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Estimation of strength anisotropy using the point-load test
Int. J. Rock Mech. Min. Sci. & Geomech. Abstr. Vol. 20, No. 4, pp. 181-187, 1983 Printed in Great Britain. All rights reserved
0148-9062/83 $3.00+0.00 Copyright '~ 1983 Pergamon Press Ltd
Estimation of Strength Anisotropy Using the Point-Load Test E. BROCH* As most rocks are of an anisotropic nature, the measurement of the ratio between the maximum and minimum strength, i.e. the strength anisotropy, is of general interest. To measure the strength anisotropy by the uniaxial compression test, core specimens drilled in different directions are needed. With the point-load test it is possible to obtain the strength anisotropy on one core only by first using the diametral test and then applying axial tests on the core pieces. The paper describes results from tests performed on 33 different rocks to find a diagram that could be used to compensate for the influence of size and shape in the axial test. Cores were drilled both parallel and normal to bedding or foliation planes. Analyses of the results show that the most reliable strength index is obtained when cores are drilled normal or near normal to weakness planes. The paper concludes with a suggested procedure for measurements and calculations.
INTRODUCTION Rocks are in general anisotropic with regard to their physical and mechanical properties. Well defined anisotropy is especially to be found among sedimentary and metamorphic rocks, where the bedding or the foliation normally is clearly visible. Igneous rocks may often look very homogeneous and isotropic, but testing reveals that many of their material properties vary with the direction of testing. Truly isotropic rocks are rare occurrences and should be regarded as exceptions. In all strength testing of rocks, it is therefore necessary to refer the obtained results to the relation between the direction of stresses and the direction of the texture of tested specimens. If possible, specimens should also be tested under the same magnitude and direction of stresses as the rocks will be subjected to at the construction site. However, it is not easy to establish future stress conditions for rock during construction. Drilling and blasting will for instance subject the rocks to very complex stress situations. Two strength values are of general interest, namely the maximum and the minimum strength of the rock. The maximum and minimum strengths are obtained when failure is initiated normal to, and respectively, parallel to the weakness planes of the rock, i.e. bedding, foliation, cleavage, etc. The ratio between these two extreme values may be regarded as the maximum strength anisotropy of the rock.
STRENGTH ANISOTROPY MEASURED BY THE UNIAXIAL COMPRESSION TEST In the uniaxial compression test the minimum strength is obtained when the inclination of weakness planes to the direction of the major principal stress is approx. 30° . Maximum strength is obtained when the inclination is either close to 0° or to 90 °. This means that the uniaxial compression test gives approximately the same maximum strength value for the two important and easily defined inclinations, namely, parallel to and normal to the weakness planes. ~Some authors find the greatest strengths in cores drilled parallel to the weakness planes [1], while others find the greatest strengths in cores drilled normal to the weakness planes [2]. For six Precambrian gneisses Svenska V~iginstitutet [3] found that the ratios between uniaxial compressive strengths measured on cores drilled parallel and normal to the foliation were 0.92, 0.92, 0.94, 1.03, 1.08 and 1.16. This means that the variations are more or less within the accuracy of the testing method. Based on uniaxial compressive strengths measured on cores drilled parallel and normal to weakness planes, it is possible to get a false impression of an isotropic material. To obtain a correct value for the maximum strength anisotropy in compression, it is necessary to test specimens drilled in varying directions relative to the weakness plane of the rock. Such a procedure is both tedious and expensive. THE POINT-LOAD STRENGTH ANISOTROPY INDEX
For the point-load test, as for other strength tests * Department of Geology,The Norwegian Institute of Technology, University of Trondheim, N-7034 Trondheim, Norway. where the specimen fails in tension, the problem of 181
182
BROCH:
E S T I M A T I O N OF S T R E N G T H A N I S O T R O P Y
e~
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Fig. 1. Diametral point-load strmagthindex, I,, as a functionof the angle, =, betweenthe foliationplane and the core axis for two gneisses and a mieasehist,from Aagaard [4]. defining the maximum and minimum strengths is considerably easier. In such tests the minimum strength is recorded when the specimen fails along a weakness plane. This has been convineingiy demonstrated by Aagaard [4] in a dissertation at the Norwegian Institute of Technology. Figure 1 shows results from this work. In 1972 a comprehensive description of the point-load strength test was published [5], in which a point-load strength index was defined as P /~ = D----~ (1) where P is the load required to break the specimen tested and D is the distance between the two platen contact points. As an appendix to that paper a "Suggested Method for Determining the Point-Load Strength Index" is described. This was adopted by the Commission on Standardization of Laboratory and Field Tests of the International Society for Rock Mechanics [6] the following year. In this suggested method a strength anisotropy index Io is defined as the ratio of the corrected median strength indices for tests perpendicular and parallel to planes of weakness. In the paper the diametral and the axial point-load test are described, and the practical use of both the point-load strength index, Is, and the strength anisotropy index, I°, are demonstrated on a core log. Since the publishing of the paper and the adoption of the method by the ISRM, a number of authors have published valuable papers on different aspects of the method and its use in practical rock engineering [7, 10--17]. It does not seem, however, that everyone is aware of the potential of the method to measure maximum and minimum strengths in one core, and thus calculate strength anisotropies. This is done by first performing diametral tests on the core, followed by axial tests on the broken core pieces. As will be shown later in the paper, this procedure may be used, provided the
angle between the weakness planes in the rock and the direction of the core does not exceed certain values. In the testing of rock strengths, specimen preparation is normally a time consuming and costly procedure. One of the great advantages of the point-load strength test is that it does not require machined specimens. As long as the influence of specimen size and shape are considered in the calculation of the strength index, any piece of rock, whether the surface is smooth or rough, can in principle be tested. Using only one core sample to obtain both the maximum and the minimum strengths of the rock is probably one of the fastest and cheapest methods in rock engineering at present. RESULTS FROM AXIAL TESTS PERFORMED ON CORE DISCS It has been shown [5] that test results obtained from axial and diametral tests on two different types of rock with three different diameters were identical provided that, in the axial test, specimens with a length/diameter ratio of 1.1 ___0.02 were used. Based on this, the ISRM Commission suggested that the axial test should be performed on core specimens with length/diameter ratios of 1.1 + 0.05. This requirement is so strict that machine cutting of specimens is in practice necessary and may be one of the reasons why the axial test has been littled used. Read et al. [7] reported that when axial tests were attempted at the suggested length/diameter ratio, the samples either rotated between the platens or broke off at the edges. Similar features have been experienced by this author, but it does not always occur. For slightly anisotropic, sound rocks it is possible to conduct valid axial tests when the length of the core is greater than the diameter. Read et al. found after some experimentation that consistent results were obtained when a ratio of 0.65 was used. This value was adopted as standard for their testing. This empirically obtained ratio is compatible with a stress analysis of cylindrical rock discs subjected to an axial, double point load by Peng [8]. His finite element model shows that the stress distribution changes slightly for length/diameter ratios greater than 1.3 and stabilizes for specimens with ratios less than 1.0. He therefore concludes that the best specimen geometry for the axial point-load is with a length/diameter ratio below 1.0. Similar results have been obtained by Sundae [9] in laboratory tests carried out on discs of three different rocks. When performing the diametrai point-load test, the ISRM Commission suggests that the distance between the contact or loading point and the nearest free end be at least 0.7 d where d is the core diameter. After diametral point-load testing, one is then normally left with core pieces with lengths in the range of 0.5-1.0 d. As the testing of rock cores in general will be performed at certain standard diameters, it is desirable to find a best possible direct way of transforming the results from the axial test to strength indices comparable with
BROCH: I00 90 80
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183
ESTIMATION OF STRENGTH ANISOTROPY
have been replotted in a semilogarithmic diagram as shOWn in Fig. 2. The dotted lines connnect points of the same core diameter, d. It is obvious that for the range of core diameters between 25 and 54ram and with length/diameter ratios varying between 0.5 and 1.5, the inclination of the lines are consistent for the two rather different rocks. It has thus been possible to fit a set of parallel lines like the solid lines in the diagram. These solid lines, which establish the combined influence of size and shape in an axial test, are replotted in Fig. 3. The lines can be described by the equation
Dolerite
70 60 50 40
30
20
L =/(1" 10 -°°25~ IO 9
n
where Ki is the constant defining where the single lines are running. (K1 = I,, when D is made equal to zero). An example for KI = 85 is shown in the right part of Fig. 3. Also included on these diagrams are the strength indices for the sandstone and dolerite discs for 25.5 and 38 mm cores as a direct function of the height, D (or length). Dotted lines parallel to the solid lines are fitted to the plotted strength indices. The big crosses mark the intersections between the dotted lines and the indices measured by the diametral test on cores from the same block of rock and of the same sizes, but drilled in a direction normal to the axially tested core discs. In these diagrams the strength indices for axially tested core discs with a diameter of 25.5 mm can be correlated to those obtained for diametrally tested cores when the height (or length) of the core disc is 28.7 ram. Correlation is obtained for 38 mm cores when the height of the disc is 39.1 mm. This clearly indicates that axially tested core pieces should have lengths slightly greater than their diameters to give commensurable strength indices. This was the bails for the earlier mentioned ISRM suggestion for the axial point load-test. In a recent paper, Greminger [10] reports valuable results from experimental studies of the influence of rock anistropy on size and shape effects in point-load testing. Four types of rock with varying strength anisotropy indices (given in parentheses) were extensively tested: Augen gneiss (Ia = 1.05), Ruhr-Sandstone (Ia = 1.15),
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Fig. 2. Point-load strength indices, I,, obtained from axial tests on sawn core discs of varying diameters, d, as functions of the ratio D/d. D is the distance between the load platens (or height of disc).
those obtained in the diametral test. Thus, when the influence of shape and size on the results from the axial test ~s considered, a true strength anisotropy index can be calculated. Returning to the earlier published paper [5], the results from axial point-load tests on carefully sawn core discs
215
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5 mm Cores
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Fig. 3. I, for axially loaded core discs as a function of the height, D. See text for further explanation.
184
BROCH:
ESTIMATION OF STRENGTH ANISOTROPY
Chiandone-Gneiss (I~ = 2.80) and Nuttlar-Slate (Ia = 5.70). Like other research workers [5, 9, 11], Greminger finds that the best fit with experimental data is obtained by a parabolic function of strength, I,, against size, D. L ~c D-° (3) He finds no indication of any dependence of the exponent a on anisotropy. He therefore draws the conclusion that the size correction factor is independent of the degree of anisotropy and of the loading direction. A shape effect is described by the relation I, oc
P oc ( d . D ) °75 ~ A °-75
~ D-°
(5)
Based on his experimental results Greminger chooses a = 0.5 and b = 0.75 which gives /~ = K2"D -"2'
(6)
where K: is a constant related to the strength of the rock tested. To compare equation (6) with equation (2) the former is also shown in the right part of Fig. 3 for a chosen value of K2 = 850. The equation is in the semilogarithmic
(7)
which is identical to an equation presented by Brook [12, 13]. In several papers he has argued that shape and size effect problems in the point-load test could be overcome by introducing a strength index P T ~ = 211.5 A0.7"--3
(4)
Combining both size and shape effects gives
,,P- ~
diagram expressed by a slightly curved line (short dashes) which to a large extent is subparallel to the straight equation (2) lines. With the chosen a and b values, equation (6) can be rewritten as
(8)
where A is the loaded area. He suggests a reference area of 500 m 2 (equivalent to diametral tests on 25 mm cores). Objections against Brook's suggestion put forward by Hassani et al. [14], are: (a) the area is often difficult to determine exactly and (b) the strength index as given by equation (1), is so widely used and accepted that it will be difficult to change. Recent talks with the chairmen of ISRM's Commission on Standardization of Laboratory and Field Tests [18, 19] confirm that the Commission has no plans for changing the definition of the Point Load Strength Index. In a revision of the "Suggested Method" to be published in the near future, references will, however, be made to all relevant research work.
Table 1. List of tested rocks with results from diametral point-load tests performed on dry and fully water-saturated specimens. Cores are drilled both parallel and normal to foliation or bedding Spec. No. 01 02 03 04 05 06 07 08 09 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33
Rock type
Locality
Geological era
Quartz-diorite Trolla Cambr.-Silur. Crystalline schist Berk/tk Cambr.-Silur. Diorite Kleft bru Cambr.-Silur. Quartzite Ringebu Eocambrian Arkosic sandstone Trenen Eocambrian Quartz-syenite Gjeller~Lsen Permian Black shale Grodalen Cambr.-Silur. Granite Lier~sen Permian Rhomb-porphyry Toverud Permian Siltstone Tyrihjelmen Cambr.-Silur. Limestone Ringerike Kaikv. Cambr.-Silur. Quartzite Modum Precambrian Basalt Steinsskogen Permian Gneiss Hambora Precambrian Gneiss-granite Hambora Precambrian Gneiss-granite Gronningen Precambrian Micashist Trlssavika Precambrian Gabbro Myrvang Cambr.-Silur. Gabbro Heggest dam Cambr.-Silur. Micashist Odtvollen Cambr.-Silur. Sandstone Sveigen Devonian Quartzite Adamselv Eocambrian Biotite-gneiss* Linde(jell Prccambrian Quartz-syenite Lindefjell Precambrian Granite Lindefjell Prec,ambrian Gneiss-granite Lisle~t ~brian Gneiss-granite Lislet Prccambrian Gneiss Gjora Pr~,ambtian Gneiss Driva Prceambrian Quartz-diorite* Stzren Cambr.-Silur. Hyperite Sohar Precambrian Gneiss lkstvoll, Fosen Prcc,ambrian Amphibolite /~t~ord Precambrian Average values for standard deviation:
* Excluded from average value calculation.
Diametral I, (MPa) with SD in ( ) Cores drilled parallel Cores drilled normal Saturated Dry Saturated Dry 7.8 (15) 11.6(12) 11.5(ll) 15.5 (10) 17.5 (14) 7.8(15) 9.6 (31) 8.5 (24) 8.0(25) 12.4(27) 6.3(18) 11.9(21) 17.0(29) 9.1(24) 9.3(16) 12.1 (10) 7.6 (21) 11.5(6) 9.0(ll) 11.4 (21) 18.7(20) 17.3 (7) 3.0 (72) 5.9 10.6 (7) I 1.7 (8) 12.3 (8) 5.5(21) 12.4(32)
12.3 (30) 11.6(26) 15.5(10) 16.0 (13) 20.3 (40) 8.6(18) 8.0 (34) 8.7 (14) 10.3 (21) 12.8(39) 6.4(18) 12.6(13) 13.7(19) 10.1 (31) 10.8(20) 14.5 (10) 8.5 (l 8) 17.9(11) 13.4(9) 9.6 (38) 17.1 (22)
8.8(30) 8.7 (14) 17.5
15.7(14) 13.3 (6) 20.2
9.3(16) 18.2(15)
4.7 (25) 5.1 (23) 10.4(10) 15.4(11) 6.3 04) 7.6(11) 8.8 (13) 6.7 (6) 5.2 (37) 7.8(21) 5.1 (38) 10.1 (14) 16.8(17) 4.9(18) 9.2(10) 8.5 (17) 3.2 (39) 9.1 (10) 7.3(15) 2.0 (33) 17.2(25) 14.7 (20) 1.6 (44) 5.3 5.7 (32) 8.4 (l 3) 7.3 (14) 3.1 (26) 2.7(29) 9.0 (! 1) 10.2(5) 8.0(15) 6.5 (11) 19.9
5.0 (29) 6.6(31) 14.8(9) 16.8 (12) 7.7 (2 l) 8.0(26) 7.8 (11 ) 7.9 (13) 7.6 (28) 8.9(28) 5.5(28) 9.5(18) 11.7(29) 7.1 (18) 9.8(15) 10.9 (12) 5.5 (26) 14.7(14) 8.7(27) 4.5 (56) 18.7(14)
3.8(21) 5.1 (21) 11.6 (11) 14.5 (6) 10.7(10) 10.2 (15) 21.3
Anisotropy 1~ Sat. Dry 1.66 2.27 l.ll 1.01 2.78 1.03 1.09 1.27 1.54 1.59 1.24 1.18 1.01 1.86 1.01 1.42 2.38 1.26 1.23 5.70 1.09 1.18 1.88 I. 1l 1.86 1.39 1.68 1.77 4.59
2.46 1.76 1.05 0.96 2.64 1.08 1.03 1.10 1.36 1.44 1.16 1.33 1.17 1.42 1.10 1.33 1.55 1.22 1.54 2.13 0.91
1.10 1.34
t.47 1.30
2.45 3.57
BROCH:
ESTIMATION OF STRENGTH ANISOTROPY
185
AXIAL TESTING OF CORE PIECES
Dry
Diametral testing of rock cores will normally produce a number of core pieces with lengths shorter than their diameter. To investigate the possibilities of employing extrapolations of axial test results along fitted lines as shown in Fig. 3, a total of 33 different Norwegian rocks have been carefully tested [15]. The ELE-point-ioad tester (from Engineering Laboratory Equipment, England) was used, and a core diameter of 31.5mm (normally referred to as 32 mm cores) was chosen. This is by far the most used core dimension in Norway. The testing procedure and the calculation of results were performed in accordance with the suggestions outlined by ISRM [6]. Cores were drilled from large blocks both parallel to and normal to bedding or foliation planes. Tests were performed on oven dried and fully water saturated cores [16]. Specimen number, type of rock, locality and geological era are listed in Table 1 together with the results of the diametral point-load test. As the table illustrates, a wide variety of rocks are represented with point-load strength indices on water saturated specimens varying from 1.6 to 18.7 MPa. Strength anisotropy indices (on saturated cores) vary between 1.01 and 4.59. The results from the axial tests were plotted as in Fig. 4. For each type of rock, both the results from cores drilled parallel to and normal to bedding/foliation planes are plotted. The results from the diametral tests (the median values) are also plotted on the diagram with the big crosses. A study of all the diagrams reveals that the scatter of the test results varies considerably from rock to rock. Rocks of high strength anisotropy tend to show a greater scatter than rocks of low anisotropy. However, this is
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not as pronounced in the diametral test as in the axial test. Most of the gneisses are good examples of anisotropic rocks with great scatter in strength results. In axial tests there is greater scatter of the data from cores drilled parallel to the foliation than normal to the foliation. On the other hand, in the diametral test the scatter is somewhat smaller for the cores drilled parallel to the foliation. The difference in the scatter of the results for the different directions is clearly less pronounced for the diametral test than for the axial test. This indicates that the most reliable results for the measurement of strength anisotropy indices on only one core should be obtained when this core is drilled normal to the foliation. Cores drilled normal to foliation / bedd=ng
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o-~.._'>...
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/s
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Fig. 4. Example of a results diagram for axial point-load testing of core p i ~ s . RMMS 2 0 / ' ~ "
1.4 8 M P o
186
BROCH: ESTIMATION OF STRENGTH ANISOTROPY
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Fig. 6. Strengthanisotropyindices measured on one core drilled parallel to (left) and normal to (right) the foliationor bedding and correlated with the strength anisotropy index measured by two diametral tests. To find what core piece lengths (D) give axial strength indices identical to the diametral strength indices, the D-values for the big crosses in the diagrams are plotted as a function of the strength, Is in Fig. 5. The data include results from dry and fully saturated cores. A few strength indices are excluded either because of too few strength tests or too wide scatter in results. The average D-value for all tests is 32.5 mm. This means that for 31.5 mm dia rock cores the axial strength index obtained on a core piece which is 1 mm longer than the diameter (or 1.03 D) should be identical to the result from the diametral test. This confirms the results presented earlier from the tests carried out on sawn core discs.
What strength anisotropy index should be regarded as the "true" one, is difficult to decide. Anisotropy measured by diametral tests on cores drilled in two directions is favoured by the fact that the diametrai test is the best controlled test. Favouring anisotropy measured by a combination of diametral and axial pointload tests on the same core is the fact that one then really knows that it is the same material that is tested in both directions. For inhomogeneous and strongly anisotropic materials this is an advantage that often may fully outrange the inaccuracies in the axial test. Furthermore, testing on one core only may considerably reduce the expense of strength testing.
CORRELATION BETWEEN POINT-LOAD STRENGTH ANISOTROPY MEASURED ON ONE AND ON TWO CORES
APPLICATION OF THE LOAD ON ANISOTROPIC CORES
When the average D-values of 32.5 mm was found, it was drawn as a vertical line in all the semilogarithmic diagrams (Fig. 4) and all the equivalent axial strength indices for water saturated cores were obtained. Strength anisotropy indices then were calculated for the results obtained from cores drilled parallel to and normal to foliation, respectively. In Fig. 6 these indices are plotted against the strength anisotropy indices calculated from diametral tests performed on cores drilled in both directions. If the diametral results are regarded as the "true" indices, it is of interest to note the core direction which gives the best correlation. Not surprisingly, the strength anisotropy index obtained on the cores drilled normal to the bedding or foliation of the rock gives the best correlation with the index obtained from measurements on two cores. A few data points deviate considerably from the regression line. These represent rocks with pronounced anisotropic properties, which in terms of testing are complicated materials with inhomogeneities and rapidly changing properties. Gneisses and micashists are examples of such rocks. The great scatter in strength test results often reflects the problems of selecting representative specimens.
When cores of anisotropic rocks are to be tested with the point-load apparatus, it is important that the load be correctly applied. To obtain readings of the maximum and minimum strength values, the load must be applied so that failure is initiated normal to and parallel to weakness planes (bedding/foliation). For cores drilled at an oblique angle to such weakness planes, Fig. 7 demonstrates the right and wrong ways of applying the load. In the diametral test, the load should be applied along the shortest axis of the elliptic weakness plane. To avoid the influence of the uncontrolled shape effects, core pieces shorter than the diameter should be used. The influence of the angle between the core axis and the weakness planes, fl, on the diametral point-load
mo0~t
Fig. 7. Right and wrong applicationof the point.loadson cores which are drilled at an oblique angle to foliation or bedding.
-I
BROCH:
ESTIMATION OF STRENGTH ANISOTROPY
187
This is consistent with the way the diametral point load strength is calculated where the use of the median value instead of the mean value will have a disproportionate effect on strongly deviating results.
8 0
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.
Acknowledgements--Financial support for these investigations was received from Norges Tekniske H6gskoles Fond. The author wishes to thank colleagues at the Department of Geology. The Norwegian Institute of Technology, Trondheim, for kind help and useful advice.
Fig. 8. The variation of the point-load strength index with the angle between the core axis and the foliation planes in a micaschist. Load applied parallel to the foliation plane, from Aagaard [4]. Received 22 December 1982; revised 25 March 1983.
strength is shown in Fig. 8. When the load is correctly applied, the results from diametral tests are only influenced by the angle of the weakness planes when they lie between 30 and 60 ° to the axis of the core. SUGGESTED PROCEDURE FOR T H E MEASUREMENT OF POINT-LOAD STRENGTH ANISOTROPY ON ONE CORE
(1) Cores to be tested should be drilled as perpendicular as possible to the weakness planes (bedding/foliation) of the rock with the deviation not exceeding 30 °. (2) Cores which are not tested as soon as they are drilled, should be stored under conditions which prevent the loss of water from the rock. (3) Diametral point-load tests are performed and strength indices calculated in accordance with the methods suggested by ISRM. (4) Axial point-load tests are performed on core pieces with lengths varying between 0.5 and 1.0 times the diameter. Each calculated point-load strength and corresponding height (or distance between loading platens) D, are plotted in a semilogarithmic diagram as shown in Figs 3 and 4. (5) A straight line with a slope defined by the equation I s ---- K f l0 -°°25D, as shown in the figures, is fitted to the points. Where this line is intersected by a vertical line through the D-value 3% greater than the diameter, the corrected axial point-load strength index is read. (6) The point-load strength anisotropy index, Io, is calculated as the ratio between the corrected axial point-load strength index and the diametral point-load strength index (In the case of cores drilled parallel to the weakness planes Io is the inverse ratio). Note: As the point-load strength is strongly dependent on the content of water in the rock [16, 17], great care should be taken to ensure that the water content is the same during both the diametral and the axial test. Points in the semilogarithmic diagram that deviate strongly from the rest of the points may be disregarded.
REFERENCES 1. Delkotz E. J., Brown J. W., Stemler O. A. and Ce L. Anisotropy of a schistose gneiss. Proc. 1st I S R M Congr., Lisboa, pp. 465-470 (1966). 2. Donath F. E. Experimental study of shear failure in anisotropic rocks. Bull. Geol. Soc. Am. 72, 985-990 (1961). 3. Svenska Viginstitutet. Methods and results from testing of rocks for road construction (in Swedish), Medd. No. 8, Stockholm (1928). 4. Aagaard B. Strength anisotropy of rocks (in Norwegian). M.Sc. dissertation, 104pp. NTH, Trondheim (1976). 5. Broch E. and Franklin J. F. The point-load strength test. Int. J. Rock Mech. Min. Sci. 9) 669-697 0972). 6. ISRM. Suggested methods for determining the point-load strength index. ISRM Commission of Laboratory Tests, Document l, pp. 8-12 (1973). 7. Read J. R. L., Thornton P. N. and Regan W. M. A rational approach to the point-load test. 3rd Australia-New Zealand Conf. on Geomechanics, Wellington, p. 2-35-39 (1980). 8. Peng S. S. Stress analysis of cyclindrical rock discs subjected to axial double point load. Int. J. Rock Mech. Min. Sci. & Geomech. Abstr. 13, 97-101 (1976). 9. Sundae L. S. Effect of specimen volume on apparent tensile strength of three igneous rocks. USBM RI 7846, Washington (1974). I0. Greminger M. Experimental studies of the influence of rock anisotropy on size and shape effects in point-load testing. Int. J. Rock Mech. Min Sci. & Geomech. Abstr. 19, 241-246 (1982). II. Guidicini G., Neible C. M. and Cornides A. T. Analysis of point-load test as a method for preliminary geotechnical classificationof rocks. Bull. Int.Ass. Engng Geol. 7, 37-52 (1973). 12. Brook N. A method of overcoming both shape and size effects in point-load testing. Proc. Conf. on Rock Engineering, Univ. of Newcastle, pp. 53-70. British Geotechnical Society, London (1977). 13. Brook N. Size correction for point-load testing. Int. J. Rock Mech. Min. Sci. & Geomech. Abstr. 17, 231-235 (1980). 14. Hassani F. P., S¢oble M. J. and Whittaker B. N. Application of the point-load index test to strength determination of rock and proposals for a new size-correction chart. Proc. 21st U.S. Symp. on Rock Mechanics, Rolla, Missouri, pp. 543-553 (1980). 15. Broch E. The point-load test and its use in engineering geology (in Norwegian). Rept No. 2, 148pp. Dept of Geology, NIT, Trondheim (1977). 16. Broch E. The influence of water on some rock properties. Proc. 3rd I S R M Congr., Denver, Vol. 2, pp. 33-38 (1974). 17. Broch E. Changes in rock strength caused by water. Proc. 4th I S R M Congr., Montreux, Vol. I, pp. 71-75. Balkema, Rotterdam (1979). 18. Bieniawski Z. T. Personal communication (March, 1983). 19. Franklin J. F. Personal communication (March, 1983).
0148-9062/83 $3.00+0.00 Copyright '~ 1983 Pergamon Press Ltd
Estimation of Strength Anisotropy Using the Point-Load Test E. BROCH* As most rocks are of an anisotropic nature, the measurement of the ratio between the maximum and minimum strength, i.e. the strength anisotropy, is of general interest. To measure the strength anisotropy by the uniaxial compression test, core specimens drilled in different directions are needed. With the point-load test it is possible to obtain the strength anisotropy on one core only by first using the diametral test and then applying axial tests on the core pieces. The paper describes results from tests performed on 33 different rocks to find a diagram that could be used to compensate for the influence of size and shape in the axial test. Cores were drilled both parallel and normal to bedding or foliation planes. Analyses of the results show that the most reliable strength index is obtained when cores are drilled normal or near normal to weakness planes. The paper concludes with a suggested procedure for measurements and calculations.
INTRODUCTION Rocks are in general anisotropic with regard to their physical and mechanical properties. Well defined anisotropy is especially to be found among sedimentary and metamorphic rocks, where the bedding or the foliation normally is clearly visible. Igneous rocks may often look very homogeneous and isotropic, but testing reveals that many of their material properties vary with the direction of testing. Truly isotropic rocks are rare occurrences and should be regarded as exceptions. In all strength testing of rocks, it is therefore necessary to refer the obtained results to the relation between the direction of stresses and the direction of the texture of tested specimens. If possible, specimens should also be tested under the same magnitude and direction of stresses as the rocks will be subjected to at the construction site. However, it is not easy to establish future stress conditions for rock during construction. Drilling and blasting will for instance subject the rocks to very complex stress situations. Two strength values are of general interest, namely the maximum and the minimum strength of the rock. The maximum and minimum strengths are obtained when failure is initiated normal to, and respectively, parallel to the weakness planes of the rock, i.e. bedding, foliation, cleavage, etc. The ratio between these two extreme values may be regarded as the maximum strength anisotropy of the rock.
STRENGTH ANISOTROPY MEASURED BY THE UNIAXIAL COMPRESSION TEST In the uniaxial compression test the minimum strength is obtained when the inclination of weakness planes to the direction of the major principal stress is approx. 30° . Maximum strength is obtained when the inclination is either close to 0° or to 90 °. This means that the uniaxial compression test gives approximately the same maximum strength value for the two important and easily defined inclinations, namely, parallel to and normal to the weakness planes. ~Some authors find the greatest strengths in cores drilled parallel to the weakness planes [1], while others find the greatest strengths in cores drilled normal to the weakness planes [2]. For six Precambrian gneisses Svenska V~iginstitutet [3] found that the ratios between uniaxial compressive strengths measured on cores drilled parallel and normal to the foliation were 0.92, 0.92, 0.94, 1.03, 1.08 and 1.16. This means that the variations are more or less within the accuracy of the testing method. Based on uniaxial compressive strengths measured on cores drilled parallel and normal to weakness planes, it is possible to get a false impression of an isotropic material. To obtain a correct value for the maximum strength anisotropy in compression, it is necessary to test specimens drilled in varying directions relative to the weakness plane of the rock. Such a procedure is both tedious and expensive. THE POINT-LOAD STRENGTH ANISOTROPY INDEX
For the point-load test, as for other strength tests * Department of Geology,The Norwegian Institute of Technology, University of Trondheim, N-7034 Trondheim, Norway. where the specimen fails in tension, the problem of 181
182
BROCH:
E S T I M A T I O N OF S T R E N G T H A N I S O T R O P Y
e~
\
I0 8
° ~ B
.-~.~
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.LI
I 15
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Fig. 1. Diametral point-load strmagthindex, I,, as a functionof the angle, =, betweenthe foliationplane and the core axis for two gneisses and a mieasehist,from Aagaard [4]. defining the maximum and minimum strengths is considerably easier. In such tests the minimum strength is recorded when the specimen fails along a weakness plane. This has been convineingiy demonstrated by Aagaard [4] in a dissertation at the Norwegian Institute of Technology. Figure 1 shows results from this work. In 1972 a comprehensive description of the point-load strength test was published [5], in which a point-load strength index was defined as P /~ = D----~ (1) where P is the load required to break the specimen tested and D is the distance between the two platen contact points. As an appendix to that paper a "Suggested Method for Determining the Point-Load Strength Index" is described. This was adopted by the Commission on Standardization of Laboratory and Field Tests of the International Society for Rock Mechanics [6] the following year. In this suggested method a strength anisotropy index Io is defined as the ratio of the corrected median strength indices for tests perpendicular and parallel to planes of weakness. In the paper the diametral and the axial point-load test are described, and the practical use of both the point-load strength index, Is, and the strength anisotropy index, I°, are demonstrated on a core log. Since the publishing of the paper and the adoption of the method by the ISRM, a number of authors have published valuable papers on different aspects of the method and its use in practical rock engineering [7, 10--17]. It does not seem, however, that everyone is aware of the potential of the method to measure maximum and minimum strengths in one core, and thus calculate strength anisotropies. This is done by first performing diametral tests on the core, followed by axial tests on the broken core pieces. As will be shown later in the paper, this procedure may be used, provided the
angle between the weakness planes in the rock and the direction of the core does not exceed certain values. In the testing of rock strengths, specimen preparation is normally a time consuming and costly procedure. One of the great advantages of the point-load strength test is that it does not require machined specimens. As long as the influence of specimen size and shape are considered in the calculation of the strength index, any piece of rock, whether the surface is smooth or rough, can in principle be tested. Using only one core sample to obtain both the maximum and the minimum strengths of the rock is probably one of the fastest and cheapest methods in rock engineering at present. RESULTS FROM AXIAL TESTS PERFORMED ON CORE DISCS It has been shown [5] that test results obtained from axial and diametral tests on two different types of rock with three different diameters were identical provided that, in the axial test, specimens with a length/diameter ratio of 1.1 ___0.02 were used. Based on this, the ISRM Commission suggested that the axial test should be performed on core specimens with length/diameter ratios of 1.1 + 0.05. This requirement is so strict that machine cutting of specimens is in practice necessary and may be one of the reasons why the axial test has been littled used. Read et al. [7] reported that when axial tests were attempted at the suggested length/diameter ratio, the samples either rotated between the platens or broke off at the edges. Similar features have been experienced by this author, but it does not always occur. For slightly anisotropic, sound rocks it is possible to conduct valid axial tests when the length of the core is greater than the diameter. Read et al. found after some experimentation that consistent results were obtained when a ratio of 0.65 was used. This value was adopted as standard for their testing. This empirically obtained ratio is compatible with a stress analysis of cylindrical rock discs subjected to an axial, double point load by Peng [8]. His finite element model shows that the stress distribution changes slightly for length/diameter ratios greater than 1.3 and stabilizes for specimens with ratios less than 1.0. He therefore concludes that the best specimen geometry for the axial point-load is with a length/diameter ratio below 1.0. Similar results have been obtained by Sundae [9] in laboratory tests carried out on discs of three different rocks. When performing the diametrai point-load test, the ISRM Commission suggests that the distance between the contact or loading point and the nearest free end be at least 0.7 d where d is the core diameter. After diametral point-load testing, one is then normally left with core pieces with lengths in the range of 0.5-1.0 d. As the testing of rock cores in general will be performed at certain standard diameters, it is desirable to find a best possible direct way of transforming the results from the axial test to strength indices comparable with
BROCH: I00 90 80
•
-
183
ESTIMATION OF STRENGTH ANISOTROPY
have been replotted in a semilogarithmic diagram as shOWn in Fig. 2. The dotted lines connnect points of the same core diameter, d. It is obvious that for the range of core diameters between 25 and 54ram and with length/diameter ratios varying between 0.5 and 1.5, the inclination of the lines are consistent for the two rather different rocks. It has thus been possible to fit a set of parallel lines like the solid lines in the diagram. These solid lines, which establish the combined influence of size and shape in an axial test, are replotted in Fig. 3. The lines can be described by the equation
Dolerite
70 60 50 40
30
20
L =/(1" 10 -°°25~ IO 9
n
where Ki is the constant defining where the single lines are running. (K1 = I,, when D is made equal to zero). An example for KI = 85 is shown in the right part of Fig. 3. Also included on these diagrams are the strength indices for the sandstone and dolerite discs for 25.5 and 38 mm cores as a direct function of the height, D (or length). Dotted lines parallel to the solid lines are fitted to the plotted strength indices. The big crosses mark the intersections between the dotted lines and the indices measured by the diametral test on cores from the same block of rock and of the same sizes, but drilled in a direction normal to the axially tested core discs. In these diagrams the strength indices for axially tested core discs with a diameter of 25.5 mm can be correlated to those obtained for diametrally tested cores when the height (or length) of the core disc is 28.7 ram. Correlation is obtained for 38 mm cores when the height of the disc is 39.1 mm. This clearly indicates that axially tested core pieces should have lengths slightly greater than their diameters to give commensurable strength indices. This was the bails for the earlier mentioned ISRM suggestion for the axial point load-test. In a recent paper, Greminger [10] reports valuable results from experimental studies of the influence of rock anistropy on size and shape effects in point-load testing. Four types of rock with varying strength anisotropy indices (given in parentheses) were extensively tested: Augen gneiss (Ia = 1.05), Ruhr-Sandstone (Ia = 1.15),
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Fig. 2. Point-load strength indices, I,, obtained from axial tests on sawn core discs of varying diameters, d, as functions of the ratio D/d. D is the distance between the load platens (or height of disc).
those obtained in the diametral test. Thus, when the influence of shape and size on the results from the axial test ~s considered, a true strength anisotropy index can be calculated. Returning to the earlier published paper [5], the results from axial point-load tests on carefully sawn core discs
215
6
38ram Cores
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Fig. 3. I, for axially loaded core discs as a function of the height, D. See text for further explanation.
184
BROCH:
ESTIMATION OF STRENGTH ANISOTROPY
Chiandone-Gneiss (I~ = 2.80) and Nuttlar-Slate (Ia = 5.70). Like other research workers [5, 9, 11], Greminger finds that the best fit with experimental data is obtained by a parabolic function of strength, I,, against size, D. L ~c D-° (3) He finds no indication of any dependence of the exponent a on anisotropy. He therefore draws the conclusion that the size correction factor is independent of the degree of anisotropy and of the loading direction. A shape effect is described by the relation I, oc
P oc ( d . D ) °75 ~ A °-75
~ D-°
(5)
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(6)
where K: is a constant related to the strength of the rock tested. To compare equation (6) with equation (2) the former is also shown in the right part of Fig. 3 for a chosen value of K2 = 850. The equation is in the semilogarithmic
(7)
which is identical to an equation presented by Brook [12, 13]. In several papers he has argued that shape and size effect problems in the point-load test could be overcome by introducing a strength index P T ~ = 211.5 A0.7"--3
(4)
Combining both size and shape effects gives
,,P- ~
diagram expressed by a slightly curved line (short dashes) which to a large extent is subparallel to the straight equation (2) lines. With the chosen a and b values, equation (6) can be rewritten as
(8)
where A is the loaded area. He suggests a reference area of 500 m 2 (equivalent to diametral tests on 25 mm cores). Objections against Brook's suggestion put forward by Hassani et al. [14], are: (a) the area is often difficult to determine exactly and (b) the strength index as given by equation (1), is so widely used and accepted that it will be difficult to change. Recent talks with the chairmen of ISRM's Commission on Standardization of Laboratory and Field Tests [18, 19] confirm that the Commission has no plans for changing the definition of the Point Load Strength Index. In a revision of the "Suggested Method" to be published in the near future, references will, however, be made to all relevant research work.
Table 1. List of tested rocks with results from diametral point-load tests performed on dry and fully water-saturated specimens. Cores are drilled both parallel and normal to foliation or bedding Spec. No. 01 02 03 04 05 06 07 08 09 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33
Rock type
Locality
Geological era
Quartz-diorite Trolla Cambr.-Silur. Crystalline schist Berk/tk Cambr.-Silur. Diorite Kleft bru Cambr.-Silur. Quartzite Ringebu Eocambrian Arkosic sandstone Trenen Eocambrian Quartz-syenite Gjeller~Lsen Permian Black shale Grodalen Cambr.-Silur. Granite Lier~sen Permian Rhomb-porphyry Toverud Permian Siltstone Tyrihjelmen Cambr.-Silur. Limestone Ringerike Kaikv. Cambr.-Silur. Quartzite Modum Precambrian Basalt Steinsskogen Permian Gneiss Hambora Precambrian Gneiss-granite Hambora Precambrian Gneiss-granite Gronningen Precambrian Micashist Trlssavika Precambrian Gabbro Myrvang Cambr.-Silur. Gabbro Heggest dam Cambr.-Silur. Micashist Odtvollen Cambr.-Silur. Sandstone Sveigen Devonian Quartzite Adamselv Eocambrian Biotite-gneiss* Linde(jell Prccambrian Quartz-syenite Lindefjell Precambrian Granite Lindefjell Prec,ambrian Gneiss-granite Lisle~t ~brian Gneiss-granite Lislet Prccambrian Gneiss Gjora Pr~,ambtian Gneiss Driva Prceambrian Quartz-diorite* Stzren Cambr.-Silur. Hyperite Sohar Precambrian Gneiss lkstvoll, Fosen Prcc,ambrian Amphibolite /~t~ord Precambrian Average values for standard deviation:
* Excluded from average value calculation.
Diametral I, (MPa) with SD in ( ) Cores drilled parallel Cores drilled normal Saturated Dry Saturated Dry 7.8 (15) 11.6(12) 11.5(ll) 15.5 (10) 17.5 (14) 7.8(15) 9.6 (31) 8.5 (24) 8.0(25) 12.4(27) 6.3(18) 11.9(21) 17.0(29) 9.1(24) 9.3(16) 12.1 (10) 7.6 (21) 11.5(6) 9.0(ll) 11.4 (21) 18.7(20) 17.3 (7) 3.0 (72) 5.9 10.6 (7) I 1.7 (8) 12.3 (8) 5.5(21) 12.4(32)
12.3 (30) 11.6(26) 15.5(10) 16.0 (13) 20.3 (40) 8.6(18) 8.0 (34) 8.7 (14) 10.3 (21) 12.8(39) 6.4(18) 12.6(13) 13.7(19) 10.1 (31) 10.8(20) 14.5 (10) 8.5 (l 8) 17.9(11) 13.4(9) 9.6 (38) 17.1 (22)
8.8(30) 8.7 (14) 17.5
15.7(14) 13.3 (6) 20.2
9.3(16) 18.2(15)
4.7 (25) 5.1 (23) 10.4(10) 15.4(11) 6.3 04) 7.6(11) 8.8 (13) 6.7 (6) 5.2 (37) 7.8(21) 5.1 (38) 10.1 (14) 16.8(17) 4.9(18) 9.2(10) 8.5 (17) 3.2 (39) 9.1 (10) 7.3(15) 2.0 (33) 17.2(25) 14.7 (20) 1.6 (44) 5.3 5.7 (32) 8.4 (l 3) 7.3 (14) 3.1 (26) 2.7(29) 9.0 (! 1) 10.2(5) 8.0(15) 6.5 (11) 19.9
5.0 (29) 6.6(31) 14.8(9) 16.8 (12) 7.7 (2 l) 8.0(26) 7.8 (11 ) 7.9 (13) 7.6 (28) 8.9(28) 5.5(28) 9.5(18) 11.7(29) 7.1 (18) 9.8(15) 10.9 (12) 5.5 (26) 14.7(14) 8.7(27) 4.5 (56) 18.7(14)
3.8(21) 5.1 (21) 11.6 (11) 14.5 (6) 10.7(10) 10.2 (15) 21.3
Anisotropy 1~ Sat. Dry 1.66 2.27 l.ll 1.01 2.78 1.03 1.09 1.27 1.54 1.59 1.24 1.18 1.01 1.86 1.01 1.42 2.38 1.26 1.23 5.70 1.09 1.18 1.88 I. 1l 1.86 1.39 1.68 1.77 4.59
2.46 1.76 1.05 0.96 2.64 1.08 1.03 1.10 1.36 1.44 1.16 1.33 1.17 1.42 1.10 1.33 1.55 1.22 1.54 2.13 0.91
1.10 1.34
t.47 1.30
2.45 3.57
BROCH:
ESTIMATION OF STRENGTH ANISOTROPY
185
AXIAL TESTING OF CORE PIECES
Dry
Diametral testing of rock cores will normally produce a number of core pieces with lengths shorter than their diameter. To investigate the possibilities of employing extrapolations of axial test results along fitted lines as shown in Fig. 3, a total of 33 different Norwegian rocks have been carefully tested [15]. The ELE-point-ioad tester (from Engineering Laboratory Equipment, England) was used, and a core diameter of 31.5mm (normally referred to as 32 mm cores) was chosen. This is by far the most used core dimension in Norway. The testing procedure and the calculation of results were performed in accordance with the suggestions outlined by ISRM [6]. Cores were drilled from large blocks both parallel to and normal to bedding or foliation planes. Tests were performed on oven dried and fully water saturated cores [16]. Specimen number, type of rock, locality and geological era are listed in Table 1 together with the results of the diametral point-load test. As the table illustrates, a wide variety of rocks are represented with point-load strength indices on water saturated specimens varying from 1.6 to 18.7 MPa. Strength anisotropy indices (on saturated cores) vary between 1.01 and 4.59. The results from the axial tests were plotted as in Fig. 4. For each type of rock, both the results from cores drilled parallel to and normal to bedding/foliation planes are plotted. The results from the diametral tests (the median values) are also plotted on the diagram with the big crosses. A study of all the diagrams reveals that the scatter of the test results varies considerably from rock to rock. Rocks of high strength anisotropy tend to show a greater scatter than rocks of low anisotropy. However, this is
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not as pronounced in the diametral test as in the axial test. Most of the gneisses are good examples of anisotropic rocks with great scatter in strength results. In axial tests there is greater scatter of the data from cores drilled parallel to the foliation than normal to the foliation. On the other hand, in the diametral test the scatter is somewhat smaller for the cores drilled parallel to the foliation. The difference in the scatter of the results for the different directions is clearly less pronounced for the diametral test than for the axial test. This indicates that the most reliable results for the measurement of strength anisotropy indices on only one core should be obtained when this core is drilled normal to the foliation. Cores drilled normal to foliation / bedd=ng
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o-~.._'>...
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o o°x
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1.4 8 M P o
186
BROCH: ESTIMATION OF STRENGTH ANISOTROPY
25
/ / / •
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Fig. 6. Strengthanisotropyindices measured on one core drilled parallel to (left) and normal to (right) the foliationor bedding and correlated with the strength anisotropy index measured by two diametral tests. To find what core piece lengths (D) give axial strength indices identical to the diametral strength indices, the D-values for the big crosses in the diagrams are plotted as a function of the strength, Is in Fig. 5. The data include results from dry and fully saturated cores. A few strength indices are excluded either because of too few strength tests or too wide scatter in results. The average D-value for all tests is 32.5 mm. This means that for 31.5 mm dia rock cores the axial strength index obtained on a core piece which is 1 mm longer than the diameter (or 1.03 D) should be identical to the result from the diametral test. This confirms the results presented earlier from the tests carried out on sawn core discs.
What strength anisotropy index should be regarded as the "true" one, is difficult to decide. Anisotropy measured by diametral tests on cores drilled in two directions is favoured by the fact that the diametrai test is the best controlled test. Favouring anisotropy measured by a combination of diametral and axial pointload tests on the same core is the fact that one then really knows that it is the same material that is tested in both directions. For inhomogeneous and strongly anisotropic materials this is an advantage that often may fully outrange the inaccuracies in the axial test. Furthermore, testing on one core only may considerably reduce the expense of strength testing.
CORRELATION BETWEEN POINT-LOAD STRENGTH ANISOTROPY MEASURED ON ONE AND ON TWO CORES
APPLICATION OF THE LOAD ON ANISOTROPIC CORES
When the average D-values of 32.5 mm was found, it was drawn as a vertical line in all the semilogarithmic diagrams (Fig. 4) and all the equivalent axial strength indices for water saturated cores were obtained. Strength anisotropy indices then were calculated for the results obtained from cores drilled parallel to and normal to foliation, respectively. In Fig. 6 these indices are plotted against the strength anisotropy indices calculated from diametral tests performed on cores drilled in both directions. If the diametral results are regarded as the "true" indices, it is of interest to note the core direction which gives the best correlation. Not surprisingly, the strength anisotropy index obtained on the cores drilled normal to the bedding or foliation of the rock gives the best correlation with the index obtained from measurements on two cores. A few data points deviate considerably from the regression line. These represent rocks with pronounced anisotropic properties, which in terms of testing are complicated materials with inhomogeneities and rapidly changing properties. Gneisses and micashists are examples of such rocks. The great scatter in strength test results often reflects the problems of selecting representative specimens.
When cores of anisotropic rocks are to be tested with the point-load apparatus, it is important that the load be correctly applied. To obtain readings of the maximum and minimum strength values, the load must be applied so that failure is initiated normal to and parallel to weakness planes (bedding/foliation). For cores drilled at an oblique angle to such weakness planes, Fig. 7 demonstrates the right and wrong ways of applying the load. In the diametral test, the load should be applied along the shortest axis of the elliptic weakness plane. To avoid the influence of the uncontrolled shape effects, core pieces shorter than the diameter should be used. The influence of the angle between the core axis and the weakness planes, fl, on the diametral point-load
mo0~t
Fig. 7. Right and wrong applicationof the point.loadson cores which are drilled at an oblique angle to foliation or bedding.
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BROCH:
ESTIMATION OF STRENGTH ANISOTROPY
187
This is consistent with the way the diametral point load strength is calculated where the use of the median value instead of the mean value will have a disproportionate effect on strongly deviating results.
8 0
L 15
I 30
I 45
I 60
l
75
I 90
.
Acknowledgements--Financial support for these investigations was received from Norges Tekniske H6gskoles Fond. The author wishes to thank colleagues at the Department of Geology. The Norwegian Institute of Technology, Trondheim, for kind help and useful advice.
Fig. 8. The variation of the point-load strength index with the angle between the core axis and the foliation planes in a micaschist. Load applied parallel to the foliation plane, from Aagaard [4]. Received 22 December 1982; revised 25 March 1983.
strength is shown in Fig. 8. When the load is correctly applied, the results from diametral tests are only influenced by the angle of the weakness planes when they lie between 30 and 60 ° to the axis of the core. SUGGESTED PROCEDURE FOR T H E MEASUREMENT OF POINT-LOAD STRENGTH ANISOTROPY ON ONE CORE
(1) Cores to be tested should be drilled as perpendicular as possible to the weakness planes (bedding/foliation) of the rock with the deviation not exceeding 30 °. (2) Cores which are not tested as soon as they are drilled, should be stored under conditions which prevent the loss of water from the rock. (3) Diametral point-load tests are performed and strength indices calculated in accordance with the methods suggested by ISRM. (4) Axial point-load tests are performed on core pieces with lengths varying between 0.5 and 1.0 times the diameter. Each calculated point-load strength and corresponding height (or distance between loading platens) D, are plotted in a semilogarithmic diagram as shown in Figs 3 and 4. (5) A straight line with a slope defined by the equation I s ---- K f l0 -°°25D, as shown in the figures, is fitted to the points. Where this line is intersected by a vertical line through the D-value 3% greater than the diameter, the corrected axial point-load strength index is read. (6) The point-load strength anisotropy index, Io, is calculated as the ratio between the corrected axial point-load strength index and the diametral point-load strength index (In the case of cores drilled parallel to the weakness planes Io is the inverse ratio). Note: As the point-load strength is strongly dependent on the content of water in the rock [16, 17], great care should be taken to ensure that the water content is the same during both the diametral and the axial test. Points in the semilogarithmic diagram that deviate strongly from the rest of the points may be disregarded.
REFERENCES 1. Delkotz E. J., Brown J. W., Stemler O. A. and Ce L. Anisotropy of a schistose gneiss. Proc. 1st I S R M Congr., Lisboa, pp. 465-470 (1966). 2. Donath F. E. Experimental study of shear failure in anisotropic rocks. Bull. Geol. Soc. Am. 72, 985-990 (1961). 3. Svenska Viginstitutet. Methods and results from testing of rocks for road construction (in Swedish), Medd. No. 8, Stockholm (1928). 4. Aagaard B. Strength anisotropy of rocks (in Norwegian). M.Sc. dissertation, 104pp. NTH, Trondheim (1976). 5. Broch E. and Franklin J. F. The point-load strength test. Int. J. Rock Mech. Min. Sci. 9) 669-697 0972). 6. ISRM. Suggested methods for determining the point-load strength index. ISRM Commission of Laboratory Tests, Document l, pp. 8-12 (1973). 7. Read J. R. L., Thornton P. N. and Regan W. M. A rational approach to the point-load test. 3rd Australia-New Zealand Conf. on Geomechanics, Wellington, p. 2-35-39 (1980). 8. Peng S. S. Stress analysis of cyclindrical rock discs subjected to axial double point load. Int. J. Rock Mech. Min. Sci. & Geomech. Abstr. 13, 97-101 (1976). 9. Sundae L. S. Effect of specimen volume on apparent tensile strength of three igneous rocks. USBM RI 7846, Washington (1974). I0. Greminger M. Experimental studies of the influence of rock anisotropy on size and shape effects in point-load testing. Int. J. Rock Mech. Min Sci. & Geomech. Abstr. 19, 241-246 (1982). II. Guidicini G., Neible C. M. and Cornides A. T. Analysis of point-load test as a method for preliminary geotechnical classificationof rocks. Bull. Int.Ass. Engng Geol. 7, 37-52 (1973). 12. Brook N. A method of overcoming both shape and size effects in point-load testing. Proc. Conf. on Rock Engineering, Univ. of Newcastle, pp. 53-70. British Geotechnical Society, London (1977). 13. Brook N. Size correction for point-load testing. Int. J. Rock Mech. Min. Sci. & Geomech. Abstr. 17, 231-235 (1980). 14. Hassani F. P., S¢oble M. J. and Whittaker B. N. Application of the point-load index test to strength determination of rock and proposals for a new size-correction chart. Proc. 21st U.S. Symp. on Rock Mechanics, Rolla, Missouri, pp. 543-553 (1980). 15. Broch E. The point-load test and its use in engineering geology (in Norwegian). Rept No. 2, 148pp. Dept of Geology, NIT, Trondheim (1977). 16. Broch E. The influence of water on some rock properties. Proc. 3rd I S R M Congr., Denver, Vol. 2, pp. 33-38 (1974). 17. Broch E. Changes in rock strength caused by water. Proc. 4th I S R M Congr., Montreux, Vol. I, pp. 71-75. Balkema, Rotterdam (1979). 18. Bieniawski Z. T. Personal communication (March, 1983). 19. Franklin J. F. Personal communication (March, 1983).