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NIOSH COMPUTER PROGRAMS FOR 

BENCH CREST FAILURE ANALYSIS IN FRACTURED ROCK 

J. Whyatt (Corresponding Author) 

Spokane Research Laboratory, NIOSH/CDC, 315 E. Montgomery, Spokane, Washington USA 

Phone (509) 354-8068, e-mail: juw6@cdc.gov

S. Miller 

University of Idaho, Moscow, Idaho USA 

J. G. Dwyer 

Spokane Research Laboratory, NIOSH/CDC, Spokane, Washington USA 
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SYNOPSIS 

 A package of bench design programs is being publicly released by the National Institute for Occupational Safety and 

Health (NIOSH). These programs are designed to provide a probabilistic estimate of the likelihood that various widths of 

catch bench will be retained. Program modules address the mechanisms of plane, plane step path, and wedge failure. 

Results are drawn from statistical and geostatistical descriptions of fracture characteristics and other input parameters, 

and reported as the statistical chance that a given width of catch bench will survive, that is, that a catch bench will remain 

wide enough to catch rolling and sliding material and prevent such material from posing hazards to miners operating 

below. The capabilities and application of this software are demonstrated through a case example. Comparing bench 

width estimates obtained using geologic data with actual widths is a key step in verifying that a program is appropriate 

for particular site conditions and that proper statistical descriptions of fracture parameters for that site have been 

developed. Such verification efforts improve confidence, and hence usefulness, of this method for designing future slope 

benches. Development and release of these programs appears particularly timely given recent progress in photoanalysis 

methods, which promise to greatly reduce the cost of collecting fracture data. 

INTRODUCTION 

 This paper was developed as part of a research program addressing accidents associated with failure of mine slopes 

initiated by the Office of Mine Safety and Health, National Institute for Occupational Safety and Health (NIOSH). It 

describes one part of the program aimed at improving design tools to enhance reliability of catch-bench design, a key 

safety element of slope design. Associated tasks include identification of hazardous geologic conditions (Girard and 

McHugh, 2000), continuous (as opposed to point) monitoring of large-scale slope movement (Dwyer, 2003), and 

development of techniques to warn of small-scale raveling and rock falls (McHugh, 2004). 

 Catch-bench crests are often broken or unstable in surface mines (Figure 

1). This is particularly true in highly fractured rock where many joints of 

limited persistence weaken the crest. Crest stability is important for two 

reasons. First, benches designed to catch raveling, sliding, and rolling slope 

material must be wide enough to halt and collect this material. Second, 

bench crests with low factors of safety may be unsafe to work on, 

particularly when heavy equipment is being operated near the crest. 

 Bench crests are often allowed to fail locally (Figures 1 and 2) since 

perfect catch benches are usually uneconomic. Most failures occur during 

excavation, but other failures may occur after weathering, vibration, freezethaw cycles, etc. These failures can be tolerated so long as a minimum 

functional bench width is maintained. 

 The reliability of catch-bench design is best described statistically, 

particularly when failures involve small-scale, pervasive geologic 

features. This problem has received considerable atten-tion, including a Ph.D. dissertation developed by one of the 

authors (Miller, 1982). This work, refined somewhat over the intervening years, is the basis for the set of programs 

described in this paper. The programs provide a statistical 

estimate of the probability that bench crests will fail and to 

what extent and are based on statistical descriptions of 

fracture set properties. Program modules—Bplane, Bstepp, 

and Bwedge—are written for plane, step path, and wedge 

modes of failure, respectively. 

 Two developments have made updating and release of 

this software particularly timely. First, computer speed has 

increased sufficiently to enable interactive and essentially 

instantaneous execution of these programs on a personal 

computer. Second, the task of inputting fracture data, 

traditionally a laborious task conducted by a geologist in 

Figure 1: Typical catch bench geometry. 

Figure 2: Plan view of realized bench width (after Ryan and 

Pryor, 2001). 
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proximity to an outcrop or bench face, is on the verge of a similar revolution. Research on remote and automated fracture 

mapping, particularly in mines where fracture traces are uncovered, is being pursued by a number of groups throughout 

the world and appears close to fruition. NIOSH is supporting some of this work at the University of Arizona through its 

grant program. Taken together, these two developments promise a breakthrough in the practicality and cost-effectiveness 

of work that was of more academic than practical interest some 20 years ago. 

 This paper briefly reviews slope ground fall accidents, provides an overview of software capabilities, and then reviews 

an example application. Detailed case studies, a user’s guide, and other references are available from the corresponding 

author and will be posted on the NIOSH Web site. 

BENCH SAFETY 

 Accident statistics collected by the Mine Safety and Health Administration (MSHA) have shown that loose material 

moving down slopes and bench failures pose significant safety hazards to miners. From 1995 through June of 2004, 

surface ground control accidents have contributed to 44 fatalities. Of these, 33 accidents occurred in metal/non-metal or 

sand and gravel mine,s while the remainder took place at coal mines. As can be seen in Figure 3, approximately 55% of 

the fatalities (24 out of 44) were a direct result of highwall failures or individual rock falls striking workers in the pit 

below. Failures of unstable ground or highwall benches beneath operating equipment are also a major concern. 

 The importance of bench integrity is well illustrated by 

two of these accidents. One occurred on the evening of 

October 5, 1998, early in the night shift. A large piece of 

rock fell 6 m from the highwall to a safety bench, split, 

then fell an additional 17 m onto the cab of a drill, 

destroying the cab (Figure 4). The rock measured about 2 

m long, 2 m wide, and 1.2 m thick. 

 Another fatal accident occurred on the morning of 

September 2, 1998, when a 67-year-old bulldozer operator 

with 40 years of mining experience was maneuvering his 

Caterpillar D8 along a bench in a limestone quarry in 

Oregon. The outside edge of the bench collapsed, and the 

dozer rolled sideways 2-1/2 times to the bottom of the pit, 

coming to rest on its side. The dozer was equipped with 

rollover protection and a seat belt. The operator was not 

wearing the seat belt and was fatally injured. 

SOFTWARE CAPABILITIES 

 The Bplane, Bstepp, and Bwedge programs are designed to 

assess the extent of small-scale failures along the crest of 

benches where rock blocks slide along natural fractures (as 

plane shears and tetrahedral wedges). Failure along a joint set 

complicated by cross jointing and failure of small bridges of 

intact rock (a step path) in a plane failure geometry is also 

considered. 

 These programs are ideal for cases where large numbers of 

discontinuities of limited extent can be grouped into fracture 

sets. They also assume that discontinuity characteristics, 

including length, spacing, and dip, can be reasonably 

described by statistical functions that are consistent 

throughout a design sector. 

Figure 3: Number of deaths attributed to highwall failure 

and rock falls, 1996-2004. 

Figure 4: Cab crushed during slope failure (MSHA 

fatalgram, www.msha.gov). 

Highwall Failure, 

16

Individual Rock 

Fall, 8

Collapse of 

Bench, 

Highwall, or 

Ground Beneath 

Equipment, 13

Material Slough 

from Stockpile, 

5
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Plane Shear Failure 

A plane shear failure occurs when a block defined by fractures and bench 

geometry slides along a single failure surface. The plane shear failure mode is said 

to be Akinematically viable@ if the average strike is parallel or nearly parallel to the 

strike of the slope face and the dip is flatter than the dip of the slope face (Hoek and 

Bray, 1981, p. 150). Failure will extend laterally along the bench to cross-cutting 

fractures, changes in bench strike, and/or newly created fractures that provide 

'release surfaces' (Figure 5). It is assumed that these surfaces will provide little 

resistance to sliding (that is, failure), so they can be neglected in assessing the 

stability of the block. 

Step-Path Plane Failure 

 The availability of a single sliding surface long enough to permit plane shear failure may be comparatively rare in 

slopes cut in rock in which single fractures are short. However, a more complex failure path comprised of multiple 

fractures is much more likely to provide the continuous path needed for sliding. From a two-dimensional standpoint, the 

most likely situation in practice is that two conjugate fracture sets form a stepped geometry (Jaeger, 1971). Both sets 

strike parallel or nearly parallel to the strike of the slope, and sliding occurs on the flatter dipping set. Figure 6 illustrates 

typical step path geometries in a fractured rock slope. 

 Step path failure geometries typically have lower probabilities of 

stability than plane shear geometries of similar scale. The differ-ence 

lies primarily in the treatment of rock bridges. Bridges are considered 

to prevent absolute failure in the plane shear model, but are checked 

for failure in the plane step path model. Experience has shown that 

for 12- to 20-m-high benches cut in crystalline rock with a tensile 

strength of 500 to 2,000 t/m2

, the probability of sliding is nearly zero 

when the fraction of intact rock exceeds approximately 0.08. Thus, 

where bridges constitute 8% or less of the total length, 

step paths that include bridges are likely to have a 

higher risk of failure than comparable plane shear 

paths. Failure becomes increasingly unlikely as the 

proportion of bridge length on the failure surface 

approaches 8%. The Bstepp program considers failure 

to be impossible if the proportion exceeds 8%. 

Wedge Failure 

 Wedge-shaped blocks often are created in benches by 

two fractures that the intersect both the bench and slope 

surfaces (Figure 7). Failing wedges move along the line 

of intersection formed by the fractures, maintaining contact on each fracture plane. In the absence of pore pressure, 

sliding will occur only when the inclination of the intersection line is steeper than the friction angle of the fractures. The 

steepest intersection lines are usually those that bear nearly perpendicular to 

the slope face. 

Program Input and Operation 

 Required geotechnical input falls into three main classes: fracture-set 

geometry, fracture shear strength, and rock mass properties. Because intact 

material is assumed to remain intact, the only rock mass properties considered 

are density and groundwater level. Any planes of weakness within the rock 

mass can be considered fractures with cohesion. Most program input is in the 

form of statistical parameters for variograms and appropriate probability 

distribution functions, rather than constants. Figure 7: Idealized wedge failure. 

Figure 5: Idealized plane shear failure.

Figure 6: Examples of step path geometries in a rock slope 

(from Call and Nicholas, 1978). Top, Continuous step path; 

bottom,. discontinuous step path with intact rock bridges.
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 The essential core of these programs is computation of the probability of sliding for a given potential failure mass. The 

fracture geometry of that failure mass is constructed with spatial rock-fracture simulations. For instance, Bplane analyzes 

plane-shear failure modes in a two-dimensional framework by simulating plane-shear fractures in the bench and then 

calculating the probability of stability for each one, as well as by identifying the corresponding backbreak distance on the 

bench. By repeating the simulation many times for a given bench, the probability of retaining various bench widths can 

be estimated. The Bstepp program conducts plane simulations for step paths in a similar manner. The Bwedge computer 

program analyzes three-dimensional wedges by simulating fractures from two fracture sets and testing whether they form 

unstable wedges. 

 The factor-of-safety (SF) equation used to evaluate the probability of sliding is assessed with the point estimation 

method for the rock slope failure mode (such as plane shear, step path, or wedge). This method provides reliable 

estimates of the mean and standard deviation of the factor-of-safety probability distribution (Miller et al., 2004). A 

gamma probability density function is used for modeling this probability distribution, because it allows only positive 

values and is flexible enough to provide symmetrical shapes and right-skewed, exponential-type shapes for the factor-ofsafety distribution. This distribution can be integrated numerically from 0 to 1 to obtain the probability of sliding (PS = 

the portion of the factor-of-safety distribution where SF <1.0). The overall probability of failure, PF, for the potential 

slope failure mass is the joint probability that the rock discontinuities are long enough to allow kinematic failure (PL) and 

that sliding occurs along the rock discontinuities (PS). That is, PF = PSPL. 

INTERPRETING ANALYSIS OUTPUT 

 Program results are reported as a probability that various bench widths will be retained for a given failure mode (that 

is, a particular failure mechanism that involves a particular set of features). The probability of retaining a particular 

bench width will be the joint probability of individual probabilities calculated for each failure mode. Joint probability is 

calculated by multiplying individual probabilities and applies individually to a short section of bench, not the entire 

bench. In the case of wedge failure, the probability gives the odds that any section of a bench as long as it is high will not 

trigger any failures that reach deeper into the bench width than a particular value. In other words, the proportion of bench 

segments that lose a section of the bench as wide as the length of the segment will be 1 minus the joint probability of 

retention. For example, a 0.80 probability of retaining 4-m-wide catch bench means that 80% of the bench run will retain 

a width of at least 4 m. 

 The probability of losing all the bench is also an important consideration. Not only do such failures eliminate any 

capability for catching loose material, but they may undermine overlying benches, leading to larger-scale failures. Thus, 

the design of overall slope angles should provide for very high probabilities (greater than 0.95) of retaining bench widths 

less than 1 m. 

 Results are typically plotted as a curve relating the probability of retaining 

bench width versus bench width. Individual curves are calculated for each bench 

slope angle. Since bench geometry has a direct influence on the overall slope 

angle, similar plots can be made for overall slope angle (Figure 8). The 

relationship between bench geometry and overall slope angle can be expressed 

as—

tan (A) = 1/[(W/H) + (1/tanB)] 

where A = overall (average) slope angle; B = bench face angle; H = vertical 

height of bench; and W = horizontal width of bench. For example, if H = 15 m, 

W = 8 m, B = 64°, then A = arctan{1/[(8/15) + (1/tan 64°)]} = 44°. 

 If an overall steeper angle is desired, then the W:H ratio of benches must be 

decreased or the bench faces cut at a steeper angle. For typical applications, 

results from bench simulations will guide the engineer in selecting the overall 

slope angle to minimize extensive loss of catch-bench width and thus minimize 

subsequent rock fall hazards. Relationships between bench geometry, catch- Figure 8: Typical results showing 

probability of retention for various 

bench widths and slope angles. 
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bench width, and overall slope angle can be displayed in graphs, which can be used to predict overall slope angles when 

the probability of retaining a given catch-bench width has been specified. 

SOFTWARE TESTING AND FIELD VERIFICATION 

 Verification of the software was an important part of this work and was pursued on two levels. The first level was 

simply verification that the calculated results were mathematically correct and numerically accurate. At this level, 

verification included the author's substantial experience with the program and his ability to recognize unreasonable 

results. Verification included dozens of parametric studies and results of unpublished 'stress tests' conducted by students 

at Montana Tech of the University of Montana, the University of Arizona, and the University of Idaho. These student 

beta testers found new and interesting ways to crash the programs, often through inappropriate and unrealistic inputs. 

This experience led to the implementation of screens to evaluate reasonable input parameters and refinement of 

numerical procedures. 

 Verification also included comparisons of program predictions based on local fracture set characteristics with actual 

bench crest failure patterns. This mode of verification has the advantage of testing assumptions underlying the code as 

well as testing whether the assumptions underlying the programs were sufficiently close to real conditions to provide 

insights into design decisions. This has been pursued through collection and development of case studies (for example, 

Ristau, 1994; Whyatt et al., 2004). One of these, which provides a good example of Bwedge use, is summarized in the 

remainder of this paper. 

 Overall, verification of the accuracy and usefulness of this software has been the cornerstone of this research. Since 

NIOSH cannot warranty this software (like any software publisher), case studies and other verification efforts are the 

user’s assurance that reasonably accurate results are produced. 

LUZENAC CASE STUDY 

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

the bench of a mine pit slope. Work included collecting and analyzing geologic data, comparing expected and observed 

bench crest performance, and conducting sensitivity studies of fracture and bench design parameters. The study was 

conducted by students at Montana Tech in cooperation with Luzenac America’s Yellowstone Mine and NIOSH. 

 Luzenac America’s Yellowstone Mine is located southwest of Ennis, MT, along the east slope of the Ruby Mountains. 

Presently the mine consists of two approximately 90-m-deep open pits. The study focused on a section of a single bench 

within the north wall of the south pit in hydrothermally altered dolomite of Precambrian age. The dolomite is heavily 

fractured, with the fractures forming at least four major sets. 

 Five representative wedge failures in this area were mapped and described by 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 previously were not seen.. Two sets of fractures delineating these and similar wedges 

were mapped by the student teams along a 90-m-long scan line on the study bench using tape and a Brunton compass. 

The first of these fracture sets was labeled the 'foliation' set and formed the left side of the wedges. The second and 

sparser of the sets was the 'joint' set. 

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

Spokane Research Laboratory and cut to determine the friction angle of saw-cut surfaces. Laboratory tests on these 

surfaces showed an average friction angle of 30.7° with a range of from 25° to 34°. Rock density tests on three rock 

fragments showed that average density was 2.76 g/cm3

. 

 The characteristics of each fracture set were described statistically and geostatistically for analysis by the Bwedge 

program. The students developed a full set of parameters describing variability of fracture dip direction, dip, spacing, 

persistence, and waviness from the mapped fractures. Although the defined fracture sets were not ideal for this purpose 
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and included a wider range of orientations and fewer fractures (especially for the joint set) than would be desired for a 

full-blown characterization study, the data were sufficient for the students to estimate all the required parameters. These 

values are listed in Table I. 

Table I: Fracture set characteristics 

Parameter Mean Standard deviation Nugget Range 

Foliation joint fracture set characteristics 

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, m Minimum 1.0 Maximum 12.0 

Joint fracture set characteristics 

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 

 A first-cut analysis of wedge stability was developed as shown in Figure 9. Bench slope, average fracture-set 

orientation, and the wedge formed by 'average' fractures were plotted to show that the wedge formed by this set 

daylighted 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, which is a typical joint friction angle. Thus, failure of such a wedge would be 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. 

 These input values overestimated retention of the bench crest, but correctly matched retention of portions of the bench 

further from the crest (Figure 10). This result is surprisingly good, especially considering that it did not incorporate 

extensive disruption of the outer portion of the bench by blasting, as noted by the mine geologist. 

 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 was 

removed. Bwedge runs using these 

weaker values more closely fit 

observations for the outer bench, but 

also underestimated retention deeper 

into the bench, which is less affected 

by blasting. This suggests that the 

student's set of parameters may well 

describe fracturing in situ prior to 

blasting. To the extent that this proves 

to be the case, the overall slope angle 

could be steepened 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, which would 

steepen the overall slope angle by 

about 5°, to roughly 45°. 

 Of course, the level of confidence 

needed for such a design study requires a somewhat larger field data set. Other operational and safety factors beyond the 

scope of this software should be considered. However, even with a limited data set, this case makes clear the power of 

this software to add new insights and precision to the design process. 

Figure 9: Stereonet plot of joint poles, joint set average orientation, and pit slope. 
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SUMMARY AND CONCLUSIONS 

 Computer software for a PC platform was 

developed to analyze bench crest failures 

stochastically in slopes excavated in heavily 

jointed rock. Three programs in the package 

analyze plane, plane step path, and wedge 

modes of failure using statistical 

descriptions of fracture sets and other 

relevant parameters. The programs are 

based on routines developed some 20 years 

ago and look particularly useful in light of 

recent advances, such as interactive 

execution of computations and automated 

fracture mapping, which promises to reduce 

the expense of fracture mapping, 

particularly where fractures are exposed in 

mine slopes and road cuts. The software 

and related manuals and case studies are available from the corresponding author and at the NIOSH Web site. Extensive 

efforts have been made to verify program operation and check results against real cases. However, complete confidence 

in the software requires verification under local conditions. As this confidence is gained, these programs should be 

valuable tools for robust designs of safe catch benches. 

ACKNOWLEDGEMENTS 

 Extensive validation as well as the case study described in this paper were undertaken as a class project for Montana 

Tech’s GeoE 5150 Slope Stability Analysis and Design course during the fall semesters of 2000, 2001, and 2002. 

Luzenac America provided a field test site at its Yellowstone Mine, an open-pit talc mine near Cameron, MT. Mike 

Cerino, Luzenac geologist, provided invaluable support, particularly for the final 2002 field campaign and follow-up data 

collection. We gratefully acknowledge the efforts of Dr. Mary MacLaughlin, the course instructor, and her students—

Dean Brower, Russell Sheets, Zachary St. Jean, Whit Adams, Kathryn Clapp, Jeremy Dierking, Meagan Duneman, Ben 

Johnston, Jennifer King, Renee Kockler, Tye Lasich, and Nate Majerus. The students collected field data, analyzed 

results, and identified faults in the Bwedge program. 

REFERENCES 

Dwyer, J.G. 2003. Novel concepts for monitoring the stability of open pit mine highwalls using radar interferometry and 

spectral imaging. M.S. thesis. Rolla, MO: University of Missouri-Rolla, 78 pp. 

Call, R.D. & Nicholas, D.E. 1978. Prediction of step-path failure geometry for slope stability analysis. In Y.S. Kim, 

(comp.), Proceedings, 19th US symposium on rock mechanics, Stateline, NV, May 1-3, 1978. Reno, NV: University 

of Nevada-Reno. 

Girard, J. & McHugh E. 2000. Detecting problems with mine slope stability. In Proceedings, 31st annual institute on 

mining health, safety, and research. Roanoak, VA, Aug. 27-30, 2000, 8 pp. 

Hoek, E. & Bray, J. 1981. Rock slope engineering, 3rd ed. London: Institute of Mining and Metallurgy, 402 pp. 

Jaeger, J.C. 1971. Friction of rocks and stability of rock slopes. Geotechnique 21: 97-134. 

La Pointe, P.R. 1980. Analysis of the spatial variation in rock mass properties through geostatistics. In Rock mechanicsa state of the art: Proceedings, 21st symposium on rock mechanics. Rolla, MO: University of Missouri-Rolla, pp. 

570-580. 

Figure 10: Estimated probability of stability at various depths into the bench 

crest based on measurements, a model using the student set of fracture 

parameters, and a set of weakened parameters. 

Depth of Bench Failure

0

10

20

30

40

50

60

70

80

90

100

012345

Distance from Crest (m)

Prob of Min Width (%)

Measured

Student

weakened
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Miller, S.M. 1982. Statistical and Fourier methods for probabilistic design of rock slopes. Ph.D. dissertation. Laramie, 

WY: University of Wyoming, 204 pp. 

Ristau, J.M. 1994. Field verification of a step-path simulation model for rock slope stability analysis. M.S. thesis. 

Moscow, ID: University of Idaho, 134 pp. 

McHugh, E. 2004. Video motion detection for real-time hazard warnings in surface mines. Presentation at annual 

meeting, Society of Mining Engineers, Feb. 23-25, 2004, Denver, CO. Preprint 04-74, 9 pp. 

Miller, S.M. et al. 2000. computer modeling of catch benches to mitigate rockfall hazards in open pit mines. In J. Girard 

et al. (eds.), Pacific rocks 2000: Rocks around the rim. Proceedings, 4th North American rock mechanics symposium, 

Seattle, WA, July 31-Aug. 3, 2000. Rotterdam: Balkema, pp. 539-545. 

Miller, S.M. et al. 2004. Application of the point estimation technique for stochastic rock slope engineering. In Gulf 

rocks 2004: Rock mechanics across borders and disciplines. Proceedings, 6th North American rock mechanics 

symposium, Houston, TX, June 5-10, 2004. Alexandria, VA: American Rock Mechanics Association, 11 pp. 

Mine Safety and Health Administration. Fatalgrams, Sept. 2, 1998, and Oct. 5, 1998. Available at www.msha.gov.

Nasrallah, J.G. et al. 2004. Rock mass characterization for slope/catch bench design using 3D laser and digital mapping. 

In Gulf rocks 2004: Rock mechanics across borders and disciplines. Proceedings, 6th North American rock 

mechanics symposium, Houston, TX, June 5-10, 2004. Alexandria, VA: American Rock Mechanics Association, 10 

pp. 

Nicholas, D.E. & Sims D.B. 2001. Collecting and using geologic structure data for slope design. Ch. 2 in W.A. Hustrulid 

et al. (eds.), Slope stability in surface mining. Littleton, CO: SME, pp. 11-26. 

Whyatt, J.K. et al. 2004. Analysis of bench crest performance at the Yellowstone Mine: A case study. In M. McLaughlin 

& R. McNearny (eds.), Proceedings, 39th symposium on engineering geology and geotechnical engineering: research 

to practice, May 18-19, 2004. Butte, MT: Montana Tech of the University of Montana, pp. 149-163.