Empirical Design Methods -UBC Geomechanics

R. Pakalnis

University of British Columbia, Vancouver, B.C., Canada

S. Vongpaisal

CANMET, Ottawa, Ontario, Canada

 ABSTRACT

 This paper summarizes the design curves that have been implemented by mine operations throughout Canada. The methodology for design is a common thread for all the design tools presented which requires the operator to address stress, structure and the prevailing rock mass. The paper presents quantified stability graph for stope design, the pillar stability curve for dimensioning sills, ribs and post pillars among others, the critical span curve for man-entry operations and support curves for the placement of stope support. The individual curves have been employed at operations throughout Canada since their introduction and have been incorporated into the design process. The paper focuses on a methodology towards design that is of applied use to the mine operator.

Introduction

A mine structure, whether it be a mine pillar or an opening, is generally influenced by numerous blocks of intact rock. Individually their properties and behaviour can be readily assessed on a laboratory scale. However, when analysed on a minewide scale, the interaction of the rock block and the rock mass behaviour is difficult if not impossible to predict employing solely a deterministic approach.

Design methods can be categorized as being either analytical, observational or empirical. Empirical methods assess the stability of 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 mature 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 observational approaches as tools to the overall process which will incorporate an empirical component towards the design.

There are inherent differences between analytical and empirical design approaches in rock mechanics. Analytical design methods are based upon an estimate of the constitutive behaviour of a rock mass. Constitutive behaviour includes an estimate of rock mass failure criteria which may be the Hoek Brown criterion (1980), Mohr-Coulomb criteria or some measure of the interaction of joint surfaces and blocks of rock. Once a constitutive rock mass behaviour has been arrived at, it becomes part of the design method and is not varied. Empirical design methods are based more on an estimate of the constitutive properties of a rock mass. Based on the collection and analyses of case histories, the relative influence on stability of factors such as joint orientation, strength and spacing are estimated. Once an estimate of these values are made they become part of the design method and are not varied. A failure criteria is then empirically derived based on weighted constitutive properties of the rock mass and a measure of the underground geometry.

Figure 1 Design Methodology Employing Stress, Structure & Rock Mass

Individually each is only a tool that requires the design to address the factors most critical to the stability of the overall underground structure: Stress, Structure and the Rock Mass as shown in Finure1. This design approach is employed to assess the potential failure mechanism. The methods of design are 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. Two prime objectives inherent with the design process are that the mine must be safe and operate as economically as possible.

Design Methodology

Instability is governed by either stress, structure or the rock mass each may occur individually or in combination in order to result in a potentially unstable condition as shown in Finure1 and must be addressed in terms of design and due diligence in assessing ground conditions.

STRESS

Design must relate the induced stress, Figure2, to the overall rock mass strength in order to assess the overall potential for instability.

Figure2: Induced pillar stress within a sill.

Numerical modeling has advanced at an accelerated pace over the last decade. It has moved from the private domain of researchers operating on large main frame computers to the desktop environment. Generally in the past, the assessment of induced stresses for a particular mine geometry was largely conducted employing two dimensional or pseudo three-dimensional plane strain modeling codes with three dimensional codes being employed in a limited capacity. Recently, numerical codes have been developed whereby true three-dimensional representation of stresses can be determined with relative ease. This allows comparisons to be made between pseudo and actual stress derived quantities. The stress model is invaluable in being able to estimate the induced load, which is fundamental to the design process. It must be recognized that the input parameters for the numerical model are guestimates at best with present levels of accuracy, in the author's opinion, of 20% at best. The level of modeling must there fore consider the input variability and how the stress results will be used subsequently. The level of accuracy should be commensurate with the input and output required.

STRUCTURE

The structural instability that may result within an opening for simplicity if termed "wedge" which has a defined three-dimensional volume of rock that can release either through sliding along a surface and/or by dead weight. This is shown in Figure 3, which requires one to assess the structure and the factors influencing the overall, potential for instability such as the cohesion and friction angle for the surfaces interacting between blocks.

In addition, the volume of the wedge coupled with the unit weight allows one to determine the amount of support required in order confining the potential wedge from being released. This requires one to install the support beyond the wedge so as to ensure that adequate bond results and full support strength is mobilized, Figure 3.

Figure 3: Structurally controlled instability.

 ROCK MASS CLASSIFICATION

The rock mass classification systems of particular reference to hard rock underground mining applications are:

• Geomechanical (RMR) Classification System (1976)
• Q-System (1976)

The systems have empirically evolved from a large database. In addition, they not only reflect the experiences of the developers but also the preceding investigators such as Terzaghi (1946), Lauffer (1958), Stini (1950), Deere (1964), Wickhaam et al. (1972) among others. The systems were primarily derived for the design of civil-engineered tunnels. However, they provide the basis for subsequent modifications that enable them to be applied to mining situations. Laubscher (1976), Mathews et al. (1981), Kendorski (1983), and Hoek (1983) have applied adjustments to the existing systems to aid in the design of mine structures. An ideal mine classification system must have the flexibility that allows it to be used for various mine applications, and it must also be simples that it can be easily assessed, understood, reproduced and applied. It is only in this manner that it can function as an important tool in the design of an operating mine. The RMR and Q Systems satisfy the above criteria. Deficiencies do exist with the two classifications but through adjustments on is able to overcome the criticisms.

The approach employed by the author is to incorporate the requirements of the design whether it being temporary or permanent and to incorporate the geometrical and excavation considerations that require one to modify the existing systems through the collection of empirical data relevant to each mining excavation. The RMR system as defined by Bieniawski in 1976 was employed for development of the database to arrive at the design curves shown in this paper.

The objective is to quantify the difference between the behaviour of a highly jointed rock mass to that of a moderately jointed to that of an intact rock as shown in Figure 4 and their implications on design. Description of the classifications in discussed in detail in Hoek and Brown (1980).

 Figure 4: Transition from very poor rock to very good rock in terms of a jointed rock mass.

Design

Three areas of design will be presented: opening, pillar and support. They are summarized in this paper; however, details are provided and referenced elsewhere.

OPENING DESIGN

This has been divided into stope wall design for footwall and hangingwall for "non entry" operations and back design for "entry" operations. It is critical that structural instability be delineated prior to defining potential rock mass instability.

STABILTY GRAPH METHOD

The Stability Graph Method for open stope design was initially proposed by Mathews et al. (1981) and subsequently modified by Potvin (1988) and Nickson (1992) to arrive at the Modified Stability Graph Method. Hadjigeorgiou (1995) further augmented the database with

Figure 5: Equivalent Linear Overbreak/Slough-ELOS

 particular reference to footwall instability. In all instances, stability was qualitatively assessed as either being stable, potentially unstable or collapses. Recent research at UBC (Mah, 1997 and Clark, 1998) have augmented the Stability Graph with stope surveys employing cavity monitoring systems (Miller et al. 1992) This has enabled one to quantify the amount of dilution employing a parameter defined as the Equivalent Linear Overbreak/Slough (ELOS by Clark, 1997) as shown in Figure 5 which attempts to express the volumetric measurements of overbreak into an average depth over the entire stope surface. This results in a design curve as shown in Figure 6"Empirical Estimation of Wall Slough" which is comprised of a database in excess of 88 observations (Clark, 1998) and is employed solely for footwalls and hangingwalls and should not be extended beyond the limits of the database. The following was employed for calculation of parameters for database shown in Figure 6.

 N'=Q'*A*B*C

Where:

Q' - The NGI rock quality index after Barton et al. (1974) with the Stress Reduction Factor (SRF) and the Joint Water Reduction Factor (Jw) equal to one as they are accounted for separately within the analysis. In addition, the database that the Stability Graph has been from mining operations which are generally dry. The following relationship is employed to convert RMR to Q:

RMR = 9lnQ + 44 (Bieniawski, 1979)

A Factor - This value is designed to accout for the influence of high stresses reducing the rock mass stability. The A ualue is determined by the ratio of the unconfined compressive strength of the intact rock divided by the maximum induced stress parallel to the opening surface. The A factor is set to 1.0 if the intact rock strength is ten (10) or more times the induced stress indicating that high stress is not a problem. The A factor is set to 0.1 if the rock strength is two (2) times the induced stress or less indicating that high stresses significantly reduce the opening stability. A value of A=1 for the stress factor was employed in Figure 6 identrfying the failure mechanism for the footwall and hangingwall as being that in a zone of relaxation. The original database (242 case histories) of Potvin (1988) and (59 case histories) Nickson (1992) support this assumption, since for all the footwall and hangingwall data points only two were assigned A values less than 1. Where numerical modelling shows that the hangingwall is in a high state of induced stress then this must be augmented by observation of the ultimate failure mechanism that prevails prior to employing a factor for the hangingwall other than 1.0.

B Factor - This value looks at the influence of the orientation of discontinuities with respect to the surface analysed. This factor states that joints oriented at 90° to a surface are not a problem to stability and a value of 1.0 is given to the value of B. Discontinuities dipping within 20° to the surface are the least stable representing structure which can topple within the stope. A value of B=0.2 is given for this condition, Figure 6.

C Factor - This value considers the orientation of the surface being analysed. A value of eight (s) is assigned for the design of vertical walls and a value of two (2) is given for horizontal backs. This factor reflects the inherently more stable nature of a vertical wall compared to a horizontal back. The C factor suggests that the Q value can be increased four (4) fold for a vertical wall as compared to a horizontal back. The curves presented in Figure 6 employ a Figure 6: Empirical Estimation of Overbreak/Slugh-Hangingwalls and Footwalls

value of C=8 for the gravity factor for all footwalls as was originally proposed by Mathews et al (1982). The ELOS values have been derived from both hangingwall and footwall points and therefore the curves of Figure 5 must be summed to arrive at the total dilution. This is described in detail in Clark et al (1997) which shows that for near vertical stope having parallel jointing in the hangingwall and footwall that the C factor for the hangingwall approaches 8, however, for the footwall this value approaches two if values as proposed by Potvin (1988) are employed. Observation shows that the footwall is generally more stable than the hangingwall and therefore a value of C=8 is employed for the footwall database as shown is Figure 6.

Hydraulic Radius - This is the surface area divided by the perimeter of the exposed wall being analysed.

 SPAN DESIGN ENTRY METHODS

This section summarizes development of critical spans for entry methods such as cut and fill operations (Lang, 1992). The critical span is defined as the diameter of the largest circle that can be drawn within the boundaries of the exposed back as viewed in plan and shown in Figure 7. This exposed span is then related to theprevailing rock mass of the immediate back to arrive at a stability condition. The design span refers to spans which have used no support and /or spans which include pattern bolting (1.8m long bolts on 1.2m ´ 1.2m) for local support. It does not include spans which are supported by more intensive ground support such as cable bolts, post pillars or timber sets (Lang, 1994 and Pakalnis et al, 1993). The "local support" is placed to confine potential blocks (loose) which may become open due to nearby blasting and/or stress redistribution caused by subsequent mining activity. The database that the "Critical Span Graph" has been derived is based upon 172 mine records from the detour Lake Mine (Lang, 1994) and augmented by data from operations throughout Canada. The design curve since being introduced has been employed at the Goldcorp operation in Red Lake, Ontario under burst prone conditions, Mah (1995) and Pakalnis/McNamarra (1997) and augmented as shown in Figure 7.

Figure 7: Critical Span Graph- Entry Methods

Figure 7 shows the span curve and the limitations are restricted to the prevailing factors influencing this database. The limitations as outlined by Pakalnis, 1993 can be summarized as follows:

• Where discrete wedges have been identified these must be supported prior to employing the Critical Span Graph
• Design span refers to backs that have local support
• Stability refers to short term stability (excess of three months)
• Critical Span Graph is considered applicable over the RMR range 40% to 85%
• Back is horizontal
• Stress induced failure does not occur within the back

The stability of the excavation is classified into three categories:

1. Stable Excavation

• There has been no uncontrolled falls of ground
• If instrumentation is available, no movement of the back has been observed
• No extraordinary support measures implemented other than required for burst prone or non burst prone ground (Mah, 1996 and Pakalnis and McNamara, 1997)

b) potentially Unstable Excavation

• Extra ground support may have been installed to prevent potential falls of ground
• Instrumentation installed in back indicates continuing back movement
• Increased frequency of ground working (Mah, 1996, and Pakalnis and McNamara, 1997)

c) Unstable Excavations

• The area has collapsed
• Support was not effective to maintain stability. At Goldcorp burst prone and non burst prone support standards dictate the use of cables to ensure stability and/or span must be minimized.

The application of the Critical Span Graph where the back is in a state of relaxation but has shallow dipping jointing (under 30° dip), the observed RMR is then reduced by 10. This value has been suggested by Bieniawski (1976) as a correction factor for adverse structure and has been found to correlate well with observations recorded for the database employed in Figure7.

The original design curve has been employed successfully at Glodcorp (Mah, 1995 and Pakalnis/McNammara 1997) within a high stress environment. This was incorporated into the design process by modifying the prevailing rock mass of the immediate back by subtracting 20 from the observed rock mass rating, Figure 7. This value has been observed through past practice at Goldcorp in comparing pre to post burst conditions to be valid. The rock mass rating prior to a burst generally has a tight condition for rating resulting in a joint condition of "20" and after the burst the joints are open and the condition approaches"0" (Bieniawski, 1976). This is also equivalent to a Stress Reduction Factor (SRF) as proposed by Barton of 10for post burst conditions. Burst prone support at Goldcorp entails the use of 1.7m #6 resin rebar with chainlink (51mm -9 gauge galvanized) screen on a 1.2m ´ 1.2m pattern. This support is employed for the back and both walls with straps in the back. Where the critical span is exceeded cable support is employed. The above support has shown that after a burst employing the reduced RMR equivalent span that the support holds and overall stability is maintained albeit requiring rehab.

PILLAR DESIGN

The approach employed is outlined by Lunder (1997) and modified by Mah (1995) for burst prone conditions as shown in Figure 8. Two primary factors are used in this design approach, a geometric term that represents pillar shape, and a strength term that includes the in situ rock strength and the predicted pillar load. The rock mass strength is dependent upon the amount of confining 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 a lower strength for a given rock type. The Pillar Stability Graph was developed by plotting the ratio of pillar load/UCS of the intact pillar material against the pillar width/pillar height ratio, Figure 8. The pillar width (Wp) is defined as the dimension normal to the direction of the induced stress as shown in Figure 8 whereas the pillar height (Hp) is measured parallel to the induced stress. The pillar load is measured at the core of the pillar whereas the unconfined compressive strength (UCS) is that recorded for the intact rock comprising the pillar. This gas been described in detail by Lunder (1994) and augmented by Mah (1995) where the Pillar Stability Graph has been related to burst potential for sill pillars for the Red Lake Mine and the adjacent Cambell Mine - Placer dome.

Figure 8: Pillar Stability Graph

SUPPORT DESIGN

CABLE SUPPORT REQUIREMENTS - BACK

Cable support within the back which have been deemed to be unstable as identified by Figure 7 employ an empirical derivation of past practice for back support as developed by Nickson (1992) and reproduced in Figure 9 whereby the Stability Graph is related to the required cable bolt density. The length of the bolts are generally in excess of 0.5 times the span as maximum failure has been observed to occur generally at a 45° arch/cone above the back (Pakalnis et al., 1995).

Figure 9: Minimum bolt density for back cable support

CABLE SUPPORT REQUIREMENTS-HANGINGWALL

The Point Anchor Design Chart is employed as shown in Figure 10 whereby Nickson (1992) defined the supported and unsupported spans as illustrated in Figure 10 and proposed the relationship between stable and caved hangingwall geometries under prevailing conditions. The design line in Figure 10 separates caved from stable cases of point anchor hangingwall support. This approach enables the design of point anchor support to be implemented in terms of identifying the optimum vertical support interval. The database that the Point Anchor HW Cable Support graph has been developed is based upon the installation of plated cables on a 2.4m ring spacing employing 5 single cables/ring.

Figure 10: Cable support - hangingwall - point anchor support

SUMMARY-SUPPORT

The support capacity for the individual rock bolt/screen/bond strengths employed at typical hard rock operations is shown is Figure 11 and have been compiled from site testing at the Detour Lake Mine-Placer Dome, Ted Lake Mine-Goldcorp, Lupin Mine-Echo Bay Mines, manufacturers specifications as well as from CAMIRO (1997). The breaking strength as well as the yield strength for the individual rock bolts is presented. The breaking strength is generally the normal design capacity employed in practice in the Canadian mining industry. This is the maximum strength of the bolt and due to the unknowns of the strength and geometry of the potential failure geometry one tends to design for dead weight and for gravity fall and not incorporate any shear strength is the design process of confining a structural instability as shown in Figure 3. In addition, the temporary nature of the support coupled with monitoring of potential blocks to ensure against unpredicted instability direct the operator towards designing employing breaking strengths for rock support. In addition, the bond strength of the support is related to the critical distance past the wedge that is required in order to assess the potential failure mechanism of the support i.e. Pull out versus exceeding the breaking strength of the bolt. In addition, support should be plated at the collar or critical bond strengths must be assessed for the potential failure block above the immediate back.

#6 refer to 6/8", #7 refer to 7/8, #8 refer to 8/8" diam. etc.

4 gauge = 0.23" diam, 6 gauge = 0.20", 9 gauge = 0.16" 11 gauge = 0.125" 12 gauge = 0.11" diam.

Shotcrete shear strength = 2 Mpa = 200 tonnes/m²

Figure 11: Rock support properties.

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, opening stability and effective 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 the UBC Geomechanics Group, the mine operations and granting agencies that participated within the above studies in particular CANMET, NSERC, USBM, Noranda Technology Centre, Westmin, Goldcorp, Detour Lake, Campbell, Lupin, Snip, Ruttan, Inco Thompson and Dome Mining Operations.

REFERENCES

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Bieniawski, Z.T. 1974. Geomechanics Classification of Rock Masses and the Application is Tunnelling. Proc. Third Intl. Congress on Rock Mechanics, ISRM, Denver, Vol 11A, pp. 27-32.

Bieniawski, Z.T. 1976. Rock Mass Classification in Rock Engineering. Proc. Symp. On exploration for Rock Engineering, Johannesburg, pp. 97-106.

CAMIRO Mining Division, 1997. Canadian Rockburst Research Program 1990-1995. Mining Research Directorate, CAMIRO Mining Division, Vol. 1-6.

Clark, L. And Pakalnis, R. 1997. An Empirical Design Approach for Estimating Unplanned Dilution from Open Stope Hangingwalls and Footwalls. Presented at the 99^th AGM-CIM, Vancouver, pp. 25.

Goris, J.M., Nickson, S.D. and Pakalnis, R. 1994. Cable Bolt Support Technology in North America, USBM Information Circular IC 9402, Washington: US Department of the Stability Graph Method for Open Stope Design, CIM-AGM, Halifax.

Hoek, E., and Brown, E.T. 1980. Underground Excavations in Rock. Institution of Mining and Metallurgy, London, p. 484.

Lang, B. 1994. Span Design for Entry-Type Excavations. MASc Thesis, University of British Columbia, pp.250.

Lunder, P. 1994. Hard Rock Pillar Strength Estimation: An Applied Empirical Approach. MASc Thesis, University of British Columbia, pp. 166.

Mah, P. 1995. Development of Empirical Design Technques in Burst Prone Ground at the A.W. White Mine, CANMET Project No.: 1-9180, CANMET DSS File No. 02SQ.23440-1-9180.

Mah, S. 1997. Quantification and Prediction of Wall Slough in Open Stope Mining Methods. MASc Thesis, University of British Columbia, pp. 290.

Miller, F., Potvin, Y., Jacob, D.

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