Empirical Methods for the Design of Mine Structure
Abstract
The design of mine structures is a major area of study within the mining and mineral Process Engineering Department at the University of British Columbia. This paper will describe empirical methods that have been developed based upon extensive field input and application. The design curves are derived from the factors critical to the stability of the mine structure, whether they be mine openings or pillars, such as geometry, rock mass quality, prevailing structure, rate of excavation, stress levels, blasting influences, production constraints among others. The methods resented in this paper are employed by mine operators for the estimation of:
1 Introduction
This paper summarizes four empirical approaches towards design developed by the authors in assisting the operator in the design of mine structures whether they be mine openings or pillars. Design methods can be categorized as being either analytical, observational or empirical. Empirical methods assess the stability
structures by the use of past practices to predict future behaviour based upon factors most critical towards the design. Empirical derivations have gained acceptance over the last fifteen years largely due to their predictive capability since conventional methods of assessment have the difficulty of identifying the jointed nature of the rock material, assigning properties thereto and establishing input parameters for subsequent numerical evaluation. The process that the authors have found to be of greatest value is to employ numerical codes, analytical tools and observation approaches as tools to the overall process which will incorporate an empirical component towards the design. Individually each is only a tool that requires the design to address the factors (Pakalnis, 1991) most critical to the stability of the overall underground structure: Stress, Structure and the Rock Mass as shown in Figure 1. The design approach is discussed in earlier papers where relationships such as relating stope dilution to the rock mass rating and maximum critical span for man-entry operations to prevailing conditions was presented (Pakalnis et al., 1993). A similar approach was adopted in this paper where methods of design where based upon a strong analytical foundation coupled with extensive field observations to arrive at a calibrated empirical approach towards the solution to a given problem. The methods presented here are compiled from extensive mine visits, literature reviews, discussions among researchers and practitioners, analytical and numerical assessments along with successful implementation at mine operations primarily within Canadian hard rock environments.
Figure 1: Design Methodology
2 Empirical Cable Support Design (Nickson, 1992)
Potvin (1988) proposed the Modified Stability Graph methodology for stope surface design, an approach that related case histories of open stope surfaces to particular design ranges on an empirical design chart. A study completed by Mickson (1992) expanded the Potvin database and redefined the Modified Stability Graph design ranges based on a statistical analysis and the addition of new data. The study also looked into cable bolt support design procedures and proposed several new design charts that could be used for back and hangingwall surface design.
The revised database incorporated 13 new unsupported and 46 new supported case histories, in addition to the 176 unsupported and 66 supported(backs) case histories assembled by Potvin (1988). The terms "supported" and "unsupported' refer to the use of cable support. A supported case history incorporates cable bolts, while an unsupported case history does not. Each point in the database is associated with a stability number, N, an hydraulic radius and a stability condition. The separation of such three dimensional multivariate data into different groups was accomplished using a form of discriminant analysis and a statistical measure of distance called the Mahalanobis distance (Seber, 1984). The method is designed to derive a linear function that will separate a database into two or more groups.
Revisions to the design ranges on the Modified Stability Graph are shown on Figure 2, in conjunction with the complete unsupported and supported data points. It is sometimes useful in the design process to locate a particular surface in reference to those in the database. A stope wall having a surface hydraulic radius of greater than 15 m for example would have limited success of stability as shown in Figure 2. The two thicker lines shown on Figure 2 were obtained from the statistical analysis that was completed to separate stable and caved case histories for both the unsupported and supported database. The statistical analysis was used to define potential revisions to the transition zones. The unsupported transition zone is the same as that suggested by Potvin (1988), but a new supported transition zone was proposed. It intersects the unsupported transition zone and suggests that there is a limit to the effectiveness of cable support with respect to large competent stope surfaces.
Figure 2: Revised Modified Stability Graph
The revised Modified Stability Graph provides a tool the mining engineer. to aid in the development of site specific design guidelines. The design of unsupported surfaces are initially suggested to be located above the unsupported transition zone. Similarly, the design of supported stope surfaces should initially be located above the supported transition zone. The design of stope surfaces into or beyond the respective transition zone will result in increasing levels of dilution and greater susceptibility to the effects of blasting and exposure time. Non-entry mining methods may tolerate initial design within the appropriate transition zone providing the level of dilution can be controlled.
A design chart for the installation of back cable support was proposed by Potvin (1988). Potvins' proposal related the cable bolt density to the relative block size factor, RQD/Jn/HR. A revised Design Chart for Back Cable Support that relates cable density to N'/HR (Figure 3) was proposed by Nickson (1992). This chart incorporates the complete stability number, N', and therefore includes a relationship to rock mass quality, surface orientation and induced stress. Potvins' relative block size factor considered only RQD and the number of joint sets (Jn) as a rough approximation of block size. The design line on the revised chart in Figure 3 was determined from a regression analysis of the stable case history data, and is recommended for the determination of minimum support levels for stope backs that plot within the stable with support zone of the revised Modified Stability Graph, The 84% confidence line on Figure 2 is suggested as a minimum design density for the supported transition zone of the Modified Stability Graph. The Design Chart for Back Cable Support is based on average conditions within a database of stable case histories, where cables are evenly distributed over the supported surface. The majority of the case histories within this database incorporate single cables and limited use of plates. The average water:cement ratio of the grout by weight was approximately 0.40. A relationship between minimum cable bolt densities and the revised Modified Stability Graph is proposed in Figure 3 for stope back cable support, based on the minimum design criteria outlined on the Design Chart for Back Cable support.
In many cases, point anchor hangingwall cable support is installed from fan rings drilled into the hangingwall, and or footwall, of a stope from a sublevel development drift. Ideally, this type of support divides a potentially unstable hangingwall into smaller stable unsupported spans. Nickson (1992) defined the supported and unsupported spans as illustrated in Figure 5 and proposed the relationship in the Design Chart for Point Anchor Cable Support illustrated in Figure 6. The design line in Figure 6 was located to separate caved from stable cases of point anchor hangingwall support. For design purposes, underground mapping and stope planning will give an indication of the relative block size factor. An acceptable design is indicated by projecting vertically up from the horizontal axis to the design line, and reading a recommended unsupported hydraulic radius on the vertical axis. The unsupported hydraulic radius can be used to evaluate an acceptable sublevel spacing. The database was based on a water:cement ratio range of 0.40 to 0.45 in conjunction with an average of five plated cables per ring at a ring spacing of 2.4 metres.
3 Empirical Pillar Design (Lunder, 1994)
A comprehensive pillar database that relates geometry, loading conditions, in-situ rock strength and stability condition has been developed. Analysis of this database has led to the development of pillar stability curves that can be used to design pillars for underground hard-rock mines. A total of 178 stability cases have been included where each case example represents a failed pillar, an unstable pillar or a stable pillar. With the use of proper calibration techniques, this method provides a reliable method of designing pillars for underground mining operations.
3.1 Database / Stability Assessment
The pillar data used to develop this methodology is a compilation of seven individual pillar stability databases that have been published worldwide. The information available is the pillar stability assessment, the predicted pillar load, and the pillar geometry. Five of the seven databases originate from massive sulphide deposits, and all of the databases have reported rock mass ratings (RMR) of 65-85% representing good to very good quality rock mass conditions. Each of the databases used similar although differing pillar stability classification definitions. These were simplified into a common three level stability classification system as representing either failed, unstable or stable pillar conditions. Figure 7 is a schematic of the observed conditions that would be encountered for each stability level. This is based upon detailed research work that showed that pillar stability levels could be assessed on a five level scale. This was simplified in order to assimilate the data with the additional databases that were collected from literature.
3.2 Pillar Strength
Two primary factors are used in this design methodology, a geometric term that represents pillar shape, and strength term that includes the in-situ rock strength and the predicted pillar load. It is an accepted fact that rock mass strength is dependent upon the amount of confined stress applied to a sample. In the case of mine pillars, the more slender a pillar, the less confining stress will be available resulting in lower strength for a given rock type. It is however, difficult to determine the actual confinement for many pillars. The Pillar Strength Curves were developed by plotting the ratio of pillar load / UCS (unconfined compressive strength) of intact pillar material against the pillar width / pillar height ratio, Figure 8. A different symbol was used for each pillar stability classification and the areas containing like classifications were subdivided by the stability lines. For a detailed review of how the stability lines were designated, the reader is referred to Lunder 1994.
3.3 Design Method
The procedure employed to design mine pillars with the pillar stability graph can be summarized as follows:
3.4 Calibration / Summary
The use of any empirical method requires that a particular site be calibrated to the empirical data. With the Pillar Stability Graph, calibration is achieved through the strength term, the pillar load / UCS ratio. This term can be calibrated utilizing either of the two terms, the means of calculating the pillar load can be modified by changing the in-situ parameters that are used in the numerical modeling program. A more practical alternative is to use a "modified" in-situ UCS value. If observed pillars are not performing as predicted, the UCS value can be modified so that pillars plot in there proper stability range.
Mah(1995) has related the Pillar Stability Graph to the burst potential for sill pillars for the Goldcorp Inc. - Red Lake Mine and the Campbell mine - Placer Dome Canada located in Red Lake, Ontario, based upon methodology as outlined in Figure 1. The database was comprised of twenty-three case histories from the Campbell Mine and 21 case histories from the Red Lake Mine. The following recommendations were made for the design of pillars in a burst prone environment:
Stable Nil to Low Burst potential |
Unstable Medium Burst Potential |
Failed High Burst Potential |
- minimal signs of deteriorate observed - ground support costs low |
- usually
temporary entry or non-entry methods - generally F.S. ranges from 1.0 to 1.4 on Pillar Stability Graph - medium burst potential - progressive or, - progressive yielding or bursting deterioration of sill pillar - moderate support costs |
- generally F.S < 1.0 on Pillar Stability Graph - high burst prone, progressive or - extensive yielding of pillars resulting in cave or near cave conditions depending upon the span - ground support costs high |
The Pillar Stability Graph presented here represents a collection of a wide range and type of mine pillar. It provides a basis for pillar design that can be used with a high degree of confidence provided that the method is calibrated to a given site.
4 Empirical Design for Estimating Overbreak/Slough from Open Stope Surfaces (Clark, 1995)
Since the introduction of the Cavity Monitoring System (CMS) in 1991 (Miller et al.,l991.) it has gained wide spread acceptance in the mining industry. The CMS system utilizes prismless laser technology and make possible detailed surveying of open stopes. This allows determination of volumes for overbreak/slough and underbreak from open stope surfaces, and permits a qualitative analysis of stope stability. Over the past year, the University of British Columbia has been compiling a large database of CMS survey data with the objective of developing an empirical method for estimating the volume of overbreak/slough from open stope surfaces(Clark, 1995). Correspondingly, the volumetric estimates can be used to predict the unplanned dilution that may be associated with a particular stope design. Development of the method is currently ongoing and the results presented hereafter should be considered as preliminary.
4.1 Description of Database
At present, the database is comprised of eighteen stope surveys from six different longhole open stope in operations located across Canada. Of the stopes examined, depths ranged from 100m to 1000m; widths varies from 2.5m to 35m, heights varied from 15m to 135m, strike lengths varied from 15m to 60m, wall dip varies between 45o and 90o, typical blasthole lengths ranged from 10m to 50m, blasthole diameters ranged from 50mm(2") to 120mm(4.75"), and generally the critical joint set with regards to stability was parallel to the hangingwall and footwall. Hangingwall cable bolt support (point anchor) was utilized in five of the stopes surveyed.
4.2 Development of Empirical Design Approach
The approach used to date has been to calculate the volume of
the overbreak/slough form the stope surface as shown in Figure 9
and to convert the volume to a parameter termed the Equivalent
Linear Overbreak/Slough (ELOS) which is equal to the volume of
slough divided by the stope surface area. This ELOS is expressed
in meters(m) and the value plotted onto a graph of the modified
Stability Number (N') vs. Hydraulic Radius as described by Potvin
(1988) and shown in Figure 10. 
The ELOS parameter is an alternative way of expressing the volumetric measurement (m3) overbreak/slough. It converts the true volumetric measurement into an average depth of slough over the entire stope surface. A schematic describing this term and its method of calculation is shown in Figure 9. The attractiveness of this term is that its meaning from a dilution point view is more readily apparent than a volumetric measurement. For example, if 5m wide stopes are being designed and the ELOS is estimated to be 2.5m, 50% (2.5/5) unplanned dilution can be expected (assuming the overbreak/slough has no grade).
Figure 10 is a plot of the results to date. Only hangingwalls and steeply dipping footwalls (dip>80° ) have been plotted (18 hangingwalls, 6 footwalls). Results to date suggest that the current methods for determining a Modified Stability Number (N') for footwalls (namely the "C" factor) requires further calibration. Footwalls which dipped steeper than 80° were arbitrary treated as vertical hangingwalls. As of yet, little effort has been made to fit any curves to the data. The stability lines shown on Figure 10 are very similar to ones presented by Scoble and Moss (1994). The graph tends to quantify terms such as Moderate Sloughing.
At this stage, Figure 10 is not recommended for detailed design purposes since more data points are required, however, it can be used to give very approximate estimates for volumes of overbreak/slough from hangingwalls and steeply dipping footwalls (>80° ).
As an example, a possible design approach for cases where the majority of unplanned dilution comes from the hangingwalls could be as follows:
Procedure for use of ELOS Dilution Estimate:
4.3 Future Work
It is expected that by the end of this study more than one hundred points will have been collected. Future work will involve: examining whether hydraulic radius is the most appropriate parameter to describe stope size and shape; determining a better method of quantifying the effect of the footwall stability (C factor); and examining the need for introducing additional parameters which account for factors such as: drilling and blasting; undercutting of stope walls, and cable bolt support (Pakalnis et al 1995).
5 Geometric Assessment for Empirical Design (Mine, 1996)
The previous sections on surface stability have used either hydraulic radius or an equivalent circle factor for assessing surface geometry. The hydraulic radius term has been used in many empirical design techniques (Potvin 1988), (Laubscher, 1990) and deserves further attention. Hydraulic radius is defined as the surface area divided by perimeter. For a rectangular surface, Equation 1 shows how this factor can also be expressed as the minimum distance from the centre of a surface to the supporting abutments
Where: a and b are the length and width of the surface.
When the hydraulic radius is expressed as a function of distance to supporting abutments, it becomes apparent why this term should be related to opening stability. There are difficulties associated with using the hydraulic radius to assess opening stability. Irregular geometries are difficult to assess and the presence of raises, pillars and brows are difficult to quantify.
A new term called the radius factor (RF) is proposed as a replacement to hydraulic radius (Milne et al., 1996). This term follows the same form as the hydraulic radius, however, it is based on the sum of many measurement to Supporting abutments, taken at small angular increments from the centre of a surface, Equation 2.
where rq is the distance to abutments measured from the surface centre.
Figure 11 shows how this term would assess a stope back with a raise present in the back, or supported by a small pillar. The data from which the Modified Stability Graph was developed has been adjusted to plot stability based on RF values instead of HR values. The resulting graph did not change significantly, as shown in Figur 12, however, more complex geometries can now be realistically assessed. The radius factor is defined at the centre of an opening surface, however, it can be calculated at an point on a surface.
Figure 12: Unsupported Case Histories Plotted on the Modified Stability Graph Using Hydraulic Radius an Radius Factor (Milne et al., 1996)
Another term called the effective radius factor (ERF) is introduced which is calculated at any point on a surface. The ERF value is at a maximum at the centre of a surface which is equal to the RF and drops to zero at an abutment, reflecting the increased stability of a surface at the abutments. Figure 13 shows RF and ERF values calculated on a stope back. The RF value of 6.5m shows the influence of the intersecting cross cut on the stope back whereas the ERF value of 3.7m is removed from the influence of the cross cut. Surface ERF values have been successfully related to relative wall dilution as well as to measured wall deformation.
It is proposed that the application of the radius factor and effective radius factor terms will improve the applicability of empirical design techniques to more complex mining geometries. Linking relative surface stability, deformation and sloughing will improve our ability to engineer surface support and economical stoping geometries.
6 Conclusions
The approach to design summarized in this paper is one whereby existing databases have been calibrated to analytical and empirical approaches and modified according to observed mine behaviour. The tools have been used successfully to predict levels of dilution, pillar stability and effective cable support requirements. The approaches presented in this paper are to be employed as a tool for the practitioner and to augment the methodology with his own database and decision making process in order to arrive at a workable solution.'
Acknowledgements
The authors would like to thank all the mine operations and granting agencies that participated within the above studies in particular Noranda Technology Centre, CAMET, NSERC, UBC, Westmin Operations, Detour Lake, Goldcorp, Campbell Mine among others.