The origin and loss of fractal scaling in simulated soil aggregates

A growing body of evidence supports the use of fractals to approximate the heterogeneous structure of soil. Fractal models of transport processes in soil indicate that the fractal dimension and the upper limit to fractal scaling (denoted ξ) determine flow rates and scaling properties. A two-dimensional Monte Carlo simulation of soil aggregation is used to identify the key processes which may lead to fractal-like scaling in the soil matrix. A bonding law is developed which parameterizes the relative importance of chemical bonding to binding by microbial by-products and fungi. We investigate the sensitivity of the fractal dimension and ξ to the nature of the bonding law, and to aggregate fragmentation, initial particle size distribution and mechanical restructuring. Fractal-like structures result from the aggregation process. However, the measured fractal dimension is insensitive to the detailed form of the bonding law. The factor that most sensitively influences the fractal dimension is found to be mechanical restructuring such as would arise from the action of roots, soil fauna and natural weathering. By contrast, ξ is most sensitive to the bonding law. The results suggest that the fractal dimension and characteristic diameter of aggregates should be uncorrelated, and that increased binding by microbial by-products and fungi should produce larger, less dense, aggregates.     

The fractal structure of soil aggregates: its measurement and interpretation

The theory of fractal geometry is presented with reference to soil structure. Recent work on relating fractal structure to pore structure in soils is reviewed. It is suggested that the connection made in previous work between the fractal dimension and soil moisture retention curves is based on simplified assumptions that complicate the interpretation of results. A simple method for estimating the fractal dimension, D, of natural aggregates which circumvents some of these assumptions is presented. Preliminary results of aggregates from soils under different management systems show that, for the soils examined, D ranged from 2.75 to 2.93. The use of D to quantify heterogeneity in soil is explored.     

The pore–solid fractal model of soil density scaling

We have developed the fractal approach to modelling variations in soil bulk density and porosity with scale of measurement or sample size. A new expression is derived for each quantity based on the pore–solid fractal (PSF) model of soil structure. This new general expression covers a range of fractal media and accommodates existing fractal models as special cases. Model outputs cover a range of scaling behaviour expressed in terms of monotonic functions, from increasing density and decreasing porosity, through constant porosity and density to decreasing density and increasing porosity with increasing scale of measurement. We demonstrate the link between this new model for the scaling of porosity and bulk density and the water retention model for the PSF. The model for scaling bulk density is fitted to data on aggregate bulk density and shown to yield good fits describing bulk density decreasing with increasing aggregate size. Porosity scaling is also inferred from the fitting of water retention data. Inferred porosities from different fittings are shown to follow decreasing, scale‐invariant and increasing values with decreasing size of structural unit, and these theoretical results emphasize the need for further experimental investigation on the basic issue of density scaling in soil science.     

Tillage effects on shear strength and bulk density of soil aggregates

An experiment was conducted to determine the effect of four tillage systems (moldboard plow, chisel plow, Paraplow and no-till) on soil aggregate shear strength and bulk density. Two soils, a Canisteo clay loam (fine-loamy, mixed (calcareous), mesic, Typic Haplaquoll) and a Haig silt loam (fine, montmorillonitic, mesic, Typic Argiaquoll) were used in this study. Soil samples were collected from the 0.075–0.15-m-depth increment in 1983 and the 0.075–0.15- and 0.225–0.30-m-depth increments in 1985. Shear strength of soil aggregates 0.02–0.03 m in diameter was measured by a fall-cone penetrometer and bulk density of the same aggregates was measured by gamma-ray attenuation. Aggregates were tested at soil water matric potentials (ψ_m) of −0.2, −1.1 and −4.0 kPa in 1983 and at ψ_m of −0.2, −1.1, −4.0 and −7.9 kPa in 1985. Tillage for the 1983 growing season was conducted under very wet conditions, whereas tillage for the 1985 growing season was conducted under much drier conditions. Samples collected in 1983 showed little tillage effect on shear strength or bulk density. In 1985, tillage had an effect on shear strength and bulk density for the Haig soil, but not for the Canisteo soil. Much of the tillage effect on soil aggregate shear strength could be explained by tillage-induced changes in the aggregate bulk density. As bulk density decreased, soil aggregate shear strength decreased.Sampling depth had no effect on soil aggregate shear strength or bulk density. Matric potential had an effect on soil aggregate shear strength and bulk density. As matric potential decreased, both shear strength and bulk density increased.     

Dependence of tensile strength of soil aggregates on soil constituents, density and load history

The compressive-tensile stress ratio at failure under unidirectional loading of air-dry samples of 10 soils was compared with their clay and CaCO₃ contents, and their surface areas. Deviations from the commonly assumed Griffith theory were found for two soils. No special relationships were found between soil constituents and associated compressive tensile stress ratio, even though this ratio tends to decrease slightly with increasing clay percentage.     

Novel impacts of nanoparticles on soil properties: tensile strength of aggregates and compression characteristics of soil

Nanoparticles (NPs) affect most soil properties but there have been no assessments of their effects on the compression behavior of soil and the strength of aggregates. Therefore, we assessed the impact of NPs on the bulk density and the confined compression and tensile strength of aggregates of a calcareous loamy soil. Using a factorial design, we assessed the effects of two factors on the soil properties, i.e., NP type (first factor) at two levels comprising Fe nano-oxide (Fe₃O₄, N₁) and Mg nano-oxide (MgO, N₂), and treatment amount (second factor) at four levels with dry mass percentages of 0%, 1%, 3%, and 5%. The soil bulk density increased with the Fe level but decreased with the Mg level in ranges of 0.02–0.04 and 0.02–0.08 g cm^–3, respectively. The compression curve characteristics were not affected by the NPs. Compared with N₁, the N₂ treatment significantly increased the soil void ratio in 86% of the applied stresses. N₁ also significantly enhanced the soil tensile strength at suctions of 30, 100, and 1500 kPa, ranging from 0.5 to 15.3 kPa. The 3% Mg and 1% Fe dosages of nano-oxides had the optimal effects, so they should be considered in future investigations.     

半湿润区长期施肥对土壤结构体分形特征的影响

利用黄土高原南部半湿润地区长达25年田间肥料定位试验020.cm土层土样,研究了长期不同施肥模式与土壤结构体大小、结构体分形特征与土壤肥力的相互关系。结果表明,长期不同施肥模式下土垫旱耕人为土结构体分形特征存在一定差异:7种施肥处理土壤结构体分形维数分布在2.4388～2.6363之间,其中以化肥+厩肥处理土壤结构体分形维数最大,不施肥土壤结构体分形维数最低,说明化肥与有机肥长期配施对土壤团聚体结构分布影响较大。相关分析发现,土壤结构体分形维数与5～2mm团聚体间具有极显著的正相关关系(r=0.994,P0.01);与土壤有机碳、全氮、硝态氮、有效磷含量均具显著正相关关系,与土壤碳氮比(C/N)呈显著负相关关系。在长期不同施肥模式下,分形维数对土壤性质变化的边际量亦有明显差异:土壤结构体分形维数每增加一个单位值,土壤有机碳、全氮、C/N、硝态氮和有效磷的变化依次为31.628%、2.404%、-6.014%、90.370%和172.760%。由边际分析可知,长期施肥条件下土壤结构体分形维数的变化对土壤有效磷、硝态氮的影响最大。     

On the relation between number-size distributions and the fractal dimension of aggregates

Number-size distributions (i.e. particle- and aggregate-size distributions) have historically been used as indicators of soil structure, and recent work has aimed to quantify this link using fractals to model the soil fabric. This interpretation of number-size distributions is evaluated, and it is shown that a number-size relation described by a power law does not in itself imply fractal structure as suggested, and a counter example is presented. Where fractal structure is assumed, it is shown that the power-law exponent, φ, describing the number-size distribution cannot be interpreted as the mass-fractal dimension, D_M, of the aggregate. If the probability of fragmentation is independent of fragment diameter, then the exponent may be identified with the boundary dimension, D_B, of the original matrix. If, however, as is likely, this probability is scale-dependent, then φ may over- or under-estimate the boundary dimension depending on whether the fragmentation probability increases or decreases with fragment size. The significance of these conclusions is discussed in terms of the interpretation of number-size distributions, and alternative methods for quantifying and interpreting soil structure are evaluated.     

Sensitivity of fractal parameters of soil aggregates to different management practices in a Phaeozem in central Argentina

Changes in soil structure often accompany changes in management practices and may affect the effectiveness of these practices. Parameters are needed to quantify these changes. Our objective was to see if fractal dimensions derived from ‘aggregate bulk density–aggregate size’ and ‘aggregate number–aggregate size’ relationships could be applied to quantify such changes. The study was conducted at the Experimental Farm of the School of Agronomy and Forestry Engineering, National University of La Plata, Argentina. A Vertic Phaeozem soil was sampled at seven locations differing in long-term management practices. The ‘aggregate bulk density–aggregate size’ and ‘number of aggregates–aggregate size’ data were obtained for seven ranges of aggregate sizes. Differences in treatments were reflected by the fragmentation fractal dimension but not the mass fractal dimension. The lowest fragmentation fractal dimensions corresponded to plots under long-term no-tillage and the highest to plots with a history of cultivation of rice (Oryza sativa L.) under water. The fragmentation fractal dimension reflected the differences in soil management whereas the mass fractal dimension appeared to be insensitive to those differences.     

生物炭碳固定于稳定性土壤团聚体中：土壤黏土矿物及其它土壤性质的作用

Aggregation and structure play key roles in water-holding capacity and stability of soils.In this study,the incorporation of carbon(C) from switchgrass biochar into stable aggregate size fractions was assessed in an Aridisol(from Colorado,USA) dominated by 2:1 clays and an Alfisol(from Virginia,USA) containing weathered mixed 1:1 and 2:1 mineralogy,to evaluate the effect of biochar addition on soil characteristics.The biochar was applied at 4 levels,0,25,50,and 100 g kg~(-1),to the soils grown with wheat in a growth chamber experiment.The changes in soil strength and water-holding capacity using water release curves were measured.In the Colorado soil,the proportion of soil occurring in large aggregates decreased,with concomitant increases in small size fractions.No changes in aggregate size fractions occurred in the Virginia soil.In the Colorado soil,C content increased from 3.3 to 16.8 g kg~(-1),whereas in the53 μm fraction C content increased from 5.7 to 22.6 g kg~(-1) with 100 g kg~(-1)biochar addition.In the Virginia soil,C content within aggregate size fractions increased for each size fraction,except the2 000 μm fraction.The greatest increase(from 6.2 to 22.0 g kg~(-1)) occurred in the 53–250 μm fraction.The results indicated that C was incorporated into larger aggregates in the Virginia soil,but remained largely unassociated to soil particles in the Colorado soil.Biochar addition had no significant effect on water-holding capacity or strength measurements.Adding biochar to more weathered soils with high native soil organic content may result in greater stabilization of incorporated C and result in less loss because of erosion and transport,compared with the soils dominated by 2:1 clays and low native soil organic content.     

Structure and stability of soil aggregates

The formation and disintegration of macroaggregates into water-stable particles in a wide range of soil water contents—from the hygroscopic moisture to the capillary saturation moisture—were analyzed. It was found that the disintegration of macroaggregates into water-stable particles follows an exponential law. As the system becomes a three-phase system, neighboring particles in the macroaggregate are pressed together due to capillary pressure, and strong molecular bonds are formed. The disintegration curve of macroaggregates is an integral informative characteristic, which reflects the dynamics of changes in the strength properties of the macroaggregates.     

长期施肥对潮土团聚体有机碳分子结构的影响

采取长期施用有机肥（CM）、一半化肥氮和一半有机肥氮（HCM）、化肥（NPK）和不施肥对照（CK）的土壤,用湿筛法分为大团聚体（2000~250 μm）、微团聚体（250~53 μm）和粉砂 黏粒组分（<53 μm）,利用固态13C-核磁共振技术分析了土壤和团聚体中有机质的分子结构特征。结果表明,随着团聚体粒径减小,烷基碳/烷氧碳比值逐渐提高,并与土壤C/N呈显著负相关（R2 = 0.421,p = 0.022）,表明随着团聚体粒径减小,有机质的分解程度不断增加。与对照土壤相比,长期施用有机肥（HCM和CM处理）提高了土壤中烷氧碳和羰基碳的相对含量,烷氧碳的增加主要是由于大团聚体中甲氧基和含氮烷基碳相对含量的增加,羰基碳则主要在大团聚体和微团聚体中积聚。施用化肥土壤提高了烷氧碳和烷基碳的相对含量,烷氧碳增加主要是由于大团聚体中甲氧基和含氮烷基碳以及微团聚体中含氧烷基碳相对含量的提高,烷基碳增加主要发生在大团聚体。有机肥和化肥处理土壤中芳基碳相对含量降低1.8%~4.6%,主要是大团聚体和微团聚体中芳基碳比例下降引起的。而在粉砂 黏粒组分中芳基碳和酚基碳均增加,烷基碳相对含量降低5.9%~7.1%,表明施肥更利于芳香碳在小粒径组分中积累,减弱烷基碳在小粒径组分中的积累。结果表明长期施用有机肥可通过大团聚体和微团聚体物理保护肥料带入的大量碳水化合物和有机酸从而提高土壤有机碳含量。     

土壤供肥量的动态结构探讨

土壤供肥量是耕作土壤重要的肥力参数之一,也是测土配方施肥所需的五大参数之一。土壤供肥量具有动态结构,有一定的弹性范围,具有不同的特征值。不同的特征值对应着不同的施肥配方,各自的准确程度也不同。要降低配方误差,应该采用缺素区代替不施肥区产量来估算施肥量,并且采用合适的目标产量。     

Effect of soil organic matter, electrical conductivity and sodium adsorption ratio on tensile strength of aggregates

The properties of soils affected by salinity and processes involving degradation of soil structure have been partly recognized. However, the effects of saline and sodic conditions on mechanical and physical properties of soils have been studied to a lesser extent. In this research, the effects of electrical conductivity (EC) and sodium adsorption ratio (SAR) on soils possessing various amounts of organic matter were assessed under laboratory conditions. The soils contained a uniform clay type, predominantly Illite. The major difference of the soils was their amount of organic matter content. The treatments consisted of solutions with definite EC and SAR (two levels of EC: 0.5 and 4 dS/m and three levels of SAR: 0, 5 and 15). The amount of tensile strength was dependent on organic matter, EC, and SAR in a way that with the increase of SAR, the tensile strength decreased. In similar SAR, treatments with higher EC exhibited greater tensile strength. Also, the soils with higher organic matter showed greater tensile strength. The analysis of variance showed the significant difference (at 1%) between the mean of parameters analyzed (soil type, sampling depth, EC, and SAR). The order of averages of tensile strength were: permanent pasture (Agropyron elengatum)Festuca arusdinaceae)相似文献   

Composition and structure of aggregates from compacted soil horizons in the southern steppe zone of European Russia

The composition and structure of aggregates from different agrogenic soils in the southern steppe zone of European Russia have been studied. It is shown that the multi-level study (from the macro- to microlevel) of these horizons makes it possible to identify soil compaction caused by different elementary soil processes: solonetz-forming, vertisol-forming, and mechanical (wheel) compaction in the rainfed and irrigated soils. The understanding of the genesis of the compaction of soil horizons (natural or anthropogenic) is important for the economic evaluation of soil degradation. It should enable us to make more exact predictions of the rates of degradation processes and undertake adequate mitigation measures. The combined tomographic and micromorphological studies of aggregates of 1–2 and 3–5 mm in diameter from compacted horizons of different soils have been performed for the first time. Additional diagnostic features of negative solonetz- forming processes (low open porosity of aggregates seen on tomograms and filling of a considerable part of the intraped pores with mobile substance) and the vertisol-forming processes (large amount of fine intraaggregate pores seen on tomograms and a virtual absence of humus–clay plasma in the intraped zone)—have been identified. It is shown that the combination of microtomographic and micromorphological methods is helpful for studying the pore space of compacted horizons in cultivated soils.     

Root growth and phosphorus uptake in relation to the size and strength of soil aggregates. I. Experimental studies

Cotton and sunflower were grown in pots containing aggregates of 6 different sizes in the range of 1–19 mm. The penetrometer pressures of individual aggregates from each pot were measured with a 1-mm diameter blunt (total cone angle 60°) probe, driven at 3 mm min⁻¹. Root lengths within aggregates, in voids and along the surface of aggregates were measured after 15 days of growth. Root hair lengths were also measured. At this time, plant tops were harvested and phosphorus concentrations in the tops were determined.Maximum penetrometer pressure was significantly higher with large than with small aggregates. Total root length and the proportion of the total length growing within aggregates was greater with small aggregates, while mean root hair length was greater with large aggregates. Dry weight and phosphorus content of plant tops was higher in beds of small aggregates than in beds of large aggregates. The lower root growth and phosphorus uptake in beds of large compared with small aggregates is attributed to greater mechanical impedance to root penetration and lower availability of phosphorus.     

Residual effects of additions of calcium compounds on soil structure and strength

Soil structure was measured from the roughness of soil fracture surfaces created by breaking unsaturated soil clods under tensile stress. Soil clods were collected in 1986 and 1987 from field plots to which calcium compounds had been applied in 1980 (to improve degraded structure) at rates of 0, 2, 4, 10, 14 and 20 t ha⁻¹, and which had not been disturbed since the initial establishment of pasture. A residual effect on the soil structure was sought. In 1987, samples were equilibrated at different water suctions in the laboratory, and physical and chemical measurements including tensile strength, penetrometer resistance, exchangeable cations and dispersible clay were made.

Exchangeable cation and dispersible clay values did not correspond with the amounts of calcium added in 1980, indicating that most of the applied calcium had leached by the time measurements were made in 1986 and 1987. The water content at which measurements were made was the dominant factor controlling the tensile strength and penetrometer resistance of the soil clods. The water content also had a major influence on the fracture surface roughness; wetter clods had rougher tensile fracture surfaces. Because most of the applied calcium was leached by the time measurements were made, the residual effect of the calcium amendments was only detectable in the microstructure (undisturbed since 1980). Soils to which greater amounts of calcium had been added tended to have clods with smoother tensile fracture surfaces. This was attributed to stabilization by calcium of aggregates with diameters up to 0.1 mm in the soil structural hierarchy. The importance of the scale at which fracture surface roughness measurements are made is emphasized.     

Modified technique to assess the wettability of soil aggregates: comparison with contact angles measured on crushed aggregates and bulk soil

Wettability parameters determined for individual soils often show a considerable variation depending on the kind of sample (aggregated or homogeneous material) and the method used. To investigate the causes of this variation, we assessed wettability of both intact and crushed aggregates and bulk soil using different methods. Wettability of intact aggregates was characterized by a modified technique where the specific infiltration rates of water and a completely wetting liquid were used to define a repellency index. Contact angles were determined on crushed aggregates and bulk soil using the Wilhelmy plate and capillary rise methods. The repellency index was found to be sensitive to slight differences in wettability and was in good agreement with Wilhelmy plate contact angles. Contact angles measured with the capillary rise method showed a strong deviation from those determined with the Wilhelmy plate method. This can be ascribed to the underlying assumptions of the capillary rise method (i.e. cylindrical and parallel capillaries) resulting in an over‐estimation of contact angle, particularly for the small‐sized particle fraction because of the impact of inertia and pore structure. No significant differences were found between intact and crushed aggregates whereas the bulk soil was slightly more water‐repellent, probably because of a somewhat larger organic carbon content. We conclude that the contact angle determined by the Wilhelmy plate method and the repellency index are appropriate parameters for characterizing soil water repellency because they detected small changes in wettability over a wide range extending from subcritical water repellency to hydrophobicity.