By: S. Shnorhokian, Mining and Materials Engineering, McGill University, Montreal, Quebec, Canada.Abstract Stope sequencing is a key design and planning tool used in underground mines. With the future forecast to take place at deeper levels, sequencing is destined to play a more significant role. Laboratory tests and data from core logs are combined to classify rock masses and assess their susceptibility to instability due to mining-induced stresses. The use of numerical tools is currently an integral part of operational planning, and an advantage of a 3D model is the ability to calculate volumes susceptible to instability for each stope se- quence quantitatively. In this paper, a simplified model of a tabular, steeply dipping orebody typically found in the Canadian Shield is constructed in FLAC3D. Stope sequences including a diminishing, 1-4-7, and 1-5-9 pillars are simulated. The brittle shear ratio is the instability criterion used in combination with volumetric analysis to assess the merits of each sequence quantitatively.IntroductionLiterature ReviewSublevel open stoping with delayed backfill placement is one of the most common underground extraction methods and is used extensively in Canadian mines (Potvin & Hudyma, 1989, 2000, Villaescusa, 2003). In general, a steeply dipping tabular orebody is exploited where the boundaries with the host rock mass formations are clear and where all the geologic units have moderate strength properties (Pakalnis & Hughes, 2011). In several of its variations, the mining method results in the formation of different types of temporary pillars that are eventually extracted. Horizontal pillars within the orebody separate between mining blocks while vertical ones serve to separate between primary, secondary, or tertiary stopes. Depending on the mining sequence implemented, the locations of these pillars and time of their extraction vary, thus affecting the concentration and magnitude of induced stresses (Pakalnis & Hughes, 2011). A vital ground control tool available to the mining engineer is to modify the stope sequence and implement the one that provides the least degree of instability (Potvin & Hudyma 2000, Castro et al., 2012).Numerical modelling is currently a standard practice in the mining industry, and it can be effectively used to predict the level of instability for multiple stope sequence alternatives in a relatively short period of time. A calibrated model can be combined with engineering criteria used for underground de sign – compressive, tensile, or shear strength, structurally-controlled instability, or rock bursting poten- tial – to examine the potential for their occurrences in each extraction sequence (Board et al., 2001; Wiles 2006; Castro et al., 2012). The use of 3D codes is essential for this type of analysis as the stopes being extracted are not necessarily coplanar with others. Another advantage of using 3D models is the ability to quantify the volume of rock mass that has been excavated or that has been designated to be "at risk" based on a particular instability criterion.Since competent rock mass properties are required for sublevel open stoping, and the method comprises the presence of pillars, rock bursting and mining- induced seismicity are common ground control challenges faced. The bilinear failure envelope reported by several authors (Martin et al., 1999; Diederichs 1999, Kaiser et al., 2000; Kim & Kaiser 2008) indi- cate a zone of microseismicity at values of deviatoric stress (σ1 – σ3) that plot above the damage threshold envelope. Castro et al., (2012) assign similar values and designate a ratio of 0.7 as the threshold for major strain bursting and rock mass damage. This is designated as the "brittle shear ratio" (BSR) and can be used in the industry as a design criterion for stope sequence alternatives (Shnorhokian et al., 2015, Heidarzadeh et al., 2019), as well as stope ge- ometrical parameters such as dimensions and dip (Heidarzadeh et al., 2018).It was already mentioned that stope sequencing is one of the key ground control tools available to the mining engineer. Combined with modelling, multiple extraction alternatives can be examined before a final approach is adopted. Villaescusa (2003) conducted an extensive global review of sequences used specifically in sublevel open stoping. Pelley (1994), Potvin & Hudyma (1989, 2000), Manchuk (2007), Bewick (2013), and Morissette et al. (2017) provided comprehensive reviews of typical sequences used at various Canadian mines. Bouzeran et al. (2019) used FLAC3D to optimize the mining sequence at Eleonore mine, while Heidarzadeh et al. (2019) examined stope stability and the impact of sequencing at the Niobec mine using numerical methods. In Africa, Kabwe (2017) analyzed the extraction sequence in the Upper Orebody at the Nchanga mine in Zambia using Examine2D and RS3. Handley et al. (2000) and Jooste & Malan (2015) studied the use of dip stabilizing pillars in deep reef mining in South Africa with modelling work, observing that a new multi-raise sequence is superior to the traditional se- quential grid mining approach in terms of production rates but similar when microseismic effects are con- sidered. In Australia, the implementation of a 1-5-9 sequence at the George Fisher mine is reported by Neindorf & Karunatillake (2000), and a 1-3-5 one at Kanowna Bell Gold Mine was presented by Cepuri- tis & Villaescusa (2006) and Cepuritis et al. (2007). Grant & de Kruijff (2000) reported the use of a chequerboard pattern in the 1100 orebody at Mount Isa Mines to relieve. Beck & Sandy (2003) provided an overview of sequencing techniques used in Western Australian to manage challenging stressrelated instability. Mgumbwa et al. (2017) studied the use of a diminishing pillar sequence in the Mist orebody. In Scandinavia, Sjöberg et al. (2012) used 3DEC to ex- amine stope sequences that would minimize fault slip in Block 19 of the Kiirunavara mine.Scope and ObjectivesIn this study, a simplified model of a steeply dipping, tabular deposit within the Canadian Shield is constructed in FLAC3D. Rock mass properties and in-situ stress tensors typically found in this geologic province are used as input parameters. Three stope sequence alternatives are simulated using simplified diminishing, 1-4-7, and 1-5-9 pillar strategies for a total of 144 stopes. A combination of the BSR criterion and volumetric analysis is used to provide in- sight as to the location, timing, and duration of un- stable rock mass within the orebody, hanging wall, and footwall on all levels of the mining block.MethodologyModel SetupThe simplified model of a typical orebody in the Canadian Shield was constructed in FLAC3D, extending for 360 m along an EW strike and dipping 80° to the south. The host formations comprised metavolcanics with a dominant greenstone formation, a stiff norite formation to the north, and ductile metasediments to the south. A swarm of igneous intrusions in the region were represented by two dykes striking WNW-ESE to the north and south of the orebody. The model dimensions were 840 m along the EW axis, 390 m along the NS one, and 300 m in depth. A total of 862,400 zones were used with a higher mesh density in the zones of interest.Based on commonly used intervals in sublevel open stoping, vertical distances between levels were set at 30 m. Stopes were dimensioned at 20 m along the strike length, 15 m in width, and 30 m in height, translating into 18 stopes longitudinally and 2 transversely for 36 on each level. Mining was simulated from the bottom up on four active levels – L1550, L1520, L1490, and L1460 – from a depth of 1550 m to 1430 m. Each stope was designed with a volume of 9,000 m3 for a total of 324,000 m3 per level and 1,296,000 m3 for four active levels. Haulage drifts were excavated in the footwall at 30 m from the ore- body, in addition to three crosscuts – western, cen- tral, and eastern – per level. Drift and crosscut di- mensions were based on those typically used in Canadian mines with a 5 m × 5 m cross-section and a 1-m arch in the back. Figure 1 presents an isometric view of the model. The mining block from L1580 to L1430 is shown in detail in Figure 2a, while details of the haulage drifts and crosscuts are presented in Figure 2b.Rock Mass Properties and Pre-mining StressesThe rock mass properties used in the model were based on a previous case study mine in the Canadian Shield.Laboratory test results on intact rock samples were combined with borehole logs indicating the rock mass rating (RMR) to derive the required rock mass properties, which are summarized in Table 1 and were used as input properties. The model was simulated in linear elastic mode to maximize induced stress magnitudes and provide a more conservative estimate of potential instability.Based on the rock mass properties of the geologic units, the BSR criterion was selected to gauge the potential for instability in the orebody and greenstone formation. The generation of pre-mining stresses in homogeneous (McKinnon, 2001) and heterogeneous rock mass (Shnorhokian et al., 2014) was achieved using boundary tractions applied on all sides of the model. Calibration was conducted to obtain model readings on L1490 within the norite formation comparable to in-situ measurements obtained at the previous case study mine. Additional model readings on L1400 and L1580 were compared to typical stress rate increases measured in the Canadian Shield (Brown & Hoek 1978, Arjang & Herget 1997).Table 2 presents a comparison of the in-situ measurements and model stress readings along the directional axes. The only significant shear stress component was σxy measured between 8.5 and 9.6 MPa on the three levels. This was very closely matched by the model readings that also varied between 8.74 and 9.42 MPa at the same locations.Stope Sequence AlternativesOnce the pre-mining stresses were generated, three stope sequence scenarios were simulated within the mining block from L1550 upwards to L1460. In the first sequence, a diminishing central pillar scenario was implemented, alternating between the eastern and western extents of the orebody while moving towards the center. In the second approach, a 1-4-7 sequence was run whereby the first, fourth, seventh, tenth, thirteenth, and sixteenth stopes on each active level were designated as primary ones. After their extraction and backfilling, stopes 2-5-8-11-14-17 were mined as secondaries and finally, stopes 3-6-9- 12-15-18 were extracted as tertiaries. The stope sequence was implemented with a lag of at least two levels between primaries-secondaries and secondar- iestertiaries. In the third case, a 1-5-9 sequence was implemented that was similar to the previous one but comprised thicker pillars between the primaries. The numerical sequence for the three alternatives is visually presented in Figure 3.In each sequence, a mining stage represented the extraction of six stopes from various locations within the four active levels. Therefore, while the total volume of ore extracted at each stage remained consistent for all sequences, their locations varied between the levels. A total of 24 stages were simulated with 6 stopes per stage, which resulted in 144 stopes being extracted.Instability Criterion and Volumetric AnalysisDue to the relatively competent nature of both host rock and orebody, and the fact that different pillar configurations were being assessed in the three sequence alternatives, the brittle shear ratio (BSR) was adopted as the instability criterion in this study. A value of 0.7 was used as the threshold above which rock mass was considered unstable and became a source of intense induced seismicity. To render a more conservative analysis, the properties of rock mass attaining a threshold of 0.7 were not reduced and a strain-softening constitutive model was not used in the simulation.The BSR was combined with volumetric analysis to conduct a quantitative comparison of unstable rock mass in the three sequence scenarios. The ore- body, footwall, and hanging wall were monitored separately at each mining stage and the volume of rock mass at risk within each domain was recorded to detect any changes in values. The cumulative volume was compared amongst the sequences at each stage to observe their impact on stability on individual levels, orebody, footwall, and hanging wall.Results and DiscussionGeneral ApproachAn overall comparative analysis was first conducted on the volume of unstable rock mass above a BSR of 0.7 for all three sequence alternatives. It allowed for a general assessment with respect to the optimum extraction approach from the standpoint of minimizing potential ground control challenges. A more detailed analysis was then conducted for individual active levels to relate increases in unstable rock mass volume to the mining front. In the final stage, instability in the footwall and hanging wall was examined for each sequence. Since the host rocks remain in place and are not extracted, the unstable volume there would constitute a region of ongoing microseismic activity and impact the extraction of other levels. The haulage drift and crosscut system was excavated in the footwall and would therefore be impacted by the volume of unstable rock mass in that region. In addition, instability in the hanging wall could result in overbreak and ore dilution during stope extraction.Impact on Overall StabilityTable 3 summarizes the volume of unstable orebody and host rock for the active levels at each stage of mining for all three sequence alternatives. The first observation is that fluctuations take place in terms of ore at risk amongst the 1-4-7 and 1-5-9 options, with the diminishing pillar one comprising the least instability for most of the mining stages. The 1-5-9 approach registers the largest volume of unstable ore in the initial and final stages of extraction from the active levels, while the 1-4-7 sequence take on this role midway through the mining operations. At the penultimate stage of mining, both the 1-4-7 and 1-5- 9 sequences report comparable values with the diminishing pillar approach registering half their volumes of ore at risk. The layout of mined and un- mined stopes for the diminishing pillar, 1-4-7, and 1- 5-9 sequences is presented at stage 14, 15, and 13, respectively, in Figure 4.The second observation is that where the footwall and hanging wall are concerned, the diminishing pillar sequence leads in the volume of unstable rock mass for most of the mining stages. Once the levels are extracted, the values amongst the other two approaches are comparable with those of the diminishing pillar one. However, although all three leave behind a similar volume of unstable host rock once ore extraction has been completed, it can clearly be observed that a diminishing pillar approach would precipitate significant volumes of microseismically active host rock during mining operations. This would undoubtedly provide more challenges than the other two alternatives for ground control strategies, especially since the haulage drift and crosscut network lies within the footwall. Larger volumes of host rock at risk could also result in ore dilution from the hanging wall side during stope extraction.1.1 Impact on active levels in orebodyTables 4, 5, and 6 present the cumulative volumes of unstable rock in the orebody on each active level for the three stope sequences, as well as in the unmined stopes on L1580 and L1430. Figure 5 visually presents the volume of unmined ore at risk for all active levels – as well as L1580 and L1430 – in all three sequences at each mining stage.In the diminishing pillar approach, instability for each active level does not exceed 25,000 m3 (7.5%) of the unmined ore except on L1460 between stages 20 and 24. This is due to the pillar decreasing in height and width in the upper two levels – L1490 and L1460 – at the end of mining stages.In the 1-4-7 sequence, instability ranges from 30,000 to 75,000 m3 (9-23%) from stage 14 onward on L1520, L1490, and L1460. It should be noted that these occur in phases on each active level – at stages 14 to 16 on L1520, at stages 16 to 20 on L1490, and at stages 20 to 22 on L1460. In the first case, slender pillars are formed on L1520 and L1490, which explains the high percentage of ore at risk on the lower level. The same scenario is repeated between stages 16 and 20 for L1460 and L1430. Similarly, stages 20 to 22 comprise the formation of the last rib pillars on L1460.In the 1-5-9 alternative, the highest percentages of ore at risk range between 25,000 and 55,000 m3 (8- 17%) from stage 14 to 20 on L1520, from stage 14 to 22 on L1490, and from stage 18 to 22 on L1460. This occurs when slender pillars extend from L1550 to L1460 at stage 14 and remain in place until the lower stopes are mined on L1550 and L1520 by stage 22.The quantitative assessment of ore at risk for each mining stage is important not only to select an option that minimizes the overall volume of unstable rock mass, but also to identify the levels that require special preventive measures at each stage. Rib pillar stability can be enhanced locally by techniques such as decreasing the volume of extraction per stage and destress blasting, and a foreknowledge of the active levels requiring these measures at a given time is a valuable ground control tool for the mining engineers.Impact on Inactive Levels in OrebodyA key contribution of the quantitative analysis done is the observation of instability in those just above (L1430) and below (L1580) the active levels. It is very interesting to observe from Tables 4 to 6 and Figure 5 that a significant volume of ore on these two levels are rendered unstable from stage 18 onward even though no mining occurs there. This is especially true for L1580 where the volume of un- stable rock mass surpasses 63,000 m3 (19%) at stage 20 in the diminishing pillar sequence, 58,000 m3 (18%) at stage 18 in the 1-4-7 approach, and 71,000 m3 (22%) at stage 22 in the 1-5-9 alternative. L1430 registers only between 30,000 and 40,000 m3 (9- 12%) of unstable rock mass at stage 22 in all sequence options.From a rock mechanics perspective, this is an expected phenomenon whereby stresses are redistributed to the remainder of the geologic formation as parts of it are extracted. As the mining front advances from the bottom to the top, L1580 acts as the principal repository of induced stresses. With the mining of the final stopes on L1460, the last vestiges of natural rock mass stress are directed towards L1430. Quantitative analysis is once again observed to be of practical value as it indicates the degree of additional stresses accumulating in L1580 for all sequence alternatives, thus allowing for the operations team to prepare a plan for its eventual extraction sometime in the future. A common trend in all three sequence alternatives is that once the active levels have been mined out, more than 80,000 m3 (25%) of ore on each of L1580 and L1430 remain above the BSR threshold of 0.7.Impact on footwall and hanging wallTables 7 and 8 presents the overall instability at each mining stage on individual levels from L1580 to L1430 for the host rock, further subdividing the readings into the footwall and hanging wall sections of the greenstone formation. The reason for this step is that instability in the footwall would cause potential issues in the haulage drift and crosscut network excavated there and impact the safety of personnel and mining operations. The information provided is invaluable for the ground control engineers as they would be able to design the ground support in these areas accordingly. Instability in the hanging wall does note pose safety issues per se as no personnel operate in an open stope. However, it would have economic ramifications since instability in that part of the host rock could cause overbreak and induce ore dilution.In general, it is observed that once the ore on all active levels is completely extracted, the total volume of rock mass at risk within the greenstone formation registers 13,500 m3 for all three sequences. It is also noted that the diminishing pillar approach induces the most voluminous instability in the greenstone formation, especially between stages 6 and 16. Since the footwall and hanging wall volumes are reported separately and indicate specific differences between the three sequences implemented.Almost no instability is observed on the inactive levels at L1580 and L1430 except for a total of 66 m3 at depth towards the end of mining operations. A second point is that the volume of rock mass at risk in the hanging wall exceeds that of the footwall by 2,000 m3 after extraction is completed on the active levels. Hence, there is more potential for microseismic activity to originate from the hanging wall side once mining operations cease in the block.The most important contribution of the comparative analysis is the differences in trends in the three options adopted. In the diminishing pillar sequence, the volume of rock mass at risk on the hanging wall side is consistently larger than its footwall counterpart. Hence, there is more potential for ore dilution in this scenario than for instability around the haulage drift and crosscut network. On the other hand, the footwall side generates more volume of unstable rock mass in the 1-4-7 sequence, thus indicating a higher potential for safety concerns around the developments. As for the 1-5-7 option, the weight of rock mass at risk shifts between the hanging wall to the footwall and then back again between various stages of mining. An indication of when these shifts take place can be extremely helpful to the ground control engineers to take the necessary preventive actions on either side of the orebody.The main contribution of this comparative analysis is underlined graphically in Figure 6 where the timing and duration of a potential instability threshold can be read. If an upper limit of 1,500 m3 of rock mass at risk was used for the installation and use of enhanced ground support in the haulage drift and crosscuts network, then this milestone is observed to occur at stage 16 in the diminishing pillar sequence, at stage 14 in the 1-4-7 one, and at stage 20 in the 1- 5-9 approach, with a duration of 8, 10, and 4 stages, respectively. In a similar manner, potential ore dilution – if expected to occur above a volume of 2,000 m3 of rock mass at risk – is anticipated at stages 18 for the diminishing pillar and 1-4-7 sequences and at stage 20 for the 1-5-9 approach.Conclusions1. Based on the figures, tables, and analyses presented in the preceding sections, it can be concluded that a quantitative volumetric comparison of ore and host rock –footwall and hanging wall sides– at risk provides critical insights for mining engineers to optimize the extraction sequence. Firstly, an overall assessment can be made with respect to the volumes of ore and host rock at risk using a specific instability criterion. In this study, the BSR was used, and it was observed that all three sequences left behind comparable volumes of ore at risk on L1580 and L1430. However, the 1-4-7 and 1-5-9 ones incurred more instability on active levels than the diminishing pillar approach at various stages of mining. Furthermore, the analysis specified the mining stage at which the volume of ore at risk begins to increase on a given level, thus enabling ground control engineers to plan for the location and timing of appropriate preventive or support measures.2. Quantitative volumetric analysis was observed to also be of practical use when applied to the footwall and hanging wall sides of the orebody. More potential existed in the latter for the diminishing pillar sequence and in the former for the 1-4-7 approach, while instability shifted between the two locations for the 1-5-9 option. A foreknowledge of when and where instability will increase for a given sequence would enable the installation of enhanced ground support on the footwall side to increase the safety of an operation, and the implementation of preventive measures on the hanging wall side to enhance its profitability.AcknowledgementsThe author acknowledges Prof. Hani Mitri from the Department of Mining and Materials Engineering at McGill University for the use of a FLAC3D license v. 4.00 in this study and is grateful for its availabil- ity.ReferencesArjang, B. & Herget, G. 1997. In situ ground stresses in the Canadian hardrock mines: an update. Int. J. Rock Mech. Min. Sci. 34(15):1-16.Beck, D.A. & Sandy, M.P. 2003. Mine sequencing for high re- covery in Western Australian mines. 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