__Clark Pakalnis AN EMPIRICAL DESIGN APPROACH FOR ESTIMATING UNPLANNED DILUTION

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AN EMPIRICAL DESIGN APPROACH FOR ESTIMATING UNPLANNED
DILUTION FROM OPEN STOPE HANGINGWALLS AND FOOTWALLS
L.M. Clark
University of British Columbia
R.C. Pakalnis
University of British Columbia
ABSTRACT
Open stope mining within Canada is the most common method of underground mining. The sizing of the
individual stopes is a major area of study at the University of British Columbia. The introduction of the Cavity
Monitoring System (CMS) has enabled one to quantify the performance of a particular design, thereby enabling
identification of parameters critical to the stability of open stope surfaces. During the past two years UBC has
developed a database of CMS surveys detailing the stability of over 100 open stope hangingwalls and
footwalls. These have been correlated to an existing qualitative method of design, the Modified Stability
Graph. A factor is introduced termed “ELOS” (equivalent linear overbreak/slough) which is a measure of the
unplanned dilution for a particular stope surface thereby enabling one to quantify stope desing in terms of
potential amount of wall slough.
1.0 INTRODUCTION
The dilution and recovery realized for a particular open stope are a measure of the quality
of the design and mining practice. A good design is one that maximizes recovery and
minimizes dilution, bearing in mind that the two measures are inter-dependent (i.e. achieving
a certain recovery may only be possible at the expense of accepting a certain level of
dilution). Figure 1 is a generalized flowsheet showing the general progression for
delineating and ultimately excavating an open stope and the various factors which may
impact dilution and recovery along the way.
Quantifying dilution and recovery in open stope mining has traditionally been very difficult
due to the non-entry nature of the mining method. Thus dilution and recovery are often
evaluated based on visual observation and/or reconciled from data such as: design tonnes vs.
mucked tonnes; design stope grade vs. mill head grade; and design stope grade vs. muck
sample grades. Due to inherent inaccuracies, evaluations of dilution and recovery with these
methods are often global estimates at best.
In recent years, actual surveying of open stopes has been made possible through the
application of non-contact laser rangefinders. The dimensions of excavated stopes can now
be accurately determined and quantifiable values for dilution and recovery can be calculated.
Over the past two years, the University of British Columbia has been compiling a database
of stope surveys with the objective of developing an empirical method for estimating the
volume of overbreak/slough from open stope hangingwalls and footwalls. Correspondingly,
the volumetric estimates can be used to help predict the dilution that may be associated with
a particular stope design.
For this study, all of the stope surveys were conducted using the Cavity Monitoring System
(CMS), refer to Figure 2. For details on this system refer to: Miller et. al., 1992; and Mah
et.al., 1995. 
2.0 DEFINING DILUTION
Dilution can be defined as the contamination of ore by non-ore material during the mining
process (Wright, 1983). The consequences of this contamination are as follows:
· the actual amount of material extracted will be larger than what is necessary to obtain the
same equivalent metal content.
· the grade of the run-of-mine ore will be lower than the estimated in-situ grade.
The consequences stated above directly increase the cost of production (ie: cost per unit
weight of metal mined) since the waste material must be: mucked; transported; crushed;
ground; processed and stored as tailings. Furthermore, a mill is designed to operate at a
given mill feed grade, lower grade material can unbalance the system resulting in decreased
mill recoveries. The mining of waste material also results in an opportunity cost since ore
is displaced by waste within the overall mine/mill circuit. This displacement effectively
increases the mine life which spreads the cash flow over a longer period of time, resulting
in an overall decrease in net present value.
Scoble and Moss (1994) define Total Dilution as the sum of the Planned Dilution and the
Unplanned Dilution. Where:
Planned Dilution is the non-ore material (below cutoff grade) that lies within the designed
stope boundaries (mining lines) as determined by: the selectivity of the mining method; the
continuity of the orebody along strike and along dip; and the complexity of the orebody
shape.
Unplanned Dilution is additional non-ore material (below cutoff grade) which is derived
from rock or backfill outside the stope boundaries (mining lines). Incorporation of this 
material is due to: blast induced overbreak; and/or sloughing of unstable wall rock or
backfill. 
Figure 3 is a schematic illustrating the above.
From the above dilution definitions it can be appreciated that CMS stope surveys can
only be used to quantify Unplanned Dilution, thus, this study only looks at half of the
dilution equation. Planned Dilution is more difficult to quantify and becomes increasingly
difficult with increasing orebody complexity. Although Planned Dilution is equally as
important, it is deserved of study on its own. The reader is referred to: Stone, 1985;
Puhakka, 1990; and Braun, 1991 for a treatise on the factors influencing Planned Dilution.
Various methods for calculating dilution exist. For this reason one should be very cautious
when comparing values from different operations. Scoble and Moss (1994) state that the two
most common methods are based on tonnage as follows:
1. Dilution = Tonnes Waste / Tonnes Ore
2. Dilution = Tonnes Waste / (Tonnes Ore + Tonnes Waste)
Pakalnis et. al. (1995) recommends using equation (1) as a standard measure of dilution since
equation (2) is much less sensitive to increases in waste. This is depicted graphically in
Figure 4.
3.0 CAVITY MONITORING SYSTEM (CMS) DATABASE
 
Referring to Figure 1, it can be appreciated that there are a number of factors that can
influence the dilution and recovery for a particular stope. To help gain a better
understanding for which factors are most critical with regard to stope wall stability, it was
deemed necessary to collect extensive data complimentary to each CMS stope survey. The
complimentary data consists of details on:
· stope geometry;
· rock mass classification;
· undercutting of stope walls;
· drilling;
· blasting;
· stope support;
· time.
Figure 5 is a schematic showing the database structure.
3.1 Description of Data
Empirical design methods are only applicable for design situations similar to those from
which the method was derived. Therefore, when using any empirical design method it is
imperative to have a good understanding of the data set used to develop the method.
To date, the main database contains 47 stope surveys from 6 mines. All of the mines in the
database utilize open stoping as the main mining method. Of the 47 stopes, 30 are considered
primary stopes (i.e. all surfaces of the stope comprised of solid rock) and 17 were mined
adjacent to backfill. Mining depths ranged from approximately 75m to 1100m with the
majority of surveyed stopes being between depths of 700m to 1100m. 
A number of histograms are presented in Figures 6 to 8 which provide a more detailed
description of the data contained in the database. 
Volumetric measurements of overbreak/slough have been recorded for: 31 unsupported
hangingwalls; 16 cable bolted hangingwalls; 39 unsupported footwalls; and 2 cable bolted
footwalls. 
In all cases where cable bolt support was used, it consisted of cables installed from the sub-
levels (point anchor approach), no pattern bolted wall surfaces were surveyed. The support
pattern was generally a fan of 3 cable bolt holes every 2 to 3m along strike. Cable bolt
lengths varied from 4.5 to 15.5m. Double cables (2 per hole) were used in the majority of
the cases. Face plates were installed on all the cables.
3.2 New Parametersto Relate Hangingwall and Footwall Stability
3.2.1 Collection and Reduction of CMS Survey Data
Conducting a CMS survey is a very straight forward task. However, obtaining surveys
which accurately represent the dimensions of the stope requires careful consideration of set-
up location (due to possible line of sight errors) and the density of data recorded. Errors can
also be introduced depending on the survey method used to locate the laser rangefinder in
space. Discussions on obtaining quality CMS surveys can be found in Mah et.al. (1995) and
Miller et. al. (1992). 
With regard to data reduction the following approach was used for this study:
1. Conduct CMS survey.
2. Download the survey results to a PC.
3. Reduce survey data into DXF file format.
4. Overlay survey on existing 3D mine model.
5. Cut cross-sections along the longhole rings. The sections should contain the following
information: ore drift(s); ore contacts or mining lines; CMS survey.
6. Plot blastholes on sections
7. On each section, calculate the area (m2) of overbreak/slough and underbreak for both the
hangingwall and footwall. Overbreak/slough and underbreak is measured relative to the
ore contacts or mining lines. Dilution from ore drift development is not included when
determining the area of overbreak/slough.
8. Based on the areas calculated on each section, calculate a volume of overbreak/slough
and a volume of underbreak for both the hangingwall and footwall. This will require that
a thickness be assigned to each section.
9. Convert the volumetric measurements into parameters termed ELOS (Equivalent Linear
Overbreak/Slough) and ELLO (Equivalent Linear Lost Ore) which are both expressed
in meters (m).
3.2.2 Description of ELOS and ELLO
ELOS and ELLO are alternate ways of expressing the volumetric measurements (m3) of
overbreak/slough and underbreak. They represent conversions of the true volumetric
measurements into an average depth (ELOS) or thickness (ELLO) over the entire stope
surface. A schematic describing ELOS and the method of calculation is shown in Figure 9.
 ELLO is calculated the same way except “volume of overbreak/slough” is replaced with
“volume of underbreak”. The attractiveness of these terms is that their meaning from a
dilution or recovery point of view is more readily apparent than a volumetric measurement.
 For example, if 10m wide stopes are being designed and the ELOS is estimated to be 1.0m,
approximately 10% unplanned dilution (by volume) can be expected. Conversely, an ELLO
of 1.0m would represent a recovery of approximately 90% (i.e. Recovery = Actual Ore
Mined / Planned Ore).
Since the focus of this paper is estimating unplanned dilution, the ELOS parameter will be
examined specifically. 
A benefit of using the ELOS parameter for empirical design is that it allows comparisons
with other mining operations. This is not possible if dilution values are used since the values
determined are a function of: stope width; grade of wall rock; and the associated tonnage
factors. 
 4.0 PRELIMINARY DEVELOPMENT OF AN EMPIRICAL APPROACH TO
ESTIMATE UNPLANNED DILUTION FROM OPEN STOPE
HANGINGWALLS AND FOOTWALLS
The Modified Stability Graph (Potvin, 1988; Nickson, 1992; Hadjigeorgiou, 1995) has
generally been well accepted by industry for open stope design. For this reason, it was
chosen as the starting point for developing an empirical method for estimating unplanned
dilution.
The Modified Stability Graph plots a stability number N’ versus the Hydraulic Radius (HR)
of the surface being analyzed, refer to Figure 10. N’ and HR are calculated using the
equations shown below:
 N’ = Q’ x A x B x C
 HR = Wall Surface Area / Wall Perimeter
Where:
 N’ = Stability Number
Q’ = Modified Tunneling Quality Index (NGI)
 with Jw/SRF set to one. (after Barton, 1974)
 A = Stress Factor
 B = Joint Orientation Factor
 C = Gravity Factor
 
4.1 Details on the Calculation of the Modified Stability Number (N’)
With regard to the calculation of the Modified Stability Number (N’) the following criteria
were used:
· the RQD was generally dictated by the spacing of the joint set parallel to the stope walls.
· Jr and Ja were based on the critical joint set with regard to stability which was always the
joint set parallel to the stope walls.
· the A factor was always set to a value of 1 (stope wall in relaxed or low stress state).
· the B factor was always set to a value of 0.3 (critical joint set with regard to stability was
parallel to the stope wall)
· the C factor equaled: 8-6cosÆ for hangingwalls (where Æ equals the hangingwall dip);
and 8 for all footwalls.
The following paragraphs discuss the assumptions made regarding the A, B, and C factors.
Stress Factor - A
The A factor accounts for the induced stress in the particular stope surface being analyzed.
 The factor is determined using the graph presented in Figure 11.
In this study, the A factor was always assumed to be equal to 1 (stope wall in a relaxed or
low stress state). The reasoning behind this assumption is as follows:
· based on several pre-mining stress measurements carried out at depths between 60m and
1890m, Arjang (1991) shows that in hardrock mines with near vertical orebodies the
maximum horizontal stress is commonly oriented approximately perpendicular to the
strike of the orebody and has a magnitude of approximately twice the vertical stress. The
minimum horizontal stress is generally aligned along strike. It can be shown through
numerical modelling that in this stress regime hangingwalls and footwalls are generally
under low stress or in relaxation.
· given the violent nature of the blasting process (ie: high vibrations and gas pressures)
there will be a zone of damaged rock extending back some distance from the excavation
perimeter. It is expected that this zone will have poor integrity and will not be an
effective transmitter of stress.
· after blasting, open stope walls generally show a somewhat erratic profile (i.e. not a
continuous hangingwall or footwall beam - due to: zones of significant blast damage;
zones of poorer rock quality; etc..), thus any stress in the walls must be thrown back into
more continuous competent rock.
The Potvin (1988) and Nickson (1992) databases support this assumption, out of all the
hangingwall and footwall data points only two were assigned A values less than 1.
A further reason to keep the A factor constant at 1 is that it is not intuitively obvious that
Figure 11 adequately accounts for the influence of induced stresses. For example, a value
of 1 (the rating most beneficial with regard to stability) is given for stope surfaces under low
stress or in a relaxed state, but, from a dilution perspective (i.e. blocks sloughing from the
stope surface) this would seem unattractive since there is little confining stress to aid with
stability. Perhaps within certain limits stress in stope walls is more beneficial to stability
than a relaxed stress state. More work is required to fully understand the effect of stress on
hangingwall and footwall stability. 
 
Joint Orientation Factor - B
This factor accounts for the orientation of structure relative to the stope walls. The factor is
determined using the chart presented in Figure 12. The structure most critical to the stability
of the wall is used to determine the appropriate B factor.
For all the stopes in the database, the critical structure with regard to stability was parallel
to the stope walls. The parallel structures were either: joint sets; bedding planes; or foliation
planes.
Gravity Factor - C
The C factor accounts for the mode of failure (buckling/slabbing vs. sliding) and the effect
of gravity. The buckling/slabbing mode of failure applies to hangingwalls whereas the
sliding mode of failure applies to footwalls. The graphs shown in Figure 13 are used to
determine the appropriate C values. 
Upon inspection the generalshape of the two graphs make intuitive sense (i.e. hangingwalls
become less stable as the dip decreases and footwalls become less stable as the dip
increases). However, what does not make intuitive sense is the actual weighting factors. For
example, a footwall with parallel structure dipping at 90° has a weighting of C=2, whereas
a hangingwall with parallel structure dipping at 90° has a weighting of C=8. In reality, there
is no difference between a 90° dipping footwall and a 90° dipping hangingwall therefore the
C factors should be equal. This suggests that the minimum C value for a footwall should be
8 and as the dip decreases the C value should increase. This concept is shown schematically
in Figure 14. This intuitively makes sense since it is well accepted that in a given rock type
the hangingwall is less stable than the footwall except at 90° where there is no difference.
 The CMS stope surveys support this statement.
For this study the buckling/slabbing graph was used to determine the C values for the
hangingwalls (C=8-6cosÆ) and a weighting of C=8 was assigned to all the footwalls. This
is the approach used with the Mathews Method (Mathews et. al, 1981) which is the method
on which the Modified Stability Graph is based. More work is required to better define the
C factor for footwalls.
4.2 Presentation of Results
 
The approach taken to incorporate ELOS onto the Modified Stability Graph was to simply
plot the location of the hangingwall and footwall data points on the graph and at each
location plot the associated ELOS value. Figure 15 is a plot of the Modified Stability Graph
with the points from the CMS database overlain. The data plots surprisingly well on the
graph providing some quantifiable meaning to the design zones shown. 
Design zones based solely on the ELOS values are presented in Figure 16. The design zones
were developed based on statistics (logistic regression) coupled with engineering judgment.
 Note that the design zones apply to unsupported surfaces. There is not enough data to
quantify the effects of cable bolt support (installed at sub-levels), however, the graph does
approximately indicate where cables may be providing some benefit and where they become
ineffective.
4.3 Additional Case Histories
As a check on the proposed design zones, CMS survey results were obtained from a mine
that is not currently in the CMS database. The following are brief notes concerning the
mine:
· mining method is transverse open stoping with paste fill (primary and secondary stopes);
· the case histories obtained are primary stopes;
· HW cable bolt support consists of cables installed at sub-levels (fan of 3 cables every
2m);
· critical joint set with regard to stability parallels the HW and FW;
· blasthole diameter 4.5 in., blasthole offset approx. 0.6m.
From the survey results 15 additional data points were collected: 6 cable bolted
hangingwalls; and 9 unsupported footwalls.
The additional case history data is shown plotted on Figure 17. The data shows no
discrepancies with the proposed design zones.
5.0 RELATIONSHIPS BETWEEN ELOS AND OTHER DATABASE
PARAMETERS
An analysis was carried out using both scatter plots and neural networks to try and
quantitatively evaluate what factors, other than those accounted for in the Modified Stability
Graph Method, influence hangingwall and footwall stability (i.e. undercutting, drilling and
blasting, adverse geometry; etc..). It was recognized from the onset, that at this stage, the
database is not large enough to warrant trying to determine additional weighting factors (i.e.
D and E factors) to incorporate into the method. Therefore, the intent of the analysis was to
provide insight into factors which may increase the probability of instability, possibly
resulting in higher ELOS values than would be estimated using the design zones presented
in Section 4.0. 
A detailed description of the analysis will not be given here, however, a summary of the
results is given below.
Factors Which May Increase the Estimated ELOS
· Irregular Wall Geometry - most of the stopes in the CMS database have regular wall
profiles (i.e. relatively planar surfaces). Both the scatter plot analysis and the neural
network analysis showed that there is a tendency for ELOS to increase as the regularity
of the wall geometry decreases.
· Undercutting of Stope Walls - the scatter plot analysis showed that the destabilizing
effect of undercutting is somewhat dependent on the stability number. Stope walls with
N’ < 5 appear to be very sensitive to undercutting. An ELOS value equal to or greater
than the undercut depth should be anticipated for rock masses with stability numbers
lower than this value.
· Blasthole Diameter and Blasthole Length - Both the scatter plot and neural network
analysis showed a relationship of increasing ELOS with increasing blasthole length and
blasthole diameter. The database is largely comprised of stopes that were excavated
using blastholes less than 65mm diameter and lengths less than 20m. The design zones
presented in Section 4.0 may underestimate ELOS where large blastholes of length
greater than 20m are used.
· Blasthole Layout - the neural network analysis indicated a relationship between ELOS
and blasthole layout. This indicates that there may be a tendency for ELOS to increase
when using fanned blastholes as opposed to parallel blastholes. The majority of
blastholes in the database were drilled parallel to the planned stope surface.
· Blasthole Offset - The majority of perimeter blastholes were offset 0 - 0.5m from the
excavation perimeter, with the average being approximately 0.3m. The design zones
presented in Section 4.0 may underestimate ELOS if small or no offsets are used in rock
masses with N’<15. This effect will likely increase with increasing blasthole diameter.
· Stope Life and Number of Stope Blasts - The scatter plot analysis showed a correlation
between ELOS and the number of stope blasts and the neural network analysis showed
a correlation between ELOS and stope life. It is expected that as stopes plot
progressively below the Blast Damage Only Zone (ELOS > 0.5m) wall stability will
become increasingly sensitive to these parameters. The majority of the stopes in the
database were open for less than 50 days and were excavated with less than 9 longhole
blasts. 
6.0 FINALIZING THE EMPIRICAL DESIGN APPROACH
A finalized version of the ELOS design chart is presented in Figure 18. The chart indicates
areas of low design confidence (dashed lines) based on the density of data in the database.
 A chart which relates: unplanned dilution; ELOS; and stope width, is included to aid in
designing stopes based on achieving a certain level of unplanned dilution. A copy of the
Modified Stability Graph (Potvin, 1988; Nickson, 1992) is also included for a cross
reference. Formal definitions for each of the ELOS design zones are presented below:
Blast Damage Only (ELOS < 0.5m)
· Potential for minimal overbreak/slough. The quantity of overbreak/slough will be highly
dependent on the quality of drilling and blasting.
· Surface is self supporting, no support is required to maintain a stable excavation.
· Time is expected to have a minimal effect with regard to stability. 
Minor Sloughing (ELOS = 0.5m - 1.0m)
· If the surface is unsupported some wall failure should be anticipated before a stable
configuration is reached. 
· Stope support should be considered. The CMS database provides some evidence that
sub-level cable support may be adequate in this design zone.
· Wall stability will be sensitive to blasting vibrations and the effects of time. Stopes
should be mined quickly and filled.
· Minor operational problems should be anticipated (i.e. some secondary blasting)
Moderate Sloughing (ELOS = 1.0m - 2.0m)
· If no stope support is installed, significant wall failure should be anticipated before a
stable configuration is reached.
· Stope support should be considered. The CMS database providessome evidence that in
this design zone sub-level cable support provides little benefit in rock masses with N’<
6. If feasible, pattern support should be installed.
· Stope stability will be very sensitive to blast vibrations and the effects of time. Stopes
should be mined quickly and filled.
· If pattern support is not installed, significant operational problems should be expected
(i.e. secondary blasting, plugged drawpoints, possible ore loss under sloughed material,
erratic production).
Severe Sloughing / Possible Wall Collapse (ELOS > 2m)
· If no support is installed, large and possibly unacceptable wall failures should be
anticipated.
· Pattern support should be considered. Sub-level cable support will provide little benefit.
· Stope stability will be very sensitive to blast vibrations and the effects of time. Stopes
should be mined quickly and filled.
· If pattern support is not installed, significant operational problems should expected (i.e.
 secondary blasting, plugged drawpoints, ore loss, erratic production, possible loss of
stope)
A point to consider when using this design approach is that not all of the estimated
overbreak/slough will necessarily be mucked out of the stope. Often the sloughed material
sits on top of the blasted rock and is slowly drawn down to the mucking level and left behind
in the stope, usually resulting in some ore loss. Other times, however, the slough
preferentially finds its way to the drawpoint or slough material gets mixed in with the ore and
everything gets mucked to the ore pass. This is influenced by factors such as drawpoint
location and mucking requirements. This is a hard factor to account for and is probably best
handled on a mine by mine basis. At the design stage it is probably best to assume that all
the estimated overbreak/slough will find its way to the ore pass.
6.1 Limitations Of This Design Approach
Limitations of this design approach are as follows:
· the main limitation is the size of the database. More data is required to give confidence
to the design zones and to refine the method.
· the method is limited to hangingwalls and footwalls in a low or relaxed stress state with
parallel structure being critical with regard to stability.
· the database is biased towards mines that use relatively small diameter blastholes (i.e.
<65mm). More data is needed from mines that utilize larger diameter blastholes.
· the database needs more large stopes and more stopes in poor quality rock.
· the effect of stope support is not addressed in great detail (need more data).
· additional factors which influence stope stability have been identified but only broad
guidelines regarding their influence have been given.
7.0 SUMMARY
An empirical design approach has been presented that can be used to estimate the amount
of overbreak/slough from open stope hangingwalls and footwalls. This in turn can be used
to estimate the unplanned dilution associated with a particular design. The method is based
on quantifiable measurements of overbreak/slough made with the Cavity Monitoring System
(CMS).
Additional factors which influence hangingwall and footwall stability, but not presently
incorporated in the design approach, have been identified through analysis of the CMS
database using scatter plots and neural networks. Broad guidelines regarding their influence
on the empirical design approach have been given. 
The main limitation of the design approach is the size of the database. Additional data is
required to verify the design zones and refine the approach. It must be recognized as with all
empirical approaches that the limitation of the predictive solution is largely governed by the
existing database and how past observations relate to the present input parameters in terms
of predicting future behaviour. 
ACKNOWLEDGMENTS
The authors would like to extend special thanks to: S. Vongpaisal (CANMET); M. Sandhu
(Echo Bay Mines Ltd.); C. Connors (HBMS); T. Whillans (Westmin Resources Ltd.); S.
Mah and K. Dunne (Placer Dome Canada); C. Wilson (Cameco); D. Milne (UBC); P.
Germain (Noranda); A. Moss and W. Forsyth (Golder Associates Ltd.); and K. Mathews.
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