Sedimentary Geology, 10 (1973) 239--247 © Elsevier Scientific Publishing Company, Amsterdam -- Printed in The Netherlands

FATIGUE EFFECTS IN QUARTZ SAND GRAINS

A.J. MOSS Sediment Transport Group, Division of Soils, CSIRO, Canberra (A.C.T., Australia)

(Accepted for publication October 17, 1973)

ABSTRACT Moss, A.J., 1973. Fatigue effects in quartz sand grains. Sediment. Geol., 10: 239--247.

Particles of quartz sand from a stream draining granite were found to exhibit note- worthy effects of fatigue. Both repeated static loading and collective movement in water weakened the particles markedly. This weakening must have significance in nature, where repeated stressing occurs in many environments, particularly in soils and during bed-load motion in both air and water. Tectonic movements may also create fatigue effects in sand grains. Fatigue effects appear also to be sufficiently pronounced to be significant in some industrial processes involving the use of sand.

INTRODUCTION

Fat igue is the progress ive decrease in a p r o p e r t y due to r epea t ed stress (Gray , 1960) .

The m o s t fami l ia r exam p l e s of fa t igue are a l te ra t ions in s t reng th and e las t ic i ty o f solid ob jec t s b y r epea t ed app l ica t ions of stresses t oo small, individual ly , to cause f rac ture , unt i l such ob jec t s are so w e a k e n e d t h a t t h e y can be b r o k e n re la t ive ly easily. A t and near the ea r th ' s surface r epea t ed stressing, resul t ing f r o m m a n y causes, is ub iqu i tous .

Qual i ta t ive evidence exists to indica te t ha t the e f fec t s o f na tura l fa t igue are p resen t in var ious f o r m s o f quar tz . Pebbles of vein quar tz or large sand grains, p ro jec t ing f r o m exposu res of gravel beds, c o m m o n l y can be b r o k e n in t w o wi th the fingers. In m a n y cases the f rac tures in te rsec t the surfaces of part icles a long lines fo l lowing the junc t ions o f air and mat r ix . These pebb les m u s t have been very m u c h s t ronger when original ly emp laced in the gravel. In sou theas t England , f l int pebb les were observed b y the a u t h o r to d isplay this p h e n o m e n o n very m a r k e d l y , even if p ro jec t ing f r o m the faces o f man- m a d e excava t ions on ly a few tens o f years old.

T h a t grani t ic qua r t z o f sand size exh ib i t ed fa t igue e f fec t s in s t r eams was suspec ted b y Moss (1972b) . La te r e x p e r i m e n t a l s tudies p rov ided m o r e de- f ini t ive evidence t ha t these grains were highly suscept ib le to fa t igue (Moss et al., 1973) . F r a g m e n t a t i o n loads, the s ta t ic loads unde r which individual par-

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ticles break into smaller fragments between parallel surfaces of hard steel (Moss, 1972a), were measured for batches of particles before and after being rotated with water for periods of hours in a sealed drum. Despite losses resulting from breakage (which, in the absence of fatigue, should, on average, make the surviving grains stronger), after some experiments the values for fragmentation load fell overall.

If the fatiguing of rocks or minerals at or near the earth's surface is widespread and well developed, then its effects must be important because any effect which facilitates breakage will aid in reduction of particle size and thus ease the task of erosive processes. The purpose of the experiments reported here is to a t tempt to determine whether or not granitic quartz can be sufficiently weakened by repeated stressing to enable the natural signifi- cance of the effects of fatigue to be assessed.

MATERIALS

The materials used were separated from a single large savnple of gravel, derived almost entirely from granite, from the headwaters of Gibraltar Creek, A.C.T. Natural breakage of this material was studied by Moss (1972b) and sieve fractions from the same sample were used for extensive experimen- tation by Moss et al. {1973).

APPARATUS

The main apparatus used has already been described (Moss, 1972a). It was a small unconfined compression-test machine in which hard-steel frustra re- place the plattens. This modification facilitates the loading of individual sand grains. The other major item was a sealable steel drum (Moss et al., 1973), one metre in circumference, which was rotated about its axis at one revolu- tion per second. In it, charges of sand and water could be processed.

RESULTS

The effect of cyclic static loading on individual grains was first tested, using the unconfined compression-test machine. Two batches of 200 granitic quartz grains from the 1.19--1.41 mm sieve fraction were used. Grains of the first batch were loaded individually with the machine set at a loading rate of 1.524 mm/min until breakage occurred (deformation of the proving ring, of course, compensated for most of the piston advance). Grains of the second batch were, again, individually loaded and at the same rate but, instead of being loaded directly to failure, they were cycled thus:

0 -~1-~ 0 -~1-~ 0-+ 2-+ 0-+ 2-~ 0-+ 3-* 0-+ 3-+ 0-+ 4-+ . . . kg

This cycling continued without changing grain orientation until failure oc- curred.

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The mean fragmentation load (the load at which breakage occurs) of the uncycled batch was 3.61 kg whereas that of the cycled grains was 3.04 kg. Despite the fact that 32 of the 200 nominally cycled grains were not actually cycled because they failed before the load reached 1 kg for the first time, these means differed at between the 1% and 21/~% levels of significance. Even more significant, physically, was the fact that 21 of the 200 cycled grains failed at loads which, in previous cycles, they had successfully withstood.

The foregoing result shows that, even with a very small number of static loading cycles~ the investigated particles were highly susceptible to fatigue.

The effect of repeated light stressing, caused by inter-particle collisions in moving water, was next tested. The rotating drum was charged with 6 1 of water and 800 g of the 1.19--1.41 mm fraction from the large gravel sample. This fraction contained about 65% granitic quartz. After a 4-h run in the drum, the solids were hand-sieved through the 1.19 mm sieve. The material remaining on the sieve was weighed and, after a small sample, for fragmenta- tion load studies, had been taken, was returned to the drum for the next run. This procedure was repeated for thirty runs totalling 120 h (approximately 450 km of travel). Unavoidably, as breakage and repeated sampling caused losses, the sand charge decreased during the experiment. Of the original 800 g charge only 292 g survived the whole thirty runs. Thus the number of collisions per grain per unit time must have gradually decreased.

Fig. 1 and 2 summarize the results obtained, Fig. 1A shows percentage weight losses per 4-h run plotted against running time. The losses are for all particle types but it has been shown (Moss et al., 1973) that, for this mate- rial, proportional quartz losses do not differ significantly from the overall losses. After giving values of 20% and 8% in the first two runs, losses per run fell less rapidly with time and, after thirty runs, were still nearly 1%. In the rotating drum, each grain must collide with others several times per second. Because of the large number of collisions experienced by each grain, one would expect, after a single 4-h drum run and in the absence of fatigue effects, that breakage would be essentially finished. Thus the loss figures, taken alone, suggest that fatigue effects are significant.

It may be expected that, in any population, the weakest particles will be destroyed preferentially by any process not capable of destroying all the particles. If the effects of fatigue are absent then, after such selective break- age, the surviving particles should, on average, have higher fragmentation loads than those of the original population. A plot of mean fragmentation load against number of drum runs (Fig. 1B) shows that, for the experimental quartz, this is not so. In fact, the mean fragmentation load falls very sharply for the first few runs. Moreover, it is surprising that these were the runs in which losses were high. After thir ty runs the mean value was still falling slightly. Again, this result bespeaks a major fatigue effect on the surviving grains; the mean fragmentation load has fallen, overall, from close to 3.0 kg to less than 2.2 kg.

"Weak" particles were defined arbitrarily as those with fragmentation load

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Fig. 1. Trends shown during sequence of thirty 4-h drum runs using 1.19--1.41 mm Gibraltar Creek material and water• A. Percentage loss per 4oh drum run against number of drum runs. B. Changes in mean fragmentation load of granitic quartz against number of drum runs. C. Changes in percentage of "weak" granitic quartz grains (fragmentation load <0.25 kg) against number of drum runs.

values o f less than 0 .25 kg. T h e y cons t i tu ted a b o u t 5% o f the original mate- rial. If fat igue e f fec t s were n o t present these " w e a k " particles should have been preferent ia l ly r e m o v e d in the early runs and n o t replaced• Fig. 1C s h o w s their p r o p o r t i o n p lo t ted against n u m b e r o f drum runs. Af ter the first run, their p r o p o r t i o n did, indeed, fall to a b o u t 4% but, thereafter , increased fairly rapidly to 12.5% and remained near this f igure for the rest o f the e x p e r i m e n t . This result s eems expl icable o n l y in t erms o f fatigue• Presuma- bly , as the init ial ly present w e a k grains are broken , t h e y are replaced by f a t i g u e - w e a k e n e d grains that , previous ly , were stronger.

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Fig. 2. Fragmentation-load distributions for granitic quartz of the 1.19--1.41 mm sieve frac.tion shown as cumulative curves. A. For 700 grains of the parent material from Gibraltar Creek. B. For 250 grains surviving in the original sieve fraction after one 4-h drum run with water. C. For 250 grains surviving in the original sieve fraction after thirty 4-h drum runs. D. Calculated distribution after thirty 4-h drum runs assuming that fatigue effects were absent. Calculation was based on known breakage losses.

Fig. 2 shows cumula t ive f r a g m e n t a t i o n load curves for the original mate - rial (A), survivors a f t e r one d r u m run (B) and survivors a f t e r t h i r t y d r u m runs (C). By assuming tha t , in the absence o f fa t igue effects , the weake r grains are p re fe ren t i a l ly d e s t r o y e d one can calcula te a d i s t r ibu t ion for the f r a g m e n t a t i o n load of the survivors of t h i r ty d r u m runs. This is also shown (D). The curves suggest t h a t all, or near ly all, o f the surviving grains were w e a k e n e d ; process ing causes the ent i re cumula t ive curves to m o v e to the left . C o m p a r e d wi th the original mate r ia l the 4-h curve shows a slight def ici t o f weak grains, bu t the 120-h curve shows a ma jo r bui ld-up o f weak grains. The ca lcula ted , fa t igue-f ree , 120-h curve differs great ly f r o m the e x p e r i m e n t a l 120-h curve. Ev iden t ly fa t igue ef fec ts have m o v e d the mean f r a g m e n t a t i o n load f r o m 5.02 kg to 2 .14 kg, a r e d u c t i o n b y a f ac to r o f 2 .34. The 90-per- cent i le has been m o v e d f r o m 8.39 kg to 4.69 kg and the 10-percent i le f r o m 2.80 kg to 0 .24 kg. T h e fa t igue e f fec t mus t t he re fo re have been large.

Studies b y Moss (1966) and Moss et al. (1973) have shown tha t grani t ic qua r t z b reaks readi ly because the grains are criss-crossed wi th pre-exis t ing, par t ia l ly hea led f rac tures . Such part icles, w h e t h e r originally monoc rys t a l l i ne or po lycrys ta l l ine , m a y be regarded as consis t ing of n u m b e r s o f re la t ively s t rong v o l u m e e l emen t s jo ined across re la t ively weak crack interfaces . A grani t ic quar tz grain will t end to c o n c e n t r a t e stress a long such cracks and,

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more particularly, along lines where cracks join. Thus, if the grain is stressed, such cracks will be "worked", bonding across them will be weakened and the whole grain will become more readily breakable. Some cracks may become virtually bond-free and the volume elements on either side of them will be able to slide, relative to each other, for short distances along the crack inter- face. During loading and unloading discrete deformations can then be ex- pected to occur as limiting friction, along crack interfaces, is overcome. Many quartz sand grains show what are apparently such effects.

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Fig. 3. Behaviour o f a proving ring pressing u p o n a single quartz sand grain, in an uncon- f ined compress ion test machine , during a loading and unloading cyc le at a cons tant p i s ton speed o f 0 . 3 0 5 m m / m i n . The ring was k n o w n to f o l l o w H o o k e ' s Law c lose ly and load was used to measure its de format ion . The t w o major deviat ions (at 8 .9 kg during loading and 1.5 kg during unloading) are therefore attr ibutable to discrete de format ions o f the sand grain. The grain was from the 1 . 6 8 - - 2 . 0 0 m m fract ion o f gravel from Gibraltar Creek, A.C.T.

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An extreme case in which discrete deformation occurred during loading and unloading is shown in Fig. 3. Load is plotted against time for a proving ring pressing upon single, rather equant, quartz grain from the 1.68-- 2.00 mm fraction. This particle was loaded to about 10 kg and unloaded again a number of times in the same orientation before finally being frac- tured under a load of 18.48 kg. Loading rate was 0.305 mm/min. The figure records a single loading and unloading cycle. The proving-ring deformation closely followed Hooke's Law until, at a load of 8.9 kg, the dial needle suddenly stood virtually still for about half a minute. The grain, not the proving ring, was accommodating the advance of the piston. On further loading, Hooke's Law was closely followed once more. The law was also followed during unloading until a load of 1.5 kg was reached when the needle stood still for about half a minute once more. Thereafter the loading and unloading curves were almost coincident

The loading deformation shown by this particle became better defined as cycling proceeded. Also the loading and unloading deformations did not always occur at the same loading, the former varying between 8.1 and 8.9 kg and the latter between 1.4 and 1.9 kg. There can be little doubt that the discrete unloading deformation involved the reversal of the internal relative movements that brought about the discrete loading deformation.

DISCUSSION

Moss (1972b) considered the possibility that the results of his fragmenta- tion-load studies of quartz from the Murrumbidgee River and its tributaries were significantly affected by fatigue. Breakage preferentially removes the weaker grains from a population. Therefore, in the absence of fatigue, com- parison of fragmentation-load data for two points on a stream enables the amount of breakage that has taken place between those points to be esti- mated. The effect of fatigue is to move the whole fragmentation load distri- bution to lower values. Therefore, breakage-loss estimates made by Moss (1972b}, large though they were for coarse granitic quartz, must still have been underestimates of the actual breakage losses.

More generally, the results show that granitic quartz grains are so highly susceptible to fatigue that its effects must be important in nature. The presently reported laboratory cycling is minor compared with the natural cycling which can take place during long periods of time. Thus stresses, too small to break particles immediately, must, nonetheless, be able to weaken them gradually and thus to facilitate their ultimate breakage.

Little doubt remains that fatigue weakening of granitic quartz grains takes place in streams. If fatigue effects are present in streams, then they must also have importance on beaches and in the more dynamic near-shore environ- ments. Fatigue could also be expected to be effective and rapid in quartz sand blown by wind.

In soils, cyclic stressing of particles, due to several causes, is widespread.

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In the present context, cycling due to freeze and thaw seems likely to be important. However, this is but one example of the coming and going of cementing materials. Hence, such stressing may not be confined to ice ac- tion. In thin sections of soil materials cemented with iron oxide, the author has commonly observed quartz grains which obviously have been fragmented in situ.

During long periods of time such processes as wetting and drying, varia- tions in temperature, mass movement (including hill-creep), loading and un- loading of superincumbent sediment, or various biological activities may all give rise to cyclic stressing. Persistence of forest cover in an area for a long period could repeatedly change the stress fields of quartz grains in the soil, by virtue both of boles occupying different positions and of major roots growing and rotting in different positions at different times.

Examples of fatigue weakening resulting from a particle's being at the junction of two environments, such as air and soil, have already been given. As particle size decreases such effects must decline but may still be impor- tant in the sand-size range. In this context, tillage is of interest because it not only causes direct stressing but changes the physical environments of parti- cles from year to year.

Tectonic activity could also cause cyclic stressing of sand grains. More particularly, near active faults, stress field changes must occur fairly fre- quently. In this context it is of interest that, in a relatively homogeneous sandstone, the percentage of quartz grains showing undulose extinction was found to increase with angle of dip and to rise to high levels in the close proximity of faults {Connolly, 1965).

Quartz-rich sand is used in many industrial processes. Some of these in- volve repeated stressing. Between pit source and delivery site concreting sand, for example, is involved in several stressing processes. If geologically nascent sands are used, it may be pertinent to enquire to what extent fatigue and breakage may alter them.

The survival of large amounts of quartz of medium-sand grade and smaller amounts of coarser quartz in mature detritus implies that, in nature, some restraints on the action of fatigue must exist. Undamaged quartz is very strong. Consequently, if particles lack significant internal flaws, minor stress- ing will probably but little affect them. After each stressing their recovery will probably be virtually complete. Also, the present results suggest that, as the treatment of particle populations progresses, the overall effect of fatigue lessens. Study of the breakage characteristics of quartz from a mature gravel has revealed that .particles smaller than 1 mm in diameter consisted domi- nantly of plutonic quartz whereas particles larger than 2 mm in diameter were " sound" quartz types (such as vein quartz). "Sound" quartz variants are normally much less damaged internally than is plutonic quartz. In the range between 1 and 2 mm a transition of quartz types occurred. It is well known that quartz pebbles of " sound" types can survive two or more major sedimentary cycles (Moss, 1966).

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Possibly some quartz grains may be made stronger, at least initially, by repeated stressing. This could sometimes happen if the opening of cracks relieved residual strain. However, no evidence suggests that this happens extensively. In nature, a two-stage strengthening effect seems more likely to be important . First, fatigue, acting either during transport or while grains are emplaced in stationary positions, may cause cracks to reach the grain sur- faces. Second, quartz may be precipitated in these cracks, thus greatly strengthening the grains. Such a precipitation could take place readily in many soils or in sandstones. Possibly, the quartz in some strongly abrasive sandstones (e.g., millstones) may have been subjected to such two-stage strengthening.

ACKNOWLEDGEMENTS

Miss M.P. Green, Messrs B.E. Butler, P.I.A. Kinnell, J.R. Sleeman and Dr. P.H. Walker kindly read the manuscript and made helpful suggestions. I also thank Dr. J.E. Sanders who suggested many improvements to the text on behalf of the editors.

REFERENCES

Connolly, J.R., 1965. The occurrence of polycrystallinity and undulatory extinction in quartz sandstones. J. Sediment. Petrol., 35: 116--135.

Gray, H.J., 1960. Dictionary o f Physics. Longmans, Green, London, 544 pp. Moss, A.J., 1966. Origin, shaping and significance of quartz sand grains. J. Geol. Soc.

Aust. , 13: 97--136. Moss, A.J., 1972a. Technique for assessment of particle breakage in natural and artificial

environments. J. Sediment. Petrol., 42: 725--728. Moss, A.J., 1972b. Initial fluviatile fragmentation of granitic quartz. J. Sediment. Petrol.,

42: 905--916. Moss, A.J., Walker, P.H. and Hutka, J., 1973. Fragmentation of granitic quartz in water.

Sedimentology, 20 (in press).