Empirical Design of Span Openings in Weak Rock based upon Support 

Type Employed 

Ouchi, A. M. 

Barrick Gold Corporation, Tulawaka Gold Mine, Tanzania, Africa
 

Norman B. Keevil Institute of Mining Engineering, University of British Columbia, Vancouver, BC, Canada 

Pakalnis, R. 

Norman B. Keevil Institute of Mining Engineering, University of British Columbia, Vancouver, BC, Canada 

Brady, T.M. 

Spokane Research Laboratory, National Institute for Occupational Safety and Health, Spokane, WA, USA 

 

ABSTRACT: Existing empirical design tools have been developed from fair-to-good quality rock masses (RMR76 >50). This 

paper presents a focus of ground control research presently being conducted by the Rock Mechanics Group in the UBC Mining 

Department in incorporating weak rock masses (RMR76 <50) into existing empirical design relationships. An emphasis is being 

placed upon the updated span design curve/critical span graph originally developed at UBC. The original database has been 

augmented with over 450 weak rock data points from mines such as the Stillwater mine (Montana), the Eskay Creek Mine (BC) 

and several mines in the Carlin Trend and other parts of Nevada. The original database is comprised of spans supported with 

“traditional” mechanical bolting. In weak rock environments however, this type of support has been found for the most part, 

ineffective. This paper presents the span and weak rock RMR76 relationship for four different support categories. This work 

attempts to provide rock mechanic tools that will enable a mine operator to make economic decisions that will also ensure a safe 

working environment. 

commenced technical mine visits. There was another 

pike in injuries in 2005. The last two years have had 

elatively low numbers of ground fall related injuries. 

owever, last year there was one fatality from a fall of 

round. Weak rock conditions are a concern and will 

ontinue to be in the years to come. 

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1. INTRODUCTION 

The University of British Columbia Geomechanics

group and the NIOSH Spokane Research Laborator

have been conducting research in the development of

safe and cost effective underground design guidelines in

weak rock environments with Rock Mass Ratings

(RMR76) [1] in the range of 20 to 50. A main area of th

research is in the augmentation of the updated spa

design curve/critical span graph. 

As “ideal” resources in competent ground conditions ar

depleted, there is an increase in the number of mines

operating in weak ground conditions. This presents

potentially difficult and hazardous mining conditions to

workers in the industry resulting in a higher frequency of

injuries and fatalities. This is evident in Nevada by th

number of injuries resulting from uncontrolled rock falls

during the time period of 1990 through 2007 (Figure 1

with a low of 2 in 2004 and a high of 28 in 1995 and

1997 [2,3]. In mid-1999 NIOSH started conducting

visits and discussions with Nevada mines regarding

weak rock and ground falls resulting in a statistica

decline of ground fall related injuries over the next two

years [4]. 2002 showed an increase in ground fall

related injuries and in the middle of that year, NIOSH

y 

e 

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e 

) 

l 

199019911992199319941995199619971998199920002001200220032004200520062007 

Injuries

35 

30 

25 

20 

15 

10 

5 

0 

Year

8 

13 

9 

12 

16 

28 27 28 

25 

19 

12 

8 

14 

7 

2 

10 

5 

7 

Figure 1: Ground Fall Related Injuries in Nevada, 1990-2007 

The Critical Span Curve is a simple and useful tool that 

aids in the design of underground man-entry openings. 

With the increasing number of mines operating in weak 

ground conditions of RMR76 less than 50, there is the 

need to update the Critical Span Curve for the RMR76
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

range of 20-50. The augmentation of this curve to 

include a larger database of points in the weak rock mass 

range will increase its accuracy and reliability in such 

conditions. For the purposes of this study, RMR76 

values of 60 and less were used. 

Surface support is almost always used in weak rock 

environments. The type of support used can vary 

widely. The development of the weak rock augmented 

Span Design Curve has also been separated into four 

different support categories; Pattern Friction Sets (A), 

Pattern Friction Sets with Spot Bolting of Rebar (B), 

Pattern Friction Sets with Pattern Rebar Bolts (C) and 

Cablebolting/“Heroics” (D). Category D includes 

cablebolts and other engineering designed support 

systems such as cemented rock fill (underhand cut and 

fill mining), significant application of shotcrete 

(typically 76mm), spiling or timber sets. 

2.	 SPAN DESIGN, MAN ENTRY 

The “critical span curve” has undergone modifications 

since its development in 1994 by Lang and the 

University of British Columbia [5]. The database was 

expanded to 292 observations in 2000 with case 

histories from an additional six mines [6]. The span 

curve and its updates (Figure 2) has been widely 

accepted in the North American mining community and 

provides a quick and simple tool to estimate a maximum 

span that may be designed based upon the observed 

RMR76 value. 

 Figure 2: Updated Critical Span Curve 

The updated database included RMR76 values from 24 to 

87 with 63% of the cases in the range of 60 to 80 [6]. 

Less than 10% of RMR76 values in the updated database 

fall below a value of 40 and less than 20% fall below a 

value of 55 [7]. The updated curve has uncertainties 

below RMR76 values of 50 and above RMR76 values of 

80. At the lower RMR76 range (and in the unstable 

zone), it has been shown in mining operations that 

openings can remain stable with only local support [8]. 

The augmentation of this curve to include a larger 

database of points and to split it into separate support 

categories in the weak rock mass range will increase its 

accuracy, reliability and usability. 

The stability of and excavation is separated into three 

categories described below. A brief description is 

presented below and the reader is referred to the detailed 

reference as outlined by Pakalnis [9]. 

i. Stable Excavations 

a.	 No uncontrolled falls of ground 

b.	 No observed movement in the back 

c.	 No extraordinary support measures 

implemented 

ii.	 Potentially Unstable Excavations 

a.	 Extra ground support has been installed to 

prevent potential falls of ground 

b.	 Movement in the back of 1mm or more in 

24 hours has been observed 

c.	 Increase in the frequency of popping and 

cracking indicating ground movement 

iii. Unstable Excavations 

a.	 Area has collapsed 

b.	 The depth of failure of the back is 0.5 

times the span (in absence of structure 

related failure) 

c.	 Support was not effective in maintaining 

stability 

When evaluating areas with shallow dipping or flat 

joints, a correction factor minus 10 is applied to the final 

calculation of RMR76. This correction factor is usually 

applied in high stress environments where these flat 

lying joints typically develop. In the weak rock 

environment, typically heavily jointed, it is expected that 

the addition of a flat lying joint set will play a minor role 

in the overall stability of the opening. Therefore, the 

application of this correction factor for flat lying joints is 

questionable. Where structures of discrete wedges have 

been identified, these must be supported prior to 

employing the use of the critical span curve. 

3. WEAK ROCK AUGMENTED SPAN DESIGN 

CURVES 

The span curve database has been augmented with a total 

of 463 points in the RMR76 range of 15-60. The weak 

rock data has been collected from 12 mines across 

Canada and the US. As shown in Figure 3, 58% (267 

points) of the data has RMR76 values below 50, 32% 

(147 points) of the data falls below 45 and 13% (60 

points) of the data falls below 40. This weak rock 

database has been split into four support type categories. 

These categories were created to be able to compare 

similar support types/capacities. 
For each category, a neural network analysis was 

performed. The Neuroshell Predictor program from 

Ward Systems was used [10]. The networks were 

trained on approximately 60% of the data and verified 

with the remaining 40%. Genetic analyses were 

preformed to obtain interpolation results. Stable points 

were given values of 1, Potentially Unstable points were 

given values of 2 and Unstable points were given values 

of 3. For the categories that achieved an acceptable 

correlation and error, the networks were used to make 

stability predictions on a grid that covered an RMR76 

range from 20 to 60 and a span range from 1.5m to 13m. 

From this data, the transitions from 1 to 2 mapped the 

Stable/Potentially Unstable transition line and the 

transitions from 2 to 3 mapped the Potentially 

Unstable/Unstable transition line. 

0 

20 

40 

60 

80 

100 

120 

140 

160 

1-5

6-10

11-1516-2021-2526-3031-3536-4041-4546-5051-5556-6061-6566-7071-7576-8081-8586-9091-95

96-100 

RMR

Frequency

Unstable 

Potentially Unstable 

Stable 

Figure 3: Weak Rock Database RMR76 Distribution 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

3.1.	 Category A: Pattern Friction Sets 

This category is comprised of spans that were pattern 

bolted (typically 1.2m x 1.2m or 0.9m x 0.9m) solely 

with frictions sets (Split Sets and/or Swellex). The 

Category A database includes 47 points from 7 mines 

across North America. RMR76 values range from 20 to 

60 with spans from 1.8m to 12.2m. The neural network 

analysis obtained a correlation of 0.90, R-squared of 

0.80 and average error of 0.18. Figure 4 shows the 

updated weak rock curves overlaid with the updated 

curve. 

50 

Exisiting Stable-PU Unstable 

0 

10 

20 

30 

40 

Span (m) 

Existing PU-Unstable 

New Stable-PU Line 

New Stable-PU Projec ion 

New PU-Unstable Line 

New PU-Unstable Projection 

Stable 

Potentially Unstable 

Unstable 

0 20 40 60 80 100

RMR76
 

Figure 4: Category A New S/PU and PU/U lines 

 

 

 

The resultant curves mimic what is seen in the field. It 

is known that stable excavations are possible at lower 

RMR76 values with smaller spans. However, once a 

certain span is exceeded, the span typically fails. This is 

shown with the new transition curves. As the RMR76 

values decrease, the transition between Stable, 

Potentially Unstable and Unstable really becomes a 

drastic transition between Stable and Unstable with a 

very small to non-existent Potentially Unstable zone 

where spans typically have warning signs prior to 

failure. On the graph, the maximum stable span at 25% 

RMR76 is 3m. Due to the small database, it is 

recommended that mines use caution around this lower 

end of the weak rock database and establish site specific 

data. 

3.2.	 Category B: Pattern Friction Sets with Spot 

Bolting of Rebar 

This category is comprised of spans that were pattern 

bolted (typically 1.2m x 1.2m or 0.9m x 0.9m) with 

frictions sets (Split Sets and/or Swellex) along with spot 

bolting using resin grouted rebar. The Category B 

database includes 176 points from 7 mines across North 

America. RMR76 values range from 30 to 60 with spans 

from 1.5m to 9.1m. The neural network analysis 

obtained a correlation of 0.89, R-squared of 0.79 and 

average error of 0.12. Figure 5 shows the updated weak 

rock curves overlaid with the updated curve. 

0 

10 

20 

30 

40 

50 

Span (m) 

Existing Stable-PU Line 

Existing PU-Unstable Line 

New Stable-PU Line 

New Stable-PU Projection 

New PU-Unstable Line 

Stable 

Potentially Unstable 

Unstable 

0 20 40 60 80 100

RMR76 

Figure 5: Category B New S/PU and PU/U lines 

The results from this category are similar to those from 

Category C and will be discussed in concurrence with 

those from Category C below. 

3.3.	 Category C: Pattern Friction Sets with 

Pattern Rebar Bolts 

This category is comprised of spans that were pattern 

bolted (typically 1.2m x 1.2m or 0.9m x 0.9m) with 

frictions sets (Split Sets and/or Swellex) and pattern 
 bolted (typically 1.2m x 1.2m or 0.9m x 0.9m) with resin 

grouted rebar. The Category C database includes 152 
 

 

 

points from 2 mines across North America. RMR76 

values range from 26 to 60 with spans from 1.8m to 

10.7m. The neural network analysis obtained a 

correlation of 0.92, R-squared of 0.85 and average error 

of 0.15. Figure 6 shows the updated weak rock curves 

overlaid with the updated curve. 

50 

Existing Stable-PU Line 

0 

10 

20 

30 

40 

Span (m) 

Existing PU-Unstable Line 

New Stable-PU Line 

New Stable-PU Projec ion 

New PU-Unstable Line 

New PU-Unstable Projection 

Stable 

Potentially Unstable 

Unstable 

0 20 40 60 80 100

RMR76 

Figure 6: Category C New S/PU and PU/U lines 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

The resultant curves for Categories B and C are a little 

surprising. The stable lines do move up indicating that 

stable excavations are possible down to RMR76 values of 

35. However, they have not moved up as much as the 

same line for Category A. Also, one would figure that 

the Potentially Unstable/Unstable lines would fit closer 

or to the left of the existing line due to the increased 

yield and bond strengths of rebar as compared to friction 

sets. The RMR76 range of the databases for Categories B 

and C have a lower range of about 35 as compared to 20 

for Category A. The trends exhibited in Categories B 

and C indicate that data in the RMR76 20-25 range for 

both graphs would be unstable. 

The authors have observed that resin grouted rebar is 

difficult to install in weak rock. Full resin coverage of 

the bolt is difficult to achieve due to the jointed nature of 

the rock mass. The resin tends to either get caught in 

open fissures of the rock mass, the tubes break part way 

into the hole or the resin spins out into the surrounding 

rock mass thus resulting in incomplete coverage of resin 

along the length of the bolt. This incomplete coverage 

would result in a decrease the in the bond strength of the 

rebar bolts. This could be a reason why there are so 

many spans in the previous Potentially Unstable zone 

that have failed. The use of resin grouted rebar in weak 

rock environments could give an operator a false sense 

of security if the bolts are not installed properly. 

3.4. Category D: Cablebolting/“Heroics” 

This category is comprised of spans that were bolted 

with cablebolts or that were supported using another 

engineering designed support system such as cemented 

rock fill (underhand cut and fill mining), significant 

application of shotcrete (typically 76mm), spiling or 

timber sets. The Category D database includes 88 points 

from 10 mines across North America. RMR76 values 

range from 15 to 55 with spans from 2.1m to 13.1m. 

This category did not achieve acceptable correlation and 

error results with the neural network analysis. This is 

most likely due to the varied engineered support systems 

which act differently on the rock mass resulting in 

distinct support mechanisms with different factors of 

safety. The data is displayed in Figure 7 to show that 

spans in the Unstable zone may be supported with 

detailed engineering support design. 

0 

10 

20 

30 

40 

50 

Span (m) 

Exiting Stable-PU Line 

Existing PU-Unstable Line 

Stable - Cables 

Potentially Unstable - Cables 

Unstable - Cables 

CRF-Shotcrete-Spiling-Timber 

20 40 60 80 100 

RMR76 

Figure 7: Category D points on Span Design Curve 

4. CONLUSIONS 

The University of British Columbia Geomechanics 

group and the NIOSH Spokane Research Laboratory 

have been conducting research in the development of 

safe and cost effective underground design guidelines in 

weak rock environments with RMR76 in the range of 20 

to 50. An update of the Span Design Curve was 

conducted for this weak rock mass range. A total of 463 

points were added to graph. 

Surface support is almost always used in weak rock 

environments. The type of support used can vary 

widely. The development of the weak rock augmented 

Span Design Curve has been separated into to four 

different support categories. 

Category A (pattern friction sets) yields good results and 

follow what is seen in the field, though caution should 

be used as the dataset is small with 47 points. 

Categories B and C yielded similar results with the 

Stable/Potenially Unstable line moving up. However the 

Potentially Unstable/Unstable line moved in to the right. 

This is unexpected, but may be explained by the 

difficulty experienced in the installation of resin grouted 

rebar. Category D, the “heroic” category did not obtain 

positive results from the neural networks analysis, but 
 

 

 

 

 

 

 

 

 

 

 

still demonstrates that spans can be stable at lower 

RMR76 values with detailed engineering support design. 

As with any empirical design, it is important to 

understand the data behind the design. The empirical 

design graphs presented in this paper are intended to aid 

the experienced operator in making safe and economical 

design decisions. 

This work would not have been possible without the 

partnership between the University of British Columbia, 

NIOSH and the mine sites involved. The mine sites 

involved include Cameco, Carlin East, Deep Post, Eskay 

Creek, Getchell, Jerritt Canyon, Midas, Myra Falls, Red 

Lake, Rodeo, Stillwater and Turquoise Ridge. 

The findings and conclusions in this paper have not been 

formally disseminated by the National Institute for 

Occupational Safety and Health and should not be 

construed to represent any agency determination or 

policy and mention of any company or product does not 

constitute endorsement by NIOSH. 

REFERENCES 

[1] Bieniawski, Z.T. 1976. Rock Mass Classification in 

Rock Engineering. In Proceedings of the Symposium 

on Exploration for Rock Engineering, Johannesburg, 

South Africa, 97-106. 

[2] Hoch, T. 2000. Ground control seminar for 

underground gold mines, Elko, NV. Sponsored by 

MSHA Ground Control Division, Pittsburgh, PA. 

[3] Brady, T. 2008. Personal communication. NIOSH. 

[4]	 Brady, T., L. Martin, and R. Pakalnis. 2005. Empirical 

approaches for open design in weak rock masses. 

Transactions of the Institution of Mining and 

Metallurgy. 114: A13-A20. 

[5] Lang, B. 1994. Span Design for Entry Type 

Excavations. MASc Thesis, University of British 

Columbia, Vancouver, BC. 

[6] Wang, J., R. Pakalnis, and D. Milne. 2000. Empirical 

underground entry type excavation span design 

modification. In Proceedings of the 53rd Annual 

Conference of the Canadian Geotechnical Society. 

[7]	 Brady, T., L. Martin, and R. Pakalnis. 2003. Empirical 

Approaches for Weak Rock Masses. In Proceedings of 

the 98th annual AGM-CIM conference, Montreal, QC. 

[8] Ouchi, A., R. Pakalnis, and T. Brady. 2004. Update of 

Span Design Curve for Weak Rock Masses. In 

Proceedings of the 99th annual AGM-CIM conference, 

Edmonton, AB. 

[9] Pakalnis, R. 2002. Empirical Design Methods – UBC 

Geomechanics Update. In Proceedings of the NARMSTAC 2002: Mining and Tunneling Innovation and 

Opportunity, eds. R. Hammah, W. Bawden, J. Curran, 

and M. Telesnicki, Vol. 1. 

[10] Ward Systems Group (Frederick, MD). 2003. 

Neuroshell Predictor Version 2.01. 

http:www.wardsystem.com.