# Fractal Characteristics of Soil Retention Curve and Particle Size Distribution with Different Vegetation Types in Mountain Areas of Northern China

^{1}

^{2}

^{*}

*Int. J. Environ. Res. Public Health*

**2015**,

*12*(12), 15379-15389; https://doi.org/10.3390/ijerph121214978

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Study Area Condition

**Figure 1.**Map of the study area generated by Auto CAD2007 software. The dot on the map indicates the study area.

#### 2.2. Sampling and Processing

^{3}cutting ring at each sample plot of the five different vegetation types. The undisturbed soil in a 100 cm

^{3}cutting rings were weighed, allowing it to soak into the water until the soil was saturated, and then, the soil water contents were measured under 1, 10, 30, 80, 100, 300, 600, 800 and 1000 kPa of pressure using the soil WRC tester [23].

Vegetation Types | Vegetation Coverage (%) | Tree Age (Year) | Elevation (m) | Slope (°) | Aspect ^{‡} | |
---|---|---|---|---|---|---|

Mixed forest | QRM site ^{†} | 90.3 | 7 | 326 | 10–15 | sunny |

PPM site | 89.4 | 7 | 344 | 15–25 | half-sunny | |

Pure forest | PTP site | 78.8 | 7 | 346 | 15–25 | sunny |

JRL site | 80.7 | 6 | 316 | 10–15 | sunny | |

Comparison | ABG site | 35.2 | − | 340 | 15–25 | sunny |

**QRM—Quercus Acutissima Carr. and Robina Pseudoacacia Linn. mixed plantation; PPM—Pinus thunbergii Parl. and Pistacia chinensis Bunge mixed plantation; PTP—Pinus thunbergii Parl.; JRL—Juglans rigia Linn.; ABG—Abandoned grassland (the species in the abandoned grassland are Zoysia japonica Steud., Rubia-manjith Roxb. ex Flem., Themeda japonica Tanaka and Setaria viridis (Linn.) Beauv., etc.).**

^{†}**The “Aspect” were divided into three classes at 90° intervals from due north, 0°–45° and 315°–360° were shady slopes, 45°–135° and 225°–315° were half-sunny slopes, and 135°–225° were sunny slopes.**

^{‡}#### 2.3. Monofractal Method

_{i}and greater $\left(V(r>{R}_{i})\right)$ () can be expressed as follows [24]:

#### 2.4. Multifractal Method

_{i + 1}/φ

_{i}) is a constant across the measurement interval of I = (0.02, 2000 μm). To meet the requirements of the multifractal method, ψ

_{i}= lg(φ

_{i}/φ

_{1}) (with I = 1,2,…, 100) was changed. Next, we received a new dimensionless interval of J = [0,5], which had 100 equidistant subintervals, J

_{i}= [ψ

_{i}, ψ

_{i + 1}], I = 1, 2 …, 100. In the interval J, 2

^{k}same-size subintervals were used (ε), ε = 5 × 2

^{−k}. Every subinterval contained at least one measured value within a k range of 1 to 6. Thus, the multifractal parameters of D

_{0}, D

_{1}and D

_{1}/D

_{0}were calculated with Equations (4) and (5) [25,26]. These multifractal parameters varied between −10 and 10, with a step size of 0.5. From these data, we determined the multifractal spectrum of the soil PSD.

_{i}(ε) is the volume percentage of every subinterval; ε is the same size subinterval; q is the given parameter; and D(q) is the information entropy. When q = 0, D(q) = D

_{0}, which is the capacity dimension, and measures the span of the soil PSD. When q = 1, D(q) = D

_{1}, D

_{1}is the information dimension, which provides the irregular degree of the soil PSD. D

_{1}/D

_{0}(the information dimension/capacity dimension) measures the degree of heterogeneity of the soil PSD.

#### 2.5. The Fractal Dimensions of the Soil WRC

_{s}is the soil saturated water content in %; h is the soil matric suction in kPa; and h

_{d}is the soil air-entry suction in kPa. h is the vertical axis, and θ is the abscissa, and then from these values, the curve was drawn. The power of the fitting curve is determined from $1/({D}^{\prime}-3)$, which can be used to calculate the D′.

#### 2.6. Statistical Data Analyses

## 3. Results and Discussions

#### 3.1. Soil PSD and Its Fractal Dimension under Different Vegetation Types

**Table 2.**Soil particles-size distribution (PSD) under the different vegetation types in the study area.

Vegetation Type | Sand Volume Content (%) | Silt Volume Content (%) | Clay Volume Content (%) | ||||
---|---|---|---|---|---|---|---|

Very Coarse Sand | Coarse Sand | Sand | Fine Sand | Very Fine Sand | |||

QRM ^{†} | 0.019 ± 0.004 ^{a} | 8.54 ± 0.58 ^{a,}* | 20.61 ± 1.84 ^{a} | 18.35 ± 1.07 ^{a} | 8.35 ± 0.74 ^{a} | 39.06 ± 3.18 ^{a} | 4.90 ± 0.51 ^{a} |

PPM | 0.020 ± 0.005 ^{a} | 4.39 ± 0.37 ^{b} | 16.43 ± 1.09 ^{b} | 25.63 ± 2.16 ^{b} | 10.86 ± 0.82 ^{b} | 38.02 ± 3.02 ^{a} | 4.65 ± 0.48 ^{a} |

PTP | 5.82 ± 0.52 ^{b} | 26.40 ± 2.12 ^{c} | 22.16 ± 1.98 ^{c} | 12.40 ± 0.96 ^{c} | 5.16 ± 0.47 ^{c} | 25.68 ± 2.35 ^{b} | 2.38 ± 0.32 ^{b} |

JRL | 8.63 ± 0.65 ^{c} | 14.28 ± 1.21 ^{d} | 24.11 ± 2.05 ^{d} | 20.96 ± 1.78 ^{d} | 7.60 ± 0.59 ^{d} | 22.00 ± 1.89 ^{c} | 2.12 ± 0.25 ^{b} |

ABG | 8.97 ± 0.62 ^{c} | 24.40 ± 2.02 ^{e} | 26.95 ± 2.35 ^{e} | 18.11 ± 1.02 ^{e} | 5.00 ± 0.38 ^{e} | 16.40 ± 1.14 ^{d} | 1.08 ± 0.12 ^{c} |

**QRM—Quercus Acutissima Carr. and Robina Pseudoacacia Linn. mixed plantation; PPM—Pinus thunbergii Parl. and Pistacia chinensis Bunge mixed plantation; PTP—Pinus thunbergii Parl.; JRL—Juglans rigia Linn.; ABG—abandoned grassland.**

^{†}*****Indicates that the columns with different letters are significantly different at p < 0.05.

Vegetation Type | D ^{†} | D_{0} | D_{1} | D_{1}/D_{0} | D′ | R^{2} |
---|---|---|---|---|---|---|

QRM ^{†} | 2.5576 ± 0.48 ^{a,}* | 0.9317 ± 0.09 ^{a} | 0.9104 ± 0.07 ^{a} | 0.9824 ± 0.10 ^{a} | 2.6165 ± 0.50 ^{a} | 0.9111 |

PPM | 2.5462 ± 0.43 ^{a} | 0.9241 ± 0.09 ^{a} | 0.9057 ± 0.06 ^{a} | 0.9773 ± 0.10 ^{a} | 2.5913 ± 0.47 ^{a} | 0.8477 |

PTP | 2.4563 ± 0.37 ^{b} | 0.9212 ± 0.08 ^{a} | 0.8799 ± 0.05 ^{b} | 0.9495 ± 0.09 ^{b} | 2.5341 ± 0.42 ^{b} | 0.8253 |

JRL | 2.4331 ± 0.35 ^{b} | 0.9205 ± 0.08 ^{a} | 0.8761 ± 0.05 ^{b} | 0.9454 ± 0.09 ^{b} | 2.5110 ± 0.40 ^{b} | 0.8511 |

ABG | 2.3288 ± 0.0.32 ^{c} | 0.9142 ± 0.07 ^{b} | 0.8542 ± 0.05 ^{c} | 0.9244 ± 0.08 ^{c} | 2.4491 ± 0.36 ^{c} | 0.8618 |

**QRM—Quercus Acutissima Carr. and Robina Pseudoacacia Linn. mixed plantation; PPM—Pinus thunbergii Parl. and Pistacia chinensis Bunge mixed plantation; PTP—Pinus thunbergii Parl.; JRL—Juglans rigia Linn.; ABG—abandoned grassland; D—monofractal dimension; D**

^{†}_{0}—capacity dimension; D

_{1}—information dimension; D

_{1}/D

_{0}—information dimension/capacity dimension; D′—is fractal dimensions of soil WRC.

*****Indicates that the columns with different letters are significantly different at p < 0.05.

**Figure 2.**Relationships between D and the percentage of different soil PSD. D—Monofractal dimension of the soil PSD; PSD—Particle size distribution.

_{0}was 0.9142–0.9317 (n = 30, R

^{2}> 0.99), and D

_{1}was 0.8542–0.9104 (n = 30, R

^{2}> 0.97). All of the multifractal parameters (D

_{0}, D

_{1}) followed a trend of D

_{0}> D

_{1}.

**Figure 3.**Multifractal spectra of soil PSD under the different vegetation types in the study area QRM—Quercus Acutissima Carr. and Robina Pseudoacacia Linn. mixed plantation; PPM—Pinus thunbergii Parl. and Pistacia chinensis Bunge mixed plantation; PTP—Pinus thunbergii Parl.; JRL—Juglans rigia Linn.; ABG—Abandoned grassland.

_{0}, D

_{1}and D

_{1}/D

_{0}values for the five vegetation types followed the same order: QRM > PPM > PTP > JRL > ABG. ANOVA results indicated that the multifractal parameters of woodlands (QRM, PPM, PTP and JRL) were significantly higher than that of ABG (p < 0.05). The multifractal parameters of mixed forests (QRM and PPM) were higher than that of pure forests (PTP and JRL) (p < 0.05). However, the two types of woodland (QRM and PPM; PTP and JRL) were not significantly different (p > 0.05) (Table 4).

**Table 4.**Correlation analysis between soil fractal parameters and soil particles content and soil WRC under the different vegetation types.

Parameter Types | Clay | Slit | Sand | D ^{†} | D_{0} | D_{1} | D_{1}/D_{0} |
---|---|---|---|---|---|---|---|

Slit ^{†} | 0.935 * | ||||||

Sand | −0.950 * | −0.999 ** | |||||

D | 0.944 * | 0.957 * | −0.963 ** | ||||

D_{0} | 0.663 | 0.685 | −0.687 | 0.849 | |||

D_{1} | 0.978 ** | 0.984 ** | −0.990 ** | 0.962 ** | 0.682 | ||

D_{1}/D_{0} | 0.969 ** | 0.971 ** | −0.978 ** | 0.914 * | 0.568 | 0.989 ** | |

D′ | 0.942 * | 0.992 ** | −0.993 ** | 0.986 ** | 0.769 | 0.982 ** | 0.952 * |

**D—monofractal dimension; D**

^{†}_{0}—capacity dimension; D

_{1}—information dimension; D

_{1}/D

_{0}—information dimension/capacity dimension; D′—fractal dimensions of soil WRC;

*****Indicates that the columns are significantly different at p < 0.05;

******Indicates that the columns are significantly different at p < 0.01.

_{0}describes the span of the soil PSD. Therefore, larger D

_{0}values indicate a wider soil PSD range, and smaller D

_{0}values indicate a narrower soil PSD range. The D

_{1}and D

_{1}/D

_{0}values reflect the irregularity and the degree of heterogeneity of the soil PSD. Greater D

_{1}and D

_{1}/D

_{0}values indicate a greater irregularity and heterogeneity in the soil PSD [25,26,27]. In our study, compared with pure forest land, the mixed forests had a wider range of soil PSDs and had greater irregularity and heterogeneity in soil PSD, while the ABG had the narrowest range of soil PSDs and the least irregularity and heterogeneity in soil PSDs. Across vegetation types, the values of D

_{0}, D

_{1}and D

_{1}/D

_{0}were positively correlated with clay and silt contents and negatively correlated with the sand content. These results further corroborate our findings on the ranking order of D of soil particles across the different vegetation types. It was potentially explained by the effects of environmental construction projects (such as Return Farmland to Forests Project) on soil structure and function in the study area. Thus, these results indicate that fractal dimensions could adequately describe the influences of different vegetation types on the soil particle composition and the soil PSD. Furthermore, fractal dimensions serve as an important index for soil improvement and development.

#### 3.2. Soil WRC and Its Fractal Dimension under Different Vegetation Types

**Figure 4.**Soil WRC of the different vegetation types in the study area. QRM—Quercus Acutissima Carr. and Robina Pseudoacacia Linn. mixed plantation; PPM—Pinus thunbergii Parl. and Pistacia chinensis Bunge mixed plantation; PTP—Pinus thunbergii Parl.; JRL—Juglans rigia Linn.; ABG—Abandoned grassland.

#### 3.3. Correlation Analysis between D′ and D of the Soil PSD

## 4. Conclusions

- (1)
- The fractal parameters of soil PSDs and soil WRCs under different vegetation types were significantly different (p < 0.05), and all analyses showed that QRM > PPM > PTP > JRL > ABG. The soil fractal dimensions of mixed forests (QRM and PPM) were higher than that in pure forests (PTP and JRL), and the soil fractal dimensions of woodlands (QRM, PPM, PTP and JRL) were significantly higher than in ABG (p < 0.05). These results indicated that the woodland vegetation types had obvious effects on improving the soil structure, preventing the loss of soil, and increasing the soil fractal dimensions. These results also indicated that fractal dimensions could adequately describe the influences of different vegetation types on the soil particle composition and the soil PSD. Furthermore, fractal dimensions served as an important index for soil improvement and development. Therefore, it was necessary to construct different ecological forest types for preventing soil erosion and improving soil structure, especially for the construction and management of mixed forests in a study area.
- (2)
- The D of the soil PSD was positively correlated with the fractal dimension of the soil WRC. Therefore, the relationship between the fractal dimension of the soil PSD and WRC could be used to describe the corresponding soil WRC.
- (3)
- The fractal parameters of the soil PSD and WRC were closely related to the soil structure and were used as quantitative indices to reflect changes in the physical properties of the soil. Thus, the fractal parameters of the soil PSD and WRC could also act as an index and theoretical basis for the construction of environmental construction projects (such as Return Farmland to Forests Project) and the evaluation of forest ecological service function in the study area.

## Acknowledgments

## Author Contributions

## Conflicts of Interest

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**MDPI and ACS Style**

Niu, X.; Gao, P.; Wang, B.; Liu, Y. Fractal Characteristics of Soil Retention Curve and Particle Size Distribution with Different Vegetation Types in Mountain Areas of Northern China. *Int. J. Environ. Res. Public Health* **2015**, *12*, 15379-15389.
https://doi.org/10.3390/ijerph121214978

**AMA Style**

Niu X, Gao P, Wang B, Liu Y. Fractal Characteristics of Soil Retention Curve and Particle Size Distribution with Different Vegetation Types in Mountain Areas of Northern China. *International Journal of Environmental Research and Public Health*. 2015; 12(12):15379-15389.
https://doi.org/10.3390/ijerph121214978

**Chicago/Turabian Style**

Niu, Xiang, Peng Gao, Bing Wang, and Yu Liu. 2015. "Fractal Characteristics of Soil Retention Curve and Particle Size Distribution with Different Vegetation Types in Mountain Areas of Northern China" *International Journal of Environmental Research and Public Health* 12, no. 12: 15379-15389.
https://doi.org/10.3390/ijerph121214978