Fractal Dimension Of Particle Size Distribution Research Articles

Fractal dimension of particle-size distribution and their relationships with alkalinity properties of soils in the western Songnen Plain, China

The purpose of this study was to identify the fractal dimension and their relationships with alkalinity properties of soils, and to evaluate the potential of fractal dimension as an indicator of alkalinity properties of soil. Six soils with an increasing salinity (electrical conductivity was 0.09, 0.18, 0.62, 0.78, 1.57 and 1.99 dS m−1, respectively) were selected from the western part of the Songnen Plain (China). Salt content, exchangeable sodium percentage, sodium adsorption ratio and other properties of the soils were determined and the soil particle-size distribution (0–2000 μm) was measured using a laser diffraction particle size analyser. Our results show that the overall fractal dimension of the selected soils ranged from 2.35 to 2.60. A linear regression analysis showed a significant negative correlation between fractal dimension and the amount of coarse sand and fine sand (r = − 0.5452, P < 0.05 and r = − 0.8641, P < 0.01, respectively), and a significant positive correlation with silt and clay (r = 0.9726, P < 0.01 and r = 0.9526, P < 0.01, respectively). Thus, soils with higher silt and clay content have higher fractal dimension values. Strong linear relationships between fractal dimension and salt content (P < 0.05), in particular a very significant positive relationship with HCO3− (P < 0.01), also exist. It is therefore possible to conclude that a soil’s fractal dimension could serve as a potential indicator of soil alkalization and the variability in alkaline soil texture.

Fractal analysis of the infiltration curve and soil particle size in a semi‐humid watershed

AbstractAlthough fractal mathematics has been commonly used to quantify particle size distribution (PSD), limited attention has been paid to the fractal dimension of the infiltration curve (DI). Therefore, it is necessary to determine whether the DI and fractal dimensions of PSD (Dm, Dclay, Dsilt and Dsand) can reflect the infiltration process, and soil erodibility and degradation. Accordingly, this study aimed to provide new information on the quantification of infiltration processes, and soil erodibility and degradation, using DI and Dm in the Soorak basin in the northern part of Iran. The soil and infiltration properties were calculated by field and laboratory practices on 46 topsoil samples and 34 infiltrometer double‐ring tests. Correlation, regression and redundancy analysis (RDA) were used to identify relationships between the infiltration curve and PSD coordinates with soil and infiltration properties. Results indicated that the DI was significantly linearly correlated with other infiltration curve characteristics, with the correlation coefficient ranging from −0.737 to −0.403 (sig. = 0.000–0.037). However, there was no significant correlation between DI and Dm, Dclay, Dsilt and Dsand. Different erodibility factors, especially KUSLE, had significant relations with Dm, Dclay, Dsilt, Dsand and DI (p &lt; .01), suggesting that these fractal dimensions are indicators of soil degradation. Other findings indicated that the land use had no significant effect on DI and infiltration properties, whereas KUSLE, Dm, Dclay, DSilt and DSand were significantly affected by land‐use patterns (p &lt; .01). These findings demonstrate that fractal dimensions of PSD and infiltration can be practicable indices to analyse soil degradation under different land‐use types.Highlights How fractal geometry adds to understanding of the infiltration process and soil degradation. Fractal dimensions of infiltration (DI) can describe the infiltration process. Fractal dimensions of soil (Dm) and DI can be used as indicators of the soil erodibility. Erodibility and fractal properties of soil were significantly affected by land use.

Fractal Features of Soil Particle Size Distributions and Their Implications for Indicating Enclosure Management in a Semiarid Grassland Ecosystem

Soil particle size distribution (PSD) is becoming an increasingly useful tool for the objective description of soil structure and intrinsic links between soil and the environment. Here we examined the fractal features of PSD and its correlation with soil physiochemical properties in grasslands under grazing and protected from grazing (enclosure) animals, before and after plant growing periods in a semiarid grassland ecosystem, in northern China. Our results showed that sand content was significantly higher in grassland soils under grazing compared with the enclosure at both sampling times (May and September), whereas their silt and clay contents followed the reverse pattern. The fractal dimensions of PSD (Dm) under enclosure were significantly greater than those found under grazing. The soil clay, silt contents and Dm were positively correlated with soil total N, total C, soil pH, and moisture content. By contrast, the soil sand content declined with increasing total N, total C, pH, and moisture content of soil. The soil fractal dimension of PSD had a positive correlation with soil clay and silt content, whereas it had a negatively correlated with sand content. From these results, we conclude installing enclosures can promote soil clay, silt, and soil particles' fractal dimension, with the latter could be used as a quantitative indicator of soil fertility characteristics. But it is unnecessary to use the fractal dimension of PSD as an index to evaluate the effects of enclosure management on degraded grassland.

Effects of frame beam on structural characteristics of artificial soil on railway cut‐slopes in southwestern China

AbstractCut‐slope restoration technologies commonly used in southwest China mainly include using simple outside soil spray seeding (OSSS) techniques, or OSSS combined with an anchor frame beam. Artificial soil used in OSSS can establish a soil layer suitable for revegetation; the addition of an anchor frame beam not only fixes soil and shallow rock, it also acts to strengthen deep rock. However, there have been few studies on the effects of frame beams on artificial soil structural characteristics on railway cut‐slopes. In order to evaluate the effects of different frame beams on artificial soil structure, soil samples from a natural slope (NS) and three cut‐slopes restored using OSSS with various frame beams (AS, arched slope; DS, diamond slope; and RS, rimless slope) were analyzed. Soil structural characteristics analyzed include particle‐size percentage and cumulative distribution curve of dry‐sieving and wet‐sieving aggregates, structural failure rate, water stability factor, soil particle size distribution (PSD), bias and peak convex coefficients, fractal dimension of PSD (Dm), and fundamental properties. Our results indicate that structural failure rate, water stability factor, fractal dimension of PSD, soil bulk density, total porosity, moisture content, and organic matter are significantly affected by the use of different frame beams. In addition, a difference in wet‐sieving soil aggregates content, PSD, clay and sand particle contents, Dm, and the area difference ΔS of cumulative distribution between AS and DS was evident. Overall, soil structure in cut‐slopes using a diamond frame anchor beam recorded the best levels of recovery after 8 years of ecological restoration.

Microstructural properties and compressive strength of lime or/and cement solidified silt: a multi-scale study

Because of its poor engineering properties, silt often needs to be treated to meet the design requirements. Solidification using binder is one of the most common methods to improve the engineering properties of silt. Lime or/and cement are often used to treat silt. However, the mechanical properties of soil are closely related to its microstructure. Although much research has been done on the mechanical properties and stabilization mechanism of lime or/and cement solidified silt, the multi-scale research between the microstructure and macroscopic mechanics properties of solidified silt has received no attention. Therefore, in this paper, unconfined compression, mercury intrusion, and scanning electron microscope (SEM) tests were conducted on lime, cement, and lime and cement mixtures (LC) solidified silt. The microstructure parameters of particle, pore, and contact zone were extracted from SEM images. Meanwhile, the effect of curing time and binder dosage on the microstructure parameters was analyzed. In addition, the relationship between micro-parameters and macro-mechanical strength was established. The results showed that the particle diameter, particle area, contact zone diameter, and contact zone area increased with increasing curing time and binder dosage, while the pore ratio, fractal dimension of particle size distribution (PSD), and fractal dimension of contact zone size distribution (CZSD) decreased with increasing binder dosage. The unconfined compressive strength (UCS) decreased with the increase of particle roundness, pore area, pore diameter, pore ratio, and fractal dimension of PSD, and increased with increasing fractal dimension of pore size distribution (PPSD). In addition, there were no obvious relationships between UCS and pore roundness, contact zone area, and fractal dimension of CZSD.

The texture, structure and nutrient availability of artificial soil on cut slopes restored with OSSS – Influence of restoration time

Outside soil spray seeding (OSSS) is widely used to restore cut slopes in southwest of China, and artificial soil is often sprayed onto cut slopes to establish a soil layer for revegetation. The stability of artificial soil layer and its supply of water and nutrients for plants is crucial for successful restoration. To evaluate the long-term effectiveness of OSSS, the texture, structure and nutrient availability of artificial soil were studied, various soil samples were obtained from three cut slopes with different restoration time (restored with OSSS in 1996, 2003 and 2007 respectively) and one natural developed slope (NS). The properties measured including soil particle size distribution (PSD), texture, fractal dimension of PSD (Dm), the bias (CS) and peak convex (CE) coefficients of aggregate size distribution, structure failure rate, bulk density, moisture, pH, soil organic carbon (SOC), calcium carbonate content, Available nitrogen (NA), Available phosphorus (PA), and Available potassium (KA). The results showed that different restoration time resulted in significant differences in soil PSD, Dm, CS, CE, structure failure rate, bulk density, moisture, pH, NA, and KA. And these properties improved with increasing restoration age. However, there is still a huge disparity in soil texture, structure, and the availability of nutrients and moisture between the cut slopes and NS over a restoration period of up to 17 years, and this is caused by the little fine particles and the lack of slow release fertilizers and organic fertilizers in the artificial soil, resulting in poorer soil structure stability, retention and availability of moisture and nutrients on the cut slopes. Overall, the OSSS technique shows a long-term effectiveness in southwest of China, but there is still room for improvement.

Fractal features of soil profiles under different land use patterns on the Loess Plateau, China

Fractal theory is becoming an increasingly useful tool to describe soil structure dynamics for a better understanding of the performance of soil systems. Changes in land use patterns significantly affect soil physical, chemical and biological properties. However, limited information is available on the fractal characteristics of deep soil layers under different land use patterns. In this study, the fractal dimensions of particle size distribution (PSD) and micro-aggregates in the 0–500 cm soil profile and soil anti-erodibility in the 0–10 cm soil profile for 10 typical land use patterns were investigated in the Zhifanggou Watershed on the Loess Plateau, China. The 10 typical land use patterns were: slope cropland, two terraced croplands, check-dam cropland, woodland, two shrublands, orchard, artificial and natural grasslands. The results showed that the fractal dimensions of PSD and micro-aggregates were all significantly influenced by soil depths, land use patterns and their interaction. The plantations of shrubland, woodland and natural grassland increased the amount of larger micro-aggregates, and decreased the fractal dimensions of micro-aggregates in the 0–40 cm soil profile. And they also improved the aggregate state and aggregate degree and decreased dispersion rate in the 0–10 cm soil profile. The results indicated that fractal theory can be used to characterize soil structure under different land use patterns and fractal dimensions of micro-aggregates were more effective in this regard. The natural grassland may be the best choice for improving soil structure in the study area.

Fractal characteristics of synthetic soil for cut slope revegetation in the Purple soil area of China

Ai, Y., Chen, Z., Guo, P., Zeng, L., Liu, H., Da, Z. and Li, W. 2012. Fractal characteristics of synthetic soil for cut slope revegetation in the Purple soil area of China. Can. J. Soil Sci. 92: 277–284. Revegetation of the cut slopes formed during railroad construction can reduce potential hazards, improve the quality of the environment, and beautify the landscape along the railways. Artificial backfill soil is required to anchor the plant roots and satisfy the plant's moisture and nutritional demands on the bare rock face. The soil particle size distribution (PSD), fertility and stability of the reconstructed topsoils are affected by the soil type used as a backfill. In this study, a fractal method was used to characterize the PSD. The relationships between the fractal dimension of the PSD and selected soil properties, including soil moisture, bulk density, and organic carbon are discussed. Various soil samples were obtained from four different land-use environments in the purple soil area in southwest, China: a cut slope reconstructed from rock fragments (RF), a cut slope reconstructed with agricultural soil (AS), a naturally developed slope (NS), and a cropland used for growing Vicia faba (CL). Analysis of the soil samples revealed that: (1) from CL to RF, the sand content increased from 59.6 to 83.9%; (2) the fractal dimension of PSD ranged from 2.605 for RF to 2.725 for CL, being the greater the sand content and the lower the fractal dimension; (3) there existed marked linear relationships between the fractal dimensions and selected physicochemical properties of the soils. Therefore, the fractal dimension of PSD can be a useful parameter with which to monitor the structural deterioration and nutrient loss of the synthetic soils used for the revegetation of a cut slope.

Soil texture fractions and fractal dimension of particle size distribution as predictors of interrill erodibility

Choosing a particular textural fraction as an erodibility predictor is often confusing because various fractions of soil particles have been introduced as erodibility index by many researchers. Recently, advances in fractal theory have introduced a scaling parameter for characterizing soil fragments. The objectives of this study were (i) to test the applicability of fractal dimension of particle size distribution (PSD) for estimation of interrill erodibility and (ii) to study the relationship between interrill erodibility and soil texture components. Samples from 36 soil series with contrasting characters were collected from northwest Iran. The sand fractions were obtained by sieving, while silt and clay fractions were determined by hydrometer. Fractal dimension (D_B) of PSD was estimated. A rainfall simulator with drainable tilting flume (1 × 0.5 m^2) at a slope of 9% was used and interrill erodibility (K_i) was calculated for 20, 37, and 47 mm h^{-1} rainfall intensities. The results showed a positive correlation between K_i and clay content. The degree of dependence of K_i to soil texture fractions (sand, silt, and clay contents) was greatly affected by the rainfall intensity level. Using either texture fractions (sand, silt, very fine sand and sand) or D_B did not affect the accuracy of the K_i- predicting models. As use of fractal dimension could follow the principles of uniqueness, fractal dimension of PSD may be applied as an alternative of texture fractions for prediction of interrill erodibility.

Fractal Dimension of Soil Particle Size Distribution Along an Altitudinal Gradient in the Alxa Rangeland, Western Inner Mongolia

The Alxa Plateau of Inner Mongolia exhibits vast differences in vertical distribution in vegetation and soil types. The plant communities range from the alpine meadows at the top of the Helan Mountain (3500 m) to the shrub desert at the foothills (1360 m). This type of ecosystem is common in the northwestern China, yet limited research has been conducted. We studied the fractal dimension (D) of particle size distribution (PSD) in the arid Alxa Plateau. Sixteen study sites were located along an altitudinal gradient of the Helan Mountain and the surrounding Alxa Desert rangeland. In the transformation from meadow, steppe to desert, the sand content in the 0 to 20-cm topsoil increased from 18% to 96%. Soil organic C (SOC) and total N decreased by 97% and 95%, respectively. Soil bulk density increased by 84%, and soil pH increased from 7.49 to 9.33. Vegetation cover decreased by 83% and biomass by 94%. The fractal dimension of PSD ranged from 2.66 to 2.06—the greater the sand content, the lower the D. Although the changes in D showed a narrow range from one range type to another, these changes were statistically significant (P < 0.0001). Vegetation cover, biomass, and soil fertility exhibited nonsignificant changes between some range types. Thus, D is a more sensitive parameter than vegetation cover, biomass, or soil fertility in monitoring the health and vigor of a range site or in estimating the degree of soil degradation. Once a trend in D is established, it could be used to monitor general directions of a particular ecosystem.

Soil fractal features of typical forest stands in Jinyun Mountain, Chongqing City, Southwest China

In order to explore the forest soil physical property in the Three Gorges Reservoir areas, the fractal theory was adopted to study the soil fractal features of the four typical forest stands (mixed Pinus massoniana-broadleaf forests, evergreen broadleaved forests, Phyllostachys pubescens forests and evergreen broadleaved shrub forests) in Jinyun Mountain, Chongqing City, and they were compared with arable land. It has been proposed that the model can be used for the analysis of the relationship between the fractal dimensions and the properties of forest soil. The impacts of fractal dimensions on the soil properties were analyzed with the elasticity analysis and marginal yield analysis. Results showed that the fractal dimension of particle size distribution (PSD), the micro-aggregate size distribution (ASD) and the soil pore size distribution (SPD) can be used as the indices to evaluate the soil structure. In the typical stands of Jinyun Mountain, the fractal dimension of PSD is 2.7–2.9, the ASD is 2.5–2.8, and the SPD is 2.3–2.8. The soil structure of evergreen broadleaved shrub forests performed best in PSD, ASD and SPD, and the soil of P. pubescens forests is the worst. There were some relationships among the PSD, ASD, SPD and some soil properties in the different forests and farmland. The related coefficients are over 0.5. Based on the elasticity analysis and marginal yield analysis, the effect of PSD was more than those of ASD and SPD. Obviously, the further study on the fractal theory application in soil structure and soil properties has important significance.

Impacts of fractal features of soil on moisture infiltration capacity of typical stands in Jinyun mountain of Chongqing city

The soil structure was expressed with fractal dimensions of particle size distribution (PSD), aggregate size distribution (ASD), and soil pore size distribution (SPD). The effect of soil fractal features on soil infiltration velocity and process was studied. The result of the fractal feature shows that fractal dimensions of PSD are obviously greater than those of ASD and SPD, and in different soil genetic horizons, the fractal dimension of ASD has the greatest variability, and shows a downtrend on the top-to-bottom genetic horizon. According to the soil infiltration process curve, the infiltration process was divided into three phases: (1) the initial phase (0–5 min), (2) the transition phase (5–30 min), and (3) the stable phase (30–180 min). In the initial phase of infiltration, the soil structure of soil genetic horizon A was the major influencing factor; in the transition phase of infiltration, the pore distribution of soil horizon AB and soil structure of horizon B were the major influencing factors; in the stable phase of infiltration, the soil structure of horizon C was the major influencing factor to the infiltration velocity. Soil infiltration process is influenced comprehensively by soil PSD, ASD, and SPD. In the overall soil water infiltration, the infiltration in shrub forest land was much faster than that in other land uses, and in the initial infiltration phase, arable land soil infiltration was much faster than that in forest land, and in the stable infiltration phase, the infiltration velocity in forest land was faster than that in arable land.

Estimating specific surface area and cation exchange capacity in soils using fractal dimension of particle-size distribution

Fractal scaling has been proposed as a method to evaluate spatial variability of soil properties. Fractal scaling of particle-size distribution, which controls many dynamic and static processes such as transmission of water and solutes, water holding capacity, heat storage and conductivity, etc., has been widely studied. We evaluated surface fractal dimensions for particle-size distributions, D s, and their relation to specific surface area, SSA, and cation exchange capacity, CEC, for 22 soils with textures, ranging from sandy loam to clay, derived from distinct parent materials under diverse soil forming processes in central Anatolia, Turkey. Values of D s ranged from 2.45 to 2.94, finer textures giving greater D s values. Relationships between D s and SSA or CEC were successfully described by second degree polynomial regression equations ( R 2 = 0.76 and 0.74 for SSA and CEC, respectively). The results revealed that D s can be used as an integrating index in estimating the SSA and the CEC of soils from particle-size distribution, which can be useful in modeling studies.

Fractal features of soil particle size distribution and the implication for indicating desertification

Some of the effects of land desertification on soil properties are manifested by the coarsening of the soil particlesize distribution (PSD) and the losses in organic C and nutrients. The changes and characteristics of PSD and selected chemical properties in soils at the 0–15 cm plough layer from different degrees of desertified croplands are analyzed in the semiarid Horqin Sandy Land, northern China. The fractal dimension of the PSD is emanated to characterize the patterns of PSD. The relationships between the fractal dimension of the PSD and selected soil properties are discussed. The results show that: (1) in the transformation from potential desertified cropland to extremely desertified cropland, the sand content at the 0–15 cm soil increased from 69% to 93%, organic C and total N contents decreased by 65% and 69%, respectively; (2) the fractal dimension of PSD ranged from 2.179 to 2.611, the more the contents of sand, the lower the fractal dimension and the higher the desertified degree of farmland. In the desertification process within the studied area, the mean fractal dimension decreased from 2.555 for the potential desertified soils to 2.298 for extremely desertified soils; (3) there existed considerable linear relationships between fractal dimension and soil properties. It was shown that fractal dimensions of PSD are useful parameters able to monitor soil degradation and to estimate the degree of soil desertification.

FRACTAL SCALING OF PARTICLE AND PORE SIZE DISTRIBUTIONS AND ITS RELATION TO SOIL HYDRAULIC CONDUCTIVITY

Fractal scaling has been applied to soils, both for void and solid phases, as an approach to characterize the porous arrangement, attempting to relate particle-size distribution to soil water retention and soil water dynamic properties. One important point of such an analysis is the assumption that the void space geometry of soils reflects its solid phase geometry, taking into account that soil pores are lined by the full range of particles, and that their fractal dimension, which expresses their tortuosity, could be evaluated by the fractal scaling of particle-size distribution. Other authors already concluded that although fractal scaling plays an important role in soil water retention and porosity, particle-size distribution alone is not sufficient to evaluate the fractal structure of porosity. It is also recommended to examine the relationship between fractal properties of solids and of voids, and in some special cases, look for an equivalence of both fractal dimensions. In the present paper data of 42 soil samples were analyzed in order to compare fractal dimensions of pore-size distribution, evaluated by soil water retention curves (SWRC) of soils, with fractal dimensions of soil particle-size distributions (PSD), taking the hydraulic conductivity as a standard variable for the comparison, due to its relation to tortuosity. A new procedure is proposed to evaluate the fractal dimension of pore-size distribution. Results indicate a better correlation between fractal dimensions of pore-size distribution and the hydraulic conductivity for this set of soils, showing that for most of the soils analyzed there is no equivalence of both fractal dimensions. For most of these soils the fractal dimension of particle-size distribution does not indicate properly the pore trace tortuosity. A better equivalence of both fractal dimensions was found for sandy soils.