Analysis of Bench Crest Performance at the Yellowstone Mine: 

A Case Study 

J. Whyatt1

, M. MacLaughlin2 and S. Miller3

A case study is presented that relates statistical descriptions of joint sets to the distribution of 

local wedge failures along the crest of a catch bench at the Yellowstone Talc Mine. The fracture 

sets and bench width were mapped by teams of geological engineering students from Montana 

Tech under the direction of Dr. Mary MacLaughlin. The students analyzed the fracture data, 

conducted physical property tests, and used a beta version of a NIOSH program “Bwedge” to 

predict the distribution of surviving bench widths. In the course of this analysis the students 

developed evidence of software performance issues that, unfortunately, frustrated their analysis. 

These have now been addressed and a full analysis completed. The analysis confirms the 

validity of the student mapping program and provides insight into the effects of blasting and 

excavation practices on the bench. It also provides a tool for exploring the pattern of bench crest 

failure that would result from variations in both bench geometry and blasting practices. 

I. Introduction 

This study was undertaken to demonstrate use of the Bwedge computer program in evaluation of 

bench crest failures in a mine pit slope. The Bwedge program provides a statistical estimate of 

wedge failures along the length of a bench crest. Results are expressed as a probability of 

retaining various usable bench widths. The effort included collection and analysis of geologic 

data, comparison of expected and observed bench crest performance, and sensitivity studies of 

fracture and bench design parameters. The initial phase of the study was conducted by a group 

of students in a graduate level slope design class at Montana Tech in cooperation with Luzenac 

America’s Yellowstone Mine and the National Institute for Occupational Safety and Health 

(NIOSH). The students discovered a number of flaws in a beta version of Bwedge. These flaws 

have been addressed and the study completed. 

II. North Bench, Yellowstone Mine 

Luzenac America’s Yellowstone Mine is located southwest of Ennis, Montana along the east 

slope of the Ruby Mountain Range. Mining is conducted using two open pits approximately 90 

m (300 ft) deep. 

The study focused on a 90 m (300 ft) section of a single bench within the north wall of the south 

pit in hydrothermally-altered dolomite of Precambrian age. This rock is overlain by Tertiary age 

Huckleberry ridge tuff. Severe fracturing of the dolomite appears to form at least four major sets 

(figure 1). Fractures are likely related, at least in part, to movement along a major fault that runs 

through the pit, striking N-NW with near vertical dip. This fault lies adjacent to the west end of 

the study scan line. The rock mass was classified as “Fair” for the RMR and “Very Poor” for the 

“Q” system (Appendix A). 

1. Mining Engineer, Spokane Research Lab, NIOSH; email – juw6@cdc.gov 

2. Associate Professor, Geological Engineering, Montana Tech of the University of Montana 

3. Professor, Geological Engineering, University of Idaho 
Figure 1: Fractured rock on a bench face. 

The overall slope angle of the north wall was measured by Brunton compass at roughly 40°. 

Benches are 7.6 m (25 ft) high with an estimated intact bench width of 5.5 m (18 ft) and bench 

face dip of 62°. However, the students found that the bench crest was intact at only a handful of 

locations along the study bench section (figure 2). Widths measured along the study bench are 

plotted in figure 3. Narrower sections of bench were caused primarily by wedge failures of 

various sizes along the bench crest (figure 4). Wedges were formed by, and have slid upon, preexisting fracture planes. 

Figure 2: Students measuring the bench width and idealized cross section. 

Base of Bench Face 4 m Wide 

62° 

Catch Bench 

5.5 m Wide 

Bench 

Crest 

Failure 
Bench Width by Chainage

0

1

2

3

4

5

6

0 15 30 45 60 75 90

Location along study bench (m)

Bench Width (m)

measured

intact

Figure 3: A plot of measured bench widths by distance along the mapped section of the study 

bench. 

Figure 4: Idealized wedge geometry showing left and right fracture planes. 
A. Fracture Geometry 

Five representative wedge failures were mapped and described by Mike Cerino, the mine 

geologist. Descriptions included fracture orientations and conditions. Three of these wedges 

had clearly moved, but not by much. Remnants of two other wedges, that had failed completely, 

were not present. Examples of disturbed and failed wedges are described in Appendix C. 

Blast fractures and (apparently) blast-crushed caliche fracture infilling were noted near the bench 

face. Mr. Cerino interpreted these observations as evidence that “blasting released wedges that 

otherwise would have remained stable...” He mapped the apex of each of these steeply plunging 

wedges in the bench face and found they daylighted at distances of 4.3 m (14 ft), 6.1 m (20 ft), 

6.7 m (22 ft), 4.6 m (15 ft) and 6.1 m (20 ft) below the bench crest (i.e. just above the next bench 

which is 7.6 m (25 ft) below the crest). In addition, he noted a number of potential wedges that 

do not daylight in the bench face (being steeper than the face). 

Two sets of fractures delineating these and similar wedges were mapped by student teams along 

a 90- m (300-ft) long scan line on the study bench, using tape and Brunton compass. The first of 

these fracture sets was labeled the “foliation” set. This set lies parallel to rock foliation with an 

average orientation of 018°/72° SE (strike/dip) and forms the left side of wedges (figure 4). The 

second and sparser of the sets is the “joint” set. It has an average orientation of 124°/52° SW 

(strike/dip) and forms the right side of these wedges. Line mapping fracture data for these sets is 

included as Appendices D and E, and individual fracture poles for these sets are plotted in figure 

5. The highly fractured nature of the rock (including two other fracture sets that did not 

contribute to wedge failure) made mapping and discrimination of fractures sets difficult. 

Figure 5: Stereonet plot of joint poles, joint set average orientations and pit slope. 
A first cut analysis of wedge stability was developed as shown in figure 5. Bench slope, average 

fracture-set orientations and the wedge formed by “average” fractures were plotted to show that 

the wedge formed by set “average” fractures daylights in the bench face. The plunge of the 

fracture set intersection beneath this wedge was found to be steeper than a 35° friction angle 

circle, a typical joint friction angle. Thus, failure of such a wedge is likely. Plane failure on the 

joint set is also possible but its apparent dip in the bench cross section is flatter than the plunge 

of the wedge fracture plane intersection. Thus, wedge failure will be preferred where both are 

possible. This tendency is evident in the predominance of wedge failures observed in the field. 

B. Fracture Strength and Rock Density 

A number of rock samples collected during the field mapping effort were tested to determine 

frictional strength of the fractures and rock density. Tilt tests of friction angle were conducted in 

the field using rock fragments found along the bench. These tests showed natural fractures had 

an average friction angle of 38.7°. Samples were also taken to the lab and cut to determine the 

friction angle of saw-cut surfaces. Laboratory tests on these surfaces showed an average friction 

angle of 30.7° (ranging 25° to 34°). Complete results from the field and lab tilt tests can be 

found in Appendix B. 

Rock samples were also taken back to the laboratory for density tests. The average density, 

based on tests on three rock fragments, was 2.76 grams per cubic centimeter. Results from 

individual density tests can be also be found in Appendix B. 

III. Fracture Set Characteristics 

The characteristics of each fracture set have to be described statistically and geostatistically for 

analysis by the Bwedge program. The students developed a full set of parameters from the 

mapped fractures. These parameters describe the variability of fracture dip direction, dip, 

spacing, persistence and waviness. The defined fracture sets were not ideal for this purpose, 

including a wider range of orientations and fewer fractures (especially for the joint set) than 

would be desired for a full-blown characterization study. However, the data was sufficient for 

the students to estimate all the required parameters. These values are listed in Table 1. 

Table 1a: Foliation Joint Set Characteristics 

Parameter Mean Std. Dev. Nugget Range

Dip Direction (deg) 108.7 11.70 80.00 16.56 

Dip (deg) 72.35 8.35 62.08 18.92 

Persistence (m) 2.63 1.82 2.54 17.62 

Spacing (m) 1.16 1.21 1.05 6.20 

Waviness (deg) Minimum - 1.0 Maximum – 12.0 
Table 1b: Joint Set Characteristics 

Parameter Mean Std. Dev. Nugget Range

Dip Direction (deg) 214.8 18.44 247.93 4.78 

Dip (deg) 51.80 13.87 148.66 4.72 

Persistence (m) 3.81 3.07 5.05 6.38 

Spacing (m) 1.89 2.13 2.62 5.27 

Waviness (deg) Minimum - 0.0 Maximum – 22.0 

IV. Bwedge Analysis 

Initial Bwedge analyses run by the students failed to match results observed in the field and 

crashed the program for particular ranges of parameters. Identification of these problems led to 

discovery and elimination of a number of flaws in Bwedge. The analysis was then repeated, 

using the student-developed set of input parameters. Results for these input values overestimated 

retention of the bench crest, but correctly matched retention of portions of the bench further from 

the crest (figure 6). This result is surprisingly good, especially considering that it does not 

consider extensive disruption of the outer portion of the bench by blasting noted by Mike Cerino. 

Figure 6. Estimated probability of stability at various depths into the bench crest based on (1) 

measurements, (2) a model using the student set of fracture parameters and (3) a set of weakened 

parameters. 

Depth of Bench Failure

0

10

20

30

40

50

60

70

80

90

100

0 1 2 3 4 5

Distance from Crest (m)

Measured

Student

weakened
An attempt was made to explore the effects of blasting on the bench model by weakening 

fracture strength. The friction angle was decreased from in situ to saw-cut values and the 

stabilizing influence of fracture waviness removed. Bwedge runs using these weaker values 

more closely fit observations for the outer bench, but also underestimate retention deeper into the 

bench – which is also more sheltered from blasting. This result suggests that the student set of 

parameters may well describe the fracturing in situ, prior to the influence of blasting. To the 

extent that this proves to be the case, the overall slope angle could be steepened, while 

preserving both bench face angle and effective bench width, through more careful blasting. If all 

blasting effects were removed, and a 90% probability of maintaining a minimum bench width 

was desired, benches could be narrowed by a full meter. The overall slope angle could be 

steepened by about 5°, to roughly 45°. 

Bwedge can also be used to explore how variations in bench face angle, bench height and initial 

bench width can influence the effective, usable width of resulting catch benches and the overall 

slope angle. For example, the depth of crest failure can be estimated for various bench face 

angles. Figure 7 is such a plot, developed with strong (intact) rock properties. As such, it is 

most relevant to considering steepening of the bench and the resulting extension of wedge 

failures deeper into the bench. Figure 8 is a similar plot for weakened (blast-impacted) 

properties relevant closer to the bench face. 

Figure 7. Probability of stability estimated at various depths into the bench for various bench 

face angles. Curves for steepened slopes are, in sequence, below and to the right of the shaded 

interval which indicates the actual bench face angle. Curves were computed with Bwedge using 

the “strong” set of fracture properties. 

Depth of Bench Failure by Bench Slope Angle - strong

0

10

20

30

40

50

60

70

80

90

100

0 1 2 3 4 5

Distance from Crest (m)

90

85

80

75

70

65

60

55

50

45

40

35

30
Figure 8. Plot of figure 7 recalculated for “weak” set of fracture properties. 

Given a desired surviving bench width, figures 7 and 8 can be used to estimate the additional 

bench width that should be developed to allow for local crest failures. That is, the design should 

consist of a “sacrificial” width that will likely fail, at least locally, and a deeper “protected” 

width that should have a high probability of survival as a functioning catch bench. Obviously, 

steepening the bench face increases the sacrificial width while cutting this angle back reduces it. 

However, it is clear from these figures that it is not possible to completely eliminate crest failure, 

only manage how much must be dealt with. 

For example, we can examine the current design for strong properties (figure 7) and a threshold 

probability of 90%. Recall that this chart is most relevant when failure extends into rock that is 

not weakened by blasting. For instance, when careful blasting practices are used or steepening 

of the bench face pushes failure deeper into the bench. With the current design, the sacrificial 

width is a little more than a meter. If the bench face were steepened to a vertical dip, the 

unreliable portion of bench width would increase to more than 3 m. The bench width would 

have to be increased by a similar amount to maintain the necessary catch bench width. 

The effect of bench face angle on the overall slope angle is determined by its effect on the total 

bench width or “footprint.” The footprint width of the bench can be broken into segments. The 

outermost segment underlies the bench slope. The middle segment underlies the sacrificial 

portion of bench width; that is, the width of bench likely to suffer crest failure. The remainder of 

the slope width is taken up by the protected (functional) width of the catch bench. 

Bench footprints can be calculated for a variety of face angles (and other parameters) and the 

results used to obtain an optimal overall slope angle. This tradeoff is illustrated for this case in 

figures 9 and 10. The absence of an inflection point in these curves shows that a vertical bench 

face is optimal, at least for the wedge bench crest failure mechanism. 

Depth of Bench Failure by Bench Slope Angle - weak

0

10

20

30

40

50

60

70

80

90

100

0 1 2 3 4 5

Distance from Crest (m)

90

85

80

75

70

65

60

55

50

45

40

35

30
Other operational concerns might limit this angle, however. These considerations might include 

handling the increased volume of relatively intact material that is likely to fall out in crest failure 

wedges. It’s also possible that other modes and scales of slope failure might be activated as the 

face is steepened. 

Bench Face Angle and Failure vs Footprint - strong

0

2

4

6

8

10

12

14

30 45 60 75 90

Bench Face Angle (deg)

Width (m)

Bench Slope Base

Base Width Savings

Failure Adj (90% min width)

Failure Adj (95% min width)

Figure 9: Bench slope footprint plotted as a function of bench face angle. The savings in 

footprint width are plotted for steepening of the bench face from an initial angle of 30°. These 

savings are then adjusted for a sacrificial segment of bench width containing crest failures with 

90% and 95% probabilities. Sacrificial segment width was calculated with Bwedge using the 

“strong” set of fracture properties. 

Bench Face Angle and Failure vs Footprint - weak

0

2

4

6

8

10

12

14

30 45 60 75 90

Bench Face Angle (deg)

Width (m)

Bench Slope Base

Base Width Savings

Failure Adj (90% min width)

Failure Adj (95% min width)

Figure 10: Plot of figure 9 recalculated for the “weak” set of fracture properties. 
V. Discussion and Conclusions 

This example exercise demonstrates the utility of the Bwedge program in assessing the 

sensitivity of a catch bench designed in closely fractured rock to various rock, fracture, and 

design parameters. The Bwedge program generated estimates of effective bench widths from 

rock and fracture properties that provided insight into bench behavior and bounded observed 

bench failure. It also highlighted the importance of blasting practice in determining the extent of 

local failure within the first couple of meters of bench width. 

These results are a credit to the Montana Tech students that collected the source data, onsite and 

in the laboratory, and performed both the geostatistical analyses of the fracture data sets and 

sensitivity analyses with respect to their input parameters. The amount of time and extent of 

mapping was limited; much more so than would be desirable for a design study. Despite this, the 

distribution of modeled and measured bench widths showed good correlation. This result is also 

a testament to the growing robustness of the Bwedge program which benefited greatly from the 

students’ thorough testing. 

Finally, these results demonstrate the practical usefulness of the Bwedge program in optimizing 

catch bench design. It provides a means for assuring adequate catch benches while limiting the 

costs of over-design. The program, and its companions Bplane (plane failures) and Bstepp (step 

path failures), are available from the author and will soon be available on the NIOSH website as 

well. The widespread availability of geostatistical software and ongoing development of 

automated fracture mapping systems based on laser and/or photogrammetric instruments promise 

to make these types of analyses even more practical in the future. 

Acknowledgements 

Montana Tech’s GeoE 5150 Slope Stability Analysis & Design course incorporated a project 

involving field validation of the new NIOSH bench slope software suite during fall semesters of 

2000, 2001, and 2002. During fall semesters 2001 and 2002, the students had the opportunity to 

collect data at Luzenac America’s Yellowstone Mine, an open pit talc mine near Cameron, 

Montana. Mike Cerino, Luzenac geologist enrolled in the course during fall semester 2001, 

provided the field site for this study and later collected supplementary geologic information. The 

other students in the fall semester 2001 course who participated in the project were Dean 

Brower, Russell Sheets, and Zachary St. Jean. The students in the fall semester 2002 course 

were Whit Adams, Kathryn Clapp, Jeremy Dierking, Meagan Duneman, Ben Johnston, Jennifer 

King, Renee Kockler, Tye Lasich, and Nate Majerus. The students contributed to collecting field 

data, analyzing results and identifying faults in the Bwedge program. These contributions were 

essential and central to the development of this paper, and are gratefully acknowledged. 
VI. Appendices 

Appendix A: Rock Mass Classification 

Q-system RMR

RQD 25 1 15

Jn 12 2 3

Jr 1.5 3 15

Ja 2 4 25

Jw 1 5 12

SRF 5 persistence 2

 separation 5

Q= 0.3125 roughness 3

 infilling 2

 weathering 3 

 rating/slopes -25 

 rating 60 

 class III 

 Description: Very poor rock Description: Fair Rock 

Appendix B: Laboratory Data 

Field Tilt Test Data Laboratory Tilt Test Data

 Specific Gravity Tests

Friction 

Angle Tan (Phi) 

Friction 

Angle Tan (Phi) 2.71 g/cc

36 0.726543 25 0.466308 2.74

46 1.03553 30 0.57735 2.84

46 1.03553 41 0.869287 

35 0.700208 25 0.466308 2.76 Average

35 0.700208 25 0.466308

40 0.8391 27 0.509525

35 0.700208 30 0.57735

41 0.869287 32 0.624869

45 1 34 0.674509

40 0.8391 35 0.700208

30 0.57735 34 0.674509

35 0.700208 

38.67 0.810272 30.73 0.600594 Average

 0.151461 0.125342 Standard Dev.

 0.186926 0.208698 SD/mean
Appendix C: Observed Wedge Failures 

Wedge 1:

• Joint striking 132°, dips 53°, 6.1m (20 ft) long, cemented caliche infill up to 13 mm (1⁄2 

inch) thick - broken in places and intact in others, waviness 26 cm (14 inches) amplitude 

over a 3 m (10 ft) wavelength. 

• Foliation fracture striking 15°, dips 72°, 3.7 m (12 ft) long, infill broken, planar. 

• Apex of partially failed wedge daylights 4.3 m (14 ft) from crest (photo below). (Note: 

4.3 m (14 ft) depth of apex is longer than the foliation fracture, because of rubble on top 

of the wedge. The actual fracture length was likely longer than 3.7 m (12 ft) before 

blasting.) 

 
Wedge 2:

• Joint striking 113°, dips 51°, 6.1 m (20 ft) long, cemented caliche infill with steps, 

waviness 2 cm (3⁄4 inch) amplitude over a 15 cm (6 inch) wavelength. 

• Foliation fracture striking 20°, dips 70°, 6.1 m (20 ft) long, open fracture with caliche 

infill. 

• Failed wedge apex daylights 6.1 m (20 ft) from crest (photo below). Arrow traces apex 

of steeply dipping wedge and lines illustrate sliding planes. Bench crest is near the top of 

the picture. 
Appendix D: Fracture Set 1 – Foliation 

Fracture # Strike Dip Persistence (m) Spacing* (m) Waviness (deg) 

1 36 63 6.10 0.24 5 

2 0 72 0.91 0.52 14 

3 28 70 0.30 2.62 2 

4 7 61 4.57 0.61 2 

5 10 69 0.61 1.31 2 

6 24 53 6.10 1.58 8 

7 30 68 3.66 4.27 6 

8 10 72 4.57 1.74 7 

9 19 76 6.10 0.30 4 

10 35 60 5.49 0.30 17 

11 0 76 0.61 0.98 4 

12 5 56 1.22 0.55 2 

13 7 80 4.57 0.94 12 

14 9 72 6.10 0.61 10 

15 13 72 3.05 2.80 17 

16 21 69 4.57 3.75 15 

17 22 73 4.57 1.37 14 

18 28 90 1.83 3.75 11 

19 35 70 2.13 0.30 7 

20 15 70 1.98 2.74 10 

21 25 76 1.52 0.91 7 

22 26 64 1.37 0.76 6 

23 8 71 1.37 0.46 26 

24 35 71 1.07 0.46 13 

25 28 74 1.22 0.61 23 

26 42 66 4.27 0.46 7 

27 22 90 1.07 4.57 7 

28 28 62 1.98 3.05 8 

29 34 70 4.57 0.46 12 

30 22 73 3.05 0.25 14 

31 37 86 1.22 0.84 5 

32 8 90 0.91 0.41 6 

33 28 76 1.83 0.61 16 

34 18 68 1.83 0.33 4 

35 6 69 1.83 0.71 10 

36 4 77 3.05 0.30 8 

37 11 80 0.91 0.28 3 

38 8 84 0.61 0.61 1 

39 22 74 0.61 0.61 12 

40 6 70 0.91 0.66 8 

41 8 80 3.05 0.25 20 

42 6 76 3.05 0.30 4 

*Estimated true spacing to the next fracture measured along a normal from the intersection of the scan line with the 

current fracture. 
Appendix E: Fracture Set 2 – Joints 

Fracture # Strike Dip Persistence (m) Spacing* (m) Waviness (deg) 

1 115 49 0.91 0.61 0.75 

2 88 54 2.13 0.58 25 

3 136 49 1.52 3.96 4 

4 118 67 3.05 0.30 4 

5 152 53 1.52 6.10 2 

6 170 50 3.05 2.26 3 

7 129 54 9.14 0.61 13 

8 160 55 9.14 3.05 3 

9 106 61 9.14 1.52 4 

10 123 25 2.74 0.30 9 

11 133 50 0.23 1.52 8 

12 90 36 2.44 1.52 5 

13 125 31 3.66 0.99 5 

14 132 47 1.22 0.76 2 

15 118 30 4.27 3.66 8 

16 108 83 3.05 0.30 0 

17 129 78 6.10 0.63 13 

18 124 43 1.52 1.22 0 

19 119 37 1.22 0.41 22 

20 114 50 6.10 0.76 16 

21 111 56 2.13 4.57 15 

22 131 54 0.91 0.43 0 

23 130 56 1.83 0.55 4 

24 127 57 9.14 2.44 3 

25 132 70 9.14 8.84 0 

*Estimated true spacing to the next fracture measured along a normal from the intersection of the scan line with the 

current fracture.