ABSTRACT 

 Mine planning for a new reserve is based on information 

obtained from exploratory coreholes. A critical component of an 

exploration program is the geotechnical evaluation. Poor 

assumptions about roof conditions greatly add to the risks of 

mining. 

 Rock mechanics testing is central to a geotechnical exploration 

program. Typically, 3 to 5 uniaxial compressive strength (UCS) 

tests are made to characterize a particular roof unit at a given 

corehole. The average (mean) of these tests is taken as “The UCS” 

for that location. Isopach contour maps are then used to show 

spatial trends in roof strength. 

 Two issues are raised by this traditional approach. The first is 

due to the large variability in UCS values that is typical even within 

a single unit from a single hole. The average UCS might be higher 

at Corehole A than it is at Corehole B, but the difference may not 

be statistically significant. 

 The second issue is whether widely spaced coreholes can 

identify valid spatial trends in rock strength. The answer depends 

upon whether rock strength changes over distances that are longer 

or shorter than the corehole spacing. This is a classical 

geostatistical problem. While geostatics have been used to 

investigate many coal quality parameters, they have seldom been 

used to evaluate rock strength. 

 This paper describes an extensive investigation of these issues 

conducted by the National Institute for Occupational Safety and 

Health (NIOSH) in collaboration with Peabody Energy. The study 

employed the Peabody Rock Mechanics Data Base which contains 

more than 10,000 individual test results. Data from four important 

roof units were subjected to statistical analysis: 

• Brereton Limestone above the Herrin 6 seam (Illinois) 

• Turner Mine Shale above the No. 9 Seam (Kentucky) 

• Sandstone above the Eagle Coal (West Virginia) 

• Shale above the Eagle Coal (West Virginia) 

 The study did not find significant spatial trends in rock strength 

in any of the cases. Perhaps there are none, or perhaps the 

exploration coreholes were just too far apart to see them. These 

results have valuable implications for the design of geotechical 

exploration programs. 

INTRODUCTION 

 Modern mine planning requires a thorough knowledge of the 

geotechnical conditions that will be encountered underground. 

Roof conditions can determine the bolting pattern, longwall pillar 

size, entry width, and the feasibility of extended cuts. Inaccurate, 

overly optimistic assumptions can mean unexpected hazards, 

higher costs, and lower productivity. Unfortunately, there are 

many examples of large investments that were lost because ground 

conditions were worse than anticipated. 

 The Westray coal mine in Canada provided a particularly tragic 

illustration of the potential consequences of inadequate 

geotechnical characterization. Westray was designed around large, 

thick seam, room-and-pillar mining equipment that had been 

successful in western Canada. The mine’s planners did not foresee 

that the thinly laminated roof shale roof at Westray could not 

support the wide intersection spans the equipment required. Major 

roof falls began to occur on a regular basis, and it was obvious that 

the very existence of the mine was in question. Senior managers 

were preoccupied with finding the solution to the ground control 

problems. The diversion of their attention from other major issues 

and hazards made a significant contribution to the deadly methane 

explosion that killed 26 miners (Richard, 1999; Comish, 1993). 

 Most of the data used in coal mine geotechnical site 

characterization come from exploration coreholes. However, the 

number and location of coreholes is usually determined by the need 

to define coal thickness and quality, not rock mechanics. The result 

is that mine planners must often make due with widely spaced data 

points. 

 Therefore, it is important to try to make the most of the data 

that are available. There are two key issues: 

• How to interpret the data from an individual hole, and; 

• How to interpolate conditions between holes. 

The purpose of this paper is to explore these two issues, and to 

begin to develop strategies for conducting geotechnical evaluations. 

UNCONFINED COMPRESSIVE STRENGTH (UCS) 

 The two most important geotechnical parameters that can be 

obtained from coreholes are: 

SPATIAL TRENDS IN ROCK STRENGTH – CAN THEY BE 

DETERMINED FROM COREHOLES? 

Christopher Mark, Section Chief, Rock Mechanics 

Linda McWilliams, Statistician 

Deno Pappas, Civil Engineer 

National Institute for Occupational Safety and Health 

Pittsburgh Research Laboratory 

Pittsburgh, Pennsylvania USA 

John Rusnak, Chief Geologist 

Peabody Energy 

St. Louis, Missouri USA 
• The thickness of the roof units (lithography), and; 

• The structural competence of each unit. 

Both are required for the Coal Mine Roof Rating (CMRR), which 

provides perhaps the most complete picture of the overall roof 

stability. 

 The UCS is probably the most widely quoted measure of the 

structural competence. UCS tests (or UCS index tests, like the 

Point Load Test) are also one of the three main elements in the 

CMRR.1

 In the U.S., 3 to 5 samples are typically tested to 

determine the UCS of a rock unit. 

 One issue with the UCS is the high variability associated with 

it. One recent study (Rusnak and Mark, 2000) found that the 

standard deviation for a typical suite of UCS is 20-30% of the mean 

(figure 1). To illustrate what this means in plain English, lets 

suppose 5 tests of a sandstone in Corehole “A” had an average 

UCS=10,000 psi with a standard deviation of 3,000 psi. A 95% 

confidence interval around the mean has an upper limit of 13,450 

psi and a lower limit of 6,555 psi. That is a pretty big range! 

 Now let us further suppose that the average UCS in nearby 

corehole “B” was 12,500 psi. Would we be right to think that the 

rock was actually stronger at Corehole B? Probably not. 

 An even more significant question is how much do we really 

know about the strength of the sandstone between our two 

coreholes. Let's suppose for a moment that the tests did tell us the 

“true” UCS. Would we expect that the sandstone’s strength 

gradually increased from 10,000 psi at Corehole A until it reach 

12,500 psi at Corehole B? This is what a contouring package 

would assume. But how do we know that the strength doesn’t 

actually fluctuate a lot between the two coreholes (see figure 2)? 

 

1

The other two elements of the CMRRR are (1) the diametral point load 

strength (a measure of bedding plane strength) and (2) the RQD or fracture 

spacing (Mark et al., 2002). 

 Spatial statistics—commonly called Geostatistics—can help us 

with the answer. 

GEOSTATISTICS 

 Geostatistics were first developed to provide better estimates of 

ore reserves. In coal mining, they have been used to evaluate 

energy content, sulfur, ash, and other quality attributes of deposits. 

In fact, geostatistics can be used to study many properties that vary 

in space, but are measured at distinct locations. Research in fields 

as diverse as hydrology, forestry, air pollution, and global warming 

have all made extensive use of geostatistics (Ledvina et al., 1994; 

Armstrong, 1998). 

 The basic idea of geostatistics is this. Suppose the goal is to 

determine the sulfur content in a coal seam. If two coreholes are 

drilled just 1 ft apart from each other, one would expect that their 

sulfur values would be very similar. If a third hole is drilled 100 ft 

away, the sulfur content might be expected to change a little, but 

still be close the original value. As more holes are drilled further 

and further away, a distance is eventually reached where the first 

holes no longer help predict the sulfur content. 

 Geostatistics helps to quantify the spatial relationships that are 

observed between coreholes. The variogram is the central tool. 

The variogram is constructed by comparing all the possible pairs of 

data points in a set of drillhole data, and then calculating for each 

pair: 

• The distance (h) between the two holes, and; 

• The difference between the values of the parameter being 

measured (sulfur, in the example above) in the two holes. 

 An idealized variogram is shown in figure 3. The x-axis is the 

distance h between the drillholes. The y-axis is the “variance” (the 

square root of the variance is the standard deviation) for all the data 

pairs with approximately the same distance h between them. Some 

valuable information that can be obtained from the variogram are: 

• Range: the distance h at which there is no spatial

relationship between the holes (the holes are still related in 

the sense that they come from the same data set); 

• Sill: Typically, the value of the variance for the entire data 

set (i.e., without considering any spatial relationships); 

Figure 1. Histograms showing standard deviation of UCS 

for various rock types as a fraction of the mean 

(after Rusnak and Mark, 2000). 

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Actual (?)

BOREHOLE LOCATION

Figure 2. Conceptualization of UCS variation between two 

coreholes. 
• Nugget: The short-range variability (i.e., the difference you 

might expect to find even with two coreholes drilled right 

next to each other). 

 Once the model variogram has been constructed, it can be used 

to obtain best statistical estimates of values throughout the entire 

reserve area using the mathematical techniques of “kriging.” One 

big advantage of kriging is that the “kriging error” can also be 

plotted. The kriging error essentially tells us how much confidence 

we can have in our estimates of what’s going on between the holes. 

 Of course, this has been a greatly simplified (and nonmathematical) explanation of geostatistics. Before we move on, 

three other points are worth mentioning: 

• Drift: Geostatistics only work when it can be assumed that 

the entire data set has a single mean and standard deviation. 

If there is a regional trend (for instance, if the sulfur values 

decrease from north to south), then that “drift” must be 

removed mathematically before the variogram is 

constructed. 

• Outliers: Because the variance is a squared function, even 

a single outlier can have a huge effect on the variogram. 

Often, the best thing to do is just remove them (Armstrong, 

1998). Outliers can also be truncated (so that they still 

represent high or low values), or their effect can be 

minimized by working with the logarithms of the data 

values. 

• Anisotropy: The simplest variograms look just at the 

distance between points, and do not consider the orientation 

of that distance. However, many geologic phenomena do 

have preferred orientations, and it is possible to construct 

variograms in different orientations (as long as enough data 

are available). Often, a look at a contour plot of the data is 

enough to determine if anisotropy might be an issue. 

AN EXAMPLE OF GEOSTATISTICS APPLIED TO 

GROUND CONTROL 

 There are very few reported examples of the application of 

geostatistics to ground control (Reifenberg, 1994, 1996; Kim et al., 

1989). In fact, of the nearly 1,000 papers included in the 22 

Conferences in this series, only three have ever mentioned 

geostatistics. 

 One notable exception is the case history presented by Ledvina 

et al. (1994). Ledvina investigated the thickness of the Brereton 

limestone in the roof above the Herrin No. 6 seam in Illinois. At 

this mine, the thickness of the limestone was the controlling factor 

behind roof stability. 

 Ledvina had three data sets to work with: 

• A large area with widely-space coreholes; 

• A smaller area with more closely-spaced surface coreholes, 

and; 

• A much smaller underground area, with very closely-spaced 

roof bolt test holes. 

 Figure 4a shows the contour plot for the limestone thickness 

from the widely-spaced coreholes. Note the large number of 

“bulls-eyes” (closely spaced contours around a single corehole) and 

large areas of seeming uniformity where data are sparse. The 

variogram (figure 4b) confirms that this drilling pattern is useless to 

predict limestone thickness between the coreholes. If there is some 

spatial relationship, it is clearly operating over distances that are 

less than the typical spacing between the holes. 

Figure 3. Idealized variogram. 

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Figure 4b. Variogram constructed from data illustrated in 

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Figure 4a. Contour plot of Brereton Limestone thickness 

from surface coreholes. Limestone thickness contour 

intervals are 0.5 ft (after Ledvina et al., 1994). 
 In contrast, clear spatial trends can easily be seen in the contour 

map from the underground drilling area (figure 5a). The contour 

lines are much more regular, and each is generally defined by 

several data points. The variogram (figure 5b) has an almost ideal 

shape, with a nugget of zero and a range of about 300 ft. The 

implication is that if the mine really needed to know the thickness 

of the limestone, the holes would have to be drilled less than 300 ft 

apart.2

 

2

Ledvina (1991) also provides details on a second case history from a mine 

working in the Springfield No. 5 seam in Illinois. This case studied the 

thickness of the Turner Mine Shale, the unit which lay directly above the 

coal. Again, Ledvina had three data sets with different hole spacings, and 

again only the underground data set displayed any meaningful spatial 

correlation, with the range of the variogram being about 300 ft. 

 It is interesting to note that for both of these data sets, the 

average limestone thickness was about 2.5 ft, and the standard 

deviation was about 2 ft. This is important because it tells us that 

even if our holes are too far apart to be spatially related, it does not 

mean that we know “nothing” about the rock in between the holes. 

We still know the approximate range of values for that rock (from 

the mean, the standard deviation, etc), we just don’t have any idea 

where the high and low values might be. 

ANALYSIS OF UCS DATA 

 The data used in this study were obtained from the Peabody 

Energy Rock Strength Data Base. Peabody Energy initiated fullscale rock mechanics testing in the fall of 1986. Testing has been 

done primarily on core samples obtained from exploration drilling 

to provide data for mine planning and design. A full range of 

testing is conducted including uniaxial compressive strength, 

indirect tensile strength, point load index, triaxial compressive 

strength, flexural strength, direct shear strength, long term creep, 

roof bolt anchorage capacity, slake durability, ultrasonic velocity, 

swelling strain and Atterberg limits. ASTM and ISRM procedures 

are followed for all rock mechanics testing. Currently, the data 

base contains rock mechanics test results from more than 1,000 

drill holes from the states of WV, IL, KY, IN, CO, and OH. 

 Four data sets were analyzed for this study: 

• Brereton Limestone above the Herrin 6 seam (Illinois) 

• Turner Mine Shale above the No. 9 Seam (Kentucky) 

• Sandstone above the Eagle Coal (West Virginia) 

• Shale above the Eagle Coal (West Virginia) 

 Table 1 contains details on each data set. The two midwestern 

data sets have more holes each, but an average of just 2 UCS tests 

per hole. In the data sets from southern West Virginia, average 

number of tests per hole was about 5. In the case of the Brereton 

limestone, the holes were distributed over an area measuring 

approximately 40 miles by 40 miles. The areas measured about 

12 miles by 12 miles in the other three cases. 

Table 1. Overall rock unit summary. 

State No. 

holes 

No. 

UCS 

tests 

UCS 

average 

(psi) 

UCS 

standard 

deviation 

UCS 

variance 

(106

) 

Size of area 

(mile2) 

Rock Unit–Brereton Limestone 

IL 108 216 15,251 7,188 51.7 1,744 

Rock Unit–Turner Mine Shale 

KY 73 135 6,991 4,040 16.3 109 

Rock Unit–Shale above Eagle Coalbed 

WV 45 207 11,457 4,757 22.6 157 

Rock Unit–Sandstone above Eagle Coal bed 

WV 50 295 15,266 3,850 14.2 165 

 The first step was to evaluate the variability of the UCS tests 

themselves. The goal is to apportion the total variability between: 

• Within-hole variability due to the range of UCS values 

encountered in each individual hole, and; 

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Figure 5b. Variogram constructed from data illustrated in 

figure 5a (after Ledvina et al., 1994). 

Figure 5a. Contour plot of Brereton Limestone thickness from 

closely-spaced underground test holes. Limestone thickness 

contour intervals are 0.5 ft (after Ledvina et al., 1994). 

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• Between-hole variability which is determined by comparing 

the average UCS values in the different holes to one 

another. 

 If the between-hole variability is not significantly larger than 

the within-hole variability, it is unlikely that any meaningful spatial 

relationship will be present. 

 Figure 6 illustrates the concept, using the Eagle Sandstone data 

set. Only holes where at least 3 UCS tests were conducted are 

shown. The variability within each hole is signified by the range of 

UCS (the high-low bar) plotted for each hole. The variability 

between the holes is indicated by the range of the mean UCS values 

for the entire data set. The figure shows that the within-hole range 

of UCS values encountered in many individual holes was similar to 

range of mean UCS values for the entire data set. Clearly, the 

within-hole variability is quite high relative to the between-hole 

variability. 

 A one-way analysis of variance (ANOVA) was used to 

compare the between-corehole variability to the within-corehole 

variability for each of the four data sets. Only the boreholes with 

two or more UCS tests were used in the analysis. Table 2 shows 

the results. First, the degrees of freedom (df) are calculated 

according to the number of holes and the total number of UCS tests 

in each data set. Then the sum-of-squares, indicating the total 

variability within each data set, is apportioned between the withinand between-hole variability. The mean square is simply the sumof-squares divided by the df. The F-value is the ratio of the mean 

squares. When the F value for the model is statistically significant 

(p < .05), this indicates that the mean UCS for at least one of the 

coreholes is different from the mean UCS of the other coreholes. 

Without a significant F-value, it is likely that all of the holes share 

a common “true mean” UCS, and it would probably make little 

sense to look for spatial relationships within the data. 

 Table 2 shows that the Eagle Sandstone data set shown in 

Figure 6 actually has the second greatest F value (i.e., the between 

hole variability is actually the largest relative to the within-hole 

variability). The other West Virginia data set has a slightly higher 

F-value. The F-values are very low for both the Midwestern data 

sets. In the case of the Turner Mine Shale, it seems that the range 

of UCS values likely to be encountered in a single hole is 

approximately the same as that in the entire data set. 

Table 2. Comparison of within- to between-corehole variability. 

Source of 

Variability dF 

Sum of 

squares 

(106

) 

Mean 

square 

(106

) 

F-value Pr > F 

Rock Unit–Brereton Limestone 

Between-Corehole 51 3,131 61.4 1.40 0.07 

Within-Corehole 108 4,725 43.8 

Rock Unit–Turner Mine Shale 

Between-Corehole 44 617 14.0 0.70 0.90 

Within-Corehole 62 1,250 20.2 

Rock Unit–Shale above Eagle Coalbed 

Between-Corehole 35 1,795 51.4 3.58 <.001 

Within-Corehole 162 2,327 14.3 

Rock Unit–Sandstone above Eagle Coal bed 

Between-Corehole 45 1,515 33.7 2.94 <.001 

Within-Corehole 245 2802 11.4 

 Computation of the variograms was the final step in the 

analysis. The results are shown in figure 7. Of the four data sets, 

only in the two strong rocks is there even a hint of a spatial 

relationship. Of these two, the Eagle Sandstone has the best 

variogram, but even here the variance is still quite high for even the 

closest holes. The variograms for the shales are essentially 

horizontal lines, indicating that there is basically no spatial 

relationship between the holes. 

CONCLUSIONS 

 The lack of spatial correlation in these four data sets has some 

important implications. First, it means that contour plots of UCS 

for these units must be treated with skepticism. This would be 

particularly true for the shale units. 

 Second, since these four units represent a fairly wide range of 

UCS, rock types, and U.S. coal basins, it seems likely that 

meaningful spatial correlations for UCS are the exception rather 

than the rule for other rock types. The most likely explanation is 

the large variability in UCS values that is regularly observed within 

single coreholes. Perhaps it is not surprising that in layered, 

sedimentary rock that the vertical variations even over small 

distance are quite large compared with the horizontal variations. 

 It is possible that the UCS of some rock types does truly vary 

from place to place, but that exploratory drillholes are just too 

widely spaced to measure it. In the past studies cited in this paper, 

Ledvina et al. (1994) found that a corehole spacing on the order of 

300 ft was necessary to accurately predict the thickness of some 

roof rock units. However, the large within-corehole variability in 

the two shale units implies that it is highly unlikely that a spatial 

relationship for UCS could be found regardless of the corehole 

spacing. 

 Finally, this paper has shown the power of geostatistics in 

helping to understand the variability of geomechanical properties of 

coal measure rock. Increased use of geostatistical methods could 

greatly improve the reliability of data used in ground control 

design. 

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Bars indicate full range of data

Figure 6. Within- and between-hole variability for the Eagle 

Sandstone data set. 
REFERENCES 

Armstrong, M. (1998). Basic Linear Geostatistics. SpringerVerlag, Berlin, 155 pp. 

Comish, S. (1993). The Westray Tragedy –A Miner’s Story. 

Fernwood, Halifax, NS, 82 pp. 

Kim, Y.C., Cervantes, J.A., Farmer, I.W. (1989). Predicting 

Rockfalls in an Underground Coal Mine Using Discriminant 

Analysis and Geostatistics. Proceedings, 7th Annual Workshop of 

the Generic Mineral Technology Center for Mine Systems Design 

and Ground Control, Blacksburg, VA, pp. 95-104. 

Ledvina, C.T., Dowding, C.H., Fowler, S., Hunt, G. and Nance, R. 

(1994). Geostatistical Guidance of Exploration in Roof Control – 

How Many Drill Holes are Enough? Proceedings, 5th Conference 

on Ground Control for Midwest U.S. Coal Mines, Collinsville, IL, 

YP Chugh and GA Beasley, Eds., pp. 14-30. 

Ledvina, C.T. (1991). Geostatistical Inference and Exploration of 

Coal Mine Roof Strata. PhD Dissertation, Northwestern 

University, Evanston, IL, 419 pp. 

Mark, C., Molinda, G.M., Barton, T.M. (2002). New 

Developments with the Coal Mine Roof Rating. Proceedings, 21st 

International Conference on Ground Control in Mining, 

Morgantown, WV, Aug. 6-8, pp. 294-301. 

Reifenberg, J. (1994). Geostatistical Modeling of Coal Mine Roof 

Quality for Hazard Mapping. Proceedings, 5th Conference on 

Ground Control for Midwest U.S. Coal Mines, Collinsville, IL, YP 

Chugh and GA Beasley, Eds., pp. 31-40. 

Reifenberg, J. (1996). Geostatistical Methods for Hazard 

Assessment and Site Characterization in Mining. Proceedings, 

15th International Conference on Ground Control in Mining, 

Golden, CO, Aug. 13-15, pp. 671-680. 

Richard, K.P. (1999). The Westray Story—A Predictable Path to 

Disaster. Chapter 10--Ground Control. Report of the Westray 

Mine Public Inquiry, Nova Scotia Department of Labor, Vol. 1, pp. 

351-385. 

Rusnak, J. and Mark, C. (2000). Using the Point Load Test to 

Determine the Uniaxial Compressive Strength of Coal Measure 

Rock. Proceedings, 19th International Conference on Ground 

Control in Mining, Morgantown, WV, Aug. 7-9, pp. 362-371.

Figure 7. Variograms constructed from the four data sets. 

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