# Evaluation of the Reinforcement Performance of Loess Slopes Affected by Rainfall Infiltration

Authors: Yongdong Yang; Hai Liu; Hongfei Li; Shengrui Su; Wanfeng Liu; Yunxiu Dong; Dong Wang
Journal: Geofluids
 (2022)

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## Abstract

The instability disaster of slope engineering is the third largest geological disaster after earthquake and debris flow, and rainfall is an important factor affecting the stability of slopes. In this study, the stability of a loess slope affected by rainfall infiltration was investigated using engineering examples, an in-depth site investigation, geotechnical physical and mechanical tests, and numerical simulations. The finite element software ABAQUS was used to establish a model of the rainfall infiltration slope to analyze the slope stability after rainfall infiltration while considering the influence of the groundwater level on slope stability and evaluated the reinforcement performance of retaining wall and biological measures on loess slope under rainfall conditions. The results showed that the displacement and pore pressure at the bottom of the slope increased after a strong rainfall. The rapid rise of the water level caused increases in the displacement and pore pressure of the slope, but the slope stability improved when the water table reached 0.8 m. Further analysis shows that under the joint action of rainfall and groundwater, the slope stability can be effectively improved by using retaining wall to strengthen the slope. Under the action of rainfall, the increase of vegetation depth and density has a certain effect on the improvement of slope stability. The ryegrass and alfalfa were the most effective slope stabilization approach if the vegetation parameters and economic factors were considered.


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## Body

## 1. Introduction

Landslide hazard is a common natural disaster and destructive, which not only threats human life and safety, but also property, environment, resources, [1]. Statistics show that most slope instability is directly caused by rainfall, such as shallow soil landslide in Nanjiang county and accumulation landslide in Dashuchang town of the Three Gorges [2–4]. A prerequisite for the accurate calculation of slope stability is an understanding of changes in the water content of slopes affected by rainfall infiltration or changes in the groundwater table [5]. In this field, many researchers have carried out a lot of studies from different directions and obtained many useful conclusions. Yuan et al. pointed out that the displacement field is helpful to evaluate the range and degree of soil disturbance on the slope [6]. Shi et al. considered that the increase of pore water pressure in soil caused by rainfall is an important reason for slope instability [7]. Sugiyama et al. studied the slope instability along the railway and concluded that the influence of rainfall on shallow landslide is more significant [8]. Many researchers study this kind of influence through numerical analysis. Tian et al. modified the rainfall infiltration boundary based on Richard equation and realized the simplified numerical simulation method of rainfall infiltration considering runoff recharge [9]. Yuan et al. developed an improved three-dimensional displacement measurement system based on MATLAB software [10]. Based on the Green-Ampt model, Wang et al. deduced a rainfall infiltration function of landslide, which more ideally described the expansion process of wetting front [11]. Cuomo Della Sala simulated the seepage of soil with different soil water characteristic curves and obtained the soil water characteristic curve, which will have a significant impact on the seepage process inside the slope [12]. The rise of groundwater is harmful to the soil slope [13]. When the groundwater level rises and the slope has high water content, the slope volume increases, the effective stress or slip resistance of the slip surface decreases, and the shear strength of the slip zone is reduced. Gao and Yin indicated that when the water level drops abruptly, the seepage of water causes a change in the weight and stress of the soil, resulting in a dynamic hydraulic force on the soil particles. At the same time, the damage to the slope of the roadbed is intensified due to the erosion at the toe of the slope by the water flow [14]. Yan et al. evaluated the effectiveness of the drainage tunnel system on the Donglingxing landslide based on field measurement data with groundwater level, water discharge, and deformation of the landslide before and after construction of the drainage tunnel [15]. Wang et al. used vector autoregressive model to establish and judged the relationship between groundwater level and slope surface displacement and the lag time of slope displacement relative to groundwater level change [16].Slope protection and reinforcement are essential aspects of slope design. The two traditional measures for slope reinforcement in engineering include reducing load and reinforcement measures (such as retaining wall reinforcement, anchor bolt reinforcement, and stabilizing pile reinforcement). The main purpose of reinforcement is to improve the stability of slope, increase its bearing capacity, and reduce deformation [17]. However, the soil abandonment after cutting slope poses a serious threat to the ecological environment, and it is expensive in terms of human, material, and financial resources. Therefore, it is crucial to investigate protection and stabilization measures for soil slopes to improve slope drainage and reinforcement. Slope ecoengineering has become a common method of slope protection due to its high stability, low cost, and the ability to restore the ecological environment of road areas, which has attracted extensive attention of researchers. The results were in agreement with the presence of root systems that can mechanically reinforce soil slope. The mechanical properties of root-soil composites are studied based on root tensile test and shear strength test [18–20]. With the improvement of computer performance, many scholars have begun to use finite element software to analyze actual engineering problems. The effect of ecological slope protection mode was analyzed by 2D or 3D finite element [21, 22]. For different slope types, factors such as climate, sunshine, water and air conditions, soil, and nutrient conditions of the slope will affect the selection of vegetation types and also affect the final function and effect of vegetation soil-fixing and slope protection. Therefore, it is necessary to establish a method of vegetation protection for loess slopes.To the authors’ best of knowledge, most researchers consider the impact of rainfall and groundwater level change on slope deformation characteristics, but there are few studies on the impact of groundwater level change and rainfall coupling action on slope deformation and failure characteristics and its impact on slope reinforcement performance. At present, there are two main viewpoints in numerical simulation to reveal the change mechanism of mechanical properties of the root-soil composite, which are the principle of pseudocohesion and the principle of frictional reinforcement. We use the principle of pseudocohesion to consider the effect of root-soil composite on slope reinforcement. In this study, the rainfall infiltration model of the loess slope was established using the finite element software ABAQUS. By comparing the variation laws of pore water pressure and displacement of the slope reference point under uniform rainfall and nonuniform rainfall, the influence of rainfall types on slope stability is studied. The influence of groundwater level change and rainfall coupling effect on slope displacement and pore pressure is further analyzed. Finally, the effects of retaining wall and vegetation protection measures on loess slope stability under rainfall conditions are discussed.


## 2. Materials and Methods

### 2.1. Loess Unstable Slope

The unstable slope is located in the south section of the northwest landslide area of Huachi County, Qingyang City, Gansu Province, China, the slope zone on the left bank of Rouyuan River and the west side of vocational high school in Huachi County. The top of the slope is a village road, and the foot of the slope is the planned land of vocational high school in Huachi County. It is 34 m long in the north-south direction, about 20 m wide in the east-west direction, with a height difference of 4.5 m. The slope gradient is 70-80° (see Figure1). The annual precipitation is 563.0 mm, and the precipitation occurs mainly during the period from July to September and occupies 71. 8% of the annual precipitation. The loess physical and mechanical parameter values of each layer are listed (see Table 1).Figure 1
The unstable slope.Table 1
Soil parameter values of the slope.
Soil layer
Water content at saturation
Saturated permeability coefficient (10-6 m/s)
Unit weight (kN/m3)
Cohesion force (kPa)
Internal friction angel(o)
φ
b
Malan loess
0.52
5.2
13.1
17.6
21.3
10.0
Lishi loess
0.53
5.6
14.9
18.7
25.4
11.4
Wucheng loess
0.56
5.7
14.2
40.3
25.2
12.3


### 2.2. Methods

ABAQUS software (version 6.14.3) was used for the calculations in this study. It was assumed that the soil was a porous medium with uniformly distributed pores in the solid. The nodal degrees of freedom were used to determine the nodal displacement and pore water pressure. Moreover, the unsaturated loess slope stability affected by rainfall infiltration and groundwater level changes was carried out using the Mohr-Coulomb damage criterion. The numerical model of the slope affected by rainfall infiltration was established in the finite element software ABAQUS (see Figure2). We used three monitoring cells: A (bottom of slope), B (middle of slope), and C (top of slope). The model without and with the retaining walls was divided into 19630 and 15300 grid cells, respectively, using C3D8RP (three-dimensional solid 8-node hexahedral reduced integral solid element) pore pressure cells. The rainfall data were obtained from the hydrological and meteorological station data, and we investigated the effects of uniform rainfall and nonuniform rainfall (real rainfall conditions) with a total rainfall of 0.2 m and rainfall time of 24 h (see Figure 3). The left axis represents the rainfall intensity of ununiform rainfall, and the right axis represents the rainfall intensity of uniform rainfall.Figure 2
Finite element model of the original slope.Figure 3
The uniform and nonuniform rainfall patterns analyzed in this study.The rainfall boundary function was expressed in terms of the rainfall intensity, i.e., the unit circulation q (m/s), and we ignored the surface water accumulation caused by rainfall. The rainfall was not confined to a specific part of the slope but affected the entire slope; thus, the rainfall infiltration analysis was performed on the entire slope.


### 2.3. Theory of Slope Rainfall Infiltration and Numerical Calculations

The Biot theory described the flow of a single fluid in saturated linear elastic (or viscoelastic) porous medium, and it had great limitations when it was applied to unsaturated soils. The fluid involved in unsaturated soil generally contained fluid and gas, and the deformation of solids was not necessarily to be linear elastic, but it was nonlinear. Besides, Fredlund and Hasen proposed a one-dimensional consolidation theory for unsaturated soils [23]. Moreover, a three-dimensional (3D) consolidation equation for unsaturated soils with five variables was developed by Fredlund and Xing [24]. Since then, many scholars have carried out research on unsaturated seepage and consolidation theory.


#### 2.3.1. Principle of Unsaturated Soil Seepage

Rainfall infiltration can be considered a process in which unsaturated soil is changed to saturated soil. The model of unsaturated soil is based on Darcy’s law, which is expressed as(1)∂∂xkijskrhc∂hc∂xi+ki3krhc+Q=Chc+θnSs∂hc∂t,where kijs is the saturation coefficient of permeability in different directions (m/s); kr is the relative permeability; hc is the pressure head (m); Chc is the water capacity; ss is the unit storage volume (m3); and n is the porosity.


#### 2.3.2. Shear Strength of Unsaturated Soils

Based on the Mohr-coulomb strength criterion, Fredlund and Xing proposed the following expression for the shear strength of unsaturated soils as [24]
(2)τf=c′+σm−uatanφ′+ua−uwtanφb,where c′ and φ′ are the effective cohesion and angle of internal friction, respectively; σm is the normal stress; and ua−uw is the matrix suction. The relationship between φb and the volumetric moisture content was proposed by Vanapalli and Fredlund and is expressed as [25]
(3)tanφb=θ−θrθs−θrtanφ,′where θ is the volumetric water content; θs is the saturated volumetric water content; and θr is the residual water content.


#### 2.3.3. Soil Water Characteristic Curves and Hydraulic Permeability Coefficients

The hydraulic infiltration coefficient is generally a constant in saturated soils but is related to the matric suction or the volumetric water content in unsaturated soils. The relationship between the infiltration coefficient and the matric suction in this analysis is defined by Equation (4), which describes the water infiltration coefficient in the soil [26]:
(4)kw=awkwsaw+bw·ua−uwcw,where kw is the infiltration coefficient; aw,bw,cw are parameters determined from the literature; kws is the infiltration coefficient of saturated soil; and ua−uw are the pore air and pore water pressures, respectively. It is also required to define the soil-water characteristic curve. The relationship between soil saturation and matric suction is calculated using [26]
(5)Sr=Si+Sn−Siasas+bsua−uwcs,where Sr is the saturability; Si is the residual saturability; sn is the maximum saturability; and as,bs,cs are parameters determined from the literature.The characteristic curves of the hydraulic infiltration coefficient and the soil-water characteristic curves are shown, respectively (see Figures4 and 5) [27].Figure 4
Characteristic curves of the hydraulic infiltration coefficient.Figure 5
Soil-water characteristic curve.


## 2.1. Loess Unstable Slope

The unstable slope is located in the south section of the northwest landslide area of Huachi County, Qingyang City, Gansu Province, China, the slope zone on the left bank of Rouyuan River and the west side of vocational high school in Huachi County. The top of the slope is a village road, and the foot of the slope is the planned land of vocational high school in Huachi County. It is 34 m long in the north-south direction, about 20 m wide in the east-west direction, with a height difference of 4.5 m. The slope gradient is 70-80° (see Figure1). The annual precipitation is 563.0 mm, and the precipitation occurs mainly during the period from July to September and occupies 71. 8% of the annual precipitation. The loess physical and mechanical parameter values of each layer are listed (see Table 1).Figure 1
The unstable slope.Table 1
Soil parameter values of the slope.
Soil layer
Water content at saturation
Saturated permeability coefficient (10-6 m/s)
Unit weight (kN/m3)
Cohesion force (kPa)
Internal friction angel(o)
φ
b
Malan loess
0.52
5.2
13.1
17.6
21.3
10.0
Lishi loess
0.53
5.6
14.9
18.7
25.4
11.4
Wucheng loess
0.56
5.7
14.2
40.3
25.2
12.3


## 2.2. Methods

ABAQUS software (version 6.14.3) was used for the calculations in this study. It was assumed that the soil was a porous medium with uniformly distributed pores in the solid. The nodal degrees of freedom were used to determine the nodal displacement and pore water pressure. Moreover, the unsaturated loess slope stability affected by rainfall infiltration and groundwater level changes was carried out using the Mohr-Coulomb damage criterion. The numerical model of the slope affected by rainfall infiltration was established in the finite element software ABAQUS (see Figure2). We used three monitoring cells: A (bottom of slope), B (middle of slope), and C (top of slope). The model without and with the retaining walls was divided into 19630 and 15300 grid cells, respectively, using C3D8RP (three-dimensional solid 8-node hexahedral reduced integral solid element) pore pressure cells. The rainfall data were obtained from the hydrological and meteorological station data, and we investigated the effects of uniform rainfall and nonuniform rainfall (real rainfall conditions) with a total rainfall of 0.2 m and rainfall time of 24 h (see Figure 3). The left axis represents the rainfall intensity of ununiform rainfall, and the right axis represents the rainfall intensity of uniform rainfall.Figure 2
Finite element model of the original slope.Figure 3
The uniform and nonuniform rainfall patterns analyzed in this study.The rainfall boundary function was expressed in terms of the rainfall intensity, i.e., the unit circulation q (m/s), and we ignored the surface water accumulation caused by rainfall. The rainfall was not confined to a specific part of the slope but affected the entire slope; thus, the rainfall infiltration analysis was performed on the entire slope.


## 2.3. Theory of Slope Rainfall Infiltration and Numerical Calculations

The Biot theory described the flow of a single fluid in saturated linear elastic (or viscoelastic) porous medium, and it had great limitations when it was applied to unsaturated soils. The fluid involved in unsaturated soil generally contained fluid and gas, and the deformation of solids was not necessarily to be linear elastic, but it was nonlinear. Besides, Fredlund and Hasen proposed a one-dimensional consolidation theory for unsaturated soils [23]. Moreover, a three-dimensional (3D) consolidation equation for unsaturated soils with five variables was developed by Fredlund and Xing [24]. Since then, many scholars have carried out research on unsaturated seepage and consolidation theory.


### 2.3.1. Principle of Unsaturated Soil Seepage

Rainfall infiltration can be considered a process in which unsaturated soil is changed to saturated soil. The model of unsaturated soil is based on Darcy’s law, which is expressed as(1)∂∂xkijskrhc∂hc∂xi+ki3krhc+Q=Chc+θnSs∂hc∂t,where kijs is the saturation coefficient of permeability in different directions (m/s); kr is the relative permeability; hc is the pressure head (m); Chc is the water capacity; ss is the unit storage volume (m3); and n is the porosity.


### 2.3.2. Shear Strength of Unsaturated Soils

Based on the Mohr-coulomb strength criterion, Fredlund and Xing proposed the following expression for the shear strength of unsaturated soils as [24]
(2)τf=c′+σm−uatanφ′+ua−uwtanφb,where c′ and φ′ are the effective cohesion and angle of internal friction, respectively; σm is the normal stress; and ua−uw is the matrix suction. The relationship between φb and the volumetric moisture content was proposed by Vanapalli and Fredlund and is expressed as [25]
(3)tanφb=θ−θrθs−θrtanφ,′where θ is the volumetric water content; θs is the saturated volumetric water content; and θr is the residual water content.


### 2.3.3. Soil Water Characteristic Curves and Hydraulic Permeability Coefficients

The hydraulic infiltration coefficient is generally a constant in saturated soils but is related to the matric suction or the volumetric water content in unsaturated soils. The relationship between the infiltration coefficient and the matric suction in this analysis is defined by Equation (4), which describes the water infiltration coefficient in the soil [26]:
(4)kw=awkwsaw+bw·ua−uwcw,where kw is the infiltration coefficient; aw,bw,cw are parameters determined from the literature; kws is the infiltration coefficient of saturated soil; and ua−uw are the pore air and pore water pressures, respectively. It is also required to define the soil-water characteristic curve. The relationship between soil saturation and matric suction is calculated using [26]
(5)Sr=Si+Sn−Siasas+bsua−uwcs,where Sr is the saturability; Si is the residual saturability; sn is the maximum saturability; and as,bs,cs are parameters determined from the literature.The characteristic curves of the hydraulic infiltration coefficient and the soil-water characteristic curves are shown, respectively (see Figures4 and 5) [27].Figure 4
Characteristic curves of the hydraulic infiltration coefficient.Figure 5
Soil-water characteristic curve.


## 2.3.1. Principle of Unsaturated Soil Seepage

Rainfall infiltration can be considered a process in which unsaturated soil is changed to saturated soil. The model of unsaturated soil is based on Darcy’s law, which is expressed as(1)∂∂xkijskrhc∂hc∂xi+ki3krhc+Q=Chc+θnSs∂hc∂t,where kijs is the saturation coefficient of permeability in different directions (m/s); kr is the relative permeability; hc is the pressure head (m); Chc is the water capacity; ss is the unit storage volume (m3); and n is the porosity.


## 2.3.2. Shear Strength of Unsaturated Soils

Based on the Mohr-coulomb strength criterion, Fredlund and Xing proposed the following expression for the shear strength of unsaturated soils as [24]
(2)τf=c′+σm−uatanφ′+ua−uwtanφb,where c′ and φ′ are the effective cohesion and angle of internal friction, respectively; σm is the normal stress; and ua−uw is the matrix suction. The relationship between φb and the volumetric moisture content was proposed by Vanapalli and Fredlund and is expressed as [25]
(3)tanφb=θ−θrθs−θrtanφ,′where θ is the volumetric water content; θs is the saturated volumetric water content; and θr is the residual water content.


## 2.3.3. Soil Water Characteristic Curves and Hydraulic Permeability Coefficients

The hydraulic infiltration coefficient is generally a constant in saturated soils but is related to the matric suction or the volumetric water content in unsaturated soils. The relationship between the infiltration coefficient and the matric suction in this analysis is defined by Equation (4), which describes the water infiltration coefficient in the soil [26]:
(4)kw=awkwsaw+bw·ua−uwcw,where kw is the infiltration coefficient; aw,bw,cw are parameters determined from the literature; kws is the infiltration coefficient of saturated soil; and ua−uw are the pore air and pore water pressures, respectively. It is also required to define the soil-water characteristic curve. The relationship between soil saturation and matric suction is calculated using [26]
(5)Sr=Si+Sn−Siasas+bsua−uwcs,where Sr is the saturability; Si is the residual saturability; sn is the maximum saturability; and as,bs,cs are parameters determined from the literature.The characteristic curves of the hydraulic infiltration coefficient and the soil-water characteristic curves are shown, respectively (see Figures4 and 5) [27].Figure 4
Characteristic curves of the hydraulic infiltration coefficient.Figure 5
Soil-water characteristic curve.


## 3. Results and Discussion

### 3.1. Effect of Retaining Walls on the Stability of Loess Slopes under Different Rainfall Conditions

The displacement of slopes due to rainfall occurs because rainfall infiltration increases the water content of the soil in the unsaturated zone of the slope and decreases the matric suction, causing strain on the unsaturated soil of the slope.The horizontal displacements of the reference points during and after the rainfall with uniform rainfall and nonuniform rainfall are shown (see Figure6). The maximum value during rainfall process and final value after rainfall process of horizontal displacement of slope reference point are equal. The horizontal displacements of the reference points are larger for uniform rainfall than for nonuniform rainfall. Compared with nonuniform rainfall, under the condition of uniform rainfall, the horizontal displacement of the reference points A, B, and C increase 37.5%, 26.7%, and 43.3%, respectively. The maximum horizontal displacement of the slope occurs at the bottom of the slope (reference point A), followed by the middle of the slope (reference point B) and the top of the slope (reference point C).Figure 6
Horizontal displacement of reference points.The maximum pore water pressure at the reference points during and after the rainfall with different rainfall patterns is shown (see Figure7). The maximum pore pressure at the middle and bottom of the slope caused by uniform rainfall pattern is greater than that caused by nonuniform rainfall. The pore water pressure during rainfall process is greater than the values of after rainfall process because of the pore pressure dissipation. The maximum pore pressure at the middle and top of the slope caused by uniform rainfall pattern is less than that caused by nonuniform rainfall, while the maximum pore pressure at the bottom of the slope is greater than that caused by nonuniform rainfall. The maximum pore pressure always occurs at the bottom of the slope (reference point A), followed by the middle of the slope (reference point B) and the top of the slope (reference point C).Figure 7
Pore water pressure of reference points.


### 3.2. Analysis of the Effect of the Groundwater Level on Slope Stability

#### 3.2.1. The Effect on Horizontal Displacement

The horizontal displacement of the slope reference points decreases as the groundwater level increases from 0.2 m to 0.8 m (see Figure8). When the water level increases from 0.2 m to 0.6 m, the horizontal displacement of the slope reference point decreases. And when the groundwater level increases from 0.6 m to 0.8 m, the horizontal displacement of the slope reference point increases. When the water level increases from 0.2 m to 0.6 m, the maximum horizontal displacement of slope reference points A, B, and C decreases by 5.6%, 6.1%, and 5.9%, respectively, and the final horizontal displacement of slope reference points A, B, and C increases by 17.9%, 46.4%, and 24.2%, respectively. When the groundwater level increases from 0.6 m to 0.8 m, the maximum horizontal displacement of slope reference points A, B, and C increases by 161.8%, respectively, 169.6% and 123.7%, and the final horizontal displacement values of slope reference points A, B, and C increased by 125.8%, 87.8%, and 107.3%, respectively. Moreover, the horizontal displacement of the slope bottom (reference point A) is the largest, the slope top is the second (reference point C), and the middle of the slope is the smallest (reference point B). The horizontal displacement is the largest at the bottom of the slope (reference point A), followed by that at the top of the slope (reference point C) and that in the middle of the slope (reference point B).Figure 8
Displacement of slope reference points A, B, and C after the end of rainfall.


#### 3.2.2. The Effect on Pore Water Pressure

The pore water pressure of the slope reference points decreases as the groundwater level increases from 0.2 m to 0.8 m with nonuniform rainfall (see Figure9). From the curves, the maximum values of the pore water pressure at slope reference points decrease when the water level increases from 0.2 m to 0.6 m. However, as the water level increases to 0.8 m, the pore water pressure increases rapidly. Moreover, the pore pressure at the bottom of the slope (reference point A) is the largest, followed by the middle of the slope (reference point B), and the top of the slope (reference point C) is the smallest. When the water level increases from 0.2 m to 0.6 m, the maximum pore pressure of slope reference points A, B, and C decreases by 14.3%, 6.8%, and 8.5%, respectively, and the final pore pressure of slope reference points A, B, and C decreases by 8.8%, 19.9%, and 3.6%, respectively. When the groundwater level increases from 0.6 m to 0.8 m, the maximum pore pressure of slope reference points A, B, and C increases by 226.5%, 300.9%, and 16.2%, respectively, and the final values of pore water pressure at slope reference points A, B and C increased by 48.6%, 56.4%, and 42.0%, respectively.Figure 9
The maximum pore water pressure at slope reference points A, B, and C.


### 3.3. Influence of Retaining Wall on Slope Protection

The influence of retaining wall on slope stability is studied based on ABAQUS finite element analysis method. The soil parameter values of each layer are listed in Table1. A numerical model of the slope affected by rainfall infiltration and retaining wall was established in the finite element software ABAQUS (see Figure 10).Figure 10
Numerical model of slope with retaining wall.


#### 3.3.1. Influence of Retaining Wall on Slope under Different Rainfall Conditions

The horizontal displacement of the slope reference points with retaining wall under uniform rainfall and nonuniform rainfall is shown (see Figure11). For the slope reference points A, B, and C, the maximum horizontal displacements are 23.1%, 28.9%, and 55.0% lower, respectively, for slopes with than without a retaining wall under nonuniform rainfall. And the corresponding values after the end of the rainfall are 26.9%, 63.2%, and 70.0%, respectively. During uniform rainfall, the maximum and final values of the horizontal displacements of the slope reference points are equal, and the maximum horizontal displacements of the slope reference points are smaller with than without a retaining wall. For slope reference points A, B, and C, the maximum horizontal displacements are 32.4%, 58.2%, and 68.8% lower, respectively, for slopes with than without a retaining wall.Figure 11
The horizontal displacement of the slope reference points with retaining wall under rainfall.The pore water pressure of the slope reference points with retaining wall under uniform rainfall and nonuniform rainfall is shown (see Figure12). During nonuniform rainfall, the maximum values of the pore pressure at the slope reference points are lower on the slope with than without a retaining wall. For slope reference points A, B, and C, the maximum pore pressure values are reduced by 23.1%, 28.9%, and 55.0%, respectively. The corresponding values of the pore pressure after the end of the rainfall are 26.9%, 63.2%, and 70.0%, respectively. During uniform rainfall, the maximum and final values of the pore pressure at the slope reference points are equal, and the maximum values of the pore pressure at the slope reference points are lower for the slope with than without reinforcement. For slope reference points A, B, and C, the maximum pore pressure values are 32.4%, 58.2%, and 68.8% lower, respectively.Figure 12
The pore water pressure of the slope reference points with retaining wall under rainfall.When uniform rainfall type rainfall is applied, the rainfall intensity is greater than the rainfall dissipation rate of the soil, so the pore pressure and displacement of the slope reaches its maximum at the end of the rainfall. However, when an uneven rainfall type rainfall is applied, after the rainfall intensity reaches its maximum intensity in the nonuniform of the rainfall, the rainfall intensity in the later part of the rainfall is less than the rainwater dissipation rate of the soil, so the displacement and pore pressure are smaller than the values during the rainfall after the end of the rainfall. It can be seen that retaining walls can effectively reduce the displacement and pore water pressure of the slope and improve the stability of the slope.


#### 3.3.2. Influence of Retaining Wall on Slope under Different Rainfall Conditions and Groundwater Level

The horizontal displacement of the slope reference points with retaining wall under different groundwater level and nonuniform rainfall is shown (see Figure13). When the groundwater levels increase from 0.2 m to 0.6 m, regardless of whether the slope is reinforced by a retaining wall, the values become lower. However, as the groundwater level increases from 0.6 m to 0.8 m, the horizontal displacement of the slope reference points increases significantly. The horizontal displacement is the largest at the bottom of the slope (reference point A), followed by that at the top of the slope (reference point C) and that in the middle of the slope (reference point B).Figure 13
The horizontal displacement at slope reference points A, B, and C with retaining wall.The pore water pressure of the slope reference points with retaining wall under different groundwater level and nonuniform rainfall is shown (see Figure14). The maximum values of the pore water pressure at slope reference points decrease when the water level increases from 0.2 m to 0.6 m. However, as the water level increases to 0.8 m, the pore water pressure increases rapidly. With the water level increases from 0.2 m to 0.6 m with retaining wall, the maximum pore water pressure decreases by 6.0%, 3.3%, and 3.9%, respectively. And when the water level increases from 0.6 m to 0.8 m with retaining wall, the maximum pore water pressure increases by 223.7%, 264.4%, and 243.4%. As the water level increases from 0.2 m to 0.4 m, the reduction in the final value of the pore water pressure of the slope reference points A, B, and C is about 17.0%, 30.0, and 5%. When the water level increases from 0.4 m to 0.8 m, the reduction in the final value is about 8.0%, 15.0%, and 11%.Figure 14
The pore water pressure at slope reference points A,B, and C with retaining wall.When the groundwater level rises from 0.2 m to 0.6 m, the floating weight of the slope increases and the overall slip resistance of the slope increases, so the increase in displacement and pore pressure of the slope under the rainfall action is relatively small. When the groundwater level increases further, the floating weight of the slope increases, and at the same time, the saturation and sliding force of the slope both increase further, so the displacement and pore pressure of the slope increase relatively large. It can be seen that when the groundwater level rises, especially to higher levels, the retaining wall can effectively reduce the displacement and pore pressure of the slope, thus improving the stability of the slope [28].


### 3.4. Influence of Vegetation on Slope Protection

The main purpose of vegetated slope protection is the reinforcing effect of the root system of plants. Thus, this method is highly effective for soil stabilization. It enhances the cohesion of the soil and increases the overall strength of the rooted soil layer by mechanical binding of the root system, increasing resistance to soil sliding. The root system covers the shallow, loosely weathered layers of the slope, extending vertically into deeper layers and more stable rock and soil layers, acting as prestressing anchors. When the slope is covered with vegetation, a root network with a relatively high tensile strength is formed by the intertwining of the lateral roots of the plants, holding the soil together as a single unit (see Figure15).Figure 15
Vegetated slope protection.


#### 3.4.1. The Soil Parameters of the Model

The parameters of the vegetated slope are listed (see Table2). M represents the rooting depth of the vegetation. M1, M2, and M3 refer to vegetation depths of 0.2, 0.5, and 0.8 m. N represents the vegetation type. N1 refers to ryegrass and clover. N2 is ryegrass and alfalfa, and N3 is ryegrass and Caragana. D represents vegetation density. D1, D2, and D3 refer to vegetation densities of 30%, 50%, and 60%, respectively. The model is shown (see Figure 16). The influence of ecological slope protection measures on slope stability under nonuniform rainfall is analyzed in this paper.Table 2
Parameters of the vegetated slope.
Rooting depth (M)/vegetation type (N)/vegetation density (D)
Saturated permeability coefficient (10-6 m/s)
Cohesion force (kPa)
Internal friction angle (°)
M1
0.08
51.0
23.3
M2
0.05
70.8
19.2
M3
0.02
71.8
24.9
N1
0.07
56.8
25.4
N2
0.05
70.8
19.2
N3
0.03
68.6
26.2
D1
0.07
52.3
21.7
D2
0.06
53.2
27.5
D3
0.06
58.1
24.1Figure 16
Schematic diagram of the vegetation rooting depth on the slope.


#### 3.4.2. Effect of Vegetation Rooting Depth on Slope Stability

In order to analyze and compare the influence of vegetation depth on slope stability, three different depths of 0.2 m, 0.5 m, and 0.8 m were selected. At the same time, when the vegetation depth increases, the economic consumption also increases. The influence of vegetation depth on slope stability is evaluated according to the comprehensive economic cost performance of slope vegetation.The effect on slope stability is analyzed at vegetation rooting depths of 0.2 m, 0.5 m, and 0.8 m (see Figure17). With the rooting depth increases, the horizontal displacement of the slope reference point decreases. As the rooting depth increases from 0.2 m to 0.5 m, the maximum values of horizontal displacement at reference points A, B, and C decrease by 0.05 m, 0.04 m, and 0.05 m, respectively. And as the rooting depth increases from 0.5 m to 0.8 m, the maximum values of horizontal displacement at reference points A, B, and C decrease by 0.02 m, 0.02 m, and 0.03 m, respectively.Figure 17
Different values of horizontal displacement at the slope reference points for different rooting depths.As the vegetation depth increases from 0.2 m to 0.5 m, the final values of horizontal displacement at reference points A, B, and C decrease by 0.02 m, 0.02 m, and 0.04 m, respectively. When the vegetation depth increases from 0.5 m to 0.8 m, the final values decrease by 0.01 m, 0.01 m, and 0.01 m, respectively. With the increase of root depth, the influence of vegetation on slope horizontal displacement decreases.When the vegetation root depth is 0.2 m, the maximum horizontal displacement of reference points A, B, and C during rainfall is reduced by 8.3%, 57.5%, and 44.4%, respectively, compared with the untreated slope. And the final values are reduced by 36.8%, 225.0%, and 160.0%.The maximum and final pore pressure values of the slope are shown (see Figure18). The pore pressure decreases as the rooting depth increases. As the rooting depth increases from 0.2 m to 0.5 m, the maximum values of the pore pressure at reference points A, B, and C decrease by 1.12 kPa, 5.62 kPa, and 4.56 kPa, respectively. When the rooting depth increases from 0.5 m to 0.8 m, the maximum values decrease by 0.87 kPa, 0.02 kPa, and 0.03 kPa, respectively.Figure 18
Different values of pore pressure at the reference points for different rooting depths.As the rooting depth increases from 0.2 m to 0.5 m, the final values of the pore pressure decrease by 1.12 kPa, 5.62 kPa, and 4.56 kPa, respectively. When the rooting depth increases from 0.5 m to 0.8 m, the final values of decrease by 0.87 kPa, 0.02 kPa, and 0.03 kPa, respectively. With the increase of root depth, the influence of vegetation on slope horizontal displacement decreases.When the vegetation root depth is 0.2 m, the pore water pressure of reference points A, B, and C during rainfall is reduced by 35.4%, 42.2%, and 42.0%, respectively, compared with the untreated slope. And the final values are reduced by 24.6%, 18.7%, and 10.9%.When the depth of vegetation roots increases, the modulus of elasticity and cohesion of the soil on the slope surface increases, the slip resistance of the slope surface increases, and permeability decreases, resulting in relatively less rainwater entering the slope. Therefore, the greater the depth of vegetation, the greater the stability of the slope. At the same time, it can be seen that when the vegetation depth is increased to a certain depth (0.5 m), the slip resistance of the soil on the slope surface is already very high and the infiltration of rainwater is very low, so that when the vegetation depth is gradually increased again, the stability of the slope does not improve significantly. This means that when vegetation is used for slope protection, the depth of vegetation should be chosen reasonably in relation to the slope, the intensity of rainfall, and the vegetation parameters.


#### 3.4.3. Influence of Vegetation Type on Slope Stability

The maximum values of the horizontal displacement at slope reference points A, B, and C decrease as the vegetation type changes from N1 to N3 (see Figure19). After the end of the rainfall, the values of slope reference points B and C decrease as the vegetation type changes from N1 to N3. However, for reference point A, its vegetation type N1 has the largest final value, followed by vegetation type N3 and vegetation type N2. In conclusion, the slope vegetation type N2 is more suitable than vegetation types N1 and N3 to reinforce this slope.Figure 19
Different values of horizontal displacement at the reference points for different vegetation types.When the vegetation types N1 is chosen, the horizontal displacement of reference points A, B, and C during rainfall is reduced by 13.0%, 62.5%, and 62.5%, respectively, compared with the untreated slope. And the final values are reduced by 44.4%, 271.4%, and 225.0%.When the vegetation type changes from N1 to N3, the maximum and final values of the pore pressure at reference points A, B, and C on the slope decrease (see Figure20). When the vegetation type N1 is chosen, the pore water pressure of reference points A, B, and C during rainfall is reduced by 45.3%, 38.0%, and 69.5%, respectively, compared with the untreated slope. And the final values are reduced by 24.6%, 18.7%, and 10.9%.Figure 20
Different values of pore pressure at the reference points for different rooting depths.


#### 3.4.4. Influence of Vegetation Density on Slope Stability

The horizontal displacement of the slope reference points decreases as the vegetation density increases (see Figure21). As the vegetation density increases from 30% to 50%, the maximum values of horizontal displacement at reference points A, B, and C decrease by 0.02 mm, 0.04 mm, and 0.05 mm, respectively; as the vegetation density increases from 50% to 60%, the maximum values decrease by 0.02 mm, 0.02 mm, and 0.03 mm, respectively.Figure 21
Different values of horizontal displacement at the reference point for different vegetation densities.As the vegetation density increases from 30% to 50%, the final values of horizontal displacement at reference points A, B, and C decrease by 0.04 mm, 0.02 mm, and 0.04 mm, respectively; as the vegetation density increases from 50% to 60%, the final values decrease by 0.02 mm, 0.01 mm, and 0.01 mm, respectively.When the vegetation density is 30%, the horizontal displacement of reference points A, B, and C during rainfall is reduced by 13.0%, 62.5%, and 62.5%, respectively, compared with the untreated slope. And the final value is reduced by 44.4%, 271.4%, and 225.0%.The pore pressure at the slope reference points decreases with the vegetation density increasing (see Figure22). As the vegetation density increases from 30% to 50%, the maximum values of the pore pressure at reference points A, B, and C decrease by 1.85 kPa, 4.89 kPa, and 1.12 kPa, respectively. The vegetation density increases from 50% to 60%, and the maximum values decrease by 2.50 kPa, 1.57 kPa, and 0.83 kPa, respectively.Figure 22
Different values of pore pressure at the reference points for different vegetation densities.As the vegetation density increases from 30% to 50%, the final values of the pore pressure decrease by 0.57 kPa, 2.34 kPa, and 1.80 kPa, respectively, the vegetation density increases from 50% to 60%, and the final values decrease by 0.87 kPa, 0.02 kPa, and 0.03 kPa, respectively.When vegetation density is 30%, the pore water pressure of reference points A, B, and C during rainfall is reduced by 45.3%, 38.0%, and 69.5%, respectively, compared with the untreated slope. And the final value is reduced by 24.6%, 18.7%, and 10.9%.When the density of vegetation increases, the modulus of elasticity and cohesion of the soil on the surface of the slope gradually increase, the slip resistance of the surface soil increases, and at the same time, the resistance of the soil to permeability also increases, so that the displacement and pore pressure of the slope decrease.


## 3.1. Effect of Retaining Walls on the Stability of Loess Slopes under Different Rainfall Conditions

The displacement of slopes due to rainfall occurs because rainfall infiltration increases the water content of the soil in the unsaturated zone of the slope and decreases the matric suction, causing strain on the unsaturated soil of the slope.The horizontal displacements of the reference points during and after the rainfall with uniform rainfall and nonuniform rainfall are shown (see Figure6). The maximum value during rainfall process and final value after rainfall process of horizontal displacement of slope reference point are equal. The horizontal displacements of the reference points are larger for uniform rainfall than for nonuniform rainfall. Compared with nonuniform rainfall, under the condition of uniform rainfall, the horizontal displacement of the reference points A, B, and C increase 37.5%, 26.7%, and 43.3%, respectively. The maximum horizontal displacement of the slope occurs at the bottom of the slope (reference point A), followed by the middle of the slope (reference point B) and the top of the slope (reference point C).Figure 6
Horizontal displacement of reference points.The maximum pore water pressure at the reference points during and after the rainfall with different rainfall patterns is shown (see Figure7). The maximum pore pressure at the middle and bottom of the slope caused by uniform rainfall pattern is greater than that caused by nonuniform rainfall. The pore water pressure during rainfall process is greater than the values of after rainfall process because of the pore pressure dissipation. The maximum pore pressure at the middle and top of the slope caused by uniform rainfall pattern is less than that caused by nonuniform rainfall, while the maximum pore pressure at the bottom of the slope is greater than that caused by nonuniform rainfall. The maximum pore pressure always occurs at the bottom of the slope (reference point A), followed by the middle of the slope (reference point B) and the top of the slope (reference point C).Figure 7
Pore water pressure of reference points.


## 3.2. Analysis of the Effect of the Groundwater Level on Slope Stability

### 3.2.1. The Effect on Horizontal Displacement

The horizontal displacement of the slope reference points decreases as the groundwater level increases from 0.2 m to 0.8 m (see Figure8). When the water level increases from 0.2 m to 0.6 m, the horizontal displacement of the slope reference point decreases. And when the groundwater level increases from 0.6 m to 0.8 m, the horizontal displacement of the slope reference point increases. When the water level increases from 0.2 m to 0.6 m, the maximum horizontal displacement of slope reference points A, B, and C decreases by 5.6%, 6.1%, and 5.9%, respectively, and the final horizontal displacement of slope reference points A, B, and C increases by 17.9%, 46.4%, and 24.2%, respectively. When the groundwater level increases from 0.6 m to 0.8 m, the maximum horizontal displacement of slope reference points A, B, and C increases by 161.8%, respectively, 169.6% and 123.7%, and the final horizontal displacement values of slope reference points A, B, and C increased by 125.8%, 87.8%, and 107.3%, respectively. Moreover, the horizontal displacement of the slope bottom (reference point A) is the largest, the slope top is the second (reference point C), and the middle of the slope is the smallest (reference point B). The horizontal displacement is the largest at the bottom of the slope (reference point A), followed by that at the top of the slope (reference point C) and that in the middle of the slope (reference point B).Figure 8
Displacement of slope reference points A, B, and C after the end of rainfall.


### 3.2.2. The Effect on Pore Water Pressure

The pore water pressure of the slope reference points decreases as the groundwater level increases from 0.2 m to 0.8 m with nonuniform rainfall (see Figure9). From the curves, the maximum values of the pore water pressure at slope reference points decrease when the water level increases from 0.2 m to 0.6 m. However, as the water level increases to 0.8 m, the pore water pressure increases rapidly. Moreover, the pore pressure at the bottom of the slope (reference point A) is the largest, followed by the middle of the slope (reference point B), and the top of the slope (reference point C) is the smallest. When the water level increases from 0.2 m to 0.6 m, the maximum pore pressure of slope reference points A, B, and C decreases by 14.3%, 6.8%, and 8.5%, respectively, and the final pore pressure of slope reference points A, B, and C decreases by 8.8%, 19.9%, and 3.6%, respectively. When the groundwater level increases from 0.6 m to 0.8 m, the maximum pore pressure of slope reference points A, B, and C increases by 226.5%, 300.9%, and 16.2%, respectively, and the final values of pore water pressure at slope reference points A, B and C increased by 48.6%, 56.4%, and 42.0%, respectively.Figure 9
The maximum pore water pressure at slope reference points A, B, and C.


## 3.2.1. The Effect on Horizontal Displacement

The horizontal displacement of the slope reference points decreases as the groundwater level increases from 0.2 m to 0.8 m (see Figure8). When the water level increases from 0.2 m to 0.6 m, the horizontal displacement of the slope reference point decreases. And when the groundwater level increases from 0.6 m to 0.8 m, the horizontal displacement of the slope reference point increases. When the water level increases from 0.2 m to 0.6 m, the maximum horizontal displacement of slope reference points A, B, and C decreases by 5.6%, 6.1%, and 5.9%, respectively, and the final horizontal displacement of slope reference points A, B, and C increases by 17.9%, 46.4%, and 24.2%, respectively. When the groundwater level increases from 0.6 m to 0.8 m, the maximum horizontal displacement of slope reference points A, B, and C increases by 161.8%, respectively, 169.6% and 123.7%, and the final horizontal displacement values of slope reference points A, B, and C increased by 125.8%, 87.8%, and 107.3%, respectively. Moreover, the horizontal displacement of the slope bottom (reference point A) is the largest, the slope top is the second (reference point C), and the middle of the slope is the smallest (reference point B). The horizontal displacement is the largest at the bottom of the slope (reference point A), followed by that at the top of the slope (reference point C) and that in the middle of the slope (reference point B).Figure 8
Displacement of slope reference points A, B, and C after the end of rainfall.


## 3.2.2. The Effect on Pore Water Pressure

The pore water pressure of the slope reference points decreases as the groundwater level increases from 0.2 m to 0.8 m with nonuniform rainfall (see Figure9). From the curves, the maximum values of the pore water pressure at slope reference points decrease when the water level increases from 0.2 m to 0.6 m. However, as the water level increases to 0.8 m, the pore water pressure increases rapidly. Moreover, the pore pressure at the bottom of the slope (reference point A) is the largest, followed by the middle of the slope (reference point B), and the top of the slope (reference point C) is the smallest. When the water level increases from 0.2 m to 0.6 m, the maximum pore pressure of slope reference points A, B, and C decreases by 14.3%, 6.8%, and 8.5%, respectively, and the final pore pressure of slope reference points A, B, and C decreases by 8.8%, 19.9%, and 3.6%, respectively. When the groundwater level increases from 0.6 m to 0.8 m, the maximum pore pressure of slope reference points A, B, and C increases by 226.5%, 300.9%, and 16.2%, respectively, and the final values of pore water pressure at slope reference points A, B and C increased by 48.6%, 56.4%, and 42.0%, respectively.Figure 9
The maximum pore water pressure at slope reference points A, B, and C.


## 3.3. Influence of Retaining Wall on Slope Protection

The influence of retaining wall on slope stability is studied based on ABAQUS finite element analysis method. The soil parameter values of each layer are listed in Table1. A numerical model of the slope affected by rainfall infiltration and retaining wall was established in the finite element software ABAQUS (see Figure 10).Figure 10
Numerical model of slope with retaining wall.


### 3.3.1. Influence of Retaining Wall on Slope under Different Rainfall Conditions

The horizontal displacement of the slope reference points with retaining wall under uniform rainfall and nonuniform rainfall is shown (see Figure11). For the slope reference points A, B, and C, the maximum horizontal displacements are 23.1%, 28.9%, and 55.0% lower, respectively, for slopes with than without a retaining wall under nonuniform rainfall. And the corresponding values after the end of the rainfall are 26.9%, 63.2%, and 70.0%, respectively. During uniform rainfall, the maximum and final values of the horizontal displacements of the slope reference points are equal, and the maximum horizontal displacements of the slope reference points are smaller with than without a retaining wall. For slope reference points A, B, and C, the maximum horizontal displacements are 32.4%, 58.2%, and 68.8% lower, respectively, for slopes with than without a retaining wall.Figure 11
The horizontal displacement of the slope reference points with retaining wall under rainfall.The pore water pressure of the slope reference points with retaining wall under uniform rainfall and nonuniform rainfall is shown (see Figure12). During nonuniform rainfall, the maximum values of the pore pressure at the slope reference points are lower on the slope with than without a retaining wall. For slope reference points A, B, and C, the maximum pore pressure values are reduced by 23.1%, 28.9%, and 55.0%, respectively. The corresponding values of the pore pressure after the end of the rainfall are 26.9%, 63.2%, and 70.0%, respectively. During uniform rainfall, the maximum and final values of the pore pressure at the slope reference points are equal, and the maximum values of the pore pressure at the slope reference points are lower for the slope with than without reinforcement. For slope reference points A, B, and C, the maximum pore pressure values are 32.4%, 58.2%, and 68.8% lower, respectively.Figure 12
The pore water pressure of the slope reference points with retaining wall under rainfall.When uniform rainfall type rainfall is applied, the rainfall intensity is greater than the rainfall dissipation rate of the soil, so the pore pressure and displacement of the slope reaches its maximum at the end of the rainfall. However, when an uneven rainfall type rainfall is applied, after the rainfall intensity reaches its maximum intensity in the nonuniform of the rainfall, the rainfall intensity in the later part of the rainfall is less than the rainwater dissipation rate of the soil, so the displacement and pore pressure are smaller than the values during the rainfall after the end of the rainfall. It can be seen that retaining walls can effectively reduce the displacement and pore water pressure of the slope and improve the stability of the slope.


### 3.3.2. Influence of Retaining Wall on Slope under Different Rainfall Conditions and Groundwater Level

The horizontal displacement of the slope reference points with retaining wall under different groundwater level and nonuniform rainfall is shown (see Figure13). When the groundwater levels increase from 0.2 m to 0.6 m, regardless of whether the slope is reinforced by a retaining wall, the values become lower. However, as the groundwater level increases from 0.6 m to 0.8 m, the horizontal displacement of the slope reference points increases significantly. The horizontal displacement is the largest at the bottom of the slope (reference point A), followed by that at the top of the slope (reference point C) and that in the middle of the slope (reference point B).Figure 13
The horizontal displacement at slope reference points A, B, and C with retaining wall.The pore water pressure of the slope reference points with retaining wall under different groundwater level and nonuniform rainfall is shown (see Figure14). The maximum values of the pore water pressure at slope reference points decrease when the water level increases from 0.2 m to 0.6 m. However, as the water level increases to 0.8 m, the pore water pressure increases rapidly. With the water level increases from 0.2 m to 0.6 m with retaining wall, the maximum pore water pressure decreases by 6.0%, 3.3%, and 3.9%, respectively. And when the water level increases from 0.6 m to 0.8 m with retaining wall, the maximum pore water pressure increases by 223.7%, 264.4%, and 243.4%. As the water level increases from 0.2 m to 0.4 m, the reduction in the final value of the pore water pressure of the slope reference points A, B, and C is about 17.0%, 30.0, and 5%. When the water level increases from 0.4 m to 0.8 m, the reduction in the final value is about 8.0%, 15.0%, and 11%.Figure 14
The pore water pressure at slope reference points A,B, and C with retaining wall.When the groundwater level rises from 0.2 m to 0.6 m, the floating weight of the slope increases and the overall slip resistance of the slope increases, so the increase in displacement and pore pressure of the slope under the rainfall action is relatively small. When the groundwater level increases further, the floating weight of the slope increases, and at the same time, the saturation and sliding force of the slope both increase further, so the displacement and pore pressure of the slope increase relatively large. It can be seen that when the groundwater level rises, especially to higher levels, the retaining wall can effectively reduce the displacement and pore pressure of the slope, thus improving the stability of the slope [28].


## 3.3.1. Influence of Retaining Wall on Slope under Different Rainfall Conditions

The horizontal displacement of the slope reference points with retaining wall under uniform rainfall and nonuniform rainfall is shown (see Figure11). For the slope reference points A, B, and C, the maximum horizontal displacements are 23.1%, 28.9%, and 55.0% lower, respectively, for slopes with than without a retaining wall under nonuniform rainfall. And the corresponding values after the end of the rainfall are 26.9%, 63.2%, and 70.0%, respectively. During uniform rainfall, the maximum and final values of the horizontal displacements of the slope reference points are equal, and the maximum horizontal displacements of the slope reference points are smaller with than without a retaining wall. For slope reference points A, B, and C, the maximum horizontal displacements are 32.4%, 58.2%, and 68.8% lower, respectively, for slopes with than without a retaining wall.Figure 11
The horizontal displacement of the slope reference points with retaining wall under rainfall.The pore water pressure of the slope reference points with retaining wall under uniform rainfall and nonuniform rainfall is shown (see Figure12). During nonuniform rainfall, the maximum values of the pore pressure at the slope reference points are lower on the slope with than without a retaining wall. For slope reference points A, B, and C, the maximum pore pressure values are reduced by 23.1%, 28.9%, and 55.0%, respectively. The corresponding values of the pore pressure after the end of the rainfall are 26.9%, 63.2%, and 70.0%, respectively. During uniform rainfall, the maximum and final values of the pore pressure at the slope reference points are equal, and the maximum values of the pore pressure at the slope reference points are lower for the slope with than without reinforcement. For slope reference points A, B, and C, the maximum pore pressure values are 32.4%, 58.2%, and 68.8% lower, respectively.Figure 12
The pore water pressure of the slope reference points with retaining wall under rainfall.When uniform rainfall type rainfall is applied, the rainfall intensity is greater than the rainfall dissipation rate of the soil, so the pore pressure and displacement of the slope reaches its maximum at the end of the rainfall. However, when an uneven rainfall type rainfall is applied, after the rainfall intensity reaches its maximum intensity in the nonuniform of the rainfall, the rainfall intensity in the later part of the rainfall is less than the rainwater dissipation rate of the soil, so the displacement and pore pressure are smaller than the values during the rainfall after the end of the rainfall. It can be seen that retaining walls can effectively reduce the displacement and pore water pressure of the slope and improve the stability of the slope.


## 3.3.2. Influence of Retaining Wall on Slope under Different Rainfall Conditions and Groundwater Level

The horizontal displacement of the slope reference points with retaining wall under different groundwater level and nonuniform rainfall is shown (see Figure13). When the groundwater levels increase from 0.2 m to 0.6 m, regardless of whether the slope is reinforced by a retaining wall, the values become lower. However, as the groundwater level increases from 0.6 m to 0.8 m, the horizontal displacement of the slope reference points increases significantly. The horizontal displacement is the largest at the bottom of the slope (reference point A), followed by that at the top of the slope (reference point C) and that in the middle of the slope (reference point B).Figure 13
The horizontal displacement at slope reference points A, B, and C with retaining wall.The pore water pressure of the slope reference points with retaining wall under different groundwater level and nonuniform rainfall is shown (see Figure14). The maximum values of the pore water pressure at slope reference points decrease when the water level increases from 0.2 m to 0.6 m. However, as the water level increases to 0.8 m, the pore water pressure increases rapidly. With the water level increases from 0.2 m to 0.6 m with retaining wall, the maximum pore water pressure decreases by 6.0%, 3.3%, and 3.9%, respectively. And when the water level increases from 0.6 m to 0.8 m with retaining wall, the maximum pore water pressure increases by 223.7%, 264.4%, and 243.4%. As the water level increases from 0.2 m to 0.4 m, the reduction in the final value of the pore water pressure of the slope reference points A, B, and C is about 17.0%, 30.0, and 5%. When the water level increases from 0.4 m to 0.8 m, the reduction in the final value is about 8.0%, 15.0%, and 11%.Figure 14
The pore water pressure at slope reference points A,B, and C with retaining wall.When the groundwater level rises from 0.2 m to 0.6 m, the floating weight of the slope increases and the overall slip resistance of the slope increases, so the increase in displacement and pore pressure of the slope under the rainfall action is relatively small. When the groundwater level increases further, the floating weight of the slope increases, and at the same time, the saturation and sliding force of the slope both increase further, so the displacement and pore pressure of the slope increase relatively large. It can be seen that when the groundwater level rises, especially to higher levels, the retaining wall can effectively reduce the displacement and pore pressure of the slope, thus improving the stability of the slope [28].


## 3.4. Influence of Vegetation on Slope Protection

The main purpose of vegetated slope protection is the reinforcing effect of the root system of plants. Thus, this method is highly effective for soil stabilization. It enhances the cohesion of the soil and increases the overall strength of the rooted soil layer by mechanical binding of the root system, increasing resistance to soil sliding. The root system covers the shallow, loosely weathered layers of the slope, extending vertically into deeper layers and more stable rock and soil layers, acting as prestressing anchors. When the slope is covered with vegetation, a root network with a relatively high tensile strength is formed by the intertwining of the lateral roots of the plants, holding the soil together as a single unit (see Figure15).Figure 15
Vegetated slope protection.


### 3.4.1. The Soil Parameters of the Model

The parameters of the vegetated slope are listed (see Table2). M represents the rooting depth of the vegetation. M1, M2, and M3 refer to vegetation depths of 0.2, 0.5, and 0.8 m. N represents the vegetation type. N1 refers to ryegrass and clover. N2 is ryegrass and alfalfa, and N3 is ryegrass and Caragana. D represents vegetation density. D1, D2, and D3 refer to vegetation densities of 30%, 50%, and 60%, respectively. The model is shown (see Figure 16). The influence of ecological slope protection measures on slope stability under nonuniform rainfall is analyzed in this paper.Table 2
Parameters of the vegetated slope.
Rooting depth (M)/vegetation type (N)/vegetation density (D)
Saturated permeability coefficient (10-6 m/s)
Cohesion force (kPa)
Internal friction angle (°)
M1
0.08
51.0
23.3
M2
0.05
70.8
19.2
M3
0.02
71.8
24.9
N1
0.07
56.8
25.4
N2
0.05
70.8
19.2
N3
0.03
68.6
26.2
D1
0.07
52.3
21.7
D2
0.06
53.2
27.5
D3
0.06
58.1
24.1Figure 16
Schematic diagram of the vegetation rooting depth on the slope.


### 3.4.2. Effect of Vegetation Rooting Depth on Slope Stability

In order to analyze and compare the influence of vegetation depth on slope stability, three different depths of 0.2 m, 0.5 m, and 0.8 m were selected. At the same time, when the vegetation depth increases, the economic consumption also increases. The influence of vegetation depth on slope stability is evaluated according to the comprehensive economic cost performance of slope vegetation.The effect on slope stability is analyzed at vegetation rooting depths of 0.2 m, 0.5 m, and 0.8 m (see Figure17). With the rooting depth increases, the horizontal displacement of the slope reference point decreases. As the rooting depth increases from 0.2 m to 0.5 m, the maximum values of horizontal displacement at reference points A, B, and C decrease by 0.05 m, 0.04 m, and 0.05 m, respectively. And as the rooting depth increases from 0.5 m to 0.8 m, the maximum values of horizontal displacement at reference points A, B, and C decrease by 0.02 m, 0.02 m, and 0.03 m, respectively.Figure 17
Different values of horizontal displacement at the slope reference points for different rooting depths.As the vegetation depth increases from 0.2 m to 0.5 m, the final values of horizontal displacement at reference points A, B, and C decrease by 0.02 m, 0.02 m, and 0.04 m, respectively. When the vegetation depth increases from 0.5 m to 0.8 m, the final values decrease by 0.01 m, 0.01 m, and 0.01 m, respectively. With the increase of root depth, the influence of vegetation on slope horizontal displacement decreases.When the vegetation root depth is 0.2 m, the maximum horizontal displacement of reference points A, B, and C during rainfall is reduced by 8.3%, 57.5%, and 44.4%, respectively, compared with the untreated slope. And the final values are reduced by 36.8%, 225.0%, and 160.0%.The maximum and final pore pressure values of the slope are shown (see Figure18). The pore pressure decreases as the rooting depth increases. As the rooting depth increases from 0.2 m to 0.5 m, the maximum values of the pore pressure at reference points A, B, and C decrease by 1.12 kPa, 5.62 kPa, and 4.56 kPa, respectively. When the rooting depth increases from 0.5 m to 0.8 m, the maximum values decrease by 0.87 kPa, 0.02 kPa, and 0.03 kPa, respectively.Figure 18
Different values of pore pressure at the reference points for different rooting depths.As the rooting depth increases from 0.2 m to 0.5 m, the final values of the pore pressure decrease by 1.12 kPa, 5.62 kPa, and 4.56 kPa, respectively. When the rooting depth increases from 0.5 m to 0.8 m, the final values of decrease by 0.87 kPa, 0.02 kPa, and 0.03 kPa, respectively. With the increase of root depth, the influence of vegetation on slope horizontal displacement decreases.When the vegetation root depth is 0.2 m, the pore water pressure of reference points A, B, and C during rainfall is reduced by 35.4%, 42.2%, and 42.0%, respectively, compared with the untreated slope. And the final values are reduced by 24.6%, 18.7%, and 10.9%.When the depth of vegetation roots increases, the modulus of elasticity and cohesion of the soil on the slope surface increases, the slip resistance of the slope surface increases, and permeability decreases, resulting in relatively less rainwater entering the slope. Therefore, the greater the depth of vegetation, the greater the stability of the slope. At the same time, it can be seen that when the vegetation depth is increased to a certain depth (0.5 m), the slip resistance of the soil on the slope surface is already very high and the infiltration of rainwater is very low, so that when the vegetation depth is gradually increased again, the stability of the slope does not improve significantly. This means that when vegetation is used for slope protection, the depth of vegetation should be chosen reasonably in relation to the slope, the intensity of rainfall, and the vegetation parameters.


### 3.4.3. Influence of Vegetation Type on Slope Stability

The maximum values of the horizontal displacement at slope reference points A, B, and C decrease as the vegetation type changes from N1 to N3 (see Figure19). After the end of the rainfall, the values of slope reference points B and C decrease as the vegetation type changes from N1 to N3. However, for reference point A, its vegetation type N1 has the largest final value, followed by vegetation type N3 and vegetation type N2. In conclusion, the slope vegetation type N2 is more suitable than vegetation types N1 and N3 to reinforce this slope.Figure 19
Different values of horizontal displacement at the reference points for different vegetation types.When the vegetation types N1 is chosen, the horizontal displacement of reference points A, B, and C during rainfall is reduced by 13.0%, 62.5%, and 62.5%, respectively, compared with the untreated slope. And the final values are reduced by 44.4%, 271.4%, and 225.0%.When the vegetation type changes from N1 to N3, the maximum and final values of the pore pressure at reference points A, B, and C on the slope decrease (see Figure20). When the vegetation type N1 is chosen, the pore water pressure of reference points A, B, and C during rainfall is reduced by 45.3%, 38.0%, and 69.5%, respectively, compared with the untreated slope. And the final values are reduced by 24.6%, 18.7%, and 10.9%.Figure 20
Different values of pore pressure at the reference points for different rooting depths.


### 3.4.4. Influence of Vegetation Density on Slope Stability

The horizontal displacement of the slope reference points decreases as the vegetation density increases (see Figure21). As the vegetation density increases from 30% to 50%, the maximum values of horizontal displacement at reference points A, B, and C decrease by 0.02 mm, 0.04 mm, and 0.05 mm, respectively; as the vegetation density increases from 50% to 60%, the maximum values decrease by 0.02 mm, 0.02 mm, and 0.03 mm, respectively.Figure 21
Different values of horizontal displacement at the reference point for different vegetation densities.As the vegetation density increases from 30% to 50%, the final values of horizontal displacement at reference points A, B, and C decrease by 0.04 mm, 0.02 mm, and 0.04 mm, respectively; as the vegetation density increases from 50% to 60%, the final values decrease by 0.02 mm, 0.01 mm, and 0.01 mm, respectively.When the vegetation density is 30%, the horizontal displacement of reference points A, B, and C during rainfall is reduced by 13.0%, 62.5%, and 62.5%, respectively, compared with the untreated slope. And the final value is reduced by 44.4%, 271.4%, and 225.0%.The pore pressure at the slope reference points decreases with the vegetation density increasing (see Figure22). As the vegetation density increases from 30% to 50%, the maximum values of the pore pressure at reference points A, B, and C decrease by 1.85 kPa, 4.89 kPa, and 1.12 kPa, respectively. The vegetation density increases from 50% to 60%, and the maximum values decrease by 2.50 kPa, 1.57 kPa, and 0.83 kPa, respectively.Figure 22
Different values of pore pressure at the reference points for different vegetation densities.As the vegetation density increases from 30% to 50%, the final values of the pore pressure decrease by 0.57 kPa, 2.34 kPa, and 1.80 kPa, respectively, the vegetation density increases from 50% to 60%, and the final values decrease by 0.87 kPa, 0.02 kPa, and 0.03 kPa, respectively.When vegetation density is 30%, the pore water pressure of reference points A, B, and C during rainfall is reduced by 45.3%, 38.0%, and 69.5%, respectively, compared with the untreated slope. And the final value is reduced by 24.6%, 18.7%, and 10.9%.When the density of vegetation increases, the modulus of elasticity and cohesion of the soil on the surface of the slope gradually increase, the slip resistance of the surface soil increases, and at the same time, the resistance of the soil to permeability also increases, so that the displacement and pore pressure of the slope decrease.


## 3.4.1. The Soil Parameters of the Model

The parameters of the vegetated slope are listed (see Table2). M represents the rooting depth of the vegetation. M1, M2, and M3 refer to vegetation depths of 0.2, 0.5, and 0.8 m. N represents the vegetation type. N1 refers to ryegrass and clover. N2 is ryegrass and alfalfa, and N3 is ryegrass and Caragana. D represents vegetation density. D1, D2, and D3 refer to vegetation densities of 30%, 50%, and 60%, respectively. The model is shown (see Figure 16). The influence of ecological slope protection measures on slope stability under nonuniform rainfall is analyzed in this paper.Table 2
Parameters of the vegetated slope.
Rooting depth (M)/vegetation type (N)/vegetation density (D)
Saturated permeability coefficient (10-6 m/s)
Cohesion force (kPa)
Internal friction angle (°)
M1
0.08
51.0
23.3
M2
0.05
70.8
19.2
M3
0.02
71.8
24.9
N1
0.07
56.8
25.4
N2
0.05
70.8
19.2
N3
0.03
68.6
26.2
D1
0.07
52.3
21.7
D2
0.06
53.2
27.5
D3
0.06
58.1
24.1Figure 16
Schematic diagram of the vegetation rooting depth on the slope.


## 3.4.2. Effect of Vegetation Rooting Depth on Slope Stability

In order to analyze and compare the influence of vegetation depth on slope stability, three different depths of 0.2 m, 0.5 m, and 0.8 m were selected. At the same time, when the vegetation depth increases, the economic consumption also increases. The influence of vegetation depth on slope stability is evaluated according to the comprehensive economic cost performance of slope vegetation.The effect on slope stability is analyzed at vegetation rooting depths of 0.2 m, 0.5 m, and 0.8 m (see Figure17). With the rooting depth increases, the horizontal displacement of the slope reference point decreases. As the rooting depth increases from 0.2 m to 0.5 m, the maximum values of horizontal displacement at reference points A, B, and C decrease by 0.05 m, 0.04 m, and 0.05 m, respectively. And as the rooting depth increases from 0.5 m to 0.8 m, the maximum values of horizontal displacement at reference points A, B, and C decrease by 0.02 m, 0.02 m, and 0.03 m, respectively.Figure 17
Different values of horizontal displacement at the slope reference points for different rooting depths.As the vegetation depth increases from 0.2 m to 0.5 m, the final values of horizontal displacement at reference points A, B, and C decrease by 0.02 m, 0.02 m, and 0.04 m, respectively. When the vegetation depth increases from 0.5 m to 0.8 m, the final values decrease by 0.01 m, 0.01 m, and 0.01 m, respectively. With the increase of root depth, the influence of vegetation on slope horizontal displacement decreases.When the vegetation root depth is 0.2 m, the maximum horizontal displacement of reference points A, B, and C during rainfall is reduced by 8.3%, 57.5%, and 44.4%, respectively, compared with the untreated slope. And the final values are reduced by 36.8%, 225.0%, and 160.0%.The maximum and final pore pressure values of the slope are shown (see Figure18). The pore pressure decreases as the rooting depth increases. As the rooting depth increases from 0.2 m to 0.5 m, the maximum values of the pore pressure at reference points A, B, and C decrease by 1.12 kPa, 5.62 kPa, and 4.56 kPa, respectively. When the rooting depth increases from 0.5 m to 0.8 m, the maximum values decrease by 0.87 kPa, 0.02 kPa, and 0.03 kPa, respectively.Figure 18
Different values of pore pressure at the reference points for different rooting depths.As the rooting depth increases from 0.2 m to 0.5 m, the final values of the pore pressure decrease by 1.12 kPa, 5.62 kPa, and 4.56 kPa, respectively. When the rooting depth increases from 0.5 m to 0.8 m, the final values of decrease by 0.87 kPa, 0.02 kPa, and 0.03 kPa, respectively. With the increase of root depth, the influence of vegetation on slope horizontal displacement decreases.When the vegetation root depth is 0.2 m, the pore water pressure of reference points A, B, and C during rainfall is reduced by 35.4%, 42.2%, and 42.0%, respectively, compared with the untreated slope. And the final values are reduced by 24.6%, 18.7%, and 10.9%.When the depth of vegetation roots increases, the modulus of elasticity and cohesion of the soil on the slope surface increases, the slip resistance of the slope surface increases, and permeability decreases, resulting in relatively less rainwater entering the slope. Therefore, the greater the depth of vegetation, the greater the stability of the slope. At the same time, it can be seen that when the vegetation depth is increased to a certain depth (0.5 m), the slip resistance of the soil on the slope surface is already very high and the infiltration of rainwater is very low, so that when the vegetation depth is gradually increased again, the stability of the slope does not improve significantly. This means that when vegetation is used for slope protection, the depth of vegetation should be chosen reasonably in relation to the slope, the intensity of rainfall, and the vegetation parameters.


## 3.4.3. Influence of Vegetation Type on Slope Stability

The maximum values of the horizontal displacement at slope reference points A, B, and C decrease as the vegetation type changes from N1 to N3 (see Figure19). After the end of the rainfall, the values of slope reference points B and C decrease as the vegetation type changes from N1 to N3. However, for reference point A, its vegetation type N1 has the largest final value, followed by vegetation type N3 and vegetation type N2. In conclusion, the slope vegetation type N2 is more suitable than vegetation types N1 and N3 to reinforce this slope.Figure 19
Different values of horizontal displacement at the reference points for different vegetation types.When the vegetation types N1 is chosen, the horizontal displacement of reference points A, B, and C during rainfall is reduced by 13.0%, 62.5%, and 62.5%, respectively, compared with the untreated slope. And the final values are reduced by 44.4%, 271.4%, and 225.0%.When the vegetation type changes from N1 to N3, the maximum and final values of the pore pressure at reference points A, B, and C on the slope decrease (see Figure20). When the vegetation type N1 is chosen, the pore water pressure of reference points A, B, and C during rainfall is reduced by 45.3%, 38.0%, and 69.5%, respectively, compared with the untreated slope. And the final values are reduced by 24.6%, 18.7%, and 10.9%.Figure 20
Different values of pore pressure at the reference points for different rooting depths.


## 3.4.4. Influence of Vegetation Density on Slope Stability

The horizontal displacement of the slope reference points decreases as the vegetation density increases (see Figure21). As the vegetation density increases from 30% to 50%, the maximum values of horizontal displacement at reference points A, B, and C decrease by 0.02 mm, 0.04 mm, and 0.05 mm, respectively; as the vegetation density increases from 50% to 60%, the maximum values decrease by 0.02 mm, 0.02 mm, and 0.03 mm, respectively.Figure 21
Different values of horizontal displacement at the reference point for different vegetation densities.As the vegetation density increases from 30% to 50%, the final values of horizontal displacement at reference points A, B, and C decrease by 0.04 mm, 0.02 mm, and 0.04 mm, respectively; as the vegetation density increases from 50% to 60%, the final values decrease by 0.02 mm, 0.01 mm, and 0.01 mm, respectively.When the vegetation density is 30%, the horizontal displacement of reference points A, B, and C during rainfall is reduced by 13.0%, 62.5%, and 62.5%, respectively, compared with the untreated slope. And the final value is reduced by 44.4%, 271.4%, and 225.0%.The pore pressure at the slope reference points decreases with the vegetation density increasing (see Figure22). As the vegetation density increases from 30% to 50%, the maximum values of the pore pressure at reference points A, B, and C decrease by 1.85 kPa, 4.89 kPa, and 1.12 kPa, respectively. The vegetation density increases from 50% to 60%, and the maximum values decrease by 2.50 kPa, 1.57 kPa, and 0.83 kPa, respectively.Figure 22
Different values of pore pressure at the reference points for different vegetation densities.As the vegetation density increases from 30% to 50%, the final values of the pore pressure decrease by 0.57 kPa, 2.34 kPa, and 1.80 kPa, respectively, the vegetation density increases from 50% to 60%, and the final values decrease by 0.87 kPa, 0.02 kPa, and 0.03 kPa, respectively.When vegetation density is 30%, the pore water pressure of reference points A, B, and C during rainfall is reduced by 45.3%, 38.0%, and 69.5%, respectively, compared with the untreated slope. And the final value is reduced by 24.6%, 18.7%, and 10.9%.When the density of vegetation increases, the modulus of elasticity and cohesion of the soil on the surface of the slope gradually increase, the slip resistance of the surface soil increases, and at the same time, the resistance of the soil to permeability also increases, so that the displacement and pore pressure of the slope decrease.


## 4. Conclusions

The slope model under the influence of rainfall infiltration is established by using the finite element software ABAQUS. Firstly, the influence of rainfall and groundwater level change on the stability of loess slope is analyzed. Then, the influence of retaining wall reinforcement measures on slope stability under rainfall and groundwater level change is evaluated. Finally, the influence of vegetation slope protection measures under rainfall on slope stability is analyzed. The conclusions are as follows:(1)
The changes of slope displacement and pore water pressure caused by rainfall and groundwater level are of great significance to the study and prediction of slope stability. This paper studies the displacement and pore pressure of the reference point of the slope under the conditions of uniform rainfall and uneven rainfall. Under the conditions of extreme rainfall, the order of the increase and change of the displacement and pore pressure at the bottom of the slope is the largest at the bottom of the slope, the second in the middle of the slope, and the lowest at the top of the slope. As the groundwater level fell, the displacement and pore pressure of the slope decreased; however, as the water level increased from 0.6 m to 0.8 m, the horizontal displacement and pore pressure of the slope increased(2)
When the slope was reinforced by retaining wall, the displacement and pore pressure of the slope decreased compared with untreated slope. The stability of the slope is effectively improved under the action of heavy rainfall and groundwater. Therefore, it is very effective to improve the stability of the slope engineering by using retaining wall reinforcement(3)
Plants can reduce the pore water pressure of the slope and improve the shear strength of the soil, which is conducive to the stability of the slope. The depth of roots and the density of vegetation have an impact on the slope stability. With the increase of the depth of vegetation roots, the slope stability increases under the action of rainfall. However, when the vegetation root depth increases to 0.5 m, the impact of vegetation depth on the slope stability decreases. The greater the density of vegetation, the greater the slope stability under the action of rainfall. Considering the external and economic factors, such as vegetation density and vegetation depth, vegetation type N2 is the most suitable for improving slope stability compared with vegetation types N1 and N3



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*Source: 5359809-2022-05-16.xml*