Journal of Applied Geophysics 71 (2010) 1–5

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Journal of Applied Geophysics

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Correlating index properties of rocks with P-wave measurements

Manoj Khandelwal a, P.G. Ranjith b,⁎a Dept of Mining Engineering, College of Technology & Engineering, Maharana Pratap University of Agriculture & Technology, Udaipur — 313 001, Indiab Monash University, Geomechanics, Bld. 60, Clayton, Victoria 3800, Australia

⁎ Corresponding author.E-mail addresses: mkhandelwal@mpuat.ac.in (M. Kh

ranjith.pg@eng.monash.edu.au (P.G. Ranjith).

0926-9851/$ – see front matter © 2010 Elsevier B.V. Aldoi:10.1016/j.jappgeo.2010.01.007

a b s t r a c t

a r t i c l e i n f o

Article history:Received 3 March 2009Accepted 29 January 2010

Keywords:Index propertiesP-wave velocityCerchar Abrasivity IndexShore HardnessProtodyakonov IndexVickers Hardness

The determination of index properties of rock, such as Cerchar Abrasivity Index, Shore Hardness,Protodyakonov Index and Vickers Hardness in laboratory or insitu conditions is time-consuming andrequires special equipment and expertise. However, the use of P-wave technology to measure the P-wavevelocity of rock is a relatively simple task because the portable equipment can be used in the laboratory or inthe field without tedious preparation of rock cores and it is non-destructive. This paper presents anexperimental study of the measurement of P-waves of several types of igneous, sedimentary andmetamorphic rock. The index properties were also determined in the laboratory to obtain correlationsbetween P-waves and various index properties. Good linear relationships were found between all the indexproperties determined and the P-wave measurements.

andelwal),

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© 2010 Elsevier B.V. All rights reserved.

1. Introduction

The index properties of rocks play a crucial role in the planning anddesign of civil and mining excavations, including the stability of dumpand rock slopes, stability of underground excavations, tunnels, dams,deep trenches and caverns. They are also very important for the studyof rock bursts and bumps in underground mines, for pillar design andthe prediction of failure of rock mass. The determination of theseindex properties in the laboratory as well as in insitu conditions istedious and time-consuming. It also requires great accuracy in thepreparation and testing of samples. There is no such direct method bywhich index properties can be obtained, without following a laboriousand time-consuming laboratory procedure. Therefore, there is a needfor a simple technique for the determination of the index properties ofrocks by an indirect but reliable method.

Ultrasonic techniques have been used for many years in geotech-nical practice and mining science. They are employed in the field forgeophysical investigations and in the laboratory for the determinationof the dynamic properties of rocks (Kahraman, 2002). Since thesetechniques are non-destructive and easy to apply, they are increas-ingly being used in geotechnical engineering (Sharma and Singh,2008). Attempts have been made to assess grouting, rock boltreinforcement and blasting efficiencies in the rock mass by seismicvelocity (Knill, 1970; Price et al., 1970; Young et al., 1985). The

predictions of rock mass deformation as well as the extent of damagezones developed around underground openings are other applica-tions of seismic techniques (Onodera, 1963; Hudson et al., 1980;Gladwin, 1982). Various researchers have found that sound velocity isclosely related to rock properties (Deere and Miller, 1966; D'Andreaet al., 1965; Saito et al., 1974; Gardner et al., 1974; Youash, 1970; Lamaand Vutukuri, 1978; Inoue and Ohomi, 1981; Gaviglio, 1989).

Themeasurement of P-wave velocity can be carried out in both fieldand laboratory environments. The P-wave technique is non-destructiveand easy to apply. Therefore, it is increasingly beingused in geotechnicalengineering,mining and petroleum engineering. The P-wave velocity ofa rock is closely related to the intact rock properties and measuring thevelocity in rock media interrogates the rock structure and texture. Theimportant influencing parameters are grain size and shape, density,porosity, anisotropy, pore water, temperature, weathering and alter-ation zones, bedding planes and joint properties, including roughness,filling material, water, dip and strike (Kahraman, 2001).

To date, there has been no direct method by which indexproperties such as Cerchar Abrasivity Index (CAI), Shore Hardness(SH), Protodyakonov Index (f) and Vickers Hardness (VH) can bedetermined. Therefore, an attempt has been made in this paper tocorrelate P-wave velocity with other index properties, such as CercharAbrasivity Index (CAI), Shore Hardness (SH), Protodyakonov Index (f)and Vickers Hardness (VH).

2. Location and type of samples collected

All rock types tested in the present study were collected fromdifferent locations in India. During sampling, representative rockmasssamples were collected to determine the index properties in the

Table 1List of rock types with class and location.

Rock type Rock class Location (in India)

Quartzite Igneous Rampur (H.P.)Granite Igneous Jalore (Raj)Dolomite Sedimentary Jodhpur (Raj)Sandstone 1 Sedimentary Jodhpur (Raj)Sandstone 2 Sedimentary Bijoliyan (Raj)Sandstone 3 Sedimentary Bundi (Raj)Limestone 1 Sedimentary Satna (M.P.)Limestone 2 Sedimentary Amreli (Guj)Shale Sedimentary Jharia (Jharkhand)Kota stone Sedimentary Ramganjmandi (Raj)Marble (white) Metamorphic Makrana (Raj)Marble (pink) Metamorphic Babarmal (Raj)Marble (green) Metamorphic Kesariyaji (Raj)

Table 2Physico-mechanical properties of various rock types.

Rock type P-wave(m/s)

CercharAbrasivityIndex (CAI)

ShoreHardness(SH)

ProtodyakonovIndex (f )

VickersHardness(VH)

Quartzite 5225 6.8 82 20 710Granite 4350 6.1 76 20 630Dolomite 3270 5 46 10.4 330Sandstone 1 2652 5.6 41 3.4 285Sandstone 2 2957 4.3 43 4.1 312Sandstone 3 3017 4.4 42 4.3 307Limestone 1 3200 4.8 35.27 8.24 240Limestone 2 3016 3.6 29.3 6.3 180Shale 1490 2.6 35.86 5.54 230Kota stone 6221 7.8 88 23 824Marble (white) 3739 5.8 53 7.2 548Marble (pink) 2844 5.3 47 5.4 483Marble (green) 2370 5.1 39 3.9 336

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laboratory. Table 1 illustrates the list of rock types with their classesand the locations where the samples were collected.

3. Laboratory investigation

Representative rock mass samples were collected from the variouslocations in India. These rock mass samples were cored in NX size(54 mm diameter) to determine their physico-mechanical properties.Core specimens were cored by a coring machine and the endstrimmed as required. The core specimens were then cut into standardsize as per the ISRM (1981) standards for different physico-mechanical properties. After coring, the rock specimens were furthersmoothened using a lathe to avoid end effects. The specimens weredried at 105 °C for 24 h to remove the moisture. For each rock type,the average of 3 to 5 sample results was determined.

3.1. P-wave measurements

The velocity of ultrasonic pulses travelling in a solid materialdepends on the density and elastic properties of that material. Thequality of some materials is related to their elastic stiffness so thatmeasurement of ultrasonic pulse velocity in such materials can oftenbe used to indicate their quality as well as to determine their elasticproperties. To determine the P-wave velocity of different rocks, rockblocks were cored in the laboratory for NX diameter with sufficientlength. P-waves were determined in the laboratory as per the ISRM

Fig. 1. Ultrasonic P-wave tester.

(1978a) standard. Fig. 1 shows the P-wave instrument used in thisstudy for the measurements of P-wave. Table 2 shows the P-wavevelocity of different rock types. In addition to P-wave measurements,Cerchar Abrasivity Index, Shore Hardness, Protodyakonov Index, andVickers Hardness tests were carried out on all selected rock samplesand brief descriptions of each test and the test procedures arediscussed below.

3.2. Cerchar Abrasivity Index

The Cerchar Abrasivity Index (CAI) test is widely accepted for theassessment of rock abrasiveness. It is considered to provide a reliableindication of rock abrasiveness (Muftuoglu, 1983; Singh et al., 1983;Atkinson et al., 1986a,b; Yaralı et al., 2008). CAI is conducted withreference to the original testing recommendation by the FrenchCERCHAR institute (Cerchar, 1986). The CAI is determined as theabrasion of ametal pin after scratching over the freshly-broken surfaceof a rock. The pin ismade of a certain steel quality (200 kg/mm2 tensilestrength or Rockwell Hardness 54–56 or Vickers Hardness 610±5)and is terminated by a 90° cone angle, sharpened on a high precisionlathe and applied to the surface of a rock specimen for approximately1 s under a static load of 68.646 N to scratch a 10 mm long groove(Suana and Peters, 1982; Yaralı et al., 2008). This procedure wasrepeated several times in various directions using a fresh pin for eachrepetition. The abrasiveness of the rock was determined by theresultant wear flat generated at the point of the stylus, which wasmeasured in 0.1 mm under a microscope (Fig. 2). The unit ofabrasiveness is defined as a wear flat of 0.1 mm, which is equal to 1CAI, ranging from 0 to 6. Table 2 shows the measured CAI values of thedifferent rock types used in this test program.

3.3. Shore Hardness

The Shore Hardness (SH) test is a convenient and inexpensivemethod for estimating rock hardness (Altindag and Guney, 2006). The

Fig. 2. The measurement of abrasiveness of point of the stylus (Thuro and Plinninger,1998). (a) New tool; (b) after wearing.

Fig. 3. Vickers Hardness tester.

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SH of a specimen was determined from the rebound height of adiamond or tungsten-carbide tipped hammer released from rest ontoa horizontal smooth surface (Rabia and Brook, 1979). A fulldescription of the apparatus can be found elsewhere (ISRM, 1978b;Misra, 1972). Originally the test was developed for determining thehardness of metal specimens, and as metals are homogeneous, onerebound reading is sufficient to give a representative value of the SH.Rocks, however, are composed of a number of minerals and a singlereading would not be representative of the whole specimen.Therefore, in this study, SH was determined by taking 20 reboundreadings at different positions on a ground surface of a rock sample asper ISRM (1978b) standards. The arithmetic mean of 20 readings wastaken as the SH of each rock. Table 2 illustrates the SH values ofdifferent rock types sourced from India.

3.4. Protodyakonov Index

Protodyakonov (1962) proposed the evaluation of the mechanicalproperties of rocks bymeans of relative strength coefficient, called theProtodyakonov Index (f). The Protodyakonov Rock Strength Scale wasoriginally devised as an index relating to compressive strength, andwas defined as the strength in kgf/cm2 divided by 100. As adetermination of this index requires extensive laboratory facilities, afield method was devised, using a mortar and falling weight to breakthe rock and a volumemeter to determine the fines below 0.5 mm. Anempirical relationship was used to relate the two methods. TheProtodyakonov Index can be determined in the laboratory by thefollowing empirical formula:

f = 20:n= h ð1Þ

Where,

n number of impacts of the drop weight on each sampleh volumeter height.

The accuracy of the Protodyakonov Index is susceptible to theduration of sieving and degree of compaction of the fines in thevolumeter, which depends on the number of blows (Paithankar andMisra, 1976). It also varies with the number of blows for the same rockdepending on the hardness of the rock. In the case of soft rocks, theremay be regrinding of fines, while in hard rock the energy may beutilised in elastic deformation and cracking of particles withoutgenerating sufficient fines. Themeasured values of the ProtodyakonovIndex of each rock are given in Table 2.

3.5. Vickers Hardness

The Vickers Hardness (VH) test was developed by Smith andSandland (1922) at Vickers Ltd. as an alternative to the Brinellmethod, which is determined by forcing a hard steel or carbide sphereof a specified diameter under a specified load into the surface of amaterial and measuring the diameter of the indentation left after thetest to measure the hardness of materials. The Vickers test is ofteneasier to use than other hardness tests, since the required calculationsare independent of the size of the indenter, and the indenter can beused for all materials irrespective of hardness. The basic principle, aswith all common measures of hardness, is to observe the questionedmaterial's ability to resist plastic deformation from a standard source.The Vickers test can be used for all rock types and has one of thewidest scales among hardness tests. Fig. 3 illustrates the VickersHardness tester.

The Vickers Hardness test method consists of indenting the testmaterial with a diamond indenter, in the form of a right pyramid witha square base and an angle of 136° between opposite faces subjectedto a load of 1 to 100 kgf. The full load is normally applied for 10 to 15 s.

The two diagonals of the indentation left in the surface of the materialafter removal of the load are measured using a microscope and theiraverage calculated. The area of the sloping surface of the indentationis calculated. The Vickers Hardness is the quotient obtained bydividing the load (kgf) by the area (mm2) of indentation.

VH = 2:F:Sin680= d2 = 1:854F = d2 approximatelyð Þ ð2Þ

Where,

VH Vickers HardnessF Load in kgfd Arithmetic mean of the two diagonals, d1 and d2 in mm

The measured Vickers Hardness value of each rock type is given inTable 2 below.

4. Results and discussions

In order to describe the relationships between P-wave velocity andCerchar Abrasivity Index (CAI), Shore Hardness, Protodyakonov Indexand Vickers Hardness of the tested rock samples, a regression analysiswas carried out. The equation of the best fit line and the coefficient ofdetermination (R2) were determined for each test result.

The best fit line and its regression analysis for each data set isillustrated in Figs. 4–7. It can be seen from the figures that, in all cases,the best fit relationships were found to be best represented by linearregression curves. However, this is only applicable under the P-waverange 1490 m/s–6221 m/s. For the lower and higher P-wave values,these equationsmay producemisleading results. Extrapolation shouldtherefore not be used to validate the results from empirical equations.

Fig. 4. Graph of P-wave and Cerchar Abrasivity Index. Fig. 6. Graph of P-wave and Protodyakonov Index.

Fig. 7. Graph of P-wave and Vickers Hardness Index.

4 M. Khandelwal, P.G. Ranjith / Journal of Applied Geophysics 71 (2010) 1–5

The plot of the P-wave as a function of Cerchar Abrasivity Index isshown in Fig. 4.

There is linear relation between P-wave velocity and CercharAbrasivity Index for all rock types. A strong correlation (R2=0.7646)was found between P-wave velocity and Cerchar Abrasivity Index forall rock types (Fig. 4). The equation of this relation is given below:

CAI = 0:0009*P‐wave + 1:9375: ð3Þ

A similar linear relationship has been observed between P-wavevelocity and Shore Hardness (SH) for all rock types. A very goodcorrelation was found (R2=0.817) between them for the tested rocktypes (Fig. 5).

SH = 0:013*P‐wave + 3:265: ð4Þ

For P-wave velocity and the Protodyakonov Index (f), the curvealso shows a linear relationship (Fig. 6). A good correlation(R2=0.801) was found between P-wave velocity and ProtodyakonovIndex for all rocks. The equation of relation is as given below.

f = 0:005*P‐wave−7:734 ð5Þ

For P-wave velocity and Vickers Hardness (VH), the curve alsoshows a linear relationship (Fig. 7). A good correlation (R2=0.774)was found between P-wave velocity and Vickers Hardness for allrocks. The equation of relation is as given below.

VH = 0:144*P‐wave−75:63 ð6Þ

Fig. 5. Graph of P-wave and Shore Hardness.

4.1. Student t-test analysis

To determine the relationship between P-wave velocity and othertests, such as Cerchar Abrasivity Index, Shore Hardness, Protodyako-nov Index and Vickers Hardness of the tested rock types, t-tests havebeen performed using the Student 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 done tocompare the means of two variables, even if they have differentnumbers of replicates.

To test the significance, one needs to set a risk level known as thealpha level. In most cases, the “rule of thumb” is to set this at 0.05, i.e.95% confidence interval. Since a 95% confidence level was chosen inthis test, a corresponding critical t-value of 2.06was obtained from therelated tables. As seen in Table 3, the two computed t-values remain inthe upper critical region. It is therefore concluded that there is acorrelation between P-wave velocity and the Cerchar AbrasivityIndex, Shore Hardness, Protodyakonov Index and Vickers Hardness,supporting the engineering use of correlations.

Table 3Tabulated results of the t-test.

Rock tests t-test

Calculatedvalue

Tabulatedvalue

1. Cerchar Abrasivity Index and P-wave velocity 9.91 2.062. Shore Hardness and P-wave velocity 9.78 2.063. Protodyakonov Index and P-wave velocity 9.90 2.064. Vickers Hardness and P-wave velocity 8.60 2.06

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In all four cases, the calculated value of the t-test is much higherthan the tabulated value as shown in Table 3. Hence, they all havesignificantly strong correlations among themselves and this may alsobe used for the prediction of these parameters using P-wave velocityfor other rock types.

5. Conclusions

In this study, P-wave velocity, Cerchar Hardness, Shore Hardness,Protodyakonov Index and Vickers Hardness for all rock types weredetermined in the laboratory. The test results were interpretedstatistically and good linear relationships were found with P-wavevelocity to Cerchar Hardness, Shore Hardness, Protodyakonov Indexand Vickers Hardness. It can be inferred that P-wave velocity shows agood statistical relationship in the range of 1490 m/s–6221 m/s withCerchar Hardness, Shore Hardness, Protodyakonov Index and VickersHardness. This implies that rocks having the above range of P-wavevelocities could be ideal sources for the determination of the indexproperties of those mentioned above.

To establish the relationship between the P-wave velocities andindex tests such as Cerchar Hardness, Shore Hardness, ProtodyakonovIndex and Vickers Hardness of the tested rocks, t-tests were carriedout using the Student t-test. This analysis reveals that the calculatedvalue is much higher than the tabulated value; hence they all havesignificantly strong correlations among themselves and the proposedcorrelation equations can be used for the determination of CercharHardness, Shore Hardness, Protodyakonov Index and Vickers Hard-ness by the simple and non-destructive P-wave velocity test.

This study reveals that Cerchar Hardness, Shore Hardness,Protodyakonov Index and Vickers Hardness can be estimated bydetermining P-wave velocity with the given empirical equationsunder the specified limits without extrapolation.

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