International Journal of Coal Geology 79 (2009) 55–60

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International Journal of Coal Geology

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Correlating static properties of coal measures rocks with P-wave velocity

Manoj Khandelwal a,⁎,1, T.N. Singh b

a Department of Mining Engineering, College of Technology and Engineering, Maharana Pratap University of Agriculture and Technology, Udaipur-313 001, Indiab Department of Earth Sciences, Indian Institute of Technology Bombay, Powai, Mumbai-400 076, India

⁎ Corresponding author. Tel.: +91 294 2471 379; fax:E-mail address: mkhandelwal@mpuat.ac.in (M. Khan

1 Present address: Dept of Civil Engineering, Monash

0166-5162/$ – see front matter © 2009 Published by Edoi:10.1016/j.coal.2009.01.004

a b s t r a c t

a r t i c l e i n f o

Article history:

Physico-mechanical proper Received 17 October 2008Received in revised form 21 January 2009Accepted 26 January 2009Available online 3 February 2009

Keywords:Physico-mechanical propertiesP-wave velocityCoalShaleSandstoneCoefficient of determination

ties of rocks are important in the planning, design, and stability of civil andmining engineering projects. The determination of these properties in laboratory is a time consuming andlaborious job and needs costly equipment and expertise, but the determination of P-wave velocity inlaboratory as well as in in-situ condition is an easy, simple, reliable, and less complicated task. So, inthis paper, an attempt has been made to correlate physico-mechanical properties of coal measures rocks withP-wave velocity. Samples of coal, shale, and sandstone has been taken from the four different coal mines ofIndia for the determination of compressive strength, tensile strength, shear strength, density, Young'smodulus, Poisson's ratio, and P-wave velocity.

© 2009 Published by Elsevier B.V.

1. Introduction

The physico-mechanical properties of rocks play a very vital andcrucial role in the planning and design of civil and mining excavationssuch as the stability of dump and rock slopes, and stability ofunderground excavation, tunnels, dams, deep trenches, caverns, etc.They are also very important for the study of rock bursts and bumps inunderground mines, pillar design, prediction of failure of rock mass,etc. The determination of these properties in laboratory as well as inin-situ condition is a tedious and time-consuming job. It also requiresgreater accuracy in preparation and testing of samples. Till now, therehas been no such method by which all the static physico-mechanicalproperties can get. Therefore, there has been a need for a simpletechnique of determining the physico-mechanical properties of rocksby some indirect but relevant and reliable methods.

The determination of P-wave velocity is an easy and simple taskand it can be determined in field as well as in laboratory.Determination of P-wave velocity is non-destructive and easy toapply, that is why it is increasingly being used in geotechnicalengineering. The P-wave velocity of a rock is closely related to theintact rock properties and measuring the velocity in rock massesdescribes the rock structure and texture. The important influencingparameters are grain size and shape, density, porosity, anisotropy,pore water, confining pressure, temperature, weathering and altera-

+91 294 2471 056.delwal).University, VIC 3800, Australia.

lsevier B.V.

tion zones, bedding planes, and joint properties (roughness, fillingmaterial, water, dip and strike, etc.) (Kahraman, 2001a).

A number of researchers (Smorodinov et al., 1970; Inoue andOhomi, 1981; Gaviglio, 1989; Boadu, 2000; Kahraman, 2001a,b;Ozkahraman et al., 2004; Yasar and Erdogan, 2004) have studied therelation between different physico-mechanical properties of rock andP-wave velocity and found that the seismic wave is closely related tophysico-mechanical properties. The P-wave velocity in a solidmaterialdepends on the density and elastic properties of that material(Rzhevsky and Novik, 1971; Franklin and Dusseault, 1989). The qualityof some materials is sometimes related to their elastic stiffness so thatmeasurement of P-wave velocity in such materials can often be usedto indicate their quality as well as to determine elastic properties(Kahraman, 2002; Sharma and Singh, 2008). Inoue and Ohomi (1981)investigated the relation between uniaxial compressive strength andP-wave velocity of soft rocks and reported very poor correlationbetween them. Relation between density and P-wave velocity wasgiven by Gaviglio (1989). Boadu (2000) predicted the transportproperties of fractured rocks from seismic waves. Kahraman (2001a)correlated P-wave velocity with the number of joints and Schmidtrebound number and found a strong influence on P-wave velocity withthe number of joints. Kahraman (2001b) evaluated uniaxial compres-sive strength using Schmidt rebound number, point load index, impactstrength index and P-wave velocity. He used 48 different rocks toestablish the correlation between them and found a non-linear relationbetween the P-wave velocity and uniaxial compressive strength.Ozkahraman et al. (2004) determined the thermal conductivityof rocks from the P-wave velocity. Yasar and Erdogan (2004)studied carbonate rocks of different origins and established a linear

Fig. 1. Sample collecting location of different coalmines.

56 M. Khandelwal, T.N. Singh / International Journal of Coal Geology 79 (2009) 55–60

relation between density, Young's modulus, and uniaxial compressivestrength with P-wave velocity. They found a higher error betweenmeasured and estimated values of uniaxial compressive strength andYoung's modulus than in density.

The aim of the present study is to correlate compressive strength,tensile strength, shear strength, density, Young's modulus, andPoisson's ratio of the coal measures rocks with the P-wave velocity.

2. Field study

Rock samples were collected from Jayant Opencast Coal mine,Singrauli, Madhya Pradesh (Northern Coalfields Ltd.); Bishrampur

Fig. 2. Measurement o

Underground Coal Mine, Chhattisgarh (South-Eastern CoalfieldsLtd.); Lodna Opencast Coal Mine, Jharia, Jharkhand (Bharat CokingCoal Ltd.), and Umred Opencast Coal Mine, Nagpur (WesternCoalfields Limited). The rocks are mainly Permo-Carboniferous-ageof Gondwana system. The locations of different mines are shown inFig. 1.

3. Laboratory investigation

Representative rock mass samples were collected from thefour different coal mines in India. These rock mass samples werecored in NX size to determine physico-mechanical properties. Core

f P-wave velocity.

Table 1Physico-mechanical properties of different types of rock with their location.

Samplenumber

Name of mine Rock type P-wave(m/s)

UCS(MPa)

Tensilestrength(MPa)

Shearstrength(MPa)

Density(t/m3)

Young'smodulus(MPa)

Poisson'sratio

1. Jayant O/C Project Coal 1741.00 8.207 1.007 1.675 1.75 1457.33 0.372. Jayant O/C Project Shale 1752.00 10.698 1.277 2.459 1.78 1500.13 0.363. Jayant O/C Project Sand stone 1758.00 11.441 1.504 2.46 1.80 1710.23 0.334. Bishrampur U/G Project Coal 1830.00 16.367 1.687 3.597 1.84 1956.91 0.285. Bishrampur U/G Project Shale 1849.00 15.829 1.739 3.768 1.82 1805.02 0.296. Bishrampur U/G Project Shaly sand stone 1881.00 17.292 1.942 3.565 1.86 2203.33 0.277. Lodna O/C Project Coal 1890.00 20.62 2.397 4.676 1.93 2412.37 0.248. Lodna O/C Project Shale 1905.00 25.327 2.638 5.22 1.89 2296.38 0.189. Lodna O/C Project Sand Stone 1968.00 32.096 3.614 6.977 1.98 2800.31 0.1810. Umred O/C Project Coal 2101.00 54.702 5.852 11.738 2.15 3213.41 0.1411. Umred O/C Project Shale 2114.00 57.192 6.117 12.273 2.14 3345.629 0.1412. Umred O/C Project Sand stone 2116.00 58.252 6.805 13.119 2.15 3365.361 0.14

57M. Khandelwal, T.N. Singh / International Journal of Coal Geology 79 (2009) 55–60

specimens were cored by coring machine and the ends trimmedas required. The core specimens were then cut into standard size asper ISRM (1981) standards for different physico-mechanical proper-

Fig. 3. Correlation between P-wave velocity and uniaxial compressive strength.

Fig. 4. Correlation between P-wave velocity and tensile strength.

Fig. 5. Correlation between P-wave velocity and shear strength.

ties. After coring the rock specimens, it was further smoothened bythe lathe machine to avoid end effects. The specimens were dried at105 °C for 24 h to remove the moisture.

Fig. 6. Correlation between P-wave velocity and density.

Fig. 7. Correlation between P-wave velocity and Young's modulus.

Fig. 8. Correlation between P-wave velocity and Poisson's ratio.

Table 2Regression analysis results.

Samplenumber

Parameters to be related Regression equation R2 value

1. UCS–P-wave UCS=0.1333⁎P-wave−227.19 0.96192. Tensile strength (TS)–P-wave TS=0.0145⁎P-wave−24.55 0.94693. Shear strength (SS)–P-wave SS=0.0291⁎P-wave−49.494 0.95794. Density (Den)–P-wave Den=0.0011⁎P-wave−0.0847 0.97195. Young's modulus (YM)–P-wave YM=4.9718⁎P-wave−7151 0.97406. Poisson's ratio (PR)–P-wave PR=8×1015⁎P-wave−5.0509 0.9434

Fig. 9. Estimated vs. measured values of uniaxial compressive strength.

58 M. Khandelwal, T.N. Singh / International Journal of Coal Geology 79 (2009) 55–60

3.1. Determination of P-wave velocity

The P-wave velocity of rock was determined using a PortableUltrasonic Non-destructive Digital Indicating Tester (PUNDIT) as perISRM (1978) standards (Fig. 2). In this, a mechanical pulse isgenerated on prepared specimens by piezo-electric transducers. Ahigh electric voltage pulse of short duration is generated by piezo-electric transducer which converts into mechanical pulse. In thissystem, the pulses are transmitted from one end and received atanother end of the specimen. The time elapsed (t) in received ofpulses on the other end transducer by distance (S) then the velocity(V) can be determined by Eq. (1).

V = S = t m=s ð1Þ

Table 1 shows the P-wave values determined for differentrock types from various locations based on average value of 3–5samples.

3.2. Determination of physico-mechanical properties

Obtaining the coal samples of NX size core was very difficult due topresence of discontinuities and weak planes. Therefore, cubicalsamples of 5 cm3 were prepared by cutting the coal blocks usinghexagonal blades and these samples were used to determine theuniaxial compressive strength and shear strength. Compressivestrength, tensile strength, shear strength, density, Young's modulus,Poisson's ratio and P-wave velocity were calculated by taking anaverage value of 3–5 samples.

The NX size rock specimens of shale and sandstone were placed inbetween the platens and loaded at constant loading rate of3.5×103 Pa/s until it fails (ISRM, 1979). The load and deformationcurve was used to determine the modulus of elasticity and uniaxialcompressive strength of the shale and sandstone samples.

Table 3Estimated and measured values of different physico-mechanical properties of coal measure

Mine name Rock type Uniaxial compressivestrength (MPa)

Tensile strength(MPa)

Shear s(MPa)

Estimated Measured Estimated Measured Estima

Jayant O/C Project Coal 4.955 8.207 0.625 1.007 1.082Jayant O/C Project Shale 6.422 10.698 0.784 1.277 1.402Jayant O/C Project Sand stone 7.222 11.441 0.871 1.504 1.576Bishrampur U/G

ProjectCoal 16.822 16.367 1.912 1.687 3.668

Bishrampur U/GProject

Shale 19.356 15.829 2.187 1.739 4.219

Bishrampur U/GProject

Shaly sandstone

23.623 17.292 2.649 1.942 5.149

Lodna O/C Project Coal 24.823 20.62 2.779 2.397 5.411Lodna O/C Project Shale 26.823 25.327 2.996 2.638 5.846Lodna O/C Project Sand Stone 35.223 32.096 3.907 3.614 7.676Umred O/C Project Coal 52.957 54.702 5.83 5.852 11.54Umred O/C Project Shale 54.691 57.192 6.018 6.117 11.918Umred O/C Project Sand stone 54.957 58.252 6.047 6.805 11.976

The strain gauges were pasted in the axial and the diametricaldirection to determine the strain in both the directions to obtain thePoisson's ratio for different rock types. Table 1 shows the physico-mechanical properties values of coal measures rocks from India.

4. Statistical analysis of test results

The results of P-wave velocity with all the six static physico-mechanical properties of the rocks were analyzed using themethod ofleast square regression method. The equation of best fit line andcoefficient of determination (R2) were determined for each regression.The values of P-wave velocity of the coal measures rocks werecorrelated with the static physico-mechanical properties of the rocks.

The graphs between P-wave velocity and static physico-mechanicalproperties of the rocks are shown in Figs. 3–8.

A very strong correlation between P-wave velocity and physico-mechanical properties of the rocks was found. It can be observed thatthere is linear relation between the physico-mechanical properties ofrocks with P-wave velocity of the coal measures rocks, except inPoisson's ratio, where power relation is providing better coefficient ofdetermination as compared to the linear one. The result of regressionequations and the coefficient of determination are presented inTable 2.

Data from each test were used in the developed empiricalequations to estimate the physico-mechanical properties of therocks. The estimated values of physico-mechanical properties of therocks were plotted against the measured values for each test (Table 3;Figs. 9–14). The error in the estimated value is represented by thedistance of each data point from the 1:1 slope line. A point lying on the

s rocks.

trength Density (t/m3) Young's modulus(MPa)

Poisson's ratio

ted Measured Estimated Measured Estimated Measured Estimated Measured

1.675 1.83 1.75 1504.904 1457.33 0.34 0.372.459 1.84 1.78 1559.594 1500.13 0.33 0.362.46 1.85 1.80 1589.424 1710.23 0.33 0.333.597 1.93 1.84 1947.394 1956.91 0.27 0.28

3.768 1.95 1.82 2041.858 1805.02 0.25 0.29

3.565 1.98 1.86 2200.956 2203.33 0.23 0.27

4.676 1.99 1.93 2245.702 2412.37 0.23 0.245.22 2.01 1.89 2320.279 2296.38 0.22 0.186.977 2.08 1.98 2633.502 2800.31 0.18 0.1811.738 2.23 2.15 3294.752 3213.41 0.13 0.1412.273 2.24 2.14 3359.385 3345.629 0.13 0.1413.119 2.24 2.15 3369.329 3365.361 0.13 0.14

Fig. 10. Estimated vs. measured values of tensile strength.

Fig. 11. Estimated vs. measured values of shear strength.

Fig. 13. Estimated vs. measured values of Young's modulus.

Fig. 14. Estimated vs. measured values of Poisson's ratio.

59M. Khandelwal, T.N. Singh / International Journal of Coal Geology 79 (2009) 55–60

1:1 slope line indicates an exact estimation, whereas, away from theline shows the error, as shown in Figs. 9–14.

5. Student's t-test

The significance of R-values can be determined by the t-test,assuming that both variables are normally distributed and theobservations are chosen randomly. The test compares the computedt-value with a tabulated t-value using the null hypothesis. It is donefor comparing the means of two variables, even if they have differentnumbers of replicates. In simple terms, the t-test compares the actualdifference between two means in relation to the variation in the data(expressed as the standard deviation of the difference between themeans).

The formula for the t-test is a ratio in which the numerator is justthe difference between the two means or averages and thedenominator is a measure of the variability or dispersion of thescores. The numerator of the formula is easy to compute, just find thedifference between themeans. The denominator is called the standarderror of the difference. To compute it, variance for each group has beentaken and divided it by the number of people in that group. These two

Fig. 12. Estimated vs. measured values of density.

values are then added and their square root is taken. The formula forthe t-test is

t =xrT − xrCffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiVarTnT

+ VarCnC

� �r ð2Þ

The t-value is positive, if the first mean is larger than the secondand negative if it is lower. Once the t value is computed, it is thencompared with the tabulated value. If the computed value is largerthan the tabulated one, then it indicates strong and significantcorrelation. To test the significance, one needs to set a risk level orcalled the alpha level. In most cases, the “rule of thumb” is to set at0.05 i.e. 95% confidence interval. Since, a 95% confidence level waschosen in this test, a corresponding critical t-value 2.07 is obtained. Asit is seen in Table 4, the two computed t-values remain in the uppercritical region. So, it is concluded that there is a real correlationbetween the P-wave velocity and uniaxial compressive strength,tensile strength, shear strength, density, Young's modulus andPoisson's ratio supporting the engineering use of correlations.

In all the above six cases, calculated value of t-test is much higherthan the tabulated value, hence, they all have significantly strong

Table 4Tabulated results of the t-test.

Rock tests t-test

Calculatedvalue

Tabulatedvalue

1. Uniaxial compressive strength and P-wave velocity 47.6 2.072. Tensile strength and P-wave velocity 47.5 2.073. Shear strength and P-wave velocity 47.6 2.074. Density and P-wave velocity 2.09 2.075. Young's modulus and P-wave velocity 47.6 2.076. Poisson's ratio and P-wave velocity 46.5 2.07

60 M. Khandelwal, T.N. Singh / International Journal of Coal Geology 79 (2009) 55–60

correlation among themselves and this may be used for prediction ofthese parameters using P-wave velocity.

6. Conclusions

The study indicates that the uniaxial compressive strength, tensilestrength, shear strength, density, Young's modulus and Poisson's ratioof various coal measures rocks types of India can be estimated fromtheir P-wave values by using simple mathematical relations. First fiveproperties showed linear relationship with P-wave velocity, whereas,Poisson's ratio showed power relation. The mathematical expressionsare as follows:

UCS = 0:1333TP‐wave − 227:19 R2 = 0:9619 ð3Þ

TS = 0:0145TP‐wave − 24:55 R2 = 0:9469 ð4Þ

SS = 0:0291TP‐wave − 49:494 R2 = 0:9579 ð5Þ

Den = 0:0011TP‐wave − 0:0847 R2 = 0:9719 ð6Þ

YM = 4:9718TP‐wave − 7151 R2 = 0:9740 ð7Þ

PR = 8 × 1015TP‐wave−5:0509 R2 = 0:9434 ð8Þ

A strong coefficient of determination was found between P-wavevelocity and physico-mechanical properties of the tested coalmeasures rocks. This was also verified by Student's t-test, whichshowed higher calculated values for each relation, rather thantabulated values.

These equations are practical, simple and accurate enough to applyfor the use in general practice to obtain important static physico-

mechanical properties of the different rocks for design and planning ofexcavation with greater safety and stability for Indian geo-miningconditions.

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