Brittleness Determination of Rocks by Different Methods V

Int. J. Rock Mech. Min. Sci. & Geomech. Abstr. Vol. 11, pp. 389-392. Pergamon Press 1974. Printed in Great Britain

Brittleness Determination of Rocks by Different Methods V. HUCKA* B. DAS* The term brittleness is used differently by different authors. An analysis is made in the present paper of the various concepts of it. The various phenomena asso- ciated with brittle substances, e.g. low value of elonoation, fracture failure, formation offines, higher ratio of compressive to tensile strenoth, higher angle of internal [biction,.formation of cracks in indentation, etc., can be used.for measuring brittleness. Experimental results based on the measurement of some of the above quantities to represent brittleness have been presented. A discussion is made to compare the results of different formulation. It appears that there is no uniformity in different formulation of brittleness, e.g. brittleness based on strain ratio, brittleness based on energy ratio, brittleness from Mohr's envelope, brittleness from compressive and tensile strength, brittleness from Protodyak- onov Impact Test, brittleness from macro- and micro-hardness, etc. Each concept of brittleness should, therefore, be treated and used separately with refer- ence to its practical utility.

INTRODUCTION books of physics and mechanics. In rock mechanics as well, brittleness is defined, conceived and used variously. Brittleness is one of the most important mechanical According to Obert and Duvall [3] it is expressed as fol- properties of rocks. But, unfortunately, there is no har- lows: materials such as cast iron and many rocks usually mony between different authors whether as to definition, terminate by fracture at or only slightly beyond the yield concept or as to measurement of brittleness. Different stress. These materials are referred to as brittle. Ramsay authors mean, express and use it differently. [4] defines brittleness as: when the internal cohesion of In view of the above fact an attempt has been made in rock materials which are deforming in their elastic range the present article to make an analysis of the concept of is broken, the rocks are said to be brittle and the stress brittleness and of the principle of its measurement as conditions at the moments of failure define the stress cri- exists or as conceived by the present authors. It may teria of brittle strength. Brittleness is further defined in then be easier to single out the principle if possible that the "Glossary of Geology and Related Sciences" [51 as may be the best in relation to the soundness of concept a property of materials that rupture or fracture with and utility. Brittleness of two different rocks is then mea- little or no plastic flow. sured following different principles and the results are From what has been discussed about brittleness it presented in tabular and graphical form. appears that the concept of brittleness is not yet made precise. However, it may be stated that with higher CONCEPT OF BRHTLENESS--DUCFILITY brittleness the following facts are observed: The definition of brittleness as a mechanical property --low values of elongation; of matter varies from author to author. Het6nyi [1"1 --fracture failure; defines it as the lack of ductility or its inverse. The degree --formation of fines; of brittleness is usually reflected in low values of percent- --higher ratio of compressive to tensile strength; age elongation or reduction in area. It is a relative term --higher resilience; since there is no universally accepted values of tensile --higher angle of internal friction; fracture strain below which a material is considered brit- --formation of cracks in indentation. tle and above which is classified as ductile. Morley [2"1 defines brittleness as the lack of ductility and the same author defines the ductility as that property of a material PRINCIPLE OF BRITTLENESS which allows of its being drawn out by tension to a MEASUREMENT smaller section. Similar definitions are there in different Because of the lack of precise definition or concept, the measurement of brittleness has not yet been standar- * Department of Mines and Metallurgy, Laval University, Quebec dized. However, the principle of reversible strain-energy 10, Quebec, Canada. is generally used. Various principles are described here. 389 390 V. Hucka and B. Das

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0 D E A/ ~o Stroin or.(Normol stress Fig. I. Determination of brittleness from stress-strain diagram. .~ -jL. I

1. Determination of brittleness from the percentage of Fig. 2. Diagram showing the determination of brittleness from the reversible strain angle of internal friction at a. = 0 from Mohr's envelope. This principle has been used by Coates [6] according to whom brittleness is the ratio of the reversible strain mum resistance to deformation is given by the following to that of the total strain at the point of failure. This con- equation (Fig. 2): cept of brittleness (termed Bt in this paper) may be R = C + ~r.tan0 expressed in relation to Fig. 1 as follows: where R--resistance to deformation; reversible strain DE C---cohesion; Bt = total.strain = OE" a.--normal stress on the plane of failure; 0--angle of internal friction. 2. Determination of brittleness from the percentage of Differentiating partially the equation (OR/&rn)= reversible energy tan 0 This concept has been used by Baron [7] which is and similar as the previous concept except that the term OR strain is replaced by the term energy. Thus with refer- : 3G. ence to Fig. 1 it may be expressed as follows: B4 = Sin 0 = {0 y reversible energy Area DCE B2 = total energy = Area OABCE B 4 = Sin 0 is taken to maintain similarity with previous where B2--brittleness based on this concept. definition B 3 where B~--brittleness determined from Mohr's .envel- 3. Determination of brittlenessfi'om tensile and compres- ope at a,, = 0. sive strengths Rate of increase in resistance with increase in confin- It is observed that the difference between the compres- ing pressure is a characteristic of brittleness and may be sive and the tensile strengths increases with increase in used in measuring the same. It is found that the ductile brittleness. Therefore, this fact may be used to measure materials are having low angle of internal friction. brittleness. In this case the brittleness may be repre- This method has the added advantage that the brittle- sented by the following equation: ness of a substance (which is found to be lower-at a

B3 = cr c -- o', higher confining pressurek can be determined at any O"c d- O"t , stage, and verified from the drop in the angle of internal friction. where B4--brittleness determined from tensile . and compressive strengths; 5. Determination of brittleness from the measurement of at--compressive strength; oblique shear tr,--tensile strength. This method is similar in fundamental with the These tests may be suitable even for friable substances method of determining brittleness from Mohr's envelope like coal. as described under the previous heading. In both cases the brittleness is calculated from the angle of internal 4. Determination of brittleness from Mohr's envelope friction; only here the practical test is different and Brittleness may be determined from Mohr's envelope. simpler. The relation between the angle of oblique shear According to Mohr's 'Theory of Strength' the maxi- plane and the angle of internal friction is given below by Brittleness Determination of Rocks by Different Methods 391 well-known Mohr's stress circle. The methods are simple Heinze [10] has established a similar relation with Vick- simple but in practice it is difficult to achieve clear rup- &s micro- and macro-hardness and so-called "fissure ture plane. factor", as expressed by him through the following equation: 2~ = ~/2 - 0. Hence, R - H~,v - H~. 2-6 0 = re/2 - 2~. where R--fissure factor; H.~---Vicker's micro-hardness; 6. Deterntination of brittleness from amount offine formed H,,~Vicker's macro-hardness. in Protodyakonov Impact Test for strength of rocks The principle of this method is only mentioned here. As stated before, formation of fines depends on brittle- as the tests based on this method are still in progress. ness. Protodyakonov Impact Test [8] for strength may therefore be used to determine the brittleness. As the formation of fines depends on impact from a certain height EXPERIMENTAL PROCEDURE AND RESULTS as well as on the strength of substance subjected to im- Four different methods have been used for determin- pact, brittleness will therefore be a function of percent- ing brittleness. The tests include: stress-strain diagram, age of fine formed in Protodyakonov Impact Test as well compressive and tensile strength tests, triaxial tests for as on the strength of the substance. It may be repre- establishing Mohr's envelope and Protodyakonov Im- sented by the following expression: pact Tests. Two different types of rock were used for the B5 = qtrc purpose of the experiment; skarn and siltstone collected from Gaspe Copper Mines (Murdochville--Quebec). where Bs--brittlenessfrom Protodyakonov Impact Specimens were prepared of usual cylindrical shape with Test; diameter equal to 1 in. and height 2 in. and were fitted q--percentage of fines (-28 mesh) formed with micro-strain gages and stress-strain diagrams were in Protodyakonov Impact Test: recorded on automatic recorder. Brazilian tests were tr¢--uniaxial compressive strength. performed for determining tensile strength. For Proto- 7. Determination of brittleness from .macro- and micro- dyakonov Impact Tests irregular specimens not exceed- hardness ing 1"5 in. were used and the tests were carried out by means of a Protodyakonov apparatus. Triaxial tests Macro-indentation hardness means hardness deter- were performed for lateral pressure: 0-7.500 psi. mined from experiments performed by means of a The results ofthe tests are presented in Tables 1-4. macro- or large size indentor as opposed to microscopic, The mean of 10 tests for each rock type and each method size indentor as in the case of a micro-indentation hard- are presented separately on the tables. The following ness [9]. It is found that macro-indentation hardness is remarks, however, may be made on the test results: always lower than the micro- one, the reason being the --brittleness determined from the ratio of elastic development of more cracks in macro-test, which in- strain to total strain is much higher than that from creases the area of the impression. Again, as the develop- energy ratio, i.e. B t > B_, (Table 1). ment of cracks is a direct function of brittleness, the dif- --different concepts of brittleness follows different ference between the micro-indentation and macro-in- trends. dentation hardness values may be taken as a measure of --it is interesting to note that brittleness determined brittleness. This method is less precise. The equation from the angle of internal friction read off from Mohr's may be deduced as follows: envelope at a, = 0 (Fig. 2 and Table 3) is almost identi- B~ - H~, - H cal to that determined from compressive and tensile K strengths (Table 2). where B6--brittleness from macro- and micro-hard- --brittleness of skarn is much higher than that of silt- ne ss; stone when determined from Protodyakonov Impact H,--micro-indentation hardness: Test; however, they are almost comparable, when deter- H--macro-indentation hardness: mined from Mohr's envelope from compressive andten- K--constant. sile strengths, and from stress-strain diagram.

TABLE 1. BRITTLENESSDETERMINATION FROM STRESS-STRAIN DIAGRAM

Total energy supplied Elastic Brittleness Ultimate Elastic up to breaking energy at the W,. x 100 strain strain point breaking point B1 - ~'' x 100 B., E, E, w, w,, ~' w,. Rock type It~cm/cml (l~cm cml tcm/kg) (cm/kg) (',',o) (%)

Skarn 793 450 3.8807 1.5233 56-74 39.25 Siltstone 851 414 2.2770 0-6986 48.71 30-70 392 V. Hucka and B. Das

TABLE 2. BRITTLENESS FROM COMPRESSIVE AND TENSILE STRENGTH CONCLUSION Brittleness At the present moment the term brittleness is used not

O"c -- O" t Compressive Tensile B 3 - x 100 exactly in a uniform way. The values of brittleness are, strength a, .strength ~rc ~'c + fir therefore, not identical. It appears that like different Rock type (kg/cm 2) (kg/cm 2) (%) types of strength it would be better to define different types of brittleness, e.g. brittleness based on strain ratio, Skarn 2323 229 82'06 Siltstone 2000 217 80.40 brittleness based on energy ratio, etc., as discussed in this paper. Each will have its use in science and technology depending on practical utility. TABLE 3. BRITTLENESS FROM MOltR'S ENVELOPE

Brittleness tan 0 Received 10 March 1974. Angle of B4 =- × 100 Rock type internal friction 1 + tan-' 0 (0) where 0 is at a, = 0

Skarn 60 ° 86.6 REFERENCES Siltstone 55 ° 81-91 1. Het6nyi M. Handbook of Experimental Stress Analysis, p. 15. John Wiley, New York (1966). TABLE 4. BRITTLENESS FROM PROTODYAKONOV IMPACT TEST 2. Morley A. Strength of Materials, p. 35. Longman, Green. London (1944). Percentage of fines Uniaxial 3. Obert L. and Duvall W. I. Rock Mechanics and the Design of Struc- ( - 28 mesh) after 5 compressive tures in Rock, p. 278. John Wiley, New York (1967). impacts strength 4. Ramsay J. G. Folding and Fracturing of Rocks, p. 289. McGraw- q a~: Brittleness Hill, London (1967). Rock type (%) (kg/cmj B~ = q. ac 5. Glossary of Geology and Related Sciences, Amer. Geolog. Inst., Washington D.C. (1960). Skarn 7.54 2323 17,515 6. Coates D. F. Experimental criteria for classification of rock sub- Sihstone 4.28 2000 8560 stances. Int. J. Rock Mech. Min. Sci. 3, 181-189 (1966). 7. Baron L. I. Determination of Properties of Rocks (in Russian). Goz- gotekhizdat, Moscow (1962). --although the value of different types of brittleness 8. Protodyakonov M. M. Mechanical properties and driUability of are different it is interesting to note that in all different rocks. Proc. 5th Spnp. Rock Mech., 103-118, University of Minnesota (1963). methods the values of brittleness of skarn are found to 9. Honda H. and Sanada Y. Hardness of coal. Fuel 35, 451 (1956). be higher than that of siltstone. I0. Heinze G. Bergbau Archly 19, 71-93 (1958). 本文献由“学霸图书馆-文献云下载”收集自网络，仅供学习交流使用。

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