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Estimation of rock engineering properties using hardness tests

Faisal I. Shalabi, Edward J. Cording, Omar H. Al-Hattamleh

PII: S0013-7952(07)00002-6DOI: doi: 10.1016/j.enggeo.2006.12.006Reference: ENGEO 2637

To appear in: Engineering Geology

Received date: 12 September 2006Revised date: 17 December 2006Accepted date: 29 December 2006

Please cite this article as: Shalabi, Faisal I., Cording, Edward J., Al-Hattamleh, OmarH., Estimation of rock engineering properties using hardness tests, Engineering Geology(2007), doi: 10.1016/j.enggeo.2006.12.006

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41Telephone: 962-5-390-333342Fax: 962-5-382-634843

1

Estimation of rock engineering properties using hardness tests12

Faisal I. Shalabi 1, Edward J. Cording2, Omar H. Al-Hattamleh334

1,3 Assistant Professor, Department of Civil Engineering, Hashemite University, 13115 Zarqa,5Jordan6

72 Professor Emeritus, Department of Civil Engineering, University of Illinois at Urbana-8

Champaign, Urbana, Illinois 61801, USA910

Abstract1112

In engineering projects such as tunnels, dams, foundations, and slope stability, the strength and13elastic properties of the intact rock affect both the project design and the construction operation.14It is sometimes expensive and time consuming to perform direct tests to evaluate the15engineering properties (such as strength, modulus of elasticity, and Poisson’s ratio) of the intact16rock. The purpose of this work is to investigate the relationships between the engineering17properties of the intact rock and the different types of hardness (Schmidt, shore scleroscope,18abrasion, and total hardness), which are relatively cheap and easy to evaluate. In this study,19dolomite, dolomitic limestone, and shale rocks were used. For simplicity, linear statistical20analyses were performed. The results show that there are good relationships between the21engineering properties of the intact rock and its hardness. Also, the results of this study are22compared well with the results obtained by other investigators conducted on different types of23rocks.24

25Keywords: abrasion, elasticity, Poisson’s ratio, Schmidt hardness, shore hardness, strength, statistical26relationships.27

281. Introduction29

30Physical and mechanical properties of intact rocks are very important in civil engineering works31

that interact with rock such as underground structures, dams, foundations on rock, and rock32

slopes. Performing direct tests to evaluate rock strength and deformation is mostly expensive33

and required considerable time, especially the preparation of rock samples for testing. Different34

indirect testing methods were developed and used to interpret the engineering properties of35

rock. The indirect tests include point load, Schmidt rebound hardness, Shore Scleroscope36

hardness, and abrasion hardness. These tests are relatively easy to perform, not expensive, and37

take short testing time.38

391 Corresponding author.40E-mail address: fshalabi@hu.edu.jo

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The physical properties of the intact rocks depend on its microstructure. Willared and44

McWilliams (1969) indicated that the micro-structure, including: minerals cleavage, grain45

boundaries, and microfractures, has an effect on the rock strength and the direction of failure.46

Merriam et al. (1970) found a good relationship between the strength of granitic rock and47

quartz content. Onodera and Kumara (1980) found that the strength of igneous rocks decreases48

linearly with the increase in grain size. Irfan, (1996) indicated that the physical properties of the49

intact rocks are highly influenced by the type, texture, percentage, and fabric of the minerals50

forming the rock.51

52Many studies had been carried out to correlate the engineering properties of rock with53

its physical index properties. Griffith (1937) correlated the unconfined compressive strength of54

different rock types (sedimentary, igneous, and metamorphic rocks) with shore scleroscope55

hardness according to the equation: UCS = 300 x (1± 0.1) Sh, where UCS is the unconfined56

compressive strength in psi, and Sh is the shore scleroscope rebound hardness. Wuerker (1953),57

based on tested rock samples, correlated the unconfined compressive strength of rock with the58

shore scleroscope hardness using very simple linear equation: UCS = 400 Sh, (UCS in psi).59

60Deere et al. (1966) performed an extensive study on large number of rock samples61

representing different types of rocks (basalt, diabase, dolomite, gneiss, granite, limestone,62

marble, quartzite, rock salt, sandstone, schist, siltstone, and tuff) to develop an engineering63

classification system for the intact rock. The researchers found that the classification is strongly64

affected by rock mineralogy, texture, and anisotropy. They also concluded that rock strength65

and modulus properties are correlated better with Schmidt hardness than Shore hardness when66

the effect of unit weight of the rock is included. Further more, they found that sonic velocity as67

an index property for rock modulus is not as good as Schmidt or shore hardness. Table 168

provides the important correlations that were developed by Deere et al. (1966) to correlate the69

engineering properties of the intact rock with its index properties.70

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Aufmuth (1973) obtained a good correlation between Schmidt hardness (HR) and both,71

unconfined compressive strength (UCS) and tangent modulus of rock (E) including the effect of72

rock density. Singh et al. (1983), based on the results of sedimentary rocks, developed a very73

simple and good relationship between UCS of rock and HR. O’Rourke (1989) obtained a good74

linear relation between UCS and HR using different types of sedimentary rocks. Sachpazis75

(1990) obtained a strong relationship (R = 0.96) between USC and HR for carbonate rocks when76

the rock density was considered. Tugrul and Zarif (1999), based on tests on granitic rocks77

obtained a strong relationship between UCS and HR. They also concluded that the strength of78

the rock depends on the mean size of the grains. Katz et al. (2000), based on tests on marble,79

limestone, granite, sandstone, chalk, and syenite, obtained a very strong relation between UCS80

and HR (R = 0.98). Yilmaz and Sendir (2002), based on experimental test results on gypsum81

rock, obtained a strong relationships (R = 0.91) between UCS and exponential of HR. Yasar and82

Erdogan (2004), based on experimental tests on limestone, sandstone, marble, and basalt,83

obtained a good statistical power relation between HR and UCS. Table 2 summarized some of84

the relationships between the Schmidt rebound hardness and both the unconfined compressive85

strength and tangent modulus of different types of rocks.86

87Other researchers tried to correlate unconfined compressive strength with shore88

scleroscope hardness (Sh). Table 3 shows that a strong power relationship (R=0.91) between89

UCS and Sh was developed by Yasar and Erdogan (2004) based on results of experimental tests90

on limestone, sandstone, marble, and basalt rocks.91

92In this work, relationships between physical index properties and engineering93

properties of different types of rocks will also be investigated. Although many researchers94

studied the relations between UCS- rebound hardness (HR), and rock modulus (E)-HR, this work95

attempts to develop new empirical relations between rock hardness and Poisson’s ratio, total96

hardness and UCS, abrasion hardness and UCS, and UCS and Poisson’s ratio. This study with97

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the new empirical relations is expected to add more information to the relationships between98

rock hardness and rock engineering properties.99

1002. Methods and Testing Procedures101

102Dolomite rock samples were collected from McCook Quarry and Joliet Road103

(Chicago), rock shale samples brought from Puerto Rico, dolomitic marble, deopside, and104

anhydrite brought from New York, and dolomite and dolomitic limestone brought from Detroit105

River Outfall. NX size (54 mm diameter) samples were used for testing. For unconfined106

compressive strength tests, the ends of the samples were cut flat and polished with special107

machine in order to be precisely perpendicular to the specimen axis. For shale and dolomitic108

marble, strain gages were fixed along and across the sides of the specimens in order to measure109

axial and lateral deformations. The samples were tested according to ISRM (1981a) suggested110

methods. 100 kips (450 kN) in capacity computerized MTS compression machine was used for111

testing. Constant stress rate of 0.2 MPa/sec. was applied to the specimens to reach the state of112

failure within approximately 5-10 minutes. Fig. 1 shows a strain-gaged rock sample ready for113

unconfined compression test.114

115For the Schmidt hardness test, L-type Schmidt hammer with 0.075 kg-m of energy was116

used. Tests were made by laying the sample inside the cradle and performing the rebound test at117

different places along the specimen (20 reading points were taken along the specimen and the118

mean value of the highest 10 points was considered). The Schmidt rebound values were119

corrected based on a correction factor: C.F = Specified standard value of the anvil /average of120

10 readings taken on the calibrated anvil (Tarkoy, 1975). Fig. 2 shows Schmidt hammer device121

with rock sample.122

123For the shore scleroscope hardness tests, C-2 type model was used. The test was124

performed by placing the sample inside the cradle. The shore hardness was measured as the125

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height of the rebound of a small diamond-point hammer which dropped from a distance of126

about 30 cm from the surface of the specimen (20 reading points were taken along the specimen127

and the mean value was calculated). The rebound values were corrected according to the128

correction factor: C.F = Specified standard values/average of 10 readings taken on standard129

steel block (Tarkoy, 1975). Fig. 3 shows the shore sleroscope hardness device with rock130

sample.131

For the abrasion hardness tests, two oven dried disks of rock samples were weighted132

and used for testing. During the test, each side of rock disk was revolved 400 revolutions133

underneath the abrasion wheel (800 revolutions for each disk). The abrade material was134

continuously removed by a vacuum and air pressure. After testing, the weight of each disk was135

recorded and the abrasion hardness was evaluated as: HA = 1/ average weight loss of the two136

rock disks in grams (Tarkoy, 1975). The total hardness (HT) was calculated according to137

Cording (1996) as: HT = HR x (HA)1/2, where HR is the Schmidt hardness and HA is the abrasion138

hardness. Fig. 4 shows two prepared disks for abrasion test.139

1403. Results and discussions141

142In this section the results of the experimental tests will be discussed. The discussion143

will focus on the statistical relationships that were developed between rock engineering144

properties and rock hardness. Table 4 summarized the results of the tests of all the tested145

samples.146

1473.1 Relationships between rock hardness and rock strength148

149Unconfined compressive strength (UCS) was correlated with Schmidt rebound150

hardness (HR), abrasion hardness (HA), and total hardness (HT) of low density dolomite (γ<23151

kN/m3) and dolomitic limestone rocks, as shown in Fig. 5 through Fig. 7. Good linear152

relationships were obtained especially between UCS and both abrasion hardness (correlation153

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coefficient, R=0.81) and total hardness (R=0.83). For high density dolomite (γ>23 kN/m3), Fig.154

8 shows the relationship between UCS and shore hardness. In this Fig., it can be seen that the155

UCS increases with the increase in shore hardness and the relation can be expressed linearly156

with R=0.80. For argillite and shale rocks, Fig. 9 shows a good linear relationship between the157

UCS and shore scleroscope hardness. For this relationship, the correlation coefficient, R is 0.85.158

1593.2 Relationships between rock hardness and elastic properties160

161In this study the relationships between the elastic properties of just shale rock were162

investigated. For the other types of rocks used in this work, no tests were performed to163

investigate these relations. Fig. 10 shows the relationship between modulus of elasticity (Et50)164

and shore hardness. In this figure, it can be seen that Et50 increases with the increase in shore165

hardness and the relationship between them can be expressed linearly with correlation166

coefficient, R = 0.92. It should be mentioned here that tangent modulus of elasticity was167

calculated from the stress strain curve at a normal stress equal to the half of the unconfined168

compressive strength because around this stress level the micro-cracks are closed and the169

stress-strain curve is linear (Deere et al. 1996). Considering the effect of rock hardness on rock170

lateral deformation, Fig. 11 shows a good linear relationship between Poisson’s ratio (v) and171

shore scleroscope hardness, with R = 0.81. In this figure it can also be seen that Poisson’s ratio172

decreases with the increase in shore scleroscope hardness.173

1743.3 Relationship between rock strength and unit weight175

176Unconfined compressive strength of dolomite rock was correlated with the dry unit177

weight as shown in Fig. 12. In this Fig., it can be seen that the trend of the data shows an178

increase in UCS with the increase in the unit weight. If this relation expressed linearly, the179

coefficient of correlation, R is 0.62.180

181

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3.4 Relationship between rock modulus and strength182183

The relationship between tangent modulus at 50% strain of failure and unconfined184

compressive strength was investigated, as shown in Fig. 13. Considering different types of185

rocks on the same scale (shale and dolomite for this case), Fig. 13 shows an increase in rock186

modulus with the increase in UCS. For linear relationship, the coefficient of correlation, R is187

0.84. If the ratio between tangent modulus and unconfined strength was considered, Fig. 13188

shows that Et50/UCS ratio is approximately considered between 1000 for shale rock and 700 for189

dolomite rock.190

1913.5 Relationships among various rock properties192

193Results of the tests of low density dolomite and dolomitic limestone rocks show that194

there is a good linear relationship (R=0.81) between abrasion hardness (HA) and Schmidt195

rebound hardness (HR) as shown in Fig. 14. On the other hand, results of the tests of high196

density dolomite shows that there is a strong linear relationship (R = 0.92) between Abrasion197

hardness and shore hardness, as shown in Fig. 15.198

199Results of the tests on shale rock show that there is a decrease in Poisson’s ratio, ν,200

with the increase in the unconfined compressive strength. Fig. 16 shows that the correlation201

coefficient of a linear relationship between ν and UCS is 0.87.202

2034. Comparison with other studies204

205Results of this study were compared with the results of other studies conducted by206

many investigators. Fig. 17 shows that the relationship between unconfined compressive207

strength and Schmidt rebound hardness is compared well with the other studies, and the results208

of this relation were matching the results obtained by Singh et al. (1983). Fig. 18 shows the209

relationships between unconfined compressive strength and Shore scleroscope hardness for210

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different studies. In this figure it can be seen that the results of this study are compared well211

with the results of the other studies.212

2135. Conclusions214

215Many studies were performed to investigate the relationship between rock strength and216

deformation and rock hardness. Different statistical simple and complex empirical models were217

derived from these studies. The correlation coefficients of the proposed models were varied218

between low and high values. This study was performed to provide more investigation and to219

add more information to the relationships between rock hardness and rock engineering220

properties.221

222In this study the properties of dolomite, dolomitic limestone, and shale rocks were tested.223

The tests include the stress-strain behavior, compressive strength, abrasion hardness, shore224

scleroscope hardness, and Schmidt rebound calibrated hardness. It should be mentioned here225

that, only shale rock was tested for stress-strain behavior. Linear regression analyses were226

performed to correlate rock hardness with rock engineering properties. The results of this study227

were compared well with the results obtained by other investigators conducted on different228

types of rocks. Tables 5 through 7 summarize the correlations among rock properties.229

230From the results of regressions the following conclusions were derived:231

(1) The unconfined compressive strength and modulus of elasticity of sedimentary232

rock can be estimated based on simple linear relations between these engineering233

properties and the hardness of the rock.234

235(2) Poisson’s ratio of rock can be predicted based on the results of unconfined236

compressive strength and hardness. The results show that Poisson’s ratio decreases237

with the increase in rock strength and hardness.238

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(3) The abrasion hardness can reasonably be estimated based on the results of rebound239

hardness.240

(4) Beside the rock type, it is very important to consider rock microstructure (including241

density, grain size, and porosity) when using rock hardness to evaluate rock242

engineering properties.243

(5) It is important to perform more studies on different types of rocks that encountered244

engineering projects in order to improve the statistical relationships between rock245

hardness and rock engineering properties. The improved relationships should be246

driven individually for each rock type.247

(6) It is important to investigate the effect of sample orientation on the relationships248

between rock hardness and its engineering properties.249

250Acknowledgements251

252The authors would like to thank Woodward-Clyde (Illinois, USA), Geoconsult (San253

Juan, Puerto Rico), PB-KBB (Texas, USA), and NTH Consultants (Michigan, USA) for254

providing most of the rock samples.255

256References257

258Atkinson, R.H., 1993. Hardness tests for rock characteristics. In: Hudson, J.A. (Ed.), Rock259

Testing and Site Characterization- Compressive Rock Engineering, vol. 3, pp. 105-117.260

Aufmuth, R. E., 1973. A systematic determination of engineering criteria for rocks. Bull.261

Assoc. Eng. Geol. 11, 235-245.262

Cording, E. (1996). Rock mechanics class notes. Dept. of civil engineering. University of263

Illinois at Urbana-Champaign, Urbana, Illinois, USA.264

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Deer, D.U., Miller, R. P., 1966. Engineering classification and index properties for intact rock.265

Tech. Report. Air Force Weapons Lab., New Mexico, No. AFWL-TR-65-116.266

Irfan, T.Y., 1996. Mineralogy, fabric properties, and classification of weathered granites in267

Hong Kong. Q. J. Eng. Geol. 29, 5-35.268

I.S.R.M., 1981a. Suggested methods for determining the uniaxial compressive strength and269

deformability of rock materials. International Society for Rock Mechanics. Commission on270

standardisation of laboratory and field tests, pp. 111-116271

I.S.R.M., 1981b. Suggested methods for determining hardness and abrasiveness of rocks, Part272

3. International Society for Rock Mechanics. Commission on standardisation of laboratory273

and field tests, pp. 101-102.274

Sachpazis, C.I., 1990. Correlating Schmidt hardness with compressive strength and Young’s275

modulus of carbonate rocks. Bull. Int. Assoc. Eng. Geol. 42, 75-83.276

Katz, O., Reches, Z., Roegiers, J., 2000. Evaluation of mechanical rock properties using a277

Schmidt hammer. Int. J. Rock Mech. Min. Sci., 37, 723-728.278

Koncagul, E.C., Santi, P.M., 1999. Predicting the unconfined compressive strength of the279

Breathitt shale using slake durability, shore hardness and rock structural properties. Int. J.280

Rock Mech. Min. Sci., 139-153.281

Merriam, R., Rieke, H.H., Kim, Y.C., 1970. Tensile strength related to mineralogy and texture282

of some granitic rocks. Eng. Geol., 4, 155-160283

Onodera, T.F., Asoka Kumara, H.M., 1980. Relation between texture and mechanical284

properties of crystalline rocks. Bull. Int. Assoc. Eng. Geol.22, 173-177.285

O’Rourke, J. E., 1989. Rock index properties for geoengineering in underground development.286

Min. Eng., 106-110.287

Tarkoy, P., 1975. Rock hardness index properties and geotechnical papameters for predicting288

tunnel boring machine performance. PhD thesis, University of Illinois at Urbana-289

Champaign, Urbana, Illinois, USA.290

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Tugrul A., Zarif, I.H., 1999. Correlation of mineralogical and textural characteristics with291

engineering properties of selected granitic rocks from Turkey. Engineering Geology, 51,292

303-317.293

Willard, R.J., McWilliams, J.R., 1969. Microstructural techniques in the study of physical294

properties of rock. Int. J. Rock Mech. Min. Sci. 6, 1-12.295

Wuerker, R., 1953. The status of testing strength of rock. Trans. Min. Eng. AIME, 1108-1113.296

Yasar, E., Erdogan, Y., 2004. Estimation of rock physicomechanical properties using hardness297

methods. Engineering Geology, 71, 281-288.298

Yilmaz, I., Sedir, H., 2002. Correlation of Schmidt hardness with unconfined compressive299

strength and Young’s modulus in gypsum from Sivas (Turkey). Engineering Geology, 66,300

211-219.301

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Fig.1. Rock sample with longitudinal and circumferential326strain gages.327

328Fig. 2. Schmidt hammer device with rock sample329

330Fig. 3. shore scleroscope hardness with rock sample331

Fig. 4. Rock disks for the abrasion test332333

Fig. 5. The relationship between unconfined compressive strength334and Schmidt hammer (low density dolomite and dolomitic limestone)335

336Fig. 6. The relationship between unconfined compressive strength337and abrasion hardness (low density dolomite and dolomitic limestone)338

339Fig. 7. The relationship between unconfined compressive strength340and total hardness (low density dolomite and dolomitic limestone)341

342Fig. 8. The relationship between unconfined compressive strength and shore343hardness of high density dolomite344

345Fig. 9. The relationship between unconfined compressive strength and346shore hardness of shale rock347

348Fig. 10. The relationship between modulus of elasticity and shore349hardness of shale rock350

351Fig. 11. The relationship between Poisson’s ratio and shore hardness of352shale rock353

354Fig. 12. The relationship between unconfined compressive strength and355unit weight of dolomitic rock356

357Fig. 13. The relationship between tangent modulus and unconfined358compressive strength of dolomite and shale rocks359

360Fig. 14. The relationship between abrasion hardness and Schmidt361hardness. Low density dolomite and dolomitic limestone362

363Fig. 15. The relationship between the abrasion hardness and shore364hardness of high density dolomite365

366Fig. 16. The relationship between Poisson’s ratio and unconfined367compressive strength of shale rock368

369Fig. 17. The relationship between unconfined compressive strength370and Schmidt rebound hardness (different studies)371

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Fig. 18. The relationship between unconfined compressive strength372and Shore scleroscope hardness (different studies)373

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