Numerical modelling of ore dilution in blasthole stoping

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International Journal of Rock Mechanics & Mining Sciences 44 (2007) 692–703 www.elsevier.com/locate/ijrmms

Numerical modelling of ore dilution in blasthole stoping John G. Henning, Hani S. Mitri Department of Mining, Metals and Materials Engineering, McGill University, 3450 University St., Montreal, Que. Canada H3A2A7 Received 12 May 2006; received in revised form 12 October 2006; accepted 7 November 2006 Available online 3 January 2007

Abstract The paper presents the results of a study of the factors causing stope wall overbreak or ore dilution in a blasthole stoping environment. A series of three-dimensional numerical models are developed and analyzed to examine the effect of mining depth, in situ stress as well as stope geometry and orientation on stope wall overbreak. A characteristic orebody and mine design configuration is adopted and used as a basis to carry out comprehensive model parametric study, from which a simple, graphical design tool is derived for the prediction of stope overbreak. It is shown that stope overbreak is significantly affected by the stope aspect ratio and the orientation of major principal in situ stresses with respect to the stope. The methodology presented in this paper can be adopted to develop mine-specific design tools for the estimation of ore dilution associated with a proposed mine design. This can be extremely helpful in the process of underground mine planning and optimization. r 2006 Elsevier Ltd. All rights reserved. Keywords: 3-D modelling; Hanging-wall dilution; Numerical modelling; Ore dilution; Overbreak; Rock mechanics; Stope type; Underground mining

1. Introduction In a global competitive market, there is pressure on mines to maximize production and increase revenue. Unplanned ore dilution has a direct and large influence on the cost of a stope, and ultimately on the profitability of a mining operation. The economic impact of dilution is due to costs associated with the mucking, haulage, crushing, hoisting, milling, and treatment of waste or low-grade rock having little or no value, displacing profitable ore and processing capacity. The additional time required for excavation and backfilling of the larger stope volumes produced by the extraction of waste rock can also lead to unscheduled delays, changes to the mining schedule, and potentially, development rehabilitation costs. Blasthole mining, also referred to as long-hole mining, is a general term applied to mining methods that employ longhole drilling for the production of ore. It is a system of largescale drilling and blasting in which large amounts of ore are broken in single blasts. Blasted slices of rock fall into an open void within the stope. The rock is extracted and the empty Corresponding author. Tel.: +1 514 398 4890; fax: +1 514 398 7396.

E-mail address: [email protected] (H.S. Mitri). 1365-1609/$ - see front matter r 2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.ijrmms.2006.11.002

stope is backfilled (delayed backfilling). The method is used to mine ore where both the ore and wall rocks are relatively strong. The method may be applied to a variety of vertical or steeply dipping orebody shapes and sizes. The blasthole mining method provides limited selectivity. Since it is a bulk method, blasthole mining results in some overbreak. The orebody should preferably be regular, as changes in orebody geometry outlines are difficult to compensate for. Production holes, commonly in the range of 50–110 mm diameter, are drilled either in a fan-shaped pattern, or in a pattern parallel to the stope dip. Drilling can be done in advance of ore extraction. Stope dimensions are determined from local ground conditions and orebody thickness. Stope blocks are accessed in transverse or longitudinal directions. Transverse stoping is common to tabular orezones of widths exceeding 5 m, where stope access is driven normal orezone strike. Narrower width orezones are mined longitudinally, with stope access driven parallel to, and within, the orezone strike. 2. Review of ore dilution assessment methods The term ‘dilution’ refers to any waste material within the mining block, including barren and subgrade rock and

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backfill. Dilution tends to be the most consistently underestimated factor in mine planning [1]. Increasing ore dilution results in a decrease of hoisted grade in comparison with the mining reserves [2]. Dilution negatively influences the profitability of mining operations by lowering the quantity of mineral or metal that can be produced from each ton of ore processed in mining/milling operations. Dilution is a qualitative parameter that enables the mine operator to evaluate quality of design [3]. Traditionally, the mining industry has used the dilution concept to define the negative differences between forecasts and production results [4]. Dilution and sacrifice of ore tend to be inseparable factors, with a trade-off between optimum recovery and impairment of grade. Inadequate attention to stope design can quickly eliminate profitability from high productivity bulk mining methods [5,6]. Dilution can refer to either a measure of external waste (unplanned dilution) that has sloughed from the stope wall, or to material that is of lower grade than cut-off, but which is included in the mineral deposit, reserve or stope outline and extracted with the mining of ore (planned dilution). Unplanned dilution, the focus of in this study, refers to additional non-ore material derived from rock or backfill outside the stope boundaries due to blast-induced overbreak, sloughage of unstable wall rock, or sloughing of backfill [7]. The term ‘overbreak’ is synonymous with unplanned wall dilution. A value of dilution is recorded by most mines, although not in an identical manner. A survey of mines throughout Canada by Pakalnis [3] identified nine variations on a definition of dilution. Dilution is usually calculated as a percentage. In their review of Canadian mining practices, Scoble and Moss [7] reported that Eqs. (1) and (2) were the most widely used. Eq. (1) was recommended as a standard measure of dilution by Pakalnis et al. [8], as it was more sensitive to wall sloughage. Dilution ¼ ðTons waste minedÞ=ðTons ore minedÞ, Dilution ¼

Tons waste mined . Tons ore mined þ tons waste mined

(1)

693

different stope geometries perform in a particular quality rockmass, or mining-induced stress environment. In assessing dilution, it is necessary to understand the way a stope operates. Empirical design techniques, such as those described in Mathews et al. [10], Potvin [11], and Pakalnis and Vongpaisal [12] have gained acceptance as a simple, ‘first-pass’ means of generating broad design guidelines for primary stopes. Empirical back-analysis of CMS stope stability data can provide useful predictions of dilution or sloughage for particular stope design [13–15]. 3. Stope design influences on dilution In a general sense, a mine is a factory with standardized practices, equipment and materials for stope design and excavation. However, no two stopes are the same, as each has numerous potential variables such as stope height, hanging-wall dip and pre-mining stress environment, which may impact recovery and unplanned dilution. 3.1. Stope height Published data suggests that unplanned dilution, particularly from the hanging-wall, is sensitive to the stope height and the dip of the hanging-wall. Increased overbreak may be associated with equipment limitations, such as increased borehole deviation, or to rockmass stability. Perron [16] describes instabilities associated with high stopes at one mining operation, which ultimately required a re-design of both the stope height and mining sequence to reduce dilution. Stopes of 60 m height  20 m width were originally designed for transverse mining. Wall instability was found to be greater than anticipated. To improve stability and to lower dilution, additional sub-levels were developed in ore, reducing stope dimensions to a more stable 30 m high  20 m wide dimension. A consequence of this conversion was a change to longitudinal mining, with a lower rate of production. 3.2. Hanging-wall dip angle

(2)

Narrow stopes, mined by blasthole method, are generally victims of considerable dilution: the narrower the zone is, the more important the border effects [4]. For example, using Eq. (1), if both the hanging-wall and footwall of a steeply dipping 1.5 m wide tabular deposit contributes 0.3 m of overbreak, then an unplanned mining dilution of 40% results. If this orezone was 3.0 m thick, mined in the same conditions, the resulting dilution factor becomes 20%. In recent years, accurate surveying of excavated stope surfaces has been made possible with the application of automated non-contact laser rangefinders. The Cavity Monitoring System (CMS), described by Miller et al. [9], offers a volume-based technique for directly measuring stope performance. CMS data provides a record of how

The influence of hanging-wall dip on overbreak can be significant. With steeply dipping orezones, vertical stresses are shed around the ore body. As the dip of the stope hanging-wall becomes shallower, vertical stresses are shed onto the ore body, leading to larger displacements. An example of the influence of hanging-wall dip on stope overbreak is described in [17], where depth of overbreak was observed to increase as the hanging-wall dip became shallower. 3.3. Stress environment When a drift, stope or other underground opening is excavated into a stressed rockmass, stresses near the new opening are disrupted and re-distributed. As a blasthole stope is mined, a zone of low stress develops [18]. Stresses

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analysing induced stress and displaying displacements, strains and stresses. The program can accommodate multistep mining sequences and multiple material zones with different material properties and stress states.

normal to the hanging-wall are shed to the abutments. This zone of elastic relaxation extends further into the hanging wall as the distance to the supporting abutments increases. According to Kaiser et al. [19], rockmass relaxation refers mostly to stress reduction parallel to the excavation wall and not to stress reductions in the radial direction or a reduction in confinement. Stresses in the tangential direction to the excavation wall (the major and/or intermediate principal stress) are reduced in the rockmass, often to values far below those predicted by linear elastic models, because the rockmass has been allowed to deform at some distance from the excavation. In the relaxation zone, the absence of significant clamping stresses is often cited as one of the main reasons for the instability of large hanging-walls [20]. The depth or volume of this relaxation zone in a stope hanging-wall is dependent upon the pre-existing stress state and the size or hydraulic radius of the hanging-wall [21]. The shape of the stope hanging-wall also influences the total volume, or average depth of the relaxation zone in the hanging-wall [22,23]. Diederichs and Kaiser [24] have also shown that relaxation, causing near-zero stress conditions tangential to excavation spans, reduces the self-supporting capacity of an excavation in fractured ground. This relaxation can also drastically reduce the performance of cablebolts, which are often used to support hanging-walls [25]. Tannant et al. [22] reported that tension can manifest itself as delamination of foliation planes and dilation of cross jointing, leading to unravelling failure in laminated rock.

4.1. Quantifying hanging-wall dilution using numerical modelling With stope excavation, principal in situ stresses rotate such that the major (s1) and intermediate (s2) principal stress are aligned parallel to the excavation hanging-wall. Minor principal stress (s3) tends to align perpendicular to the excavation boundary, as shown in Fig. 1. Overbreak occurs due to the loss of confinement in the radial direction to the stope wall and a decrease in s1 and s2 [27]. The tangential stresses s1 and s2 may decrease in addition to the decrease of s3 causing a larger area of caving or this may bring stable hanging-walls to failure. The zone of relaxation defines an envelope within which gravity-driven block failures may occur. It can be assumed that the volume of hanging-wall relaxation represents a potential volume of unplanned dilution. Sloughage potential is assumed to be a function of loss of confinement, which results in the creation of zones of relaxation, and the exploitation of this confinement loss by structures or planes of preferential weakness within that zone. The nature of the structures determines the tensile strength of the rockmass in question. In massive to moderately jointed rock, residual tensile load bearing strength arising from incomplete fracturing or from rock bridges separating non-persistent jointing is a key factor in the control of ultimate gravitydriven failure of jointed or stress damaged ground [18]. The notion that a simple confining stress (tensile strength) criterion can be used to assess hanging-wall stability and dilution potential has been reported by many, including [28,29]. A potential for sloughage exists in the region of confinement loss (s3 ¼ 0 MPa iso-contour). However, not all of this zone will fail if the rockmass has some self-supporting capacity. The occurrence and potential severity of this sloughage is influenced by the tensile strength of the rockmass. In turn, the tensile

4. Numerical modelling Most underground excavations are complex threedimensional (3-D) shapes with irregular form. Complexity increases on a larger, mine-wide, scale since these individual mine openings are frequently grouped close to other excavations. The sensitivity of controlling stope geometry and stope setting on potential overbreak was examined parametrically using the 3-D numerical modelling program Map3D [26]. Map3D is capable of constructing 3-D geometries,

a

b σ3 σ1 σ3 Ore

Excavation

σ2 σ1

Initial condition

σ2

After excavation

Fig. 1. Principal stress orientation before and after stope excavation, after [27].

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strength depends on the material properties of the rock and the structures present within it. A common practice is to reconcile stope overbreak, measured from CMS survey, using numerical modelling. In a case example described by Martin et al. [30], the distribution of three principal stresses within a hangingwall, obtained from 3-D elastic modelling, was plotted against the surveyed stope profile. Results from this study suggested that the contours of minimum principal stress at s3 ¼ 0 best reflected the observed geometry. 4.2. Modelling parameters For the parametric study, values representative of the Canadian Shield mining environment were adopted for modelling input parameters. Parameters were examined under a range of conditions, as indicated below. Pre-mining or in situ stresses are usually reported in terms of principal stresses s1, s2 and s3 and their associated orientations in terms of trend and dip. In the Canadian Shield the major and intermediate principal stresses s1 and s2 tend to be near horizontal with plunges between zero and approximately 101, and the minor principal stress s3 is approximately vertical [31]. Consequently, the maximum and minimum horizontal stresses sH and sh and the vertical stress sv are used synonymously with s1, s2 and s3, respectively. For the parametric study, stress regimes at three depths were considered, separated in 750 m intervals of depth. Shallow depth corresponds to a 750 m depth. A depth of 1500 m was considered moderate; while deep mining was represented by stopes at a depth of 2250 m, see Table 1. Horizontal-to-vertical stress ratio decreases from 1.9 to 1.5 with depth. Stress magnitudes were determined from relationships suggested by Diederichs [20], based on a re-evaluation of documented stress data. Three categories of rockmass quality were considered for the parametric study, ranging across the spectrum of rockmass qualities common to Canadian mines employing long-hole mining [32,33]. They are: very good quality rock, good quality, and fair quality rock. Rockmass conditions were classified using the Geological Strength Index (GSI) system, developed for Canadian mining and described in [34]. The GSI system considers the qualitative characteristics of the rockmass as a whole, rather than assessing the quantitative characteristics of discrete joint sets. With the GSI approach, the rockmass is assessed by the visual geological description of its block size and joint surface condition or by its typical block size [35]. Rockmass quality

695

decreases as the structure of the exposed rock face becomes less interlocked. Rockmass quality is further diminished as quality of the joint surfaces is reduced. Hoek–Brown strength parameters mb and s; as well as elastic modulus E, can be determined from GSI values for design purposes. Equations for obtaining generalized Hoek–Brown criterion for jointed rock masses are described in [36]. Input parameters for numerical modelling are summarized in Table 2. For the parametric study a uniaxial compressive strength value of sc ¼ 175 MPa was used, which corresponds to a mid-range strong rock. With blasthole mining, in order to maximize ore recovery, it is common to mine pillars following primary mining recovery. As this is done, large surface areas of backfill may be exposed as a free standing wall. It is necessary that the backfill has sufficient strength to remain free standing during and after pillar extraction. For the parametric study, mined stopes were backfilled using parameters listed in Table 3. 4.3. Modelled stope geometry Numerical modelling was undertaken to examine the influence of mine depth, hanging-wall dimensions, hanging-wall dip angle, the orientation of pre-mining stress with respect to stope hanging-wall, and stope type on ore dilution. Stope geometries common to Canadian long-hole mining operations were selected for the numerical model. For this parametric study, stope dimensions varying from 10 to 40 m in both strike length and vertical stope height were assessed. Modelled stopes were assigned a width of 10 m. Two values of hanging-wall dip were assessed: 801 and 601. Footwall dip was kept parallel to the modelled hangingwall dip angle, to maintain the tabular nature of the orebody. A ‘typical’ stope with an 801 hanging-wall and footwall dip, and dimensions measuring 30 m high  10 m thick, with a strike range of 10–40 m was selected as a base case; see Fig. 2. The setting of the base-case stope was at moderate depth (Z ¼ 1500 m), in moderately strong rock, with mid-range rockmass quality (GSI ¼ 65) for both the orezone and host rock. 4.3.1. Stope type A stoping sequence common to many Canadian mines employing blasthole methods uses a pyramidal or chevron mining front. Stopes are sequenced to maintain a

Table 1 Pre-mining stress magnitudes associated with shallow, moderate and deep mining Depth category

Depth below surface

K

sH

sh

sv

Shallow Moderate Deep

750 m 1500 m 2250 m

1.9 1.6 1.5

37.3 MPa 64.2 MPa 89.3 MPa

25.2 MPa 47.1 MPa 68.4 MPa

19.5 MPa 39.0 MPa 58.5 MPa

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Table 2 Model parameters for host and orezone rock Very good rockmass quality

Good rockmass quality

Fair rockmass quality

Material values GSI Uniaxial compressive strength, (sc) Hoek-Brown constant for intact rock, (mi)

80 175 MPa 25

65 175 MPa 25

50 175 MPa 25

Rockmass values calculated with GSI value Rockmass elastic modulus (Erm) Hoek–Brown ‘m’ Hoek–Brown ‘s’ Rockmass tensile strength, (st) Global rockmass compressive strength, (scm)

56,234 MPa 12.24 0.108 1.55 MPa 91.5 MPa

23,713 MPa 7.16 0.021 0.50 MPa 64.6 MPa

10,000 MPa 4.19 0.004 0.16 MPa 47.5 MPa

Table 3 Model parameters for consolidated rockfill

orezone

Parameter

Material value

Uniaxial compressive strength, sc Elastic modulus, E Cohesive strength Internal angle of friction

3 MPa 2500 MPa 0.1 MPa 351

80° HW dip 30m

triangular shape to the mined-out area by mining vertically with a lead stope, then outward along the rill of the triangle towards its base. The lead primary stope, subjected to elevated stresses as a result of the high level of confinement, creates a ‘bow wave’ effect that tends to distress adjacent primary stopes and shed stresses to the abutments. This ‘halo’ of failed ground in the bow wave of the lead stope should allow improved ground conditions in subsequent panels [37]. With careful scheduling, adjacent primary stopes are mined and filled for two vertical lifts before mining of the secondary stope between them is started [32,38]. An important, sometimes overlooked, parameter affecting unplanned dilution is the local stope setting within the mining sequence. Depending on its placement within a planned mining sequence, a stope may be bound by rock on both walls (a primary stope), or it may have backfill on one or both walls (a secondary stope). Five stope categories were identified, based on their setting within the orezone mining sequence; see Fig. 3. The stope categories consisted of three primary (Type P1, P2 and P3) and two secondarytype stopes (Type S1 and S2). Type P1 stope refers to an isolated primary stope, with rock on both side walls. Type P2 stope refers to a primary stope, located above a backfilled P1-type stope, with rock on both side walls. A rock pillar of height equal to two stopes occurs on at least one side wall of the stope. Lastly, Type P3 stope refers to a primary stope, located above a backfilled P2-type stope, with rock on both side walls. A rock pillar of height equal to three stopes occurs on at least one side wall of the stope.

10 to 40m

10m

Fig. 2. ‘‘Typical’’ stope geometry used for the model parametric study.

Sub Level P3 Sub Level P2

S2

P2

S1 Sub Level

P1

S2

P1

S2

P1

S2

P1

S1 Main Level

Fig. 3. Stope categories within mining block.

Type S1 stope refers to a secondary stope, with rock on one side and above. Other side wall is against backfill. S1type stopes are common to pillarless stope sequence extraction sequences and to longitudinal mining methods. The other secondary stope, Type S2, refers to a secondary stope having both side walls against backfilled primary

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697

stopes. S2-type stopes are common to transverse mining methods. For the parametric study, a block of equally dimensioned stopes measuring three stopes high by three stopes wide were generated in Map3D. Individual stopes were modelled in accordance to the five stope categories. 5. Numerical model parametric study 5.1. Estimation of overbreak volume As mentioned in Section 2, stope width influences the calculated value of percent dilution. To express dilution independently of stope width, Dunne and Pakalnis [39] and Clark and Pakalnis [40] suggest that dilution values be calculated average metres of wall slough per square metre of wall (m3/m2), rather than percent dilution. Equivalent Linear Overbreak/Slough (ELOS) is a method of converting the volumetric CMS measurement into an average sloughage depth over the entire stope surface. An advantage of reporting stope sloughage in terms of ELOS is that the source of unplanned dilution can be associated with individual stope walls, such as hanging-wall or footwall. For a given stope surface, ELOS is calculated as follows:

Fig. 4. Grid plane position at stope mid-height and mid-span. Secondary (S2) stope model shown.

ELOS ðmÞ ¼

Volume of measured overbreak from stope surface ðm2 Þ . Area of stope surface ðm3 Þ

ð3Þ In this study, relaxation depth was determined from isocontours of minimum principal stress (s3), located on a vertical plane located at the stope mid-spans. For the parametric study, hanging-wall relaxation depth was defined as the maximum depth of the s3 ¼ 0 contour relative to the excavation boundary, measured from the center of the stope wall. With the Map3D models, hanging-wall stresses were plotted onto grids placed at the mid-span and mid-height of the stope, as illustrated in Fig. 4. Grid planes were orientated normal to the hanging-wall dip, and extend a distance of 15 m away from the stope boundary. The extent of the potential relaxation zone associated with a given stope geometry of setting was determined from contours of minimum stress. The volume of potential hanging-wall relaxation simulated by a 3-D elastic numerical model for a given 3-D stope geometry was estimated using an approach described in [41], in which the overbreak volume was represented as the volume of half a prolate ellipsoid, illustrated in Fig. 5. The volume (V) of hanging-wall relaxation, represented by the half-prolate ellipsoid, is calculated as V ¼ ð2p=3Þr1 r2 r3 ðm3 Þ.

(4)

In Eq. (4), r1, r2 and r3 correspond to the perpendicular, vertical and horizontal radius distances from center (midspan and mid-height) of stope hanging-wall contact.

Fig. 5. Illustration of overbreak envelope in a stope hanging-wall.

A potential for overbreak exists within the envelope of confinement loss, defined by s3p0 MPa.The height of such envelope was determined from iso-contours of minimum principal stress (s3), located on a vertical and horizontal planes located at the stope mid-span and mid-height, respectively, as illustrated in Fig. 5. To quantify modelled ore dilution from the 3-D simulations, the ore Dilution Density (DD) is a term introduced in this study to denote potential hanging-wall overbreak. DD ¼

Volume of half prolate ellipsoid ðm3 Þ . Surface area exposed ðm2 Þ

(5)

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Such a definition allows for the estimation of dilution density at any location in the stope wall—the inherent feature of this definition is that DD is not constant over the surface area examined. Thus, referring to Fig. 5, it can be seen that DD ¼ 0 along the edges of the stope wall and is maximum at the centre where DD ¼ r1, the height of the prolate ellipsoid. DD as calculated from the above equation is similar to the parameter ELOS, in that both express a measure of overbreak. As for the estimation of the size of the overbreak zone, typically the zero stress contour (s3 ¼ 0 MPa) or the rockmass tensile strength contour (s3 ¼ st) are used to define the boundary of such zone. 5.2. Modelling results

1.4

DD (m)

698

5.2.2. Dilution density relationship with varying stope height and strike length Unlike factors such as mine depth and hanging-wall dip angle, which are outside of the control of the mine

40m Strike length

1

30m Strike length

0.8 0.6 0.4 0.2

20m Strike length

15m Strike length 10m Strike length

0 750

1500

2250

Mining Depth (m) Fig. 6. Modelled dilution density trend lines as a function of mining depth, s3 ¼ 0 MPa contour.

Parametric modelling was performed to examine relationships of hanging-wall dilution with depth, stope dimension, dip angle, stress setting and stope type.

1 0.8 DD (m)

5.2.1. Effect of mining depth The influence of mining depth (or stress setting) on the envelope of potential overbreak was assessed using Map3D. The base-case stope (30 m vertical height, 801 dip, GSI ¼ 65, s11 perpendicular to hanging-wall, P1 type primary stope), with strike lengths ranging from 10 to 40 m, was modelled across the shallow, moderate and deep mining range of stope settings described in Section 4.2. Results were expressed as modelled DD. Two DD values were calculated: (i) The s3 ¼ 0 MPa, represents the volume of relaxed ground available for overbreak, assuming the rockmass has no tensile strength; (ii) DD values were also determined for the s3 ¼ st contour, which accounts for rockmass tensile strength. For GSI ¼ 65, rockmass tensile strength was calculated to be st ¼ 0.5 MPa (Table 2). Trends associated with DD for the s3 ¼ 0 MPa contour are presented in Fig. 6. For a given stope dimension, the stress model suggests that the DD remains relatively uniform. Trend lines between the data points show only marginal increase, in the range of 0.02 m DD per 500 m increase in depth. Of greater impact on DD increase is the influence of strike length, which is examined further in Section 5.2.2. Trends associated with DD for the s3 ¼ 0.5 MPa contour, shown in Fig. 7 show a relationship influenced by depth. The envelope defined by the s3 ¼ 0.5 MPa contour, representing the rockmass tensile strength of a good quality (GSI ¼ 65) rockmass, increases with depth. At shallow depth, this contour generates minimal (nearzero) DD values. However, with depth the value of DD increases. The s3 ¼ 0.5 MPa contour also varies with strike length. At stope strike lengths of 15 m or less, minimal (near-zero) DD occurs. Increased strike length leads to increased DD values.

1.2

0.6

Strike length 40 m 30 m 20 m

0.4 0.2 0 750

1500

15 m 10 m 2250

Mining depth (m) Fig. 7. Modelled dilution density trend lines as a function of mining depth, s3 ¼ 0.5 MPa contour.

operator, stope dimensions are a variable factor that influences overbreak, which can be established during the initial mine design. Selection of stope dimensions, and in particular stope height, represents a compromise between ‘acceptable’ overbreak and the cost and time required to establish additional lateral infrastructure in order to mine smaller, more stable blocks. For example, mining of a 120 m high orezone in 30 m vertical increments would require four lateral mine horizons. Mining of the same block in 20 m vertical increments may generate a more stable hanging-wall, resulting in less overbreak, but would require six mine levels, or 50% more lateral development. The influence of stope hanging-wall dimensions (height and strike length) on potential overbreak was assessed using Map3D. The results from the study into the effect of mine depth on dilution density suggest that mining depth does not play a significant role in the extent of s3 ¼ 0 MPa contour within the hanging-wall. When investigating trends associated with varying stope dimensions, data from stopes in a shallow, moderate and deep mine setting was collected. As there was little scatter in the data points, analysis is based on averaged values. The base-case stope was applied across a range of dimensions. Results for the s3 ¼ 0 MPa contour were expressed in terms of DD values. Trends associated with DD for the s3 ¼ 0 MPa contour as a function of strike length and vertical stope height are presented in Fig. 8. Fig. 8 represents a design tool, plotting contours of anticipated dilution density against stope

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Strike length of exposed wall Aspect ratio ¼ . True height of exposed wall

(6)

5.2.3. Effect of hanging-wall dip angle The influence of the hanging-wall dip angle on overbreak has been discussed by others, including [17,43]. With a shallower hanging-wall dip, the distribution of low s3 stress contours becomes increasingly asymmetric, as illustrated in Fig. 10, leading to a favorable orientation for release of unstable wedge intersections from the exposed hangingwall. Another factor to consider is the true height of exposed hanging-wall, which increases as the hanging-wall dip angle decreases. True height can be calculated from dip angle and vertical height using. True height ¼ Vertical height=sin f

(7)

where f is the hanging-wall dip angle (measured from horizontal). 0.1m

0.2m

0.5m

0.75m

1.0m

DD =1.0m

DD = 0.50m

40 DD = 0.75m Stope Height (m)

dimension for the base case stope. Villaescusa [42] qualitatively described a similar hyperbolic curve defining a stable/unstable region. Fig. 8 suggests that stope wall stability (with minimal dilution) improves by either excavating openings having long vertical and short horizontal dimensions, or openings having long horizontal and short vertical dimensions. Similarly, Fig. 9 plots dilution density values for the range of stopes modelled against stope geometry. Here, stope geometry is described by its aspect ratio (see Eq. (6)) and vertical height. From this plot, it can be seen that stopes with a small vertical height or tall stopes with a short strike length generate the lowest DD. Severity of DD increases as the aspect ratio of the hanging-wall approaches unity.

699

DD = 0.25m

30

20

10

2:1

1:1

0.5:1

0.33:1

Aspect Ratio (length/height) Fig. 9. Dilution Density associated with stope height and aspect ratio for the base case stope, s3 ¼ 0 MPa contour.

The influence of hanging-wall dip angle on the envelope of potential overbreak was assessed using Map3D. Stopes with true height of 20, 30 and 40 m were examined in the base-case model setting at moderate (1500 m) depth. Hanging-wall dip angles of 801 and 601 were considered. DD results, defined by the s3 ¼ 0 MPa contour, were determined. Trends associated with DD for varying hanging-wall dip angles are presented in Fig. 11. DD values cluster together for strike lengths p20 m. As shown previously, smaller stopes have more stable geometry. Hanging-wall dip influences stope overbreak as strike length increases beyond 20 m. At a 30 m strike length, the DD associated with a 30 m stope height increased by 28% with the shallower hanging-wall dip. At a 40 m strike length, the DD increased by 52% with the shallower hanging-wall dip of 601.

40

Vertical height (m)

30 1.0m 0.75m 20 0.5m

10

0.2m 0.1m

10

15

20

30

5.2.4. Effect of pre-mining stress orientation The influence of major principal stress orientation with respect to the stope hanging-wall was assessed using Map3D. Base case stopes with hanging-wall dip angles of 801 and 601 were examined. Two major principal stress orientations were considered: (i) s11 perpendicular to stope strike, and (ii) s11 parallel to stope strike. DD trends, defined by the s3 ¼ 0 MPa contour, associated with varying s1 orientations are found in Fig. 12. DD values cluster together for strike lengths p20 m. Major principal stress orientation influences stope overbreak as strike length increases beyond 20 m. DD is reduced when s1 is parallel to the strike of the stope. The amount of DD reduction ranged from 14% for a stope with an 801 hanging-wall dip angle, to 17% for a stope with a 601 hanging-wall dip angle.

40

Strike length (m) Fig. 8. Dilution Density (DD) as a function of stope hanging-wall dimension for the base-case stope, s3 ¼ 0 MPa contour.

5.2.5. Effect of stope type A parameter affecting unplanned ore dilution is the local stope setting within the mining sequence. Depending on its

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Fig. 10. Distribution of relaxation zone under varying hanging-wall dip angles.

Vertical Height

1.8

40m

1.6

30m

1.4

20m

1.2 DD (m)

60° dip

40m 30m

1

80° dip

0.8 0.6

20m

0.4 0.2 0 10

20

40

30 Strike Length (m)

Fig. 11. Influence of hanging-wall dip on overbreak. Base-case stope, s3 ¼ 0 MPa contour.

1.6 σ1° perpendicular

1.4

60° dip

DD (m)

1.2

σ1° parallel

1

σ1° perpendicular

0.8

σ1° parallel

80° dip

0.6 0.4 0.2 0 10

20

30

40

Strike Length (m) Fig. 12. Influence of major principal stress orientation on overbreak. Base-case stope, s3 ¼ 0 MPa contour.

placement within a planned mining sequence, a stope may be bound by rock on both walls (a primary stope), or it may have backfill on one or both walls (a secondary stope). The base-case stope setting (30 m vertical height, 801 dip,

GSI ¼ 65, s11 perpendicular to the hanging-wall) was modelled over strike lengths ranging from 10 to 40 m. A P1 stope is an isolated mine block, and is the basis for other parametric modelling described in this chapter. With the

ARTICLE IN PRESS J.G. Henning, H.S. Mitri / International Journal of Rock Mechanics & Mining Sciences 44 (2007) 692–703

P2, P3, S1 and S2 stope types, previously mined stopes were backfilled. Two DD values were calculated: (i) defined by the s3 ¼ 0 MPa, represents the volume of relaxed ground available for overbreak, assuming the rockmass has no tensile strength; (ii) DD values were also determined for the s3 ¼ st ¼ 0.5 MPa contour, which accounts for rockmass tensile strength. Trends associated with DD for the s3 ¼ 0 MPa contour are presented in Fig. 13. Compared against the P1 stope, extraction of the P2 and P3 stopes is associated with greater values of DD. For a 20 m long stope, a DD increase of 32% occurred between P1 and P2 mining. Subsequent extraction of the P3 stope resulted in only a minor DD increase of 3% over the P2 stope, or 36% greater than the P1 stope. DD values for the secondary stopes are significantly greater than those associated with the P1 stope. For the 20 m long stope, DD associated with the S1 stope increased by 0.67 m or 132% compared against the P1 stope. The S2 stope generated a DD increase of 1.6 m or 320% compared against the P1 stope. Compared to averaged DD values for 20 m long primary stopes, the S1 stope overbreak increased by 0.55 m or 90%, while S2 stope overbreak increased by 1.49 m or 244%.

3 2.5

DD (m)

2 1.5 1

P1 P2 P3 S1 S2

0 10

6. Discussion Parametric numerical modelling studies were undertaken to examine the impact of a variety of factors on hangingwall ore dilution. The parametric study considered two criteria for overbreak: (i) the volume of relaxed ground available for overbreak, assuming the rockmass has no tensile strength, represented by the s3 ¼ 0 MPa; and (ii) the s3 ¼ st contour, which considers rockmass tensile strength. Modelling results found that these two criteria did not parallel each other. When comparing overbreak associated with the s3 ¼ 0 MPa and s3 ¼ st contours against depth (Fig. 14), it was found that the s3 ¼ 0 MPa contour remained near-constant with depth for a given stope geometry or hanging-wall dip. Conversely, potential overbreak associated with the contour of rockmass tensile strength increased with depth for a given stope geometry or hanging-wall dip. To quantify modelled overbreak, two terminologies, illustrated schematically in Fig. 15, are introduced. Notension overbreak (DD0), corresponding to the s3 ¼ 0 MPa contour represents overbreak that may happen, assuming that the rockmass has no inherent strength. The Notension overbreak contour varies with stope geometry and hanging-wall dip, and is roughly independent of depth. Confinement overbreak (DDT), corresponding with the s3 ¼ st contour represents slough that will happen. The extent of Confinement overbreak increases with depth for a given stope geometry or hanging-wall dip angle. DDT is a less conservative estimate of ore dilution density than DD0. DDT oDD0 .

0.5

15

20

30

40

Strike Length (m) Fig. 13. Influence of stope type on Dilution Density. Base-case stope at s3 ¼ 0 MPa contour.

(8)

Several observations of the sensitivity of individual factors on potential overbreak were made. It was found that mine depth does not play a significant role in increasing the volume of potential dilution corresponding to the s3 ¼ 0 MPa contour, (DD0). For example, as the mining depth increases from 750 to 2250 m, the increase in DD is only 0.05 m or 8.6% for a 20 m long stope. However, for stopes with strike lengths exceeding 15 m, located at moderate and greater mining depths, the severity of potential dilution associated with the s3 ¼ st contour,

1.2 40m Strike length 1

30m Strike length

DD (m)

0.8 0.6

20m Strike length

σ3= 0 MPa 40 m 30 m

0.4 15m Strike length 0.2 0 750

20 m

10m Strike length 1500

701

Strike length

σ3= τt=-0.5 MPa

15 m 10 m 2500

Mining depth (m) Fig. 14. Map3D results for stope of 30 m vertical height. Values associated with s3 ¼ 0 and s3 ¼ st ¼ 0.5 MPa contours plotted.

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σ3 = 0 contour “No-tension overbreak” DD0

Mined stope

a

σ3 = 1t contour “Confinement overbreak” DDT

Mined stope

Mined stope

b

c

Fig. 15. Schematic illustration of influence of mining depth on hanging-wall overbreak regimes: (a) shallow depth, (b) moderate depth, (c) deep.

(DDT) increased. With a 20 m long stope, DDT increases from 0.02 to 0.2 m between shallow and moderate depth. As mining depth increases from 1500 to 2250 m depth, DDT increases from 0.2 to 0.28 m. Varying stope dimensions influences the magnitude of DD0. Stopes with large or small axial ratios are more stable than large rectangular stopes. Rectangular stopes with vertical height and strike lengths of 15 m or less are more stable than large rectangular stopes. Severity of overbreak increases as the hanging-wall dip angle became increasingly shallow. For a 30 m high  30 m long stope, overbreak increases by 0.22 m or 29% when the dip angle changes from 801 to 601. The influence of hanging-wall dip angle on overbreak is more pronounced as strike length increases. Major principal stress orientation influences stope overbreak as strike length increases beyond 20 m for a 30 m high stope. The severity of overbreak was reduced in a mine setting where the orientation of principal pre-mining stress is parallel to the strike of the orebody. A decrease in DD by 0.08 m or 16% occurs when pre-mining stresses are parallel rather than perpendicular on a 20 m long stope. Stope type influences severity of modelled overbreak. Five stope types were identified, based on their position within a tabular blasthole mining sequence. Three stope types are classified as primary (P1, P2 and P3) and two are secondary stopes (S1 and S2). Overbreak potential increased slightly between the three primary stope types, and increased significantly when comparing the primary and secondary stope types. In a general sense, this can be expressed as DDP oDDS1 oDDS2 ,

(9)

where, DDP is the DD generated by primary (P1, P2 and P3) type stopes, DDS1 the DD generated by S1-type stopes, DDS2 the DD generated by S2-type stopes. Two other factors influence the likelihood of dilution occurring within (and beyond) the envelope of no-tension

overbreak. External Factors (DDE) represent physical conditions of the stope setting that influence hanging-wall stability. These conditions include rockmass quality, orientation of principal stress, and stope type. Construction Factors (DDCf) are human influences impacting overbreak. Construction Factors include blasting, drillhole deviation, and undercutting. 7. Conclusion New terminologies have been introduced to quantify modelled overbreak. No-tension overbreak (DD0) represents overbreak that may happen, depending largely on the severity of Construction Factors (DDCf) in damaging the tensile capacity of the rockmass. Confinement overbreak (DDT), which increases with depth, represents dilution that will occur as a result of tensile failure of the hanging-wall rock into the mined stope. The magnitude of overbreak may be further increased by External Factors (DDE). The numerical modelling methodology presented in this paper has proven to account for what might be considered the most critical parameters for stope design and ore dilution estimation. Such methodology can be adopted to develop mine-specific design tools for the estimation of ore dilution associated with a proposed mine design. This can prove extremely helpful in the process of underground mine planning and optimization. References [1] Taylor HK. Ore reserves, mining and profit. CIM Bull 1994;87:38–46. [2] Planeta S, Bourgoin C, Laflamme M. The impact of rock dilution on underground mining: operational and financial considerations. In: Proceeding of the 92nd CIM annual general Meeting, Ottawa, 6–10 May 1990. [3] Pakalnis RC. Empirical stope design in Canada. PhD thesis, University of British Columbia, Vancouver, 1986. 276pp. [4] Valle´e M, David M, Dagbert M, Desrochers C. Guide to the evaluation of gold deposits. CIM Spec 45, 1992. ISBN:0-919086-31-4.

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