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The effect of Schmidt hammer type on uniaxial compressive strength prediction of rock
ARTICLE IN PRESS
International Journal of Rock Mechanics & Mining Sciences 44 (2007) 299–307 www.elsevier.com/locate/ijrmms
Technical note
The effect of Schmidt hammer type on uniaxial compressive strength prediction of rock I.S. Buyuksagisa, R.M. Goktanb, a
Department of Marble Technology, Afyon Kocatepe Universitesi, Afyon, Turkey Department of Mining Engineering, Eskisehir Osmangazi Universitesi, Meselik Kampusu, Eskisehir, Turkey
b
Accepted 28 July 2006 Available online 26 September 2006
Keywords: Uniaxial compressive strength (UCS); Schmidt hammer test procedures; L-type hammer; N-type hammer
1. Introduction The estimation of rock and concrete strength by nondestructive test methods is of great interest both to civil and mining engineers involved in various design projects. The Schmidt hammer rebound hardness is one of the most frequently used methods for non-destructive testing of concrete and rock since 1950s, due to its cost-effectiveness and easy handling. Schmidt hammer tests can be performed in either the field or the laboratory to provide preliminary information on the relative quality of the material being investigated. Although originally developed to test the surface rebound hardness of concrete, it has since also been adapted for the indirect strength estimation of rock. The operation mechanism of the instrument is rather simple. A spring-loaded mass is released against a plunger when the hammer is pressed on to the surface of a test material. The plunger impacts the surface and the mass recoils. The rebound distance is proportional to the total energy absorbed by the impact surface. The rebound distance of the plunger is read directly from a numerical scale on the instrument and is called the rebound number (R) [1]. On account of its precision, cost-effectiveness and easy handling, wide application of this instrument has been made in rock engineering. Some common extensions of the use of the Schmidt hammer include: the estimation of uniaxial compressive strength and Young’s modulus of rock [2–12], determination of rock weathering [2,13,14], Corresponding author. Tel.: +90 222 239 28 40; fax: +90 222 239 36 13. E-mail address: [email protected] (R.M. Goktan).
1365-1609/$ - see front matter r 2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.ijrmms.2006.07.008
assessing joint separation and discontinuities [15,16], estimation of underground large-scale in situ strength [11,17] mine-roof control [18], rock abrasivity [19], rock rippability and rock mass excavatability classification [20,21], abrasion resistance of rock aggregates [22], penetration rate prediction of drilling machines [23–26] and, prediction of roadheader and tunnel boring machine performance [27–31]. Despite its consistency and reproducibility [32–34], a number of factors are associated with the obtained Schmidt hammer rebound values, among which are: calibration and improper functioning of the instrument [34], surface irregularities of the rock [6], weathering state of the tested rock [2,35], nearby discontinuities [36,37] rock surface moisture content [38], test specimen size [39,40], spacing between the impacts [12,39,40], orientation of the hammer [12,42,43], the adopted test procedure [27,32,33,41], and type of hammer and available impact energy [2,41]. The rebound number values obtained by Schmidt hardness method reflect an interrelated combination of rock properties such as elasticity, strength and hardness. It is known from theoretical physics that the coefficient of restitution (r) for the fall and rebound of one body on a second body can be expressed by: pffiffiffiffiffiffiffiffiffiffi r ¼ h=H , (1) where h is the rebound height and H is the drop height. In treatises on rock mechanics, the dimensionless quantity h/ H is known as rebound number, rebound hardness or rebound strength [44]. The coefficient of restitution (r) is a measure of the elasticity of the collision between two bodies. If the collision is perfectly elastic, r ¼ 1. If the collision is completely inelastic, r ¼ 0 and in this case the
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two colliding bodies will stick together and there will be no rebound. The kinetic energy possessed by the falling body just before impact is, upon impact, divided into three parts. These are elastic potential energy which is given back in the form of rebound energy (height), and elastic kinetic energy which is converted into heat energy owing to localized deformation, plastic flow and friction [44]. In the case of Schmidt hammer rebound testing, the h/H ratio is a function of the test hammer design (available impact energy) and the elastic/plastic properties of the rebound surface. This point is of vital importance for the interpretation of the obtained rebound values, as the obtained rebound number will be a function of the hammer design when the properties of the tested surface remain the same. The Schmidt hammer models are designed in different levels of impact energy, but the types L and N are more commonly adopted for the testing of rock and concrete. The provided impact energy levels of the L- and N-type hammers are 0.735 and 2.207 Nm, respectively. Although the L-type hammer is usually adopted for the testing of relatively softer materials, usable range of this type of hammer (with respect to rock strength or elasticity) is still uncertain and much discussed [2]. There are several organizations such as the International Society for Rock Mechanics (ISRM) and the American Society for Testing and Materials (ASTM) which have published Suggested Methods and testing standards, respectively, on the appropriate use of this instrument. It is suggested by the ISRM [45] that the L-type of hammer should be used for the hardness characterization of rocks which have 20–150 MPa uniaxial compressive strength (UCS). Since the use of N-type of Schmidt hammer is not endorsed by the ISRM for rock characterization, it appears that the hardness testing of rocks using this instrument is applicable to those rocks in the UCS range of 20–150 MPa. On the other hand, the ASTM [40] does not specify a hammer type, but suggests that the use of this instrument is best suited for rocks which have UCS in the range of 1–100 MPa. However, despite these suggestions and limitations suggested by such organizations, a comprehensive literature survey conducted by Aydin and Basu [2] reveals that both types of hammers have been used in rock engineering for strength estimation of various rocks having UCS up to approximately 350 MPa. Considering the brief discussion made above, it is possible to arrive to the conclusion that there is still much uncertainty regarding the selection of an appropriate hammer type for a particular application. Therefore, the present research has been conducted with a view to improve the understanding of the influence of Schmidt hammer type on strength estimation of rocks. To achieve this goal, the Schmidt hammer rebound tests of a total of 27 different rocks were carried out in the laboratory, using both the L- and N-type of hammers. The obtained rebound values, using five different Schmidt hammer recording techniques, were then correlated with the UCS values of
the tested rocks. Finally, statistical performance analyzes were performed in order to be able to check and compare the prediction capabilities of both hammer types. 2. Experimental procedures Twenty-seven different rocks including granites, marbles, limestones and travertines collected from various stone processing plants in Turkey were sampled and tested for the execution of the study. The mineralogical compositions of the tested rocks are given in Table 1, along with their textural, structural and granular descriptions. Thin sections of the rock samples were examined under a petrographic microscope for mineral type, mineral content and mean grain size. The point-count method was employed for the modal analyses. To determine silica content and other elements present in the rock, an automatic X-ray analyzer was used. For both the L- and N-type Schmidt hammers, the rebound tests were carried out on prismatic rock blocks having approximately 110 mm height, 200 mm width and 500 mm length (Fig. 1). All tests were made with the hammer held vertically downwards and at right angles to horizontal faces of the blocks. In order to avoid edge effects, the recordings were made at least two plunger diameters away from the edges of the specimen blocks. To ensure a reasonable smoothness and flatness of the surfaces covered by the plunger, the specimen surfaces were cut in precision by diamond segmented circular sawblades in the processing plants and were ground by hand with a carborundum wheel when necessary. Test locations on the samples were marked and separated by at least the diameter of the plunger. The calibration of the instrument was regularly checked according to the instructions provided by the manufacturer. Each test procedure was repeated three times on any rock sample, and the average value was recorded as the rebound number (R). The Schmidt hammer test set up is shown in Fig. 1. For the execution of this study, considering the wide procedural variations reported in the literature [27], it was found necessary to perform five different recognized Schmidt hammer test procedures (Table 2) on any one rock type. For the strength determination of the rocks, the standard test method for UCS of dimension stone suggested by ASTM [46] was followed on 70 mm cubes. The results of the Schmidt hammer and UCS tests are listed in Table 3. 3. Evaluation of experimental data In order to be able to determine the best empirical correlations between Schmidt hammer rebound values (R) and UCS of the tested rocks, regression curves for different test procedures are drawn in Figs. 2–11. As can be followed from Figs. 2–11, valid for all test procedures followed, the correlations derived between rebound values and UCS of rocks by using the type
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Table 1 Mineralogical properties of the tested rocks Sample No.
Rock type
Minerals
1
Nero Zimbabwe Black Gabbro
2
Giresun Vizon Granite
Orthoclase Plagioclase Pyroxene Opaque Quartz
10.3 44.0 44.0 1.5 14.9
Aksaray Yaylak Granite
Orthoclase Plagioclase Biotite Hornblende Opaque Quartz
64.7 13.1 2.9 3.7 0.5 32.0
Rosa Porrino Granite
Orthoclase Plagioclase Biotite Hornblende Cloride Opaque Quartz
46.4 17.4 0.9 0.1 0.1 2.8 10.0
Santiago Red Granite
Orthoclase Plagioclase Biotite Hornblende Opaque Quartz
80.6 4.0 3.8 0.8 0.5 23.3
African Red Granite
Orthoclase Plagioclase Biotite Opaque Quartz
70.4 3.3 1.8 1.0 41.7
7
Usak Green marble
Orthoclase Opaque Calcite
56.8 1.3 495
8
Afyon Sugar marble
Calcite
495
9
Manyas White marble
Calcite
495
10
Afyon Tiger Skin marble
Calcite
495
11
Ku¨tahya Violet marble
Calcite
495
12 13
Mugla White marble Usak Grey marble
Calcite Calcite
495 495
14
Burdur limestone
Calcite
495
15
So¨gu¨t limestone
Calcite
495
16
Aksehir Black limestone
Calcite
495
17 18
Bilecik limestone Korkuteli limestone
Calcite Calcite
495 495
19
Osmaniye Serpentine Breccia
Serpentine Calcite
3
4
5
6
Proportion (%)
83 16
Texture, structure and grain shape
Poikilitic and interlocking, fine- grained, angular, mostly anhedral and subhedral crystals, tight crystal boundaries.
Hypidiomorphic, coarse- grained, subhedral and angular crystals, strongly bonded.
Holocrystalline, perhitic texture and twinned crystals, coarse- grained, subhedral and angular crystals.
Hypidiomorphic, coarse- grained, subhedral and angular crystals, most crystals not uniformly distributed.
Myrmekitic texture, mostly euhedral crystals, very coarsegrained.
Perthitic and interlocking, hard, coarse- grained, strongly bonded, very angular crystals and very tight grain boundaries.
Microcrystalline, cataclastic deformation, very finegrained. Granoblastic and local polygonal texture, microcrystalline, very fine-grained. Macrocrystalline, mostly metamophic and very coarsegrained. Cataclastic texture, cryptocrystalline, mostly metamorphic and very fine-grained. Cryptocrystalline, mostly metamorphic and very finegrained. Coarse crystals, mostly metamophic and coarse-grained. Cryptocrystalline, cataclastic texture, mostly metamorphic. Fractures filled by sparry calcite, recrystallion, finegrained. Foraminifera fragments, micritic texture, cryptocrystaline, pellets, sparry limestone. Recrystallized limestone, cataclastic texture, discrete bands, fine-grained. Pellets, sparry limestone, fine to medium-grained. Microcrystalline, mostly metamorphic and very finegrained. Ophiolitic breccia, secondary fractures filled by calcite, named ophicalcite.
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302 Table 1 (continued ) Sample No.
Rock type
Minerals
Proportion (%)
Texture, structure and grain shape
20
Sivrihisar limestone
Calcite
495
21 22
Afyon Tabaklar travertine Usak Yellow travertine
Calcite Calcite
495 495
23
Ku¨tahya Red travertine
Calcite
495
24
Ankara Polatlı Travertine
Calcite
495
25
Denizli Ilik travertine
Calcite
495
26 27
Denizli Ece travertine Denizli Ivory travertine
Calcite Calcite
495 495
Pelletic, fossiliferous (foraminifera), micrite matrix, finegrained, pelbiomicrite. Fractures filled by sparry calcite, fine- grained. Microcrystalline, microfissure and cavity, fractures filled by sparry calcite, fine- grained. Oolitic structures, microcrstaline, microfissur and cavity, fractures filled by sparry calcite, fine- grained. Microcrystalline, microfissure and cavity, fractures filled by sparry calcite, fine- grained. Microcrystalline, microfissure and cavity, fractures filled by sparry calcite, fine- grained. Microcrystalline, microfissure and cavity, fine- grained. Microcrystalline, microfissure and cavity, fractures filled by sparry calcite, fine-grained.
Fig. 1. A typical rock sample used and calibration block with range of Schmidt hammers used in the tests.
N-hammer are consistently higher than those of the L-type, as also observed by Aydin and Basu [2]. In order to be able to further check and compare the prediction capabilities of both hammer types, statistical performance indices root mean square error (RMSE) and variance account for (VAF) were also used: vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u N u1 X RMSE ¼ t (2) ðy y^ i Þ2 , N i¼1 i varðyi y^ i Þ VAF ¼ 1 100%, varðyi Þ
(3)
where yi is the measured value, y^ i is the predicted value, N is the number of samples, and var symbolizes the variance. The interpretations of the above performance indexes are as follows [47]. The lower the RMSE, the better the model performs. RMSE also accounts for a bias in the model, i.e. an offset between the measured and predicted data. The higher values of VAF indicate an improvement
on the prediction capability. For example, a VAF of 100% means that the measured UCS has been predicted exactly. When the RMSE, VAF and standard error of estimate performance indices are considered (Table 4), it is clear that the N-type hammer outperforms the L-type hammer, and thus can be used to produce a more accurate and reliable estimate of rock uniaxial compressive strength in the range of approximately 20–290 MPa UCS, valid for the rock types tested in this study. Since the rebound values obtained by the N-type hammer were consistently higher than those of the L-type (Table 3), it is possible to state that higher impact energy transmitted to the rock surface with this hammer type aids in a better characterization of rock strength. This finding is in good agreement with the results of a recently published study [2] where it is stated that higher impact energy (corresponding to probing a larger volume of material by a deeper and wider penetration) should reduce scatter in rebound values on a heterogeneous surface, provided that the hammer impact results in uniform compaction (i.e., the rock does not disintegrate or fracture under the impact action of the hammer). The results of the statistical analysis shown in Table 4 also reveal that the prediction performances of the test procedures that are based on continuous impacts at a point (test procedures 3 and 4) are consistently better than those based on single impacts (test procedures 1, 2 and 5). It is interesting to note that the prediction superiority of the test procedures based on continuous impacts is valid for both L- and N-type of hammers. Such a finding supports the suggestions made by some other researchers [32,43] that rebound value recordings made by continuous impacts at a point are more repeatable and consistent than single impacts.
4. Conclusions and recommendations The uniaxial compressive strength (UCS) of rock is regarded as the most widely used design parameter in the
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Table 2 The followed Schmidt hammer test procedures Author/Institution
Test Procedure
(1) ISRM [39]
Test Procedure 1: Record 20 rebound values from single impacts separated by at least a plunger diameter, and average the upper 10 values. Test Procedure 2: Record at least 10 single impact readings, discarding those differing from the average by more than 7 units, and averaging those left. Test Procedure 3: Select the peak rebound value from five continuous impacts at a point. Average the peaks of three sets of tests conducted at three separated points. Test Procedure 4: Select the peak rebound value from 10 continuous impacts at a point. Average the peaks of the three sets of tests conducted at three separated points. Test Procedure 5: Record 20 rebound values from 20 single impacts separated by at least a plunger Diameter. Reject outlier values by using Chauvenet’s criterion, and average the remaining readings.
(2) ASTM [40] (3) Poole & Farmer [32] (4) Hucka [43] (5) Goktan and Ayday [33]
Table 3 Rebound values and uniaxial compressive strength values of the tested rocks Sample No.
Uniaxial Compressive Strength (MPa)
Schmidt hammer rebound value L-type hammer
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27
292.0 168.0 155.9 134.1 159.9 161.5 77.7 56.5 40.8 65.9 90.5 55.2 51.9 36.4 59.3 56.9 69.8 58.0 33.1 46.9 74.7 31.9 67.0 49.0 44.5 50.9 18.4
N-type hammer
RL1
RL2
RL3
RL4
RL5
RN1
RN2
RN3
RN4
RN5
63.1 57.9 56.5 51.6 50.9 58.2 50.9 47.5 33.3 45.7 52.7 38.6 36.7 41.4 43.3 45.2 47.2 43.6 39.7 42.2 45.7 34.5 45.6 41.9 40.2 43.4 30.3
61.1 55.9 54.5 49.8 47.8 56.2 48.9 45.5 30.4 43.6 49.7 36.5 33.7 38.8 40.6 42.5 45.6 40.5 37.2 39.6 41.8 32.2 42.6 40.7 37.9 41.3 27.9
66.7 60.2 58.7 57.5 53.7 60.5 51.2 46.2 32.5 48.2 51.2 42.5 38.7 42.7 45.5 48.5 52.2 46.0 40.2 42.5 48.2 36.2 49.2 44.7 45.5 46.7 32.5
70.2 59.3 59.0 60.5 56.5 63.5 52.3 48.5 35.5 52.5 54.5 43.0 39.2 43.0 46.0 49.0 54.5 46.5 41.0 43.0 49.0 37.0 48.7 47.5 46.5 47.0 33.0
61.1 55.9 54.5 49.8 47.8 56.2 48.9 45.5 29.9 43.6 49.7 36.5 33.7 38.4 40.3 42.1 45.6 40.4 36.7 39.2 40.7 29.2 42.6 41.0 36.1 41.3 27.9
81.6 71.2 68.1 60.7 67.0 66.5 58.5 52.5 40.1 54.1 59.0 48.5 44.7 47.5 51.2 51.6 55.3 50.6 45.3 49.5 55.8 42.2 55.6 50.4 52.7 53.2 40.1
79.6 70.0 66.1 57.7 64.2 63.6 56.7 50.5 37.4 52.0 56.9 46.6 42.6 45.4 48.5 49.0 53.5 48.8 42.2 47.6 52.8 40.3 53.6 48.2 50.4 50.7 37.4
82.7 73.0 68.5 64.5 70.2 70.7 58.2 56.2 45.0 55.7 61.2 53.2 50.7 48.5 52.0 52.5 56.0 51.0 47.5 50.2 57.0 42.5 56.2 52.0 54.2 54.2 40.7
83.2 73.6 69.5 66.0 71.0 71.5 59.0 56.7 45.5 57.0 62.0 55.0 53.2 49.5 52.5 52.0 56.2 51.5 48.0 49.5 57.5 43.0 55.5 53.5 54.5 56.5 41.5
79.6 70.2 66.1 57.7 64.2 63.6 56.7 50.8 37.1 52.0 56.9 46.6 43.0 45.4 48.2 48.6 54.1 49.2 42.1 47.9 52.8 40.3 53.6 48.2 50.4 50.3 36.8
*Numbers 1–5 (RL1-RL5, RN1-RN5) refer to the test procedures given in Table 2.
general field of rock engineering. As a non-destructive, portable and cost-effective device for hardness testing, the Schmidt hammer is often used to obtain an indirect estimation of UCS. Different Schmidt hammer models are commercially available providing different levels of impact energy, but the types L and N are commonly
adopted for rock property determinations. However, a literature survey has shown that some confusion still exists concerning the selection of an appropriate hammer type for UCS prediction purposes. Although the procedure for Schmidt hardness testing has been standardized by both the ISRM [39] and ASTM [40], the accurate application
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350 Uniaxial compressive strength (MPa)
Uniaxial compressive strength (MPa)
350 300 250
y = 2.4817e0.0725x
200
R2 = 0.8763
150 100 50
300 250 y = 2.6363e0.0659x
200
R2 = 0.8889
150 100 50 0
0 20
30
40
50
60
30
70
Schmidt hammer rebound value (RL1)
50
60
70
80
Fig. 5. Relation between RL4 (L-hammer, Test Procedure 4) and UCS.
350
350 Uniaxial compressive strength (MPa)
Uniaxial compressive strength (MPa)
Fig. 2. Relation between RL1 (L-hammer, Test Procedure 1) and UCS.
40
Schmidt hammer rebound value (RL4)
300 250 y = 3.2126e0.0705x
200
R2 = 0.8625
150 100 50 0 20
30
40
50
60
300 250 y = 3.6834e0.0679x
200
R2 = 0.8561
150 100 50 0
70
20
Schmidt hammer rebound value (RL2)
30
40
50
60
70
Schmidt hammer rebound value (RL5)
Fig. 3. Relation between RL2 (L-hammer, Test Procedure 2) and UCS.
Fig. 6. Relation between RL5 (L-hammer, Test Procedure 5) and UCS.
400 300 250 y = 2.4736e0.0691x
200
R2 = 0.883 150 100 50 0 30
40
50
60
70
Schmidt hammer rebound value (RL3) Fig. 4. Relation between RL3 (L-hammer, Test Procedure 3) and UCS.
Uniaxial compressive strength (MPa)
Uniaxial compressive strength (MPa)
350
350 300 250
y = 2.5328e0.06x
200
R2 = 0.9129
150 100 50 0 20
40
60
80
100
Schmidt hammer rebound value (RN1) Fig. 7. Relation between RN1 (N-hammer, Test Procedure 1) and UCS.
ranges of L- and N-type hammers have not been clearly defined. Furthermore, despite the existence of different Schmidt hammer models are pointed out by the ISRM [39],
only the type L hammer is suggested for the determination of rebound hardness. Consequently, in this study, a comprehensive experimental programme was undertaken
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400 Uniaxial compressive strength (MPa)
Uniaxial compressive strength (MPa)
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350 300 250
y=
3.0192e0.0593x
R2 = 0.9069
200 150 100 50 0 30
40
50
60
70
80
Schmidt hammer rebound value (RN2)
350 300 250
y = 3.0652e0.059x R2 = 0.9091
200 150 100 50 0 30
40
50
60
70
80
90
Schmidt hammer rebound value (RN5)
Fig. 8. Relation between RN2 (N-hammer, Test Procedure 2) and UCS.
Fig. 11. Relation between RN5 (N-hammer, Test Procedure 5) and UCS.
Uniaxial compressive strength (MPa)
400 350
After analyzing all the obtained experimental data by using various statistical performance indices, the following main conclusions were drawn:
300 250 y = 2.101e0.0613x
200
R2 = 0.9506
150 100 50 0 30
40
50
60
70
80
90
100
Schmidt hammer rebound value (RN3) Fig. 9. Relation between RN3 (N-hammer, Test Procedure 3) and UCS.
Uniaxial compressive strength (MPa)
350 300 250 y = 2.0656e0.0608x R2 = 0.9444
200 150 100 50 0 30
40
50
60
70
80
90
Schmidt hammer rebound value (RN4) Fig. 10. Relation between RN4 (N-hammer, Test Procedure 4) and UCS.
with the main objective of ascertaining the best Schmidt hammer type suitable for UCS prediction of rocks, special attention also given to the test procedures recommended by different organizations and authors.
(a) Valid for the rock types tested, compared to the L-type hammer, the N-type hammer appears to be a more effective tool in strength estimation of rocks for the approximate UCS range of 20–290 MPa. This finding may be attributed to the higher impact energy provided by the N-type hammer which helps to better characterize rock strength over a wider and deeper scale on the tested sample. (b) Valid for both type of hammers, Schmidt hammer test procedures that are based on continuous impacts at a point provide a more reliable and accurate estimation of UCS than those that are based on single impacts at a point. This finding may be related to the higher consistency and repeatability of continuous impacts recording technique, as claimed by some other authors in the literature. Although a great number of various petrologic rock types were tested in the present study, for further work it is suggested that the general validity of the findings mentioned above should also be checked for other rock types such as the sedimentary and volcanic group. If the relative effectiveness of N-type hammer is confirmed by other experimental studies in the future, it is thought that the suggestion made by the ISRM [39] that ‘the L-type hammer should be used for the determination of Schmidt rebound hardness’ may call a possible revision. This point is particularly important when one considers that the Schmidt hammer rebound values are not generally used independently in practice, but in conjunction or in comparison with the uniaxial compressive strength of rock material.
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Table 4 Results of the statistical analysis Test procedure
Procedure Procedure Procedure Procedure Procedure
1 2 3 4 5
R2
Standard error of estimation
RMSE (%)
L-type
N-type
L-type
N-type
L-type
N-type
L-type
N-type
18.50 19.45 15.38 16.71 19.91
14.00 15.46 10.42 9.75 15.46
19.08 20.00 16.69 16.82 20.61
14.73 16.25 11.74 10.43 16.08
89.74 88.77 92.22 92.01 88.02
93.78 92.43 96.05 96.88 92.59
0.87 0.86 0.88 0.89 0.86
0.91 0.91 0.95 0.94 0.91
Acknowledgements The authors would like to thank Prof. Y. Kibici (Afyon Kocatepe University) and Prof. M.R. Bozkurt (Eskisehir Osmangazi University) for their help in the study of thin sections and petrographic descriptions of the rock samples.
References [1] Soiltest Inc. Operating instructions—concrete test hammer. Evanston, IL: Soiltest Inc.; 1976. [2] Aydin A, Basu A. The Schmidt hammer in rock material characterization. Eng Geol 2005;81:1–14. [3] Yasar E, Erdogan Y. Estimation of rock physico-mechanical properties using hardness methods. Eng Geol 2004;71:281–8. [4] Yilmaz I, Sendir H. Correlation of Schmidt hardness with unconfined compressive strength and young’s modulus in gypsum from Sivas (Turkey). Eng Geol 2002;66:211–9. [5] Kahraman S. A correlation between P-wave velocity, number of joints and Schmidt hammer rebound number. Int J Rock Mech Min Sci 2001;38:729–33. [6] Katz O, Reches Z, Roegiers JC. Evaluation of mechanical rock properties using a Schmidt hammer. Int J Rock Mech Min Sci 2000;37:723–8. [7] Cargill JS, Shakoor A. Evaluation of empirical methods for measuring the uniaxial strength of rock. Int J Rock Mech Min Sci Geomech Abstr 1990;27:495–503. [8] Sachapazis CI. Correlating Schmidt hardness with compressive strength and Young’s modulus of carbonate rocks. Bull Int Assoc Eng Geol 1990;42:75–83. [9] Xu S, Grasso P, Mahtab A. Use of Schmidt hammer for estimating mechanical properties of weak rock. Proceedings of the 6th International IAEG Congress 1990; Vol. 1, Balkema, Rotterdam, p. 511–9. [10] Haramy KY, DeMarco MJ. Use of Schmidt hammer for rock and coal testing. Proceedings of the 26th US Symposium on rock mechanics. 1985, Rapid City. Balkema, Rotterdam, p. 549–5. [11] Shorey PR, Barat D, Das MN, Mukherjee KP, Singh B. Schmidt hammer rebound data for estimation of large scale in-situ coal strength. Int J Rock Mech Min Sci Geomech Abstr 1984;21:39–42. [12] Deere DU, Miller RP. Engineering classifications and index properties of intact rock. Tech. Report No. AFWL-TR 65-116, University of Illinois, 1966. [13] Gokceoglu C, Aksoy H. New approaches to the characterization of clay-bearing, densely jointed and weak rock masses. Eng Geol 2000;58:1–23. [14] Karpuz C, Pasamehmetoglu AG. Field characterization of weathered Ankara andezites. Eng Geol 1977;46:1–17. [15] Greco R, Sorriso-Valvo M. Relationships between joint apparent separation, Schmidt hammer rebound value, and distance to faults, in rocky outcrops, Calabria, Southern Italy. Eng Geol 2005;78:309–20.
VAF (%)
[16] Young RP, Fowell RJ. Assessing rock discontinuities. Tunnels Tunnelling 1978:45–8. [17] Singh R, Singh AK, Mandal PK. Cuttability of coal seams with igneous intrusions. Eng Geol 2002;67:127–37. [18] Kidybinski A. Rebound number and the quality of mine roof strata. Int J Rock Mech Min Sci 1968;5:283–92. [19] Janach W, Merminod A. Rock abrasivity test with a modified Schmidt hammer. Int J Rock Mech Min Sci Geomech Abstr 1982;19:43–5. [20] Karpuz C. A classification system for excavation of surface coal measures. Min Sci Technol 1990;11:157–63. [21] Duncan N. Engineering geology and rock mechanics, Vol. 1. London: Leonard Hill; 1969. [22] Kazi A, Al-Mansour ZR. Empirical relationship between Los Angeles Abrasion and Schmidt hammer strength tests with application to aggregates around Jeddah. Q J Eng Geol 1980;13:45–52. [23] Kahraman S, Bilgin N, Feridunoglu C. Dominant rock properties affecting the penetration rate of percussive drills. Int J Rock Mech Min Sci 2003;40:711–23. [24] Kahraman S, Balcı C, Yazıcı S, Bilgin N. Prediction of the penetration rate of rotary blast hole drills using a new drillability index. Int J Rock Mech Min Sci 2000;37:729–43. [25] Li X, Rupert G, Summers DA, Santi P, Liu D. Analysis of impact hammer rebound to estimate rock drillability. Rock Mech Rock Engng 2000;33:1–13. [26] Kahraman S. Rotary and percussive drilling prediction using regression analysis. Int J Rock Mech Min Sci 1999;36:981–9. [27] Goktan RM, Gunes N. A comparative study of Schmidt hammer testing procedures with reference to cutting machine performance prediction. Int J Rock Mech Min Sci 2005;42:466–72. [28] Bilgin N, Dincer T, Copur H. The performance prediction of impact hammers from Schmidt hammer rebound values in I˙stanbul metro tunnel drivages. Tunnel Underground Space Technol 2002;17:237–47. [29] Bilgin N, Seyrek T, Shahriar K. Roadheaders glean valuable tips for Istanbul metro. Tunnels Tunnelling 1990;October:29–32. [30] Howarth DF, Adamson WR, Berndt JR. Correlation of model tunnel boring and drilling machine performances with rock properties. Int J Rock Mech Min Sci Geomech Abstr 1986;23:171–5. [31] Poole RW, Farmer IW. Geotechnical factors affecting tunnelling machine performance in coal measures rock. Tunnels Tunnell 1978;December:27–30. [32] Poole RW, Farmer IW. Consistency and repeatability of Schmidt hammer rebound data during field testing. Int J Rock Mech Min Sci Geomech Abstr 1980;17:167–71. [33] Goktan RM, Ayday C. A suggested improvement to the Schmidt rebound hardness ISRM suggested method with particular reference to rock machineability. Int J Rock Mech Min Sci Geomech Abstr 1993;30:321–2. [34] Day MJ, Goudie AS. Field assessment of rock hardness using the Schmidt test hammer. Br Geomorphol Res Group Tech Bull 1977;18:19–29. [35] Matthews JA, Shakesby RA. The status of the Little Ice Age in southern Norway: Relative-age dating of Neoglacial moraines with Schmidt hammer and lichenometry. Boreas 1984;13:333–46.
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[41] Ayday C, Goktan RM. Correlations between L and N-type Schmidt hammer rebound values obtained during field testing. Proc. of the Int. Symp. on Rock Characterization, EUROCK’92, 1992, Chester, UK. P. 47–50. [42] Basu A, Aydin A. A method for normalization of Schmidt hammer rebound values. Int J Rock Mech Min Sci 2004;41:1211–4. [43] Hucka V. A rapid method for determining the strength of rocks in situ. Int J Rock Mech Min Sci Geomech Abstr 1965;2:127–34. [44] Das B. Rebound strength of the coal series. Fuel 1973;52:118–20. [45] ISRM. Suggested methods for the quantitative description of discontinuities in rock masses. Int J Rock Mech Min Sci Geomech Abstr 1978;15:319–68. [46] ASTM. Standard test method for compressive strength of dimension stone. ASTM C170. [47] Alvarez Grima M. Neuro-fuzzy modeling in engineering geology. Rotterdam: A.A. Balkema; 2000 244p.
International Journal of Rock Mechanics & Mining Sciences 44 (2007) 299–307 www.elsevier.com/locate/ijrmms
Technical note
The effect of Schmidt hammer type on uniaxial compressive strength prediction of rock I.S. Buyuksagisa, R.M. Goktanb, a
Department of Marble Technology, Afyon Kocatepe Universitesi, Afyon, Turkey Department of Mining Engineering, Eskisehir Osmangazi Universitesi, Meselik Kampusu, Eskisehir, Turkey
b
Accepted 28 July 2006 Available online 26 September 2006
Keywords: Uniaxial compressive strength (UCS); Schmidt hammer test procedures; L-type hammer; N-type hammer
1. Introduction The estimation of rock and concrete strength by nondestructive test methods is of great interest both to civil and mining engineers involved in various design projects. The Schmidt hammer rebound hardness is one of the most frequently used methods for non-destructive testing of concrete and rock since 1950s, due to its cost-effectiveness and easy handling. Schmidt hammer tests can be performed in either the field or the laboratory to provide preliminary information on the relative quality of the material being investigated. Although originally developed to test the surface rebound hardness of concrete, it has since also been adapted for the indirect strength estimation of rock. The operation mechanism of the instrument is rather simple. A spring-loaded mass is released against a plunger when the hammer is pressed on to the surface of a test material. The plunger impacts the surface and the mass recoils. The rebound distance is proportional to the total energy absorbed by the impact surface. The rebound distance of the plunger is read directly from a numerical scale on the instrument and is called the rebound number (R) [1]. On account of its precision, cost-effectiveness and easy handling, wide application of this instrument has been made in rock engineering. Some common extensions of the use of the Schmidt hammer include: the estimation of uniaxial compressive strength and Young’s modulus of rock [2–12], determination of rock weathering [2,13,14], Corresponding author. Tel.: +90 222 239 28 40; fax: +90 222 239 36 13. E-mail address: [email protected] (R.M. Goktan).
1365-1609/$ - see front matter r 2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.ijrmms.2006.07.008
assessing joint separation and discontinuities [15,16], estimation of underground large-scale in situ strength [11,17] mine-roof control [18], rock abrasivity [19], rock rippability and rock mass excavatability classification [20,21], abrasion resistance of rock aggregates [22], penetration rate prediction of drilling machines [23–26] and, prediction of roadheader and tunnel boring machine performance [27–31]. Despite its consistency and reproducibility [32–34], a number of factors are associated with the obtained Schmidt hammer rebound values, among which are: calibration and improper functioning of the instrument [34], surface irregularities of the rock [6], weathering state of the tested rock [2,35], nearby discontinuities [36,37] rock surface moisture content [38], test specimen size [39,40], spacing between the impacts [12,39,40], orientation of the hammer [12,42,43], the adopted test procedure [27,32,33,41], and type of hammer and available impact energy [2,41]. The rebound number values obtained by Schmidt hardness method reflect an interrelated combination of rock properties such as elasticity, strength and hardness. It is known from theoretical physics that the coefficient of restitution (r) for the fall and rebound of one body on a second body can be expressed by: pffiffiffiffiffiffiffiffiffiffi r ¼ h=H , (1) where h is the rebound height and H is the drop height. In treatises on rock mechanics, the dimensionless quantity h/ H is known as rebound number, rebound hardness or rebound strength [44]. The coefficient of restitution (r) is a measure of the elasticity of the collision between two bodies. If the collision is perfectly elastic, r ¼ 1. If the collision is completely inelastic, r ¼ 0 and in this case the
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two colliding bodies will stick together and there will be no rebound. The kinetic energy possessed by the falling body just before impact is, upon impact, divided into three parts. These are elastic potential energy which is given back in the form of rebound energy (height), and elastic kinetic energy which is converted into heat energy owing to localized deformation, plastic flow and friction [44]. In the case of Schmidt hammer rebound testing, the h/H ratio is a function of the test hammer design (available impact energy) and the elastic/plastic properties of the rebound surface. This point is of vital importance for the interpretation of the obtained rebound values, as the obtained rebound number will be a function of the hammer design when the properties of the tested surface remain the same. The Schmidt hammer models are designed in different levels of impact energy, but the types L and N are more commonly adopted for the testing of rock and concrete. The provided impact energy levels of the L- and N-type hammers are 0.735 and 2.207 Nm, respectively. Although the L-type hammer is usually adopted for the testing of relatively softer materials, usable range of this type of hammer (with respect to rock strength or elasticity) is still uncertain and much discussed [2]. There are several organizations such as the International Society for Rock Mechanics (ISRM) and the American Society for Testing and Materials (ASTM) which have published Suggested Methods and testing standards, respectively, on the appropriate use of this instrument. It is suggested by the ISRM [45] that the L-type of hammer should be used for the hardness characterization of rocks which have 20–150 MPa uniaxial compressive strength (UCS). Since the use of N-type of Schmidt hammer is not endorsed by the ISRM for rock characterization, it appears that the hardness testing of rocks using this instrument is applicable to those rocks in the UCS range of 20–150 MPa. On the other hand, the ASTM [40] does not specify a hammer type, but suggests that the use of this instrument is best suited for rocks which have UCS in the range of 1–100 MPa. However, despite these suggestions and limitations suggested by such organizations, a comprehensive literature survey conducted by Aydin and Basu [2] reveals that both types of hammers have been used in rock engineering for strength estimation of various rocks having UCS up to approximately 350 MPa. Considering the brief discussion made above, it is possible to arrive to the conclusion that there is still much uncertainty regarding the selection of an appropriate hammer type for a particular application. Therefore, the present research has been conducted with a view to improve the understanding of the influence of Schmidt hammer type on strength estimation of rocks. To achieve this goal, the Schmidt hammer rebound tests of a total of 27 different rocks were carried out in the laboratory, using both the L- and N-type of hammers. The obtained rebound values, using five different Schmidt hammer recording techniques, were then correlated with the UCS values of
the tested rocks. Finally, statistical performance analyzes were performed in order to be able to check and compare the prediction capabilities of both hammer types. 2. Experimental procedures Twenty-seven different rocks including granites, marbles, limestones and travertines collected from various stone processing plants in Turkey were sampled and tested for the execution of the study. The mineralogical compositions of the tested rocks are given in Table 1, along with their textural, structural and granular descriptions. Thin sections of the rock samples were examined under a petrographic microscope for mineral type, mineral content and mean grain size. The point-count method was employed for the modal analyses. To determine silica content and other elements present in the rock, an automatic X-ray analyzer was used. For both the L- and N-type Schmidt hammers, the rebound tests were carried out on prismatic rock blocks having approximately 110 mm height, 200 mm width and 500 mm length (Fig. 1). All tests were made with the hammer held vertically downwards and at right angles to horizontal faces of the blocks. In order to avoid edge effects, the recordings were made at least two plunger diameters away from the edges of the specimen blocks. To ensure a reasonable smoothness and flatness of the surfaces covered by the plunger, the specimen surfaces were cut in precision by diamond segmented circular sawblades in the processing plants and were ground by hand with a carborundum wheel when necessary. Test locations on the samples were marked and separated by at least the diameter of the plunger. The calibration of the instrument was regularly checked according to the instructions provided by the manufacturer. Each test procedure was repeated three times on any rock sample, and the average value was recorded as the rebound number (R). The Schmidt hammer test set up is shown in Fig. 1. For the execution of this study, considering the wide procedural variations reported in the literature [27], it was found necessary to perform five different recognized Schmidt hammer test procedures (Table 2) on any one rock type. For the strength determination of the rocks, the standard test method for UCS of dimension stone suggested by ASTM [46] was followed on 70 mm cubes. The results of the Schmidt hammer and UCS tests are listed in Table 3. 3. Evaluation of experimental data In order to be able to determine the best empirical correlations between Schmidt hammer rebound values (R) and UCS of the tested rocks, regression curves for different test procedures are drawn in Figs. 2–11. As can be followed from Figs. 2–11, valid for all test procedures followed, the correlations derived between rebound values and UCS of rocks by using the type
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Table 1 Mineralogical properties of the tested rocks Sample No.
Rock type
Minerals
1
Nero Zimbabwe Black Gabbro
2
Giresun Vizon Granite
Orthoclase Plagioclase Pyroxene Opaque Quartz
10.3 44.0 44.0 1.5 14.9
Aksaray Yaylak Granite
Orthoclase Plagioclase Biotite Hornblende Opaque Quartz
64.7 13.1 2.9 3.7 0.5 32.0
Rosa Porrino Granite
Orthoclase Plagioclase Biotite Hornblende Cloride Opaque Quartz
46.4 17.4 0.9 0.1 0.1 2.8 10.0
Santiago Red Granite
Orthoclase Plagioclase Biotite Hornblende Opaque Quartz
80.6 4.0 3.8 0.8 0.5 23.3
African Red Granite
Orthoclase Plagioclase Biotite Opaque Quartz
70.4 3.3 1.8 1.0 41.7
7
Usak Green marble
Orthoclase Opaque Calcite
56.8 1.3 495
8
Afyon Sugar marble
Calcite
495
9
Manyas White marble
Calcite
495
10
Afyon Tiger Skin marble
Calcite
495
11
Ku¨tahya Violet marble
Calcite
495
12 13
Mugla White marble Usak Grey marble
Calcite Calcite
495 495
14
Burdur limestone
Calcite
495
15
So¨gu¨t limestone
Calcite
495
16
Aksehir Black limestone
Calcite
495
17 18
Bilecik limestone Korkuteli limestone
Calcite Calcite
495 495
19
Osmaniye Serpentine Breccia
Serpentine Calcite
3
4
5
6
Proportion (%)
83 16
Texture, structure and grain shape
Poikilitic and interlocking, fine- grained, angular, mostly anhedral and subhedral crystals, tight crystal boundaries.
Hypidiomorphic, coarse- grained, subhedral and angular crystals, strongly bonded.
Holocrystalline, perhitic texture and twinned crystals, coarse- grained, subhedral and angular crystals.
Hypidiomorphic, coarse- grained, subhedral and angular crystals, most crystals not uniformly distributed.
Myrmekitic texture, mostly euhedral crystals, very coarsegrained.
Perthitic and interlocking, hard, coarse- grained, strongly bonded, very angular crystals and very tight grain boundaries.
Microcrystalline, cataclastic deformation, very finegrained. Granoblastic and local polygonal texture, microcrystalline, very fine-grained. Macrocrystalline, mostly metamophic and very coarsegrained. Cataclastic texture, cryptocrystalline, mostly metamorphic and very fine-grained. Cryptocrystalline, mostly metamorphic and very finegrained. Coarse crystals, mostly metamophic and coarse-grained. Cryptocrystalline, cataclastic texture, mostly metamorphic. Fractures filled by sparry calcite, recrystallion, finegrained. Foraminifera fragments, micritic texture, cryptocrystaline, pellets, sparry limestone. Recrystallized limestone, cataclastic texture, discrete bands, fine-grained. Pellets, sparry limestone, fine to medium-grained. Microcrystalline, mostly metamorphic and very finegrained. Ophiolitic breccia, secondary fractures filled by calcite, named ophicalcite.
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302 Table 1 (continued ) Sample No.
Rock type
Minerals
Proportion (%)
Texture, structure and grain shape
20
Sivrihisar limestone
Calcite
495
21 22
Afyon Tabaklar travertine Usak Yellow travertine
Calcite Calcite
495 495
23
Ku¨tahya Red travertine
Calcite
495
24
Ankara Polatlı Travertine
Calcite
495
25
Denizli Ilik travertine
Calcite
495
26 27
Denizli Ece travertine Denizli Ivory travertine
Calcite Calcite
495 495
Pelletic, fossiliferous (foraminifera), micrite matrix, finegrained, pelbiomicrite. Fractures filled by sparry calcite, fine- grained. Microcrystalline, microfissure and cavity, fractures filled by sparry calcite, fine- grained. Oolitic structures, microcrstaline, microfissur and cavity, fractures filled by sparry calcite, fine- grained. Microcrystalline, microfissure and cavity, fractures filled by sparry calcite, fine- grained. Microcrystalline, microfissure and cavity, fractures filled by sparry calcite, fine- grained. Microcrystalline, microfissure and cavity, fine- grained. Microcrystalline, microfissure and cavity, fractures filled by sparry calcite, fine-grained.
Fig. 1. A typical rock sample used and calibration block with range of Schmidt hammers used in the tests.
N-hammer are consistently higher than those of the L-type, as also observed by Aydin and Basu [2]. In order to be able to further check and compare the prediction capabilities of both hammer types, statistical performance indices root mean square error (RMSE) and variance account for (VAF) were also used: vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u N u1 X RMSE ¼ t (2) ðy y^ i Þ2 , N i¼1 i varðyi y^ i Þ VAF ¼ 1 100%, varðyi Þ
(3)
where yi is the measured value, y^ i is the predicted value, N is the number of samples, and var symbolizes the variance. The interpretations of the above performance indexes are as follows [47]. The lower the RMSE, the better the model performs. RMSE also accounts for a bias in the model, i.e. an offset between the measured and predicted data. The higher values of VAF indicate an improvement
on the prediction capability. For example, a VAF of 100% means that the measured UCS has been predicted exactly. When the RMSE, VAF and standard error of estimate performance indices are considered (Table 4), it is clear that the N-type hammer outperforms the L-type hammer, and thus can be used to produce a more accurate and reliable estimate of rock uniaxial compressive strength in the range of approximately 20–290 MPa UCS, valid for the rock types tested in this study. Since the rebound values obtained by the N-type hammer were consistently higher than those of the L-type (Table 3), it is possible to state that higher impact energy transmitted to the rock surface with this hammer type aids in a better characterization of rock strength. This finding is in good agreement with the results of a recently published study [2] where it is stated that higher impact energy (corresponding to probing a larger volume of material by a deeper and wider penetration) should reduce scatter in rebound values on a heterogeneous surface, provided that the hammer impact results in uniform compaction (i.e., the rock does not disintegrate or fracture under the impact action of the hammer). The results of the statistical analysis shown in Table 4 also reveal that the prediction performances of the test procedures that are based on continuous impacts at a point (test procedures 3 and 4) are consistently better than those based on single impacts (test procedures 1, 2 and 5). It is interesting to note that the prediction superiority of the test procedures based on continuous impacts is valid for both L- and N-type of hammers. Such a finding supports the suggestions made by some other researchers [32,43] that rebound value recordings made by continuous impacts at a point are more repeatable and consistent than single impacts.
4. Conclusions and recommendations The uniaxial compressive strength (UCS) of rock is regarded as the most widely used design parameter in the
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Table 2 The followed Schmidt hammer test procedures Author/Institution
Test Procedure
(1) ISRM [39]
Test Procedure 1: Record 20 rebound values from single impacts separated by at least a plunger diameter, and average the upper 10 values. Test Procedure 2: Record at least 10 single impact readings, discarding those differing from the average by more than 7 units, and averaging those left. Test Procedure 3: Select the peak rebound value from five continuous impacts at a point. Average the peaks of three sets of tests conducted at three separated points. Test Procedure 4: Select the peak rebound value from 10 continuous impacts at a point. Average the peaks of the three sets of tests conducted at three separated points. Test Procedure 5: Record 20 rebound values from 20 single impacts separated by at least a plunger Diameter. Reject outlier values by using Chauvenet’s criterion, and average the remaining readings.
(2) ASTM [40] (3) Poole & Farmer [32] (4) Hucka [43] (5) Goktan and Ayday [33]
Table 3 Rebound values and uniaxial compressive strength values of the tested rocks Sample No.
Uniaxial Compressive Strength (MPa)
Schmidt hammer rebound value L-type hammer
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27
292.0 168.0 155.9 134.1 159.9 161.5 77.7 56.5 40.8 65.9 90.5 55.2 51.9 36.4 59.3 56.9 69.8 58.0 33.1 46.9 74.7 31.9 67.0 49.0 44.5 50.9 18.4
N-type hammer
RL1
RL2
RL3
RL4
RL5
RN1
RN2
RN3
RN4
RN5
63.1 57.9 56.5 51.6 50.9 58.2 50.9 47.5 33.3 45.7 52.7 38.6 36.7 41.4 43.3 45.2 47.2 43.6 39.7 42.2 45.7 34.5 45.6 41.9 40.2 43.4 30.3
61.1 55.9 54.5 49.8 47.8 56.2 48.9 45.5 30.4 43.6 49.7 36.5 33.7 38.8 40.6 42.5 45.6 40.5 37.2 39.6 41.8 32.2 42.6 40.7 37.9 41.3 27.9
66.7 60.2 58.7 57.5 53.7 60.5 51.2 46.2 32.5 48.2 51.2 42.5 38.7 42.7 45.5 48.5 52.2 46.0 40.2 42.5 48.2 36.2 49.2 44.7 45.5 46.7 32.5
70.2 59.3 59.0 60.5 56.5 63.5 52.3 48.5 35.5 52.5 54.5 43.0 39.2 43.0 46.0 49.0 54.5 46.5 41.0 43.0 49.0 37.0 48.7 47.5 46.5 47.0 33.0
61.1 55.9 54.5 49.8 47.8 56.2 48.9 45.5 29.9 43.6 49.7 36.5 33.7 38.4 40.3 42.1 45.6 40.4 36.7 39.2 40.7 29.2 42.6 41.0 36.1 41.3 27.9
81.6 71.2 68.1 60.7 67.0 66.5 58.5 52.5 40.1 54.1 59.0 48.5 44.7 47.5 51.2 51.6 55.3 50.6 45.3 49.5 55.8 42.2 55.6 50.4 52.7 53.2 40.1
79.6 70.0 66.1 57.7 64.2 63.6 56.7 50.5 37.4 52.0 56.9 46.6 42.6 45.4 48.5 49.0 53.5 48.8 42.2 47.6 52.8 40.3 53.6 48.2 50.4 50.7 37.4
82.7 73.0 68.5 64.5 70.2 70.7 58.2 56.2 45.0 55.7 61.2 53.2 50.7 48.5 52.0 52.5 56.0 51.0 47.5 50.2 57.0 42.5 56.2 52.0 54.2 54.2 40.7
83.2 73.6 69.5 66.0 71.0 71.5 59.0 56.7 45.5 57.0 62.0 55.0 53.2 49.5 52.5 52.0 56.2 51.5 48.0 49.5 57.5 43.0 55.5 53.5 54.5 56.5 41.5
79.6 70.2 66.1 57.7 64.2 63.6 56.7 50.8 37.1 52.0 56.9 46.6 43.0 45.4 48.2 48.6 54.1 49.2 42.1 47.9 52.8 40.3 53.6 48.2 50.4 50.3 36.8
*Numbers 1–5 (RL1-RL5, RN1-RN5) refer to the test procedures given in Table 2.
general field of rock engineering. As a non-destructive, portable and cost-effective device for hardness testing, the Schmidt hammer is often used to obtain an indirect estimation of UCS. Different Schmidt hammer models are commercially available providing different levels of impact energy, but the types L and N are commonly
adopted for rock property determinations. However, a literature survey has shown that some confusion still exists concerning the selection of an appropriate hammer type for UCS prediction purposes. Although the procedure for Schmidt hardness testing has been standardized by both the ISRM [39] and ASTM [40], the accurate application
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304
350 Uniaxial compressive strength (MPa)
Uniaxial compressive strength (MPa)
350 300 250
y = 2.4817e0.0725x
200
R2 = 0.8763
150 100 50
300 250 y = 2.6363e0.0659x
200
R2 = 0.8889
150 100 50 0
0 20
30
40
50
60
30
70
Schmidt hammer rebound value (RL1)
50
60
70
80
Fig. 5. Relation between RL4 (L-hammer, Test Procedure 4) and UCS.
350
350 Uniaxial compressive strength (MPa)
Uniaxial compressive strength (MPa)
Fig. 2. Relation between RL1 (L-hammer, Test Procedure 1) and UCS.
40
Schmidt hammer rebound value (RL4)
300 250 y = 3.2126e0.0705x
200
R2 = 0.8625
150 100 50 0 20
30
40
50
60
300 250 y = 3.6834e0.0679x
200
R2 = 0.8561
150 100 50 0
70
20
Schmidt hammer rebound value (RL2)
30
40
50
60
70
Schmidt hammer rebound value (RL5)
Fig. 3. Relation between RL2 (L-hammer, Test Procedure 2) and UCS.
Fig. 6. Relation between RL5 (L-hammer, Test Procedure 5) and UCS.
400 300 250 y = 2.4736e0.0691x
200
R2 = 0.883 150 100 50 0 30
40
50
60
70
Schmidt hammer rebound value (RL3) Fig. 4. Relation between RL3 (L-hammer, Test Procedure 3) and UCS.
Uniaxial compressive strength (MPa)
Uniaxial compressive strength (MPa)
350
350 300 250
y = 2.5328e0.06x
200
R2 = 0.9129
150 100 50 0 20
40
60
80
100
Schmidt hammer rebound value (RN1) Fig. 7. Relation between RN1 (N-hammer, Test Procedure 1) and UCS.
ranges of L- and N-type hammers have not been clearly defined. Furthermore, despite the existence of different Schmidt hammer models are pointed out by the ISRM [39],
only the type L hammer is suggested for the determination of rebound hardness. Consequently, in this study, a comprehensive experimental programme was undertaken
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400 Uniaxial compressive strength (MPa)
Uniaxial compressive strength (MPa)
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350 300 250
y=
3.0192e0.0593x
R2 = 0.9069
200 150 100 50 0 30
40
50
60
70
80
Schmidt hammer rebound value (RN2)
350 300 250
y = 3.0652e0.059x R2 = 0.9091
200 150 100 50 0 30
40
50
60
70
80
90
Schmidt hammer rebound value (RN5)
Fig. 8. Relation between RN2 (N-hammer, Test Procedure 2) and UCS.
Fig. 11. Relation between RN5 (N-hammer, Test Procedure 5) and UCS.
Uniaxial compressive strength (MPa)
400 350
After analyzing all the obtained experimental data by using various statistical performance indices, the following main conclusions were drawn:
300 250 y = 2.101e0.0613x
200
R2 = 0.9506
150 100 50 0 30
40
50
60
70
80
90
100
Schmidt hammer rebound value (RN3) Fig. 9. Relation between RN3 (N-hammer, Test Procedure 3) and UCS.
Uniaxial compressive strength (MPa)
350 300 250 y = 2.0656e0.0608x R2 = 0.9444
200 150 100 50 0 30
40
50
60
70
80
90
Schmidt hammer rebound value (RN4) Fig. 10. Relation between RN4 (N-hammer, Test Procedure 4) and UCS.
with the main objective of ascertaining the best Schmidt hammer type suitable for UCS prediction of rocks, special attention also given to the test procedures recommended by different organizations and authors.
(a) Valid for the rock types tested, compared to the L-type hammer, the N-type hammer appears to be a more effective tool in strength estimation of rocks for the approximate UCS range of 20–290 MPa. This finding may be attributed to the higher impact energy provided by the N-type hammer which helps to better characterize rock strength over a wider and deeper scale on the tested sample. (b) Valid for both type of hammers, Schmidt hammer test procedures that are based on continuous impacts at a point provide a more reliable and accurate estimation of UCS than those that are based on single impacts at a point. This finding may be related to the higher consistency and repeatability of continuous impacts recording technique, as claimed by some other authors in the literature. Although a great number of various petrologic rock types were tested in the present study, for further work it is suggested that the general validity of the findings mentioned above should also be checked for other rock types such as the sedimentary and volcanic group. If the relative effectiveness of N-type hammer is confirmed by other experimental studies in the future, it is thought that the suggestion made by the ISRM [39] that ‘the L-type hammer should be used for the determination of Schmidt rebound hardness’ may call a possible revision. This point is particularly important when one considers that the Schmidt hammer rebound values are not generally used independently in practice, but in conjunction or in comparison with the uniaxial compressive strength of rock material.
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Table 4 Results of the statistical analysis Test procedure
Procedure Procedure Procedure Procedure Procedure
1 2 3 4 5
R2
Standard error of estimation
RMSE (%)
L-type
N-type
L-type
N-type
L-type
N-type
L-type
N-type
18.50 19.45 15.38 16.71 19.91
14.00 15.46 10.42 9.75 15.46
19.08 20.00 16.69 16.82 20.61
14.73 16.25 11.74 10.43 16.08
89.74 88.77 92.22 92.01 88.02
93.78 92.43 96.05 96.88 92.59
0.87 0.86 0.88 0.89 0.86
0.91 0.91 0.95 0.94 0.91
Acknowledgements The authors would like to thank Prof. Y. Kibici (Afyon Kocatepe University) and Prof. M.R. Bozkurt (Eskisehir Osmangazi University) for their help in the study of thin sections and petrographic descriptions of the rock samples.
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