In situ estimation of roof rock strength using sonic logging

David C. Oyler ⁎,

⁎ Corresponding author.

E-mail addresses: dbo1@cdc.gov (D.C. Oyler), cnm7@cdc.gov (C. Mark),

gdm4@cdc.gov (G.M. Molinda).

Christopher Mark, Gregory M. Molinda

NIOSH-Pittsburgh Research Laboratory, Pittsburgh, PA, United States

abstract

Sonic travel time logging of exploration boreholes is routinely used in Australia to obtain estimates of coal

mine roof rock strength. Because sonic velocity logs are relatively inexpensive and easy to obtain during

exploration, the technique has provided Australian underground coal mines with an abundance of rock

strength data for use in all aspects of ground control design. However, the technique depends upon reliable

correlations between the uniaxial compressive strength (UCS) and the sonic velocity. This paper describes

research recently conducted by NIOSH aimed at developing a correlation for use by the U.S. mining industry.

From two coreholes in Illinois, two from Pennsylvania, and one each from Colorado, western Kentucky and

southern West Virginia, sonic velocity logs were compared with UCS values derived from Point Load tests for

a broad range of coal measure rock types. For the entire data set, the relationship between UCS and sonic

travel time is expressed by an exponential equation relating the UCS in psi to the travel time of the P-wave in

μs/ft. The coefficient of determination or R-squared for this equation is 0.72, indicating that a relatively high

reliability can be achieved with this technique. The strength estimates obtained from the correlation

equation may be used to help design roof support systems. The paper also addresses the steps that are

necessary to ensure that high-quality sonic logs are obtained for use in estimating UCS.

1. Introduction

Uniaxial compressive strength (UCS) is perhaps the material

property that is most frequently quoted in rock engineering (Hoek,

1977). In recent years, the trend has been to replace laboratory UCS

tests with simpler, faster, “indirect” methods such as the point load

test (Cargill and Shakoor, 1990; Karacan, 2009a). Sonic logging has

been routinely used for many years in Australia to obtain estimates of

the UCS of coal mine roof rock for use in roof support design (McNally,

1987 and McNally, 1990). The estimates are obtained through log

measurements of the travel time of the compressional or P wave,

determined by running sonic geophysical logs in coreholes, which are

then correlated with UCS measurements made on core samples from

the same holes. In McNally's classic original study, conducted in 1987,

sonic velocity logs and drill core were obtained from 16 mines

throughout the Australian coalfields. The overall correlation equation

McNally obtained from least-squares regression was:

− UCS = 143 0:035t ; 000e ð1Þ

Where UCS is in psi and t is the travel time of the P-wave in μs/ft.

Fig. 1 shows a typical data set collected by McNally, in this case from

the German Creek Formation (McNally, 1987).

Today, most Australian mines employ mine-specific correlations in

preference to the generic McNally equation (Zhou et al, 2001). Once

an acceptable correlation has been developed for a mine or mining

district, mine planners have easy access to a wealth of rock strength

data for use in mine design. The sonic travel time data can be obtained

from logs run in either cored holes or rotary drilled holes. In actual

practice the amount of coring and core testing are probably reduced,

but not eliminated even after acceptable correlations are developed.

The Crinum Mine in Queensland gives an example of the use of

sonic log data (Payne, 2008). At Crinum a sonic velocity-to-UCS

correlation was established during initial mine exploration by running

sonic logs and testing 150 core samples. Sonic logs were obtained

from all subsequent exploration holes, and the correlations were

applied to the bolted horizon and contoured over the workings. These

correlations allow for continuous mapping of the roof rock UCS in

each borehole. After several panels, it became clear that areas of

difficult ground corresponded closely with regions of low sonic

velocity and estimated UCS less than 1500 psi. Currently, boreholes

are drilled every 450 ft along each gateroad, and the derived UCS

values are contoured as part of the hazard plan (Fig. 2). These contour

plots are used to select bolting densities and the location of secondary

support.

In contrast to the Australian situation, only limited research has

been conducted in North America to use borehole geophysics to

characterize the geotechnical properties of coal measure rocks (Wade

and Hickinbotham, 1997). Recently, full wave sonic logs have been

used to determine the Young's, shear and bulk moduli, as well as
porosity and Poisson's ratio, for coal mine degasification and methane

production applications (Karacan, 2009a,b).

The goal of the NIOSH research reported in this paper was to

demonstrate that the logging tools and techniques available in the US

could be used to obtain a McNally type equation correlation with a

coefficient of determination (R2

) of similar magnitude to that

commonly considered acceptable in Australian practice (R2≥0.7). A

secondary objective was to report on the best practices for obtaining

quality sonic logs for use in estimating UCS.

Fig. 1. Sonic travel time versus UCS data from the Australian German Creek seam. Data

after McNally (1987).

Fig. 2. Contour plot of UCS of the immediate roof above a gateroad at the Crinum mine,

Queensland, Australia (after Payne, 2008). UCS data computed from sonic travel time

log data, with black representing the weakest roof and light gray to white the strongest

roof. Vertical scale 0 to 40 ft. Plot width approximately 8000 ft.

2. Sonic logging tools

Sonic logging tools contain one or more transmitters which generate

high frequency (generally 20 to 24 kHz) sound waves, which then travel

through fluid in the borehole and the formation, and are received by two

or more detectors. The difference in arrival times of the sonic wave train

received by two detectors is then used to determine the travel time of

the first arrival of the compressional (or P) wave, the fastest component

of the sound. It is also possible to measure the shear wave (S wave)

traveltime, but most companies logging coal coreholes are not prepared

to do so. Generally sonic data are displayed in travel time per foot, with

the travel times for almost all sedimentary rocks falling in the range of

40 to 140 μs/ft. An overview of sonic logging may be found in the

Schlumberger Log Interpretation Principles and Applications manual

(Schlumberger, 1991). The sonic logging tools currently available fall

into two broad groupings, larger diameter tools designed for oil and gas

logging and smaller diameter tools designed for minerals logging. The

tools used for logging oil and gas wells are generally “compensated”,

meaning that they have two transmitters and 4 receivers and the

additional data can be used to correct for tool misalignment in the hole.

The spacing between the receivers is usually 2 ft, which improves their

depth of investigation, but reduces their vertical resolution. Minerals

logging tools frequently have only one transmitter and two receivers

and are not compensated. The receiver spacings available in the US are

usually 1 ft, although tools with multiple spacings and slightly shorter

spacings (20 cm or 8 in.) exist and are frequently used in Australia.

Although data sampling intervals can vary, the sonic data collected for

this paper were all sampled at 0.1 ft intervals. The large quantities of

data which must be transmitted uphole by sonic tools probably make

sampling intervals shorter than 0.1 ft impractical, but not impossible, if

the need was demonstrated. On the other hand more frequent sampling

does not improve the vertical resolution, which would be more useful in

ground control applications.

3. Vertical resolution differences between log and test specimens

It is important to note that since the logging tool measures the

sound wave's travel time between the two receivers, the travel time it

records is actually the average travel time of all the rock layers contained

within that 1- to 2-ft interval. UCS test specimens, on the other hand,

are no more than a few inches long. This “averaging” that is inherent in

the design of the sonic tool has several important implications. Since

test specimens are typically much shorter than sonic log receiver

spacings, it is possible to exactly correlate the core and log depths and

still obtain a poor correlation between the rock strength and sonic log

travel time, due to averaging by the sonic log of rocks of greatly

differing velocities. In this study the samples tested ranged in length

from 0.05 to 0.2 ft, generally averaging 0.125 ft in length. The receiver

spacing on the Century 9321 tools1

1 Mention of company name or product does not constitute endorsement by the

National Institute of Occupational Safety and Health.

that were used to run all of the sonic

logs obtained for this NIOSH study is approximately 1.1 ft. To obtain

travel times from the 9321 tool comparable to point load strengths,

sonic data must be collected from zones of uniform properties greater

than 1.1 ft in length and not closer than 0.5 ft from a bed boundary.

Rock units containing thin beds of alternating properties, such as thin

interbedded shales and sandstones are likely to show poor agreement

between the strength of individual samples and the sonic log travel

time even when those samples have been taken far from the bed

boundaries. Where possible, such zones should be avoided when

attempting to correlate UCS and travel time data.

Analysis of the data from the coreholes suggests three alternative

techniques for handling the differences in vertical resolution between

logs and core samples.

1. Select sonic travel readings only from homogeneous	 zones of

thickness greater than twice the sonic tool receiver spacing and test

specimens from as close to the center of those zones as possible.

2. Perform multiple point load tests in each suitable rock unit meeting

condition 1 and determine the average UCS for the 1-ft zone

centered on the location of the sonic velocity measurement to be

compared to the averaged UCS data.

3. If sufficient point load tests are available, compute a moving

average UCS of 1-ft intervals of the borehole and correlate those to

the sonic readings. This technique actually best mirrors the sonic

travel time log itself, which essentially averages the travel times of

all the rocks that the sonic pulse encounters as it travels between

the near and far receivers.

Techniques 1 and 2 are not mutually exclusive and to some extent

form a logical progression. Technique 3 requires testing of thin beds

and near bed boundaries and much more testing, and is incompatible

with technique 1. Tests run near bed boundaries and in thin beds

probably will not improve the correlation until sufficient tests have

been conducted to obtain good moving averages; so technique 3

requires a decision about the number of tests to run and the resources

to be committed to the testing process. Technique 3 is much more
time consuming, but can provide a very detailed picture of rock

strength in a zone of particular interest, such as the immediate roof of

a coal seam. However, it can be difficult to obtain adequate coverage

over intervals of weak rocks where it may be difficult to obtain good

point load measurements.

In the work conducted for this paper Technique 3 was not used.

Instead a mix of Techniques 1 and 2 was used depending upon the

amount of core and testing time available. The results obtained from

each of the three techniques will be described in the “Discussion and

results” section.

4. Sonic log errors

A major source of errors in a UCS/sonic travel time correlation is

from errors in the measured sonic travel times. Sonic tools are

designed to detect the arrival of the first signal of the sonic wavetrain

(the first arrival of the compressional wave), which consists of a series

of roughly sinusoidal waves at the tool's operating frequency. The

peaks arrive at intervals of approximately 42 μs. The detectors

measure the amplitude of the arriving signal and the time of the

arrival is recorded when a threshold signal amplitude is detected. For

tools containing two receivers the difference between the arrivaltimes

at the two receivers is computed and presented as the travel time. If

however, the amplitude of the first arrival is too small to trigger the

detector, it is possible for the detector to trigger on the second, or a

later arrival. If this happens to only one of the detectors, it can cause

travel time shifts in 42 μs steps. This type of error is usually referred to

as a cycle skip. Typically the far detector is affected and the shift is

toward longer travel times, but cycle skipping by the near receiver

(less likely, but still possible) can lead to reduced travel times. Cycle

skipping can be caused by misalignment or decentralization of the tool

with the axis of the hole, either of which will cause destructive

interference of the sonic signal and reduction of the signal amplitude.

Other causes of cycle skipping include incorrect tool gain settings, gas

flowing into the hole (causing both attenuation of signal and increased

travel times) and noise from the tool or centralizers scraping on the

wall ofthe hole and attenuation across joints or fractures. The presence

of joints and fractures can sometimes cause cycle skipping, although

the sources of cycle skips are usually not identifiable. The sonic tool is

sometimes suggested as an instrument for identifying joints and

fractures through the observation of cycle skipping or the shape of the

sonic wavetrain, but there is no generally accepted technique for

identifying fractures or joints using standard sonic logging tools.

Fig. 3. Illinois corehole A. Sonic travel time versus UCS, with best fit relationship.

5. Discussion and results

NIOSH collected data from seven coreholes (Fig. 4), two in Illinois,

two in southwestern Pennsylvania, one in north central Colorado, one

in southern West Virginia and one in western Kentucky.

Fig. 4. Location map of the coring sites from which core and log data were collected for this paper.

In the eastern

coreholes the sonic logs core were run by Geological Logging Systems,

a Division of Marshall Miller & Associates, using a Century Geophysical

Corp model 9321 sonic tool. The Colorado logs were run by Century

Geophysical Corp, also using the 9321 model sonic tool. The 9321 is an

uncompensated sonic tool with one transmitter and two receivers,

and is typical of the sonic tools available for minerals industry use.

Although the UCS data were not restricted to any one source, all of

the UCS data collected for this paper were obtained from cores provided

to NIOSH by cooperating mining companies and point load tested by

NIOSH personnel. In all cases except the Colorado corehole the core was

collected in the field by NIOSH personnel. The point load data were

obtained using a point load tester manufactured by GCTS (Tempe, AZ).

The GCTS tester consists of a hand pump, a hydraulic cylinder and two

60° cone shaped platens to break the samples. Itincorporates a pressure

transducer and potentiometric position transducer, along with hardware and software to allow recording of sample loading and

deformation by a laptop computer. Sample deformation was measured

for all of the samples tested for this paper and all strength calculations

were made using the sample heights at the time of failure.

The testing and calculations followed the procedures outlined in

the ISRM recommended method for determination of point load

strengths (ISRM, 1985). The equation proposed by Rusnak and Mark

(2000), which was based upon approximately 10,000 point load and

UCS tests of coal measure rock, was used to convert point load data to

UCS:

UCS = 21*Is50 ð2Þ

Where Is50 is determined from the point load test using the

standard ISRM procedures.
The GCTS hardware and software were upgraded in late 2007, after

testing the core from Illinois corehole A, with an increased sensitivity

pressure transducer, longer stroke position sensor and a higher

resolution analog to digital data card. The upgrades were primarily

needed to allow more accurate estimates of the strength of very weak

rocks, such as those commonly found in the Illinois basin, and to

facilitate the measurement of the dimensions of larger diameter core

samples. The Illinois basin and Colorado cores were 3 in. in diameter

and obtained through rotary drilling with coring of selected intervals,

while the eastern cores (West Virginia and Pennsylvania) were 2 in. in

diameter and obtained by wireline continuous coring.

Most, but not all, of the cores collected in the study were from

intervals adjacent to coalbeds to be mined. However the depths of the

samples vary over a wide range so Table 1 has been included to

provide data on the distribution of sample depths.

Table 1

Depths of samples from each corehole.

Depth

Min

range (ft)

Max Average Median

Illinois A 576.2 599.3 587.8 589.1

West Virginia A 185.1 410.3 300.3 300.7

Pennsylvania A 46.3 542.8 292.2 282.8

Illinois B 1008.4 1142.1 1068.1 1041.3

Pennsylvania B 349.5 735.3 577.2 605.9

Colorado A 965.1 1034.4 984.7 975.6

Kentucky A 800 940.1 872.1 887.3

Fig. 3 and 5 through 10 show sonic travel time, in μs/ft graphed

versus uniaxial compressive strength, as determined from point load

data, for each of the seven coreholes. For all seven coreholes most of

the points represent a UCS measurement from a single core sample

versus the sonic log travel time reading at that depth, but in a few

cases they represent the average of a group of UCS readings (2 to 5)

plotted versus the sonic log reading at the midpoint of the group.

Averaging was always performed over intervals less than or equal to 1

foot in length, in order to match the sonic response to the UCS data.

The majority of the data points represent single UCS measurements.

Fig. 5. Illinois corehole B. The large open circles are data from carbonaceous shales. The

dashed correlation curve uses all the data, including the carbonaceous shale samples.

The solid correlation curve does not use the carbonaceous shale samples. Data points

represent point load tests and sonic travel time measurements from individual tests.

Fig. 6. Kentucky corehole A. The large open circles are data from carbonaceous shales.

The dashed correlation curve uses all the data, including the carbonaceous shale

samples. The solid correlation curve does not use the carbonaceous shale samples. Data

points represent point load tests and sonic travel time measurements from individual

tests.

Fig. 7. Pennsylvania corehole A. Filled circles represent individual sample points.

Table 2 summarizes the correlation equations, coefficients of

determination, and numbers of samples for each corehole and for

several groupings of the data, including the three Illinois basin

coreholes, the two Pennsylvania coreholes, the six eastern US

coreholes, and a composite of all seven coreholes. The composite

equation reported in 2008 (Oyler, et. al., 2008) using data from three

coreholes and the general McNally equation (units converted from

MPa to psi) are also included in the table for comparison. All of the

graphs are reproduced in Fig. 11 to show the spread in the strength

estimates from the different data sets. Where data points have been

included on the graphs the smaller filled circles represent data used in

the correlation, while the larger open circles represent carbonaceous

shale samples, which have not been included in the data used to

compute the least squares exponential correlation equations, and

which will be discussed in greater detail later in this paper.

Fig. 12 summarizes the correlations computed for all test data

collected. The general Australian McNally equation (McNally, 1987),

converted from MPa to psi, has been added for comparison. The

equation for the combined data set

− UCS = 329 100e 0:0505t ; ð3Þ

is similar in shape and range to the Australian equations. This

composite correlation has a coefficient of determination (R2

) of 0.72

and is based upon 1015 data points (a few derived from averaging

several samples). In Eq. (3), UCS is the computed rock strength in psi,

and t is the travel time read directly from a sonic log, in μs/ft. Fig. 11

summarizes all of the correlations in graphical form, allowing

comparison of the various correlations. Table 3 reproduces the

regression statistics for Eq. (3), obtained by transforming the

exponential equation to a linear one by taking the natural log of

both sides of the equation and taking the natural log of the measured

UCS values. In table 3 the Intercept Coefficient, 12.704 is the natural

log of the constant coefficient of Eq. (3); 329,100. Similar statistical

analyses were run for the other data sets, but have not been

reproduced in this paper. With the exception of the general McNally

equation and the correlation from Colorado A, the correlations show a

tight grouping for travel times over 80 μs/ft and a wider spread for

lower travel times. This is a helpful trend, since greater accuracy in

estimating UCS values is more critical when evaluating weak rocks,

and not as critical with stronger rocks.
Fig. 8. Pennsylvania corehole B. The large open circles are data from carbonaceous

shales. The dashed correlation curve uses all the data, including the carbonaceous shale

samples. The solid correlation curve does not use the carbonaceous shale samples. Data

points represent point load tests and sonic travel time measurements from individual

tests, with six samples averaged in groups of three.

Fig. 9. West Virginia corehole A. Filled circles represent individual sample points.

Fig. 10. Colorado corehole A. Filled circles represent individual sample points.

Table 2

Sonic travel time versus UCS (from point load data) correlationa

.

Corehole or group Coefficient Ab Coefficient B R2 N

Illinois A 250,000 −0.0521 0.34 121

Illinois B 320,800 −0.0492 0.77 141

Kentucky A 243,000 −0.0497 0.57 235

Colorado A 137,200 −0.0343 0.50 106

Pennsylvania A 211,700 −0.0429 0.77 139

Pennsylvania B 765,000 −0.0627 0.59 150

West Virginia A 715,400 −0.0610 0.63 127

All coreholes (7)c 329,100 −0.0505 0.72 1015

Eastern coreholes (6) 339,600 −0.0515 0.75 909

Illinois basin (3) 270,000 −0.0497 0.75 493

Pennsylvania (2) 298,500 −0.0488 0.63 289

2008 composite (3)d 468,000 −0.054 0.87 316

McNallye 143,000 −0.035 N/A N/A

a Correlations do not include carbonaceous shale sample data. b A and B are coefficients of an equation of the form, UCS=Ae−Bt. c Number in parentheses indicates the number of coreholes included in the data set. d Correlation of unaveraged Illinois A sample data, Pennsylvania A and West Virginia

A data, as reported by Oyler et al. (2008). e From McNally (1987). Equation converted from metric units (MPa) to psi.

5.1. Carbonaceous shales

Although some spread was observed in the measured UCS values

of all rock types when compared to the travel time readings,

carbonaceous shales were found to frequently exhibit much higher

measured UCS values than other types of rock for the observed travel

times. This anomalous response was not noted until the fourth

corehole, Illinois B, from which data were collected in August 2008.

Prior to that hole almost no carbonaceous shale had been encountered. The large open circles in Figs. 5, 6, 8 and 12 show the

carbonaceous shale data. The travel times for the samples from Illinois

corehole B ranged from 100 to130 μs/ft, while the strengths ranged

from 6000 to 12,000 psi. Normally shales with those travel times

would range in strength from a few hundred to 4000 psi. In late 2009

core was collected from above the Herrin (#11) and Springfield (#9)

in western Kentucky (Kentucky A, Fig. 6). Again anomalous correlations were observed for carbonaceous shales.

Most of the anomalous carbonaceous shale samples tested during

this project were from two marine carbonaceous shales found in the

Illinois basin, the Anna shale, found directly above the Herrin #6 (#11

in Kentucky) and the Turner Mine shale, found directly above the

Springfield #5 (#9 in Kentucky). The tested UCS values of samples of

both of these shales were much higher than would be predicted from

the sonic log travel times. Fig. 13 shows a set of typical carbonaceous

shale samples, in this case from corehole Kentucky A. Five of the

samples are from the Anna shale; the upper right sample is from the

Turner Mine shale. The samples were chosen to illustrate the wide

range of strengths possible in the carbonaceous shales, and the lack of

visual indication of the strength of the samples. The travel time data of

the pictured samples cover a narrow range of 110 to 119 μs/ft. The

correlation equation predicts UCS values between 670 and 1030 psi.

The actual strengths were between 2400 and 15,900 psi.

Samples from carbonaceous shale directly above the Bakerstown

coal, from a Pennsylvania corehole, were also tested during the

preparation of this paper. The average UCS value for the 16 samples

tested in the 2 ft interval was 8000 psi, with a standard deviation of

1300 psi. The high UCS values suggested that the sonic response in

this shale is also anomalous, but no sonic data were available for this

interval so the results are inconclusive.

One possible source of the anomalous response of carbonaceous

shales is the amount of organic material contained in them. The

possibility of correlating organic material content to geophysical log

response was not pursued in this study, but has been studied by other

researchers (Fertl et al., 1986) using a wide range of geophysical logs.

Variation in the organic matter content could help explain the wide

range of and high UCS values observed from carbonaceous shales

tested in this study.

Two observations can be made from the data. First, the

carbonaceous shales should be excluded from the data when

developing a general sonic travel time-to-UCS correlation because

they clearly form a distinct, anomalous rock type. Second, it appears

that carbonaceous shales are usually stronger than the general

correlation would predict, so it would be conservative to use the

general correlations to design support systems in roof containing the

shales.

5.2. Application to roof design

The primary purpose of this paper is to lay out for the reader the

development of a tool to be used to aid in roof control design. The use

of sonic log data combined with the correlations developed in this

paper can provide continuous estimates of the UCS of the rocks in the
immediate mine roof. These UCS estimates can also be used to map

roof strata and may aid in interpolation of and/or prediction of

changes in roof conditions. The UCS obtained from sonic logs is also

one of the key input parameters for the Coal Mine Roof Rating (Mark

and Molinda, 2005).

This paper does not attempt to determine whether local UCS/

travel time correlations on a mine-by-mine basis, as is Australian

practice, or correlations using basin wide or regional data give better

results. The authors have presented regional correlations rather than

local correlations because it was possible to do the former and not the

latter and because we believe that the regional correlations can be

useful, but we cannot be completely certain that local mine-by-mine

correlations would not give better results.

The paper also does not attempt to provide guidelines for using

UCS data, whether estimated from sonic logs or from testing of rock

samples, for the design of mine roof support systems. Current

Australian research (Hatherly, et al., 2005; Hatherly, et al., 2007) is

focused on employing the full suite of geophysical logs, including

density, sonic, gamma ray and neutron logs, to develop a more

complete strata characterization. This work has resulted in the

development of the Geophysical Strata Rating (GSR), which has

been calibrated by comparison with the Coal Mine Roof Rating

(CMRR), but is derived solely from geophysical log data (Hatherly,

2006). NIOSH is currently conducting a study to compare CMRR unit

ratings determined using data from core samples to the geophysical

log derived GSR ratings. Both ratings attempt to take into account

moisture sensitivity, bedding and other factors besides rock strength.

Fig. 11. Graphed correlation equations for data from each of the seven coreholes and

including an Illinois basin correlation, Pennsylvania correlation, Eastern US correlation,

a correlation using all seven coreholes, and a previously published correlation based

upon three of the coreholes (Oyler, et al., 2008). The general McNally Australian

equation (in psi units) (McNally, 1987) is shown for comparison.

Fig. 12. Correlation using data from all seven coreholes. The large open circles are data

from carbonaceous shale samples not used in computing the correlation equation

shown. The general McNally equation (McNally, 1987) is shown by the dashed curve.

Table 3

Regression statistics for the data from all 7 coreholesa

.

R-squared Adj R-squared MSE F # Obs

0.7231 0.7229 0.5333 2645.8 1015

Source df SS MS

Model 1 752.4890 752.4890

Residual 1013 288.1109 0.284414

Total 1014 1040.5999

Coefficientb Std. err. t stat P-value 95% conf. int.

Intercept 12.70397818 0.080478 157.8565 0 12.5461 12.8619

X variable −0.0504562 0.00098 −51.43691 0.0000 −0.05238 −0.04853

a Exponential equation transformed to a linear equation by taking the natural log of both sides of the equation and performing a linear regression using the natural log of the UCS

values (ln(UCS)). b The intercept coefficient is ln(A)= 12.704, the natural log of the exponential coefficient (A); A= 329,100.

6. Conclusions

The study demonstrated that sonic travel time logs can be used to

estimate the UCS of US coal measure rocks. It appears that both the

geological conditions and the available geophysical logging technology in the US are suitable for developing and using the sonic travel

time versus unconfined compressive strength correlations. The results

were consistent across several coal provinces and represent the broad

range of rock encountered over the major US coalfields, although the

western data are limited. The general correlation shown in Eq. (3) and

repeated below in Eq. (4) appears to apply to coal measure rocks

throughout the coalfields of the continental United States.

− UCS 0:0505t = 329; 100e ð4Þ

Carbonaceous shales present in the Illinois basin and possibly

present in the Appalachian or other regions, were the only rock type

that did not fit the general equation. Additional work is warranted to

understand the reasons why the tested UCS of carbonaceous shales is

significantly higher than would be expected based on the travel times

measured in the shales. Coal samples were generally not tested,

partially due to lack of availability, and were also not included in the

correlations.

The ability to use sonic logs to estimate rock strength provides the

US coal industry with a powerful new tool for improving ground

control design. The availability of uniaxial compressive strength data

is essential to effective roof support selection, gate entry design, and

many other aspects of ground control. Widespread use of sonic logs
during the exploration phase could vastly increase the quantity of

geotechnical data that is available for mine design.

The study also suggests that high-quality sonic logs are essential if

the technique is to be successful. Careful attention to the details of the

logging process, including use of appropriate logging tools, use of

effective logging tool centralizers, accurate depth correlations and

elimination of logging errors, such as “cycle skips”, can all help to

improve the correlations.

Fig. 13. Carbonaceous shale samples from corehole Kentucky A. The samples have been tested and the halves oriented to show a top view and a view of the failure surface. All

samples are from the Anna shale, except the top right sample, which is from the Turner Mine shale. The samples were chosen to illustrate the wide range of UCS values observed in

the carbonaceous shales, despite a narrow range of logged travel times. Depths in feet, UCS in psi and Delta T in μs/ft.

Acknowledgements

The authors would like to thank Collin Henkes of Patriot Coal,

Murali Gadde and John Rusnak of Peabody Energy, Brian Schaeffer and

Scott Wade of Pennsylvania Services Corp. (Alpha Natural Resources),

Ernest Thacker and Gregory Smith of Alliance Coal, and Consulting

Geologist Jeff Padgett for providing drill cores for testing and access to

drill sites for geophysical logging.

References

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