experimental studies of the influence of rock anisotropy on size and shape effects in point-load...

Int. J. Rock Mech. Min. Sci. & Geomech. Abstr. Vol. 19, pp. 241 to 246, 1982 0148-9062]82/050241-06103.00/0 Printed in Great Britain. All rights reserved Copyright © 1982 Pergamon Press Ltd

Technical Note

Experimental Studies of the Influence of Rock Anisotropy on Size and Shape Effects in Point-Load Testing M. GREMINGER*

INTRODUCTION

In the last decade the point-load strength test, a simple indirect tensile test, has gained considerable inter- national approval. However, in tensile testing important scale effects must be expected, especially if stress gradients are produced, as is the case in indirect tensile tests [2]. The influence of specimen shape on the point- load strength of rock cores was considered by Reich- muth [3], who proposed a rather complex relationship for the determination of a constant tensile strength, whose practical value was questioned by Broch & Franklin [1]. They recommended as a replacement for the tensile strength a point-load strength index:

P It = D-~ (MPa) (1)

where It = strength index, P = fracture load, D = distance between loading cones. However considerable variations of It, dependent on both size and shape were found by Broch & Franklin. Consequently, the introduction of a reference index I~(50) was recommended, which corresponds to the point-load strength index of a diametrally loaded rock core of 50 mm dia. If other core sizes are tested the respective point-load strength indices must be reduced to I~(50). In effect, they propose a size correction factor for the point-load strength index, which is a function of the distance between the loading points only, and can be obtained from empirical correction-curves or a nomogram. The considerably larger shape effect should be avoided by testing specimens with specified geometries.

The strength anisotropy index, la, the ratio of point- load strengths in the strongest and weakest directions, serves as a quantitative measure for the anisotropy of point-load strength. Any influence of rock anisotropy on the scale effect was not mentioned by Broch & Franklin.

Further studies of the scale effect in point-load testing have been conducted by Brook [4, 5]. He developed

* Arbei tsgruppe Felsmechanik, Inst i tut fiir Geologic, Ruhr-Univer- sit,it Bochum, 4630 Bochum, F.R. Germany.

a relationship between strain energy and strained volume in point-load testing and found the fracture load, P, and the cross-sectional area, A, of the loaded specimen to be the relevant quantities for determining the point-load strength. His relationship

m ~ 0.75 P = C. A', C = constant (2)

requires no restriction on specimen geometry and is therefore applicable to arbitrary sizes and shapes. Size effects again are eliminated by reduction to a reference- index, which is now related to a cross-sectional area A * = 500mm 2 ( D _ 25 mm). A shape correction is obtained by using the cross-sectional area, A, instead of the distance, D, between the loading points. The size and shape corrected value of the point-load strength is, after Brook [5],

P(A) 5000.75 T~00 = ~zv-~" 500 (MPa) (3)

Any influence of anisotropy on the scale effect and its correction is, however, not mentioned by Brook.

An experimental study has been initiated, therefore, to investigate the directional dependence of size and shape effects of the point-load strength of anisotropic rocks. In addition, the applicability of Broch & Frank- lin's [1] empirical relation between the uniaxial compressive strength, a¢, and the point-load strength reference-index, I,(50), has been examined for anisotropic rocks. Their result

trc = 24 I~(50) (4)

has been confirmed later by Bieniawski [6] and Brook [4,5], but none of these previous investigators took strength anisotropy into consideration. Pells [7] com- pared measured values of compressive strengths of twelve rock types with those predicted by equation (4). He reports significant differences between these values for six rock types, emphasizing that four of them were isotropic.

241

242 Technical Note

A critical investigation of the validity of uniaxial compressive strength prediction by point-load index with respect to anisotropic rocks appears therefore necessary.

TEST RESULTS

Correction of size and shape effects in point-load testing

Numerous point-load tests have been performed on four rock types with various degrees of strength anisotropy (Io = 1.05 to la = 5.7) in order to evaluate these effects. Two extreme directions, i.e. parallel and normal to the plane of weakness were considered. Because of the wide range of strength anisotropies covered by the rocks chosen, the results should be applicable to other anisotropic rocks in spite of the limited number of rock types investigated in this study. The following rock materials have been tested: a medium-grained, weakly bedded Carboniferous Ruhr- Sandstone with a quartz content of 70%, 209/0 feldspar minerals, 8% mica and additional minerals and 2% por- osity; a Devonian slate from Nuttlar (Rhenish massive) with a content of phyllo silicates of 80%, 10% calcite, and 10% quartz plus feldspar; an Alpine Oligocenic gneiss from Sondrio (Switzerland) called Chiandone- Gneiss with 45% of quartz, 35% feldspar minerals, 18%/o mica, and 2% additional minerals, and a Mesozoic augen gneiss from Graubiinden (Switzerland) with 15% augen of microcline and quartz and 85%/0 ground mass consisting of 55% quartz, 25% mica, 15% feldspar minerals, and 5% additional minerals.

The mechanical properties of these rocks are listed in Table 1 for the two principal directions. The test results (Figs 1-4) from diametrically loaded cores with diam- eters of 30, 44, and 62 mm and of constant shape show that point-load strength indices for the small diameter cores can be up to two times larger than those for the larger diameter cores. This clearly demonstrates the existence of a size effect. The additional shape effect was evaluated in axial point-load tests on specimens of different width to height ratios. For constant D but different LID ratios the point-load strength index shows a variation, which can exceed a ratio of 5 to 1

(see Figs 1-4). All width to height ratios have been equal to or greater than 1, as recommended by Peng [8]. The deviation (95% interval) of in the average twelve point-load tests per configuration usually amounts to _ 10-25%, with the understandable excep- tion of Nuttlar-Slate loaded parallel to the planes of weakness.

This large variability of ls(D) could greatly limit its use as a strength index value, unless reference is made to a standard size and respective correction factors for size and shape effects are available. Scale effects cer- tainly could be avoided by using specimens of reference-dimensions only. Although desirable, this however would be rather impractical since it would eliminate the great advantage of the point-load test that no sample preparation is required. The application of suitable scale correction procedures is therefore indispensable. Because of the qualitative similarity of the curves of Figs 1-4 (full curves) it is to be expected that scale effects are independent of rock type and loading direction.

In order to establish suitable correction factors by way of analytical functions for the size and shape dependence and in particular to detect any dependence on the degree of anisotropy, linear, exponential, and parabolic functions were determined from the experimental data by regression analysis. The best fit with the experimental data could be obtained by a parabolic function, as formely ascertained by e.g. Guidicini et al. [9] or Sundae [10].

The variation of Is(D) with sample size (diametral and axial tests) is best described by

Is(D) oc D -a with 0.466 ~ a ~< 0.577 (5)

with no indication of any dependence of the exponent a on anisotropy. A very important conclusion is therefore, that the size correction factor is independent of the degree of anisotropy and of the loading direction. It can be written in the form

C o = with D * = 5 0 m m (6)

with a reference-dimension of 50 mm recommended by ISRM [11]. Setting by approximation a = 0.5 results in

TABLE 1. MECHANICAL ROCK PROPERTIES IN THE TWO PRINCIPAL DIRECTIONS

Loading Type of rock direction ac (MPa) E (MPa) v2 (km/sec) p (kN/m 3)

Augen gneiss IISchistosity 150 48,800 4.14 26.5 _LSchistosity 178 34,500 2.68 26.5

Ruhr-Sandstone IIBedding 153 39,000 4.18 25.5 &Bedding 177 34,600 3.57 25.5

Chiandone-Gneiss IISchistosity 104 38,900 3.51 26.6 _LSchistosity 164 37,800 2.81 26.6

Nuttlar-Slate IISchistosity 104 60,600 5.66 27.7

trc: uniaxial compressive strength. E: tangent Young's modulus. v L : longitudinal wave velocity. p: density.

Technical Note 243

o Q.

30

20

B e f o r e correction + L / D = 4 • L / D = :5 • L / D = 2 • L / D = 1.5 • L / D = I

Af ter correction +

o L ' 3 0 mm " • n L ' 4 4 m m

& L - 6 2 mm o OL =E

""m -.. m.,...., m"

I0

% .•x%

\m.

I I I I I I 0 20 40 60 0 20 40 6 0

D, m m D, mm

(a) (b)

Fig. I. Point- load strength of augen gneiss loaded (a) parallel and (b) normal to schistosity,

o O-

30

20

I0

30

" o ~ • . 2 0

I0

\ "aN.

4 2.

I I I I I I 0 20 40 60 0 20 40 60

D, mm D, mm

(a) (b)

Fig. 2. Point- load strength of Ruhr-Sandstone loaded (a) parallel and (b) normal to the bedding planes.

R.M.M.S, 19/5--C

2O

o a .

IO

30 ~- 30

20 o

fit. ~E

"•'"; ""-m- I 0

e

. . . .

i I I 1 I I 0 20 40 60 0 20 40 60

D, mm D, mm

(a) (b)

Fig. 3. Point- load strength of Chiandone-Gneiss loaded (a) parallel and (b) normal to schistosity.

244 Technical Note

30 -

20

30

~E

I0

+

. . . . .

zo 4 0 60

D, mm

20

W IO

4,

\ ,

I I I 0 0 20 40 60

D, mm

(a) (b)

Fig. 4. Point- load strength of Nuttlar-Slate loaded (a) parallel and (b) normal to schistosity.

errors smaller than ___ 5~o for the interval 25 < D < 75 mm, which lie well within the accuracy of the test data. The following size correction is therefore recommended:

•,(50) = I,(D)" \ O * ] - D1.5 ' D,O. 5. (7)

The quality of this correction, i.e. the corrected values for 1,(50) differ less than 1 MPa, justifies the application of a uniform and anisotropy-independent size correction factor.

Similarly, the shape effect is best described by the relation

I , (D) oc (8)

The exponent b, derived by regression analysis from the experimental data, was found to be

0.719 ~ b ~ 0.893

with no significant dependence on the degree of anisotropy or on the loading direction. Thus, also the shape correction factor can be assumed to be independent of rock type and loading direction. Although the mean value for b lies closer to 0.8, setting b = 0.75 still does not introduce errors, which exceed 7 ~ within the practically relevant interval of 500 < ( D . L ) < 5000 mm. Combining both, size (equation 5) and shape (equation 8) corrections leads to the relation

I,(D) = D- ~ oc • (9)

Inserting the found values for a = 0.5 and b = 0.75 yields

P oc (L" D) °'7s ~ A 0"75 (10)

which is identical to equation (2), theoretically derived by Brook [4, 5]. It is felt important that this agreement

should be maintained, and since this can be achieved by setting b = 0.75 instead of the experimentally found value of 0.8 without introducing significant errors, the shape correction factor therefore adopted is

C r = ( D ) °'75. (11)

For the practical determination of I, (50) three simplified cases can be distinguished:

P 1,(50) = I ,(D). Co - D1.5. D,0.5, (12a)

if

if

A = D 2 . x (circle);

1,(50) = I , ( D ) ' C o ' C L = P

(D" L) °'75" D *°'5' (12b)

if

7~ A = D . L . ~ (ellipse);

/rt\0.75 1,(50) = I , ( O ) ' C o ' C r ' ~ ) =

A = D" L (rectangle).

0.834 P (D. L)O.VS. D,O.5'

(12c)

For the rock types used in the investigation reported here, full correction of size and shape effects could not be achieved for specimens with width to height ratios greater than three. Ratios larger than this should be avoided (see dotted curves in Figs 1-4). The accuracy of < +1 MPa obtained for all other configurations is satisfactory for the point-load strength as an index value. In order to demonstrate the attainable precision,

Technical Note

TABLE 2. POINT-LOAD STRENGTH INDICES Is(50) OF THE ROCKS INVESTIGATED

ls(50)ll (MPa) L(50)~ (MPa) Type of rock I 2 3 I 2 3

Augen gneiss 6.4 6.6 6.1 6.9 6.9 6.8 1.05 Ruhr-Sandstone 7.9 7.9 7.8 8.9 8.5 8.9 i.15 Chiandone-Gneiss 3.6 3.8 3.6 10.6 10.0 10.6 2.80 Nuttlar-Slate l.l 1.4 1.5 8.5 8.2 8.4 5.70

I. Determined from test results by interpolation between 44 and 62 mm. 2. Determined by size correction of diametral test results. 3. Determined by size and shape correction of axial test results.

245

mean values of I~(50) determined by different methods are listed in Table 2.

Comparison between uniaxial compressive strength and point-load strength of anisotropic rocks

From experimental studies Broch & Franklin [1] and other authors (e.g. Bieniawski [6]) found despite a considerable scattering of the data a linear relation between uniaxial compressive strength ac and the point- load strength index:

ac = 24 I~(50) (4)

The accuracy obtained for assessing a~ has been assumed satisfactory.

Direction-controlled predictions of compressive strength by means of I,(50) have not been considered so far. In order to examine the validity of equation (4) for anisotropic rocks, unconfined compression tests have been performed on the same types of rock and in the same loading directions as in the point-load tests. The diameter of the cores used for this purpose was 62 mm; all height to diameter ratios were 2.5 to 3.0. A size effect in compressive tests was considered to be negligible.

A comparison using the Student-t-test of measured compressive strengths with those predicted by means of equation (4) was successful only for augen gneiss (Io = 1.05). Errors between these values were found to be probable for the slightly more anisotropic Ruhr-

Sandstone (la --- 1.15) and significant or highly significant for both highly anisotropic rocks, Chiandone- Gneiss (I, = 2.8) and Nuttlar-Slate (I, = 5.7) (see Fig. 5).

This result is not surprising since the directional variation of the uniaxial compressive strength is rather different from that of the point-load strength. The point- load strength reaches its maximum at a loading direction normal to the planes of weakness and its minimum parallel to the planes of weakness, whereas the uniaxial compressive strength normal to the planes of weakness is generally higher than that parallel to it. The minimum of ac, however, is generally observed and also predicted by the Mohr-Coulomb criterion [12] for a load direction at an angle of 45 ° - ~b/2 to the planes of weakness.

The answer to the question of a possible correlation between the minimum and maximum values of compressive strength of anisotropic rocks and the appro- priate values of point-load strength appears to be therefore a negative one. The experimental results show a particularly poor correlation for the maximum compressive strength, since there significant errors of up to 60~ were observed between measured and predicted values. The test results clearly indicate that for the four rock types of this study neither degree nor direction of anisotropy agree between uniaxial and point-load tests.

Although the limited number of rock types investigated in this study does not allow a final conclusion

L o a d e d L o a d e d para l le l pe rpend icu la r

Augen gneiss v • Io - Ruhr sandstone o • t - - • - - I

Ch iandone gneiss o • I • I

N u t t l a r s la te A -

o •

IE

% [ 5 0 ] • 2 4 I s [501 o

!

I I I I 0 50 I 0 0 1 5 0 2 0 0

o c [ 5 0 ) , MPo

Fig. 5. Relationship between uniaxial compressive strength a, and point-load strength index I,(50).

246 Technical Note

regarding the use of the point-load test for predicting the uniaxial compressive strength, the considerable prediction errors observed for anisotropic rocks cannot and must not be overlooked. The prediction should therefore be used only with great caution.

The results of both parts of this study lead to the conclusion that the point-load strength index should preferably be used as an independent strength parameter. Unconfined compression tests should be added whenever especially required.

to significant errors. The point-load strength index should therefore be used as an independent parameter and additional unconfined compression tests should be performed whenever required.

Acknowledgements--The author would like to thank Professor H. K. Kutter for initiating this study, for his permanent interest, and numerous discussions.

Received 17 March 1982.

CONCLUSIONS

(1) Size and shape effects in point-load testing of anisotropic rock were experimentally shown to be independent of the degree of rock anisotropy and independent of the loading direction. Standard size and shape correction factors could therefore be applied to the four rock types tested. The obtained accuracy (< +1 MPa) is sufficient for an index value.

(2) Because of the wide range of the degree of anisotropy (I, = 1.05 to I, = 5.7) of the point-load strength examined in this study, the results should apply to all other rocks considering even the small number of investigated rock types.

(3) Specimens of standard size (D = L = 50mm) should be tested whenever possible, e.g. diametrally compressed cores of 50 mm dia. The existence of size and shape correction factors permits, however, also the testing of specimens of arbitrary geometries, provided that 1 ~ LID ~ 3. Maximum specimen size is determined by the load capacity of the testing machine. Specimens of less than 30 mm dia should not be used, since there the loaded areas can no more be considered to be point-shaped in relation to the specimen size.

(4) Estimation of uniaxial compressive strength of anisotropic rock (I, > 1.1) by means of Is(50) can lead

REFERENCES

1. Broch E. & Franklin J. A. The point-load strength test. Int. J. Rock Mech. Min. Sci. 9, 669-697 (1972).

2. Paterson M. S. Experimental Rock Deformation--The Brittle Field, 254 pp. Springer, Heidelberg (1978).

3. Reichmuth D. R. Point-load testing of brittle materials to deter- mine tensile strength and relative brittleness. Proc. 9th Syrup. on Rock Mechanics, Colorado School of Mines, 1967, pp. 134-159. Am. Inst. Min. Metall. Petrol. Engrs. New York 0968).

4. 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. Br. Geotech. Soc., London (1977).

5. Brook N. Size correction for point-load testing, Technical Note. Int. J. Rock Mech. Min. Sci. & Geomech. Abstr. 17, 231-235 (1980).

6. Bieniawski Z. T. The point-load test in geotechnical practise. Engng Geol. 9, 1-11 (1975).

7. Pells P. J. N. The use of point-load test in predicting the compressive strength of rock materials, Technical Note. Aust. Geo- mech. 2. G5, N1, 54-56 (1975).

8. Peng S. S. Stress analysis of cylindrical rock discs subjected to axial double point-load. Int. J. Rock Mech. Min. Sci. & Geomech. Abstr. 13, 97-101 (1976).

9. Guidicini G., Nieble C. M. & Cornides A. T. Analysis of point- load test as a method for preliminary geotechnical classification of rocks. Bull. Int. Assoc. Engng Geol. 7, 37-52 (1973).

10. Sundae L. S. Effect of specimen volume on apparent tensile strength of three igneous rocks. USBM RI 7846, Washington (1974).

11. ISRM. Suggested Methods of determining the point-load strength index. ISRM Committee on Laboratory Tests. Document I, 8-12 (1973).

12. Jaeger J. C. & Cook N. G. W. Fundamentals of Rock Mechanics 2rid edn. Chapman & Hall, London (1976).

experimental studies of the influence of rock anisotropy on size and shape effects in point-load...

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