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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
This is a PDF file of an unedited manuscript that has been accepted for publication.As a service to our customers we are providing this early version of the manuscript.The manuscript will undergo copyediting, typesetting, and review of the resulting proofbefore it is published in its final form. Please note that during the production processerrors may be discovered which could affect the content, and all legal disclaimers thatapply to the journal pertain.
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41Telephone: 962-5-390-333342Fax: 962-5-382-634843
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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
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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
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deformability of rock materials. International Society for Rock Mechanics. Commission on270
standardisation of laboratory and field tests, pp. 111-116271
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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
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Schmidt hammer. Int. J. Rock Mech. Min. Sci., 37, 723-728.278
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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
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properties of crystalline rocks. Bull. Int. Assoc. Eng. Geol.22, 173-177.285
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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
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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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D M
ANU
SCR
IPT
ACCEPTED MANUSCRIPT
31
1200120112021203120412051206120712081209121012111212121312141215121612171218121912201221122212231224122512261227122812291230123112321233123412351236123712381239124012411242124312441245
ACC
EPTE
D M
ANU
SCR
IPT
ACCEPTED MANUSCRIPT
32
1246124712481249125012511252125312541255125612571258125912601261126212631264126512661267126812691270127112721273127412751276127712781279128012811282128312841285128612871288128912901291
ACC
EPTE
D M
ANU
SCR
IPT
ACCEPTED MANUSCRIPT
33
1292129312941295129612971298129913001301130213031304130513061307130813091310131113121313131413151316131713181319132013211322132313241325132613271328132913301331133213331334133513361337
ACC
EPTE
D M
ANU
SCR
IPT
ACCEPTED MANUSCRIPT
34
1338133913401341134213431344134513461347134813491350135113521353135413551356135713581359136013611362136313641365136613671368136913701371137213731374137513761377137813791380138113821383
ACC
EPTE
D M
ANU
SCR
IPT
ACCEPTED MANUSCRIPT
35
1384138513861387138813891390139113921393139413951396139713981399140014011402140314041405140614071408140914101411141214131414141514161417141814191420142114221423142414251426142714281429
ACC
EPTE
D M
ANU
SCR
IPT
ACCEPTED MANUSCRIPT
36
1430143114321433143414351436143714381439144014411442144314441445144614471448144914501451145214531454145514561457145814591460146114621463146414651466146714681469147014711472147314741475
ACC
EPTE
D M
ANU
SCR
IPT
ACCEPTED MANUSCRIPT
37
1476147714781479148014811482148314841485148614871488148914901491149214931494149514961497149814991500150115021503150415051506150715081509151015111512151315141515151615171518151915201521
ACC
EPTE
D M
ANU
SCR
IPT
ACCEPTED MANUSCRIPT
38
1522152315241525152615271528152915301531153215331534153515361537153815391540154115421543154415451546154715481549155015511552155315541555155615571558155915601561156215631564156515661567
ACC
EPTE
D M
ANU
SCR
IPT
ACCEPTED MANUSCRIPT
39
1568156915701571157215731574157515761577
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