding of stope behaviour. However, the value added to operations from this effort remains limited in many cases because the initial stages of mining are completed, the mine infrastructure is in place, and opportunities for modifying stopes layout are restricted.

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DISCUSSION AND CONCLUSION

By definition, empirical design is based on observation and experience. The stability-graph method owes its popularity in its ease of use, its application at early stages of mining, and the fact that it can provide a reference for stope performance. Invariably, it cannot provide a successful prediction for every stope at every operation because the complexity of ground conditions and operating practices can influence stope performance. It has been argued in the past that the method only reaches its full potential when it is "site-calibrated." The basic assumption is that, as more data become available, the design recommendations can be modified through back analysis. Obviously, this is an important step in better understanding the site conditions. If the reconciliation exercise is done rigorously, it can reveal important information on the efficiency of mine practices such as blasting, prereinforcement, and sequencing. However, this should not detract from the main objective of the method as a design tool at the feasibility stage when no such data is available, but when the critical decision must be made. The extensive calibration of the method worldwide makes it very robust and ideal for designing open-stope dimension at the

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feasibility-assessment stage. The added value of a very refined site-specific graph towards the end of a mine life can only be limited. Over the years, there has been a proliferation of design charts aiming to refine the method or expand on its applicability. Design charts that are not backed by field data have limited use. Similarly, modifications that rely on limited sites should be viewed with caution. Complex charts bring new and interesting ideas, but one should keep in mind that the method can be no better than the quality of input data available. This is particularly true at the feasibility stage where data are limited by access. Introducing many zones to the graph has limited application at the design stage because the designer has to come up with a hydraulic radius number for each domain. The transition between stable and unstable and the potential for increasing dimensions by using pattern cable bolts remain the basis for stope design S O „14

REFERENCES

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