# Study on the Fractal Characteristics of the Plant Root System and Its Relationship with Soil Strength in Tailing Ponds

Authors: Qingchao Yang; Wenjing Cheng; Zhe Hao; Qian Zhang; Dongxu Yang; Da Teng; Ying Zhang; Xiaoming Wang; Hongxia Shen; Shengyou Lei
Journal: Wireless Communications and Mobile Computing
 (2022)

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## Abstract

To study the fractal characteristics of plant roots in tailing ponds and their effect on soil strength, the rhizosphere soil and roots ofAmorpha fruticosa and Hippophae rhamnoides, which are widely distributed in ecological restoration areas, were collected. The fractal dimension, root fractal characteristics, soil strength characteristics, and interaction relationships of the two rhizosphere soils were studied. Fractal theory was used to derive the formula for calculating the safety factor of the slope considering the soil and root fractals. The results showed that (1) the fractal dimension of rhizosphere soil of A. fruticosa and H. rhamnoides decreased with increasing vertical profile depth. (2) The fractal dimensions of roots of A. fruticosa and H. rhamnoides decreased with increasing soil depth. (3) The cohesion of the root-soil complex first increased and then decreased, and the fractal dimension of roots was significantly positively correlated with the increase in cohesion. (4) The slope safety factor was positively correlated with the fractal dimension of the soil and root system. It established the theoretical formula of the slope safety factor modified according to the fractal dimension.


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## Body

## 1. Introduction

At present, the theory of soil fixation by vegetation roots has been extensively explored and studied [1, 2]. Fan [3] analysed the effect of plant roots on soil shear resistance based on a model. Moresi et al. [4] evaluated root system sample indices and analysed the role of the root system in slope stability by combining root system mechanical properties. Yildiz et al. [5] conducted mechanical tests on root-soil complexes using a large direct shear instrument and analysed the shear properties and the mechanical effects of root consolidation on slope protection. Through the analysis of the morphological characteristics of Vetiver grass root systems and the direct shear test, Hamidifar et al. [6] concluded that the plant roots can improve the shear strength parameters of the soil body to different degrees. Maffra et al. [7] evaluated the effect of plant roots on the shear strength of clay and sandy soils. Badhon et al. [8] quantified the effect of plant roots on soil shear strength enhancement using an improved mathematical model based on in situ experiments on naturally grown Chrysopogon zizanioides land. Nguyen et al. [9, 10] used field monitoring data and direct shear tests and found that the C. zizanioides root-soil complex can improve the stability of shallow slopes by increasing the shear strength of slope soil. Wu et al. [11] investigated the distribution characteristics of Lespedeza bicolor root under different growing side slope stand conditions to reveal the variation and adaptation strategies of root plant growth in different locations. Zhang et al. [12] quantified the horizontal and vertical conformational fractal dimensions and fractal abundance characteristics of plant root systems to analyse the ability of plants to reinforce the soil mass. Ghestem et al. [13] analysed the mechanical action of soil using the morphological and structural characteristics of three plant roots. Lionel et al. [14] studied the mechanical response of different root morphologies and soil types. Huang et al. [15] analysed the effect of the root fractal characteristics of two herbaceous plants on the shear strength index. Arnone et al. [16] proposed a new method to estimate the shear strength exerted by the root system on slopes based on the fractal characteristics of the root system of trees and irrigation plants. Hairiah et al. [17] analysed the fractal differences in the vertical and horizontal distributions of the root systems of different grass and irrigation plants on the reinforcement of slope soils.From the current state of research on the effect of plant roots on soil shear resistance [3–10], no studies have carried out fractal characterization of plant roots to improve the reliability of quantitative descriptions of root morphological parameters. From the current state of research on the effect of plant roots on soil shear resistance [11–17], although research on the fractal characteristics of plant roots has been carried out, the interaction between soil fractal dimension, root fractal characteristics, and soil strength properties has not been considered. In terms of plant root fractal structure, root fractals can reflect the spatial branching status [18] and complexity of plant roots, as well as the ability of root expansion in the soil layer [19], which has obvious fractal characteristics [20, 21]. However, studies on the effect of such fractal characteristics on tailing soils have not been carried out. Further studies on the relationship between soil slope stability problems and fractal dimensions have not been carried out. Therefore, the root architecture characteristics of A. fruticosa and H. rhamnoides were analysed by using fractal theory. The interactions between the fractal dimension of rhizosphere soil, the fractal characteristics of roots, and the strength characteristics of soil were examined in combination with the shear strength test of shallow soil enhanced by roots. The theoretical formula of the slope safety factor modified based on the fractal dimension was derived to provide theoretical support for the study of tailing pond vegetation slope protection.


## 2. Experimental Scheme

### 2.1. General Situation of Tailing Ponds

The Waitoushan Iron Mine in Benxi city, China, is a valley-type second-class tailing pond. At present, the elevation is 280 m, the relative height is approximately 100 m, the total length of the dry beach of the tailing pond is approximately 250 m, and the total length of the tailing dam crest is approximately 1600 m. The total green area on the tailing dam with a length of approximately 2000 m from east to west is approximately 780000 m2. The ecological restoration plants are mainly deciduous small trees; torch trees; shrubs such as A. fruticosa, L. bicolor, and H. rhamnoides; and herbs such as dogtail grass and alfalfa. A. fruticosa and H. rhamnoides are typical pioneer plants for the ecological restoration of tailing dams [22]. Therefore, this paper takes the representative plants, A. fruticosa and H. rhamnoides, as experimental samples.


### 2.2. Test Materials

In this experiment, we selected a dam slope platform with a planting time of 4 years in Waitoushan in August 2020 and established 5 sampling areas, each of which was100mlong×100mwide, with an interval of 200 m. Four sampling points for A. fruticosa and four sampling points for H. rhamnoides were set in each sampling area. The sampling points were centred on A. fruticosa and H. rhamnoides plants, and undisturbed samples of the root-soil complex and plant roots were sampled. ① Collection of undisturbed samples of the root-soil complex: the profile stratification sampling method was used. The 0~2 cm surface impurities were removed, and at each sampling point, a profile of 1.5 m long, 0.6 m wide, and 0.8 m deep was made. The plant was the centre from the surface down to collect the profile 0~20 cm, 20~40 cm, 40~60 cm, and 60~80 cm root-soil complex in situ samples. The collection steps were detailed in a previous study [23]. The same method was used to collect the plain tailing soil as the control, while the fractal dimension of soil particles was measured by using a small shovel to collect the soil downwards at a certain angle. Each soil sample was approximately 1 kg, and the soil samples of the same level in each collection area were mixed. The samples were packed and sealed before being sent to the laboratory for treatment. In addition, while collecting undisturbed root-soil complex and plain tailing soil samples, a certain quality soil sample was prepared at the same time corresponding to the same depth layer and placed in an aluminium box to determine the water content of different soil layers. ② Root collection: roots were collected by the root tracing method and stratified whole plant excavation method [24]. The roots were excavated from the centre of the plant at depths of 0~20 cm, 20~40 cm, 40~60 cm, and below 60 cm. Each layer of roots was marked to prevent water dissipation and quickly transferred to the laboratory with the roots and soil wrapped together for subsequent experiments. The root systems of A. fruticosa and H. rhamnoides are shown in Figure 1.Figure 1
Plant root systems at the tailing pond.
(a)
A. fruticosa roots(b)
H. rhamnoides roots


### 2.3. Soil Sample and Root Treatment and Determination

Soil sample treatment and determination: ① the aluminium box was taken back to the laboratory, and the moisture content was measured by the drying method. ② The mass percentage of soil with different particle sizes was obtained by the sieving method and hydrometer method for the samples used to determine the fractal dimension of the soil particles. Through the fractal model of soil particles, the fractal dimensionD1 of soil particles distributed at different depths could be obtained. The calculation steps were detailed in previous studies [25] [26].Root measurement: the roots brought back were rinsed with running water, and the number of roots, root length, root area, and the characteristic values of root volume at each sampling site were selected as morphological parameters of the root system at the sampling site. ① The roots ofA. fruticosa and H. rhamnoides with diameter class d≥2mm were measured with electronic vernier callipers and tape, and the average diameter of the root system and the amount of root length (L) were determined using the root branching model [27]. Using the formulas L=4V/πd2 and S=4V/d and the measuring cylinder overflow method [28], the root surface area (S) and the volume (V) of each layer were calculated. ② The root system of the 0<d<2mm diameter class was scanned by Win RHIZO image software, and the root scanning data of each sampling point were averaged for quantitative analysis of root morphological parameters. The root scanning maps of two plants with a diameter class of 0<d<2mm were randomly selected, as shown in Figure 2.③ The roots were spread flat on a flat surface and photographed at different scales with a high-resolution camera. The root system images were analysed by preprocessing, image matrix meshing, and division results in MATLAB [29]. The fractal dimension of the root system was solved by the box dimension method. The calculation steps were detailed in previous studies [30] [31].Figure 2
Scanning diagrams of the plant root systems with a0<d<2mm diameter from the tailing pond.
(a)
A. fruticosa roots(b)
H. rhamnoides roots


### 2.4. Mechanical Test

① Tensile test: vernier callipers were used to measure the average diameter of the upper, middle, and lower roots of each sample as the diameter of the sample, the tensile rate of the universal tester was set to 10 mm/min, and the ratio of the sum of the single tensile strength values of the selected samples and the number of samples was taken as the average tensile strength value.② Direct shear test: undisturbed samples were ready according to the standard geotechnical test method GB/T50123-2019 and a previous study [32]. For each undisturbed sample of the root-soil complex, four ring knife samples were successively prepared according to the above sample preparation methods as a group of undisturbed samples of the root-soil complex. Under loads of 100, 200, 300, and 400 kPa, the 0.8 mm/min rapid shear test of plain tailing soil and root-soil composite samples was performed by a ZJ direct shear instrument. The average value of repeating specimens was used as the index of shear strength. In addition, when the root-soil composite shear test was completed, the specimen was removed from the shear box and placed in a geotechnical sieve to wash the roots in the composite with water. Growth volume indicators were counted according to Method 2.2 above.


### 2.5. Technology Line

The research work plan diagram is shown in Figure3.Figure 3
Technology roadmap.


## 2.1. General Situation of Tailing Ponds

The Waitoushan Iron Mine in Benxi city, China, is a valley-type second-class tailing pond. At present, the elevation is 280 m, the relative height is approximately 100 m, the total length of the dry beach of the tailing pond is approximately 250 m, and the total length of the tailing dam crest is approximately 1600 m. The total green area on the tailing dam with a length of approximately 2000 m from east to west is approximately 780000 m2. The ecological restoration plants are mainly deciduous small trees; torch trees; shrubs such as A. fruticosa, L. bicolor, and H. rhamnoides; and herbs such as dogtail grass and alfalfa. A. fruticosa and H. rhamnoides are typical pioneer plants for the ecological restoration of tailing dams [22]. Therefore, this paper takes the representative plants, A. fruticosa and H. rhamnoides, as experimental samples.


## 2.2. Test Materials

In this experiment, we selected a dam slope platform with a planting time of 4 years in Waitoushan in August 2020 and established 5 sampling areas, each of which was100mlong×100mwide, with an interval of 200 m. Four sampling points for A. fruticosa and four sampling points for H. rhamnoides were set in each sampling area. The sampling points were centred on A. fruticosa and H. rhamnoides plants, and undisturbed samples of the root-soil complex and plant roots were sampled. ① Collection of undisturbed samples of the root-soil complex: the profile stratification sampling method was used. The 0~2 cm surface impurities were removed, and at each sampling point, a profile of 1.5 m long, 0.6 m wide, and 0.8 m deep was made. The plant was the centre from the surface down to collect the profile 0~20 cm, 20~40 cm, 40~60 cm, and 60~80 cm root-soil complex in situ samples. The collection steps were detailed in a previous study [23]. The same method was used to collect the plain tailing soil as the control, while the fractal dimension of soil particles was measured by using a small shovel to collect the soil downwards at a certain angle. Each soil sample was approximately 1 kg, and the soil samples of the same level in each collection area were mixed. The samples were packed and sealed before being sent to the laboratory for treatment. In addition, while collecting undisturbed root-soil complex and plain tailing soil samples, a certain quality soil sample was prepared at the same time corresponding to the same depth layer and placed in an aluminium box to determine the water content of different soil layers. ② Root collection: roots were collected by the root tracing method and stratified whole plant excavation method [24]. The roots were excavated from the centre of the plant at depths of 0~20 cm, 20~40 cm, 40~60 cm, and below 60 cm. Each layer of roots was marked to prevent water dissipation and quickly transferred to the laboratory with the roots and soil wrapped together for subsequent experiments. The root systems of A. fruticosa and H. rhamnoides are shown in Figure 1.Figure 1
Plant root systems at the tailing pond.
(a)
A. fruticosa roots(b)
H. rhamnoides roots


## 2.3. Soil Sample and Root Treatment and Determination

Soil sample treatment and determination: ① the aluminium box was taken back to the laboratory, and the moisture content was measured by the drying method. ② The mass percentage of soil with different particle sizes was obtained by the sieving method and hydrometer method for the samples used to determine the fractal dimension of the soil particles. Through the fractal model of soil particles, the fractal dimensionD1 of soil particles distributed at different depths could be obtained. The calculation steps were detailed in previous studies [25] [26].Root measurement: the roots brought back were rinsed with running water, and the number of roots, root length, root area, and the characteristic values of root volume at each sampling site were selected as morphological parameters of the root system at the sampling site. ① The roots ofA. fruticosa and H. rhamnoides with diameter class d≥2mm were measured with electronic vernier callipers and tape, and the average diameter of the root system and the amount of root length (L) were determined using the root branching model [27]. Using the formulas L=4V/πd2 and S=4V/d and the measuring cylinder overflow method [28], the root surface area (S) and the volume (V) of each layer were calculated. ② The root system of the 0<d<2mm diameter class was scanned by Win RHIZO image software, and the root scanning data of each sampling point were averaged for quantitative analysis of root morphological parameters. The root scanning maps of two plants with a diameter class of 0<d<2mm were randomly selected, as shown in Figure 2.③ The roots were spread flat on a flat surface and photographed at different scales with a high-resolution camera. The root system images were analysed by preprocessing, image matrix meshing, and division results in MATLAB [29]. The fractal dimension of the root system was solved by the box dimension method. The calculation steps were detailed in previous studies [30] [31].Figure 2
Scanning diagrams of the plant root systems with a0<d<2mm diameter from the tailing pond.
(a)
A. fruticosa roots(b)
H. rhamnoides roots


## 2.4. Mechanical Test

① Tensile test: vernier callipers were used to measure the average diameter of the upper, middle, and lower roots of each sample as the diameter of the sample, the tensile rate of the universal tester was set to 10 mm/min, and the ratio of the sum of the single tensile strength values of the selected samples and the number of samples was taken as the average tensile strength value.② Direct shear test: undisturbed samples were ready according to the standard geotechnical test method GB/T50123-2019 and a previous study [32]. For each undisturbed sample of the root-soil complex, four ring knife samples were successively prepared according to the above sample preparation methods as a group of undisturbed samples of the root-soil complex. Under loads of 100, 200, 300, and 400 kPa, the 0.8 mm/min rapid shear test of plain tailing soil and root-soil composite samples was performed by a ZJ direct shear instrument. The average value of repeating specimens was used as the index of shear strength. In addition, when the root-soil composite shear test was completed, the specimen was removed from the shear box and placed in a geotechnical sieve to wash the roots in the composite with water. Growth volume indicators were counted according to Method 2.2 above.


## 2.5. Technology Line

The research work plan diagram is shown in Figure3.Figure 3
Technology roadmap.


## 3. Morphological and Fractal Characteristics of the Soil and Root System

### 3.1. Characteristics of Soil Gradation

The composition of soil particles under different shrub types is shown in Table1. Therefore, the percentage content of soil particle mass in different size distribution ranges of each soil sample had a nonuniform distribution.Table 1
Soil particle distribution under different shrub types.
Sample plotSoil depthGravel (%)Sand (%)Silt (%)Soil clay (%)cm20-2 mm2-0.5 mm0.5-0.25 mm0.25-0.075 mm0.075-0.005 mm<0.005 mmTailing soil0~200.30A6.30A13.60B69.30A6.80B3.70A20~400.10A7.20B12.30B71.20A7.30A2.20A40~600.30A6.50A12.50B71.20A7.30A2.20A60~800.50B5.40B13.60A73.50A4.60A2.40A0~800.30A6.35B13.00A71.10A6.35A2.90AA. fruticosa plot0~205.60B2.30A4.60A66.20A20.70A4.60A20~400.10Aa0.50Aa3.30A76.10A15.80A4.20A40~600.50Aa0.60B3.80A82.70Aa9.20Aa3.20A60~802.30Aab6.10abc9.10Aabc70.60A9.00Aa2.90A0~802.13B2.38A5.20B72.90A13.68B3.73AH. rhamnoides plot0~200.20A3.30A5.70A66.80A16.90A7.10A20~402.40Ba1.30A5.60A72.30A13.60A4.80A40~600.90A5.60A7.00A68.60A13.40A4.50A60~801.60A12.60Aabc10.20A65.30A7.30A3.00A0~801.28A5.70B7.13B68.25A12.80B4.85BNote (same below): different uppercase letters indicate significant differences in the mechanical composition of soil particles under different shrubs in the same soil section, and different lowercase letters indicate significant differences in the mechanical composition of soil particles under the same shrub in different soil sections (P<0.05).Table1 shows that there were differences in particle composition between shrub rhizosphere soil formed by plant growth and bare tailing soil. The percentage mass of soil particles significantly differed (P<0.05) between the different particle sizes in the study area, with the highest percentage distribution of soil particles in a range of 0.25-0.075 mm. In the 0-80 cm soil layer of A. fruticosa and H. rhamnoides rhizosphere soil, the weight percentage of gravel was the lowest, only 1.3%-2.1%, which was higher than that of bare tailing soil. There were significant differences in the percentage of soil particles of each size fraction under tailing shrubs (P<0.05).


### 3.2. Soil Fractal Dimension

The fractal dimension of rhizosphere soil in different soil layers under shrubs is shown in Figure4.Figure 4
Fractal dimension variation of rhizosphere soil in different soil layers under shrubs.Figure4 shows that due to the different heights and branching densities of A. fruticosa and H. rhamnoides, the particle composition of the soil layers at different depths of 0-80 cm under shrubs was different. The root-soil of the two shrub plants had a phenomenon in which the fractal dimension decreased with increasing depth. The difference in fractal dimension between the 0-20 cm and 20-40 cm root-soil of the same species was significant (P<0.05), but the variability in fractal dimension of root-soil in other soil layers was not significant. The fractal dimension of root-soil was notably higher in A. fruticosa (2.482) and H. rhamnoides (2.503) than in tailing soil (2.374).


### 3.3. Morphological Characteristics of the Root System

#### 3.3.1. Root Number

Root number is an important parameter for the qualitative description of root water absorption and the evaluation of plant water absorption functions [33]. The root number of different diameter classes of A. fruticosa and H. rhamnoides in different soil layers is shown in Figure 5.Figure 5
The number of roots in different soil layers at different root diameters. Note (same below): ① the number of roots is the average of the number of roots in the upper and lower parts of different soil layers. ② The above data are the average of the samples collected.Figure5 shows that the number of roots of A. fruticosa and H. rhamnoides decreased with increasing soil depth, and the reduction range of the number of roots increased gradually. A. fruticosa and H. rhamnoides with diameter d≥2mm accounted for 22.59% and 17.38% of the total number of individual roots, respectively. The d≥2mm primary root system that played an anchoring role in the dam body from 40 to 60 cm and below 60 cm accounted for less than 5% of the total. Two plant root systems with diameter classes at 0<d<2mm accounted for 77.41% and 82.62% of the total root mass, respectively. The 0<d<2mm fibrous roots in a depth range of 0-40 cm accounted for more than 60% of the total. The main and fibrous roots of the two shrubs provide a combined anchoring and reinforcing slope protection effect on the dam.


#### 3.3.2. Root Length

Root length is a parameter that reflects the absorption level of roots in soil and is also a parameter used to evaluate the erosion resistance of plant roots [34]. The root length of each diameter stage in different soil layers is shown in Figure 6.Figure 6
Root length of each diameter stage in different soil layers.In Figure6, we can see that the root length of A. fruticosa and H. rhamnoides showed a decreasing trend with increasing soil depth. The diameter class d≥2mm accounted for 18.8% and 13.49% of the total root length of each shrub, respectively. The main root system can reach below 60 cm of the soil layer, which plays a certain anchoring role for the surface soil structure of the slope. The roots of A. fruticosa and H. rhamnoides are mainly fibrous roots less than 2 mm. The diameter class 0<d<2mm accounted for 81.2% and 86.51% of the total root length of each shrub, respectively. A soil depth of 0~40 cm was the main range of fibrous root distribution. The reinforcing capacity of fibrous roots in soil is also an important indicator of soil stability, and the roots of A. fruticosa and H. rhamnoides have good integrated slope protection effects.


#### 3.3.3. Root Surface Area

Root surface area can reflect the ability of roots to absorb nutrients and water. A larger root surface area indicates a stronger root absorption function and a stronger rooting and soil-fixing capacity of the plant root system [35, 36].In Figure7, we can see that the root surface area of A. fruticosa and H. rhamnoides decreased with increasing soil depth. The root surface area of the two diameter classes, 0<d<2mm and d≥2mm, accounted for 76.44% and 72.69% and 23.56% and 21.01% of the total root surface area at different depths of the soil layer, respectively. Among them, the 0<d<2mm fibrous roots in a range of 0~40 cm accounted for 70.58% and 72.69% of the total surface area, respectively, and the fibrous root reinforcement capacity played an important role in the stability of the tailing soil.Figure 7
Root surface area of each diameter stage in different soil layers.


#### 3.3.4. Root Volume

Root volume is an important parameter for measuring the spatial growth and distribution of plant roots in the soil layer [37]. It reflects the spatial distribution of plant roots in the process of soil growth and the vertical spatial extension of plant roots, thus directly reflecting the reinforcement effect of plant roots on soil.Figure8 shows that the root volume of A. fruticosa and H. rhamnoides showed an obvious downwards trend with increasing depth in each root-soil layer. The root volumes of the two diameter classes, 0<d<2mm and d≥2mm, accounted for 7.44% and 5.97% and 92.56% and 94.03% of the total root volume of each shrub at different depths of the soil layer, respectively, indicating the dominance of the taproot volume. In the soil layer from 0 to 40 cm depth, the root volume of the d≥2mm diameter class reached more than 80%, indicating that the main stem roots were mostly distributed in the superficial soil layer at the surface. The root volumes of A. fruticosa and H. rhamnoides were evenly distributed. A certain amount of fibrous roots and taproots was distributed in the soil layer of each root, which could effectively enhance the root anchorage and erosion resistance.Figure 8
Root volume at different soil layers at different root diameter stages.


### 3.4. Root Fractal Dimension

Through the fractal calculation of roots with different diameters, the average fractal dimension of roots with different vertical profile depths was obtained, as shown in Figure9.Figure 9
The average fractal dimension of roots at different vertical profile depths.The criterion for determining that the object of analysis has fractal characteristics is that the fractal dimension of the root system should be greater than 1.1 [38]. Figure 9 shows that the average fractal dimension of both the A. fruticosa (1.588) and H. rhamnoides root systems (1.661) was higher than 1.1; therefore, the A. fruticosa and H. rhamnoides root systems had obvious fractal characteristics. The fractal dimension of H. rhamnoides roots was greater than that of A. fruticosa by 4.60%, which indicated that H. rhamnoides roots had higher fullness and more fine roots in the soil, which was consistent with the actual distribution of root parameters in the soil as calculated in Section 3.3. The root fractal dimension of A. fruticosa and H. rhamnoides showed a more obvious trend of increasing and then decreasing, which may be because the plant roots started to divide and grow from 0 to 20 cm, and the maximum number of root divisions was found at depths of 20-40 cm, resulting in a higher number of roots and a larger root fractal dimension in that depth range of the soil layer. The fractal dimension of the root system decreased from 40 to 60 cm depth, mainly because the number of roots, root diameter, and root length all decreased with increasing soil depth [39, 40].


## 3.1. Characteristics of Soil Gradation

The composition of soil particles under different shrub types is shown in Table1. Therefore, the percentage content of soil particle mass in different size distribution ranges of each soil sample had a nonuniform distribution.Table 1
Soil particle distribution under different shrub types.
Sample plotSoil depthGravel (%)Sand (%)Silt (%)Soil clay (%)cm20-2 mm2-0.5 mm0.5-0.25 mm0.25-0.075 mm0.075-0.005 mm<0.005 mmTailing soil0~200.30A6.30A13.60B69.30A6.80B3.70A20~400.10A7.20B12.30B71.20A7.30A2.20A40~600.30A6.50A12.50B71.20A7.30A2.20A60~800.50B5.40B13.60A73.50A4.60A2.40A0~800.30A6.35B13.00A71.10A6.35A2.90AA. fruticosa plot0~205.60B2.30A4.60A66.20A20.70A4.60A20~400.10Aa0.50Aa3.30A76.10A15.80A4.20A40~600.50Aa0.60B3.80A82.70Aa9.20Aa3.20A60~802.30Aab6.10abc9.10Aabc70.60A9.00Aa2.90A0~802.13B2.38A5.20B72.90A13.68B3.73AH. rhamnoides plot0~200.20A3.30A5.70A66.80A16.90A7.10A20~402.40Ba1.30A5.60A72.30A13.60A4.80A40~600.90A5.60A7.00A68.60A13.40A4.50A60~801.60A12.60Aabc10.20A65.30A7.30A3.00A0~801.28A5.70B7.13B68.25A12.80B4.85BNote (same below): different uppercase letters indicate significant differences in the mechanical composition of soil particles under different shrubs in the same soil section, and different lowercase letters indicate significant differences in the mechanical composition of soil particles under the same shrub in different soil sections (P<0.05).Table1 shows that there were differences in particle composition between shrub rhizosphere soil formed by plant growth and bare tailing soil. The percentage mass of soil particles significantly differed (P<0.05) between the different particle sizes in the study area, with the highest percentage distribution of soil particles in a range of 0.25-0.075 mm. In the 0-80 cm soil layer of A. fruticosa and H. rhamnoides rhizosphere soil, the weight percentage of gravel was the lowest, only 1.3%-2.1%, which was higher than that of bare tailing soil. There were significant differences in the percentage of soil particles of each size fraction under tailing shrubs (P<0.05).


## 3.2. Soil Fractal Dimension

The fractal dimension of rhizosphere soil in different soil layers under shrubs is shown in Figure4.Figure 4
Fractal dimension variation of rhizosphere soil in different soil layers under shrubs.Figure4 shows that due to the different heights and branching densities of A. fruticosa and H. rhamnoides, the particle composition of the soil layers at different depths of 0-80 cm under shrubs was different. The root-soil of the two shrub plants had a phenomenon in which the fractal dimension decreased with increasing depth. The difference in fractal dimension between the 0-20 cm and 20-40 cm root-soil of the same species was significant (P<0.05), but the variability in fractal dimension of root-soil in other soil layers was not significant. The fractal dimension of root-soil was notably higher in A. fruticosa (2.482) and H. rhamnoides (2.503) than in tailing soil (2.374).


## 3.3. Morphological Characteristics of the Root System

### 3.3.1. Root Number

Root number is an important parameter for the qualitative description of root water absorption and the evaluation of plant water absorption functions [33]. The root number of different diameter classes of A. fruticosa and H. rhamnoides in different soil layers is shown in Figure 5.Figure 5
The number of roots in different soil layers at different root diameters. Note (same below): ① the number of roots is the average of the number of roots in the upper and lower parts of different soil layers. ② The above data are the average of the samples collected.Figure5 shows that the number of roots of A. fruticosa and H. rhamnoides decreased with increasing soil depth, and the reduction range of the number of roots increased gradually. A. fruticosa and H. rhamnoides with diameter d≥2mm accounted for 22.59% and 17.38% of the total number of individual roots, respectively. The d≥2mm primary root system that played an anchoring role in the dam body from 40 to 60 cm and below 60 cm accounted for less than 5% of the total. Two plant root systems with diameter classes at 0<d<2mm accounted for 77.41% and 82.62% of the total root mass, respectively. The 0<d<2mm fibrous roots in a depth range of 0-40 cm accounted for more than 60% of the total. The main and fibrous roots of the two shrubs provide a combined anchoring and reinforcing slope protection effect on the dam.


### 3.3.2. Root Length

Root length is a parameter that reflects the absorption level of roots in soil and is also a parameter used to evaluate the erosion resistance of plant roots [34]. The root length of each diameter stage in different soil layers is shown in Figure 6.Figure 6
Root length of each diameter stage in different soil layers.In Figure6, we can see that the root length of A. fruticosa and H. rhamnoides showed a decreasing trend with increasing soil depth. The diameter class d≥2mm accounted for 18.8% and 13.49% of the total root length of each shrub, respectively. The main root system can reach below 60 cm of the soil layer, which plays a certain anchoring role for the surface soil structure of the slope. The roots of A. fruticosa and H. rhamnoides are mainly fibrous roots less than 2 mm. The diameter class 0<d<2mm accounted for 81.2% and 86.51% of the total root length of each shrub, respectively. A soil depth of 0~40 cm was the main range of fibrous root distribution. The reinforcing capacity of fibrous roots in soil is also an important indicator of soil stability, and the roots of A. fruticosa and H. rhamnoides have good integrated slope protection effects.


### 3.3.3. Root Surface Area

Root surface area can reflect the ability of roots to absorb nutrients and water. A larger root surface area indicates a stronger root absorption function and a stronger rooting and soil-fixing capacity of the plant root system [35, 36].In Figure7, we can see that the root surface area of A. fruticosa and H. rhamnoides decreased with increasing soil depth. The root surface area of the two diameter classes, 0<d<2mm and d≥2mm, accounted for 76.44% and 72.69% and 23.56% and 21.01% of the total root surface area at different depths of the soil layer, respectively. Among them, the 0<d<2mm fibrous roots in a range of 0~40 cm accounted for 70.58% and 72.69% of the total surface area, respectively, and the fibrous root reinforcement capacity played an important role in the stability of the tailing soil.Figure 7
Root surface area of each diameter stage in different soil layers.


### 3.3.4. Root Volume

Root volume is an important parameter for measuring the spatial growth and distribution of plant roots in the soil layer [37]. It reflects the spatial distribution of plant roots in the process of soil growth and the vertical spatial extension of plant roots, thus directly reflecting the reinforcement effect of plant roots on soil.Figure8 shows that the root volume of A. fruticosa and H. rhamnoides showed an obvious downwards trend with increasing depth in each root-soil layer. The root volumes of the two diameter classes, 0<d<2mm and d≥2mm, accounted for 7.44% and 5.97% and 92.56% and 94.03% of the total root volume of each shrub at different depths of the soil layer, respectively, indicating the dominance of the taproot volume. In the soil layer from 0 to 40 cm depth, the root volume of the d≥2mm diameter class reached more than 80%, indicating that the main stem roots were mostly distributed in the superficial soil layer at the surface. The root volumes of A. fruticosa and H. rhamnoides were evenly distributed. A certain amount of fibrous roots and taproots was distributed in the soil layer of each root, which could effectively enhance the root anchorage and erosion resistance.Figure 8
Root volume at different soil layers at different root diameter stages.


## 3.3.1. Root Number

Root number is an important parameter for the qualitative description of root water absorption and the evaluation of plant water absorption functions [33]. The root number of different diameter classes of A. fruticosa and H. rhamnoides in different soil layers is shown in Figure 5.Figure 5
The number of roots in different soil layers at different root diameters. Note (same below): ① the number of roots is the average of the number of roots in the upper and lower parts of different soil layers. ② The above data are the average of the samples collected.Figure5 shows that the number of roots of A. fruticosa and H. rhamnoides decreased with increasing soil depth, and the reduction range of the number of roots increased gradually. A. fruticosa and H. rhamnoides with diameter d≥2mm accounted for 22.59% and 17.38% of the total number of individual roots, respectively. The d≥2mm primary root system that played an anchoring role in the dam body from 40 to 60 cm and below 60 cm accounted for less than 5% of the total. Two plant root systems with diameter classes at 0<d<2mm accounted for 77.41% and 82.62% of the total root mass, respectively. The 0<d<2mm fibrous roots in a depth range of 0-40 cm accounted for more than 60% of the total. The main and fibrous roots of the two shrubs provide a combined anchoring and reinforcing slope protection effect on the dam.


## 3.3.2. Root Length

Root length is a parameter that reflects the absorption level of roots in soil and is also a parameter used to evaluate the erosion resistance of plant roots [34]. The root length of each diameter stage in different soil layers is shown in Figure 6.Figure 6
Root length of each diameter stage in different soil layers.In Figure6, we can see that the root length of A. fruticosa and H. rhamnoides showed a decreasing trend with increasing soil depth. The diameter class d≥2mm accounted for 18.8% and 13.49% of the total root length of each shrub, respectively. The main root system can reach below 60 cm of the soil layer, which plays a certain anchoring role for the surface soil structure of the slope. The roots of A. fruticosa and H. rhamnoides are mainly fibrous roots less than 2 mm. The diameter class 0<d<2mm accounted for 81.2% and 86.51% of the total root length of each shrub, respectively. A soil depth of 0~40 cm was the main range of fibrous root distribution. The reinforcing capacity of fibrous roots in soil is also an important indicator of soil stability, and the roots of A. fruticosa and H. rhamnoides have good integrated slope protection effects.


## 3.3.3. Root Surface Area

Root surface area can reflect the ability of roots to absorb nutrients and water. A larger root surface area indicates a stronger root absorption function and a stronger rooting and soil-fixing capacity of the plant root system [35, 36].In Figure7, we can see that the root surface area of A. fruticosa and H. rhamnoides decreased with increasing soil depth. The root surface area of the two diameter classes, 0<d<2mm and d≥2mm, accounted for 76.44% and 72.69% and 23.56% and 21.01% of the total root surface area at different depths of the soil layer, respectively. Among them, the 0<d<2mm fibrous roots in a range of 0~40 cm accounted for 70.58% and 72.69% of the total surface area, respectively, and the fibrous root reinforcement capacity played an important role in the stability of the tailing soil.Figure 7
Root surface area of each diameter stage in different soil layers.


## 3.3.4. Root Volume

Root volume is an important parameter for measuring the spatial growth and distribution of plant roots in the soil layer [37]. It reflects the spatial distribution of plant roots in the process of soil growth and the vertical spatial extension of plant roots, thus directly reflecting the reinforcement effect of plant roots on soil.Figure8 shows that the root volume of A. fruticosa and H. rhamnoides showed an obvious downwards trend with increasing depth in each root-soil layer. The root volumes of the two diameter classes, 0<d<2mm and d≥2mm, accounted for 7.44% and 5.97% and 92.56% and 94.03% of the total root volume of each shrub at different depths of the soil layer, respectively, indicating the dominance of the taproot volume. In the soil layer from 0 to 40 cm depth, the root volume of the d≥2mm diameter class reached more than 80%, indicating that the main stem roots were mostly distributed in the superficial soil layer at the surface. The root volumes of A. fruticosa and H. rhamnoides were evenly distributed. A certain amount of fibrous roots and taproots was distributed in the soil layer of each root, which could effectively enhance the root anchorage and erosion resistance.Figure 8
Root volume at different soil layers at different root diameter stages.


## 3.4. Root Fractal Dimension

Through the fractal calculation of roots with different diameters, the average fractal dimension of roots with different vertical profile depths was obtained, as shown in Figure9.Figure 9
The average fractal dimension of roots at different vertical profile depths.The criterion for determining that the object of analysis has fractal characteristics is that the fractal dimension of the root system should be greater than 1.1 [38]. Figure 9 shows that the average fractal dimension of both the A. fruticosa (1.588) and H. rhamnoides root systems (1.661) was higher than 1.1; therefore, the A. fruticosa and H. rhamnoides root systems had obvious fractal characteristics. The fractal dimension of H. rhamnoides roots was greater than that of A. fruticosa by 4.60%, which indicated that H. rhamnoides roots had higher fullness and more fine roots in the soil, which was consistent with the actual distribution of root parameters in the soil as calculated in Section 3.3. The root fractal dimension of A. fruticosa and H. rhamnoides showed a more obvious trend of increasing and then decreasing, which may be because the plant roots started to divide and grow from 0 to 20 cm, and the maximum number of root divisions was found at depths of 20-40 cm, resulting in a higher number of roots and a larger root fractal dimension in that depth range of the soil layer. The fractal dimension of the root system decreased from 40 to 60 cm depth, mainly because the number of roots, root diameter, and root length all decreased with increasing soil depth [39, 40].


## 4. Analysis of the Mechanical Properties of Plant Root Tailing Soil Complexes

### 4.1. Tensile Strength of the Root Strip

The diameters of the selected root samples ofA. fruticosa ranged from 1.43 mm to 5.76 mm, with a mean diameter of 2.49±0.23mm. The diameters of the H. rhamnoides root samples ranged from 0.95 mm to 6.33 mm, with a mean diameter of 3.74±0.18mm. The average tensile strengths of single roots were obtained from the single root tensile strength tests: 22.31±1.22MPa and 16.77±1.14MPa for A. fruticosa and H. rhamnoides, respectively.Table2 shows that the tensile strength of A. fruticosa and H. rhamnoides decreased with increasing root diameter and shows a power function relationship. The average tensile strength of the two shrubs was A. fruticosa > H. rhamnoides, which may be related to the plant growth conditions and root microstructure. The maximum tensile strength of a single plant root reinforcement was equal to 2.7% and 1.9% of the ultimate tensile strength of Grade I reinforcement, respectively. This shows that the two kinds of roots have good tensile properties and that the plant roots are of great significance for improving the slope consolidation capacity and the construction of soil and water conservation vegetation.Table 2
Single tensile strength and diameter fitting equations.
Plant typeCorrelation formulaR2PearsonA. fruticosaT=9.332d−0.1350.843P<0.05H. rhamnoidesT=8.687d−0.1850.768P<0.05


### 4.2. Shear Strength of Composite Soil

#### 4.2.1. Shear Strength of the Root-Soil Complex

Through the direct shear strength test of the root-soil complex, the shear strength index of the stratified sample was obtained, as shown in Figure10.Figure 10
Shear strength index of the stratified sample.
(a)
Cohesion(b)
Angle of internal frictionFigure10(a) shows that the cohesion of the root-soil complex increases greatly compared with that of plain tailing soil. The cohesion of the A. fruticosa root-soil complex increased by 25.57%-56.69%, and that of the H. rhamnoides root-soil complex increased by 51.05%-73.94%. The results show that the two kinds of root-soil complexes can improve soil cohesion. However, Figure 10(b) shows that the internal friction angle of the two soil complexes has no obvious change with increasing soil depth. The results showed that the average value of H. rhamnoides root-enhanced soil cohesion was higher than that of A. Fruticosa and H. rhamnoides roots improved soil shear strength better.


#### 4.2.2. Cohesion Increase and Root Fractal Dimension of Soil with Roots

Figure11 shows the relationship between the fractal dimension of roots of A. fruticosa and H. rhamnoides and the increased cohesion of the root-soil complex.Figure 11
Curve of the fractal dimension and added value of cohesion in the root-bearing soil layer.Figure11 shows that the change in root fractal dimension is consistent with root reinforcement ability [41]. When the root fractal dimension increases, plant roots have an enhanced effect on both soil consolidation and regional soil and water conservation [42, 43]. At a certain critical value [38], the root fractal dimension can lead to a maximum increase in the soil shear strength. Correlation analysis was performed between the fractal dimension of the root system and the value of increased cohesion of root-bearing soil layers. It can be concluded that there was a remarkably significant correlation between the fractal dimension of roots of the same shrub and the added value of cohesion of the root-soil complex, while the contribution of different plant roots to the increase of complex cohesion was significantly different, which was mainly due to plant differences in root diameter, morphological character, and root uniformity [39, 40, 44, 45].


## 4.1. Tensile Strength of the Root Strip

The diameters of the selected root samples ofA. fruticosa ranged from 1.43 mm to 5.76 mm, with a mean diameter of 2.49±0.23mm. The diameters of the H. rhamnoides root samples ranged from 0.95 mm to 6.33 mm, with a mean diameter of 3.74±0.18mm. The average tensile strengths of single roots were obtained from the single root tensile strength tests: 22.31±1.22MPa and 16.77±1.14MPa for A. fruticosa and H. rhamnoides, respectively.Table2 shows that the tensile strength of A. fruticosa and H. rhamnoides decreased with increasing root diameter and shows a power function relationship. The average tensile strength of the two shrubs was A. fruticosa > H. rhamnoides, which may be related to the plant growth conditions and root microstructure. The maximum tensile strength of a single plant root reinforcement was equal to 2.7% and 1.9% of the ultimate tensile strength of Grade I reinforcement, respectively. This shows that the two kinds of roots have good tensile properties and that the plant roots are of great significance for improving the slope consolidation capacity and the construction of soil and water conservation vegetation.Table 2
Single tensile strength and diameter fitting equations.
Plant typeCorrelation formulaR2PearsonA. fruticosaT=9.332d−0.1350.843P<0.05H. rhamnoidesT=8.687d−0.1850.768P<0.05


## 4.2. Shear Strength of Composite Soil

### 4.2.1. Shear Strength of the Root-Soil Complex

Through the direct shear strength test of the root-soil complex, the shear strength index of the stratified sample was obtained, as shown in Figure10.Figure 10
Shear strength index of the stratified sample.
(a)
Cohesion(b)
Angle of internal frictionFigure10(a) shows that the cohesion of the root-soil complex increases greatly compared with that of plain tailing soil. The cohesion of the A. fruticosa root-soil complex increased by 25.57%-56.69%, and that of the H. rhamnoides root-soil complex increased by 51.05%-73.94%. The results show that the two kinds of root-soil complexes can improve soil cohesion. However, Figure 10(b) shows that the internal friction angle of the two soil complexes has no obvious change with increasing soil depth. The results showed that the average value of H. rhamnoides root-enhanced soil cohesion was higher than that of A. Fruticosa and H. rhamnoides roots improved soil shear strength better.


### 4.2.2. Cohesion Increase and Root Fractal Dimension of Soil with Roots

Figure11 shows the relationship between the fractal dimension of roots of A. fruticosa and H. rhamnoides and the increased cohesion of the root-soil complex.Figure 11
Curve of the fractal dimension and added value of cohesion in the root-bearing soil layer.Figure11 shows that the change in root fractal dimension is consistent with root reinforcement ability [41]. When the root fractal dimension increases, plant roots have an enhanced effect on both soil consolidation and regional soil and water conservation [42, 43]. At a certain critical value [38], the root fractal dimension can lead to a maximum increase in the soil shear strength. Correlation analysis was performed between the fractal dimension of the root system and the value of increased cohesion of root-bearing soil layers. It can be concluded that there was a remarkably significant correlation between the fractal dimension of roots of the same shrub and the added value of cohesion of the root-soil complex, while the contribution of different plant roots to the increase of complex cohesion was significantly different, which was mainly due to plant differences in root diameter, morphological character, and root uniformity [39, 40, 44, 45].


## 4.2.1. Shear Strength of the Root-Soil Complex

Through the direct shear strength test of the root-soil complex, the shear strength index of the stratified sample was obtained, as shown in Figure10.Figure 10
Shear strength index of the stratified sample.
(a)
Cohesion(b)
Angle of internal frictionFigure10(a) shows that the cohesion of the root-soil complex increases greatly compared with that of plain tailing soil. The cohesion of the A. fruticosa root-soil complex increased by 25.57%-56.69%, and that of the H. rhamnoides root-soil complex increased by 51.05%-73.94%. The results show that the two kinds of root-soil complexes can improve soil cohesion. However, Figure 10(b) shows that the internal friction angle of the two soil complexes has no obvious change with increasing soil depth. The results showed that the average value of H. rhamnoides root-enhanced soil cohesion was higher than that of A. Fruticosa and H. rhamnoides roots improved soil shear strength better.


## 4.2.2. Cohesion Increase and Root Fractal Dimension of Soil with Roots

Figure11 shows the relationship between the fractal dimension of roots of A. fruticosa and H. rhamnoides and the increased cohesion of the root-soil complex.Figure 11
Curve of the fractal dimension and added value of cohesion in the root-bearing soil layer.Figure11 shows that the change in root fractal dimension is consistent with root reinforcement ability [41]. When the root fractal dimension increases, plant roots have an enhanced effect on both soil consolidation and regional soil and water conservation [42, 43]. At a certain critical value [38], the root fractal dimension can lead to a maximum increase in the soil shear strength. Correlation analysis was performed between the fractal dimension of the root system and the value of increased cohesion of root-bearing soil layers. It can be concluded that there was a remarkably significant correlation between the fractal dimension of roots of the same shrub and the added value of cohesion of the root-soil complex, while the contribution of different plant roots to the increase of complex cohesion was significantly different, which was mainly due to plant differences in root diameter, morphological character, and root uniformity [39, 40, 44, 45].


## 5. Limit Equilibrium Analysis of Slope considering Root Effects

### 5.1. Calculation Method of the Safety Factor of Plant Slope Protection

The morphological characteristics and mechanical properties of the plant root system were combined to establish a mechanical model and analyse the mechanism of the plant root system on the slope consolidation and slope protection of tailing dams. The stress analysis of the slip zone soil is detailed in Figure12.Figure 12
Force analysis diagram of the sliding body.We assume that the side slope soil is in ultimate equilibrium when using the static equilibrium condition. The shear strength expression of the following sliding zone soil is established.(1)F=c+σtanφL=cL+Wcosβtanφ.Based on Section4.2.1, it is assumed that the increase in root slip resistance is equal to the increase in cohesion (Δc); therefore, the total slip resistance F′ can be obtained.
(2)F′=cL+Wcosβtanφ+Δc,F=Wsinβ.WhenW is the gravity of the slope sliding mass, F is the sliding force, L is the arc length of the landslide mass, β is the slope degree, and Δc is the increased resistance of plant roots to sliding.The coefficient of safety of the slope against sliding stability is(3)K=F′F=cL+Wcosβtanφ+ΔcLWsinβ=Wcosβtanφ+cL+ΔcLWsinβ.According to fractal theory and Section3.2, the fitting formula of cohesion and fractal dimension of tailing soil is obtained.
(4)c=m1D1+n1,where m1 and n1 are the coefficients, which are related to the soil properties.In combination with Section4.2.2, it is known that it relies on the test to establish the general expression for the increase in shear strength of the soil by roots.
(5)c=m2D2+n2,where m2 and n2 are the coefficients, which are related to the root type and characteristics.Formulas (4) and (5) are replaced by Formula (3), and the slope factor of safety is
(6)K=F′F=Wcosβtanφ+cL+ΔcLWsinβ=Wcosβtanφ+m1D1+n1+m2D2+n2LWsinβ,where f is defined as m1D1+n1+m2D2+n2; therefore, Formula (6) is further simplified as
(7)K=F′F=Wcosβtanφ+fLWsinβ,where f is the general cohesive force related to D1 and D2. Therefore, the factor of safety K of the whole sliding soil is positively correlated with the fractal dimension of the soil and root system.


## 5.1. Calculation Method of the Safety Factor of Plant Slope Protection

The morphological characteristics and mechanical properties of the plant root system were combined to establish a mechanical model and analyse the mechanism of the plant root system on the slope consolidation and slope protection of tailing dams. The stress analysis of the slip zone soil is detailed in Figure12.Figure 12
Force analysis diagram of the sliding body.We assume that the side slope soil is in ultimate equilibrium when using the static equilibrium condition. The shear strength expression of the following sliding zone soil is established.(1)F=c+σtanφL=cL+Wcosβtanφ.Based on Section4.2.1, it is assumed that the increase in root slip resistance is equal to the increase in cohesion (Δc); therefore, the total slip resistance F′ can be obtained.
(2)F′=cL+Wcosβtanφ+Δc,F=Wsinβ.WhenW is the gravity of the slope sliding mass, F is the sliding force, L is the arc length of the landslide mass, β is the slope degree, and Δc is the increased resistance of plant roots to sliding.The coefficient of safety of the slope against sliding stability is(3)K=F′F=cL+Wcosβtanφ+ΔcLWsinβ=Wcosβtanφ+cL+ΔcLWsinβ.According to fractal theory and Section3.2, the fitting formula of cohesion and fractal dimension of tailing soil is obtained.
(4)c=m1D1+n1,where m1 and n1 are the coefficients, which are related to the soil properties.In combination with Section4.2.2, it is known that it relies on the test to establish the general expression for the increase in shear strength of the soil by roots.
(5)c=m2D2+n2,where m2 and n2 are the coefficients, which are related to the root type and characteristics.Formulas (4) and (5) are replaced by Formula (3), and the slope factor of safety is
(6)K=F′F=Wcosβtanφ+cL+ΔcLWsinβ=Wcosβtanφ+m1D1+n1+m2D2+n2LWsinβ,where f is defined as m1D1+n1+m2D2+n2; therefore, Formula (6) is further simplified as
(7)K=F′F=Wcosβtanφ+fLWsinβ,where f is the general cohesive force related to D1 and D2. Therefore, the factor of safety K of the whole sliding soil is positively correlated with the fractal dimension of the soil and root system.


## 6. Conclusions

In this paper, we make use of fractal theory to characterize the plant root system configuration. Combined with the test of root strengthening and the shear strength of shallow soil, the fractal description of plant roots in the tailing pond and its influence on soil strength were examined.(1)
The average particle fractal dimension of the three types of soils, namely, tailings,A. fruticosa and H. rhamnoides exhibited a decreasing trend with increasing soil depth, and the average particle fractal dimension of the three types of sorting was H. rhamnoides (2.503) > A. fruticosa (2.482) > tailings (2.374). The root fractal characteristics of A. fruticosa and H. rhamnoides were very noticeable. The order of the average root fractal dimension was H. rhamnoides (1.588) > A. fruticosa (1.661)(2)
The root number, length, surface area, and volume ofA. fruticosa and H. rhamnoides were used as root morphological indicators. The root morphological index and root fractal dimension progressively decreased with increasing soil depth. The roots of A. fruticosa and H. rhamnoides had significant stratification phenomena and were mainly distributed in the soil layer from 0 to 40 cm depth. There were a certain amount of fibrous roots and main roots distributed in each soil layer, which have a comprehensive slope protection effect of anchoring and reinforcement for the dam body(3)
The cohesion of the root-soil complex ofA. fruticosa and H. rhamnoides was greater than that of the tailing soil. The average cohesion of the H. rhamnoides root-soil complex was higher than that of A. fruticosa. The increasing range of the two was 121.98% ~15.52%, showing a trend of increasing and then decreasing, but the change in the internal friction angle was not significant. The fractal dimension was significantly and positively correlated with the increase in soil cohesion(4)
Using fractal theory to derive the formula for calculating the safety factor of slopes considering soil fractal and root fractal dimensions, the safety factor of sliding soil was positively correlated with the soil and root fractal dimensions(5)
Root system grows in the soil and is a function of soil environment with complex and variable morphology and three-dimensional spatial distribution. This study mainly focuses on the study of static morphology and distribution characteristics of root systems. The fractal dimension describes its morphology slightly singularly. The study of fractal dimensional characteristics of the dynamic growth of the root system in the subsurface is the next direction to be performed



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*Source: 9499465-2022-05-05.xml*