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DIVISION S-1-SOIL PHYSICS

Three-Dimensional Quantification of Macropore Networks in Undisturbed Soil Cores

^a Dep. of Agricultural and Biosystems Engineering, McGill Univ., 21111 Lakeshore Rd., Ste-Anne-de-Bellevue, QC, Canada, H9X-3V9
^b Dep. of Chemical and Petroleum Engineering, Univ. of Calgary, 2500 University Dr. N.W., Calgary, AB, Canada, T2N-1N4
^c Dep. of Chemistry, Univ. of Calgary, 2500 University Dr. N.W., Calgary, AB, Canada, T2N-1N4

prasher{at}agreng.lan.mcgill.ca

	ABSTRACT

TOP ABSTRACT INTRODUCTION Terminology Materials and methods Results and discussion Summary and conclusions REFERENCES

 
The role of macropores in soil and water processes has motivated many researchers to describe their sizes and shapes. Several approaches have been developed to characterize macroporosity, such as the use of tension infiltrometers, breakthrough curve techniques, image-analysis of sections of soils, and CAT scanning. Until now, efforts to describe macropores in quantitative terms have been concentrated on their two-dimensional (2-D) geometry. The objective of this study is to nondestructively quantify the three-dimensional (3-D) properties of soil macropores in four large undisturbed soil columns. The geometry and topology of macropore networks were determined using CAT scanning and 3-D reconstruction techniques. Our results suggest that the numerical density of macropores varies between 13421 to 23562 networks/m³ of sandy loam soil. The majority of the macropore networks had a length of 40 mm, a volume of 60 mm³, and a wall area of 175 mm². It was found that the greater the length of networks, the greater the hydraulic radius. The inclination of the networks ranged from vertical to an angle of 55° from vertical. Results for tortuosity indicated that most macropore networks had a 3-D tortuous length 15% greater than the distance between their extremities. More than 60% of the networks were made up of four branches. For Column 1, it was found that 82% of the networks had zero connectivity. This implies that more than 4/5 of the macropore networks were composed of only one independent path between any two points within the pore space.

Abbreviations: CAT, computer-assisted tomography • CT, computed tomography • ECD, equivalent cylindrical diameter • HU, Hounsfield Units • 2-D, two-dimensional • 3-D, three-dimensional

	INTRODUCTION

TOP ABSTRACT INTRODUCTION Terminology Materials and methods Results and discussion Summary and conclusions REFERENCES

 
SOIL STRUCTURE consists of a 3-D network of pores. Large pores play an important role in allowing roots, gas, and water to penetrate into the soil. The higher the macropore density, the more the soil can be exploitable by plant roots (Scott et al., 1988a). Similarly, the more continuous the macropores are, the more freely gases can interchange with the atmosphere. Continuous macropores also have a direct effect on water infiltration and solute transport in soil.

According to Sutton (1991), the size of pore openings is more important for plant growth than is the overall soil porosity. Although existing pores constrain the penetration of roots, they provide favorable conditions for root growth. Several studies have shown that the presence of continuous macropores in soil significantly benefits root growth (Bennie, 1991). One of the most important factors influencing soil fertility, besides water and nutrient content, is soil aeration (Hillel, 1980; Glinski and Stepniewski, 1985). Large soil pores are the paths available for gas exchange between soil and atmosphere (Sutton, 1991). In natural soils, water movement follows paths of least resistance (i.e., preferential flow paths). Intuitively, large and continuous pores facilitate water transport. It is now well known that the size and connectivity of soil pores play a major role in the flow characteristics of water and the transport of solutes through soil (Ma and Selim, 1997). Jury and Flühler (1992)(p. 192) stated that "fluid transport through well defined structural voids is not predictable unless the distributions of the voids, aperture sizes and shapes, depths of penetration, and interconnectivity are known."

The importance of macropores in many soil–plant–roots processes has motivated many researchers to describe their sizes and shapes. Several approaches have been developed to characterize macroporosity. Among them are tension infiltrometers (Everts and Kanwar, 1993; Timlin et al., 1994; Logsdon et al., 1993), breakthrough curve techniques (Ahuja et al., 1995; Jabro et al., 1994; Li and Ghodrati, 1994; Ma and Selim, 1994), and image-analysis of sections of soils (Koppi and McBratney, 1991; Moran and McBratney, 1992; Singh et al., 1991; Vermeul et al., 1993). Warner et al. (1989), Grevers et al. (1989), Anderson et al. (1990), Hanson et al. (1991), Tollner et al. (1995), Asare et al. (1995), and Heijs et al. (1996) have also recognized the great potential offered by computer-assisted tomography (CAT) scanning for characterizing soil macroporosity.

Nevertheless, efforts to describe macropores in quantitative terms have not yet resulted in a comprehensive theoretical framework that allows a complete representation of their geometry. This is partly due to the fact that macropores are very difficult to observe and characterize, bearing in mind that the macropore networks are complex 3-D structures. Up to now, most of the work done on the quantification of soil macropores concentrated on their 2-D geometry. A few researchers, such as Hanson et al. (1991), Heijs et al. (1996), and Perret et al. (1997), have used reconstructive imagery, allowing 3-D visualization of the macropore space, but have not quantified soil macroporosity in three dimensions. Transport phenomena in porous media strongly depend on the 3-D pore structure (Chatzis and Dullien, 1977). Very little work has been done to characterize the macroporosity of intact soil cores in terms of its 3-D parameters. Tollner et al. (1995) pointed out the need for additional research to investigate reliable approaches for computing tortuosity and connectivity of soil macropores. Imaging in three dimensions and quantification of 3-D parameters of soil macroporosity are critical in order to accurately correlate soil pore structure with preferential flow phenomena and much additional work is needed in this area (Hanson et al., 1991).

The present investigation is a study of the 3-D properties of soil macropores. The main characteristics of a porous medium that affect fluid flow are porosity, numerical density, pore shape (size, length, volume, hydraulic radius, tortuosity), and pore interconnectivity or genus per unit volume (Constantinides and Payatakes, 1989). Therefore, the objective of this study is to quantitatively determine the above parameters of soil macropores in four undisturbed soil columns through a 3-D reconstruction from 2-D matrices generated by an x-ray CAT scanner. The results of this work show promise for future studies in the area of soil macropore quantification.

	Terminology

TOP ABSTRACT INTRODUCTION Terminology Materials and methods Results and discussion Summary and conclusions REFERENCES

 
Various standard geometrical parameters are meaningful to quantify the structure of 3-D macropore networks, such as their relative position, length, volume, specific wall area, and orientation. Such parameters are explicit and do not need to be defined. However, several terms that are used to describe soil structure and their 3-D attributes are fuzzier and need to be clarified. Some of these terms are defined below:

Macropore
At first, the definition of a macropore may seem simple. However, as we come to consider the complexity of a macropore, its definition may become hazy and ambiguous. By strict definition, macropore implies a large pore. However, large is a relative term and this lack of clarity has led to several conflicting definitions.

It would be useful to have a general agreement on pore terminology, just as one exists for the definitions of sand, silt, and clay. However, up to now there has been little or no consensus for the definition and terminology used for classifying pores in general. A large number of classification schemes based on the equivalent cylindrical diameter (ECD) and several contradicting definitions can be found in soil literature (Table 1) .

Up to now, definitions of macropore make no specific reference to its size or shape in a 3-D context. The lack of information describing their shapes has led to the generality used in defining macropores (Kwiecien, 1987). Part of the goal of this study is to characterize the shapes and other 3-D parameters of macropore networks with the aid of computer programs, in order to describe macropore geometry and, eventually, to help clarify the definition of a soil macropore.

Macropore Network and Branches
In a porous medium, a network is a set of macropores that are interconnected such that there is a passage from any part of the set to every other part (Scott et al., 1988a). Thus, the concept of a macropore network implies a 3-D structure. A branch is a portion of the macropore network connecting to the rest of the network.

Tortuosity
Tortuosity () is one of the most meaningful 3-D parameters of pore structure. Carman (1937) introduced the concept of tortuosity as the square of the ratio of the effective average path in the porous medium (L_e) to the shortest distance measured along the direction of the pore (L). Several researchers have reviewed this definition (Hillel, 1982; Marshall and Holmes, 1988; Jury et al., 1991; Sahimi, 1995) and have redefined tortuosity (Eq. [1]):

(1)

Tortuosity is a dimensionless factor always greater than one, which expresses the degree of complexity of the sinuous pore path (Fig. 1) . Tortuosity can easily be related to the conductivity of a porous medium since it provides an indication of increased resistance to flow due to the pore system's greater path length (Dullien, 1979). The term continuity is sometimes used to describe pore tortuosity. Richter (1987) has defined pore continuity as the reciprocal of tortuosity.

View larger version (108K): [in this window] [in a new window]   Fig. 1 Tortuosity of a soil macropore

(2)

Necks can therefore be easily located by identifying local minima in the hydraulic radii of macropores. The reason for using the hydraulic radius as a measure of pore throat is that it is a useful measure of size in the case of irregularly shaped pores (Dullien, 1992). The hydraulic radius can provide a good indication of the pore neck position and of the pore expansion–contraction.

Topology of Macropore Networks
A complete description of pore structures requires geometrical as well as topological information (Macdonald et al., 1986). Topology deals with properties of an object in a space that remain unaltered when that space is deformed. The topology of macropore networks concerns essentially the number per unit volume and the degree of connectivity of macropore networks, regardless of their shape. The number of networks, defined later as numerical density, is a measure of the complexity of pore structure (Scott et al., 1988a). Topological parameters characterizing the morphology of a porous medium are the numerical density, coordination number, connectivity, and genus (Dullien, 1992). Each of these terms is defined below.

Numerical Density of Networks
The number of networks per unit volume, regardless of their size or shape, is the numerical density. Scott et al. (1988a) pointed out that it is very difficult to determine this quantity. Up to now, this information was roughly estimated by cutting parallel plane sections through soil. Essentially, numerical density was only accessible in two dimensions. One of the major drawbacks of this approach is that there is not a one-to-one correspondence between the number of networks estimated in the 2-D sections and those in three dimensions (Scott et al., 1988a).

Coordination Number
One of the simplest concepts for characterizing pore topology is the coordination number (Z). It is defined as the number of pore throats that meet at a given point along a pore (Sahimi, 1995). In other terms, the coordination number determines the number of branches meeting at one node. Until now, the only approach to determining the coordination number has been to reconstruct a branch-node chart of the pore structure (Fig. 2) from a series of parallel sections of the porous medium (Dullien, 1992).

View larger version (36K): [in this window] [in a new window]   Fig. 2 Schematic representation of (a) pore space, and (b) coordination number on a branch-node chart (after Dullien, 1992)

View larger version (33K): [in this window] [in a new window]   Fig. 3 Illustration of the concept of connectivity and genus (from Macdonald et al., 1986)

Although these topological concepts have recently been given increased attention in the field of petroleum recovery, these concepts have not yet been used to describe the spatial characteristics of a soil macropore network. For this study, we propose evaluating the coordination number and the connectivity–genus of soil macropores in order to describe their complex geometry.

	Materials and methods

TOP ABSTRACT INTRODUCTION Terminology Materials and methods Results and discussion Summary and conclusions REFERENCES

 
Soil Cores
In July 1995, four undisturbed soil columns, 800 mm in length and 77 mm in diam., were taken from a field site at the Macdonald Campus of McGill University in Ste-Anne-de-Bellevue, QC. The columns were extracted from an uncultivated field border that had been covered for many years by a combination of quack grass [Elytrigia repens (L) Desv. ex Nevski], white clover (Trifolium repens L.), and wild oat (Avena fatua L.). Periodic mowing during the summer was the only cultural practice used. The land slope was <1%. Column size was selected based on the need for a sample that was large enough to represent macropore distribution, yet small enough to be handled easily when full of soil. The hydraulic bucket of a backhoe was used to drive polyvinyl chloride (PVC) pipes in small increments of about 80 mm. The objective was to obtain soil cores that were disturbed as little as possible to obtain samples that were representative of natural conditions. The soil belonged to the Chicot series. The Chicot series is a type of soil encountered in the Montreal area following the Canadian soil taxonomy. These soils are developed from sandy materials over a calcareous till and, as a result, they are generally well drained (Lajoie and Baril, 1954). The soil was predominantly a sandy loam with an A horizon thickness of 0.4 m.

The soil columns were scanned under dry as well as saturated conditions. To reach dry conditions, the soil columns were placed under a set of 10 300-W light bulbs for a period of 6 wk. The cores were rotated periodically to accelerate evaporation.

A 1-mm-i.d. polyethylene tube was inserted into one of the soil columns to verify the ability of the CAT scanner to portray the size and the location of a known macropore.

X-Ray CAT Scanning
A modified medical ADVENT HD200 whole-body CAT scanner (Universal Systems, Solon, OH) was used for this study at the TIPM laboratory in Calgary, AB. Computed tomography (CT) or computer-assisted tomography (CAT) is a method of diagnostic imaging used for nondestructive imaging of cross-sectional slices of the human body or an object. This scanner incorporates a fourth-generation scan geometry with scan times as short as 2s/scan and a high pixel resolution (up to 195 x 195 µm). In most CAT scanners, the actual collection of patient data occurs in the gantry where the patient lies horizontally. However, the ADVENT HD200 was modified to allow vertical scanning. For that purpose, the CAT scanner gantry was rotated 90° and positioned on a metal frame designed to hold the whole gantry horizontally. Figure 4 shows the rotated gantry of the CAT scanner.

View larger version (192K): [in this window] [in a new window]   Fig. 4 View of the rotated gantry of the Advent HD200

The position of the core was set mechanically for each scan with a digital indexing ruler having a precision of ±0.001 mm. A total of 360 sections or scans was obtained for each column, leaving no space between two consecutive scans.

Data from each scan were recorded on a magnetic tape, transferred to a SUN4 workstation running under the UNIX operating system, and converted to a bulk density value. First, the scans were stored in matrices composed of CT numbers that were expressed in a dimensionless quantity known as Hounsfield Units (HU). The CT number for water is roughly 0 and -420 for air. The CT values are a function of the electron density (bulk density) and atomic number of the material. It has been previously demonstrated that the CT numbers are linearly related to the bulk density of the soil (Anderson et al., 1988). The soil columns were mounted inside a core holder assembly made of a hollow Plexiglas annulus, partitioned into four chambers filled with two liquids. Water and mineral oil were used as reference materials. By plotting CT numbers vs. the bulk density of reference materials and using a simple linear regression, a calibration curve that relates bulk density to the CT number of the scanned material was derived. A FORTRAN 77 program was developed to compute the calibration line of each scan. Once the linear calibration equations were established, a computer algorithm transformed CAT-scan arrays into matrices of bulk density. Part of the algorithm also allowed for computation of the soil section's porosity distribution on a voxel (i.e., volume element) basis. The remaining analysis was done using the PV-WAVE language on a 300 MHZ Pentium II with 128 Mb of RAM.

3-D Reconstruction of Macropores
The PV-WAVE language was chosen for computer programming in this study. The PV-WAVE language is a comprehensive programming environment that integrates state-of-the-art numerical and graphical analyses. This programming language is widely used for analyzing and visualizing technical data in many fields, such as medical imaging, remote sensing, and engineering. PV-WAVE is an ideal tool for working with large arrays such as our CAT-scan data, because of its array-oriented operators and ability to display and process data in the ASCII and binary I–O formats. Another reason that motivated this choice was PV-WAVE's ability to be used under both UNIX and PC environments.

Four computer programs were developed to reconstruct, visualize and quantify 3-D macropore structures in soil columns. The first program, called Filterjo.pro, thresholds the macropores in the 360 2-D bulk density matrices before isolating macropore networks in three dimensions. Each pixel can represent only two states of the dry soil columns, pore space, or soil matrix. The first task accomplished by Filterjo.pro is to partition 2-D matrices into regions of 1 for pores and 0 for soil matrix. The pores contain either water or air (i.e., density <1). Thus, the pore can be isolated by applying a threshold on all the pixels in the bulk density matrices having a value less than 1. This transformation is called segmentation. The program then regroups pixels belonging to the same pore (clustering) by following a set of rules described by Perret et al. (1997). A filtering subroutine is then executed. For that purpose, a criterion is used to determine if the pore belongs to the macropore domain. The criterion is based on the size of the pore. If the pore has an ECD <1 mm, it is removed from the matrix. After filtering, a median smoothing is applied on each matrix with a neighborhood of two pixels. This process is similar to smoothing with an average filter, but it does not blur edges larger than the neighborhood. Median smoothing was used since it has been found to be effective in removing noise (Visual Numerics, 1994). Each pixel in the resulting matrix is then multiplied by -1. Therefore, matrix elements have a value of 0 (i.e., soil) or -1 (i.e., macropores). The resulting 2-D matrices are then stored in a file ready for the 3-D analysis.

A second computer program, called Netjo.pro, was developed to recognize and isolate 3-D macropore networks. The first step in developing this program was to establish a set of rules, which were used to determine how the macropore spaces in each 2-D matrix were connecting to each other in 3-D. Several different clustering criteria were used. The first algorithm was based on the six nearest neighboring voxels rule in three dimensions (Fig. 5a) . With this algorithm, similar voxels (with a value of -1) are clustered together if they are beside, above, or below one another. In other words, all clustered voxels are joined by at least one planar face. Although this algorithm was fast, it did not cluster all voxels belonging to a network in a single pass when the network's 3-D structure was very complex and showed a high degree of connectivity. Therefore, a second clustering algorithm was developed, based on the 26 neighboring voxels rule (Fig. 5b). This algorithm clusters all voxels belonging to the macropore domain around the voxel of interest if they share a face, an edge, or even a corner by visiting the top and bottom 2-D matrices. In other words, two voxels will be registered as part of the same group of pore volume if they have a value of -1 and share a common corner. Thus, the clustering algorithm examines the 26 nearest neighboring voxels in three dimensions. To do so, each cross-section of the soil column is analyzed by superimposing its adjacent sections (Fig. 5c). A 3-D filtering algorithm was incorporated in Netjo.pro to eliminate all networks having a length 10 mm. These macropores were removed because we assumed they were not contributing to preferential flow. The output of this program is a large 3-D matrix that contains matrix elements of 0 (i.e., soil matrix domain) and 1, 2, 3, ... , n for the macropore domain, where each integer represents a network. In other words, each voxel belonging to a network has an integer value. For instance, if a soil column has 45 independent macropore networks, all voxels of the last network will have a value of 45. This approach was successfully implemented in the recognition and reconstruction of macropore networks.

View larger version (60K): [in this window] [in a new window]   Fig. 5 Illustration of (a) the six nearest neighboring voxels rule and (b) 26 neighboring voxels rule; (c) superposition of consecutive 2-D matrices for the 3-D algorithm

View larger version (15K): [in this window] [in a new window]   Fig. 6 Three-dimensional reconstruction of macropore networks in Column 1

View larger version (20K): [in this window] [in a new window]   Fig. 7 Flow diagram of the PV-WAVE program Branjo.pro

	Results and discussion

TOP ABSTRACT INTRODUCTION Terminology Materials and methods Results and discussion Summary and conclusions REFERENCES

View larger version (39K): [in this window] [in a new window]   Fig. 8 Number, relative position, and vertical length of macropore networks in the four soil columns

One would expect that the number of macropore networks per unit volume would have a consequential effect on macroporosity. More precisely, it would make sense that soil columns with a large numerical density would have a large macroporosity and vice-versa. However, our results do not confirm this supposition or indicate a direct relationship between numerical density and macroporosity. For instance, Column 1, which has the smallest numerical density (i.e., 13421 macropore networks/m³), has the greatest macroporosity. Column 3 (with a numerical density of 23562 networks/m³) exhibits a much smaller macroporosity (i.e., 2.59%). These results can be explained by the difference in the average network volume. The average network volume in Column 1 is more than 2.5 times that of Column 3. This explains the relatively high macroporosity of Column 1. Therefore, one cannot use numerical density as an indication of macroporosity.

The vertical length and position of macropore networks can be evaluated, as shown in Fig. 8. This provides a good indication of the long networks that might have a significant impact on vertical water and chemical displacement. The artificial macropore (i.e., polyethylene tubing) running through the soil in Column 4 has been readily detected and identified as Network 1.

Figure 9 shows the frequency distributions of the length of the macropore networks in the four soil columns. The distributions peak at 40 mm for all soil columns. This indicates that the majority of the macropore networks have a length of 40 mm. As expected, the distributions are skewed to the left, showing the presence of a few long networks, especially for Columns 1 and 4.

View larger version (18K): [in this window] [in a new window]   Fig. 9 Frequency distributions of the length of macropore networks in the four soil columns

View larger version (19K): [in this window] [in a new window]   Fig. 10 Frequency distributions of volume of macropore networks in the four soil columns

The distributions of the wall area of macropore networks have been also evaluated (Fig. 11) . The results suggest the same bimodal pattern for all soil columns. The mode of the distributions is 175 mm². A secondary peak, however, can be observed for networks having a wall area of 1200 mm². The prevailing macropore network length of 40 mm implies that two sizes of networks may be found in this soil. The first category, which accounts for about 18 to 28% of the networks, represents networks with an equivalent diam. of 1.4 mm, and the second category delineates networks with an ECD of 9.5 mm.

View larger version (20K): [in this window] [in a new window]   Fig. 11 Frequency distributions of wall area of macropore networks in the four soil columns

View larger version (35K): [in this window] [in a new window]   Fig. 12 Hydraulic radius of macropore networks in the four soil columns

The frequency distributions of hydraulic radii were also assessed for every column and are shown in Fig. 13 . The distributions of hydraulic radii are almost symmetrical with a mode of 0.13. Here again, networks in all soil columns show a similar trend.

View larger version (20K): [in this window] [in a new window]   Fig. 13 Frequency distributions of hydraulic radius of macropore networks in the four soil columns

View larger version (20K): [in this window] [in a new window]   Fig. 14 Frequency distributions of macropore network inclination

Figure 15 shows the distributions of the tortuosity of macropore networks found in the four columns. The distributions are similar and skewed to the right, with a mode of 1.15. Most of the networks have a tortuosity in the range 1 to 1.4. Thus, the majority of the macropore networks have a 3-D tortuous length 15% greater than the distance between their extremities. Some macropore networks have a tortuosity as high as 2.4.

View larger version (20K): [in this window] [in a new window]   Fig. 15 Frequency distributions of tortuosity of macropore networks

View larger version (15K): [in this window] [in a new window]   Fig. 16 Frequency distributions of number of branches per macropore network

The distributions of branch lengths of Networks 6, 18, 19, 32, and 44 in Column 1 are presented in Fig. 17a . Only networks that have a length greater than average were selected. As indicated in Fig. 8, Networks 6, 18, 19, 32, and 44 of Column 1 have a length greater than the average macropore network. Fig. 17a suggests that more than 60% of the branches of Networks 6, 18, and 19 have a length of 10 mm. Since Network 32 has only one 150-mm long branch, and Network 44 has only one 79-mm long branch, a single peak reaching 100% in their distributions was observed.

View larger version (25K): [in this window] [in a new window]   Fig. 17 Frequency distributions of (a) length and (b) tortuosity of branches for selected networks of Column 1

One of the simplest concepts for characterizing pore topology is the coordination number (Z), which is defined as the average number of branches meeting at a connecting node. In mathematical terms, the average coordination number of a network can be written as in Eq. [3]:

(3)

where Z_i is the number of branches connected to a node of type i, and _i is the relative frequency of such nodes. A branch-node chart was constructed for Network 6 of Column 1 to illustrate the concept of average coordination number (Fig. 18) . A branch-node chart is a representation of the 3-D arrangement of the pore networks in a 2-D plane. Network 6 was selected because of its high number of branches. The branch-node chart of Network 6 gives an idea of its ability to transmit a fluid. More precisely, it indicates branches that may act as preferential flow paths, as well as a dead-ended set of branches that will not be part of the main channels.

View larger version (25K): [in this window] [in a new window]   Fig. 18 Branch-node chart for Network 6 of Column 1

(4)

The average number of branches meeting at a node is 3.09. Like tortuosity, this gives an indication of increased resistance to flow due to the degree of branchedness of the macropore network.

The genus or connectivity of Network 6 was also evaluated. This was achieved by counting the number of nonredundant loops enclosed in Network 6. Two nonredundant loops can be isolated in Fig. 18. Thus, the connectivity of Network 6 is equal to 2. Similarly, the connectivity was calculated for every network of Column 1. Results are shown in Fig. 19 . The number of branches per network should increase the probability of finding nonredundant loops in the 3-D structure of the networks. Therefore, the connectivity and the number of branches were plotted on the same graph to verify this relationship for each macropore network. However, no direct relationship can be observed in Fig. 19. Macropore networks with one branch do not contain loops and therefore have a connectivity equal to 0. As mentioned earlier, the term connectivity density is sometimes used to define the connectivity per unit volume. In the case of Column 1, the connectivity density is equal to 4772 loops/m³.

View larger version (16K): [in this window] [in a new window]   Fig. 19 Connectivity of macropore networks and their number of branches (Column 1)

	Summary and conclusions

TOP ABSTRACT INTRODUCTION Terminology Materials and methods Results and discussion Summary and conclusions REFERENCES

Our results suggested that the numerical density varies between 13421 to 23562 macropore networks/m³ of soil. No direct relationship could be observed between numerical density and macroporosity. The position and the length of macropore networks were evaluated. The artificial macropore installed in one of the soil columns was readily detected. It was found that the majority of the macropore networks had a modal length of 40 mm, a volume of 60 mm³, and a wall area of 175 mm². However, some macropore networks, although representing only a small percentage, could reach a length of 750 mm, a volume of 10000 mm³, and a wall area of 50000 mm².

The hydraulic radius in three dimensions was also assessed as an indication of the ability of the networks to convey water. It was found that the greater the length of networks, the greater the hydraulic radius. On average, macropore networks had a hydraulic radius of 0.13 mm.

Our results on network inclination suggest that it ranges from vertical to an angle of about 55° from the vertical. The overall tendency of network inclination distributions suggests that the smaller the inclination, the greater the number of macropores.

Results for tortuosity indicated that the majority of the networks had a tortuosity between 1 and 1.4. The mode of the tortuosity distributions suggested that most macropore networks had a 3-D tortuous length 15% greater than the distance between its extremities. It was found that some macropore networks had a tortuosity as high as 2.4.

More than 60% of the networks were made up of four branches. Our results for Column 1 suggested that 82% of the networks had a connectivity of 0 (zero). The connectivity density was equal to 4772 nonredundant loops/m³.

The 3-D arrangement of networks of soil macropores plays a determining role in the rate of water and solute movement through soil. These results can be used to determine and quantify the effect of 3-D geometry of macropore network on solute transport through soil columns.

	ACKNOWLEDGMENTS

 
The authors wish to thank Daniel Marentette for his help and suggestions in the technical part of this work. The authors also gratefully acknowledge the financial support provided by the Natural Sciences and Engineering Research Council of Canada (NSERC) and the Environmental Science and Technology Alliance Canada (ESTAC).

Received for publication September 28, 1998.

	REFERENCES

TOP ABSTRACT INTRODUCTION Terminology Materials and methods Results and discussion Summary and conclusions REFERENCES

 

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