# Strength of Vegetated Coal-Bearing Soil under Dry-Wet Cycles: An Experimental Study

Authors: Gang Huang; Mingxin Zheng
Journal: International Journal of Corrosion
 (2021)

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## Abstract

Strength of vegetated coal-bearing soil is of great significance to evaluate the shallow stability of vegetated slopes in coal-bearing soil regions. This paper takes D-W cycles, dry density, water content, and vegetation root (VR) content as four factors and carries out the triaxial test for the orthogonal design of vegetated coal-bearing soil in southern China. The strength curves of vegetated coal-bearing soil under four factors were obtained. The Taguchi method was used to quantitatively analyse the effects of four factors. The microstructure of coal-bearing soil under D-W cycles and the theory of soil reinforcement by VR were discussed. The results indicated that D-W cycles had a significant effect on the cohesion and internal friction angle (P<0.05). The internal friction angle was little affected by the water content and VR content, which had considerable influence on the cohesion. The cohesion could be improved with less than 2% VR content. The cohesion was the largest for no D-W cycles, 10% water content, and 2% VR content. The links between mineral particles go from a stable layered structure to unsteadiness chain structure with the increase in the number of D-W cycles.


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## Body

## 1. Introduction

Coal-bearing soil, which consists of fully weathered carbonaceous mudstone or limestone weathered from coal-bearing strata, is poorly adhesive and easily expansive. With the rapid development of infrastructure in China, increasing quantities of coal-bearing soil are being weathered as coal-bearing strata are excavated during construction in southern China. Generally, coal-bearing soil is difficult to exploit because of its low raw coal content (low carbon content). Thus, the excavated coal-bearing soil layers typically remain in place and often experience shallow landslides during the rainy season, which can result in considerable harm to nearby traffic [1], which brings huge harm to traffic. The investigation found that the landslide was caused by atmospheric variation that caused fissures to accelerate the infiltration of rainwater [2]. Shallow landslides of coal-bearing soil were closely related to strength reduction [3]. Therefore, an urgent problem which could be solved is how to prevent fissures and improve the strength of coal-bearing soil [4]. So far, study on coal-bearing soil was fairly limited and mainly focused on the influence of water content on the strength characteristics of coal-bearing soil. The coal-bearing soil was sensitive to water [2, 5]. To address this issue, some researchers revealed that the cohesion of powered coal-bearing soil declines with water content increases in the form of exponential function [6]. The effect of water content on the shear strength of coal-bearing soil is related to the microstructure and conforms to the fractal theory [7]. Through scanning electron microscope scanning (SEM) and discrete element method (DEM), the microstructure characteristics of the coal-bearing soil with water content had an obvious variation [8, 9]. The repeated variety of water content could cause dry-wet (D-W) cycles, which was a well-known weathering process. Fissures gradually appear on the surface of the coal-bearing soil slope induced by D-W cycles. However, the study on D-W cycles of coal-bearing soil is still scarce.In recent years, relative studies indicated that the protection of coal-bearing soil has gradually started to utilise vegetation ecological protection technology instead of traditional engineering protection technology [10–12], mainly because of its significant role in reducing slope instability and erosion and improving the environment [13, 14]. The presence of vegetation could reduce the occurrence probability of shallow instability [15, 16]. Vegetation had been proven to be available for shallow slope stability, which is due to a series of hydrodynamic effects of vegetation roots (VR) and leaves [17]. A large number of studies have shown that the main effects of vegetation on slope stability were mechanical reinforcement and hydromechanical effects of VR [18]. Mechanical reinforcement refers to increasing the shear strength of the slope through the mechanical properties of VR, which improve the stability of slope soil and reduce the occurrence of the shallow landslide [19]. The role of VR in improving the shallow stability of the slope has been established through the tensile test, straight shear test, and triaxial test, etc. [20]. Hydrological effect refers to the absorption and transpiration of roots to increase the substrate suction of soil, thereby improving the stability of shallow slopes [21]. At present, research on the effects of hydrological on the stability of shallow slopes has become a hot topic. Relevant scholars in Hong Kong have conducted experiments to study the effect of roots on pore water pressure and the factor of safety (FOS) of a shallow slope in the atmospheric environment, moving towards the fundamental understanding of atmosphere-plant-soil interaction [22]. A mathematical model for the rate of root water uptake has been developed, including the root growth rate considering topographic factors, the type of vegetation, and climatic parameters [23, 24].Existing studies have shown that the factors affecting soil strength mainly include water content, D-W cycles, and VR. In addition, dry density will affect the pore and permeability characteristics of the soil, and it will also affect soil strength indicators [25, 26]. However, the existing water content test studies only consider some of the above factors. Considering the dry density, D-W cycles, water content, and VR content, and introducing these influencing factors into the strong model of the coal-bearing soil, the triaxial test study has not been reported. Therefore, our study is the first attempt to understand the strength of the vegetated coal-bearing soil caused by the D-W cycles, dry density, water content, and VR content.The aim of this paper is to understand the strength characteristics of the vegetated coal-bearing soil. This article takes vegetated coal-bearing soil as a research object and conducts a large number of D-W cycle triaxial compression tests. The effects of dry density, D-W cycles, water content, and VR content on the strength of compacted coal-bearing soil are comprehensively considered in the test. The microstructures were analysed by SEM test, and the digital model of soil reinforcement by VR was established. The research conclusions can provide a reference for the analysis of strength characteristics of vegetated coal- bearing soil and slope shallow protection.


## 2. Materials and Methods

### 2.1. Sample Preparation

The research object is the vegetated coal-bearing soil in Shangli County district of the Changli Expressway (Figure1). The Changli Expressway is the most convenient passageway between the capital cities of Hunan and Jiangxi provinces. The project was located in the western Jiangxi region and belongs to the humid subtropical monsoon climate. Summer accounts for 40% of annual precipitation, and it is the rainy season from mid-May to mid-July. The annual average precipitation was about 1603, and the maximum monthly precipitation was about 165. The rainfall was large and concentrated, which adversely affected the stability of the slope.Figure 1
Sampling location.The coal-bearing soil specimens were taken out with a shovel and placed in a plastic bag to seal storage. The indoor soil property test determined that the dry density of the reshaped coal-bearing soil was 1.55 g/cm3, the optimal water content was 10.5% (geotechnical test method standard GBT 50123-2019), the liquid limit was 10.5%, the liquid limit was 14.1%, and the plasticity index was 9.1%; the grain size composition is shown in Table 1. The unevenness coefficient Cu was 27.5, and the curvature coefficient Cc was 2.64. The engineering classification of coal-bearing soil was SW according to the Unified Soil Classification System, ASTM D 2487-10 [27], which was a well-graded soil.Table 1
Grain size composition of powdered coal-bearing soil.
Grain size range (mm)Content (%)Grain size range (mm)Content (%)>57.80.5~0.259.65~24.10.25~0.0758.52~0.554.6<0.07515.4The coal-bearing soil specimens were first placed in an oven at 105°C for 24 hours to ensure that coal-bearing soil specimens could be dried. The dried coal-bearing soil was crushed and passed through a two-millimeter sieve. The sieved coal-bearing soil was sprayed with water in layers with the optimal water content of 10% and left to stand for 2 hours to make the water uniform in coal-bearing soil specimens. Finally, the coal-bearing soil and simulated VR (hemp rope) were made into a standard triaxial sample with a diameter of 39.1 mm and a height of 80 mm by a geotechnical test method, as shown in Figure2.Figure 2
The specimen of triaxial text.


### 2.2. D-W Cycle Process

Triaxial tests were performed after the coal-measure-soil specimens were subjected to 1, 2, 3, 4, and 5 dry-wet cycles. The D-W cycles includes two steps: drying and wetting. The process of drying and wetting under atmospheric conditions due to rainwater infiltration, water table rise, and transpiration is similar to 1D water migration. Furthermore, the water-content gradient influences the development characteristics of soil fissures. To simulate the influence of D-W cycles on the shear strength of soil under natural conditions, we adopted the method of approximately simulating 1D moisture transfer. During drying and wetting, the sides of the specimen were wrapped with a rubber film, which ensured that water in the soil could be transferred through the upper and lower sides of the specimen. The D-W cycling process used in the study was as follows: heating for 8 h at 70°C→water injection for 4 h→heating for 8 h at 70°C→water injection for 4 h. The total period of each cycle was 12 h. The water content of the specimens during D-W cycles was controlled at a time by controlling the total amount of the specimen, and the accuracy was ±0.1 g.


### 2.3. Simulation of VR

The effect of VR in the shallow layer of the slope could play the role of mechanical reinforcement on the soil. The VR had great differences in morphology and properties according to different vegetated species. The tensile strength of VR was between 5 MPa and 100 MPa (tensile test), the plastic deformation was 2%-3%, and the deformation modulus is 100-6000 kPa [28, 29]. The hemp rope was made of vegetated material. Because hemp rope is made from plant material, its mechanical properties are basically the same as those of plant roots, and it can mimic the roots of different plant species. Root bending resistance was not considered according to the direction of prevention. Through the tensile test, the average tensile strength was 35 MPa, and the plastic deformation was 2%. The hemp rope was selected as the root simulation material, which was consistent with the general VR characteristics. The hemp rope was arranged one quarter away from the two ends of the sample in three layers. Each layer was arranged in three sections, which was the chiasma type, as shown in Figure 3.Figure 3
The arrangement of the rope in the sample.


### 2.4. Orthogonal Experimental Design and Taguchi Method

For undisturbed vegetated soil, the difference in dry density affects the strength index of powdery coal-bearing soil [30]. Therefore, it is of practical significance to study the effect of dry density on the strength effect of vegetated coal-bearing soil.The influence degree and regularity of the number of D-W cyclesN, dry density ρ, water content w, and VR content R on the strength of vegetated coal-bearing soil were analysed. Variables and values are shown in Table 2. The water content w and VR content R were percent by weight. In this paper, the triaxial test of the vegetated coal-bearing soil adopted the orthogonal test method. By using the method of extremum and variance, the influence degree and significance level of each factor on the strength parameters were ranked. Orthogonal design is shown in Table 3.Table 2
Variables and values.
LevelVariablesNw (%)R (%)ρ (g/cm3)10501.45211011.50331521.55452031.60Table 3
Orthogonal design.
Test#Nw (%)R (%)ρ (g/cm3)10501.45201011.50301521.55402031.6051521.50611031.45711501.60812011.5593531.551031021.601131511.451232001.50135511.601451001.551551531.501652021.45The effects of the four considered factors (N, ρ, w, and R) on the strength index were calculated using an analysis of variance (ANOVA) with Duncan’s multiple range test and paired t-tests. Correlations with P values less than 0.05 were considered significant. All statistical tests were performed using SPSS Statistics 23.The Taguchi method utilises an orthogonal array to design experiments and analyse the data. The method has been widely used in scientific experiments, quality control, and manufacture [31, 32]. It was specially developed to check the relative importance of multivariables, as listed in Table 4.Table 4
Examples of Taguchi’s method for range analysis.
TestVariable AVariable BVariable CEvaluated parameter1A1B1C1Y12A1B2C2Y23A2B1C2Y34A2B2C1Y4K1Y1+Y2Y1+Y3Y1+Y4K2Y3+Y4Y2+Y4Y2+Y3Vi222K1¯K1/ViK1/ViK1/ViK2¯K2/ViK2/ViK2/ViRange (R)MaxK1¯,K2¯- minK1¯,K2¯The equipment for the test was the Tsz-3 triaxial strain control system (Figure4). The loading mode was that of displacement loading; the loading rate was 0.01 mm/s.Figure 4
Triaxial test.


## 2.1. Sample Preparation

The research object is the vegetated coal-bearing soil in Shangli County district of the Changli Expressway (Figure1). The Changli Expressway is the most convenient passageway between the capital cities of Hunan and Jiangxi provinces. The project was located in the western Jiangxi region and belongs to the humid subtropical monsoon climate. Summer accounts for 40% of annual precipitation, and it is the rainy season from mid-May to mid-July. The annual average precipitation was about 1603, and the maximum monthly precipitation was about 165. The rainfall was large and concentrated, which adversely affected the stability of the slope.Figure 1
Sampling location.The coal-bearing soil specimens were taken out with a shovel and placed in a plastic bag to seal storage. The indoor soil property test determined that the dry density of the reshaped coal-bearing soil was 1.55 g/cm3, the optimal water content was 10.5% (geotechnical test method standard GBT 50123-2019), the liquid limit was 10.5%, the liquid limit was 14.1%, and the plasticity index was 9.1%; the grain size composition is shown in Table 1. The unevenness coefficient Cu was 27.5, and the curvature coefficient Cc was 2.64. The engineering classification of coal-bearing soil was SW according to the Unified Soil Classification System, ASTM D 2487-10 [27], which was a well-graded soil.Table 1
Grain size composition of powdered coal-bearing soil.
Grain size range (mm)Content (%)Grain size range (mm)Content (%)>57.80.5~0.259.65~24.10.25~0.0758.52~0.554.6<0.07515.4The coal-bearing soil specimens were first placed in an oven at 105°C for 24 hours to ensure that coal-bearing soil specimens could be dried. The dried coal-bearing soil was crushed and passed through a two-millimeter sieve. The sieved coal-bearing soil was sprayed with water in layers with the optimal water content of 10% and left to stand for 2 hours to make the water uniform in coal-bearing soil specimens. Finally, the coal-bearing soil and simulated VR (hemp rope) were made into a standard triaxial sample with a diameter of 39.1 mm and a height of 80 mm by a geotechnical test method, as shown in Figure2.Figure 2
The specimen of triaxial text.


## 2.2. D-W Cycle Process

Triaxial tests were performed after the coal-measure-soil specimens were subjected to 1, 2, 3, 4, and 5 dry-wet cycles. The D-W cycles includes two steps: drying and wetting. The process of drying and wetting under atmospheric conditions due to rainwater infiltration, water table rise, and transpiration is similar to 1D water migration. Furthermore, the water-content gradient influences the development characteristics of soil fissures. To simulate the influence of D-W cycles on the shear strength of soil under natural conditions, we adopted the method of approximately simulating 1D moisture transfer. During drying and wetting, the sides of the specimen were wrapped with a rubber film, which ensured that water in the soil could be transferred through the upper and lower sides of the specimen. The D-W cycling process used in the study was as follows: heating for 8 h at 70°C→water injection for 4 h→heating for 8 h at 70°C→water injection for 4 h. The total period of each cycle was 12 h. The water content of the specimens during D-W cycles was controlled at a time by controlling the total amount of the specimen, and the accuracy was ±0.1 g.


## 2.3. Simulation of VR

The effect of VR in the shallow layer of the slope could play the role of mechanical reinforcement on the soil. The VR had great differences in morphology and properties according to different vegetated species. The tensile strength of VR was between 5 MPa and 100 MPa (tensile test), the plastic deformation was 2%-3%, and the deformation modulus is 100-6000 kPa [28, 29]. The hemp rope was made of vegetated material. Because hemp rope is made from plant material, its mechanical properties are basically the same as those of plant roots, and it can mimic the roots of different plant species. Root bending resistance was not considered according to the direction of prevention. Through the tensile test, the average tensile strength was 35 MPa, and the plastic deformation was 2%. The hemp rope was selected as the root simulation material, which was consistent with the general VR characteristics. The hemp rope was arranged one quarter away from the two ends of the sample in three layers. Each layer was arranged in three sections, which was the chiasma type, as shown in Figure 3.Figure 3
The arrangement of the rope in the sample.


## 2.4. Orthogonal Experimental Design and Taguchi Method

For undisturbed vegetated soil, the difference in dry density affects the strength index of powdery coal-bearing soil [30]. Therefore, it is of practical significance to study the effect of dry density on the strength effect of vegetated coal-bearing soil.The influence degree and regularity of the number of D-W cyclesN, dry density ρ, water content w, and VR content R on the strength of vegetated coal-bearing soil were analysed. Variables and values are shown in Table 2. The water content w and VR content R were percent by weight. In this paper, the triaxial test of the vegetated coal-bearing soil adopted the orthogonal test method. By using the method of extremum and variance, the influence degree and significance level of each factor on the strength parameters were ranked. Orthogonal design is shown in Table 3.Table 2
Variables and values.
LevelVariablesNw (%)R (%)ρ (g/cm3)10501.45211011.50331521.55452031.60Table 3
Orthogonal design.
Test#Nw (%)R (%)ρ (g/cm3)10501.45201011.50301521.55402031.6051521.50611031.45711501.60812011.5593531.551031021.601131511.451232001.50135511.601451001.551551531.501652021.45The effects of the four considered factors (N, ρ, w, and R) on the strength index were calculated using an analysis of variance (ANOVA) with Duncan’s multiple range test and paired t-tests. Correlations with P values less than 0.05 were considered significant. All statistical tests were performed using SPSS Statistics 23.The Taguchi method utilises an orthogonal array to design experiments and analyse the data. The method has been widely used in scientific experiments, quality control, and manufacture [31, 32]. It was specially developed to check the relative importance of multivariables, as listed in Table 4.Table 4
Examples of Taguchi’s method for range analysis.
TestVariable AVariable BVariable CEvaluated parameter1A1B1C1Y12A1B2C2Y23A2B1C2Y34A2B2C1Y4K1Y1+Y2Y1+Y3Y1+Y4K2Y3+Y4Y2+Y4Y2+Y3Vi222K1¯K1/ViK1/ViK1/ViK2¯K2/ViK2/ViK2/ViRange (R)MaxK1¯,K2¯- minK1¯,K2¯The equipment for the test was the Tsz-3 triaxial strain control system (Figure4). The loading mode was that of displacement loading; the loading rate was 0.01 mm/s.Figure 4
Triaxial test.


## 3. Triaxial Test Results

### 3.1. Stress-Strain Curves

The stress-strainσ1‐σ3ε1 curves of each group were obtained through triaxial tests of unconsolidated and nondrained (UU) powdered coal-bearing soil under the action of D-W cycles. The stress-strain curves of different numbers of D-W cycles are plotted in Figure 5. The peak shear stress or the shear stress of 15% axial strain (there is no peak) of the stress-strain curves was taken as the shear strength.Figure 5
The stress-strain curves variation of vegetated coal-bearing soil specimens: (a) no D-W cycles; (b) one D-W cycles; (c) three D-W cycles; (d) five D-W cycles.
(a)(b)(c)(d)It can be seen from the stress-strain curves in Figure5 that the shear stress increases with increasing strain. The stress-strain curves show a nonlinear relationship. With increasing stress, the strain softening increments rapidly increase. The more the numbers of D-W cycles, the smaller the shear strength. This is because D-W cycles change the arrangement of particles in the sample soil, and the bite force of particles decreases.


### 3.2. Shear Strength Parameters

#### 3.2.1. Cohesion

To investigate the effect of four factors on cohesion, the relationship between the factor and cohesion is plotted in Figure6.Figure 6
(a) Cohesion vs. number of W-D cycles; (b) cohesion vs. water content; (c) cohesion vs. VR content; (d) cohesion vs. dry density.
(a)(b)(c)(d)As plotted in Figure6(a), when the number of D-W cycles was less than one, the relationships between the number of D-W cycles and cohesion were not obvious. When the water content was greater than one, the cohesion was decreasing with the increase in the number of D-W cycles. D-W cycles had a great influence on the cohesion of coal-bearing soil (P<0.05).The cohesion decreases up to 13.2 kPa for every D-W cycle. It indicated that D-W cycles were very sensitive to the strength of vegetated coal-bearing soil. This is because coal-bearing soil shrunk and expanded repeatedly. When the environment is drying, the water molecules in clay minerals in vegetated coal-bearing soils begin to evaporate, and the soils shrink and structural damage occurs beyond a certain threshold. When the environment turns wet, the structural damage of vegetated coal-bearing soil is accelerated by the wedge pressure of water and the expansion pressure of clay minerals [33].As plotted in Figure6(b), when the water content is less than 10%, the cohesive force increases as the water content increases. However, when the water content was greater than 10%, with the increase of water content, the cohesion was decreasing. When the water content was 10%, the cohesion was the maximum. The water has an influence on the cohesion of vegetated coal-bearing soil (P<0.05). When the water content was large, the cohesion decreases up to 3 kPa for every 1% increase in water content. It indicated that water was also affecting the strength of vegetated coal-bearing soil. Water and coal-bearing soil interactions were intense, leading to a decrease in strength and landslide [2].As plotted in Figure6(c), when the VR content was less than 2%, the cohesion slowly increases. When the VR content was greater than the critical value, the cohesive force decreased as the VR content increased.As plotted in Figure6(d), the relationship between dry density and cohesion was not very significant (P>0.05). According to the average cohesion, it was found that with the increase of dry density, the cohesion change amplitude was only 10 kPa, which shows that the effect of dry density was not significant (P>0.05).To investigate the effect of four influencing factors on cohesion, the analysis of cohesion was carried out, as listed in Table5. Range of D-W cycle was 53.6. The D-W cycles were the dominating factor affecting cohesion, followed by VR content and water content. Dry density had little effect on the cohesion. From the above data, the range of D-W cycles was twice as large as the other factors. When the number of D-W cycles was over one, the swelling force of coal-bearing soil is under dry conditions, and liquid bridge force is under wet conditions, the liquid bridge force has reached a threshold repeatedly, resulting in the occurrence of the fissure, which is reducing the cohesion. When the roots were in the proper amount, the VR exerts its tensile properties, which was beneficial to the cohesion of coal-bearing soil. When a lot of VR impede the adhesion of coal-bearing soil, it was easy to form a weak surface at the simulated interface. Therefore, VR reduces coal-bearing soil cohesion. When the water content was 10%, the VR content effect was obvious, which results in the stable internal structure of coal-bearing soil. Besides, when the water content was over 10%, the contact surfaces between the water and the soil were increased, resulting in the available decrease in cohesion. As for the small effect of dry density and cohesion, the possible reason was that the increase in dry density only reduced the voids of coal-bearing soil and did not increase the cohesiveness of soil particles. The amount of dry density did not cause the deterioration of coal-bearing soil to be significant, and it is difficult to affect the cohesion.Table 5
Range analysis for cohesion.
Test #Nw (%)R (%)ρ (g/cm3)c (kPa)10501.4589201011.5087.9301521.5560402031.6021.751521.5090.8611031.4558.5711501.6076.2812011.5580.192531.5528.21021021.6071.51121511.4556.11222001.5042.2133511.6017.41431001.5527.61531531.50201632021.4526K1¯64.756.454.353.9K2¯76.461.460.460.2K3¯49.553.162.149.0K4¯22.842.533.846.7Range53.718.928.313.5


#### 3.2.2. Internal Friction Angle

To investigate the effect of four factors on the internal friction angle, analysis of the internal friction angle was carried out, as listed in Table6. It can be seen that the order of Table 6 is slightly different from that of Table 5. The D-W cycles were still the main factors affecting the internal friction angle, and the effect of VR content was undermined. The relationship between the number of D-W cycles and the internal friction angle is plotted in Figure 7. According to Figure 7, the internal friction angle decreased with the increasing number of D-W cycles (P<0.05). However, the internal friction angle slowly increased with the increasing number of D-W cycles after reaching a valley value of 19.9°. It indicated that the variation of the atmospheric environment for coal-bearing soil particles causes the particles to wear and fissure, reducing the internal friction angle. The range of cohesion for D-W cycles was more than twice the internal friction angle. The effect of the water content on cohesion degeneration was not as significant as that of D-W cycles.Table 6
Range analysis for internal friction angle.
Test #Nw (%)R (%)ρ (g/cm3)K1¯39.726.726.326.6K2¯32.227.230.225.2K3¯19.930.630.035.1K4¯23.430.730.029.4Range19.84.03.99.9Figure 7
The relationship between the number of D-W cycles and internal friction angle.


## 3.1. Stress-Strain Curves

The stress-strainσ1‐σ3ε1 curves of each group were obtained through triaxial tests of unconsolidated and nondrained (UU) powdered coal-bearing soil under the action of D-W cycles. The stress-strain curves of different numbers of D-W cycles are plotted in Figure 5. The peak shear stress or the shear stress of 15% axial strain (there is no peak) of the stress-strain curves was taken as the shear strength.Figure 5
The stress-strain curves variation of vegetated coal-bearing soil specimens: (a) no D-W cycles; (b) one D-W cycles; (c) three D-W cycles; (d) five D-W cycles.
(a)(b)(c)(d)It can be seen from the stress-strain curves in Figure5 that the shear stress increases with increasing strain. The stress-strain curves show a nonlinear relationship. With increasing stress, the strain softening increments rapidly increase. The more the numbers of D-W cycles, the smaller the shear strength. This is because D-W cycles change the arrangement of particles in the sample soil, and the bite force of particles decreases.


## 3.2. Shear Strength Parameters

### 3.2.1. Cohesion

To investigate the effect of four factors on cohesion, the relationship between the factor and cohesion is plotted in Figure6.Figure 6
(a) Cohesion vs. number of W-D cycles; (b) cohesion vs. water content; (c) cohesion vs. VR content; (d) cohesion vs. dry density.
(a)(b)(c)(d)As plotted in Figure6(a), when the number of D-W cycles was less than one, the relationships between the number of D-W cycles and cohesion were not obvious. When the water content was greater than one, the cohesion was decreasing with the increase in the number of D-W cycles. D-W cycles had a great influence on the cohesion of coal-bearing soil (P<0.05).The cohesion decreases up to 13.2 kPa for every D-W cycle. It indicated that D-W cycles were very sensitive to the strength of vegetated coal-bearing soil. This is because coal-bearing soil shrunk and expanded repeatedly. When the environment is drying, the water molecules in clay minerals in vegetated coal-bearing soils begin to evaporate, and the soils shrink and structural damage occurs beyond a certain threshold. When the environment turns wet, the structural damage of vegetated coal-bearing soil is accelerated by the wedge pressure of water and the expansion pressure of clay minerals [33].As plotted in Figure6(b), when the water content is less than 10%, the cohesive force increases as the water content increases. However, when the water content was greater than 10%, with the increase of water content, the cohesion was decreasing. When the water content was 10%, the cohesion was the maximum. The water has an influence on the cohesion of vegetated coal-bearing soil (P<0.05). When the water content was large, the cohesion decreases up to 3 kPa for every 1% increase in water content. It indicated that water was also affecting the strength of vegetated coal-bearing soil. Water and coal-bearing soil interactions were intense, leading to a decrease in strength and landslide [2].As plotted in Figure6(c), when the VR content was less than 2%, the cohesion slowly increases. When the VR content was greater than the critical value, the cohesive force decreased as the VR content increased.As plotted in Figure6(d), the relationship between dry density and cohesion was not very significant (P>0.05). According to the average cohesion, it was found that with the increase of dry density, the cohesion change amplitude was only 10 kPa, which shows that the effect of dry density was not significant (P>0.05).To investigate the effect of four influencing factors on cohesion, the analysis of cohesion was carried out, as listed in Table5. Range of D-W cycle was 53.6. The D-W cycles were the dominating factor affecting cohesion, followed by VR content and water content. Dry density had little effect on the cohesion. From the above data, the range of D-W cycles was twice as large as the other factors. When the number of D-W cycles was over one, the swelling force of coal-bearing soil is under dry conditions, and liquid bridge force is under wet conditions, the liquid bridge force has reached a threshold repeatedly, resulting in the occurrence of the fissure, which is reducing the cohesion. When the roots were in the proper amount, the VR exerts its tensile properties, which was beneficial to the cohesion of coal-bearing soil. When a lot of VR impede the adhesion of coal-bearing soil, it was easy to form a weak surface at the simulated interface. Therefore, VR reduces coal-bearing soil cohesion. When the water content was 10%, the VR content effect was obvious, which results in the stable internal structure of coal-bearing soil. Besides, when the water content was over 10%, the contact surfaces between the water and the soil were increased, resulting in the available decrease in cohesion. As for the small effect of dry density and cohesion, the possible reason was that the increase in dry density only reduced the voids of coal-bearing soil and did not increase the cohesiveness of soil particles. The amount of dry density did not cause the deterioration of coal-bearing soil to be significant, and it is difficult to affect the cohesion.Table 5
Range analysis for cohesion.
Test #Nw (%)R (%)ρ (g/cm3)c (kPa)10501.4589201011.5087.9301521.5560402031.6021.751521.5090.8611031.4558.5711501.6076.2812011.5580.192531.5528.21021021.6071.51121511.4556.11222001.5042.2133511.6017.41431001.5527.61531531.50201632021.4526K1¯64.756.454.353.9K2¯76.461.460.460.2K3¯49.553.162.149.0K4¯22.842.533.846.7Range53.718.928.313.5


### 3.2.2. Internal Friction Angle

To investigate the effect of four factors on the internal friction angle, analysis of the internal friction angle was carried out, as listed in Table6. It can be seen that the order of Table 6 is slightly different from that of Table 5. The D-W cycles were still the main factors affecting the internal friction angle, and the effect of VR content was undermined. The relationship between the number of D-W cycles and the internal friction angle is plotted in Figure 7. According to Figure 7, the internal friction angle decreased with the increasing number of D-W cycles (P<0.05). However, the internal friction angle slowly increased with the increasing number of D-W cycles after reaching a valley value of 19.9°. It indicated that the variation of the atmospheric environment for coal-bearing soil particles causes the particles to wear and fissure, reducing the internal friction angle. The range of cohesion for D-W cycles was more than twice the internal friction angle. The effect of the water content on cohesion degeneration was not as significant as that of D-W cycles.Table 6
Range analysis for internal friction angle.
Test #Nw (%)R (%)ρ (g/cm3)K1¯39.726.726.326.6K2¯32.227.230.225.2K3¯19.930.630.035.1K4¯23.430.730.029.4Range19.84.03.99.9Figure 7
The relationship between the number of D-W cycles and internal friction angle.


## 3.2.1. Cohesion

To investigate the effect of four factors on cohesion, the relationship between the factor and cohesion is plotted in Figure6.Figure 6
(a) Cohesion vs. number of W-D cycles; (b) cohesion vs. water content; (c) cohesion vs. VR content; (d) cohesion vs. dry density.
(a)(b)(c)(d)As plotted in Figure6(a), when the number of D-W cycles was less than one, the relationships between the number of D-W cycles and cohesion were not obvious. When the water content was greater than one, the cohesion was decreasing with the increase in the number of D-W cycles. D-W cycles had a great influence on the cohesion of coal-bearing soil (P<0.05).The cohesion decreases up to 13.2 kPa for every D-W cycle. It indicated that D-W cycles were very sensitive to the strength of vegetated coal-bearing soil. This is because coal-bearing soil shrunk and expanded repeatedly. When the environment is drying, the water molecules in clay minerals in vegetated coal-bearing soils begin to evaporate, and the soils shrink and structural damage occurs beyond a certain threshold. When the environment turns wet, the structural damage of vegetated coal-bearing soil is accelerated by the wedge pressure of water and the expansion pressure of clay minerals [33].As plotted in Figure6(b), when the water content is less than 10%, the cohesive force increases as the water content increases. However, when the water content was greater than 10%, with the increase of water content, the cohesion was decreasing. When the water content was 10%, the cohesion was the maximum. The water has an influence on the cohesion of vegetated coal-bearing soil (P<0.05). When the water content was large, the cohesion decreases up to 3 kPa for every 1% increase in water content. It indicated that water was also affecting the strength of vegetated coal-bearing soil. Water and coal-bearing soil interactions were intense, leading to a decrease in strength and landslide [2].As plotted in Figure6(c), when the VR content was less than 2%, the cohesion slowly increases. When the VR content was greater than the critical value, the cohesive force decreased as the VR content increased.As plotted in Figure6(d), the relationship between dry density and cohesion was not very significant (P>0.05). According to the average cohesion, it was found that with the increase of dry density, the cohesion change amplitude was only 10 kPa, which shows that the effect of dry density was not significant (P>0.05).To investigate the effect of four influencing factors on cohesion, the analysis of cohesion was carried out, as listed in Table5. Range of D-W cycle was 53.6. The D-W cycles were the dominating factor affecting cohesion, followed by VR content and water content. Dry density had little effect on the cohesion. From the above data, the range of D-W cycles was twice as large as the other factors. When the number of D-W cycles was over one, the swelling force of coal-bearing soil is under dry conditions, and liquid bridge force is under wet conditions, the liquid bridge force has reached a threshold repeatedly, resulting in the occurrence of the fissure, which is reducing the cohesion. When the roots were in the proper amount, the VR exerts its tensile properties, which was beneficial to the cohesion of coal-bearing soil. When a lot of VR impede the adhesion of coal-bearing soil, it was easy to form a weak surface at the simulated interface. Therefore, VR reduces coal-bearing soil cohesion. When the water content was 10%, the VR content effect was obvious, which results in the stable internal structure of coal-bearing soil. Besides, when the water content was over 10%, the contact surfaces between the water and the soil were increased, resulting in the available decrease in cohesion. As for the small effect of dry density and cohesion, the possible reason was that the increase in dry density only reduced the voids of coal-bearing soil and did not increase the cohesiveness of soil particles. The amount of dry density did not cause the deterioration of coal-bearing soil to be significant, and it is difficult to affect the cohesion.Table 5
Range analysis for cohesion.
Test #Nw (%)R (%)ρ (g/cm3)c (kPa)10501.4589201011.5087.9301521.5560402031.6021.751521.5090.8611031.4558.5711501.6076.2812011.5580.192531.5528.21021021.6071.51121511.4556.11222001.5042.2133511.6017.41431001.5527.61531531.50201632021.4526K1¯64.756.454.353.9K2¯76.461.460.460.2K3¯49.553.162.149.0K4¯22.842.533.846.7Range53.718.928.313.5


## 3.2.2. Internal Friction Angle

To investigate the effect of four factors on the internal friction angle, analysis of the internal friction angle was carried out, as listed in Table6. It can be seen that the order of Table 6 is slightly different from that of Table 5. The D-W cycles were still the main factors affecting the internal friction angle, and the effect of VR content was undermined. The relationship between the number of D-W cycles and the internal friction angle is plotted in Figure 7. According to Figure 7, the internal friction angle decreased with the increasing number of D-W cycles (P<0.05). However, the internal friction angle slowly increased with the increasing number of D-W cycles after reaching a valley value of 19.9°. It indicated that the variation of the atmospheric environment for coal-bearing soil particles causes the particles to wear and fissure, reducing the internal friction angle. The range of cohesion for D-W cycles was more than twice the internal friction angle. The effect of the water content on cohesion degeneration was not as significant as that of D-W cycles.Table 6
Range analysis for internal friction angle.
Test #Nw (%)R (%)ρ (g/cm3)K1¯39.726.726.326.6K2¯32.227.230.225.2K3¯19.930.630.035.1K4¯23.430.730.029.4Range19.84.03.99.9Figure 7
The relationship between the number of D-W cycles and internal friction angle.


## 4. Discussion

### 4.1. Microstructure Characterization Affected by D-W Cycles

Research on geotechnical microstructure using SEM has become the most common geotechnical technique [34]. Many studies show that the strength properties of soil are closely related to the microstructure [35, 36]. To study the relationship between water and coal-bearing soil, the mineral composition and chemical composition are analysed by Sigma 300 scanning electron microscopy (SEM). Figure 8 is a comparison of the microstructure of powdered coal-bearing soil before and after the D-W cycles. As the D-W cycles increase, small pores increase and microfractures can also be clearly observed. Notably, several edge-to-edge contacts can be observed between mineral particles. Chain structures at the edges of clay minerals can be observed. It is inferred that the D-W cycles have caused the basic structural units and contact relationships of the particles to readjust; the links between mineral particles have stable layered structures through surface-to-surface contact to chain structures through edge-to-edge, which is different from Han et al. [8] in microstructure change. The microstructure from surface-to-surface to surface-to-edge contact was studied under different levels of water content. It can be seen from the figure that the D-W cycles have caused the basic structural units and contact relationships of the particles to change. Clay minerals had the high swelling-shrinking ability under D-W cycle conditions [37–39].Figure 8
SEM image at a magnification of 1000: (a) no D-W cycles; (b) one D-W cycles; (c) three D-W cycles; (d) five D-W cycles.
(a)(b)(c)(d)As the number of D-W cycles increases, the number of edge debris increased. The degree of particle fragmentation and the pores increase visibly. With increase of the number of D-W cycles, the contact relationship gradually changed from surface-to-surface contact to edge to-edge contact. The multiplication of pores and the development of microcracks simultaneously affected the shear strength. The microcracks provided the necessary conditions for water and coal-bearing soil interaction [40]. The variation of the basic structural unit and contact relationship of the particles caused the strength softening of the powdery coal-bearing soil. The water was a polar molecule and a solvent. Coal-bearing soil contains a variety of soluble components, such as clay minerals. Clay minerals had high expansive characteristics under D-W cycle conditions (Figure 9). When the environment was drying, the water molecules in clay minerals in coal-bearing soils began to evaporate and the soil shrink, and structural damage occurred beyond a certain threshold. When the environment turned wet, the structural damage of coal-bearing soil was accelerated by the wedge pressure of water and the expansion pressure of clay minerals, and microcracks appear. Some particles began to separate from the coal with the washing effect of water. After dry-wet cycles, the clay mineral particles were clustered together under the interaction of liquid bridge force and interparticle force [41].Figure 9
Coal-bearing soil with expansive characteristics.


### 4.2. Theoretical Analysis of Soil Reinforcement by Vegetation Roots

#### 4.2.1. Theoretical Analysis

Vegetation can protect the slope from shallow landslides, mainly because the underground root system strengthens the surface soil. When the coal-bearing soil slope has frequent rainfall in the south of the Yangtze River in summer, on the one hand, the erosion chain formed under the erosive force of the rainfall will bring the soil particles down the slope; on the other hand, the permeable layer will be formed after the water infiltrates, reducing the soil resistance. The shear strength affects the stability of the shallow soil of the slope. This section combines the basic theory of unsaturated soils, establishes a mathematical formula to explain the root failure mechanism and analyses the reinforcement mechanism of roots on unsaturated soils.The formula for the shear strengthτf of unsaturated soil is
(1)τf=c′+σ−uatanϕ′+ua−uwtanϕ′θ−θrθs−θr,where c′ and ϕ′ are the effective cohesion and the effective angle of internal friction of soil mass, respectively; σ−ua is the net stress of unsaturated soil; ua−uw is the matric suction; θ, θr, and θs are the current, residual, and saturated moisture contents of the soil, respectively.The cohesionc′ of the root-soil is mainly composed of two parts: (1) the effective cohesion cs′ of the soil; (2) the cohesion Δcr′ induced by the root system, namely,
(2)c′=cs′+Δcr′.According to the improvement of the Wu model by Preti and Schwarz [42], the root-induced cohesion Δcr′ is
(3)Δcr′=0.4⋅RAR⋅TNδ,where RAR is the root area ratio, TN is the maximum tensile stress caused by the root, and δ is a parameter related to the root direction, which can be expressed as
(4)δ=cosαi+sinαitanϕ′,where αi is the angle of the first deforming root to the horizontal plane.The model is extended to estimate the contribution of plant roots to the cohesive force increaseΔcr′ under a certain displacement, by considering the root failure mode observed in the triaxial test which is the cohesive force Δcr′ produced by elongated roots.According to Figure10(a), the vertical slip length ΔL of the root is
(5)ΔL=L2‐L‐L1‐Δd2+Δt2,whereL1 is the root which has no vertical length of horizontal movement and L2 is the vertical length of the horizontal movement of the root.Figure 10
Schematic diagram of root stress and deformation: (a) vertical root deformation; (b) inclined root deformation.
(a)(b)It can be seen from Figure10(b) that the inclination angle α2 between the deformed root and the horizontal is
(6)tanα2=ΔtΔt/tanβ+Δd,where Δd is the shear displacement, Δt is the shear length of the root, and β is the angle of the shear segment of the root deformation.The elongation of the rootsω is
(7)ω=L2‐L‐L1‐Δd2+Δt2L.The energy generated by the root elongation is(8)E=12Tiω=12ke2,where k is the elastic modulus of the root and e is the root elongation.Tensile stress generated by thei tensile root is
(9)Ti=kL2sinα2+L−L1sinα2‐Δttanα2+Δd2+Δt2.The cohesionΔcr produced by root elongation is
(10)Δcr=0.4⋅∑i=0m1RARi⋅Ti⋅cosαi+sinαitanϕ′,wherem1 is the number of severed roots in the roots.
(11)τf=0.4⋅∑i=0m1RARi⋅Ti⋅cosαi+sinαitanϕ′+σ−uatanϕ′+ua−uwtanϕ′θ−θrθs−θr.


#### 4.2.2. The Example Analysis

According to root damage in the direct shear test, root parameters (such as root geometry, tensile strength, Young’s modulus, and root orientation) are shown in Table7. The results of cohesion predicted by the model and the experimental results are shown in Figure 11. According to Wu, the root direction parameter is 1.2. As shown in Figure 11, the model prediction is in good agreement with the experimental results. Figure 11(a) shows the experimental results of cohesion of soil with roots at different depths, and Figure 11(b) shows the model prediction results. An acceptable agreement between the experimental and predicted values can be observed. These results verify that the mechanical effect of root system on soil reinforcement is a function of growth period and soil depth, and the proposed digital model can predict the experimental trend.Table 7
Root parameters.
Diameter (cm)Elasticity modulus (kN/m2·mm-1)Length (cm)Shear thickness (cm)L1 (cm)L2 (cm)Δd (cm)Mobile length (cm)Tensile strength (kN/m2)Mean soil depth (cm)0.3100001727.67.61.40.93100002.90.21100001426.36.31.40.93100002.60.12100001024.64.61.40.23100002.00.3410000922.52.51.40.23100004.40.23100001528.68.61.40.93100002.10.621000015212.312.41.40.931000042.60.52100001529.69.61.40.23100002.00.3100001522.52.51.40.23100002.40.21100001529.69.61.40.23100002.00.34100001522.52.51.40.23100002.4Figure 11
Cohesion of root-bearing soil at different growth periods and different depths: (a) test value; (b) predicted value.
(a)(b)


## 4.1. Microstructure Characterization Affected by D-W Cycles

Research on geotechnical microstructure using SEM has become the most common geotechnical technique [34]. Many studies show that the strength properties of soil are closely related to the microstructure [35, 36]. To study the relationship between water and coal-bearing soil, the mineral composition and chemical composition are analysed by Sigma 300 scanning electron microscopy (SEM). Figure 8 is a comparison of the microstructure of powdered coal-bearing soil before and after the D-W cycles. As the D-W cycles increase, small pores increase and microfractures can also be clearly observed. Notably, several edge-to-edge contacts can be observed between mineral particles. Chain structures at the edges of clay minerals can be observed. It is inferred that the D-W cycles have caused the basic structural units and contact relationships of the particles to readjust; the links between mineral particles have stable layered structures through surface-to-surface contact to chain structures through edge-to-edge, which is different from Han et al. [8] in microstructure change. The microstructure from surface-to-surface to surface-to-edge contact was studied under different levels of water content. It can be seen from the figure that the D-W cycles have caused the basic structural units and contact relationships of the particles to change. Clay minerals had the high swelling-shrinking ability under D-W cycle conditions [37–39].Figure 8
SEM image at a magnification of 1000: (a) no D-W cycles; (b) one D-W cycles; (c) three D-W cycles; (d) five D-W cycles.
(a)(b)(c)(d)As the number of D-W cycles increases, the number of edge debris increased. The degree of particle fragmentation and the pores increase visibly. With increase of the number of D-W cycles, the contact relationship gradually changed from surface-to-surface contact to edge to-edge contact. The multiplication of pores and the development of microcracks simultaneously affected the shear strength. The microcracks provided the necessary conditions for water and coal-bearing soil interaction [40]. The variation of the basic structural unit and contact relationship of the particles caused the strength softening of the powdery coal-bearing soil. The water was a polar molecule and a solvent. Coal-bearing soil contains a variety of soluble components, such as clay minerals. Clay minerals had high expansive characteristics under D-W cycle conditions (Figure 9). When the environment was drying, the water molecules in clay minerals in coal-bearing soils began to evaporate and the soil shrink, and structural damage occurred beyond a certain threshold. When the environment turned wet, the structural damage of coal-bearing soil was accelerated by the wedge pressure of water and the expansion pressure of clay minerals, and microcracks appear. Some particles began to separate from the coal with the washing effect of water. After dry-wet cycles, the clay mineral particles were clustered together under the interaction of liquid bridge force and interparticle force [41].Figure 9
Coal-bearing soil with expansive characteristics.


## 4.2. Theoretical Analysis of Soil Reinforcement by Vegetation Roots

### 4.2.1. Theoretical Analysis

Vegetation can protect the slope from shallow landslides, mainly because the underground root system strengthens the surface soil. When the coal-bearing soil slope has frequent rainfall in the south of the Yangtze River in summer, on the one hand, the erosion chain formed under the erosive force of the rainfall will bring the soil particles down the slope; on the other hand, the permeable layer will be formed after the water infiltrates, reducing the soil resistance. The shear strength affects the stability of the shallow soil of the slope. This section combines the basic theory of unsaturated soils, establishes a mathematical formula to explain the root failure mechanism and analyses the reinforcement mechanism of roots on unsaturated soils.The formula for the shear strengthτf of unsaturated soil is
(1)τf=c′+σ−uatanϕ′+ua−uwtanϕ′θ−θrθs−θr,where c′ and ϕ′ are the effective cohesion and the effective angle of internal friction of soil mass, respectively; σ−ua is the net stress of unsaturated soil; ua−uw is the matric suction; θ, θr, and θs are the current, residual, and saturated moisture contents of the soil, respectively.The cohesionc′ of the root-soil is mainly composed of two parts: (1) the effective cohesion cs′ of the soil; (2) the cohesion Δcr′ induced by the root system, namely,
(2)c′=cs′+Δcr′.According to the improvement of the Wu model by Preti and Schwarz [42], the root-induced cohesion Δcr′ is
(3)Δcr′=0.4⋅RAR⋅TNδ,where RAR is the root area ratio, TN is the maximum tensile stress caused by the root, and δ is a parameter related to the root direction, which can be expressed as
(4)δ=cosαi+sinαitanϕ′,where αi is the angle of the first deforming root to the horizontal plane.The model is extended to estimate the contribution of plant roots to the cohesive force increaseΔcr′ under a certain displacement, by considering the root failure mode observed in the triaxial test which is the cohesive force Δcr′ produced by elongated roots.According to Figure10(a), the vertical slip length ΔL of the root is
(5)ΔL=L2‐L‐L1‐Δd2+Δt2,whereL1 is the root which has no vertical length of horizontal movement and L2 is the vertical length of the horizontal movement of the root.Figure 10
Schematic diagram of root stress and deformation: (a) vertical root deformation; (b) inclined root deformation.
(a)(b)It can be seen from Figure10(b) that the inclination angle α2 between the deformed root and the horizontal is
(6)tanα2=ΔtΔt/tanβ+Δd,where Δd is the shear displacement, Δt is the shear length of the root, and β is the angle of the shear segment of the root deformation.The elongation of the rootsω is
(7)ω=L2‐L‐L1‐Δd2+Δt2L.The energy generated by the root elongation is(8)E=12Tiω=12ke2,where k is the elastic modulus of the root and e is the root elongation.Tensile stress generated by thei tensile root is
(9)Ti=kL2sinα2+L−L1sinα2‐Δttanα2+Δd2+Δt2.The cohesionΔcr produced by root elongation is
(10)Δcr=0.4⋅∑i=0m1RARi⋅Ti⋅cosαi+sinαitanϕ′,wherem1 is the number of severed roots in the roots.
(11)τf=0.4⋅∑i=0m1RARi⋅Ti⋅cosαi+sinαitanϕ′+σ−uatanϕ′+ua−uwtanϕ′θ−θrθs−θr.


### 4.2.2. The Example Analysis

According to root damage in the direct shear test, root parameters (such as root geometry, tensile strength, Young’s modulus, and root orientation) are shown in Table7. The results of cohesion predicted by the model and the experimental results are shown in Figure 11. According to Wu, the root direction parameter is 1.2. As shown in Figure 11, the model prediction is in good agreement with the experimental results. Figure 11(a) shows the experimental results of cohesion of soil with roots at different depths, and Figure 11(b) shows the model prediction results. An acceptable agreement between the experimental and predicted values can be observed. These results verify that the mechanical effect of root system on soil reinforcement is a function of growth period and soil depth, and the proposed digital model can predict the experimental trend.Table 7
Root parameters.
Diameter (cm)Elasticity modulus (kN/m2·mm-1)Length (cm)Shear thickness (cm)L1 (cm)L2 (cm)Δd (cm)Mobile length (cm)Tensile strength (kN/m2)Mean soil depth (cm)0.3100001727.67.61.40.93100002.90.21100001426.36.31.40.93100002.60.12100001024.64.61.40.23100002.00.3410000922.52.51.40.23100004.40.23100001528.68.61.40.93100002.10.621000015212.312.41.40.931000042.60.52100001529.69.61.40.23100002.00.3100001522.52.51.40.23100002.40.21100001529.69.61.40.23100002.00.34100001522.52.51.40.23100002.4Figure 11
Cohesion of root-bearing soil at different growth periods and different depths: (a) test value; (b) predicted value.
(a)(b)


## 4.2.1. Theoretical Analysis

Vegetation can protect the slope from shallow landslides, mainly because the underground root system strengthens the surface soil. When the coal-bearing soil slope has frequent rainfall in the south of the Yangtze River in summer, on the one hand, the erosion chain formed under the erosive force of the rainfall will bring the soil particles down the slope; on the other hand, the permeable layer will be formed after the water infiltrates, reducing the soil resistance. The shear strength affects the stability of the shallow soil of the slope. This section combines the basic theory of unsaturated soils, establishes a mathematical formula to explain the root failure mechanism and analyses the reinforcement mechanism of roots on unsaturated soils.The formula for the shear strengthτf of unsaturated soil is
(1)τf=c′+σ−uatanϕ′+ua−uwtanϕ′θ−θrθs−θr,where c′ and ϕ′ are the effective cohesion and the effective angle of internal friction of soil mass, respectively; σ−ua is the net stress of unsaturated soil; ua−uw is the matric suction; θ, θr, and θs are the current, residual, and saturated moisture contents of the soil, respectively.The cohesionc′ of the root-soil is mainly composed of two parts: (1) the effective cohesion cs′ of the soil; (2) the cohesion Δcr′ induced by the root system, namely,
(2)c′=cs′+Δcr′.According to the improvement of the Wu model by Preti and Schwarz [42], the root-induced cohesion Δcr′ is
(3)Δcr′=0.4⋅RAR⋅TNδ,where RAR is the root area ratio, TN is the maximum tensile stress caused by the root, and δ is a parameter related to the root direction, which can be expressed as
(4)δ=cosαi+sinαitanϕ′,where αi is the angle of the first deforming root to the horizontal plane.The model is extended to estimate the contribution of plant roots to the cohesive force increaseΔcr′ under a certain displacement, by considering the root failure mode observed in the triaxial test which is the cohesive force Δcr′ produced by elongated roots.According to Figure10(a), the vertical slip length ΔL of the root is
(5)ΔL=L2‐L‐L1‐Δd2+Δt2,whereL1 is the root which has no vertical length of horizontal movement and L2 is the vertical length of the horizontal movement of the root.Figure 10
Schematic diagram of root stress and deformation: (a) vertical root deformation; (b) inclined root deformation.
(a)(b)It can be seen from Figure10(b) that the inclination angle α2 between the deformed root and the horizontal is
(6)tanα2=ΔtΔt/tanβ+Δd,where Δd is the shear displacement, Δt is the shear length of the root, and β is the angle of the shear segment of the root deformation.The elongation of the rootsω is
(7)ω=L2‐L‐L1‐Δd2+Δt2L.The energy generated by the root elongation is(8)E=12Tiω=12ke2,where k is the elastic modulus of the root and e is the root elongation.Tensile stress generated by thei tensile root is
(9)Ti=kL2sinα2+L−L1sinα2‐Δttanα2+Δd2+Δt2.The cohesionΔcr produced by root elongation is
(10)Δcr=0.4⋅∑i=0m1RARi⋅Ti⋅cosαi+sinαitanϕ′,wherem1 is the number of severed roots in the roots.
(11)τf=0.4⋅∑i=0m1RARi⋅Ti⋅cosαi+sinαitanϕ′+σ−uatanϕ′+ua−uwtanϕ′θ−θrθs−θr.


## 4.2.2. The Example Analysis

According to root damage in the direct shear test, root parameters (such as root geometry, tensile strength, Young’s modulus, and root orientation) are shown in Table7. The results of cohesion predicted by the model and the experimental results are shown in Figure 11. According to Wu, the root direction parameter is 1.2. As shown in Figure 11, the model prediction is in good agreement with the experimental results. Figure 11(a) shows the experimental results of cohesion of soil with roots at different depths, and Figure 11(b) shows the model prediction results. An acceptable agreement between the experimental and predicted values can be observed. These results verify that the mechanical effect of root system on soil reinforcement is a function of growth period and soil depth, and the proposed digital model can predict the experimental trend.Table 7
Root parameters.
Diameter (cm)Elasticity modulus (kN/m2·mm-1)Length (cm)Shear thickness (cm)L1 (cm)L2 (cm)Δd (cm)Mobile length (cm)Tensile strength (kN/m2)Mean soil depth (cm)0.3100001727.67.61.40.93100002.90.21100001426.36.31.40.93100002.60.12100001024.64.61.40.23100002.00.3410000922.52.51.40.23100004.40.23100001528.68.61.40.93100002.10.621000015212.312.41.40.931000042.60.52100001529.69.61.40.23100002.00.3100001522.52.51.40.23100002.40.21100001529.69.61.40.23100002.00.34100001522.52.51.40.23100002.4Figure 11
Cohesion of root-bearing soil at different growth periods and different depths: (a) test value; (b) predicted value.
(a)(b)


## 5. Conclusions

(1)
D-W cycles had a significant effect on cohesion and internal friction angle (P<0.05). With the number of D-W cycles increasing, the cohesive decreases; the internal friction angle is just the opposite(2)
The water content had a small effect on the internal friction angle but had a large effect on the cohesion. When the water content was less than 10%, the cohesion could be improved(3)
The factor levels of the large cohesive stage were as follows: the water content was 10%, VR content was 2%, dry density was 1.50 g/cm3, and the number of D-W cycles was less than one(4)
Coal-bearing soils have many clay minerals and react violently with water. With the increase of D-W cycles, the links between mineral particles have a stable layered structure with unsteadiness chain structure(5)
The digital model of soil reinforcement by VR was established to quantify the enhancement effect of VR on the cohesion and shear strength of coal-bearing soils



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*Source: 6657160-2021-10-21.xml*