Experimental Research on Erosion Characteristics of Ecological Slopes under the Scouring of Non-Directional Inflow

Abstract

Considering environmental sustainability, ecological embankments are often adopted in rivers, which benefit both the erosion resistance and the ecological balance of the bank. In this paper, the effectiveness of different types of dominant grass species in ecological slope protection and their impact mechanisms, as well as the impact of non-directional inflow on erosion characteristics, were investigated. Based on the principle of similarity theory in hydraulic modeling and the characteristics of flood erosion in riverbanks, a test model system for hydraulic ecological simulation was designed, including a vegetation bank slope and channels. Three types of dominant grass species were selected, and 12 series of erosion experiments were conducted in the grassed slope of the test model. Three types of root–soil composites and a reference plain soil were involved in the tests, and soil mechanical indicators such as shear strength were collected. Experimental results show that root–soil composite is a special elastic–plastic material, which provides additional cohesive force to the soil due to its root consolidation and reinforcement effects, Δc. The shear strength index reflecting soil cohesion was increased by 15% to 20%. The primary factor affecting slope erosion is the flushing velocity, and both the average erosion depth and the unit soil erosion loss present an exponential function with respect to this factor, while presenting a linear function with the angle of incoming flow. Compared with the plain soil slope, the ecological slope could decrease erosion significantly. The sand loss of the ecological slope is only 50~60% that of the plain soil slope as the flushing velocity is 3–4 m s⁻¹. In vertical flushing, the sand loss in the plain soil slope is 1.73–2.43 times that of the ecological slope. This research might provide technical support for the anti-scourability design of the ecological embankment.

1. Introduction

Ecological slope protection not only has the function of traditional slope protection; it also integrates various aspects such as landscape, culture, and ecology, thereby achieving the maintenance and restoration of natural ecosystems. The plant roots on the bank slope exhibit certain hydrological and mechanical effects, forming anti-erosion and slope protection engineering properties [1]. Ng et al. [2] have specifically studied the problems of soil stability in ecological slope protection construction and proposed targeted solutions. Meijer et al. [3] pointed out that plant roots can improve the shear strength of soil, while grass roots can reduce the stress level in shallow soil, which can change the stress–strain state of the soil and increase the cohesion of shallow soil, which is beneficial for stabilizing slopes. By comparing it with plain soil, Zhou and Qi [4] found that root systems can increase the ultimate principal stress difference of soil and enhance its ability to resist damage. By means of the limit equilibrium equation, Boldrin et al. [5] established a stability calculation formula for root system slope stabilization and analyzed the stability of root system slope stabilization from local and global perspectives. Yamase et al. [6] investigated the biomechanical corrosion resistance mechanism of root–soil composites of different type of grass species by means of a root–soil composite body plastic structure. The ANS (anti-impact index), soil shear strength index, and four soil permeability parameters were measured.

The anti-erosion effectivity of plant slope protection is attributed to its ability to inhibit the runoff impact on the bank slope, the soil reinforcement of root systems, and its ability to decrease sand loss in the slope. It has been found that grass roots can improve the structure and physicochemical properties of soil, enhancing the structural stability and soil erosion resistance of root–soil composites [7]. The experimental research of Hao et al. [8] found that the stems and leaves of herbaceous plants can decrease the damage caused by flow flushing, and the soil reinforcement effect of roots plays an important role in resisting erosion. The research of Fraccica et al. [9] indicated that root density is one of the key factors affecting the anti-erosion effectivity of soil, and the amount of sand loss in soil is inversely proportional to root density. Nguyen et al. [10] pointed out that fibrous root systems with a diameter less than 1 mm can increase the number of aggregates in soil and improve soil structure, enhancing the soil integrity, stability, and corrosion resistance. The erosion amount can be calculated by using relevant formulae, such as the slope erosion resistance safety coefficient [11,12,13,14]. Su et al. [15] focused on the erosion resistance performance of the slope after combining the slope form and vegetation types and found that the slope protection effectivity of the combination of terraces and grass shrubs under rainfall erosion is the optimal, with a resistance efficiency of sand loss of 80.2%. Shen et al. [16] found that plant stems and leaves can effectively weaken the impact of rainwater on soil particles through experimental research. When the rain intensity is strong, the interception and energy dissipation effect of the forest canopy stems and leaves can be more than twice that of bare land. Wang et al. [17] investigated the relationship between plant roots and the stability of the riverbank slope structure by means of physical simulation. Monitoring showed that the size of the root structure determined the impact area of the plant on the slope as well as the anti-erosion performance of the slope. He et al. [18] revealed the associations among the anti-erosion characteristics of Bermuda grass, such as planting density and plant height, and its biological characteristics through channel erosion experiments in plant model slopes. Xiao et al. [19] simulated the rainfall runoff erosion in grass slopes, revealed the erosion process of the plant slope protection, and provided evaluation criteria for the degree of slope damage.

During the flood season, the impact of river flood on bank slopes might lead to severe erosion and damage of the local slope [20]. Therefore, Morgan [21] proposed using ecological engineering to control slope erosion after investigating the mechanism of soil stabilization and erosion resistance of plant slopes. Other slope protection technology also were developed, such as thick-layer substrate spraying, vegetation concrete, and so on, which have become new directions in plant slope protection research [22]. In summary, the research on ecological slope protection is currently being rapidly and broadly applied in river and road slope protection projects.

The coherent effect of the roots and soil on soil consolidation and the anti-erosion effect of the dominant herbaceous roots, as well as the response of the composite structures to the flow flushing force, play a role in revealing the anchoring effect of dominant roots and the anti-erosion performance parameters of ecological slopes [23]. The planar shape of the natural river is mainly curved and would change in flood periods, which results in the adjustment of centrifugal inertia forces in the curved channel, leading to the unsteady flow velocity and direction of the mainstream [24]. The local inflow at certain directions and angles would cause erosion to the bank slope. The contact erosion damage to the slope vegetation is crucial for the safety and stability of embankments [25]. However, research on the erosion resistance of vegetation slopes under non-directional mainstream flushing in rivers is currently rare. Therefore, it is necessary conduct research on the erosion damage mechanism and erosion resistance performance of ecological slopes under the condition of non-directional mainstream flushing in rivers.

In this paper, we focus on the anti-erosion performance and mechanism of the ecological bank slope in response to non-directional flows. Flushing tests in typical ecological slopes were conducted under multiple vegetation and flow conditions. The flushing flow conditions were designed to reflect the characteristics of mainstream flushing of river floods, i.e., various flow directions and velocity. To ensure the accuracy of the experiments, a hydraulic flushing test device system was designed and manufactured to simulate different bank slope environments, and a series of experiments was conducted. The research results might provide parameters and technical support for the design and promotion of ecological slope projects.

2. Research Objects and Methods

2.1. Research Subjects

2.1.1. Dominant Grass Species and Root–Soil Composite

Through data review and local field research sampling, we identified some dominant grass species with well-developed root systems and growth advantages. Finally, through screening, we selected three dominant grass species with dense plant roots, root lengths of 15–30 cm, and plant irrigation heights of 10–30 cm: Poa pratensis, Zoysia japonica, and Bermuda grass (as shown in Figure 1). The grass species from different surface environments were selected, and the sampling location is near Jialu River. The sampling is based on a soil layer thickness of 8–10 cm. After taking the sample, we removed any grass outside of this sample. These are the root–soil composite samples of the three dominant grass species used in the experiment.

2.1.2. River Embankment Protection Slope: Plain Soil Slope and Ecological Slope

An investigation was conducted on the ecological slope of Jialu River in the suburbs of Zhengzhou. Local soil samples were taken to create grass planting soil tanks and model test slopes. The initial soil sample had a density of 1.78 g/cm³, a dry density of 1.49 g/cm³, a moisture content of 26%, a cohesive force of 18.65 kpa, and an internal friction angle φ. The parameters of 23.22° are similar to the actual slope soil of the Jialu River. We cultivated the same type of soil as the outdoor grass system on the plain soil slope and avoided applying external forces during the process of taking and transporting the plain soil to maintain its original state and fill it evenly and fully. Grass cultivation was carried out in the undisturbed soil on the natural water pit slope of the outdoor experimental field. Before planting, the soil was thoroughly moistened, and the seeds of the dominant grass species, such as Poa pratensis and Bermuda grass, were selected for regional sowing. The sowing density was 1400 g/667 m², and after sowing, we covered 1–2 cm of local soil and keep the soil moist. After sowing, we regularly removed weeds, loosened soil, and supplemented organic fertilizer appropriately. We sprinkled 2 kg of urea every 667 square meters. Grasses were immediately watered after each fertilization. During maintenance, timely replanting was carried out to maintain a uniform density of grass planting. After about 50 days of growth, when the diameter of the main stem reached 2–2.5 mm or more, the root system had developed, and the planting density was 1250 g/667 m². Then, according to the specifications of the experimental box, we carefully collected the overall grass soil composite and placed it in the experimental box to continue watering and cultivation. The ecological slope model is shown in Figure 2, after the transplanted grass seeds were stable, we prepared for the water flow flushing test.

2.2. Research Methods

2.2.1. Soil Mechanics Test of Root–Soil Composite

Through indoor soil mechanical shear tests and root topology analysis, the anchoring mechanism of composite soil is studied, and the shear strength and failure surface mechanical characteristic values of the root–soil composite are obtained. The experimental conclusions can further provide relevant evidence for the study of the erosion resistance mechanism of grass systems [26,27]. Taking Bermuda grass, Zoysia grass, and Kentucky bluegrass as objects, indoor direct shear tests were carried out on root–soil composite samples at different soil depths to obtain the shear resistance characteristics indices (cohesion c and internal friction angle φ) of three soil conditions. In addition, we obtained its variation pattern with soil depth. The changes in shear resistance and distribution of root morphology characteristics of root–soil composites provide an analytical basis for the study of the erosion failure mechanism of plant slopes under sheeted water flow.

2.2.2. Ecological Water Tank Test

(1)

Design of Hydraulic Ecological Model

Based on the principle of similarity in natural models, and taking into account the general characteristics of river erosion banks, a generalized treatment was carried out on river embankment slopes, inflow conditions, and herbaceous vegetation [5]. A hydraulic sand ecological simulation test system was designed for a single-side vegetation bank slope and some river channels. The simulation system included some river channels, a herbaceous plant slope, an adjustable flushing flow subsystem, a sand erosion collection subsystem, and a scouring process camera device, as shown in Figure 3.

The model has a longitudinal length of L = 2.0 m, a transverse width of B = 1.2 m, and a height of H = 0.45 m. There is a grassy soil bank slope with a slope of 1:2.25 on one side (accounting for 2/3B), and the rest is a simulated river channel (accounting for 1/3B). There is a water and sand collection device at the end of the model. The single-bank slope adopts pure soil slope and the herbaceous ecological slope is used as the control group; while the ecological slope adopts the selected dominant grass species of Poa pratensis and Bermuda grass, which are compared with each other.

The flood inflow and flushing subsystem mainly consists of a variable-frequency booster pump and a flushing angle adjustment platform. The power of the variable frequency booster pump is 100–600 w, and the flushing flow rate can be adjusted and controlled by adjusting the pressure. The maximum flow rate can reach 4 m·s⁻¹. The flushing angle adjustment platform can freely adjust and control the angle and direction of the flushing water flow. At the 1/2 slope corresponding to the horizontal direction of the flushing water outlet, the angle between the flushing water outlet and the slope surface can be adjusted by 180°, and the distance between the automatic adjustment platform and the centerline of the slope is 0.8 m. This is only an approximate simulation of the local flushing effect of the water flow, and the effective range of the corresponding bank slope flushing is related to the diameter D of the jet water column, which is generally about (4–6) D. The difference between the simulated local flushing test and the actual river flood flushing needs to be verified and corrected through measured data.

To quantitatively observe the erosion degree of various bank slope soil under different inflow angles and flow velocity conditions, a self-made erosion soil collection device was developed. The erosion soil collection device is located immediately at the downstream slope foot of the model. In order to ensure the accuracy of measurement, the depth of slope erosion is measured using high-precision measuring rulers. In the early stage of the experiment, the height and slope profile of the slope have been marked and recorded on transparent organic glass. After each set of jet tests, the erosion depth of each fixed measuring point (Figure 4) on the slope is measured, counted, and recorded, and the vegetation damage is observed and analyzed.

(2)

Test principles and methods

The non-directional flushing bank slope of floods is the main cause of river embankment damage. Generally, two indicators can be used to reflect the flushing conditions of floods, namely, the flushing velocity (the velocity at which the incoming flow acts on the bank slope) and the flushing angle (the angle between the incoming flow and the slope shoreline) [28,29,30]. This article conducts flood erosion simulation experiments under different inflow velocities and angles on slopes covered with different vegetation types to study the anti-erosion mechanisms of slopes in different bank slope environments. The river channel with the ecological slope is generalized as a plant slope simulation test system, and the non-directional flood mainstream flushing is generalized as a flushing water flow simulation system with adjustable angle and velocity. The experimental research approach is as follows:

(1)

Design an embankment slope environment that includes vegetation free soil and several types of grass ecological slope, conduct simulation experiments on flood erosion under different conditions, observe the state of erosion damage, and study the mechanism of slope erosion;

(2)

Measure and analyze the erosion situation and soil loss on the slope surface in the designated erosion area, study the erosion characteristics and soil loss patterns of the bank slope under different erosion conditions (flow velocity, jet angle combination), and compare and analyze the soil fixation characteristics and anti-erosion effects of different vegetation slope. Through a comprehensive analysis of slope damage and soil loss, the anti-erosion and failure mechanisms of the ecological slope under different flood washes are revealed.

Due to the close proximity of the soil collector to the foot of the slope, there is no other soil loss channel in the middle, as shown in Figure 3. According to the binary constant flow and mass conservation, it can be assumed that almost all the soil washed down from the ecological slope flushing area flows into the soil collection device, and the soil mass in the soil collection device is the soil erosion amount in the ecological slope flushing area. Using the developed sand collection instrument to measure the sand loss, we collect, dry, and weigh the sand washed by each experimental group. The dry weight of the sand obtained is divided by the effective flushing area A’ of micro activity and the flushing time, which is the unit sand loss M_L. At the same time, the sand sample is analyzed for sand particle size.

(3)

Data processing and parameter introduction

A systematic analysis was conducted on the soil test data of the root–soil composite of three dominant grass species, and the following important parameters were introduced to comprehensively reflect the mechanical properties of the root–soil composite.

➀ Shear stress τ

τ = KR

(1)

In the formula, K denotes the force ring coefficient (kPa/0.01 mm). R represents the difference between the reading of the force measuring ring dial indicator during shearing and the final reading during shearing failure.

➁ Normal stress σ

We calculate the corresponding shear stress based on the data of different specimens τ, reduce the applied normal stress σ corresponding to the calculated shear stress τ, and draw the σ–τ curve. Using regression analysis method, it can be fitted to obtain normal stress σ, the calculation formula for which is as follows:

σ = β τ + c

(2)

➂ Shear stress influence coefficient β

The shear stress influence coefficient reflects σ–τ. The slope of the curve is calculated as follows:

β = tg φ

(3)

where φ denotes the internal friction angle of the soil.

From this, the corresponding cohesion c and internal friction angle are obtained, φ. Finally, based on the overall experimental data (moisture content, root content, internal friction angle, cohesion), the differences and changes in the data between the composites of different root systems and rootless soil were compared. The test data at 400 kpa are shown in

Table 1. Test data at a load of 400 kpa.

Grass Seed	Test Number	Shear Strength τ/kPa	Cohesive Force c/kPa	Internal Friction Angle φ/°
(Bluegrass) (ω = 28%)	BL1	344.96	49.63	36.60
	BL2	314.88	29.72	35.00
	BL3	262.87	52.72	27.50
	P1	216.88	10.09	27.30
(Zoysia) (ω = 21%)	ZO1	400.10	111.50	34.84
	ZO2	410.80	86.10	38.61
	ZO3	390.90	106.70	35.61
	P1	369.00	42.50	38.64
(Bermuda-grass) (ω = 22%)	BE1	462.10	119.20	40.95
	BE2	471.50	115.35	42.08
	BE3	478.34	124.18	42.09
	P1	432.00	87.75	37.98

Note: BL is a root–soil composite of Bluegrass roots and soil; ZO is a Zoysia grass root–soil composite; and BE is a root–soil composite of Bermuda grass and soil. P1 is the local rootless plain soil.

.

➃ Average erosion depth D_AE

In order to ensure the accuracy of measurement, the depth of the slope jet is measured using high-precision measuring needles. In the early stage of the experiment, the height and slope profile of the slope were marked and recorded on transparent organic glass. After each set of erosion tests, high-precision measuring rulers are used to measure the fixed measuring points and calculate the average value, which is the average erosion depth, D_AE:

D_AE = D_TE/N

(4)

In the formula, D_TE is the cumulative value of scouring depth at each measuring point, cm. N is the number of measurement points, and in this experiment, 28 points were taken.

➄ Decrease value of average erosion depth ∆D_AE

The definition formula for ΔD_AE of the average erosion depth reduction value (compared with plain soil slopes) is as follows:

∆D_AE = D_AEP − D_AEE

(5)

where D_AEP denotes the average erosion depth in plain soil slope, and D_AEE denotes the average erosion depth in the ecological slope.

⑥ Decrease rate of average erosion depth P_RD

The decrease rate of average erosion depth in the ecological slope under different flushing velocity gradients and erosion angle gradients is defined as P_RD:

P_RD= ∆D_AE/D_AEP × 100%

(6)

where ∆D_AE denotes the decrease value of average erosion depth in various ecological slopes, and D_AEP denotes the average erosion depth in a plain soil slope.

3. Test Results

3.1. Soil Mechanical Properties of Root–Soil Composite

3.1.1. Shear Strength of Different Grass Species

Root–soil composite is a special type of elastic–plastic material, whose principal stress difference and axial strain curve exhibit smooth non-linear characteristics. The influence of confining pressure is significant, and as the root diameter increases, the cohesion of the root–soil composite increases significantly. Through a series of indoor shear strength tests, the shear strength data of the root–soil composite and plain soil of Poa pratensis, Zoysia japonica, and Bermuda grass were obtained. Relevant scatter plots were drawn and then fitted to obtain the fitting curves under different root systems. Figure 5 was used to evaluate the stability of the cohesion value Δc. The characteristics of c changes are shown in

Table 2. Comparing analysis on the values of Δc under various conditions.

Root–Soil Composite	Category Number	Δc (KPa)	Range of Δc	Difference in Total Change of Δc (KPa)
Bluegrass	1	39.54	19.63~42.63	23
	2	19.63
	3	42.63
Zoysia japonica	1	69	44.05~69.00	24.95
	2	44.05
	3	62.4
Bermuda grass	1	31.45	27.00~31.45	4.45
	2	27.6
	3	36.43

.

From Table 1 and Figure 5, it can be seen that the strength envelope of root–soil is above that of non-root–soil, indicating the presence of roots, which significantly increases the shear strength index c value of the root–soil composite compared to the c value of plain soil with the same moisture content. The increase in internal friction angle φ is small, which indicates that the impact of root system on φ is minor. The composite soil formed by adding roots can improve the shear strength of the soil to a certain extent, and the cohesion c increases the specific internal friction angle φ. The increase is significant, as shown in Figure 5 of Table 2, where the slope of the shear strength envelope of the root–soil and the plain soil is almost the same, indicating the internal friction angle between the root–soil composite and the plain soil φ. The difference is not significant, indicating that the improvement of the shear strength index of the root–soil composite by the root system is mainly to enhance the cohesion of the soil, while it has almost no effect on the internal friction angle.

3.1.2. Additional Cohesion of Root–Soil Composite

From Table 2 and Figure 5, it can also be seen that the intercept between the strength envelope of the root–soil and the y-axis is larger than that of the plain soil, indicating that the reinforced root system provides an additional cohesive force for the soil Δc, moving the strength envelope of the plain soil up by one Δc. The interval of c greatly increases the shear strength of the soil, increases the bearing capacity of the root–soil composite, and strengthens the stability of the shallow soil where the root system is located.

The natural moisture content is generally between 20% and 30% for all three types of vegetation. The test samples selected in their respective growth environments each highlight their good shear strength properties compared to the plain soil state, and the shear strength increases linearly, once again reflecting the ability of the root system to enhance the shear strength of the soil. The mechanism involved might be that the soil of the ecological slope is intertwined with plant roots and forms a root–soil composite, which can be regarded as reinforced soil. The reinforced root system provides additional cohesion for the soil, which would greatly increase the shear strength of the reinforced soil. Plant roots secrete sticky substances such as root mucus. These substances can form a gel-like material on the surface of soil particles and roots, increasing the adhesive forces between particles. Furthermore, these secretions can bind with water molecules in the soil, forming a gelatinous substance that further enhances the shear strength of the soil.

Sample analysis method was applied to evaluate the stability of cohesion value and analyze the characteristics of the changes in Δc, the fluctuation of the before and after changes of Bermuda grass (4.45 kPa) are relatively smaller than the samples of Poa pratensis and Zoysia japonica, indicating that the root–soil composite of this grass has a relatively stable shear resistance, strong adaptability to the environment, and also indicates that it is more adaptable to the soil quality of the growth environment. Comprehensive experimental analysis and comparison show that Bermuda grass has certain advantages as a form of river slope protection, and it can be used in trials for river slopes or other soil slopes.

3.2. Erosion Characteristics on Ecological Slopes under Non-Directional Flood Flushing Conditions

Experimental research has found that there are two key influencing factors on the erosion of plant slopes under the condition of water flow flushing: flushing velocity and flushing angle. The impact of these two factors on plant slope erosion is mainly reflected in the depth, amount, and process of erosion. Among them, the depth of erosion and the amount of erosion are comprehensively reflected by the average erosion depth, D_AE, and the slope sand loss, M_L, respectively.

3.2.1. Impact of Flushing Velocity on Slope Erosion

(1)

Impact on average erosion depth D_AE

Statistical analysis of the average erosion depth (D_AE) of jet erosion tests under various conditions shows that the average erosion depth of plant slopes varies under different erosion velocities and angles. The average erosion depth of plain soil slopes is significantly greater than that of Poa pratensis slope and Bermuda grass slopes.

In Figure 6, the variation curves of average erosion depth with flushing velocity under four different erosion angles are shown. It can be seen that under the condition of a certain scouring angle, i.e., the directional angle of flushing flow with the bank, the variation laws of the Poa pratensis slope, Bermuda grass slope, and natural plain soil slope with the flushing flow velocity are highly consistent. The average erosion depth of the three slopes demonstrates an exponential function relationship with the jet flow velocity; that is, the scouring depth is greater with the increase in flow velocity, and the change rate of the average erosion depth increases with the increase in flow velocity. Based on data analysis, the overall trend of the average erosion depth values corresponding to different flow velocities under four different erosion angles is as follows: plain soil > Bermuda grass > Poa pratensis. From the perspective of slope failure mechanism, after the erosion depth exceeds 8 cm, the rate of change in the erosion depth increases with the increase in Poa pratensis and Bermuda grass.

(2)

The influence of flushing velocity on the sand loss M_L on the bank slope

We organized and analyzed the trend of unit sand loss M_L data based on the changing factors of flushing velocity, as shown in Figure 7, where panel (a) to (d) show the trend of unit sand loss with flushing velocity under four different erosion angles.

From the figures above, it can be seen that as the flushing velocity increases, the loss of soil on the bank slope gradually increases, in which the amount of soil loss in the plain soil slope without vegetation protection is the maximum. Due to the above-ground stem diameter of ecological slope grass being over 10 cm and the underground root system being over 20 cm, the soil loss amount is significantly lower than that of the plain soil bank slope under the comprehensive effect of grass stem, leaf energy dissipation, and root network soil fixation. Under the condition of high-intensity flow flushing, the loss amount is only 50~60% that of the plain soil bank slope. It played a role in protecting the bank slope. When the flow velocity at the shore is less than 1.6 m·s⁻¹, especially under the condition of a large angle flushing, the soil loss of the ecological slope is very small, i.e., only 45% that of the plain soil slope. Even under strong scouring conditions, i.e., flow velocity bigger than 4.0 m·s⁻¹ on the shore, soil loss is only about 50% that of the plain soil slope. The soil fixation effect of Poa pratensis in the ecological slope is slightly better than that of Bermuda grass root, i.e., 10~36%.

Under the condition of a certain scouring angle, the erosion soil loss of the Poa pratensis slope, Bermuda grass root slope, and natural plain soil slope is closely related to the scouring velocity. Under the three bank slope conditions, the unit sand loss demonstrates an exponential function relationship with the scouring velocity, as shown in

Table 3. Fitting relationship between scouring velocity and unit sand loss on bank slope.

Slope Type	Angle of Impact (°)	Fitting Curve Equation
Poa pratensis	5	ML = 0.1374exp(0.6745v)
	30	ML = 0.1767exp(0.6668v)
	60	ML = 0.3703exp(0.5210v)
	90	ML = 0.4853exp(0.5264v)
Bermuda grass	5	ML = 0.2486exp(0.5427v)
	30	ML = 0.3872exp(0.4731v)
	60	ML = 0.4772exp(0.4633v)
	90	ML = 0.5809exp(0.5000v)
Plain soil	5	ML = 0.3314exp(0.6018v)
	30	ML = 0.5364exp(0.5383v)
	60	ML = 0.8806exp(0.4229v)
	90	ML = 1.3205exp(0.4146v)

Note: Angle of impact denotes the angle of flushing flow with the bank.

. It can be expressed as follows:

M_L = αe^βv

(7)

where M_L is the unit sand loss, and v is the flushing velocity. α and β refer to the corresponding coefficients and indices, respectively.

From the analysis of the experimental data, it was found that the coefficients in the above functional relationship α and index β all change in a quadratic function manner with the adjustment of the incidence angle of the incoming stream, as shown in Figure 8 and Figure 9 and Table 3.

The experimental data show that the coefficients and indices of the loss formulae for the three types of the slope are related to the attack angle, as shown in Formula (8):

y = aθ² + bθ + c

(8)

where y denotes α or β, and θ denotes the impact angle. Based on over 60 sets of experimental data, the coefficients in the equation can be determined according to

Table 4. The change trend of fitting the coefficient in Formula (8) with α and β of incoming flow.

Type	Plain Soil		Poa pratensis		Bermuda Grass
Coefficient	α	β	α	β	α	β
a(10−5)	6.000	2.000	2.000	1.000	−2.000	3.000
b(10−2)	0.630	−0.450	0.290	−0.300	0.530	−0.370
c	0.298	0.632	0.109	0.706	0.228	0.559

.

The above analysis also indicates that the amount of soil loss is actually influenced by various factors, such as flow velocity and impact angle, and has a composite function characteristic.

3.2.2. Impact of the Direction of Flushing Flow on Erosion

(1)

Impact on erosion depth D_AE

Statistical analysis of the average erosion depth (D_AE) of jet erosion tests under various operating conditions shows that the average erosion depth of plant slopes varies under different erosion velocities and angles of flushing flow with the bank. The average erosion depth of the plain soil slope is significantly greater than that of the Poa pratensis slope and Bermuda grass slope.

The relationship between the erosion angle and the average erosion depth (D_AE) under five different erosion velocities is shown in Figure 10. It can be seen that under the condition of a certain scouring velocity, the variation law of the Poa pratensis slope, the Bermuda grass root slope, and the natural plain soil slope with the scouring angle is consistent. The average erosion depth of the three soil conditions has a linear function relationship with the jet angle. With the increase in scouring angle, the average erosion depth is larger, which is related to the fitting equation. At the same flow rate, the average erosion depth reaches its maximum when the erosion angle reaches 90°, indicating that the direction of water flow and the direction formed by the slope have a certain impact on the erosion of the slope. When the water flows towards the slope, the erosion damage caused is the greatest. By comparing the average erosion depths under three soil conditions, the average erosion depth distribution with the change of angle under each flushing velocity is basically as follows: Poa pratensis < Bermuda grass < plain soil, in which Poa pratensis is close to Bermuda grass.

(2)

The influence of erosion angle on the amount of sand loss M_L on the bank slope

The impact angle of flood flow on the bank slope is another important factor affecting the amount of sand loss. Using experimental data, we analyzed the impact and trend of changes in the erosion angle on the unit sand loss M_L. Figure 11a–e shows the response curves of unit sand loss with the change of scouring angle under three different soil conditions on the bank slope, given the scouring velocity.

By comparing the curves of five conditions in Figure 11 above, it can be seen that the characteristics and changing trends of each curve are similar. Under the flushing of any directional flow, the anti-scourability of plain soil is the minimum, and the amount of sand loss is greater than that of the ecological slope from the beginning of the flow close to the bank. After the erosion angle exceeds 30 degrees, the gradient of increased sand loss is even bigger. When the erosion is vertical, the sand loss on the plain soil bank slope is almost 1.73~2.43 times that of the ecological slope.

During the process of gradually increasing the angle of erosion, although the amount of sand loss in the ecological slope is slowly increasing, the energy dissipation of vegetation stems and leaves and the soil fixation and erosion prevention of roots always play a role. Therefore, the increased rate of sand loss is relatively low, showing a linear relationship with the low growth rate. Due to the lack of protection on the plain soil bank slope, when the erosion angle increases, the sand loss increases at a rate of 2.3 to 3.5 times higher than that of the ecological slope, while also maintaining an approximate linear relationship with it. This also indicates that among the two factors of flood flushing, the effect of increasing the flushing angle is lower than that of increasing flow velocity.

The relationship between the scouring angle and the sand loss on the slope surface is analyzed in Figure 11. Under the condition of setting the scouring velocity, the sand loss on the slopes of Poa pratensis, Bermuda grass, and natural plain soil has a relatively close linear functional relationship with the scouring angle, and can be defined as follows:

M_L = kθ + ε

(9)

In Formula (9), M_L is the unit sand loss mass, with the same unit as before; θ is the scouring angle, i.e., directional angle of the flushing flow with the bank, in degrees.

K and ε denote the loss intensity coefficient and auxiliary parameters, respectively. The analysis of experimental data shows that both parameters are closely related to the impact velocity, as shown in

Table 5. The fitting functions of unit sand loss M_L with impact angle θ of flushing flow.

Slope Type	Flushing Velocity (m·s−1)	Fitting Curve Equation
Poa pratensis	0.8	ML = 0.0066θ + 0.1515
	1.6	ML = 0.0071θ + 0.3612
	2.4	ML = 0.015θ + 0.5592
	3.2	ML = 0.016θ +1.1341
	4.0	ML = 0.0218θ + 1.7218
Bermuda grass	0.8	ML = 0.0045θ + 0.3913
	1.6	ML = 0.0092θ + 0.5069
	2.4	ML = 0.0143θ + 0.8726
	3.2	ML = 0.0158θ + 1.245
	4.0	ML = 0.0215θ + 1.9288
Plain soil	0.8	ML = 0.015θ + 0.4018
	1.6	ML = 0.0204θ + 0.7271
	2.4	ML = 0.0266θ + 1.167
	3.2	ML = 0.0223θ + 2.06
	4.0	ML = 0.0416θ + 3.3539

. Based on experimental data analysis, k and ε, the correlation with the flow velocity is shown in Figure 12 and Figure 13. This correlation can be represented by the following fitting relationship:

y = av + b

(10)

where y denotes k or ε, and v is the flow velocity. Based on fitting more than 60 sets of experimental data, the coefficients in the equation can be determined according to

Table 6. The change trend of fitting coefficient a and b in Formula (10) with k and ε.

Type	Plain Soil		Poa pratensis		Bermuda Grass
Coefficient	k	ε	k	ε	k	ε
a (10−2)	0.69	90.46	0.49	48.92	0.51	47.66
b (10−2)	0.87	−62.92	0.15	−38.85	0.09	−15.5

. The above analysis indicates that the amount of sand loss is actually influenced by multiple factors and is not a simple linear relationship with a single factor in form.

4. Discussion

4.1. The Variation Pattern of ∆D_AE in the Decrease in Average Erosion Depth

The P_RD variation decrease with flushing flow velocity and angle of impact, i.e., the directional angle of the flushing flow with the slope, is shown in Figure 14. It can be seen that when the erosion angle is constant, the P_RD of Poa pratensis is generally larger, reaching up to 52%, and the highest is 37% for Bermuda grass. This reflects that plant slopes have better resistance to vertical erosion compared to plain soil slopes, and the overall erosion resistance effect of Poa pratensis is better than that of Bermuda grass. According to the trend of change, it can be concluded that the ∆D_AE of both plant slopes is relatively large at various angles when the flow rate is below 1.6 m·s⁻¹. After the flow rate is above 1.6 m·s⁻¹, the ∆D_AE gradually decreases, indicating that the erosion resistance of grass soil fixation decreases as the erosion flow rate increases to a certain limit. When the scouring flow rate is constant, the average changes in P_RD of Poa pratensis and Bermuda grass are 17% and 14%, respectively, indicating that slopes planted with vegetation have a certain erosion resistance compared with plain soil slopes. According to the changing trend, it can be seen that with the increase in scouring angle, P_RD has a decreasing trend, indicating that an increase in the angle between channel flow and slope surface will reduce the erosion resistance of the root–soil.

4.2. Characteristics of the Sand Loss Intensity on Bank Slopes under Flood Flushing

It can be seen in Figure 11 that the increase in sand loss is faster as the impact velocity increase, and the curves of various inflow (impact angle) conditions almost present a similar trend. In order to reflect the change rate of sand loss on the slope, the slope erosion increase gradient dM_L/d_v is introduced to characterize it, and it can be defined as follows:

$$\frac{\mathrm{d}{M}_{\mathrm{L}}}{\mathrm{d}v}=\frac{\mathrm{d}(\alpha e^{\beta v})}{\mathrm{d}v}=\alpha \beta e^{\begin{array}{l}\\ \beta v\end{array}}$$

(11)

The meanings of each physical quantity in the equation are the same as before.

Here, typical working conditions with attack angles of 60° and 90° are selected to investigate the variation pattern of the increasing slope erosion gradient. By using three types of slope-fitting formulae obtained from experimental data (see Table 2), the relationship between the flushing velocity and the gradient of slope erosion increase can be obtained, as shown in Figure 15.

From Figure 15, it can be seen that for the three types of slope—Poa pratensis, Bermuda grass, and plain soil—the trend of the slope erosion gradient with the increase in flushing velocity is basically consistent; all present an exponential function. Regardless of whether the erosion angle is 60° or 90°, the changes in slope erosion gradients of the three types of slope have the same characteristics. First, the curves of the plain soil slope are much higher than those of the other two types of ecological slope. This indicates that under different flushing velocity conditions, the total amount and increase rate (erosion gradient) of the plain soil slope are the biggest. The slope erosion gradient of planting Poa pratensis and Bermuda grass slope decreased significantly (30~43%), and as the flushing velocity increased, the difference between the ecological slope erosion gradient and the plain soil slope erosion gradient also increased. This indicates that the anti-erosion ability of the ecological slope is more effective at high flow rates. The slope erosion gradient of Bermuda grass is also slightly higher than that of Poa pratensis. However, as the flushing velocity increases, the slope erosion gradients of the two become closer and closer. At a flush velocity of 4 m·s⁻¹, the erosion gradient of the two is basically the same. From the perspectives of erosion loss and the increasing gradient, the anti-scourability of Poa pratensis is better than that of Bermuda grass. Therefore, in the design of river channel slopes, a combination of the Poa pratensis slope and the anti-erosion frame can be considered to achieve higher-flow-velocity embankment slope safety.

4.3. The Mechanism of Slope Erosion Resistance during Erosion Process

To analyze the impact of flood flushing conditions on different bank slopes, comparative experiments were conducted under multiple operating conditions. Introducing corrosion resistance here (δ), in order to characterize the anti-erosion and soil consolidation effect of the ecological slope, the formula is as follows:

δ_r = ∆M_L/M_Ls = (M_Ls − M_Lp)/M_Ls

(12)

In the formula, M_Ls and M_Lp, respectively, represent the sand loss per unit area of plain soil embankment slopes and ecological protection slopes caused by water flow flushing (unit: kg·m⁻²). ∆M_L is the decrease in sand loss of the ecological slope compared to the plain soil embankment slopes, using the same unit as above. The corrosion resistance rate, δr, can also be expressed as a percentage.

Based on experimental data, the erosion resistance curves of the two dominant grass species for the ecological slope were plotted under different erosion velocities and angles, as shown in Figure 7. From the perspective of slope vegetation, the anti-erosion performance of the Poa pratensis slope is better than that of the Bermuda grass slope; when the flow rate does not exceed 2.75 m·s⁻¹, the erosion resistance rate of the Poa pratensis slope is 12~15% higher than that of the Bermuda grass slope. Afterwards, the difference in corrosion resistance between the two gradually decreased. From the perspective of erosion factors, the role of flow velocity in scouring bank slopes and reducing erosion resistance is greater than that of the erosion angle; the maximum decrease in corrosion resistance due to flow velocity is 24~34%, while the maximum decrease in corrosion resistance due to impact angle is only 6.6~9.2%. These results are consistent with the results of Ng et al. [2,8,10,21].

When the flow velocity on the bank is below 2.0 m·s⁻¹, the erosion resistance of both types of ecological slope is relatively high: Poa pratensis slope, δr > 55%; Bermuda grass, slope δr > 45%. However, after the flow velocity on the bank has exceeded 2.0 m·s⁻¹, the aggregate erosion resistance of the two types of slope grass roots to the slope soil decreases. Both erosion resistance rates gradually decrease with the increase in flow velocity. When the flow velocity on the bank reaches 4 m·s⁻¹, the impact force of water flow on the bank slope greatly reduces the bonding force of the root–soil composite; so, the erosion resistance rate of the ecological slope δr drops to 24%.

It can also be seen In Figure 16b that an increase in the attack angle will reduce the anti-erosion performance of the ecological slope. The anti-erosion rate of the Poa pratensis slope is generally higher than that of Bermuda grass slope (6–8%), indicating that the Poa pratensis slope has better anti-erosion performance.

5. Conclusions

By means of scouring experiments, soil mechanical and composites tests, the erosion characteristics of ecological slopes planted with dominant grasses were assessed. Through on-site sampling, soil mechanical tests were conducted on three dominant grass root–soil composites and comparison soil. The soil mechanical and erosion indicators were analyzed, and the mathematical models were proposed based on the test data.

In order to simulate the flood mainstream flushing embankment slope, a hydraulic ecological test model that can adjust the inflow angle and flow velocity was designed, in which the vegetation of the bank slope could be replaced. By using the hydraulic ecological test model, the sand loss of the ecological slope could be collected precisely when conducting scouring experiments. Moreover, the average erosion depth and the data on the erosion amount were also measured and collected.

The soil mechanical indicators of the five types of soil under different loads were analyzed. It is indicated that the root–soil composite provides an additional cohesive force ∆c for the soil. Our experimental data show that the cohesive force of the soil was improved significantly, and the shear strength index was increased by 15 to 20%. The reasons for this should be the root system effect and reinforcement effect. The soil of the ecological slope is intertwined with plant roots and forms a root–soil composite, i.e., reinforced soil, which provides additional cohesion and greatly increases the shear strength. Moreover, the sticky substances secreted by plant roots can form gel-like material on the surface of soil particles and roots, increasing the adhesive forces between particles. These secretions can bind with water molecules in the soil, forming a gelatinous substance. The particles’ adhesive forces and the shear strength of the soil were further enhanced.

The average erosion depth reduction value ∆D_AE of Poa pratensis at various flow rates is generally slightly greater than that of Bermuda grass. When the scouring angle is constant, the ∆D_AE at each angle of the two plant slopes is the highest when the scouring velocity is 1.6 m·s⁻¹. After the velocity exceeds 1.6 m·s⁻¹, it gradually decreases. When the scouring velocity is constant, the ∆D_AE shows a decreasing trend as the scouring angle increases. Both planting grasses for the ecological slope demonstrated a good anti-erosion performance, and the root network has a good protective effect on sticky fine particles. At high-velocity flushing, the sand loss of the ecological slope was only 50~60% that of the plain soil slope; during vertical flushing, the sand loss on the plain soil bank slope was 1.73–2.43 times that of the ecological slope. The soil fixation and anti-erosion performance of Poa pratensis roots was shown to be better than that of Bermuda grass by 10~36%.