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a UMR Environnement et Grandes Cultures, INA P-G/INRA, 78850 Thiverval-Grignon, France
b CSIRO Land and Water, Pye Laboratory, GPO Box 1666, Canberra, ACT 2601, Australia
c The Institute of Soil, Water and Environmental Sciences, Volcani Center, A.R.O., P.O.B. 6, Bet-Dagan 50250, Israel
* Corresponding author (Louis-Marie.Bresson{at}grignon.inra.fr).
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ABSTRACT |
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 TOP ABSTRACT INTRODUCTIONMATERIALS AND METHODSRESULTS AND DISCUSSIONCONCLUSIONSREFERENCES |
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INTRODUCTION |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTS AND DISCUSSIONCONCLUSIONSREFERENCES |
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 | [1] |
0 is the initial bulk density (g cm–3), s is the bulk density at the crust surface (g cm–3), z is the depth (mm), and 
is a factor (mm–1) describing the particular interaction between soil and rain. The poor vertical resolution of available methods for bulk density measurement did not allow a direct validation of the model, and an inverse method was applied to test it from infiltration data. Furthermore, the model suggests that the crust hydraulic properties, namely, the water retention curve and the hydraulic conductivity function, can be estimated using the initial undisturbed soil properties and the crust bulk density distribution with depth (Eq. [1]). Consequently, bulk density profiles could be used to model (i) the evolution of a given soil structure to the crusted state and (ii) the related changes in the hydraulic properties of the soil surface (Assouline and Mualem, 1997). The model was found to simulate and predict accurately flow processes under crusting conditions for a wide range of soil and rainfall properties (Assouline and Mualem, 2000).
Studying the relationships between crust bulk density and texture, Roth (1997) suggested that a sigmoidal function (Fig. 1) could be more appropriate than the exponential one because once the maximum compaction at the surface has been attained, further raindrop impacts would be likely to induce maximum compaction at increasing depth as suggested by Moss (1991). The empirical function suggested by Roth (1997) to describe this assumption is:
 | [2] |
0, s, and z are as above, and 
(mm–1) and 
(without dimension) are shape factors related to the soil–rain system. Inspection of this function reveals that is inversely related to the depth at which the maximum compaction is transmitted, and that is, like in Eq. [1], directly related to the rate of bulk density decrease with depth. Roth (1997) tested the exponential and the sigmoidal models by sampling 2 by 2 cm specimens of various thicknesses, as suggested by Mualem and Assouline (1989). The bulk density of these specimens was measured by immersion in water after saturation by low viscosity oil, and then bulk density depth functions could be computed. Both models showed a good fit to measured data, the exponential appearing to represent the initial stages of crust formation, and the sigmoidal, the later stages. However, the procedure used to generate the bulk density depth functions from the bulk density of specimens of various thicknesses is based on the assumption that the specimens are replicates of the same crust, which is compromised by crust lateral heterogeneity. Quantitative measurement of soil bulk density and water content of undisturbed soil samples have been obtained using X-ray tomography (e.g., Anderson et al., 1988; Heijs et al., 1995), but the vertical resolution of X-ray scanners is rather poor (usually around 1 mm for practical reasons). Moreover, X-ray scanners are very expensive and might not be easily accessible.
The aim of this work was to evaluate the two functions for crust bulk density distribution with depth (Eq. [1] and [2]) and to refine them if necessary. For this purpose, we used high-resolution images from calibrated X-ray radiography of resin-impregnated soil slices (Bresson and Moran, 1998) to generate high-resolution bulk density depth functions. Previous studies have shown that the microstructure and the related hydraulic properties of surface crusts greatly depend on the processes involved in their formation according to the soil, climatic, and management conditions (Valentin and Bresson, 1992; West et al., 1992; Bresson and Valentin, 1994). Therefore, various structural crust types, that is, slaking, infilling and coalescing, were formed using repacked seedbeds and rainfall simulation, and using different soil materials and initial water contents. The measured bulk density depth distributions were discussed in terms of crusting processes and the exponential and sigmoidal crusting models of were compared. Further, the structure of the seedbed underlying the crust was also considered because wetting is likely to cause structural collapse (slumping) within the whole seedbed (Bresson and Moran, 1995, 2004).
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MATERIALS AND METHODS |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTS AND DISCUSSIONCONCLUSIONSREFERENCES |
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A coalescing crust was formed on a repacked seedbed using a highly unstable silty loam soil (Typic Hapludalf) from Englesqueville (France) (Bresson et al., 2001). The main physical and chemical data of the soil material are given in Table 1. The water content was maintained as sampled in the field. Aggregates ranging from 0 to 30 mm were gently packed in a 10 by 30 by 10 cm box, with an initial bulk density of about 1.1 g cm–3 as measured on a replicate (Bresson et al., 2001). The seedbed was subjected to the same conditions of simulated rainfall as used to form the other crusts, using deionized water (Le Bissonnais et al., 1995).
Following rainfall simulation, all samples were air-dried and impregnated using polystyrene resin. Once cured, one vertical 2-mm thick slice, 8 cm wide and 4 to 8 cm high, was prepared from each resin-impregnated crust type.
Generation of High-Resolution Bulk Density Images
High-resolution X-ray images were obtained using a standard X-ray generator for X-ray diffractometry. A Co anode tube, with a Fe ß filter, was fitted to the top of a 2.5-m high lead-lined chamber and run at 35 kV and 20 mA. Films were digitized on a flat bed scanner at 360 dpi resolution (pixel size: 70 µm). Bulk density images were generated using the calibration procedure of Bresson and Moran (1998). In brief, the digitized image gray levels were calibrated in terms of glass thickness using images of a glass staircase, then the ratio between the attenuation coefficients of glass and soil were determined using images of remolded soil bricks of known bulk density.
Generation of Bulk Density Depth Distributions
Surface crusts are generally thin and do not have a horizontal and smooth surface. Therefore, horizontal lines cannot be used for generating depth distributions. We generated lines that were first equidistant from the soil surface then were smoothed to linearize with depth.
To define the soil surface, each column of the image was scanned from the top until a pixel with bulk density >0.5 g cm–3 was located. The resulting line was then slightly smoothed using a running mean to take into account the possible macropore openings to the atmosphere. This line defined the soil surface.
The topography of the soil surface controls only the crust conditions over a limited depth range. Therefore, at some depth below the surface, it is desirable that the line across which the mean density is measured becomes horizontal. This was achieved by smoothing the line slightly at each depth increment, starting with the 51st line that is, 3.5-mm depth (Fig. 2). Smoothing was performed using a running mean whose window length was proportional to the depth below the surface. It is possible that smoothing the line could result in some pixels belonging to more than one line. Therefore, the minimum increase in depth for each line was computed to avoid any line overlapping.
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Fitting of Functions
To test the validity of Eq. [1] and [2] (Fig. 3a,b), fitting using the least squares method was performed. In the case of Eq. [2], one parameter of the function was fixed, namely, the initial bulk density, 0, derived from the fit of Eq. [1].
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-ray attenuation. This arises because of additional densification processes that can affect the whole seedbed, that is, aggregate settling and fine particle agglomeration resulting from capillary forces on wetting, and aggregate coalescence induced by overburden pressure. Assuming that the main densification process below a crust is aggregate coalescence, and considering the small range of overburden pressure within a seedbed, it could be assumed that the increase in bulk density is linearly related to overburden pressure, and therefore to depth. This is not a process-based slumping model because the physics of compaction under overburden pressure is not explicitly taken into account. A semi-empirical function that describes seedbed slumping is:
 | [3] |
0 and z are as above, and m (g cm–3 mm–1) is a factor depending on the rheological properties of the soil material.
We applied this linear slumping model below the crust and either the exponential or the sigmoidal functions through the crust, as combined models of seedbed dynamics. First, we fitted the linear slumping model (Eq. [3]) to the data below the morphologically defined crust where the crusting processes are likely to be negligible, using least squares fit (Fig. 3b). Then, the measured data were corrected for the slumping effect, and the exponential and sigmoidal crusting functions (Eq. [1] and [2]) were fitted, with the initial density (0) being fixed at the value derived from the fit of the slumping effect (Fig. 3c). Eventually, the combined slumping–crusting models could be produced (Fig. 3d).
The quality of the fitting was evaluated by a qualitative appraisal of the shape of the fit compared with the shape of the density profile, and by the root mean square error (RMSE).
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RESULTS AND DISCUSSION |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTS AND DISCUSSIONCONCLUSIONSREFERENCES |
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The new type of information provided by the X-ray analysis raises the question of the regularity of the crust, both horizontally and vertically. The standard deviation along a "horizontal line" was quite large (0.4 in average for the whole seedbed), but a bit smaller within the morphologically defined crust (0.35 in average). The bulk density depth function measured here (Fig. 3b) was more irregular than expected by Mualem and Assouline (1989). Irregularity refers to the variation about the mean density that is predicted using a functional fit. This irregularity was related to the presence of coarse aggregates and large pores, because the horizontal section of soil probed by each measuring line was small (2 by 80 mm, i.e., 1.6 cm2) compared with the cross-section of coarse aggregates (2.6 cm diameter; i.e., 5.3 cm2). The depth functions generated by Roth (1997) on 2 by 2 cm wide samples (i.e., 4 cm2 horizontal section area) were more regular, but samples without aggregates greater than 6 mm had been selected (Roth, 1997).
The bulk density at the soil surface measured here is significantly smaller than those published by Roth (1997): 1.35 g cm–3 compared with 1.60, 1.64, 1.80, and 1.88 g cm–3. This disagreement might be due to differences in (i) crust properties, (ii) sampling procedures, and (iii) measurement techniques. Roth's initial bulk densities were much greater than the one used here (about 1.4 and 1.06 g cm–3, respectively), which might have lead to much denser crusts. Actually, it is clear from the bulk density image (Fig. 3a) that significant macroporosity still exists in this crust. Also, selecting samples without aggregates >6 mm (Roth, 1997) might have lead to selection of the densest parts of the crust. Finally, the immersion procedure used by Roth might have lead to overestimation of the bulk density because any macropore is expected to drain before the sample is immersed in the oil. This is the reason why Roth (1997) corrected his measurements with a 0.974 factor, but this correction might have been a bit too small. Conversely, the smoothing used here to define the surface line accounted for crust macropores opened to the surface
The bulk density at the soil surface was smaller (by about 0.15 g cm–3) than that of the structure induced by capillary rise wetting in a poorly aggregated seedbed prepared from the same material (Bresson and Moran, 1995; Bresson and Moran, 1998). This is consistent with the role of the aggregate (or fragment) size distribution in the tightness of packing: the maximum density attained at the soil surface with slaked aggregate fragments is smaller than the theoretical maximum density attained by packing of primary particles.
The fitted parameters of the exponential and the sigmoidal crusting models are given in Table 2. The sigmoidal model apparently provided a better fit of the crust bulk density distribution with depth than the exponential model. The RMSE was smaller (Table 4) and, qualitatively, the sigmoid shape fitted the data better (Fig. 3b). This indicates that the crust has reached its maximum density under the prevailing conditions (Roth, 1997). Eventually, if the exponential function is applied for deriving hydraulic properties, as suggested by Mualem and Assouline (1989), it is likely that the hydraulic conductivity is underestimated at the surface and overestimated within the crust.
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0, was close to the value measured on a replicate (1.08 and 1.06 g cm–3, respectively). Then the data corrected for slumping were fitted to the exponential and sigmoidal functions (Fig. 3c and Table 3). As evidenced by the reduced RMSE (Table 4), the combined slumping–crusting models resulted in a better fit, not only within the underlying layers of the seedbed, but also within the crust (Fig. 3d).
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The maximum bulk density of the crust was larger in the infilling crust compared with the slaking crust (1.49 g cm–3 instead of 1.39 g cm–3). Le Bissonnais (1996) showed that slaking tends to release aggregate fragments rather than primary particles. On the contrary, infilling crusts result from the clogging of interaggregate packing voids by primary particles detached by raindrop impact (Bresson and Cadot, 1992), which leads to tighter packing.
The slumping effect was larger in the infilling crust compared with the slaking crust (Table 3). In the infilling crust, prewetting induced some slaking at the bottom of the seedbed and therefore enhanced aggregate coalescence as observed in similar seedbeds by Bresson and Moran (1995)(2004). In the slaking crust, which was dry before rain simulation, slaking at the bottom of the seedbed might have not occurred because the wetting rate was likely to have been rather slow due to the rapid development of the overlying crust.
The exponential model and the sigmoidal models were fitted to the data corrected for slumping (Table 3). The fit was slightly better for the sigmoidal model (Table 4), even though it underestimated the bulk density at the surface (Fig. 4b). Qualitatively (Fig. 4b), however, the bulk density profile indicates that the maximum compaction was not attained at the top of the crust, which is consistent with the slow development of infilling crusts related to prewetting (Bresson and Cadot, 1992).
Coalescing Crust
The coalescing crust was formed by coalescence under plastic state (Bresson and Boiffin, 1990) rather than by aggregate breakdown. The whole seedbed was affected, which resulted in a strong global slumping. The bulk density image (Fig. 5a) showed a continuous dense material with convexo-concave voids that typically result from the coalescence of large aggregates. Coalescence of smaller aggregates could also be observed, with the initial aggregates still visible as they form a dense, continuous matrix (Fig. 5a).
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The fitted parameters for the slumping model, and the exponential and sigmoidal models are given Table 3. It is clear from the bulk density profile (Fig. 5b) and from the RMSE (Table 4) that the sigmoidal function is a better model for that crust than the exponential one. This shows that, in this highly unstable material, which was already dense due to slumping, the maximum bulk density of the crust was quickly attained and therefore propagated up to 4 mm deep under further raindrop impact.
Because wetting caused significant slumping to the aggregate bed below the crust, it is very likely that the measurement of the initial, that is, before rainfall, hydraulic properties would induce such a slumping. Therefore, deriving the hydraulic properties of a crusted bed using the changes in bulk density as a correcting factor requires that the initial density profile be measured after the hydraulic properties are determined, that is, on the slumped seedbed, rather than on the initial dry seedbed.
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CONCLUSIONS |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTS AND DISCUSSIONCONCLUSIONSREFERENCES |
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Given the small number of crusts and the absence of replicates, the above results only (i) illustrate the potential of the method to model the bulk density profiles resulting from crusting and slumping, (ii) show that the existing exponential and sigmoidal crusting models must be coupled with a slumping model. Characterizing crust types would have required new experiments involving a larger set of crusts and using more replicates.
Further research should now address the issue of determining the specific bulk density versus hydraulic properties relationships of the main types of structural crusts. These relationships are likely to be different in crusts formed by coalescence, which barely affects the aggregate/fragment-size distribution, compared with those formed by slaking or infilling, which rather involve aggregate disruption.
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ACKNOWLEDGMENTS |
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Received for publication July 21, 2003.
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTS AND DISCUSSIONCONCLUSIONSREFERENCES |
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