ENGINEERING GEOLOGY ELSEVIER
Engineering Geology37 ( 1994) 149-159
The influence of cataclasis on abrasion resistance of granitic rocks used as road surface aggregates Bjorge Brattli Department of Geology and Mineral Resources Engineering, Universityof Trondheim, The Norwegian Institute of Technology, 7034 Trondheim, Norway (Received November 2, 1993; revised version accepted February 3, 1994)
Abstract
The research described in this paper is performed on cataclastic rocks of granitic composition. The petrography is described and classified according to Higgens. All rocks appear with primary cohesion and range from cataclasite to mylonite gneiss. A crystallinity index for quartz minerals based on the degree of resolution of the d, X-ray reflection at 1.3820A is examined. It is found that the crystallinity index corresponds fairly well with the degree of distruction/annealing in cataclastic rocks. It is concluded that the index can be used as a quantitative measure of the state of ductile deformation in cataclastic rocks. However, an attempt to explain the relationship between the abrasion value, i.e., the hardness of the rocks, and the crystallinity index as a simple linear association, failed. It is believed that this at least partly is due to the grain size distribution in the rocks which has a stronger impact upon the strength properties than the ductile deformation, causing scatter in the regression model.
1. Introduction
The object of this paper is to draw attention to the possible relationship between ductile deformation and some mechanical strength properties of rocks. A relationship between mechanical strength and brittle deformation represented by joints and cracks in the materials has been demonstrated in several papers (e.g., Griffith, 1920, 1924; Spunt and Brace, 1974; Onodera and Asoka Kumara, 1980). However, investigations of how the ductile deformation affects the strength properties in the rocks are sparse. A study carried out by Brattli (1990, 1992), on how geological factors act upon mechanical properties of some important road surface aggregates, revealed a possible relation between the abrasion 0013-7952/94/$7.00© 1994ElsevierScienceB.V. All rights reserved SSDI 0013-7952 (94) 00007-0
resistance (i.e., the hardness of the rock) and the type of ductile deformation. The mechanical parameters which were analyzed were the impact value, the flakiness value and the abrasion value. The parameters are international mechanical strength indices which are used to describe the suitability of road surface aggregates. Quantifiable petrological parameters were the mineralogy of the rocks and the mean grain size. In addition, the micro textures, like grain shape, grain boundary relations, mineral orientation, and degree of alteration and deformation, have been qualitatively described. The relationship between the mechanical strength indices and the geological parameters was investigated by multiple regression analyses and the results have been discussed and reported in Brattli (1990, 1992). The investigated rocks were all crushed igneous
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rocks, which have been divided into two groups, one which consists of mafic rocks and one which includes intermediate to felsic rocks. A complete gradation from fresh to extreme metamorphosed samples exists. Two of the samples in the felsic group have suffered intense deformation under conditions where the recrystallization processes are low, i.e., high pressures and relatively low temperatures. Both rocks show a higher abrasion resistance (that means a higher hardness) than expected from texture (mean grain size, etc.) and mineralogy. As high quality aggregates are in short supply, the observation was considered as important. It was decided to supplement the analyzed samples with different kind of cataclastic rocks in an attempt to find out if there could be any systematic variation between the degree of ductile deformation and the hardness in the rocks.
2. Rock sampling The rocks are all quartzo-feldspatic in composition (Table 1). The samples have been collected from thrust/fault zones in different parts of Norway, except for one (1195501), which was collected from an undeformed felsic intrusive. It has been stressed that the deformation of the rocks should represent various physical conditions, i.e., various temperatures, effective stresses, etc., which affect the genesis of cataclastic rocks. In order to distinguish between different types of cataclastic
rocks, the samples have carefully been studied under the microscope. Description and classification of thin sections of the rocks are according to Higgens ( 1971 ).
3. Description of microstructures Two of the rocks (samples 1621501 and 1413501, Table 1) belong to the series where neomineralization-recrystallization is subordinate to cataclasis. Sample 1621501 has a typical fluxion structure with small porphyroclasts (generally larger than 0.2 mm; see Fig. 1 ). The porphyroclasts are mostly feldspar grains showing twinning and fractures. The quartz is converted to a fine-grained aggregate, which together with recrystallized epidote constitute the fluxion structure. Some quartz may be recrystallized, but the dominant texture is cataclastic. The rock is classified as a mylonite. Sample 1413501 represents an intensely fractured rock (Fig. 2). The fragments may range in size from visible to naked eye to about 0.2 mm. The large feldspar fragments often appear with microfractures. The grains and fragments show no sign of being sheared or rolled and they appear without any orientation. Some quartz may be recrystallized, especially along microfractures which seem to be filled with neomineralized quartz. As the rock totally lacks any fluxion structure, it has been classified as a microbreccia. The other rock samples (1924503, 1228501, 1246504, 1263504, 1130501, see Table 1) all belong
Table 1 Important parameters of the quartzose rock Samples
Abrasionvalue Crystal index
Meangrain size Quartz (mm) (%)
Feldspar (%)
Mica (%)
1228501 1246504 1621501 1263504 1130501 1413501 1924503 1195501
0.24 0.29 0.30 0.33 0.34 0.37 0.42 0.45
0.031 0.130 0.125 0.160 0.107 0.250 0.197 0.400
62 72 41 67 38 73 44 57
5 10 5
7.58 7.55 5.40 7.93 8.71 6.89 7.36 9.82 10.0
28 17 23 28 31 22 38 35
14 7 6
E p i d o t Rocknames (%)
30 2 28 3 8
Blasto-mylonite Mylonite gneiss Mylonite Mylonitegneiss Mylonitegneiss Micro-breccia Mylonitegneiss Granite Euhedral quartz
B. Brattli/Engineering Geology 37 (1994) 149-159
151
Fig. 1. Mylonite. Porphyroclasts of twinned and fractured feldspar in a matrix of fine-grained cataclastic quartz and recrystallized epidote (cross polars × 40).
Fig. 2. Microbreccia. Fragments of feldspar grains often with microfractures, appear in a matrix of deformed quartz. The rock totally lacks fluxion structure (cross polars x 20).
to the series where neomineralization-recrystallization is dominant over cataclasis. The rocks resemble mylonite or protomylonite, but the texture is a result of combined cataclasis and crystoblastic processes. Most of the samples appear with augen structure in a surrounding, more or less recrystallized and neomineralizied groundmass. The augen
are usually feldspar and although some recrystallizaton has taken place, they preserve evidence of typical cataclastic textures. The recrystallization in the groundmass varies considerably. In sample 1924503 (Fig. 3) quartz forms lenses of polygonal grains, which altemate with thin bands of partly not recrystallized minerals. In sample 1130501 the
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B. Brattli/Engineering Geology 37 (1994) 149-159
Fig. 3. Lenses of recrystallized/neomineralized polygonal quartz, alternate with thin bands of very fine-grained, more or less mylonitized minerals (cross polars x 20).
texture seems to be even more intense recrystallized as the minerals appear as stable grains throughout the whole thin section area. The rocks have been classified as mylonite gneiss and blastomylonite according to the approximate size of most porphyroclasts, the quantity and the mean grain size of the matrix (Table 1). The undeformed rock is represented by sample 1195501. Thin section studies indicate an almost primary texture with little evidence of deformation. Some quartz grains may appear with a slight undulose extinction and the grain size varies slightly. But no minerals appear with any elongation or preferred orientation. The rock is classified as a granite, according to Le Maitre (1989).
4. Abrasion value
As mentioned above, the mechanical parameter which is of particular interest in this investigation is the abrasion value. This parameter measures the material's abrasive durability. This describes the crushed rocks (aggregates) resistance to mechanical strength wear. The method is, together with the impact test (see intro-
duction), mainly applied as an assessment of the quality of additive to bituminous road materials. A representative proportion of aggregate clasts from the fraction 11.2-12.5 mm is cast firmly on a square plate. The grains are pressed against a rotating plate coated with a standard abrasive powder. Wear or abrasion is defined as the sample's loss in volume in cubic centimeters within a given time. Low abrasion values means high hardness. For further description of the test procedure, see Hrbeda (1989). In Norway the road authorities use the following classification, based on the abrasion values: <0.35 0.35-0.45 0.45-0.55 0.55-0.65 >0.65
very good good medium good poor very poor
The results of the abrasion tests are given in Table 2. The values range in order from 0.24-0.42 with a mean value of 0.32. Five of the cataclastic rock samples are classified as very good (<0.35), while two are classified as good. In a previous investigation on 21 granites (Brattli, 1990), the
B. Brattli/Engineering Geology 37 (1994) 149-159 Table 2 Classification of the cataclastic rocks based upon the abrasion values Samples
Abrasion value
Names
Quality
1228501 1246505 1621501 1263504 1130501 1413501 1924503
0.24 0.29 0.30 0.33 0.34 0.37 0.42
Blastomylonite Mylonite gneiss Mylonite Mylonite gneiss Mylonite gneiss Micro breccia Mylonite gneiss
Very good Very good Very good Very good Very good Good Good
abrasion value ranged from 0.37-0.71, with a mean value of 0.47 (Table 3). None of the rock samples could be classified as very good.
5. An index of crystallinity for quartz Since the object of this investigation is to examine any possible relationship between the degree of ductile deformation in cataclastic rocks and the hardness, the qualitative description of the deformation should be supplemented by a quantative Table 3 Classification of the granites based on the abrasion values Samples
Abrasion value
Names
Quality
0402514 0135505 0926503 1871503 0711506 0417501 0211501 0602501 1630505 0928503 0928501 0928502 0115501 0115503 1519501 0935501 0926501 0919501 0113508 0103501 1842501
0.37 0.38 0.39 0.40 0.41 0.42 0.42 0.43 0.45 0.45 0.48 0.49 0.49 0.49 0.51 0.52 0.52 0.53 0.54 0.54 0.71
Granite Granite Granite Granite Granite Granite Granite Granite Granite Granite Granite Granite Granite Granite Granite Granite Granite Granite Granite Granite Granite
Good Good Good Good Good Good Good Good Medium good Medium good Medium good Medium good Medium good Medium good Medium good Medium good Medium good Medium good Medium good Medium good Poor
153
one. Minerals that have suffered deformation will exhibit a distorted crystal lattice. As the deformation proceeds (especially at low temperatures) the lattice distortion will increase. This will affect the X-ray diffraction pattern of the mineral. Several authors (Hathaway, 1972; Fournier, 1973; Murata and Norman, 1975, 1976) have shown that a profile of certain X-ray diffraction peaks, particularly a set of five peaks at 20 of 67 ° to 69 ° CuK~ radiation, is sensitive to the crystallinity of quartz in deep-sea sediments. In zoned agate nodules, consisting of a rim of chalcedony around a solid core of coarsely granular quartz, Murata and Norman (1976) found that the crystallinity of the coarse quartz of the core is high and virtually constant (9.0-9.3") whereas that of the chalcedonic rim ranges from < 1.0 to 4.7. They further demonstrated that quartz from granite and pegmatite exhibit a rather high crystallinity index (8.4-9.1), while clear euhedral quartz shows the maximum resolution of this reflection. Shoval et al. (1991) proposed a semiquantative method for measuring quartz-crystallinity by using infrared spectroscopy. They found a good correlation between the IR-results and the crystallinity measured by X-ray diffraction. Murata and Norman pointed out that the index seems to be a function of grain size (up to about 1 ~ diameter), and also a function of lattice distortion induced by mechanical stress. However, a relation between the crystallinity index of quartz and the degree of ductile deformation has never been tested. It was, therefore, of particular interest to see (a) if such a relation exists and (b) if so, could the crystallinity index be used to characterize quantitatively the degree of ductile deformation in the cataclastic rocks and hence the possible relation between the deformation and the abrasion value (i.e., hardness of the rocks).
6. Analytical procedure The fine grinding and mounting of the samples in an aluminium holder were performed according to common laboratory procedures. The 20 interval *The crystallinity index ranges from < 1.0 to 10.0.
154
B. Brattli/Engineering Geology 37 (1994) 149-159
of 60 ° to 70 ° is scanned at 1/4 ° per minute with nickel filtered copper radiation. A counting rate of 320 counts per second was used. For every sample three separate slits or separate mounts were made, and the crystallinity index is the mean value of the three determinations. The crystallinity index is calculated from the intensity of the (212) peak at 67.74 ° according to the procedure given by Murata and Norman (1976). The equation for the crystallinity index is: C.L = lOa/b × F
where: a = the height (intensity) of the peak at 67.74°; and b = the total height of the peak above background. In order to express crystallization on a familiar scale the maximum determined value for the crystallization index is raised to 10 by using a scaling factor F. This factor probably varies from one diffractometer to another. In this case the maximum index determined on a clear euhedral quartz crystal is 5.8. The value is raised to 10 by setting F e q u a l to 1.724. The spectrometer tracings of the studied rocks are shown in Fig. 4(a-i). The relative intensity of the peaks are arranged in order of increasing crystallinity of quartz from (a) to (i). The determined indices are given in Table 1.
7. Results The crystallinity index ranges in order from 5.4-9.82. The lowest values, 5.4 and 6.89, are from the rocks where cataclasis clearly dominate over recrystallization/neomineralization, (samples 1621501 and 1413501, see thin section descriptions). The rocks are classified as mylonite and microbreccia. It is interesting to see that the mylonite has a lower crystallinity index than the microbreccia, which means that the crystal distortion must be greater. However, during the formation of a mylonite, the applied stress is to a larger extent stored in the crystal lattice, causing distorting and bending of the minerals, while during the formation of a microbreccia, much of the applied stress is released by crushing. The crystallinity index values ranging from 7.36
to 8.71 are from the rocks where the annealing processes dominate over the destruction processes. Going from the samples 1924503 to sample 1130501 (C.I. =7.36-8.71) there is an increase in growth of new minerals, especially quartz. In 1924503 (C.I. = 7.36) neomineralizied quartz appears in thin lenses and bands in a surrounding, very fine-grained groundmass. The matrix may have suffered recovery and to some extent primary recrystallization, but most usually it appears without any pronounced neomineralization. In sample 1130501 (C.I. =8.71) the texture is dominated by quartz which appears as stable aggregates of more or less polygonal grains with homogeneous extinction. According to Bell and Etheridge (1976), Hobbs et al. (1976) and Suppe (1985), this indicates far advanced neomineralized textures where primary recrystallization and normal grain growth are the dominating processes. The highest crystallinity index (C./. =9.82) is found in quartz from the granite (sample 1195501 ). The granite quartz has a considerably higher index than the most recrystallized cataclastic rock (sample 1130501). However, the index is lower than for the euhedral quartz crystal (Table 1). This is perhaps surprising, but the granitic quartz shows slight undulose extinction in thin section, which indicates some distortion of the crystal lattice, due to late deformation. This may be the reason why the crystallinity index of the granitic quartz is lower than the index of the euhedral quartz. The investigation seems to suggest an interesting relationship between the intensity of the (212) peak in quartz and the degree of cataclasis or ductile deformation in quartzo-feldspatic rocks, as studied in thin section. The X-ray determined crystallinity indices correlate fairly well with the observation of the deformation of rocks in thin section. Despite the small number of rocks which were examined, it is suggested that the crystal index can be used as a quantitative measure of the deformation/annealing in cataclastic rock.
8. Simple linear regression In order to express the possible relationship between the hardness of the rocks and the state of
155
B. Brattli/Engineering Geology 37 (1994) 149-159
f
=o
b
68
7
66 °
I 69
a
I 68
I 67
I 66 °
~1 69
b
i
i
i
68
67
66 °
C
,.,
b
6o
68
67
g
66 °
6
69
68
h
67
66 °
69
68
67
66 °
;
Fig. 4. Spectrometer tracing of the five peaks at 20 of 67° to 69°. The peak at 67.74° is measured to obtain the crystallinity index. (a) (1621501) C./. =5.40, (b) (1413501) C.I. =6.89, (c) (1924503) C.L =7.36, (d) (1246504) C.I. =7.55, (e) (1228501) C.I. =7.58, (f) (1263504) C.1. =7.93, (g) (1130501) C.I. =8.71, (h) (1195501) C.I. =9.82, (i) (euhedral quartz) C.I. = 10.
B. Brattli/Engineering Geology37 (1994) 149-159
156 0.50
9. Discussion , 1195501 .1924505
0.40 ,1413501 • 1130501
Q
• 1263504
, 1621501
0.30
• 1246500
.<
, 1228501
0.20
0.10 4.00
5.00
6.00
7.00
Crystallinity
a
8.00
9.00
I0.00
index
0.50 , }195501 , 1924503
0.40 , 1413501
,1130501 ,1263504
©
0.30 -<
, 1228501
0.20 r
0.10 ~ , , , , , , , i , , , , , , , , , E ~ , , , , r , l , l , , , , r , , , , i , , , i , , 1 1 1 0.00 0.10 0.20 0.30 Mean grain size
=
0.87
0.40 (mm)
I
0.50
Fig. 5. (a) Scatter plot of the abrasion value plotted against the crystallinity index. (b) The same parameter plotted against the mean grain size.
ductile deformation, the abrasion values have been plotted against the crystallinity indices. Figure 5a presents the scatter plot for the investigated parameters. As can be seen from the figure there is no simple linear relationship between the parameters. As several previous investigations (Olsson, 1974; Onodera and Kumara, 1980; Gosawami, 1984; Singh, 1988; Brattli, 1990, 1992) have shown that the mean grain size represents a very important geological factor acting upon the strength of the rocks, the abrasion value has also been plotted against the mean grain size (Fig. 5b). As can be seen from this figure the degree of linear association between the parameters is positive and fairly good (r = 0.87). This means that the abrasion value decreases (getting better) as the mean grain size decreases.
Comparing the abrasion values of Tables 2 and 3 it is obvious that the cataclastic quartzofeldspathic rocks represent a group or population with better abrasion values (higher hardness) than the undeformed granite, despite the fact that the mineral compositions are very similar. One reason could very well be the grain size distribution within the two rock groups. As mentioned above the strength of the rocks depends upon the grain size, diminishing as the grain size increases. In general, the mean grain size in cataclastic rocks is smaller than in granitic rocks, which also is the case in this investigation. However, some samples from the granitic group appear with a grain size which lies within the same range as the cataclastic rocks. The parameter could, therefore, not fully explain why all the samples of the cataclastic rock appear with a higher abrasive durability (lower abrasion value). Comparing the two groups, the most spectacular difference between them is the mylonitic texture in the cataclastic rocks versus the nearly undeformed texture in the granites. In order to explain how the deformation acts upon the rock strength properties during a shock metamorphism, one has to understand what is going on at the atomic scale as the deformation proceeds. The investigated rocks have suffered deformation under physical conditions where the destructive processes compete with the annealing processes. Intense deformation at low temperatures leads to very high concentration of dislocations, especially in minerals like quartz. On the atomic scale, a dislocation represents a linear region in which atoms are not in their proper crystallographic positions, that is, the atomic arrangement has been elastically distorted. In its simplest form a dislocation is the termination of an extra plane of atoms in the lattice. All materials seem to have such irregularity in the crystal structure and the linear defect can be made to move in response to shear stress, thereby producing slip within the crystal (Hobbs et al., 1976; Suppe, 1985). The stress needed to activate a dislocation source is thought to be the critical shear stress for translation gliding and hence ductile deformation of the crystal.
B. Brattli/Engineering Geology 37 (1994) 149-159
The dislocations are associated with a stress field because they disturb the normal atomic regularity in the crystal. The end of the extra half-plane in an edge dislocation causes a compressive stress field above the end of the half-plane and a tensile stress field below. The stress fields associated with the dislocations interact with each other and cause some to repel and others to attract. However, in general, the more dislocations within a crystal, the higher their total repulsion and the higher the stress required to move them. This is partly because of the force exerted on the dislocations by others, and partly because of the creation of extra segments of dislocation lines that do not lie in the slip plane and hence are difficult to move. As the deformation increases (under low temperatures), there will be formed a three-dimensional network of very tightly "bound" dislocations in the crystal which will prevent new dislocations to slip through. The increased difficulty of movements is responsible for strain hardening in crystals. In material science, cold rolling (cold working deformation) is a common method used for increasing the material strength (hardness). In pure aluminium and copper the yield strength can be increased as much as hundred times the value before cold rolling (N~ess, 1981). However, the capability of consuming shear stress by translation gliding along the atomic planes decreases. The result is a material with high hardness and low ductility. Further deformation will cause the material to break into pieces. In nature these mechanism can be compared with deformation under high shear stress and relatively low temperature. The rocks which are formed under such conditions belong to the cataclasite-mylonite series (in this investigation; samples 1621501, 1413502). The elastic distortion in the lattice also means that there is strain energy associated with a dislocation, so that the introduction of dislocations increases the free energy of the crystal. Dislocations are, therefore, unstable and if the crystal is heated, the dislocation density will decrease. According to Suppe (1985) the mechanisms of annealing take place both within the individual crystals by climb, migration and grouping of dislocation and by growth of new strain free grains at the expense of the high energy
157
deformed grains. As these processes proceed, the original properties of the materials will gradually be re-established. Rocks formed under such conditions belong to the mylonite gneiss series (in this investigation; samples 1924503, 1228501, 1246504 and 1263504). The physical conditions during the deformation are, therefore, of great importance regarding the strength properties of the rocks. The studied rocks are all more intensively deformed by ductile deformation than the granites. According to the dislocation theory it is reasonable that the group exhibits a higher abrasive strength than the more or less undeformed granites. However, as the studied rocks seem to represent different stages in the destruction/annealing processes, one should expect a systematic variation in the abrasion values when going from the cataclastic/mylonitic rocks (1621501, 1413502) to the mylonitic gneiss (1924503, 1228501, 1246504 and 1263504). Figure 5 shows that this is not true. The abrasion values for the mylonite/microbreccia lie within the same range as the mylonite gneisses. As previously mentioned the variation in the strength properties of the rocks is strongly affected by the variation in the mean grain size. Brattli (1990, 1992) pointed out that the mean grain size has a significantly greater impact on the strength properties than the variation in the mineral content within a rock group. It is reasonable to believe that the effect of the mean grain size on the strength parameters also in this case overweights the effect of the destruction/annealing prosesses. This would explain the absence of the expected systematic relation between the crystallinity index and the abrasion value. The good correlation between the abrasion value and the mean grain size also indicates that grain size is one of the main factors, not to say the main factor, controlling the strength properties within the rock group.
I0. Conclusions
(1) The crystallinity index ranges from 5.4 to 9.82. The lowest values, 5.4 and 6.89, are from rocks where cataclasis clearly dominates over recrystallisation/neomineralization.
158
/R Brattli/Engineering Geology 37 (1994) 149-159
(2) The values from 7.36 to 8.71 represent rocks where annealing dominates over destruction, this means rocks of the mylonite gneiss series. (3) The highest crystallinity index is found in quartz from the granite. The values are considerably higher than for the most recrystallized cataclastic rocks, but lower than for the euhedral quartz crystal. (4) It is suggested that the crystallinity index can be used as a quantitative measure of the deformation/annealing condition in cataclastic rocks. However, as the number of samples examined in the present work is relatively small, the examination should be confirmed by further work. (5) The cataclastic quartzo-feldspathic rocks represent a group with considerable better abrasion values, i.e., higher hardness or higher abrasive durability, than granites of similar composition. According to the Norwegian classification, 72% of the investigated cataclastic rocks are classified as very good and 28% as good. None of the samples are classified as medium good or poor. In the granite group, 38% is classified as good, 57% as medium good and 5% as poor. None of the samples are classified as very good. (6) The reason why the cataclastic rock group exhibits a higher hardness than the granite is related to: (a) the grain size distribution within the group, and the fact that the strength parameters are improving as the mean grain size decreases. In general, cataclastic rocks have smaller grain size than granite; and (b) the degree of ductile deformation. At least some of the rocks that belong to the cataclastic rock series, have a very high concentration of dislocations. As the dislocation density in a crystal increases, the capability of consuming shear stress by translation gliding along an atomic plane decreases. This leaves a material with high hardness, but low ductility. (7) The association between the degree of ductile deformation, expressed by the crystallinity indices and the abrasion values can not be described by a simple linear regression model. This is probably the result of the strong impact from the grain size on the strength properties, which in turn overweighs a possible relationship between the two parameters and causes scatter in the model.
Acknowledgements This work was financed by The Norwegian Institute of Technology, University of Trondheim. The Geological Survey of Norway (NGU) provided the aggregates for the investigation. The paper was written during a sabbatical year at Colorado School of Mines, USA. To these institutions I offer my sincere thanks. Professor Stephen Lippard kindly reviewed and improved the manuscript.
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B. Brattli/Engineering Geology 37 (1994) 149-159 Olsson, W.A., 1974. Grain size dependence of yield stress in marble. J. Geophys. Res., 79(32): 4859-4862. Onodera, T.F. and Asoka Kumara, H.M., 1980. Relation between texture and mechanical properties of crystalline rocks. Bull. Int. Assoc. Eng. Geol., 22: 173-177. Singh, S.K., 1988. Relationship among fatigue strength, mean grain size and compressiv strength of a rock. Rock Mech. Rock Eng., 21: 271-276.
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Shoval, S., Ginott, Y. and Natan, Y., 1991. A new method for measuring the crystallinity index of quartz by infrared spectroscopy. Min. Mag., 55:579 582. Spunt, E.S. and Brace, W.F., 1974. Direct observation of microcavities in crystalline rocks. Int. J. Rock Mech. Min. Sci., Geomech. Abstr., 11: 139-150. Suppe, J., 1985. Principles of Structural Geology. PrenticeHall, Inc., New Jersey, N.J., 537 pp.