Sedimentary Geology, 39 (1984) 87-93 87 Elsevier Science Publishers B.V., Amsterdam - Printed in The Netherlands

P A C K I N G IN A C L A S T I C S E D I M E N T : C O N C E P T A N D M E A S U R E S

H.S. PANDALAI and S. BASUMALLICK

Department of Applied Geology, Indian School of Mines, Dhanbad 826004 (India)

(Received March 28, 1983; revised and accepted August 11, 1983)

ABSTRACT

Pandalai, H.S. and Basumallick, S., 1984. Packing in a clastic sediment: concept and measures. Sediment. Geol., 39: 87-93.

Packing has been defined as the effective utilization of space by mutual arrangement of the constituent grains of an aggregate. The effective utilization of space is governed both by the material aspect of the constituent grains (size range, size ratio, shape, etc.) of a clastic sediment and the mechanism aspect (the manner of deposition) of the agent. Three new measures of packing have been introduced: (1) intrinsic packability factor (Pf) denoting the maximum packing attainable with a particular set of grains: (2) packing efficiency (Pc), denoting how far the agent is capable of attaining the said maximum; and (3) packing index (Pi), denoting the resultant of the material aspect and the mechanism aspect. For proper appreciation of the packing of a clastic sediment, all the three packing parameters need to be determined.

INTRODUCTION

Though pack ing has been regarded as a f undamen ta l p rope r ty of an aggregate,

there is nei ther a unique def in i t ion of the concept nor a unique measure of packing.

In their exhaust ive paper , which is still quo ted as a bas ic reference, G r a t o n and

F r a s e r (1935) def ined pack ing as " a n y manner of arrangement of solid units in which

each cons t i tuent uni t is suppor t ed and held in place in the ear th ' s g rav i ta t iona l f ield

b y tangent ia l contac t with its ne ighbours" . Obvious ly G r a t o n and F rase r (1935)

emphas ized the pure ly geometr ica l a r r angemen t aspect of the cons t i tuent par t ic les of

an aggregate. Others ( A G I Glossa ry as quo ted by Blat t et al., 1972, p. 71; Griff i ths ,

1967, p. 164) prefer red to def ine pack ing as the spacing or density pattern or spatial density. The la t ter aspect is evident ly dependen t on the a r rangement of the con-

s t i tuent part icles . W h e n a t t empts were m a d e to reduce the concept of pack ing to

ope ra t iona l procedures , invest igators have d i f fe ren t ia ted more than one p rope r ty

(Griff i ths , 1967, p. 165). The i m p o r t a n t measures of pack ing p roposed so far can be

g rouped into two categories (Table I), one emphas iz ing the spat ia l dens i ty (grain

volume) aspect and the o ther p r inc ipa l ly dea l ing with the a r rangement aspect.

003%0738/84/$03.00 © 1984 Elsevier Science Publishers B.V.

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TABLE I

Measures of packing

Spatial density aspect Arrangement aspect

Packing index (Fairbairn, 1943) Coordination number and symmetry Packing density (Scott, 1960) Packing fraction (Yerezunis et al., 1962) Concentration (Allen, 1970)

Packing index * (Emery, 1954, as referred to in Griffths, 1969) Grain volume fraction (Vinopal and Coogan, 1978) Packing density * (Kahn, 1956) A structural factor related to density * (Smalley, 1964a, b)

(Graton and Fraser, 1935)

Number and contacts per grain ** (Taylor, 1950) Shape of contact ** (Taylor, 1950)

Packing index ** (Mason, 1951, as referred to in Griffiths, 1967) Packing proximity * * ( Kahn. 1956)

* Two-dimensional areal density; ** two-dimensional arrangement.

In the case of purely geometrical arrangements of unisized spheres, it is possible

to calculate the coordinat ion number and symmetry which specify a particular

regular structure. But this is too simple a model to be of any significant use to

natural clastic sediments, which consist of irregular-shaped particles of varied size

and size range, packed in a random rather than regular structure. The arrangement

aspect is very difficult to quantify in cases of r andom structure where symmetry

characteristics are absent. As rightly pointed out by Dallavalle (1948, p. 123), no

comprehensive relationship between variables (size ratio, sorting, shape, etc.) de-

scribing a packing arrangement has thus far been established. Therefore we are

forced to use empirical and experimental approaches in evaluating packing of

natural sediments.

Packing is hereby defined as the effective utilization of space by mutual arrange- ment of the constituent grains of an aggregate. In a natural aggregate the effective utilization of space is dependent on two factors: (1) the nature of consti tuent grains

(size ratio, size frequency, shape and roundness); and (2) the mode of deposition. The grain-volume fraction, which can be easily determined experimentally, is usually regarded as a measure of packing (Vinopal and Coogan, 1978). Though grain-volume

fraction is a result of packing, it does not fully express the more fundamental aspect of arrangement, which gives rise to effective utilization of space. For example two

packs having the same grain-volume fraction need not have the same arrangement of

the constituent particles. This necessitates introduction of new measures to evaluate

the nature of packing in a natural aggregate. It is also necessary to distinguish, between close packing and open packing. It is

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proposed to define close packing as one in which the constituent particles touch one another at one or more points. Packing which does not satisfy the criterion of close

packing would be regarded as open packing. For example an aggregate of stellar bodies or an aggregate of subatomic particles in an atom may be considered as open packing. From the point of view of the presense or absence of symmetry and repetition characteristics, a packing can be regarded as ordered (" piles" of Bernal,

1965) or random ("heaps" of Bernal, 1965), respectively. It should be noted at this point that all clastic sediments have close packing, ranging from minimum density close random or "loose" (Scott, 1"960) packing to maximum density close random or "dense" (Scott, 1960) packing.

INTRINSIC PACKABILITY FACTOR

It is a common finding that mixing grains of different sizes causes an increase in grain-volume fraction (Furnas, 1929; Fraser, 1935; Yerezunis et al., 1962; Epstein and Young, 1962). The diameter ratio and the percentage of each size component play a vital role in this process. Though such increase in grain-volume fraction is a common experimental finding, it was only Yerezunis et al. (1962) who gave a satisfactory theoretical explanation for the same. The explanation given by them for binary mixtures of spheres may be rewritten for the natural sediment as follows. In one extreme, the addition of a large-particle to a small-particle regime results in the replacement of small particles producing an increase in grain volume by excluding microvoids associated with the small-particle regime which is replaced. This replace- ment process may be continued only up to that point at which larger particles are themselves arranged in dense random packing. At the other extreme, small particles can be added to an array of large particles, resulting in the partial filling of the existing voids. This addition process may be continued until the macrovoids formed by the large particles are entirely filled by small particles in dense random packing.

The reduction in space or increase in grain volume fraction is a tangible effect of packing of hetero-sized particles and a term intrinsic packability factor (P f) is proposed here to signify the maximum possible utilisation of the packing space, with a particular set of grains. Pf is given by:

xE Pf=~

Where V~ = volume occupied by a pack of constituent grains of a particular size range, packed in dense random state, and V a -- pack volume when all the grains are packed together in dense random state.

In the case of~unisized material, the value of Pf will be 1. For hetero-sized material, the intrinsic packability increases with increasing size range. Size range, size ratio, percent frequency of particles in each size class, and shape and roundness of the grain appear to be the controlling factors of intrinsic packability. However,

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the exact mathematical relationship between the intrinsic packability factor and the above-mentioned grain parameters is not yet known.

PACKING EFFICIENCY

As already mentioned all natural elastic sediments are not packed in the tightest possible manner and their packing can range from loose random packing to dense random packing, depending on their mode of deposition. For example grain flow and grain fall processes on slip faces of dunes or dune-like bodies should not be as efficient at packing arrangement as traction transport processes operating on hori- zontal or gently sloping surfaces. The term packing efficiency is used to denote how far a natural aggregate has approached the tightest possible arrangement, i.e. maximum density close packing, obtainable with that particular set of grains. Thus for a given set of particles, the packing efficiency (P~) will be given by:

where V B = bulk volume of natural aggregate of a given set of particles, and V d = pack volume when the same set of particles is repacked artificially in the dense state.

Evidently, as V B approaches V d it implies better efficiency of the depositional agent. J. Harrell (pers. commun., 1982) independently arrived at the concept of packing efficiency. He defined packing efficiency as the ratio of the minimum possible porosity of sand (estimated from volumetric porosity of an artificially compacted sand) to the actual depositional porosity for the same sand (estimated from a plane section of a sand impregnated with epoxy in the field).

PACKING INDEX

To compare the state of packing of two or more samples from two or more natural environments, packing efficiency alone is not sufficient, since the intrinsic packability of the component grains of the different samples may vary. A new measure packing index, relating both intrinsic packability and packing efficiency is hereby introduced, and is given by:

PROCEDURE FOR DETERMINATION OF PROPOSED PACKING PARAMETERS

The procedure recommended for the determination of packing parameters (packability factor Pf, packing efficiency Pe and packing index Pi) is as follows:

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(1) A representative portion of a natural aggregate (clastic sedimentary rock or laquer-impregnated/epoxy impregnated sediments) is selected and its bulk volume ( V B) measured.

(2) After disaggregation (following standard procedure) the grains are sieved using suitable g interval screens.

(3) Each size fraction is packed individually in dense random state by tapping, jolting or vibration, till no further volume reduction is observed (the diameters of the measuring cylinders should be greater than at least six times the grain diameter to eliminate wall effect). The individual pack volumes in the dense state (V i) are measured.

(4) All the grains are artificially repacked in the dense state and the resulting volume (V d) noted.

RESULTS AND DISCUSSION

To test the efficacy of the proposed measures of packing, experiments were conducted with two river-sand samples and two beach-sand samples, following the procedure mentioned above. Table II shows the results of the measurements of V i, V B and ~ , and the values of the packing parameters for each sample.

The results suggest that fdr natural clastic sediments taken from different environments, all the packing parameters are discernible and they have individual significance with respect to different aspects of packing. The intrinsic packability factor between river and beach sands does not show significant difference. Though poorer sorting of the river sands may favour better intrinsic packability, the latter may be adversely affected by their slightly greater angularity. Probably other factors besides sorting and roundness (such as percent frequency of particles in each size range, size ratios and sphericity) also control the intrinsic packability. There exists the possibility of establishing an empirical relation between intrinsic packability and the above-mentioned factors by their concurrent determination on a large number of clastic sediments from known environments. The value of packing index suggests that although there may be little difference in the intrinsic packability of the river and beach material, due to different packing efficiency of the depositional agents, the effective utilization of space is notably better in the beach as compared to the river sands under study. Since packing efficiency is controlled by the mode of deposition, it has the potentiality of environmental differentiation (see also Harrell, 1980, fig. 31). However, packing efficiency does not provide information about the material aspect or intrinsic packability and therefore can not be used to compare the effective utilization of space of two or more samples, Conversely, the packing factor, which gives the maximum possible utilization of space of the component grains, does not provide information about how far that specific maximum has been attained. Packing index, however, provides the resultant of the interaction between the material aspect (Pr) and the depositional aspect (Pe) and hence can be used to

92

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93

compare the state of packing of two or more samples. However, in order to ascertain

whether the effective uti l ization of space is due more to intr insic packabil i ty or to

packing efficiency, all the three packing parameters need to be determined.

CONCLUSION

Packing, defined as the effective uti l ization of space, appears to be governed both

by the material aspect of the const i tuent grains and the mechanism aspect of the

deposi t ional agent. Intr insic pack'ability factor is a measure of the material aspect,

whereas packing efficiency denotes the capabil i ty of the medium towards achieving

m a x i m u m uti l ization of space possible with a part icular set of grains of certain

intr insic packabili ty. Packing index gives the resultant of the material and mecha-

n i sm aspects of packing and can be used to compare the packing of two or more

na tura l aggregates.

ACKNOWLEDGEMENT

The authors are indebted to Dr. A. Chakrabar t i of I.I.T., Kharagpur , for kindly

providing the Digha beach samples.

REFERENCES

Allen, J.R.L., 1970. Physical Processes of Sedimentation. Allen and Unwin, London, 248 pp. Bernal, J.D., 1965. Liquids: Structures, Properties, Solid Interactions. Elsevier, Amsterdam, pp. 25-47. Blatt, H., Middleton, G. and Murray, R., 1972. Origin of Sedimentary Rocks. Prentice Hall, Englewood

Cliffs, N.J., 634 pp. Dallavalle, J.M., 1948. Micromeritics, Pitman, London, 555 pp. Epstein, N. and Young, M.J., 1962. Random loose packing of binary mixtures of spheres. Nature, 196:

885-886. Fairbairn, H.W., 1943. Packing in Ionic Minerals. Bull. Geol. Soc. Am., 54: 1305-1374. Fraser, H.J., 1935. Experimental study of the porosity and permeability of clastic sediments. J. Geol. 43:

910-1010. Furnas, C.C., 1929. Flow of gases through beds of broken solids. U.S. Bur. Mines Bull, 307. Graton, L.C. and Fraser, H.J., 1935. Systematic packing of spheres with particular reference to porosity

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characterization and new methodologies. Unpubl. Ph.D. Thesis, Univ. of Cincinnati. Kahn, J.S., 1956. The analysis and distribution of the properties of packing in sand sized sediments, 1. On

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