A technique for identifying structural domain boundaries at the EKATI Diamond Mine

Engineering Geology 74 (2004) 247 – 264 www.elsevier.com/locate/enggeo

A technique for identifying structural domain boundaries at the EKATI Diamond Mine Michael W. Martin, Dwayne D. Tannant * School of Mining and Petroleum Engineering, Department of Civil and Environmental Engineering, University of Alberta, Edmonton, Alberta, Canada T6G 2G7 Received 3 September 2003; accepted 8 April 2004 Available online 9 June 2004

Abstract Over 10,000 discontinuity orientations from various sources at the EKATI Diamond Mine in northern Canada were collected and amalgamated into a common database. A new technique in which structural domains were determined in the area of three closely spaced active pits by quantitatively comparing stereonets from different regions was developed. The frequencies of discontinuity poles plotting in orientation windows on stereonets were determined and compared using a correlation coefficient to quantify the degree of similarity between different stereonets. Structural boundaries between regions were established wherever their associated stereonets display low correlation coefficients. The technique was able to determine boundaries in the vertical direction as well as radially in a number of pie-shaped zones extending around the kimberlite pipes. D 2004 Elsevier B.V. All rights reserved. Keywords: Structural domains; Joint sets; Diamond drill core; Correlation coefficient; Stereonet

1. Introduction The BHP-Billiton-operated EKATI Diamond Mine is located approximately 300 km northeast of Yellowknife in the Northwest Territories of Canada, an area of continuous permafrost. A number of kimberlite pipes are currently being mined. Three of these, Koala, Koala North and Panda, are in close proximity (Fig. 1). Surface mining has been completed at Koala North and underground mining begun. Underground

* Corresponding author. Fax: +1-780-492-0249. E-mail address: [email protected] (D.D. Tannant). 0013-7952/$ - see front matter D 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.enggeo.2004.04.001

operations will ultimately expand to include Koala and Panda pipes once open pit mining is finished. For both surface and underground mining methods, discontinuities such as joints and faults control excavation stability. Of critical importance to the safety and economic viability of underground operations will be stability of the open pit walls and exposed gloryhole created at the base of each pit. Proper design, monitoring and stabilization methods for these exposed faces requires knowledge of the orientation of dominant joint sets at various locations around the kimberlite pipes. To facilitate engineering analysis of rock mass stability, the approach usually taken is to divide the rock mass

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Fig. 1. EKATI mine looking southwest in 2002 showing three open pits under construction.

into zones or regions of similar geological conditions and hence similar physical properties and expected behaviour. The Eocene (53 Ma) age pipes were originally covered by small lakes prior to dewatering. Consequently, the kimberlite is located within a talik or unfrozen zone (Harvey, 2003). The geometry of each pipe in plan view is roughly circular. As seen in Fig. 2, the pipes are carrot-shaped with steeply dipping sides (80j and 90j), with several areas of reverse dip resulting in pipe wall ‘overhangs’. The diamonds themselves are generally much older than the host kimberlite pipe, which is the transportation system for the diamonds and not the actual source rock where their formation occurs.

The dominant Archean age country rock surrounding the pipes consists of medium-grained biotite granodiorite or quartz diorite, occasionally showing gneissose texture (Harvey, 2003). Generally, the host rock is unaltered and contains well-developed discontinuities that are planar and continuous, with minor locking of asperities and minimal joint aperture. Most discontinuities appear to be joints as no evidence of shear displacements along the discontinuities was found. The batholith surrounding the three pipes is generally covered by a thin (1 –5 m) glaciofluvial till. The host rock outside the talik zone is in a state of permafrost to a depth of approximately 300 m. The three pits are close to each other, and due to the relatively homogeneous nature of the host rock mass, share similar geologic domains. As all kimberlitic material is extracted, only structures in the host rock are considered. Most cases of rock slope instability at EKATI have been caused by individual discontinuities. This is because the intact rock is typically strong to very strong (unconfined compressive strength in the range of 50 to 200 MPa), with the result that the preexisting discontinuities (mostly joints) are the weakest link. At some locations, unfavourable joint orientations have necessitated the use of cable bolting along with rock mass monitoring systems. Given the importance of joints on the rock mass stability at EKATI, it was necessary to examine the spatial distribution of joints (especially their orientation) to identify regions or structural domains that exhibited similar joint sets. Geological contacts between different rock types could not be used to identify potential structural domains because the rock around each pipe was essentially the same. Diamond drill core logs in combination with surface discontinuity mapping were used to create a structural geology database of the region containing the orientation and coordinates of over 10,000 dis-

Fig. 2. Vertical cross-section showing the location of the kimberlite pipes and the open pits.

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continuities (Martin, 2003) gathered around three open pits: Panda, Koala North and Koala. The Panda pit will be the deepest, having terminated at approximately 165 m above sea level. Surface elevation of the pipe was 465 m, making the final pit 300 m deep. The pit is roughly circular in plan view with a diameter of about 700 m. Commercial production at Panda started in the fall of 1998 and completed in mid 2003. Underground mining of the kimberlite pipe commenced in 2004. The small Koala North pipe is already in the underground mining stage. Open pit mining from 2000 to 2001 removed the top 70 m of ore from the Koala North pipe, ending at 405 m above sea level where the pipe is only 75 m in diameter. The Koala pipe is larger in diameter than Panda, but operations will not proceed as deep due to less favourable diamond grade. It is projected that underground development will start in late 2005.

2. Sources and processing of structural data A variety of sources were available from which structural data could be extracted. The most important of these included diamond drill hole core logs (DDH), large-scale cell mapping (LSCM) and small-scale cell mapping (SSCM). Small-scale surface mapping was only performed in the Koala pit. In addition to discontinuity coordinate and orientation data, strength parameters were also available. One large database was created from these data sources. Table 1 shows the number of discontinuity orientations collected from the three available sources, which are discussed next.

Table 1 Structural geology data sources Pit

Data source

Koala Koala North Panda Sum

DDH DDH DDH

Koala Panda Sum

LSCM LSCM

Koala Sum

SSCM

Total

No.

Percentage of data

5889 1220 1469 8578

81

751 373 1124

11

834 834

8

10536

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2.1. Diamond drill core logging The logging of the core collected from diamond drill holes was the only method employed that is capable of determining orientations of structures that do not daylight on an exposed face. Consequently, data collected via this method gives information on structures existing at depth (i.e., below current open pit operations). Given that the objective of the geotechnical data collection was intended to aid future mine planning and design, the data collection was focused on obtaining information at depth using diamond drill holes. Eighty-one percent of the raw discontinuity orientations used in this paper came from diamond drill cores. Double-tube core barrels were used when drilling to maximize core recovery. This is especially important when looking for in-filled joints (clay and calcite) or fault gouge. Double-tube core barrels also minimize disturbance to the core, thus making it easier to determine its orientation. Both HQ and NQ core were drilled; HQ core has a nominal diameter of 65 mm while NQ has a nominal diameter of 50 mm. A clay imprint of the bottom of the hole is taken every 9.1 m (30 ft or every 3rd run). This imprint is matched to the top of the succeeding core run, the drill core is pieced together, and a reference line representing the drill hole is scribed on each core using a procedure similar to that described by Call et al. (1982). Fracture orientations are then measured relative to the reference line and core axis. Unfortunately, in areas of highly fractured core and/or poor core recovery this reference line is frequently lost. Upon completion of the hole, electronic instrumentation such as a Maxibore (optical instrument) or Gyroscope (inertial instrument) was lowered down the hole to determine the actual orientation of the drill hole itself. The drill hole survey information is required when determining discontinuity orientations. The survey is also used to determine the amount of drill hole deviation that occurred. The recovered core is logged for other geotechnical parameters including joint roughness, alteration and infilling. The depth along the drill hole to discontinuity features is noted. Orientations of discontinuities in the drill core are measured relative to the core axis and a reference line using a goniometer, as shown in Fig. 3.

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radial distance, angle and elevation). After the appropriate conversions and transformations, all data were placed into a common database. 2.2. Large- and small-scale cell mapping

Fig. 3. Core orienting goniometer.

Spatial coordinates for each measurement were then computed from the orientation and collar coordinates of each drill hole. Clustering of data sampling can be seen in Fig. 4, where all 8578 drill hole sample points are plotted. The 1958 points from surface mapping are also shown and are distinguished by being located near the top of the sample clustering and by occurring in horizontal arcs that define the open pit bench locations. As stereonets are used for dealing with orientation data, the plunge and trend of each discontinuity’s pole was calculated. It is common for open pits to be separated into pie-like pieces that represent different structural domains. In order for structural domains to be analyzed later, a central reference point was therefore assigned to each open pit and all nearby data points were assigned cylindrical coordinates (i.e.,

Scan-line mapping is a systematic spot sampling method in which a measuring tape is stretched along the bench face or outcrop to be measured. For all discontinuities along the tape, the orientation, length, roughness, filling type and thickness are recorded (Nicholas and Sims, 2000). Cell mapping is similar to the above but involves identifying the above discontinuity features within a window on the bench face. This method is sensitive to the condition of the exposed bench face (i.e., muck obscuring face, obstruction due to ravelled material, degree of damage from blasting, etc.). In large-scale cell mapping, only larger discontinuities that extend for the full height of the bench (15 m at EKATI) or longer are recorded. In small-scale mapping, a window on the bench face 1.5 m up from the bench floor and extending horizontally is mapped for all discontinuities (measurements made at midheight). Cell mapping may be used to indicate if the discontinuity crosses completely through the window or terminates inside, thus giving a rough indication of a discontinuity’s trace length (something not possible when logging diamond drill core). Large- and smallscale cell mapping provided 11% and 8%, respectively, of all the raw discontinuity orientation data used in this paper.

Fig. 4. Oblique view looking NW showing the locations of 8578 discontinuity measurements.

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2.3. Correcting for bias in orientation data Before any analysis is performed on the discontinuity orientation data set, corrections must be applied to account for the bias owing to the orientation of the sampling line (be it drill hole data or any form of surface window and scan-line mapping). This bias arises from the fact that the orientation of drill holes and of scan-lines commonly lack sufficient variety to ensure a representative sampling of the joint sets present in the domain (Terzaghi, 1965). Note also that data collected from surface mapping is often along a horizontal line, whereas drill holes commonly tend towards the vertical. This fact alone can lead to serious differences in measured orientation of dominant discontinuity sets (Park and West, 2002). A linear sample line will tend to preferentially intersect those discontinuities that have a pole at the same orientation as the sample line, thereby tending to heavily bias the frequency of occurrence of those discontinuities. In order to reduce the bias introduced by the sampling method, all joints are adjusted using to the angle of intersection between a scan-line and the normal to the discontinuity, d. Essentially, this is a declustering procedure whereby each joint orientation is assigned a weight based on its probability of

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occurrence. The angle of intersection d can be determined using Eq. (1) (Priest, 1993). cos d ¼ Acosðan  as Þcos bn cos bs þ sin bn bs A

ð1Þ

Note that an and bn are the trend and plunge of the joint pole and as and bs are the trend and plunge of the scan line or borehole. Once d is determined, the Terzaghi (1965) correction factor, given in Eq. (2), can be applied. Terzaghi Correction ðTCFÞ ¼

1 cos d

ð2Þ

By applying the correction factor to joint sets, their adjusted frequencies of occurrence become equal. To simplify later processing of the data, the correction factor associated with a particular joint was rounded to the nearest integer; this integer represents calculated frequency of occurrence of this particular joint. In other words, the continuous function represented by Eq. (2) was replaced with a simple step function such that the frequencies of occurrence or correction factors for each joint were assigned values of 1, 2, or 3 corresponding respectively to ranges of d varying from 0j to 48j, from 48j to 66j and from 66j to 90j. This is illustrated in Fig. 5 for discontinuity data recorded from an

Fig. 5. (a) Raw discontinuity orientation data from a diamond drill hole showing the correction factors used to correct for orientation bias in three different zones and (b) location of blind zone associated with a diamond drill hole (70j from borehole axis).

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At the EKATI mine, the practice when logging drill core is to classify any discontinuities with an angle of intersection d greater than 70j as a core axis fracture because in practise reading the dip from the goniometer becomes unreliable at these angles. Unfortunately, there is a negative side effect to the core axis classification, namely that discontinuities with intersection angles greater than 70j usually go unsampled along a given scan line or borehole. Thus, for every sample line (e.g., drill hole), there is an associated blind zone where few poles are recorded (Yow, 1987). As this data is effectively censored, or not sampled, weighting cannot restore the underlying population. A 20j blind zone where relatively few discontinuity poles plot for data collected from a single drill hole is shown in Fig. 5. Any discontinuities with poles that occur in the blind zone are often not sampled. One way to identify features located within the blind zone is to obtain discontinuity orientations in a nearby drill hole that is orientated such that their blind zones do not overlap. This approach is preferred as applying large correction factors (>3) to the few poles that do plot in the blind zone can degrade the quality of the data set (Yow, 1987). Fig. 6 shows the effect of the bias correction applied to the data plotting in Fig. 5. A comparison of contours for the raw or uncorrected data with the corrected data shows that the steeply dipping discontinuities that were less likely to be intersected by

inclined diamond drill hole. The orientation of the diamond drill hole is shown on a stereonet along with the poles of all associated discontinuity orientation measurements. The conical zones encompass discontinuity data that fall within the three d ranges, each with a different correction factor to be applied. The weighting of poles rises from 1 to 3 when moving away from the diamond drill hole orientation. Reproducing discontinuity data such that the total number of orientation occurrences in the database was equal to the correction factor created an orientation bias-corrected database. Rounding to the nearest integer introduces some error, but was deemed sufficient to remove most of the orientation bias. A comparison between use of Eq. (2) and a step-wise approximation of Eq. (2) showed only minor differences and the use of integer values greatly simplified subsequent data processing in spreadsheet form. Table 2 shows the number of additional or duplicated data points (number of correctors) added to the database once the correction for orientation bias was applied. The maximum weighting factor applied to any discontinuity measurement is approximately 3 (i.e., 1/cos 70j). This is necessary because when the angle of intersection approaches 90j, the correction factor goes to infinity. Therefore, the logged discontinuities or scan line mapped discontinuities having an angle of intersection greater than 70j are given a weighting of 3.

Table 2 Raw and bias corrected structural data set No. of correctors

Total

Percent correctors

q*

5889 1220 1469 8578

2869 557 492 3918

8758 1777 1961 12 496

33% 31% 25% 31%

0.94 0.96 0.98

LSCM LSCM

751 373 1124

601 322 923

1352 695 2047

44% 46% 45%

0.93 0.93

SSCM

834 834

648 648

1482 1482

44% 44%

0.87

10 536

5489

16 025

34%

Pit

Data source

No. of raw data

Koala Koala North Panda Sum

DDH DDH DDH

Koala Panda Sum Koala Sum Total

* Correlation coefficient between raw and corrected data using technique presented later.

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Fig. 6. Contour plots of (a) data shown in Fig. 5 and (b) data after applying the bias correction.

the 60j plunging drill hole become more dominant after the correction is applied. Nevertheless, a blind zone is still present and can only be overcome by having data collected from a borehole (or scan line) in a different orientation.

3. Structural domains The delineation of structural domains and the definition of the characteristics of the joint sets within each domain are essential steps required before design of surface or underground excavations

can proceed (Nicholas and Sims, 2000). A variety of methods have been developed to divide a rock mass into domains. A domain represents a volume of rock mass with similar characteristics, typically defined by the orientations of dominant joint sets, their strength characteristics and the rock type. When dealing with joints or other such discontinuity orientations, the term structural domain is applied. While other joint characteristics such as surface roughness, infilling, spacing, etc., are important, the joint orientation is usually the principal characteristic affecting the behaviour of excavations in jointed rock masses.

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3.1. Joint set identification

3.2. Techniques for identifying structural domains

A stereonet is a projection of orientation data on a reference hemisphere such that the relative frequencies of discontinuity orientations in an area can be evaluated. Many techniques exist for analysing joints plotted on a stereonet to identify joint sets (e.g., Shanley and Mahtab, 1976; Mahtab and Yegulalp, 1982; Dershowitz et al., 1996; Hammah and Curran, 1998; Marcotte and Henry, 2002; Zhou and Maerz, 2002). These techniques are useful for processing a collection of joint orientation measurements taken from one specific structural domain to obtain properties for each of the joint sets. The more advanced techniques use more than just the discontinuity orientation to identify joint sets. For example, Zhou and Maerz (2002) present a multivariate clustering technique that groups discontinuities into joint sets using orientation, spacing and roughness. They also presented a graphical technique for visualizing the joint sets plotted on a stereonet at multiple locations along a borehole. Although the data is plotted along the borehole, determining the boundary between structural domains is still somewhat subjective. An important step that must be completed before performing detailed joint set analysis is to determine or verify the structural domains boundaries such that only data from one domain is used for subsequent joint set analysis. Otherwise, misleading or inaccurate conclusions may be obtained. Often, this can be easily accomplished using geological contacts between different rock types as the structural boundaries. When traversing around any of the open pits in the granodiorite rock mass at EKATI, one can observe subtle variations in joint orientations and spacing. The pit walls are all located in the same rock type and the locations for structural domain boundaries are not obvious. Therefore, a new method was devised to quantitatively use the orientations and the spatial distribution of the joints to identify the boundaries. Conceptually, this method for domain identification involves plotting stereonets of joint data for various volumes of the rock mass, then looking for significant differences between stereonets that can be attributed to a structural change between the physical areas they represent (i.e., a structural boundary).

Traditionally, domains have been delineated by analyzing discontinuity orientations plotted as poles on a stereonet and determining the dominant joint sets and then visually comparing stereonets with data taken from different areas of the rock mass. Experienced geologists or engineers then usually subjectively determine where sufficient differences exist between stereonets from adjacent regions in the rock mass to warrant the creation of a structural boundary. However, when fracture orientations appear dispersed and random on the plots, visual comparisons are not sufficient to determine whether the samples were obtained from the same structural domain (Miller, 1983). Using joint orientations measured along a scan line, Piteau and Russell (1971) and Piteau (1973) used a cumulative sums technique to determine trends in joint orientations (dip or strike) relative to a particular reference value and were able to determine the location along the scan line where significant and consistent changes in joint orientation occur, hence, indicating the location of a structural domain boundary. This technique treats joint dip and strike separately and can only deal with the presence of multiple joint sets by filtering the scan line data using previous information about dominant joint set orientations before application of the cumulative sums technique. Furthermore, it is difficult to analyse and interpret data coming from multiple sources and orientations. At the EKATI Mine, the host rock for the three kimberlite pipes is the same around the three pipes and the joint strength characteristics such as roughness and alteration are essentially constant everywhere. Although joint spacing and trace length are observed to vary from one location to another around the open pits, the use of discontinuity orientation data to identify the structure domains was deemed most useful given the large amount of orientation data that had been collected, much of it coming from oriented core. Hence, the orientation characteristics of the discontinuities themselves at different locations around the pipes were used to determine structural domains. Another approach could be to use joint or discontinuity spacing to help partition the rock mass into structural domains using the approach suggested

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by Escuder Viruete et al. (2001). This approach ignores joint orientations and uses geostatistics to extrapolate fracture density from known locations such as boreholes to the nearby volumes of rock. Dershowitz et al. (1998) presented a method for using discontinuity orientations and spacing to define transitions from one structural domain to another along a scan line or a borehole. They determined the mean dip and dip direction over an interval of a borehole and a measure of orientation dispersion to quantify the overall joint orientation characteristics. The joint orientation and fracture frequency were then tracked for different intervals along a borehole to identify potential boundaries between structural domains. One problem with this approach is that two different populations of discontinuity orientations can give similar values for the mean dip and dip direction and dispersion, and, hence, these summary statistics do not capture the full distribution of orientations. A new method is presented to accomplish structural domain identification in a quantitative manner. The discontinuity spacing was not used here. Other discontinuity features such as joint roughness, spacing, persistence and trace length were not used to determine the structural domains, but are used to characterize the properties of joint sets that lie inside each domain once its boundaries are identified. The specific properties of joint sets that were eventually found within each domain are beyond the scope of this paper. The new method involves the following procedure to identify the domains: 

Select data from a particular region in space. Regions may be blocks, pie slices, layers or other somewhat arbitrary divisions of space. Using knowledge gathered from local geology in conjunction with operational experience at the mine site, appropriate shapes and volumes of the rock mass can be selected.  Plot discontinuity orientation data for each region as poles on a stereonet.  Determine the frequency that discontinuity poles plot in a number of ‘windows’ on the stereonet.  Calculate a correlation coefficient that compares the frequency of discontinuity occurrence in each window between two stereonets representing data from two adjacent regions.

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Repeat the process using data from different regions in space and plot the correlation coefficient versus location.  Low correlation coefficients signify significant differences between stereonets and indicate the existence of structural domain boundaries. A major advantage of this technique is that knowledge about joint sets is not required; all discontinuity data in a given volume is simply statistically compared or correlated to an adjacent volume. The technique could also be modified to also include information such as fracture frequency, joint roughness, joint infilling, rock type, etc., using multivariate analysis.

4. Stereonet representation of data When establishing structural domains, the discontinuity orientations of two regions are analyzed to see if they are similar enough to be grouped into one region. The stereonet (Leyshon and Lisle, 1996) is a useful tool for displaying discontinuity orientations, which are typically plotted as poles on the stereonet. The degree of similarity between two stereonets can be obtained by looking in a given trend/plunge window and comparing the relative frequencies of pole occurrence. If most windows contain similar frequencies of poles, it is justifiable to include the two areas in the same domain. It is important to normalize the data and to compare frequencies, not the actual number of poles, in a given orientation range. Choosing appropriately sized windows within the stereonet can be difficult. Windows too large tend to overly smooth the data, thereby masking important trends. Windows too small inevitably contain few data, and any trends are rendered unrecognizable due to the sporadic plotting of random poles to discontinuities. The EKATI data set has a large number of discontinuity orientations. One may argue that a window that is 20j trend by 10j plunge is the smallest size window that is practical when aiming for an average of at least four discontinuity poles plotted per window on the stereonet. This would give 162 windows on the stereonet. Having smaller window sizes would result in many containing little to no discontinuity data.

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The optimal window size depends on the number of discontinuity orientations that will be plotted. Even though the corrected discontinuity orientation database had over 10,000 measurements, 162 windows were too many for the sizes of the data subsets that needed to be plotted. Fewer and, hence, some larger windows were desired. By considering the influence of discontinuity orientations on rock slope stability, poles of discontinuities clustered near the centre of a stereonet, representing subhorizontal sets, could be placed in bigger windows. From an engineering behaviour point of view, the trend of such shallow dipping features is often not as important as the steeply dipping discontinuities, and all shallow dipping discontinuities can be grouped in the same window. On the other hand, poles near the perimeter of the stereonet represent sub-vertical features, the trends of which are very important with respect to the orientation of a bench face or gloryhole wall. Thus, it is desired to have larger windows near the bottom of the hemisphere with the windows progressively becoming smaller towards the sides. Mahtab and Yegulalp (1984) used such a division of the hemispherical surface for their analysis. This division scheme is pictured in Fig. 7 and when plotted on a stereonet, the divisions shown in Fig. 7 result in 100 orientation windows with approximately equal areas. This facilitates statistical comparison of the number of poles lying in each window on the stereonet. Having 100 windows also makes it easier to interpret the frequency of pole occurrence in any given window in terms of percentage. The use of more or less windows

and windows of different shape does not affect the technique presented here for identifying structural domains.

5. Stereonet similarity using the correlation coefficient The primary tool for identifying a structural domain boundary is the ability to quantify the discontinuity orientation differences between two regions in the rock mass, their data represented on stereonets divided into 100 nearly equal-area windows. This comparison is a statistical problem. A statistical parameter known as the covariance is used to assess the relationship between similar windows of the two regions in the following way. The data are frequency of pole occurrence in a particular window; the data from two regions are represented by random variables X and Y. If X tends to be large when Y tends to be large, and X is small when Y is small, then X and Y will have a positive covariance. The standardized covariance is known as the correlation coefficient. The correlation coefficient gives the strength of the association between the two variables. When determining the correlation between the stereonets of two regions there will be 100 X variables and 100 Y variables. The correlation coefficient q can then be calculated via Eq. (3) (where n is equal to 100, the number of windows selected for use on the lower hemisphere). n X

Xi Yi =n 

i¼1

n X

! Xi =n

i¼1

n X

! Yi =n

i¼1

q ¼ vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u2 !2 32 !2 3 u X n n n n X X X u4 5 4 t Xi Xi =n  Xi =n Yi Yi =n  Yi =n 5 i¼1

i¼1

i¼1

i¼1

ð3Þ

Fig. 7. Lower hemispherical surface divided into 100 windows.

The covariance term is the numerator in Eq. (3). By dividing the covariance by the standard deviations of the two variables, the correlation coefficient will always be between 1 and 1; providing an index that is independent of the magnitude of the data values. A q value of 1 entails perfect negative correlation, 0 entails no correlation and 1 entails perfect positive correlation. In the latter case, the frequency value of

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every window in region 1 would be the same as the frequency value of every window in region 2 (i.e., the stereonets are identical). If these results were obtained it would be justifiable to combine regions 1 and 2 into a single representative domain. This method is somewhat similar to the approach used by Miller (1983), although they used a chisquared test to evaluate structural homogeneity between stereonets. The chi-squared test has limitations in terms of the minimum number discontinuity orientations needed in the windows. Kulatilake et al. (1990) used Miller’s (1983) and Mahtab and Yegulalp’s (1984) methods combined with a visual comparison of stereonets to identify structurally homogeneous regions. The proposed method has advantages in that windows containing no discontinuities are easily accounted for and clustering of poles into joints sets is not required.

6. Similarity of data sources The ability to calculate correlation coefficients between stereonets is also useful for purposes other than identifying structural domain boundaries. For example, the data obtained from different logging techniques located within the same open pit can be compared to identify anomalies that may indicate certain data types not being as reliable as others. All discontinuity orientations from one source were compared to all discontinuity orientations from another source within each open pit. Table 3 is a summary table showing the correlation coefficients between various data types. Table 3 Correlation coefficients between data types using raw and corrected data from each pit location Pit

Data source

Raw data

q

Corrected data

q

Koala

DDH LSCM

5889 751

0.26

8758 1352

0.61

Koala

DDH SSCM

5889 834

0.30

8758 1482

0.73

Koala

LSCM SSCM

751 834

0.77

1352 1482

0.73

Panda

DDH LSCM

1469 373

0.27

1961 695

0.59

257

Table 3 shows that low correlation coefficients (0.26 – 0.30) are obtained when raw discontinuity orientation data collected from diamond drill holes are compared with raw discontinuity orientations collected from cell mapping. This is expected given that the diamond drill holes plunge steeply and the scan lines used for the cell mapping are horizontal. Therefore, the orientation bias is quite different for the two sources of data. When the raw data from the small- and large-scale cell mapping are compared with each other one obtains a much higher correlation (0.77) as expected since both sources of data have similar orientation bias. Application of the step-wise correction factor (Eq. (2)) helps remove the effects of orientation bias and greatly improves the similarity between discontinuity orientations obtained from different methods. The correlation coefficients between the data from diamond drill holes and cell mapping is at least two times higher once the correction is applied. The last column in Table 2 shows the correlation coefficient between raw and corrected data acquired with the same collection method. The data obtained from diamond drill holes has a high correlation. After correcting the data, the correlations between the data collection methods (i.e., diamond drill hole data, large- and small-scale cell mapping) are quite good, ranging from roughly 0.6 to 0.7. These data types appear to support one another, but they are not identical and may need to be treated separately. The magnitude of the correlation coefficients probably reflects both inherent limitations in the ability for one method to fully sample a population of discontinuity orientations as well as different locations from where the data were acquired since all the data are treated as if they come from one structural domain. As diamond drill hole data are by far the most abundant, they will be solely used when determining the structural domains in the region. It is recommended that the surface mapping data be used to supplement the core logs. For instance, when working in a certain area of an open pit it will be in a certain structural domain determined from diamond drill hole data. Cell mapping represents additional knowledge and can be used to help make decisions in the vicinity of where the mapping occurred. Also, note that with the diamond drill hole data, joint sets are considered ubiquitous within the domain. Another strength of cell

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mapping is in identifying discrete planes or discontinuity intersections along which failure is probable. It is now possible to delineate the structural domains within each open pit, making use of diamond drill hole data. The diamond drill hole database corrected for orientation bias is the only data used in the next section. No effort was made to compare results with a similar analysis using the raw data, because fundamentally only bias-corrected data should be used for identifying structural domain boundaries.

7. Structural domain determination 7.1. Depth correlations (slice to slice comparison) Of particular importance to the mining operations at EKATI are changes in rock mass properties and discontinuity orientations with depth. This knowledge is needed to answer questions about whether underground operations will be working in a similar structural environment as surface operations. To determine if structural changes are occurring with depth, each open pit was analyzed independently. For all cases, horizontal slices encompassing all data at that level were used to vertically segregate the data near each open pit. Table 4 depicts the slices and number of discontinuity orientations used for the Koala, Koala North and Panda mining areas. Somewhat arbitrarily, a 60-m slice thickness was used at Koala whereas a 50-m slice was used at Panda and Koala North where the data did not cover as large a vertical extent.

Table 5 Correlation coefficients between slices Slices compared

Koala

Koala North

Panda

1–2 2–3 3–4 4–5 5–6 6–7 7–8

0.82 0.84 0.78 0.70 0.67 0.48 0.29

0.63 0.77 0.49

0.70 0.88 0.79 0.82 0.56

A given vertical distance was not considered if relatively few points occurred within it. This was usually the case at depth. As well, some very near surface data were not included in the analysis. Over 94% of the data were utilized for each pit. The next step involved calculating the correlation between horizontal slices in the same open pit. In this way, it is possible to see if changes occur with depth, indicating perhaps a structural boundary. The results of this analysis are shown in Table 5. Table 5 indicates that for the Koala area, correlations are lower for slices 7 and 8, thereby lowering the overall correlation. It is inferred that around 75 m above sea level some structural change occurs. Table 4 shows that slices 7 and 8 contain fewer data points than most others, so this difference could partially be attributed to lack of representative data. However, the amount of data contained in the lower slices is still substantial, and the change in correlation is significant enough to justify dividing the Koala area into two separate domains in the vertical direction, with the boundary located at the elevation of the boundary between slices 6 and 7. Therefore, it appears that the upper portion of the rock mass at Koala has a fairly

Table 4 Horizontal slices for each open pit showing the total number of corrected discontinuity measurements contained in each slice Slice

1 2 3 4 5 6 7 8

Koala

Koala North

Panda

Bottom elevation (m)

Top elevation (m)

Data

Bottom elevation (m)

Top elevation (m)

Data

Bottom elevation (m)

Top elevation (m)

Data

375 315 255 195 135 75 15  45

435 375 315 255 195 135 75 15

2001 2447 1036 749 746 638 401 344

400 350 300 250

450 400 350 300

620 387 373 381

400 350 300 250 200 150

450 400 350 300 250 200

197 471 475 339 180 181

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consistent distribution of discontinuity orientations but below an elevation of about 75 m the discontinuity orientations begin to change and the changes continue with depth. From Table 5, Koala North and Panda are analyzed in similar fashion. The last slice in each appears to be substantially less correlated to those above. In the case of Koala North, it may be incorrect to assume that a structural boundary exists at that depth due to lack of information below. Once additional diamond drill hole data are available at greater depths, this decision can be made with more certainty. For now, it is assumed that only one vertical domain exists at Koala North. Concerning the Panda data, lack of data below the last slice might lead to the same conclusion as at Koala North. However, the change in correlation is so large (occurring at approximately 200 m above sea level) that it cannot be ignored. Thus, it is suspected that two vertical domains exist in the Panda area. While the upper domain is well sampled, a relative lack of data in a possible lower domain will preclude further analysis for the time being. 7.2. Depth correlations (moving slice method) The Koala area contains more data than both Koala North and Panda combined, thus, it is possible to place more accurately the vertical structural boundary. The previous analysis was limited by the selection of fixed horizontal slices (Table 4), thus, a boundary could only be determined to the nearest pre-selected slice (60 m vertical resolution). Using a moving window analysis, the boundary can be determined to the nearest 15 m. In the moving window analysis, two overlapping 60 m horizontal slices containing discontinuity orientation measurements are compared. A vertical overlap of 30 m was used. The two slices are moved together in 15-m vertical increments and the comparison is repeated. Fig. 8 shows a plot of the correlation coefficient versus elevation of the boundary between the two moving slices. The lowest correlations would occur when two slices straddled a structural boundary, the midpoint of the overlapping sections was taken to be the division line. While Fig. 8 shows scatter, the overall trend is quite clear. It appears that around 75 m elevation (above sea level), the lowest correlation occurs, therefore indicating a horizontal boundary. This agrees

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Fig. 8. Koala vertical correlation versus depth using a moving 60-mhigh slice.

with the previous finding; therefore, it seems that the fixed windows were fortuitously chosen, as they happened to correspond to the 75 m elevation. Since there is good agreement, no further effort need be put into the moving window analysis (i.e., varying slice depths and offsets) in order to define more clearly the trends. In summary, the Koala area is subdivided into two domains, separated at a horizontal boundary 75 m above sea level. 7.3. Radial correlations In current practice, the structural domains at the three open pit mining areas are divided into pieshaped pieces. Due to the nature of kimberlite pipe emplacement where a weakness must have existed in the earth’s crust to allow transport to surface, as well as new discontinuities created upon emplacement, this pie-shaped division of domains seems reasonable. Practically speaking, domains whose boundaries are perpendicular to bench faces make stability analysis much easier to visualize and compute. Each discontinuity measurement was assigned cylindrical coordinates, so it is possible to create domains in the above fashion. Taking an arc (i.e., pie piece) containing drill hole data, rotating it in increments to 360j, and comparing

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the coefficients of correlation between adjacent overlapping arcs enabled structural boundaries to be identified radially around the three open pits. The arc size and increment angle (which affects the degree of overlap) were chosen after consideration of the borehole locations and their influence on the results. The arc size and angle were then varied in order to smooth the data and identify the dominant changes in the correlation coefficient. Initially, an arc angle of 120j was chosen. Smaller angles had problems capturing sufficient data due to the sampling distribution (borehole locations). The angle was also increased to 150j to see how sensitive the results are to the arc angle. Using an arc larger than 150j overly smoothed the data, therefore potentially masking a domain boundary. A rotation increment of 15j was initially tried, which gave an overlap of 105j with a 120j arc. This rotation increment was found to be too small and masked any trends in the correlation coefficient. Once the increment was increased to 20j and 30j, the trends became progressively clearer. With increments larger than 30j the precision is lost when locating the domain boundary. Note that the optimal arc angles and increment angles are a function of the data quantity and spacing. This moving window analysis is considered superior to a static window analysis. In a static analysis, the pit is divided up into a number of pie slices and each slice is correlated to its neighbours. With a static window, the effects of drill hole blind zones may artificially reduce correlations. With a moving window, these effects are minimized, although not eliminated, by smoothing the data. If relatively low correlations were found between two concurrent arcs, the bisector of the two mid-arc angles was taken to be the division line; the lowest correlation would be found when concurrent arcs straddle the domain boundary. The results for the three pit areas are plotted in Fig. 9. For Koala, the correlation coefficient occurring around 245– 270j is relatively low, leading to the belief that a structural boundary exists along this bearing. The correlation near 75– 130j is also quite low, although to a lesser extent than the previous case. Thus, it was determined that two structural boundaries exist at around 90j and 255j. There is no correlation magnitude or threshold that dictates where a structural

Fig. 9. Correlation plots between pie-shaped regions for each pit area; the angle is a bearing from North.

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boundary should be placed; rather, the overall trends of the correlations are observed, and major troughs correspond to boundaries. After dividing all the data around the Koala pipe into two domains using 90j and 255j, the correlation coefficient between the data lying in the two radial domains was found to be 0.58, confirming the distinct zones. Stereonet plots of the discontinuity poles for both domains are shown in Fig. 10. Both domains contain a dominant sub-horizontal joint set and steeply dipping joints. However, there are differences in the NE – SW striking joint set between both domains.

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These findings agree favourably with domains previously in use at Koala, where boundaries are located at approximately 100j and 260j. Insufficient information is available to analyze the lower domain located below 75 m above sea level, although a preliminary analysis shows that two major radial boundaries still exist but are offset slightly from the domains that lie above. In summary, four domains are evident in the Koala area, although at this time, only the upper two radial divisions and the elevation division are well delineated. The radial domain boundaries for all pits are shown in Fig. 11.

Fig. 10. Stereonet of contoured discontinuity poles in Koala structural domains 1 and 2.

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Fig. 9, the domain boundaries should be located at about 130j and 255j. There is some agreement between the two systems, although by the correlation method the domain boundaries at Koala and Panda are actually quite similar (both have a 255j boundary), perhaps indicating that emplacement of the kimberlite pipes occurred along the same plane of weakness and thus created similar radial jointing patterns. In summary, at least three domains have been found in the Panda mining area, although at this time only the upper two are well delineated.

8. Conclusions

Fig. 11. Summary of structural domains near three kimberlite pipes.

Similar procedures were carried out on both the Koala North and Panda mining areas. Results are plotted in Fig. 9. At Koala North, three boundaries are evident, occurring at 45j, 165j and 315j (Fig. 11). Due to lack of data at depth, these domains are simply extrapolated downwards. The correlation coefficients between data located in adjacent domains are 0.40, 0.45 and 0.72. The correlation of 0.72 occurs across the boundary at 315j and is obviously less significant than the others, though it may still be enough to warrant separate treatment. Further experience with this technique of identifying structural domains at other locations is needed before better guidance can be offered when deciding what correlation value(s) signify valid transitions from one domain to another. Analysis for Panda (Fig. 9) used only data from the upper domain (i.e., elevation >200 m). Insufficient information was available to analyze the lower domain. In the Panda upper area, two structural boundaries are quite evident, occurring at approximately 130j and 255j. The correlation between these two areas is 0.86. This is perhaps high enough to justify combining the areas such that one domain sufficiently describes the entire Panda area. Domain divisions previously in use by BHP-Billiton at Panda are located at 23j, 158j and 248j. From

A method has been proposed to delineate structural domains in a rock mass that is composed of essentially one rock type given discontinuity orientation data. The method is more quantitative, unbiased and applicable than previously used methods. The method can be easily implemented in a spreadsheet or standalone computer program. Once a database of discontinuity orientations and coordinates in space has been established, stereonet plots of data from selected regions are generated. The frequencies of discontinuity poles plotting in a number of orientation windows on the stereonets are then determined. Stereonets from different regions are compared with each other using a statistical measure, correlation coefficient, to quantify the degree of similarity between them. Structural domains boundaries between regions can be established wherever their associated stereonets display significant differences (relatively low correlation coefficients). The technique was found to work best using a moving volume analysis in which discontinuity orientations found within two similar shaped, partially overlapping volumes of rock are compared as the volumes are translated or rotated in space. The use of correlation coefficients to determine structural domains was applied to a large database (10,000 measurements) of discontinuity orientations at the EKATI Diamond Mine. The method was able to determine possible boundaries in the vertical direction as well as in a number of pie-shaped zones extending around the kimberlite pipes. Knowledge of these structural domain boundaries allows a better

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understanding of the distribution of geologic structures and their implications on surface and underground excavation stability at the EKATI Diamond Mine. The proposed method works well if many discontinuity orientations are available and they are well dispersed throughout the volume of rock of interest. Typically, corrections due to orientation bias from boreholes or scan lines should be applied before attempts are made to identify structural domain boundaries. The proposed method can be extended to incorporate multivariate statistics to allow other discontinuity characteristics such as space and roughness to be incorporated into the analysis.

Acknowledgements We extend our gratitude to the engineering and geology staff at the EKATI Diamond Mine for their significant assistance during the data collection stages of the program. A NSERC Collaborative Research and Development Grant and BHPBilliton provided funding for this research. Jody Todd, Darin Anonby and Gary Baldwin granted access to geotechnical data. Larry Long provided tours and computer models of underground mining operations. Dave Gill of Connors Drilling kindly answered any questions pertaining to diamond drilling. Suggestions to broaden the literature review from an anonymous reviewer helped strengthen the historical context of this work.

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