EARTH SURFACE PROCESSES AND LANDFORMS, VOL. 8,465-472 (1983)

QUANTIMET IMAGE ANALYSIS OF SOIL PORE GEOMETRY: COMPARISON WITH TRACER BREAKTHROUGH CURVES

P. J. C. WALKER AND S. T. TRUDGILL Department of Geography, University of Shefield, SiO 2TN. U.K.

Received 27 August 1982 Revised 6 December 1982

ABSTRACT

The relationships between two-dimensional image analysis of soil thin-sections and tracer breakthrough curves has been studied for a silty clay loam brown earth soil under saturated conditions. Initial tracer breakthrough is well in advance of one pore volume. Discrepancies between Quantimet image analysis and breakthrough curve characterization were related by inference to the role of infrequently occurring macropores not necessarily sampled on the two-dimensional images. A fundamental difficulty found in the use of image analysis is the uncertain nature of the relationship betwet-n the two- dimensional image and the three-dimensional pore system. Caution is needed in using Quantimet image analysis to describe gross properties of the three-dimensional pore system.

KEY WORDS Quantimet Pore size Macropores Dye-tracing Image analysis

INTRODUCTION

Quantimet image analysis provides a quantitative measure of soil pore geometry. Anderson and Bouma (1973) have shown that measurements of pore size and shape can be related to the hydraulic conductivity of some structured soils. Bullock and Thomasson (1979) have shown that Quantimet measurements of pore size distribution are comparable to those obtained using suction-plate apparatus. It should therefore be possible to use Quantimet to quantify pore geometry in a study of the effect of pore geometry on miscible displacement in soil.

Recent research has shown that under saturated conditions flow through many soils does not take place in a uniform manner (Thomas and Philips, 1979; Germann and Beven, 1981; Smettem and Trudgill, 1982). Miscible displacement under these conditions shows extensive inhomogeneity. This has been explained by the presence of macropores in the soil which act as bypass channels to the rest of the pore system. A critical minimal diameter for these pores is not yet agreed upon (Bouma, 1981; Beven, 1981; Skopp, 1981). Scotter (1978) proposes a cut off at 100 pm for cracks whilst Germann and Beven (1981) believe it to be in the region of 1-2 mm. Smettem and Trudgill have shown preferential movement down macropores visible to the naked eye, using dye tracing and staining techniques. They argue, in accordance with Germann and Beven, that such macropores exist either at the interface of peds or are biological in origin, such as earthworm and root channels.

The existence of well-connected macropores can lead to highly asymmetric breakthrough curves showing an early initial breakthrough with a rapid rise of C/Co to 1.0, where C/Co is ef€luent tracer concentration/original input tracer concentration (Bouma and Wosten, 1979). Quantimet image analysis provides an objective and quantitative means of measuring the size and shape of pores as seen on thin-section and as such it may be of use in ascertaining the role of macropores in miscible displacement.

01 97-9337/83/050465-08$01 .OO 0 1983 by John Wiley & Sons, Ltd.

466 P. J. C. WALKER AND S. T. TRUDGILL

The object of this paper is to determine whether Quantimet image analysis provides a sufficiently appropriate and accurate description of the three-dimensional pore system to explain its effect upon the shape of the breakthrough curve.

MATERIALS

The materials used in the soil columns to derive the breakthrough curves came from two sources. Firstly, 24 of the columns were filled with soil of the Nordrach non-stoney series. This soil is described by Johnson (1971). It is a silty clay loam occurring, in the north Derbyshire location from which it was sampled, under agricultural land. Samples were taken from three adjoining fields. Four intact soil columns were excavated from field one which had been ploughed and harrowed two months prior to sampling, seven from field two which had been under continuous pasture for five years, and six from field three which had been under continuous pasture for at least twenty years. Undisturbed cores were taken from each of these fields. In addition, material collected from field one was sieved through a 9 mm diameter sieve and packed into seven additional soil columns. Ten soil columns were filled with a washed sand. The material was chosen to provide a wide range of structural complexity, ranging from the simple homogeneous sand through the sieved soil and recently ploughed soil, to the well developed structures of the soils under permanent pasture. The increasing level of structural complexity was expected to be associated with an increase in the occurrence of macropores.

DESIGN

Breakthrough curves were obtained from thirty-four soil columns, in the laboratory, using a fraction collector after the manner described by Smettem and Trudgill(1983) with the fluorescent dye Lissamine Yellow F.F. asa tracer. The material used to fill the soil columns is described below. The columns were 25 cm long with a diameter of 15 cm. Two parameters were derived from each breakthrough curve: the skewness of the curve and the holdback of the curve, (the magnitude of the deviation from piston flow) as described by Danckwerts (1953). Upon completion of miscible displacement, the columns were drained and sub-sampled for thin- sectioning. Four sub-samples (7 cm in diameter by 5 cm high) were taken sequentially down the vertical axis of each column. A vertical thin-section, randomly orientated with respect to the horizontal axis, was taken from each sub-sample after the methods of Bascomb and Bullock (1974). Upon each thin-section, four areas of 2 x 2 cm were examined by Quantimet (using a 30 cm2 screen). For each area, the individual area of each pore

and the number of pores in each of the following size and shape classes was recorded. Three shape and four size classes were defined, following the classification devised by Bouma et al. (1977). The size classes calculated from mean pore diameter, are > loo0 pm, 1000-300 pm, 3W100 pm, and c 100 pm. The shape classes are based on the ratio of pore area to pore perimeter squared ( A / P 2 ) ; three classes are defined: > 044,0.04-0.015, and c 0015. Following collection of the data the statistical validity of the sample size, for each size and shape class, was tested. The occurrence of pores in each size and shape class was then tested for correlation with each of the breakthrough curve parameters, using the non-parametric Spearman’s rank test, and any correlations examined to assess the validity of using Quantimet to describe soil pore geometry in this particular situation.

RESULTS

The mean values for skewness and holdback are shown in Table I. The pore size and shape data for each group are shown in Table I1 and Table 111. Under uniform displacement, breakthrough curves should possess zero skewness. All the breakthrough curves examined in this research are positively skewed (see Table I). This indicates that initial movement of tracer through the soil column was more rapid than expected or that there was an attenuation of the final stages of miscible displacement. Examination of the breakthrough curves shows them all to be displaced to the left of Po = 1, C/Co = 0.5 (where Po = pore volume of efRuent having passed through the soil column) after the manner of the curve shown in Figure 1. Classical hydrodynamic dispersion theory predicts that the curve should pass through this point. The holdback of a breakthrough curve is a measure of the quantity of water not fully participating in miscible displacement, i.e. that being held back in

TWO AND THREE DIMENSIONAL IMAGE ANALYSIS 467

Table I. Mean values for breakthrough curve parameters for each soil column group

Column group Skewness Holdback Hydraulic conductivity (cm/min)

Washed sand 2348 0.309 0.48 Sieved soil (field one) 2.541 0608 020 Undisturbed soil (field one) 3.808 0698 1.38 Undisturbed soil (field two) 3.658 0713 0.93 Undisturbed soil (field three) 1 *963 0.583 077 Mean values 2.864 0582 0.75

Table 11. Mean pore area (mm’) and number of pores per size class for each column group

Class 1 Class 2 Class 3 Class 4 Column group Mean Number Mean Number Mean Number Mean Number

area of pores area of pores area of pores area of pores

Washed sand 1.89 4.6 0.19 18.6 0.02 292 3.96 64.1 Sieved soil (Field one) 1.51 6.5 019 21.8 0.02 34.9 5.45 250 Undisturbed soil (Field one) 276 3.3 0.14 13.1 012 24.9 5.49 18.1 Undisturbed soil (Field two) 12.37 6.7 0.14 13.5 002 17.4 5.98 12.6 Undisturbed soil (Field three) 3.17 4 0 0.13 17.2 0.04 34-9 5.58 24-3 Mean values 498 5.02 0.15 16.8 002 28.3 5.29 28.8

Class 1 = > 1000pm mean diameter. Class 2 = 1000-300 pn mean diameter. Class 3 = 300-100pm mean diameter. Class 4 = < 100pm mean diameter (areas shown in mm2 x lo-’)).

Table 111. Mean pore area and number of pores for each pore shape class

Class 1 Class 2 Class 3

Column group Mean area

Washed sand 0.017 Sieved soil 0.062 Undisturbed soil (Field one) 0.195 Undisturbed soil (Field two) 1.023 Undisturbed soil (Field three) 0038

Number of pores

89.2 64.8 45.0 36.7 60.9

Mean area

0.087 0.198 0.213 0.155 0.116

Number of Mean Number of pores area pores

21.2 0.469 7.9 20.2 0.846 3.7 12.0 1.246 3.6 9.6 1.096 2.3

17.1 1.469 5.4

Class 1: A / P 2 = > 0.04 area in mm2. Class 2 A/P2 = 0.04-0015 area in rum2. Class 3 A / P 2 = < 0.015 area in mm2 x lo-’.

poorly connected and dead-end pores. The holdback values for all the breakthrough curves obtained from undisturbed cores are greater than those which would be obtained under uniform displacement, thus indicating the passage through the soil column of a greater volume of tracer, by the time Pu = 1, than would be the case under uniform displacement. However, for most of the sand-filled cores and for one core of sieved soil, holdback is substantially reduced. Increases in holdback are generally associated with a transition of the breakthrough curve to the left of the point PY = 1.0, C/Co = 0.5. The observed reduced holdbacks are caused

468 P. J. C. WALKER AND S. T. TRUDGILL

Pore Volumes

Figure 1. Representative breakthrough curve, with breakthrough well before 1 pore volume and 0.5 C/Co at c 0.2 Pu

by a delay in the appearance of the tracer in the effluent, followed by a rapid increase in tracer concentration to C/Co = 05, thus creating a reduced spread of the breakthrough curve.

Skewness is highly correlated with holdback, at a confidence level of greater than 95 per cent, thus supporting the contention that high skewness values are at least partly caused by an initial rapid movement of tracer down the soil column, bypassing a large proportion of the pore system, rather than wholly by a slow leaking of resident water from poorly connected pores, which would extend the final tail of the breakthrough curve.

The statistical validity of the thin-section sample size was tested using Equation 1. This equation enables the confidence levels of the means of the parameters measured on the thin-sections to be calculated:

2 . t ( N - l), a125 3 . N

a =

where tl =: confidence level of K, N = number of samples (16), S = an estimate of the population standard deviation, K = sample mean, and t = critical value from student’s ‘t’ test. The confidence levels found in this way for each group of columns and for each thin-section variable are shown in Tables IV and V.

Most of the variables possess acceptable confidence levels of between 87 and 95 per cent. The two variables which show low confidence levels, the number of pores in size class 1 and shape class 3, represent large pores and elongate pores. As can be seen from Tables I1 and 111, these pores occur relatively rarely in the soil, on average less than ten times per sample. Estimates suggest that to provide a measure of large and elongate pore occurrence, with a confidence level of greater than 90 per cent, would require an increase in sample size from 16 to around 40.

Tables 11 and 111 also show that elongate pores tend to be large in size often being comparable with pores in size class 1. It is postulated that size class 1 and shape class 3 represent the same pores, large inter-aggregate and bio-pores which occur infrequently in the soil, compared with the smaller, possibly intra-aggregate, pores.

The correlations obtained using the Spearmans Rank correlation test, between the breakthrough curve and thin-section parameters, are shown in Table VI.

From the results of past workers it can be concluded that there should be a positive correlation between the occurrence of macropores in the soil and the holdback of the breakthrough curve. This relationship will be influenced by such factors as the degree of connectivity of the macropores, their tortuosity and the number of constrictions along their length. Further, as the number of macropores active as bypass channels increases, the

TWO AND THREE DIMENSIONAL IMAGE ANALYSIS 469

Table IV. Confidence limits, expressed as percentages, for mean values of number of pores/size class for each group of soil columns

Confidence limits for number of pores/size class Class 1 Class 2 Class 3 Class 4

Washed sand 75 87 90 92 Sieved soil 77 89 91 86 Undisturbed soil (Field one) 73 85 92 87 Undisturbed soil (Field two) 74 83 88 85 Undisturbed soil (Field three) 73 89 93 91

Table V. Confidence limits, expressed as percentages, for mean values of number of pores/shape class for each group of soil columns

Confidence limits for number of pores/shape class Class 1 Class 2 Class 3

~

Washed sand 93 84 75 Sieved soil 95 90 71 Undisturbed soil (Field one) 93 83 68 Undisturbed soil (Field two) 91 82 67 Undisturbed soil (Field three) 95 88 66 x 93 85 69

proportion of water being held back in the soil will decrease, as a larger proportion of the pore volume takes part in the rapid transmission of water.

Using the same argument, skewness should also be correlated with macropore occurrence. However, skewness is a measure taken from the whole of the breakthrough curve. This means that a positive skew can be caused not only by an initial rapid breakthrough, but also by a long tail-off of the breakthrough curve. Such a tailing-off would be caused in a structured soil when water is slowly released from intra-aggregate sites.

If the Quantimet measurements used here are a true measure of pore geometry, then the above relationships should be apparent in the correlations between the breakthrough curve parameters and the Quantimet data.

Dealing first with the relationship between skewness and the pore shape data. Skewness is seen to be most highly correlated with the number of pores in shape class 1 (see Table V).

Shape class 1 represents rounded pores. These are the most frequently occurring pores on the thin-sections. They are also the shape class with the smallest average diameter. In miscible displacement they Will act as a partial sink for resident water, which will be slowly displaced, thus diluting the incoming tracer. The initial very rapid increase in tracer concentration during the first stage of the breakthrough curves masks this dilution and it only becomes apparent during the final stages of the breakthrough curve, causing an elongation of the curve. If the pores in shape class 1 are intra-aggregate pores, then the more pores that are seen on thin-section the more likely they are to be connected in the third dimension, since these pores will be clustered together in intra- aggregate sites. Resident pore water will be displaced more effectively from well connected pores than from poorly connected ones since a poorly connected system will contain a higher proportion of slowly transmitting and stagnant pores than will a well connected system. Thus the fewer small pores that exist, the more prolonged will be their dilution effect upon the incoming tracer and thus the more extended will be the final stages of the breakthrough curve. Obviously this relationship must break down at some minimum value when the effects of these smaller pores becomes too slight to be detected on the breakthrough curve. It would be expected, therefore, that high skewness values should be associated with intermediate values of shape class 1 occurrence, and low skewness values with both high and very low values of shape class 1 occurrence. Examination of Figure 2 shows that this does in fact occur. Further evidence for this theory can be seen in the correlations between skewness and the pore shape classes. Skewness is most highly negatively correlated with the number of pores in size class 3, which contain pores of a similar size to those in shape class 1.

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P. J. C. WALKER AND S. T. TRUDGILL

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Figure 2 .The relationship between skewness and n, the number of pores in shape class one

If the above postulations concerning intra-aggregate pores are true, then a complementary set of postulations should exist concerning inter-aggregate pores. Thus it is postulated that inter-aggregate pores are the larger and more elongate pores, those in shape class 3 and size class 1. The more effective these large pores are at transmitting water, the greater will the skewness and holdback values of the breakthrough curve be. The data are ambiguous. As Table VI shows, a negative relationship exists between skewness and the number of pores in shape class 3 and no significant relationship exists between skewness and size class 1. However, if the occurrence of pores in size class 1 is expressed as a proportion of the total pore area then a positive correlation with a 90 per cent confidence level is found. As skewness is dependent upon the shape rather than the absolute position of the breakthrough curve, the proportion of pores in size class 1 may be a more valid measure of pore Occurrence than absolute pore number.

Table VI. r' values and confidence levels for Spearman's Rank correlations between breakthrough curve variables and pore geometry variables (confidence levels of less than

90 per cent are not shown)

Skewness Holdback

Shape class 1 - 0477 -0.638

Shape class 2 -0430 -0.575

Shape class 3 -0236 -0.450

Size class 1 -0166 -0.176

99 % 99 %

99 % 99 %

90 % 99 % - -

Size class 2 -0.383 -0.327 95 % 95 %

99 % 90 %

95 % 99 %

Size class 3 - 0.428 - 0.237

Size class 4 -0347 - 0-745

TWO AND THREE DIMENSIONAL IMAGE ANALYSIS 47 1

Holdback will be maximized when the incoming tracer bypasses most of the pore system through a few large diameter continuous pores. It must be remembered that holdback, unlike skewness, is dependent upon the absolute volume of water passing through the soil column and not just upon the relative shape of the breakthrough curve. Further, an increase in the number of bypassing channels, or a decline in their connectivity, will lead to a decrease in holdback. This suggests that a negative relationship might be expected between holdback and the number of large pores as seen on thin-section. Such a relationship was found with size class 2 but not class 1. It must be remembered, however, that the values for size class 1 occurrence have low confidence levels. Pores in size class 2 are still large enough to be regarded as inter-aggregate pores (Scotter, 1978).

DISCUSSION

In general it seems that Quantimet image analysis is providing a quantitative and understandable measure of pore geometry. The research has, however, highlighted two related groups of inherent problems.

Firstly there is the question of the relationship between the two-dimensional image and the three- dimensional pore system of which it is an abstraction. The two-dimensional image provides very little information on pore connectivity, particularly when dealing with macropores which occur less frequently on thin-section than other groups of pores. It is inevitable that the two-dimensional image will underestimate the connectivity of the macropores. The use of staining (Bouma et al., 1979), mercury porosimetry (Lawrence et al., 1979) or serial sections (Hall and Dalrymple, 1979), may minimize this problem. Allied to this problem is the description of pore size. For a spherical pore, only a thin-section through the exact centre of the pore will provide a true record of the pore diameter, all other sections will tend to underestimate it. The same holds true for other pore shapes. Further, on the question of pore shape, the present methodology does not distinguish between pores with crenulous edges and tortuous pores, or pores, as seen on thin-section, containing constricting necks. A more suitable measure of pore shape needs to be devised which distinguishes between these different types of pores.

In this research the supposition has been used that an increase in the pore density upon thin-section implies an increase in the connectivity of these pores. Whilst this supposition appears logically valid, it is based on information not directly obtainable from the thin-section. This therefore leaves the nature of such phenomena, as seen on thin-section, open to interpretation.

Secondly, there is the problem of sample size. The large pores which appear to be having such a strong influence on the breakthrough curve occur relatively infrequently in the soil. This greatly reduces the probability of them being picked up on thin-section in sufficient numbers to provide a representative picture of the total macropore population. It is estimated that a sample size of at least 40, 2 x 2 cm samples would be needed to give an adequate picture of macropore occurrence in the soil used in the present research.

These two problems, the relationship between the two-dimensional sample and the three-dimensional real system, and the necessary sample size, are closely related. When calculating sample size, one can only calculate the sample size necessary to sample a population of thin-sections of pores, not the three-dimensional pore system. This means that thin-sections can never be regarded as absolute samples on the three-dimensional pore geometry. They must always be regarded as a surrogate measure which bears a close but undefined relationship to the three-dimensional reality. Their chief advantage is that they provide an objective and quantifiable measure of some aspects of both pore size and shape. This fact must always be borne in mind when using image analysis to explain other gross properties of the soil.

CONCLUSIONS

Quantimet image analysis provides an objective and quantifiable measure of pore geometry as seen on thin- section. However, the relationship between thin-sectioned pores and the three-dimensional pore system is still unclear. The image area necessary to effectively sample pore geometry varies for different sizes and shapes of pores. The sample size ultimately calculated is a sample size for a population of thin-sectioned pores and not

472 P. J. C. WALKER AND S. T. TRUDGILL

for the three-dimensional pore population. Quantimet image analysis has a potential for quantitatively describing the soil pore system but it must be treated with caution until more is known about the relationship between the image pore population and the thtee-dimensional pore population.

ACKNOWLEDGEMENTS

The authors wish to acknowledge Christian Voluntary Service for providing financial assistance to carry out this research, and K. Smettem for providing useful criticism during the preparation of the paper.

REFERENCES

Anderson, J. L. and Bouma, J. 1973. ‘Relationships between saturated hydraulic conductivity and morphometric data of an argillic

Bascomb, C. L. and Bullock, P. 1974. ‘Sample preparation and stone content’, in Soil Survey Laboratory Methods (Technical monograph,

Beven, K. 198 1. ‘Micro-, meso-, macroporosity and channeling Row phenomena in soils’, Soil Science Society ofAmerica Journal, 45,1245. Bouma, J. 1981. ‘Comment on “Micro-, meso-, and macroporosity of Soil”’, Soil Science Society of America Journal, 45, 1244-1245. Bouma, J., Jongerius, A., Boersma, O., Jager, A. and Schoonderbeek, D. 1977. ‘The function of different types of macropores during

Bouma, J., Jongerius, A. and Schoonderbeek, D. 1979. ‘Calculation of hydraulic conductivity of some saturated clay soils using micro-

Bouma, J. and Wosten, J. H. M. 1979. ‘Flow patterns during extended saturated Row in two, undisturbed swelling clay soils with different

Bullock, P. and Thomasson, A. J. 1979. ‘Rothamsted studies of soil structure. 11, Measurement and characterisation of macroporosity by

Danckwerts, P. V. 1953, ‘Continuous flow systems (distribution of residence times)’, Chemical Engineering Science, 2, 1-13. Germann, P. and Beven, K. 1981. ‘Water flow in soil macropores. 3, A statistical approach’, Journal ofsoi l Science, 32, 31-40. Hall, N. W. and Dalrymple, J. B. 1979. ‘A method for making serial thin sections of soilsand other unconsolidated materials’, Earth Suface

Johnson, P. A. 1971. Soils in Derbyshire 1, Sheet SK 17 (Tideswell), Soil Survey Record No. 4., Harpenden, Herts. Lawrence, G. P., Payne, D. and Greenland, D. J. 1979. ‘Pore size distribution in critical point and freeze dried aggregates from clay

Scotter, D. R. 1978. ‘Preferential solute movement through large soil voids. I: Some computations using simple theory’, Australian Journal

Skopp, J. 1981. ‘Comment on “Micro-, meso-, and macroporosity of soil”’, Soil Science Society of America Journal, 45, 1246. Smettem, K. and Trudgill, S. T. 1983. ‘An evaluation of some fluorescent and non-fluorescent dyes in the identification of water

Thomas, G. W. and Philips, R. E. 1979. ‘Consequences of water movement in macropores’, Journal ofEnoironmental Quality, 8,149-156.

horizon’, Soil Science Society of America Proceedings, 37,408-413.

Soil Survey, No 6), Rothamsted Experimental Station, Harpenden, 7-13.

saturated flow through four swelling soil horizons’, Soil Science Society of America Proceedings, 41, 945-950.

morphometric data’, Soil Science Society of America Journal, 43, 261-265.

macrostructures’, Soil Science Society of America Journal, 43, 16-22.

image analysis and comparison with data from water retention measurements’, Journal of Soil Science, 30, 391-413.

Processes, 4, 8588.

subsoils’, Journal of Soil Science, 30, 499-516.

of Soil Research, 16, 257-267.

transmission routes in soils’, Journal ofsoi l Science, 34 (4). In press.