Open AccessArticle

Model Test of Dynamic Response of Living Poles Slope Under Train Loads

Guangdong Provincial Key Laboratory of Green Construction and Intelligent Operation & Maintenance for Offshore Infrastructure, Guangzhou Maritime University, Guangzhou 510725, China

School of Civil Engineering, Central South University of Forestry and Technology, Changsha 410018, China

Authors to whom correspondence should be addressed.

^†

These authors contributed equally to this work.

Appl. Sci. 2024, 14(23), 11355; https://doi.org/10.3390/app142311355

Submission received: 18 September 2024 / Revised: 2 December 2024 / Accepted: 2 December 2024 / Published: 5 December 2024

(This article belongs to the Special Issue Soil–Water–Plant–Atmosphere Interactions and Processes: Bioengineering of Slopes)

Download

Browse Figures

Figure 1
Profile of prototype slope. "> Figure 2
Model of the stump and rail: (a) Stump; (b) Rail. "> Figure 3
Construction of model box and layout of energy absorbing foam board: (a) construction of model box; (b) energy absorbing foam board. "> Figure 4
Layout of monitoring points in physical model. "> Figure 5
Layout of strain measuring points of living pole. "> Figure 6
Photo of slope model under excitation force. "> Figure 7
The curve of inspire force. "> Figure 8
Vertical dynamic pressure response data at different depths. "> Figure 9
Variation curve of peak pressure response with depth: (a) frequency; (b) axle load; (c) amplitude. "> Figure 10
Displacement distribution of slope under different axial loads. "> Figure 11
Time curve of strain of Z2 on pole A under working condition 1. "> Figure 12
Peak bending moment of the living poles under different axial loads: (a) bending moment of living poles A; (b) bending moment of living poles B; (c) bending moment of living poles C. "> Figure 13
The curve of stress of the lateral roots under working condition 2: (a) axial force of living poles A; (b) axial force of living poles B; (c) axial force of living poles C. ">

Review Reports Versions Notes

Abstract

Live stump-supported slopes are an environmentally friendly form of support that utilizes the powerful anchoring and reinforcing effects of deep-rooted plants to enhance slope stability. In order to ensure the safety and stability of embankment slopes during their service life, it is necessary to carry out research on the dynamic characteristics and stability of live stump slopes under train vibration loading. In this study, a large-scale indoor dynamic loading model test with a geometry of 1:7 was carried out on the live stump slope of a ballasted passenger railroad track to explore the attenuation characteristics of additional dynamic stresses, the dynamic displacement response law of the slope surface and the stress response characteristics of the live stumps, and to further investigate the influence of the live stumps on the stability of the slope under the dynamic loading. The results are as follows. (i) Additional dynamic stresses decayed at the bed surface and bed floor at a greater rate than the embankment body, and were significantly affected by dynamic loading when the vertical depth was less than 0.89 m. (ii) The dynamic displacement of the foundation bed is larger than that of the embankment body. The displacement response of the slope near the top and about 1/4 of the elevation of slope is the largest. (iii) The taproot of the living poles has many reverse bending points, and the bending moment of the taproot between the lateral roots shows the law of being larger on the top and smaller on the bottom. (iv) The slope facing has an amplifying effect on the vibration load of the train, and the farther away from the track, the smaller the amplifying effect. The research results have reference significance for the theoretical research and engineering application of living poles.

Keywords:

soil slope; train load; living poles; dynamic response; experimental study

1. Introduction

Plant roots have been widely used for the ecological protection of slopes because of their role in reinforcing shallow soils, alleviating topsoil erosion, preventing soil erosion, and being friendly to the environment [1,2,3]. The effectiveness of existing plant slopes to control deep landslides (>2 m) is limited by the fact that the root system of most plants is distributed in the shallow layer (1–2 m) of the ground surface [4]. Using living poles is a new form of plant slope support, which comprises living tree poles (willow or elm, etc.) with high vitality implanted into the deep soil layer or its branch cuttings inserted into the deep soil layer. After a period of time, the poles will grow roots and branches, thus playing the role of reinforcement and protection for the slope [5], aiming to enhance the stability of the slope through the reinforcement and anti-slip effect of its deep root system.

To date, it has been proven that living poles implanted in deep layers can achieve reinforcement of deep landslides, and their slope stability under static conditions is significantly improved compared with slopes without living poles [6,7,8]. Most of the model tests or numerical analyses for living pole support were studied under static conditions. Different types of living poles were planted on the slopes and the slopes were analyzed using the finite element software PLAXIS [9]. They demonstrated that the safety factor of the slope increased significantly due to the reinforcement effect of the living poles. The stability of the slope increased with the depth and the number of living poles set. In the medium and long term of the implanted living poles, the root system grew outward along the woody stem and formed a complex with the soil, which not only provided mechanical reinforcement, but also reduced the hydraulic conductivity of the soil to reduce the rainfall infiltration [10]. Living pole support has been applied as an engineering method for slope stabilization in high seasonal rainfall areas of natural forests in New Zealand to combat slope creep and more rapid slope movement [11,12]. Support slopes with willows, shrubs, and small tree species have proven effective in temperate regions such as Central Europe (Switzerland and Austria), the United Kingdom, and the United States [13,14].

The application of live stumps to embankment slopes of small height and gentle slope is a useful attempt, but the construction of a large number of railroads puts the embankment slopes in the high-intensity vibration environment of trains, which are inevitably subjected to periodic or non-periodic vibration loads in frequency and amplitude at any time, and the vibration load of the trains is the most direct causative factor of the dynamic response of the embankment slopes [15,16,17]. The literature contains very few studies that examine the dynamic response of the slopes supported by living poles under the action of dynamic train loads. It is important and urgent to investigate the dynamic response characteristics of the slopes supported by living poles.

Therefore, we designed and produced an indoor model of a soil embankment slope supported by living poles according to similar principles. We simulated the train vibration load on the slope by using a hydraulic pulsation testing machine, and studied the mechanical behavior and deformation of the living poles slope model under the action of train vibration, to provide a reference basis for the prevention and control of the road and railroad slope disasters.

2. Model Test of the Living Poles Slope Under the Action of Train Vibration

2.1. Original Slopes

A typical embankment slope site of a railway was selected for the model test. The section form of the embankment at the site was a non-electrified double-line passenger and freight common line railway ballast track structure. The design speed was 160 km/h, the embankment height was 10 m, the track bed with a thickness of 0.5 m was filled with graded gravel, and the foundation bed surface with a thickness of 0.6 m was filled with A1 gravel. The bottom layer of the foundation bed with a thickness of 1.9 m was filled with B1 soil, the embankment with a thickness of 7 m was filled with red clay, and the tilt angle of the slope was 1:1. The slope of the test model was strengthened by living poles. Three rows of piles were arranged, and the roots were simplified. The diameter of the taproot pile was 0.14 m in the upper part and 0.035 m in the lower part, the length of the taproot was 2.1 m, the length of the main side root was 1.05 m, and the distance between the poles was 2.6 m. The cross-sectional form is shown in Figure 1.

2.2. Similar Materials

In model testing, the similarity between the model and the prototype is crucial, and it determines the success or failure of the model simulation prototype. In order to make the model test truly reflect the dynamic characteristics of the prototype, the similarity relationship between the model and the prototype was derived by using the method of dimensional analysis. Since the prototype embankment slope was symmetrical from left to right, one side of the embankment slope was taken for simulation to save labor and material resources. The dimensions of the slope model in this test were about 2.5 m × 1.3 m × 1.6 m, and the dimensions of the original slope were about 17.5 m × 9.1 m × 11.2 m, with a dimensional similarity factor of seven. The main similarity constants of the model are shown in Table 1,

C = p r o t o t y p e / m o d e l

The model materials were composed of graded gravel, quartz sand, red clay, and water. The filling materials were selected for the slope model by trial matching method combined with geotechnical tests. The living poles as root analogs of complex geometry in the experiment were made of Acrylonitrile butadiene styrene (ABS) plastic by 3-D printing, which simulated strength (Tr) and stiffness (E) much more realistically than previously used materials (e.g., wood or rubber dowels) [18]. Due to material and technical limitations, simplified simulations of the root system of a living tree stump were required in the tests: (i) The root systems were all circular in cross-section, with the cross-sectional area decreasing linearly from the top to the bottom. (ii) The deformation of the root system in the test occurred within the elastic range. (iii) Only one main root and eight lateral roots were simulated. (The rest of the fine root system had less of an anchoring effect on the soil.) To increase the friction between the living poles and the soil, a layer of quartz sand was evenly glued on the surface of the living poles using epoxy resin as a binder. The completed live stump model was produced as shown in Figure 2a. Track structure simulation was mainly aimed at sleeper and rail components. The rail sleeper should have the necessary elasticity and sturdiness to enable it to fix the rail as well as the ability to resist transverse and longitudinal displacement. The rail must have sufficient bending stiffness, aiming to distribute the train load to more adjacent sleepers to reduce the concentrated load on a single sleeper. After calculating the similarity ratio, moment of inertia and bending stiffness, this test chose to select No. 5 hot-rolled ordinary channel steel (h is 50 mm, b is 37 mm) as the analog track, and fixed the contact position of the track and sleeper by spot welding. The rail model is shown in Figure 2b.

2.3. Model Box and Model Boundary Condition

In the model test, the selection of mold is extremely important, which needs to be stable and not easy to deform, and the space must meet the conditions of the size similar to the prototype. The main frame of the model box in this test was welded by 10-gauge hot-rolled channel steel, and the acrylic plate was laid inside and fixed on the channel steel frame by bolts. A medium and high-density black polyethylene foam board with a thickness of 5 cm was laid around the model box, which was used as the boundary energy absorbing material to weaken the dynamic boundary effect of the model box on the slope body. The headroom size was 2.75 m (length) × 1.28 m (width) × 1.78 m (height). The stratum and shape of the slope model were marked on the foam board. This is shown in Figure 3.

2.4. Filling the Embankment Slope

Artificial compaction was used in the test, and similar materials were stratified and compacted. After several trials of compaction, it was known that it was advisable to control the final compaction height of each layer at about 6 cm. According to the geotechnical test, the optimal moisture content of the soil used in the embankment body was 13%, and the maximum dry density was 1.87 g/cm³. According to the “Design Specification for Railway subgrade TB 10001-2016” [19], it was necessary to control the compaction coefficient K above 0.90, so the water content of the filling was controlled at 12–14%. The dry density had to be controlled above 1.69 g/cm³. The moisture content and compaction degree of the embankment body at different buried depths were measured, and the results are shown in Table 2.

2.5. The Layout Scheme of Monitoring Point

To study the dynamic response characteristics of embankment slopes and live stumps under different working conditions, a dynamic response monitoring system was arranged in the model. To monitor the variation law of soil pressure response with depth, the PV1~PV5 were the miniature earth pressure cells buried at 0.14 m, 0.39 m, 0.64 m, 0.89 m, and 1.14 m, respectively. To monitor the horizontal displacement of the slope, five displacement meters (D1~D5) were arranged on the central axis of the slope with a spacing of 0.3 m, as shown in Figure 4. Living poles with 3 × 3 dimensions were implanted in the slope, and strain gauges were pasted on the three living poles on the central axis. The three living poles were numbered from top to bottom as A to C. Seven strain measuring points were arranged on the primary root of poles A to C, and Z1 to Z7 was 4 cm, 9 cm, 12 cm, 15 cm, 18 cm, 22 cm, and 25 cm away from the top of the primary root for measuring the bending strain of primary root. Four strain measurement points, Aa1~Aa4 (X-directional growth) and Ab1~Ab4 (X-directional growth), were arranged on each of the two main lateral roots on the vertical slope of pole A. The distance of Aa1~Aa4 from the primary root was marked in Figure 5 as 2.5 cm, 4.5 cm, 6.5 cm, and 8.5 cm, respectively, for measuring the axial tensile and compressive strains of the lateral roots. Pole B and pole C were arranged with the same strain measuring points as pole A.

2.6. Vibration Exciter and Data Acquisition System

The model was loaded by a hydraulic pulsation test system, which consisted of an actuator, test force holding mechanism, counterforce frame, etc. The vibration exciter generated a periodic unidirectional pulsation that acted as a sinusoidal load on the top of the slope. The concentrated loads generated by the vibration exciter were converted into uniformly distributed loads acting on the track model by a distributive girder. This is shown in Figure 6. The test data acquisition system is the German imc CRONOSflex integrated measurement and control system, which has a signal bandwidth of up to 48 kHz per channel and a total sampling rate of up to 2 MSamples/s, covering almost all the frequency ranges of the physical, mechanical, and electromechanical signals, and it can simultaneously monitor a number of indicators, such as the slope dynamic soil pressure and the strain of the live stump.

2.7. Test Scheme of Exciting Force

The magnitude and running speed of the train load in the test were reflected by the output load and vibration frequency of the hydraulic pulsation test machine, which was the same method used in the tests of domestic and foreign parties [20,21]. The model was loaded under nine working conditions, and the vibration of each working condition sustained 3 s. The earth pressure and strain before each excitation were returned to zero, and only the dynamic stress response caused by the train load was considered. According to the model similarity rate and the railway train load schema in “Code for Design of Railway Subgrade”, four 250 kN axle loads were converted into line loads and then converted into the model. The dynamic load peak value of the servo shaker was calculated by the following formula:

P_{d} = \frac{P_{j}}{d \times C_{L}} \times l \times (1.4 + i) = \frac{250}{1.4 \times 7} \times 0.6 \times (1.4 + 0.5) = 29.1 k N

(1)

In the formula, the peak value of loads applied on the model was denoted as P_d. The axle loads were denoted as P_j. The space between axles was denoted as d. The geometric similarity ratio of the model was denoted as C_L. The longitudinal length of the model track was denoted as l. The combination coefficient of the live load was 1.4. The i was the impact factor and was taken as 0.5. The specific test conditions are shown in Table 3.

3. Dynamic Response of Living Poles Slope Under the Train Loads

The dynamic response of the embankment slope under nine action conditions consisting of different vehicle speeds, axle loads, and impact loads was studied. In order to verify the effect of the actuator, the pressure on the top of the model was analyzed first. The magnitude of the force feedback from the pressure sensor in real time under the action of working condition 2 is shown in Figure 7.

It can be seen from Figure 7 that the real-time feedback force of the pressure sensor is a sinusoidal load with a static load of 15 kN superimposed with an amplitude of 14.1 kN and a period of 1/3 s. The force is the same as the condition set in the excitation scheme, indicating that the actuator has an ideal excitation effect.

3.1. Dynamic Stress Response of Embankment Slope Under Train Load

The earth pressure response data at different depths under working condition 2 are shown in Figure 8.

As can be seen from Figure 8, when the vibration frequency is 3 Hz, the dynamic pressure at different depths of the embankment slope changes in a period of 1/3 s, with an obvious periodic peak. The curve of earth pressure is similar to the waveform of the test force, indicating that the response of earth pressure in the embankment slope has a good corresponding relationship with the excitation force.

3.1.1. Variation Law of Earth Pressure Response Peak with Different Train Loads

The variation curves of the peak earth pressure at different depths under different excitation frequencies, coaxial loads, and vibration amplitudes are shown in Figure 9. It can be seen from Figure 9a that the earth pressure was gradually improving with the raising of the excitation frequency. It is also noted that the earth pressure of the bed surface layer increased by 5.2% and 7.5%, respectively, during the raising of excitation frequency from 2 Hz to 4 Hz (using 2 Hz data as the reference point), which indicates that the increase of train speed and the rise of excitation frequency will lead to the improvement of earth pressure of the bed surface layer, and with the increase of depth, the sensitivity of earth pressure changes with frequency decreases. The earth pressure decayed rapidly along the depth direction. Taking the 0.14 m data as the reference, the earth pressure at the bottom of the foundation bed decayed by 43.6%, and the earth pressure at the embankment body decayed by 63.5%, 86.9%, and 86.5%, respectively. The slope of the change curve shows that the decay rate of soil pressure is gradually decreasing with the increase of burial depth, showing a trend of first fast and then slow. Another observation was that the depth that was influenced by the train loads was 0.89 m, and the earth pressure had decayed very little beyond 0.89 m. When the buried depth was below 0.89 m, the earth pressure was similar in magnitude, which was less affected by the train loads. The reason for this rule is mainly related to the gravel grading, the thickness of the ballast layer, and the mechanical properties of the embankment filling. The gravel grading meets requirements, and the ballast thickness slightly exceeds specification, and the embankment filling is mainly silty clay, resulting in the test of the embankment slope damping being larger.

As can be seen from Figure 9b, with the raise of axle load, the earth pressure gradually increases. In the process of the axle load increasing from 12.24 kN to 20.52 kN (taking 12.24 kN data as the reference point), the earth pressure on the surface of the foundation bed improved by 14.5%, 23.8%, and 34.3%, respectively. It is interesting to observe that the increase in train axle load led to the improvement of the soil pressure on the surface layer of the bed. The slope of the change curve shows that the sensitivity of earth pressure with the change of static axial load decreases with the increase of depth. As shown in Figure 9c, with the improvement of vibration amplitude, the earth pressure gradually increases. In the process of the vibration amplitude improving from 11.1 kN to 20.1 kN (taking 11.1 kN data as the reference point), the earth pressure on the surface of the foundation bed increased by 9.7%, 15.1%, and 20.6%, respectively. Increasing the train’s vibration amplitude resulted in higher soil pressure on the surface layer of the bed. The slope of the change curve shows that the sensitivity of the soil pressure to the change in vibration amplitude decreases with increasing depth. The greater the vibration frequency is borne by the embankment surface, the higher the axial load and vibration amplitude, and the faster the attenuation speed of earth pressure in the embankment. It is shown in the figure that the larger the earth pressure is, the greater the absolute value of the slope of the attenuation curve is. Another observation was that the increased rate of earth pressure in different axial load conditions was greater than in different vibration amplitude conditions. However, it is interesting to observe that the 2.76 kN of the increase step by step of axle load is less than the 3 kN of the improved step-by-step of vibration amplitude. It shows that the influence of the axial load on the earth pressure of the embankment slope is greater than that of the vibration amplitude.

3.1.2. Distribution Law of Slope Displacement of the Embankment Slope

By analyzing the influence of loads on earth pressure, it is found that the peak value of earth pressure is larger in different axial load conditions. Therefore, the displacement distribution of the slope surface under different axial loads is analyzed in this paper. Figure 10 shows the displacement distribution of the slope surface under the action of the axial load from 12.24 kN to 20.52 kN, with the slope foot as the zero point in elevation.

As can be seen in Figure 10, the maximum displacement of the slope surface occurred in the foundation bed. With the decrease in elevation, the displacement of the slope surface gradually reduced, and the displacement increased at about 1/4 of the slope elevation from the slope foot, and the displacement near the slope foot was the smallest. Measuring points D1 and D2 were most affected by the change in train axle load. The dynamic displacement amplitude improved with the increasing of the axle load. D3, D4, and D5, the lowest of the height of measuring points, were less affected by the change of train axle load. This is similar to the experimental conclusion drawn by Wenbin Jian that the closer the measurement point on the slope is to the load source and the higher the load intensity, the stronger its response to the load [22]. This indicates that the influence of train load on slope displacement gradually decreases with the increase of distance, which may be caused by the attenuation of moving earth pressure in the slope body. In engineering, to enlarge the survival rate of living poles and reduce the impact of vibration load on their growth, living poles should be implanted on the embankment body, especially near the upper part of the embankment body, and about 1/4 of the slope elevation from the slope foot should be strengthened.

3.2. Dynamic Stress Response Law of Living Poles Under Train Load

In the test process, the taproot and lateral roots of living poles produced a strain response, and the bending moment and stress at the corresponding measurement point can be calculated by

M = W ∙ ε ∙ E_{s}

and

σ = ε ∙ E_{s}

. The bending moment of the taproot of the living poles is M, the stress of the lateral root of the living poles is σ, the flexural cross section coefficient of the taproot section is W, the elastic modulus of the living poles is E_s, and the strain generated by the root system is ε.

3.2.1. Bending Moment of Taproot of Living Poles

The strain time–history curve of measuring point Z2 on living pole A in working condition 1 is shown in Figure 11.

There was no additional load on the slope before 400 s, so the curve fluctuation before that time had nothing to do with the train load. In the process of vibration excitation, the train load deformed the slope body, and then the strained the living poles, so the bending moment of the pole body gradually increased. As can be seen from Figure 11, the fluctuation amplitude of the bending moment of the living poles in the excitation process is the same as that before the excitation. The repeated tension and compression deformation of the living poles cannot be caused because the soil dynamic stress is transmitted to the living poles decays to a smaller value, leading to no significant change in the amplitude of the bending moment.

The distribution of the peak bending moment of the taproot under different coaxial loads is shown in Figure 12. The measuring point with a buried depth of 25 mm on the living pole B failed to collect data. And the buried depth in Figure 12 refers to the vertical distance between the measuring point and the slope surface.

As can be seen from Figure 12, the larger the axle load of the train, the larger the bending moment generated by the living poles. This rule is especially obvious at the measuring point with a depth of 9 cm. It may be that when the axle load is larger, the earth pressure transmitted by the soil to the living poles is greater, and then the living poles produce a bigger bending moment. The bending moment generated on the taproot segment between the buried depth of 9 cm and 14 cm gradually decreased to 0 with the increase of the buried depth, while the bending moment generated on the taproot segment between the buried depth of 14 cm and 18 cm gradually enlarged with the increase of the buried depth. As can be seen from Figure 12, the bending moment between the buried depth of 9 cm and 18 cm changes almost linearly. The reason for this rule may be that the deformed soil exerts an X-direction horizontal force on the taproot, under the action of the load, a reverse bending point b was produced. Between the taproot and lateral root, the upper around 2/3 taproot was X side in tension, and approximately 1/3 of the lower section was under tension on the opposite side. It is agreed that the bending moment is negative when the taproot is under tension on the X side.

As the slenderness ratio of the taproot is relatively big, it is a flexible structure, so it is easy to produce many anti-bending points in the process of supporting. The peak bending moment distribution diagrams in Figure 12 all show three inflection points. The position of the inflection point a and c are very close to the lateral roots, probably due to the rigid connection between the lateral roots and the taproots. The forces generated by the deformation of the lateral roots are simplified to stresses and bending moments in different directions at the rigid nodes, and the bending moments at the rigid nodes make the bending moments on the taproots change abruptly, so the taproots have opposite moments above and below the lateral roots. The inflection points shown in Figure 12 do not overlap with the positions of the lateral roots due to the errors in the positions of the monitoring points and the test data.

3.2.2. Stress Distribution of Lateral Roots

The stress time–history curves of the measuring points on the lateral roots of the living poles under the excitation condition 2 are shown in Figure 13. Due to the damage of the strain gauge, the stress measurement points at Aa2, Ba2, and Bb2 had no data.

As can be seen from Figure 13, under the same working condition, lateral roots with different directions are subjected to opposite tensile and compressive stresses. The lateral roots of living poles A and B pointing in the direction of X were subjected to compressive stress, and the lateral roots in the direction of X were subjected to tensile stress. Lateral roots growing toward the inside of the slope face produce a positive axial force and are subject to tensile stress, which exerts the tensile strength of the root system when supporting the slope; lateral roots growing toward the outside of the slope face produce a negative axial force and are subject to compressive stress, which exerts the compressive strength of the root system when supporting the slope. The tensile force of the inner roots of the live stump and the pressure of the outer roots together play the role of stabilizing the main root of the live stump. The inner roots are similar to anchors and the outer roots are similar to supports, which together enhance the role of the main root as a sliding pile, and thus it can be seen that the root system of the live stump has a relatively stable structure when supporting slopes.

In contrast, the middle of the lateral root on the living pole C, which pointed towards X, was subjected to tensile stress, and the lateral root in the opposite direction of X was subjected to compressive stress. This phenomenon may be caused by slope deformation. As the soil under the sleeper was squeezed by the train loads, its compactness was increased, and the slope surface within the elevation of living poles A and B produced shrinkage deformation. The lateral root in the opposite direction of X was affected by the shrinkage of the soil, resulting in tensile stress. The force generated by the shrinkage deformation was mainly borne by the lateral root and the taproot perpendicular to the x-direction, and the lateral root in the x-direction was subjected to the deformation of the slope soil in the opposite direction to X, resulting in compressive stress. The lateral root of living poles in the opposite direction of X located at the foot of the slope was subjected to compressive stress due to the soil expanding outward. By comparing the stress of the lateral root in the X direction of living poles A and B, it can be seen that the compressive stress of the lateral root of pole A is significantly greater than that of pole B, mainly because of the large shrinkage deformation in the elevation of pole A. Therefore, attention should be paid to the expansion of soil around the slope foot and the retraction of a slope near the foundation bed in the process of supporting.

The stress fluctuation peak of the lateral roots of the three piles at the same distance from the slope is marked in Figure 13. Number b4 is 26 cm away from the slope, and a4 is 8 cm away from the slope. By comparing the stress fluctuation amplitude of two lateral roots of the same living pole, it can be seen that the stress fluctuation amplitude of lateral root X of pole A and pole B is significantly larger than that of reverse lateral root X, indicating that the slope face has amplification effect on train vibration load. This amplification effect is influenced by elevation. The stress fluctuation amplitude of Aa4 was about 2.88 kPa for pole A located at the top of the slope, 1.79 kPa for Ba4 on pole B located in the middle of the slope, and 1.71 kPa for Ca4 on pole C located at the foot of the slope, indicating that the amplification effect for vibration is smaller as the slope is further away from the train load.

4. Discussion

4.1. Transfer of Dynamic Additional Stress in the Slope Body

The classical Boussinesq’s formula and Burmister’s theory of soil stress distribution calculation are based on some assumptions for derivation, such as that the concentrated force acts on the surface of the elastic half-space, the soil layer is an isotropic elastomer, and there is no positive and shear stresses outside the range of the first layer of the surface load distribution of the soil, etc. These are aimed at providing theoretical solutions to stresses and displacements of single-layer and multilayer elastic systems subjected to axisymmetric loads. Theoretical solutions for stresses and displacements are the basic theory for soil simulation and selected influences.

In this test, the embankment side slopes and live stumps make the constraints in the direction of adjacent slopes disappear, and the additional stresses in the foundation appear in the form of asymmetric diffusion. The ballast layer leads to a very complicated load distribution on the surface of the first soil layer, and it is not possible to substitute the test values into the basic theory equations to verify the additional stress transfer law of the embankment slope with live stumps under train loading. However, the additional stress in the vertical direction in the basic theory is inversely proportional to the square of the depth, and the additional stress decays downward, and the decay rate is upward fast and downward slow, which is similar to the law obtained in this paper.

It is difficult to predict with the help of theoretical equations how the load transfer in the slope will change under the specific influence of live stumps, so it is essential to use model tests or finite element simulations that can reflect real train loads in the study of power transfer in roadbeds. According to the results obtained from the finite element calculation model, the root system of the live stump, which forms the “anchor-support” effect, redistributes the soil stress, resulting in the concentration of shear stress in the soil near the live stump, which is especially significant at the toe of the slope. The presence of live stumps hinders the transfer of soil shear stresses and inhibits the connectivity of the plastic zone of the soil [23].

4.2. The Effect of Living Poles on the Stability of the Embankment Slope

According to the existing theories [24,25], it is speculated that the taproot of the living poles plays a role similar to that of the anti-slip pile in the slope. The uneven displacement will happen in the soil at the loaded end. Due to the heterogeneity of displacement, the soil particles will be compressed and “wedged” with each other, resulting in an “arch effect” in a certain range of soil layers. Since the geometric properties of the living poles are quite complex, it is difficult to describe the distribution and morphology of the soil arches in the soil as in the case of pile foundations, but the basic generation mechanism is similar. The root anchored into the sliding bed at a certain depth is used to stabilize the sliding body from slipping out between the roots utilizing frictional resistance with the living pole stress section and the soil behind the pole and the roots to form a soil arch effect. According to the conclusion of the research [26], the growth pattern of lateral roots can form a reticulation structure, which can effectively bind soil particles, and the vertical root system has higher stiffness and tensile strength, and grows vertically along the depth direction, which is the skeleton of the whole reticulation structure. Under the joint action of the taproot and lateral root systems, a strong overall structure is formed, which can withstand the shear stress of the soil and ultimately improve the stability of the slope.

In the process of supporting slopes, the hydrological function of living poles also plays a crucial role, and the hydrological function of living poles under dynamic load is also worth studying. The material of the living poles used in this paper is the same as Liang and Knappett et al., although it can simultaneously model the stiffness, strength, and complex structure of the root, and can better simulate the strength and stiffness of the root system than traditional materials (wood or rubber pins) [27]. This material cannot simulate the hydrological characteristics of the root system. Bengough A used young roots of plants to simulate mature roots for centrifuge tests. He believed that when appropriate growth time (2 months) and scaling factor (N = 15) were selected, young plants could simulate mature roots in terms of the mechanical and hydrological effects of roots [18]. If more studies prove the usefulness of young roots, it will be feasible to study the mechanical and hydrological interactions between living poles and soil under dynamic loading in tests.

5. Conclusions

In this paper, we designed and completed the dynamic response model test of the slope supported by living poles under the train load. The distribution of earth pressure, slope displacement response, and the force of living poles under different excitation forces and different excitation frequencies were compared and analyzed. The main conclusions are as follows.

(1): With the increase of excitation frequency, peak value under excitation, and excitation amplitude, the earth pressure on the embankment slope improve continuously, which reflects that the higher the train speed, the larger the train axle load and the greater the impact load caused by track unevenness, the more significant the dynamic response of the embankment slope is. For the living poles embankment slope in this test, the earth pressure gradually decays along the depth direction, with the rate of decay being faster on the upper and slower on the lower. The attenuation is faster on the surface of the foundation bed and at the bottom of the foundation bed than in the body of the embankment, and the depth mainly affected by the dynamic load is about 0.89 m.
(2): The dynamic displacement of the slope surface increases with the raising of the train axle load, and the dynamic displacement of the bed layer is larger than that of the embankment slope body. However, the foundation bed is not suitable for the support of living poles. For the body of the embankment slope, the displacement response of the upper part of the embankment slope body and the position about 1/4 slope elevation from the slope foot is the largest. When the support of living poles is carried out, the support should be strengthened at these two positions.
(3): The bending moment of the taproot and the stress of the lateral root increase with the raising of the train axle load, and the stress response of the living pole located at the slope top of the embankment is the largest. By comparing and analyzing the stress amplitudes of the measured points on the lateral root with different distances from the slope surface, it is known that the slope face has an amplification effect on the train vibration load, and the farther away from the track, the smaller the amplification effect is. In addition, due to the presence of lateral roots, the taproot of the living stump had multiple points of contra flexure, and the bending moment of the taproot part between the lateral roots showed a law of larger on the top and smaller on the bottom.

Author Contributions

All authors contributed to this study’s conception and design. conceptualization and funding acquisition, X.J.; Investigation, writing—original draft preparation, Z.W.; supervision and validation, H.Y.; data curation and formal analysis, H.W. All authors commented on previous versions of the manuscript. All authors have read and agreed to the published version of the manuscript.

Funding

This study was supported by the Special Projects in Key Fields of Higher Education in Guangdong Province (2023ZDZX4044), the Special Projects in Key Fields of Higher Education in Guangdong Province (2023ZDZX4045), the Research Capacity Enhancement Project of Key Construction Discipline in Guangdong Province (2022ZDJS092), the National Natural Science Foundation of China (31971727), the Forest Science and Technology Innovation Program of Hunan Province (XLK202105-3), and supported by Hunan Provincial Natural Science Foundation of China (2022JJ31005).

Institutional Review Board Statement

Not applicable.

Informed Consent Statement

Not applicable.

Data Availability Statement

The original contributions presented in the study are included in the article, and further inquiries can be directed to the corresponding authors.

Conflicts of Interest

The authors declare no conflicts of interest.

References

Zhu, H.; Zhang, L. Root-soil-water hydrological interaction and its impact on slope stability. Georisk Assess. Manag. Risk Eng. Syst. Geohazards 2019, 13, 349–359. [Google Scholar] [CrossRef]
Yamase, K.; Todo, C.; Torii, N.; Tanikawa, T.; Yamamoto, T.; Ikeno, H.; Ohashi, M.; Dannoura, M.; Hirano, Y. Dynamics of soil reinforcement by roots in a regenerating coppice stand of Quercus serrata and effects on slope stability. Ecol. Eng. 2021, 162, 106169. [Google Scholar] [CrossRef]
Wang, X.; Hong, M.-M.; Huang, Z.; Zhao, Y.-F.; Ou, Y.-S.; Jia, H.-X.; Li, J. Biomechanical properties of plant root systems and their ability to stabilize slopes in geohazard-prone regions. Soil Tillage Res. 2019, 189, 148–157. [Google Scholar] [CrossRef]
Xu, Z.-M.; Huang, R.-Q.; Tang, Z.-G.; Wang, S.-D. Limitations of biotechnical slope protection and contribution of vegetation to deep seated landslide preparation. Yanshilixue Yu Gongcheng Xuebao/Chin. J. Rock Mech. Eng. 2005, 24, 438–450. [Google Scholar]
Schiechtl, H.M.; Stern, R. Ground Bioengineering Techniques for Slope Protection and Erosion Control; Wiley-Blackwell: Hoboken, NJ, USA, 1996. [Google Scholar]
Zhu, Y.; Yang, H.; Liu, Y.; Jiang, X.; Deng, R.; Huang, L.; Yin, P.; Lai, G. Numerical simulation of the combined slope protection effect of living stump and bamboo anchor. Geotech. Geol. Eng. 2021, 40, 635–645. [Google Scholar] [CrossRef]
Niu, J.; Zhou, Y.; Zhang, J.; Duan, D.; Chen, K.P. Tensile strength of root and soil composite based on new tensile apparatus. J. Southwest JiaoTong Univ. 2022, 57, 191–199. [Google Scholar]
Niu, J.; Zhang, J.; Yan, S.; Jiang, X.; Wang, F. Seismic stability analysis of shallow overburden slopes with vegetation protection. Environ. Earth Sci. 2024, 83, 477. [Google Scholar] [CrossRef]
Prasad, A.; Kazemian, S.; Kalantari, B.; Huat, B.B.; Mafian, S. Stability of tropical residual soil slope reinforced by live pole: Experimental and numerical investigations. Arab. J. Sci. Eng. 2012, 37, 601–618. [Google Scholar] [CrossRef]
Kamchoom, V.; Leung, A.K. Hydro-mechanical reinforcements of live poles to slope stability. Soils Found. 2018, 58, 1423–1434. [Google Scholar] [CrossRef]
Stokes, A.; Atger, C.; Bengough, A.G.; Fourcaud, T.; Sidle, R.C. Desirable plant root traits for protecting natural and engineered slopes against landslides. Plant Soil 2009, 324, 1–30. [Google Scholar] [CrossRef]
Zhang, J.-J.; Niu, J.-Y.; Fu, X.; Cao, L.-C.; Xie, Q. Shaking table test of seismic responses of anchor cable and lattice beam reinforced slope. J. Mt. Sci. 2020, 17, 1251–1268. [Google Scholar] [CrossRef]
Leal, D.; Winter, M.G.; Seddon, R.; Nettleton, I.M. A comparative life cycle assessment of innovative highway slope repair techniques. Transp. Geotech. 2020, 22, 100322. [Google Scholar] [CrossRef]
Maffra, C.R.B.; Sousa, R.d.S.; Sutili, F.J.; Pinheiro, R.J.B. Evaluation of live cuttings effect on slope stability. Floresta Ambiente 2018, 26, e20170738. [Google Scholar] [CrossRef]
Ren, X.; Wu, J.; Tang, Y.; Yang, J. Propagation and attenuation characteristics of the vibration in soft soil foundations induced by high-speed trains. Soil Dyn. Earthq. Eng. 2019, 117, 374–383. [Google Scholar] [CrossRef]
Tang, Y.; Yang, Q.; Ren, X.; Xiao, S. Dynamic response of soft soils in high-speed rail foundation: In situ measurements and time domain finite element method model. Can. Geotech. J. 2019, 56, 1832–1848. [Google Scholar] [CrossRef]
Qu, S.; Yang, J.; Zhu, S.; Zhai, W.; Kouroussis, G.; Zhang, Q. Experimental study on ground vibration induced by double-line subway trains and road traffic. Transp. Geotech. 2021, 29, 100564. [Google Scholar] [CrossRef]
Liang, T.; Bengough, A.; Knappett, J.; MuirWood, D.; Loades, K.W.; Hallett, P.D.; Boldrin, D.; Leung, A.K.; Meijer, G. Scaling of the reinforcement of soil slopes by living plants in a geotechnical centrifuge. Ecol. Eng. 2017, 109, 207–227. [Google Scholar] [CrossRef]
TB 10001-2016; Code for Design of Railway Earth Structure. Chinese National Standard: Beijing, China, 2016.
Cox, S.; Wang, A.; Morison, C.; Carels, P.; Kelly, R.; Bewes, O. A test rig to investigate slab track structures for controlling ground vibration. J. Sound Vib. 2006, 293, 901–909. [Google Scholar] [CrossRef]
Liu, H.; Sun, G.; Kong, G.; Li, H. Experimental study on dynamic soil pressure distribution law of X-shaped pile-raft composite foundation for ballastless track. Chin. J. Geotech. Eng. 2016, 38, 1933–1940. [Google Scholar]
Jan, W.B.; Hu, Z.Z.; Fan, X.F. Response of slope to cyclic loading. J. Rock Mech. Eng. 2008, 27, 2562–2567. [Google Scholar]
Jiang, X.L.; Wang, Z.H.; Yang, H. Dynamic response law and stability of living stump slopes under train loading. J. Vib. Eng. 2023, 1–10. [Google Scholar]
Long, J.; Li, M.; Cui, L.; Zhang, L.; Lu, J. A method for calculating stabilizing pile spacing by integrating the mechanical characteristics of soil arching. Arab. J. Geosci. 2022, 15, 299. [Google Scholar] [CrossRef]
Zhuang, Y.; Wang, K. Finite element analysis on the dynamic behavior of soil arching effect in piled embankment. Transp. Geotech. 2018, 14, 8–21. [Google Scholar] [CrossRef]
Jiang, X.L.; Liu, W.J.; Yang, H. Study on Mechanical Characteristics of Living Stumps and Reinforcement Mechanisms of Slopes. Sustainability 2024, 16, 4294. [Google Scholar] [CrossRef]
Liang, T.; Knappett, J.; Bengough, A.; Ke, Y.X. Small-scale modelling of plant root systems using 3D printing, with applications to investigate the role of vegetation on earthquake-induced landslides. Landslides 2017, 14, 1747–1765. [Google Scholar] [CrossRef]

Figure 1. Profile of prototype slope.

Figure 2. Model of the stump and rail: (a) Stump; (b) Rail.

Figure 3. Construction of model box and layout of energy absorbing foam board: (a) construction of model box; (b) energy absorbing foam board.

Figure 4. Layout of monitoring points in physical model.

Figure 5. Layout of strain measuring points of living pole.

Figure 6. Photo of slope model under excitation force.

Figure 7. The curve of inspire force.

Figure 8. Vertical dynamic pressure response data at different depths.

Figure 9. Variation curve of peak pressure response with depth: (a) frequency; (b) axle load; (c) amplitude.

Figure 10. Displacement distribution of slope under different axial loads.

Figure 11. Time curve of strain of Z2 on pole A under working condition 1.

Figure 12. Peak bending moment of the living poles under different axial loads: (a) bending moment of living poles A; (b) bending moment of living poles B; (c) bending moment of living poles C.

Figure 13. The curve of stress of the lateral roots under working condition 2: (a) axial force of living poles A; (b) axial force of living poles B; (c) axial force of living poles C.

Table 1. Similarity constants of model.

Physical Quantity	Similarity Relation	Similarity Factor	Postscript
$Size (L$ )	$C_{L}$	7	controlled quantity
$Density (ρ$ )	$C_{ρ}$	1	controlled quantity
$elasticity modulus (E$ )	$C_{E}$	1	controlled quantity
$cohesive force (c$ )	$C_{c} {= C}_{E}$	1
$internal friction angle (φ$ )	$C_{φ}$	1
$poisson ratio (μ$ )	$C_{μ}$	1
$Load (P$ )	$C_{P} {= {(C_{L})}^{2} C}_{ρ}$	49
$Frequency (f$ )	$C_{f} = {(C_{L})}^{- 1} {(C_{ρ})}^{- 1 / 2} {(C_{E})}^{1 / 2}$	0.14
Displacement (u)	$C_{u} {= C}_{L}$	7
$Strain (σ$ )	$C_{σ} {= C}_{E}$	1
Time (t)	$C_{t} = (C_{L}) {(C_{ρ})}^{1 / 2} {(C_{E})}^{- 1 / 2}$	7

Table 2. Relevant physical property indexes of embankment body.

Burial Depth/m	Moisture Content/%	Dry Density/g∙cm⁻³	Compacting Factor/K
−0.45	12.3	1.79	0.96
−0.65	11.9	1.78	0.95
−0.85	12.5	1.78	0.95
−1.05	13.1	1.85	0.98
−1.25	12.8	1.76	0.94

Table 3. Conditions of excitation test.

Working Conditions	Frequency/Hz	Axle Load/kN	Amplitude/kN	Peak/kN
1	2	15	14.1	29.1
2	3	15	14.1	29.1
3	4	15	14.1	29.1
4	3	12.24	14.1	26.65
5	3	17.76	14.1	31.86
6	3	20.52	14.1	34.62
7	3	15	11.1	25.1
8	3	15	17.1	32.1
9	3	15	20.1	35.1

Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content.

© 2024 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

Share and Cite

MDPI and ACS Style

Jiang, X.; Wang, Z.; Yang, H.; Wang, H. Model Test of Dynamic Response of Living Poles Slope Under Train Loads. Appl. Sci. 2024, 14, 11355. https://doi.org/10.3390/app142311355

AMA Style

Jiang X, Wang Z, Yang H, Wang H. Model Test of Dynamic Response of Living Poles Slope Under Train Loads. Applied Sciences. 2024; 14(23):11355. https://doi.org/10.3390/app142311355

Chicago/Turabian Style

Jiang, Xueliang, Zihao Wang, Hui Yang, and Haodong Wang. 2024. "Model Test of Dynamic Response of Living Poles Slope Under Train Loads" Applied Sciences 14, no. 23: 11355. https://doi.org/10.3390/app142311355

APA Style

Jiang, X., Wang, Z., Yang, H., & Wang, H. (2024). Model Test of Dynamic Response of Living Poles Slope Under Train Loads. Applied Sciences, 14(23), 11355. https://doi.org/10.3390/app142311355

Note that from the first issue of 2016, this journal uses article numbers instead of page numbers. See further details here.

Article Menu