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 geometry theory has been used to describe natural bodies and phenomena displaying complicated shapes and self-similar characteristics 1,2 . Soil is a porous medium with a varied particle-size distribution as well as having irregular shapes and a self-similar structure, hence displaying fractal characteristics 3,4 . At present, several researchers have explored different ways of analysing the fractal dimension of materials. Early work by Turcotte 2 found that fractal concepts can be used as a measure of the fragility of fragmented material 2 . Tyler and Wheatcraft 4 and Yang et al. 5 developed a mass-based distribution model to calculate the fractal dimension of particle-size distribution. Following this, researchers have studied features of the fractal dimension of different soils and found that fractal theory was a useful tool for describing the soil particle-size distribution (PSD) and structure 6,7 . However, with more comprehensive studies, the hypothesis of the same density of soil particles with different sizes has been questioned 8,9 . Based on previous research, Wang et al. 9 developed a volume-based model to quantify the fractal dimension of PSD. The volume-based model has been widely used in particle size analysis, as the parameters and data required can be easily and accurately obtained using a laser particle-size analyser, thus allowing the assumption of the same density of soil particles of different sizes to be avoided 10 . Yang et al. 11 compared the volume-based and mass-based models, and found the former underestimated the clay content. To date, fractal theory has been used to describe soil particle-size distribution, aggregate-size distribution, and pore-size distribution 12 . Compared with traditional methods for characterizing soil particle-size distribution, fractal theory describes it well because it can characterize the local shape, size, structure and function of the material and any similarities between the part and the whole 10 .
Fractal theory has been developed and widely used as a "bridge" for describing and quantifying the correlation between the distribution of soil particle-size and the physical and chemical attributes of soils. Several studies

Materials and methods
Study area. The study area is located in the Saline-alkaline Wetland Ecological Experiment Station in the Western Songnen Plain in Northeast China (123° 08′ to 123° 21′ E and 44° 57′ to 45° 45′ N, Fig. 1). This region has an elevation of 110 m to 140 m a.s.l, where the terrain is a low flood plain, with slope gradients ranging from 1/7000 to 1/10,000. It is located within a transition zone between semi-arid to semi-humid and has a continental monsoon climate. Annual rainfall is approximately 396 mm with 73% of it occurring between June and August. The average annual evaporation is 1817 mm, and the average temperature is 2-5 °C 35 . The study area is one of the three major salt-affected areas in the world, with the area of salt-affected soil being close to 3.42 × 10 6 hectares, representing approximately 19.7% of the plain's total area. The salt composition is dominated by NaHCO 3 and Na 2 CO 3 , and it is a typical alkaline soil 35 . Salt-affected soils in the study area are divided into three categories: saline, sodic (alkaline) and saline-sodic meadow soils. Saline soil is mainly distributed around the low flood plain, which has a shallow groundwater level was 1.0-1.5 m. This saline soil shows a patchy distribution, and has an excessive soluble salt content ranging from 1 to 2% at the surface layer. Alkaline soil is distributed about the relatively high levels of the micro-topography, where the groundwater level is 1.5-2.0 m. The salt composition is dominated by sodium bicarbonate, with a pH of more than 9.0 and highly dispersed soil colloids. Saline-sodic meadow soil formed under the influence of micro-topography and is distributed in patches amongst saline and alkaline soils, with the groundwater level being more than 2.0 m below the surface. The zonal vegetation is dominated by meadow plants, with the dominant species being Aneurolepidium Chinese and Chloris virgata. Azonal vegetation is mainly dominated by salt-tolerant plants such as Phragmites australics, Suaeda glauca and Puccinellia tenuiflora. The azonal vegetation presents a mosaic distribution amongst the zonal vegetation 34 .
Sampling design and analysis. The distribution of plant communities is a function of the area's climate and soil, therefore, different plant communities reflect the differences in their environment 36,37 . In the case of this work, halophytes can reflect the degree of salinization and salt composition of an area 38,39 . Several researchers have attempted to explain the vegetation distribution of the Songnen Plain 40,41 . The distribution of plant communities in saline-alkaline land is greatly affected by micro-topography, and different topographies often see the distinctive distribution of plant communities 34 . For example, Suaeda glauca and Artemisia suaeda communities are distributed around depressions, where generally, Artemisia suaeda is found outside of the depression while Suaeda glauca is distributed within it. In the local depression or slightly watery alkaline spots, Pucinellia tennislora communities dominant. Halophytes, such as Suaeda glauca and Artemisia suaeda, grow on the alkaline spots near lakes, while Aneurolepidium Chinese and weeds are mainly distributed across the flat terrain. Phragmites australis communities gradually increase in extent as the soil moisture increase, and sometimes the vegetation composition will transform from grassland formed by Aneurolepidium Chinese to marsh formed by Phragmites australis. In areas where alkaline spots are exposed to the surface, there is often a barren portion where the grass is bare. Some mounds that are far away from river channels, and are low in water content may be reclaimed as arable land and are mainly used to cultivate corn in this region.
Scientific Reports | (2020) 10:20603 | https://doi.org/10.1038/s41598-020-77676-w www.nature.com/scientificreports/ Six sampling sites (i.e., cropland (CL, disturbed by tillage and crops), Aneurolepidium Chinese (AC), Phragmites australis (PA), Chloris virgata (CH), Suaeda glauca (SG), and bare land made up of saline-sodic soil (BL)) were selected at study area in August 2019. As shown in Table 1, the order of the six sampling sites exhibited an increasing trend in salinization. Except for CL, all sites were naturally salt-affected soils without disturbance by tillage or grazing. Surface plant residue and stones were carefully removed, and three soil samples were  Table 1. Physical and chemical properties of soil samples in different plant communities. ECe, ESP, SAR is electrical conductivity of saturated paste extract, exchangeable sodium percent, sodium adsorption ratio of saturated paste extract, respectively; SD is standard deviation, CV is coefficient of variation; CL, AC, PA, CH, SG, BL are different plant communities and stand for cropland, Aneurolepidium Chinese, Phragmites australics, Chloris virgata, Suaeda glauca, and bare land of saline-sodic soil, respectively; NS means normal soil, SS1-SS5 stand for different degree of sodic soil. The value of soil property parameters expressed by average ± standard deviation (n = 3). www.nature.com/scientificreports/ collected using a stainless-steel auger to a depth of 30 cm at each sampling site. All collected soils were placed in polyethylene bags and labelled. After air-drying at room temperature for approximately 20 days, the samples were sieved through a 2-mm sieve to remove coarse debris, roots and stones. A portion of each soil sample was used for determining the particle-size distribution (PSD) by a laser diffraction particle-size analyser (Malvern Instruments 2000, Malvern, England). The range of particle sizes that can be measured by this instrument is 0.02-2000 μm, which provides a continuous volume percentage of particle sizes, with a repeat error of < 2%. Following the United States Department of Agriculture Soil Taxonomy, the particle sizes were classified into three grades, clay (< 2 μm), silt (2-50 μm) and sand (50-2000 μm). Then, in order to yield an appropriate number of data points per sample to allow the linear fitting of the fractal dimension in the next steps, the three grades are artificially subdivided into twenty-four sub-intervals making The rest of the soil samples were used for determining their chemical properties. Soil pH was found by a pH meter (model: FiveEasy Plus in Mettler Toledo) for a slurry consisting of 1:5 (w/v) soil/distilled water. Soil electrical conductivity (EC e ) was determined by measuring the saturated paste extract 42 . All soluble salt ions were measured in a 1:5 soil-water suspension. The total soluble carbonate (CO 3 2− ) in soil, expressed as the CaCO 3 -equivalent (CCE), was found by a rapid-titration method, and the bicarbonate (HCO 3 − ) content were measured by the neutral titration method 42 . The cation exchange capacity (CEC) was measured using sodium acetate (1 M NaOAc) at pH 8.2 43 . Exchangeable Na + (ENa + ) was determined by the CaCO 3 -CO 2 exchange neutral titration method 44 . Soluble sodium ions (Na + ) and potassium ions (K + ) were measured using flame photometry 45 , and the soluble calcium (Ca 2+ ) and magnesium (Mg 2+ ) were measured in the same extract by atomic absorption spectrometry 42 . Chloridion (Cl − ) content was determined by titration of sliver nitrate, and sulfion (SO 4 2− ) content was found by the barium sulfate turbid metric method 46 . The total salt content (SC) was calculated as the sum of the measured cations and anions. Exchangeable sodium percentage (ESP) and sodium adsorption ratio (SAR) were calculated using measured soluble cations 47 : where ENa + is the content of exchangeable sodium (mg kg −1 ), CEC is the cation exchangeable capacity (mg kg −1 ), and Na + , Ca 2+ and Mg 2+ are the concentrations (mg kg −1 ) of these ions, respectively.
The selected soils were classified by the US Salinity Laboratory Staff 48 numerical criteria for salt-affected soils 48 . Based on this scheme, a soil having a EC ≥ 4 dS m −1 and SAR > 13 is categorized as a saline-sodic soil, those having a EC ≥ 4 dS m −1 and SAR < 13 are defined as saline soils, and those with a EC < 4 dS m −1 and SAR ≥ 13 are classed as sodic (or alkaline) soils.

Calculation of parameters of PSD.
In this study, we used a volume-based model to calculate the fractal dimension (D) of PSD 9 .
where r is the soil particle size (μm), R i is the soil particle of some grade (μm), V r<Ri is the cumulative volume of particle sizes less than R i (%), V T is the sum volume of soil particles (%), R max is the maximum soil particle size (μm), and D is the fractal dimension.
Taking the logarithm of both sides in Eq. (3a), we derived Eq. (3b) below to solve for D. Scatter diagrams are produced, with the left side of Eq. (3b) being the y-axis and the right side the x-axis. We then used least-squares regression for linear fitting, where 3-D was equal to the slope of the fitted straight line. We can derive the D value from the Eq. (3c).
The fractal dimension therefore is a function of the PSD, and the soil particle grade will reflect the range of particle sizes and evaluate the soil grade is missing or continuous. The uniformity coefficient (Cu) and curvature coefficient (Cc) were then used for determining how well or poorly graded were the studied soils. These parameters are calculated according to the Unified Soil Classification System (USCS) described in ASTM D2487-11 (2011) 49 :  30 and d 60 are effective, median and constrained particle size (μm), respectively. Cu describes the uniformity degree of soil particle-size composition. A soil having a Cu ≤ 5 is called a homogenous soil, meaning the composition of the soil particle size is singular and poorly graded. In contrast, a soil is inhomogeneous when Cu > 5 50 . The higher the Cu value, the wider is the PSD. However, Cu exceeding a certain threshold means the possibility of a particle size of soil being missing, which is a discontinuous grade and must be judged in conjunction with Cc. Experience shows that when Cu > 5 and 1 < Cc < 3, then the soil is well graded; otherwise, it is poorly graded 50 .
Statistical analysis. The statistical analyses were performed using the SPSS 19.0 statistic software package (SPSS, Inc., Chicago, IL, USA). A correlation analysis was applied to determine the correlation between fractal dimension and soil properties. Significant differences were evaluated at the 0.05 and 0.01 levels (two-tailed: significant at P < 0.05, very significant at P < 0.01). The figures were created using the Origin Pro 9.0 software (Origin Lab Inc., Northampton, MA, USA).

Results
Soil properties. The characteristics of the distribution of anions and cations and the statistics describing the selected soils' properties are provided in Fig. 2 and Table 1. As shown in Fig. 2, HCO 3 − was the major anion in the study area, with percentages ranging from 46.87 to 66.71% and an average of 57.24%. This is followed by Na + , whose content ranges from 1.35 to 24.03%, with an average of 14.68%, and Ca 2+ , with a content ranging from 6.97 to 15.63% and an average of 10.65%. Cl − content was slightly less than Ca 2+ , with an average of 8.33%. The average content of the other ions considered was CO 3 2− (4.02%) > Mg 2+ (2.28%) > SO 4 2− (1.68%) > K + (1.11%). These results therefore indicate that sodium bicarbonate is the main salt component. represents the heterogeneity of the distribution of the soil properties. We note that the CV of CL is the lowest (6.85%), a product of the low-variability between its soil properties, while CV for the other soil types ranged from 78.19 to 89.01%, hence representing a moderate level of variability. The studied soils were therefore classified, following the scheme of the US Salinity Laboratory Staff 48 , as being normal soils (cropland, coded as NS), and sodic soils (the soils of Aneurolepidium chinese, Phragmites australics, Chloris virgata, and the bare land of saline-sodic soil, coded as SS1, SS2, SS3, SS4, and SS5, respectively). Fractal dimension of the particle-size distribution. The PSD of six soils are shown in Table 2. The PSD for the different soils are similar, with fine sand being the most common particle, followed by silt, coarse sand and clay. The predominant soil particles were fine sand and silt, with percentages ranging from 49.48 to 77.78% and 10.66 to 34.23%, respectively. The coarse sand and clay content were relatively low, ranging from 4.97 to 15.45% and 2.4 to 10.68%, respectively. For clay, silt and sand, the soils' ranks (following the classification outlined in the previous section) were SS4 > SS2 > SS5 > SS1 > SS3 > NS, SS3 > NS > SS1 > SS5 > SS2 > SS4, and NS > SS3 > SS1 > SS5 > SS4, respectively. These results showed that the sand content was very high and that the clay and silt contents were relatively low. According to the classification system of the United States Department of Agriculture, the selected soils correspond to four textural classes: NS was a typical fine sand, SS1 and SS3 were loamy fine sand, SS2 and SS5 were fine sandy loam, and SS4 was very fine sandy loam.
A linear regression analysis considering Eq. (3) was conducted, with lg(R i /λ v ) as the x-axis and lg(V r<Ri / V T ) as the y-axis, from which the fractal dimension of the PSD was calculated. As shown in Fig. 3, there was a strong correlation between lg(R i /λ v ) and lg(V r<Ri /V T ), with correlation coefficients (r) greater than 0.9. Results for estimating the fractal dimension ranged from 2.35 to 2.60, with an average of 2.48. The lowest value of D (2.35) corresponded to the soil type NS, which had the highest sand content (86.94%), but the lowest clay (2.40%) and silt (10.66%). The highest D (2.60) was found in the soil SS4, which had the highest content of clay (10.68%) and silt (34.23%) of the studied soils.
For further analysis of the particle-size distribution, the Cu and Cc parameters (Eqs. 4 and 5) were used to determine whether the soil particle-size distribution was continuous. As shown in Table 2, Cu was between 5.87 and 40.67, hence greater than 5. Cc ranged from 2.11 to 8.74, with the Cc values for NS and SS4 being less than 3. Overall, NS and SS4 satisfy the condition Cu > 5 and 1 < Cc < 3. Hence, the soils NS and SS4 are considered to be well graded, and the other soils poorly graded, based on their Cc values. However, if the Cu value is much greater than 5, it indicates that this soil is likely to be missing part of the particle-size distribution. This result can also be observed from the cumulative distribution curve of soil particle size, as shown in Fig. 4. We note that the NS curve gradually changed within the range of 0-2000 μm, while the other curves tended to be almost horizontal by the point when d was approximately equal to 500 μm. This means that the component of the soil with a size d > 500 μm was fairly small, and effectively missing in all soils, except for NS.
Relationship between particle-size distribution and fractal dimension. A simple linear regression analysis was performed to establish the relationships between the inferred D of the PSD, and with sand, silt and clay content. As shown in Fig. 5, the D of the PSD showed a significant negative correlation with coarse sand (r = − 0.5452, P < 0.05), a very significant negative correlation with the fine sand content (r = − 0.8641, P < 0.01), and a very significant positive correlation with the silt and clay content (r = 0.9726, P < 0.01 and r = 0.9526, P < 0.01, respectively).
Correlation between fractal dimension of soil and its properties. The correlation coefficients and significance between the D of the PSD and properties of the soils are listed in Table 3. The correlation analysis indicated that D has a significant positive correlation with the total salt content (SC) (P < 0.05) and a very significant positive correlation with HCO 3 − content (P < 0.01). Similarly, the SC and HCO 3 − contents displayed a significant negative Table 2. Soil particle-size distribution in different plant communities. NS means normal soil, SS1, SS2, SS3, SS4, SS5 stand for different degree of sodic soil; Cu and Cc stand for uniformity coefficient and curvature coefficient, respectively. Soil particle percentage content expressed by average value ± standard deviation (n = 3).    , SC, and CEC content, respectively; ESP and SAR is exchangeable sodium percent, sodium adsorption ratio of saturated paste extract, respectively; Sand, silt and clay is the sand, silt and clay content (%), respectively. **Means significant at the 0.01 level, * means significant at the 0.05 level. www.nature.com/scientificreports/ correlation with sand content (P < 0.05), and a significant positive correlation with the silt (P < 0.05) and clay contents (P < 0.01). However, for all studied soil samples, there was no clear correlation between D and the other chemical parameters considered, such as Na + , ENa + , ESP and CEC.

Discussion
The fractal dimension of particle-size distribution. Soil PSD is a basic fundamental physical parameter and is commonly used for classifying and judging soil texture 51 . Previous studies have shown that the fractal dimension of debris flow and glacial material is approximately 2.6, and that of river and lake sediments is generally less than 2.6 52 . The fractal dimension of soils with finer textures and abundant nutrients typically ranges from 2.60 to 2.80, and those with coarse sand and poor structure range from 1.83 to 2.64 53 . In this study, the samples were collected from a flood plain, and had a fractal dimension ranging from 2.35 to 2.61, with an average of 2.48. Hence, our results are in line with previous findings. Furthermore , Liu X et al. (2009) reported that the fractal dimension of well-structured soils is approximately 2.75 54 . However, since the sampled soils in this study had fractal dimension of less than 2.75, this suggests they have poor structure and are missing part of particle-size composition. This can be confirmed from Fig. 4, which shows that for most samples, the cumulative volume reaches approximately 98% when the soil particle diameter reaches 500 μm, with the cumulative volume of particle diameters between 500 and 2000 μm accounting for only 2%. The cumulative volume of the particle sizes ranging between 50 and 250 μm accounted for 49.48 to 77.78%, indicated fine sand with a majority, hence leading to a coarse texture and poor structure, which are not conducive to soil water and nutrients conservation. Fractal dimension reflected a significant correlation with alkaline soil particle-size distribution. Here, fractal dimension showed a very significant negative correlation with sand content (P < 0.01), and a significant positive correlation with silt and clay content (P < 0.01). Zhu et al. 55 investigated the influence of adding fly ash and montmorillonite-enriched sandstone on the particle-size distribution in a alkaline soil with loamy fine sandy texture, and the results indicated that the fractal theory could be used to quantify the relationships between fractal dimension and particle-size distribution in amended soil. Our results confirmed that the fractal dimension of the PSD increases as the particle size becomes finer. Several previous studies of soils not affected by salt and our study in alkaline soils have revealed the consistent correlation between fractal dimension and the particle-size distribution 7,18 . For example, the negative correlation between sand content and fractal dimension indicates that the fractal dimension would decrease as the sand content increased. Such correlations suggest that fractal dimension has the potential to be a useful tool for simulating and characterizing the PSD of the soils 7 .
Fractal dimension and soil properties. Considering non-saline and non-alkaline soils, numerous studies have shown that there are significant statistical correlations between the fractal dimension of the PSD of soils, and their physicochemical properties 51 . Considering the analysis of the relationships between fractal dimension and alkalinity properties of soils carried out in this work, our results indicate that the fractal dimension showed a significant positive correlation with salt content (P < 0.05), and a significant positive correlation with the HCO 3 − (P < 0.01). While the study area in this work was located at a transition zone between semi-arid to semi-humid environments with the salt component dominated by bicarbonate and carbonate, Zhao et al. 32 considered an arid zone whose salt content was mainly comprised of sulfate and chloride. They also found fractal dimension and salt content were positively correlated, and in agreement with our results, determined that the fractal dimension increased with fine particle content, but decreased with increasing coarse particles content. Hu et al. 56 considered an arid mulched drip irrigation system, and determined that the soil PSD dominated the soil water and salt distribution, especially the surface soil salt content and the deep soil water content.
However, alternate results have also been presented in the literature. For example, Gui et al. 31 , who investigated the vegetation and soil conditions from elevations of 1960 to 4070 m on the north slope of the Kunlun Mountains, China, found that the fractal dimension was negatively correlated with total salt content. As described by Gui et al. 31 , the soil fine fractions increased gradually with increasing elevation. Therefore, we inferred that soil salt is mainly concentrated in the coarse particles and this is likely to have a close relationship with the soil's parent material. Nonetheless, overall, the fractal dimension has been seen to have a close relationship with soil salt content. However, no significant correlation was been found between fractal dimension and exchangeable Na + in this study.
In this study, salt content and HCO 3 − increased with the increasing fine particle content (clay and silt particles) and decreased with increasing sand contents. That is, salt content and HCO 3 − content were inversely proportional to the particle size. In a chloride-sulfate and sulfate soil, Zhao et al. 32 similarly showed that both the content of HCO 3 − and SO 4 2− show a positive correlation with clay and silt content, and a negative correlation with sand content at different soil depths 32 . Other studies have shown that soil nutrients and metal ions tend to be aggregated with fine particles (silt and clay) rather than with coarser material 57,58 . Hence, when fine particle content is higher, the greater is the specific surface area and thus the stronger the adsorption 59 . However, no significant correlation has been found between exchangeable Na + , Ca 2+ and particle-size distribution in this study.

Conclusions
The results of this work have found that the fractal dimension of the particle-size distribution of the studied soils have a close relationship with alkalinity properties of soils and soil texture. A significant negative correlation was observed between the fractal dimension and both coarse sand (P < 0.05) and fine sand content (P < 0.01), and a positive correlation between fractal dimension and silt (P < 0.01) and clay content (P < 0.01). In other words, there is an increase in the fractal dimension as the soil texture changes from coarse to fine. Salt content, particularly HCO 3 − content, was inversely proportional to soil particle size. A correlation analysis showed that the typical characteristics of alkaline soil, such as the Na + , ENa + and Ca 2+ content, had no obvious relationship with fractal Scientific Reports | (2020) 10:20603 | https://doi.org/10.1038/s41598-020-77676-w www.nature.com/scientificreports/ dimension. However, a significant positive relationship was shown between fractal dimension and salt content (P < 0.05), and in particular, a very significant positive correlation with HCO 3 − content (P < 0.01). Our results therefore indicate that the fractal dimension of soil can be used as an indicator of its alkalinity and texture.