# Microscopic Bearing Behavior of Horizontally Loaded Vertical Plate Anchors in Sandy Soil

Authors: Sifeng Zhang; Yushuai Wang; Chao Li; Qing Li; Dong Yang
Journal: Advances in Civil Engineering
 (2022)

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## Abstract

Vertical plate anchors are an effective technique to enhance the stability of various structures, such as retaining walls and sheet piles. More research has been devoted to their bearing capacity and macroscopically affecting parameters, while less research can be found on their microscopic bearing behavior. In this paper, the microscopic bearing behavior of vertical plate anchors subjected to a horizontal pullout load in sandy soil was investigated with the particle flow code (PFC) based on the model test results. Results show that the larger-sized anchor plates withstand greater soil pressure and affect a broader range of soil during the pullout process. The soil not behind the anchor plate is pressed, and the pressure in front of the anchor plate increases with increasing size. The soil close to the plate anchor suffers larger pressure while the soil far away from the plate anchor is less affected, and the soil is redistributed to a more stable state during the pullout process of the plate anchor. The particles with a long axis distributed in the horizontal direction are the most stable, while those with a long axis distributed in the vertical direction are the most unstable.


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## Body

## 1. Introduction

Plate anchors are widely used in rock and soil anchoring engineering because of their simple installation and low cost. The vertically installed plate anchor, by which the drawing force of the rod or cable is converted into the compressive stress on the surrounding but not behind rock or soil, provides an effective technique to enhance the stability of different structures. Because of its excellent bearing capacity and deformation resistance, the vertical plate anchor is often used in permanent anchoring engineering, such as retaining walls, sheet piles, etc. [1, 2]. Because the bearing capacity design has been a focus [3], the bearing behavior of vertical plate anchors becomes critical for its theoretical basis significance.At present, many hypotheses and theoretical methods have been used to analyze and study the working mechanism of plate anchors. Cheng et al. [4] established a finite element model to calculate anchor resistance, and determined the method of the overall cyclic loading coefficient Ucy∗ to determine the cyclic anchor resistance. Ali and Aziz [5] studied the uplift ability of horizontal anchor plates in non-cohesive soil and concluded that the ultimate uplift capacity of anchor plate increases with an increase in the burial depth of the anchor plate. Cheng et al. [6] used the three-dimensional finite element method to simulate the cyclic deformation process of vertically loaded anchors (VLAs) in soft soil, determined the failure displacement of VLAs under shallow and deep-embedded conditions, and revealed the variation rule of cyclic displacement, average displacement, and the cyclic bearing capacity of anchor bolts with the number of cycles. Al Hakeem and Aubeny [7] adopted the large deformation finite element (LDFE) analysis method to determine the bearing capacity and motion characteristics of vertical strip plate anchor in uniform non-cohesive soil. Jesmani et al. [8] used the finite element method to determine the pulling-out resistance of anchor plates at different positions in different soils and concluded that the pulling-out resistance of plates with deeper burial depths increases with size. Based on discrete element method (DEM), Evans and Zhang [9] concluded that when the burial depth is shallow, no matter if the particle combination is dense or loose, the rupture coefficient linearly increases with an increase in burial depth ratio. In addition, the roughness of the bolt has little influence on the resistance of the plate anchor. El Sawwaf and Nazir [10] concluded that adding row piles in front of a bolt can improve the ultimate bearing capacity of the bolt plate. Pile row, pile length, pile spacing, pile diameter relative to anchorage plate position, and pile inclination affect the anchorage ability. Based on the finite element method, Chen et al. [11] studied the soil failure mechanism of a square plate in the drawing process of non-heavy earth and self-weight earth. They observed three different types of pulling-out failure. Bhattacharya [12] used the 3D finite element method (3D-FEM) to establish a reference solution of the ultimate translational resistance through plastic limit analysis and found that shear resistance decreases with increased plate length and is less affected by plate thickness. Niroumand et al. [13] conducted a parameterization study on symmetric anchor plates. They concluded that, compared with square and circular anchor plates, rectangular anchor plates have a higher pulled-out response, and symmetric rectangular anchor plates have greater lifting resistance in deeper burial depths. Tho et al. [14] used the finite element method to conduct simulation tests and concluded that the pullout force of a plate anchor in soil with a linear increase in strength was lower than that in uniform soil. Tilak and Samadhiya [15], through the ultimate pullout ability test of a multi-plate horizontal bolt, determined that, compared with a single-plate bolt, the pullout ability of a multi-plate bolt in shallow layers decreased and that of a multi-plate bolt in deep layers increased. Choudhary and Dash [16] showed that plate anchor failure displacement and bearing capacity are closely related to soil density and burial depth. Srinivasan et al. [17] studied the interaction of anchor groups and concluded that when the anchor spacing is smaller, the displacement is larger, and the pulling force is smaller. Zhang et al. [18] studied the pullout characteristics of plate anchor in structural soft clay in combination with laboratory tests and finite element analysis. Han et al. [19] used centrifugal tests and LDFE analysis to determine the performance of a plate anchor under continuous loading in normally consolidated clay. They established the continuous uplift deformation mechanism of soil around the anchor under different mono-bearing capacity ratios. Sabermahani and Nasirabadi [20] used particle image velocimetry (PIV) technology to found that the pullout ability and sand deformation of a bolt are greatly affected by the burial depth. Kumar and Rahaman [21] concluded that the vertical pullout resistance of water plate anchors in sand decreased with an increase in the eccentricity and vertical incline angle. Athani et al. [22] adopted the discrete element method to found that both the ratio of a bolt to grain size and the angle of internal friction in sandy soil affect the pull ability. Through model experiments, Yang et al. [23] concluded that the pullout resistance of a bolt with a plate is affected by the slope foot and margin ratio, and the peak resistance of a bolt decreases with an increase in the slope foot and increases with an increase in the margin ratio. Liu et al. [24] used digital image cross-correlation (DIC) technology to determine that the unearthed density and the embedded depth of anchor significantly impact the pullout performance of a plate anchor and soil deformation. Liu et al. [25] obtained the prediction method of the pullout capacity coefficient of a rectangular bolt with a wide range of parameters by using the finite element method. Yang et al. [26] proposed an analysis method for a plate anchor to evaluate the ultimate embedding depth and bearing capacity.Although numerous studies have been devoted to the bearing behavior of vertical plate anchors, the present body of work is concentrated on the macroscopic bearing capacity. For the microscopic bearing behavior of vertical plate anchors, such as the state variation of the soil particles, less work can be found. Therefore, it is necessary to conduct further studies on vertical plate anchor’s microscopic bearing mechanical evolution. In this paper, by employing particle flow code (PFC), the microscopic bearing behavior of the vertical plate anchor was investigated based on the model test results. The results provide a theoretical basis for plate anchor design and guidance for engineering practice.


## 2. Model Test of Plate Anchor

### 2.1. Test Scheme and Design

When plate anchor anchors soil, the surrounding soil’s displacement is difficult to observe. There are few studies on microscopic deformation of the surrounding soil. Moreover, monitoring the stress variation of an anchor plate in practical engineering requires an extended period, and the test results are difficult to obtain in real-time. In this paper, digital photographic deformation measurement technology (DPDM) and laboratory visual model tests were used to analyze the soil displacement and deformation around an anchor plate. Microscopic changes in displacement were obtained, and the stress of the anchor plate was experimentally studied. In the laboratory model tests, measurement analysis was carried out by the non-punctuation method.The test model device is shown in Figure1. The glass case’s length, width, and height were 650 mm × 300 mm × 500 mm. A row of square holes with a spacing of one centimeter was drilled left at the edge of one side of the baffle, the diameter of which was slightly more than one centimeter, allowing a bolt to pass through, as shown in Figure 2.Figure 1
Test model equipment.Figure 2
Detailed test model equipment.The rod body of the plate anchor used in the test was square in section, with a side length of 10 mm. The shape of the anchor plate was semicircular. The diameterD of the anchor plate was D = 3 cm and D = 5 cm. After smooth treatment of the surface of the plate anchor, its friction with sand was able to be ignored. The style of the plate anchor is shown in Figures 3 and 4 show the assembled overall model diagram. In this section, three earth pressure gages were mounted on the anchor plate with thickness of 7 mm, surface diameter of 25 mm and maximum range of 40 kPa). And Donghua DH-3816 static strain gauge was used together with earth pressure gauge, which can timely monitor the stress of the soil in front of the anchor plate, as shown in Figures 5 and 6.Figure 3
Plate anchor style.Figure 4
Assembled model.Figure 5
Soil pressure gauge.Figure 6
Static strain gauge.The soil samples were mixed with Fujian Pingtan standard sand and Yellow River soil in Shandong Province. The particles with a diameter greater than 0.65 mm accounted for 3%, 0.45–0.65 mm accounted for 40.5%, 0.25–0.45 mm accounted for 51.5%, and the particles with a diameter less than 0.25 mm accounted for 6%. The physical properties of the sand are shown in Table1.Table 1
Physical properties of sand.
Particle specific gravityGsMaximum dry densityρdmax (g/cm3)Minimum dry densityρdmin (g/cm3)Maximum porosityemaxMinimum porosityeminThe average particle sized50 (mm)2.6431.741.430.8480.5190.34Coefficient of nonuniformityCuThe curvature coefficientCcRelative densityDr (%)Angle of internal frictionφ (°)Void ratioeDensityρ (kg/m3)1.5421.10423∼3230.20.8231450


### 2.2. Bearing Behavior of Plate Anchor

#### 2.2.1. Load-Displacement Behavior

The displacement variation of a plate anchor can directly reflect the influence of the anchor plate on the surrounding soil. Therefore, the displacement analysis of a plate anchor under pulling action was carried out to explore the change in the surrounding soil during the pullout process. Figure7 shows the load-displacement results of the anchor plate with D = 5 cm.Figure 7
Load-displacement curve of a vertical plate anchor.The load-displacement curve of the plate anchor loading process can be divided into three stages. When a pulling drawing force is applied to the anchor, the displacement linearly increases in the initial stage. The displacement gradually decreases with pulling tension, from a straight line to a curve, and the curve slope gradually becomes smaller. When the displacement curve is close to the horizontal direction, the displacement suddenly increases. In this stage, the soil suffers shear failure, and the plate anchor is pulled out.The analysis of the curve variation trend shows that in the initial loading stage, the interaction between soil and the anchor plate is low. The anchor plate easily compresses the soil, and the displacement increases linearly. As the soil is gradually compressed, the effect of embedment and compression between the soil particles are enhanced. The soil can resist a larger force from the anchor plate and limit the anchor plate’s displacement. With the continuous increase in tension, the soil has a limited bearing effect, and finally, failure occurs.To study the influence of anchor plate size on the surrounding soil, two anchor plates (D = 3 cm and D = 5 cm) with the same rod length were selected for the model test. The obtained soil displacement variation is shown in Figure 8. As can be seen from the figure, an approximately circular area appears near the anchor plate. This area is caused by the compression of the soil by the anchor plate in front. The range of influence of anchoring plate when D = 5 cm is more extensive than that of anchor plate when D = 3 cm, indicating that the influence of an anchor plate with a larger area is more significant. There is a prominent small circular area along the rod body at the left end. This is because the bearing capacity of the small-diameter anchor plate is poor, leading to a slight swing up and down of the soil.Figure 8
Soil displacement of with different anchor plate diameters. (a)D = 3 cm. (b) D = 5 cm.
(a)(b)


#### 2.2.2. Stress of the Anchor Plate

The pressure of the anchor plate was tested during the pullout process. A continuous load was applied to ensure a uniform increase in external load as far as possible until the tensile failure of the anchor plate. The stress of the two anchor plates with different diameters of 3 cm and 5 cm are shown in Figure9.Figure 9
The stress of the anchor plates with different diameters.Because of the stress of the anchor plate, the anchoring plate with a diameter of 5 cm is subjected to a pressure value greater than that of 3 cm. It shows that the anchor plate with a larger diameter has a more substantial bearing capacity. Because of the stress variation, the stress reaches a peak value as the loading process continues. The stress variation shows that the surrounding soils have a limited bearing capacity, exceeding the relative motion, and redistribution of the soils occurs. When the loading process continues, the soil is destroyed, and the stress of the anchor plate rapidly decreases.


## 2.1. Test Scheme and Design

When plate anchor anchors soil, the surrounding soil’s displacement is difficult to observe. There are few studies on microscopic deformation of the surrounding soil. Moreover, monitoring the stress variation of an anchor plate in practical engineering requires an extended period, and the test results are difficult to obtain in real-time. In this paper, digital photographic deformation measurement technology (DPDM) and laboratory visual model tests were used to analyze the soil displacement and deformation around an anchor plate. Microscopic changes in displacement were obtained, and the stress of the anchor plate was experimentally studied. In the laboratory model tests, measurement analysis was carried out by the non-punctuation method.The test model device is shown in Figure1. The glass case’s length, width, and height were 650 mm × 300 mm × 500 mm. A row of square holes with a spacing of one centimeter was drilled left at the edge of one side of the baffle, the diameter of which was slightly more than one centimeter, allowing a bolt to pass through, as shown in Figure 2.Figure 1
Test model equipment.Figure 2
Detailed test model equipment.The rod body of the plate anchor used in the test was square in section, with a side length of 10 mm. The shape of the anchor plate was semicircular. The diameterD of the anchor plate was D = 3 cm and D = 5 cm. After smooth treatment of the surface of the plate anchor, its friction with sand was able to be ignored. The style of the plate anchor is shown in Figures 3 and 4 show the assembled overall model diagram. In this section, three earth pressure gages were mounted on the anchor plate with thickness of 7 mm, surface diameter of 25 mm and maximum range of 40 kPa). And Donghua DH-3816 static strain gauge was used together with earth pressure gauge, which can timely monitor the stress of the soil in front of the anchor plate, as shown in Figures 5 and 6.Figure 3
Plate anchor style.Figure 4
Assembled model.Figure 5
Soil pressure gauge.Figure 6
Static strain gauge.The soil samples were mixed with Fujian Pingtan standard sand and Yellow River soil in Shandong Province. The particles with a diameter greater than 0.65 mm accounted for 3%, 0.45–0.65 mm accounted for 40.5%, 0.25–0.45 mm accounted for 51.5%, and the particles with a diameter less than 0.25 mm accounted for 6%. The physical properties of the sand are shown in Table1.Table 1
Physical properties of sand.
Particle specific gravityGsMaximum dry densityρdmax (g/cm3)Minimum dry densityρdmin (g/cm3)Maximum porosityemaxMinimum porosityeminThe average particle sized50 (mm)2.6431.741.430.8480.5190.34Coefficient of nonuniformityCuThe curvature coefficientCcRelative densityDr (%)Angle of internal frictionφ (°)Void ratioeDensityρ (kg/m3)1.5421.10423∼3230.20.8231450


## 2.2. Bearing Behavior of Plate Anchor

### 2.2.1. Load-Displacement Behavior

The displacement variation of a plate anchor can directly reflect the influence of the anchor plate on the surrounding soil. Therefore, the displacement analysis of a plate anchor under pulling action was carried out to explore the change in the surrounding soil during the pullout process. Figure7 shows the load-displacement results of the anchor plate with D = 5 cm.Figure 7
Load-displacement curve of a vertical plate anchor.The load-displacement curve of the plate anchor loading process can be divided into three stages. When a pulling drawing force is applied to the anchor, the displacement linearly increases in the initial stage. The displacement gradually decreases with pulling tension, from a straight line to a curve, and the curve slope gradually becomes smaller. When the displacement curve is close to the horizontal direction, the displacement suddenly increases. In this stage, the soil suffers shear failure, and the plate anchor is pulled out.The analysis of the curve variation trend shows that in the initial loading stage, the interaction between soil and the anchor plate is low. The anchor plate easily compresses the soil, and the displacement increases linearly. As the soil is gradually compressed, the effect of embedment and compression between the soil particles are enhanced. The soil can resist a larger force from the anchor plate and limit the anchor plate’s displacement. With the continuous increase in tension, the soil has a limited bearing effect, and finally, failure occurs.To study the influence of anchor plate size on the surrounding soil, two anchor plates (D = 3 cm and D = 5 cm) with the same rod length were selected for the model test. The obtained soil displacement variation is shown in Figure 8. As can be seen from the figure, an approximately circular area appears near the anchor plate. This area is caused by the compression of the soil by the anchor plate in front. The range of influence of anchoring plate when D = 5 cm is more extensive than that of anchor plate when D = 3 cm, indicating that the influence of an anchor plate with a larger area is more significant. There is a prominent small circular area along the rod body at the left end. This is because the bearing capacity of the small-diameter anchor plate is poor, leading to a slight swing up and down of the soil.Figure 8
Soil displacement of with different anchor plate diameters. (a)D = 3 cm. (b) D = 5 cm.
(a)(b)


### 2.2.2. Stress of the Anchor Plate

The pressure of the anchor plate was tested during the pullout process. A continuous load was applied to ensure a uniform increase in external load as far as possible until the tensile failure of the anchor plate. The stress of the two anchor plates with different diameters of 3 cm and 5 cm are shown in Figure9.Figure 9
The stress of the anchor plates with different diameters.Because of the stress of the anchor plate, the anchoring plate with a diameter of 5 cm is subjected to a pressure value greater than that of 3 cm. It shows that the anchor plate with a larger diameter has a more substantial bearing capacity. Because of the stress variation, the stress reaches a peak value as the loading process continues. The stress variation shows that the surrounding soils have a limited bearing capacity, exceeding the relative motion, and redistribution of the soils occurs. When the loading process continues, the soil is destroyed, and the stress of the anchor plate rapidly decreases.


## 2.2.1. Load-Displacement Behavior

The displacement variation of a plate anchor can directly reflect the influence of the anchor plate on the surrounding soil. Therefore, the displacement analysis of a plate anchor under pulling action was carried out to explore the change in the surrounding soil during the pullout process. Figure7 shows the load-displacement results of the anchor plate with D = 5 cm.Figure 7
Load-displacement curve of a vertical plate anchor.The load-displacement curve of the plate anchor loading process can be divided into three stages. When a pulling drawing force is applied to the anchor, the displacement linearly increases in the initial stage. The displacement gradually decreases with pulling tension, from a straight line to a curve, and the curve slope gradually becomes smaller. When the displacement curve is close to the horizontal direction, the displacement suddenly increases. In this stage, the soil suffers shear failure, and the plate anchor is pulled out.The analysis of the curve variation trend shows that in the initial loading stage, the interaction between soil and the anchor plate is low. The anchor plate easily compresses the soil, and the displacement increases linearly. As the soil is gradually compressed, the effect of embedment and compression between the soil particles are enhanced. The soil can resist a larger force from the anchor plate and limit the anchor plate’s displacement. With the continuous increase in tension, the soil has a limited bearing effect, and finally, failure occurs.To study the influence of anchor plate size on the surrounding soil, two anchor plates (D = 3 cm and D = 5 cm) with the same rod length were selected for the model test. The obtained soil displacement variation is shown in Figure 8. As can be seen from the figure, an approximately circular area appears near the anchor plate. This area is caused by the compression of the soil by the anchor plate in front. The range of influence of anchoring plate when D = 5 cm is more extensive than that of anchor plate when D = 3 cm, indicating that the influence of an anchor plate with a larger area is more significant. There is a prominent small circular area along the rod body at the left end. This is because the bearing capacity of the small-diameter anchor plate is poor, leading to a slight swing up and down of the soil.Figure 8
Soil displacement of with different anchor plate diameters. (a)D = 3 cm. (b) D = 5 cm.
(a)(b)


## 2.2.2. Stress of the Anchor Plate

The pressure of the anchor plate was tested during the pullout process. A continuous load was applied to ensure a uniform increase in external load as far as possible until the tensile failure of the anchor plate. The stress of the two anchor plates with different diameters of 3 cm and 5 cm are shown in Figure9.Figure 9
The stress of the anchor plates with different diameters.Because of the stress of the anchor plate, the anchoring plate with a diameter of 5 cm is subjected to a pressure value greater than that of 3 cm. It shows that the anchor plate with a larger diameter has a more substantial bearing capacity. Because of the stress variation, the stress reaches a peak value as the loading process continues. The stress variation shows that the surrounding soils have a limited bearing capacity, exceeding the relative motion, and redistribution of the soils occurs. When the loading process continues, the soil is destroyed, and the stress of the anchor plate rapidly decreases.


## 3. Numerical Simulation of Plate Anchor

### 3.1. Establishment of Numerical Model

Based on the particle flow theory and the PFC2D program, the physical and mechanical properties of plate anchors subjected to horizontal pullout load were studied using numerical simulations. PFC can simulate the mechanical properties and behaviors of the object from the microscopic perspective. It represents the macroscopic mechanical properties of the object by setting the mechanical and geometric properties of particles and bonds. The basic numerical simulation model boundary was composed of four walls, with a horizontal width of 6 m and a vertical height of 5 m. The soil had an initial porosity of 30% and was simulated using circular particles with a radius ranging from 10 mm to 12 mm that were generated according to gaussian normal distribution within the closed rectangular range walls. Gravity was applied to the generated particles to simulate soil particles. Under the action of gravity, the particles began to cycle down and compress each other, forming the initial stress field. When the particles were in an equilibrium state under circulation, the circulation ended, simulating the original state of the soil. The particles in the height range of 2.16–2.24 m in they-direction and a width range of 3.96–4.04 m in the x-direction were deleted to form reserved holes for bolts and anchor plates. The anchor plates were set at the reserved holes with bolts with a diameter of 8 cm. The plates had a height of 1 m. Simulation model of plate anchor is shown in Figure 10. Mechanical parameters of the simulation model are shown in Table 2. The number and position of the measuring circles are shown in Figure 11.Figure 10
Simulation model of plate anchor.Table 2
Mechanical parameters of the soil particles.
NameFriction coefficientμThe normal stiffnessKn (N/m)Shear stiffnessKs (N/m)Particle radius (mm)Normal bond strength (N)Tangential bond strength (N)The wall11e81e8———Anchor particles2.01e101e10401e301e30Anchor plate particles10.01e101e10401e301e30Sand particles61e71e710–121e71e7Figure 11
Measuring circle arrangement diagram.


### 3.2. Verification of Numerical Model

In this paper, the maximum horizontal pulling force of the anchor was applied step by step, and the appropriate horizontal load was 160 kN. Similarly, the displacement variation of the plate anchor was observed. The normalized values of the simulation results were compared with the test results, as shown in Figure12. The figure shows the consistency of the two results. The displacement increases rapidly when the anchor plate is initially subjected to the drawing force. With an increase in the running time step, the displacement stabilizes and does not increase. This is because when the soil is initially loaded, the anchor compresses the soil and reduces the porosity. The reverse force of the anchorage system caused by the soil particles is small, leading to the apparent displacement of the anchor. With the continuous compaction of the soil particles by the anchor plate, the internal stress of the soil is redistributed, and the resistance of the soil particles to the anchorage system increases. At this time, the resistance is equal to the applied load on the plate anchor, and the soil particles and the anchorage system reach a new equilibrium state.Figure 12
Displacement-time step curve of the plate anchor.Figure13 is the displacement vector diagram of the soil particle under the action of the anchor plate. The anchor plate compresses the soil and “pushes” the soil forward. This part of soil moves along the plate anchor position and away from the plate anchor in the vertical direction perpendicular to the plate anchor. The soil particles above the rear side of the anchor plate have evident falling displacement, pointing to the position of the anchor plate. The anchor plate pushes the soil mass in front and forms a pullout area. The upper soil particles fall to fill the pullout area due to gravity, forming a prominent falling zone. In addition, the displacement of soil particles near the rod body also became apparent, which is due to the contact friction between the soil particles and the plate anchor. The friction force drives the nearby particles to move.Figure 13
Displacement vector diagram of the soil particles.


## 3.1. Establishment of Numerical Model

Based on the particle flow theory and the PFC2D program, the physical and mechanical properties of plate anchors subjected to horizontal pullout load were studied using numerical simulations. PFC can simulate the mechanical properties and behaviors of the object from the microscopic perspective. It represents the macroscopic mechanical properties of the object by setting the mechanical and geometric properties of particles and bonds. The basic numerical simulation model boundary was composed of four walls, with a horizontal width of 6 m and a vertical height of 5 m. The soil had an initial porosity of 30% and was simulated using circular particles with a radius ranging from 10 mm to 12 mm that were generated according to gaussian normal distribution within the closed rectangular range walls. Gravity was applied to the generated particles to simulate soil particles. Under the action of gravity, the particles began to cycle down and compress each other, forming the initial stress field. When the particles were in an equilibrium state under circulation, the circulation ended, simulating the original state of the soil. The particles in the height range of 2.16–2.24 m in they-direction and a width range of 3.96–4.04 m in the x-direction were deleted to form reserved holes for bolts and anchor plates. The anchor plates were set at the reserved holes with bolts with a diameter of 8 cm. The plates had a height of 1 m. Simulation model of plate anchor is shown in Figure 10. Mechanical parameters of the simulation model are shown in Table 2. The number and position of the measuring circles are shown in Figure 11.Figure 10
Simulation model of plate anchor.Table 2
Mechanical parameters of the soil particles.
NameFriction coefficientμThe normal stiffnessKn (N/m)Shear stiffnessKs (N/m)Particle radius (mm)Normal bond strength (N)Tangential bond strength (N)The wall11e81e8———Anchor particles2.01e101e10401e301e30Anchor plate particles10.01e101e10401e301e30Sand particles61e71e710–121e71e7Figure 11
Measuring circle arrangement diagram.


## 3.2. Verification of Numerical Model

In this paper, the maximum horizontal pulling force of the anchor was applied step by step, and the appropriate horizontal load was 160 kN. Similarly, the displacement variation of the plate anchor was observed. The normalized values of the simulation results were compared with the test results, as shown in Figure12. The figure shows the consistency of the two results. The displacement increases rapidly when the anchor plate is initially subjected to the drawing force. With an increase in the running time step, the displacement stabilizes and does not increase. This is because when the soil is initially loaded, the anchor compresses the soil and reduces the porosity. The reverse force of the anchorage system caused by the soil particles is small, leading to the apparent displacement of the anchor. With the continuous compaction of the soil particles by the anchor plate, the internal stress of the soil is redistributed, and the resistance of the soil particles to the anchorage system increases. At this time, the resistance is equal to the applied load on the plate anchor, and the soil particles and the anchorage system reach a new equilibrium state.Figure 12
Displacement-time step curve of the plate anchor.Figure13 is the displacement vector diagram of the soil particle under the action of the anchor plate. The anchor plate compresses the soil and “pushes” the soil forward. This part of soil moves along the plate anchor position and away from the plate anchor in the vertical direction perpendicular to the plate anchor. The soil particles above the rear side of the anchor plate have evident falling displacement, pointing to the position of the anchor plate. The anchor plate pushes the soil mass in front and forms a pullout area. The upper soil particles fall to fill the pullout area due to gravity, forming a prominent falling zone. In addition, the displacement of soil particles near the rod body also became apparent, which is due to the contact friction between the soil particles and the plate anchor. The friction force drives the nearby particles to move.Figure 13
Displacement vector diagram of the soil particles.


## 4. Microscopic Bearing Behaviour of Soil Particles

### 4.1. Stress of Soil Particles

When the vertical plate anchor is subjected to a horizontal load, it dramatically influences the surrounding soil. In this paper, the axial stress and shear stress were analyzed, and the research scope was within the range of the four rows of measuring circles above and below the plate anchor (as shown in Figure11). The average stress values obtained from each row of measuring circles were monitored and extracted for comparative analysis.Figures14 and 15 show the change of contact stress between soil particles before and after loading, respectively. Thicker the black lines in the figure indicate more significant contact stress between the particles.Figure 14
Contact stress before loading.Figure 15
Contact stress after loading.Before loading, the contact stress between particles is mainly distributed under the plate anchor. After loading, the contact stress between soil particles under the anchor plate increases, and significant contact stress also appears above the plate anchor caused by the friction between the plate anchor and soil particles and compaction of the nearby soil. However, the contact stress between soil particles behind the anchor plate decreases significantly, indicating that with the movement of the anchor plate, the front soil is gradually compacted, while a certain gap forms in the rear. The nearby soil particles fill in the gap, and the compactness decreases. The contact between the soil decreases. Overall, in such projects, sufficient compaction should be ensured before prestressing the anchor plate to reduce the displacement caused by the anchor plate, reduce the disturbance to the soil behind the anchor plate, and improve the overall stability.Figures16 and 17 show the mean soil stress in the x-direction monitored by the four rows of measuring circles above and below the plate anchor. During the whole loading process, the average x-direction soil stress above and below the anchor is negative, indicating that the soil within this range is under pressure from the anchor. The average absolute value of the stress in the x-direction obtained by the following four rows of measuring circles is generally more significant than that obtained by the above four rows of measuring circles. Among the above measuring circles, the closer the distance to the plate anchor, the greater the value, indicating that the external load spreads outward along the radial direction of the plate anchor body. Among the average stress obtained by the following four rows of measuring circles, the value measured by the next row of measuring circles near the plate anchor is the largest, indicating that the plate anchor greatly influences this area.Figure 16
Upper average soil stress in thex-direction.Figure 17
Lower average soil stress in thex-direction.Figures18 and 19 show the average shear stress of the soil obtained from the four rows of measuring circles above and below the plate anchor, respectively. Overall, the average shear stress is greater near the plate and decreases with distance. With an increase in the time step, the average shear stress increases rapidly, then decreases slightly, and finally gradually stabilizes. The stress of the upper soil decreases after reaching its maximum value, and the value stabilizes after falling to a certain extent. However, the lower soil stress continuously increases, and the reduction is no longer evident after reaching its maximum value. The results show that the soil particles move and change the internal stress due to the plate anchor’s influence when compressed by the plate anchor load. The particles resist the shear force from the plate anchor. Due to the limited space, the shear resistance of the soil under the anchor continues to increase until it reaches equilibrium with the anchor. However, the soil particles above the anchor continue to move after the shear stress reaches its maximum value, decreasing the average shear stress and the phenomenon of decline.Figure 18
Average shear stress of upper soil.Figure 19
Average shear stress of lower soil.


### 4.2. Microscopic Parameters of Soil Particles

Soil is a granular material, and the variation of its microscopic parameters affects the properties of the soil. In this section, the bearing characteristics of the plate anchor and the evolution law of the soil particles are studied by analyzing the porosity, coordination number, and rotation of the soil particles.Figures20 and 21 show the soil porosity variation obtained from the four rows of measuring circles above and below the plate anchor. When a horizontal load is applied to the plate anchor, the average porosity of the measured circles decreases both above and below the anchor. The law of the four rows of measuring circles above the plate anchor is the same as that in the x-direction stress of the soil above the plate anchor. The variation rule of the average porosity obtained from each row of measured circles below the anchor is from the upper soil section. Furthermore, porosity was the least at the deepest values (fourth row), similar to the x-direction stress at the same position. The above trends show that the porosity variation between soil particles is closely related to the x-direction stress variation, which is affected by the plate anchor and the depth of the position; the influence of the dead weight stress is indispensable.Figure 20
The porosity of upper soil particles change with increased load.Figure 21
The porosity of the lower soil particles change with increased load.The particle coordination number is the degree of contact between soil particles and is a way to reflect the variation of force transmission between particles. It also represents the variation process of particles subjected to a horizontal load. A coordination value of 3 is the minimum index to maintain a stable state between two-dimensional circular particles.Figures22 and 23 show the soil particle coordination number variations obtained from the four rows of measuring circles above and below the plate anchor, respectively. The average coordination values obtained from the fourth row vary little, indicating that the force exerted by the horizontal load on the plate anchor is dispersed in the transmission process by the depth of the fourth row. The overall direct influence range is within three rows, here about 1.2 m.Figure 22
Coordination number above the plate.Figure 23
Coordination number below the plate.Also, the mean coordination number variation is closely related to the time step. The measured average coordination number curve fluctuated in the first 10,000 steps, decreasing first and then increasing. However, after the 10,000th time step, the variation of the average coordination number decreased, and the degree of fluctuation of the curve decreased and stabilized. The average coordination number in the four rows of the lower part of the anchor was greater than that in the upper part of the anchor. This is because the particles below the anchor are in closer contact due to gravity acting on the particles.When the plate anchor is loaded, the average coordination number of the first row of measured circles above the plate anchor varied greatly, decreasing rapidly from 3.17 to below 3, indicating that the particles are in a chaotic and unstable state and could no longer resist the external tension load. With an increase in time, the average coordination number gradually increased and finally stabilized, indicating that the load on the soil near the plate anchor is redistributed and stabilized once again. The first row below the anchor has the same variation trend as the previous row, but it is overall more stable. The minimum value of the coordination number in the next row is greater than 3, indicating no severe instability among particles within this range. The overall variation value ranges between 3.0 and 3.6, which also verifies the influence of the dead particle weight.Particle rotation is the particle rotation value over time under an external load. In this model, the change of rotation quantity reflects the shear change between soil particles and the anchor plate. A larger particle rotation indicates a more substantial shear effect of the anchor plate.Figures24 and 25 show the rotation variation of the soil particles obtained from the four rows of measuring circles above and below the plate anchor, respectively. With the increase in the time step, the rotation obtained by each row of measured circles first increases and then stabilizes, indicating that the external load’s influence gradually decreases. With a continued external load, particle rotation mainly occurs within the range of the first and second rows of measuring circles, and the rotation angle has a nonlinear relationship with the running time step. In the radial direction along the bolt body, the rotation variation gradually decreases, and the values measured in the first, second, and fourth rows were greater than those in the third and fourth rows, indicating that with an increase in radial distance from the plate body, the influence of the external load gradually decreases. The values measured in the third row of the upper and lower measuring circles are larger than those in the second row, indicating that the soil further from the plate anchor is initially less affected when a load is applied. With the redistribution of the overall force on the model, the force on the soil near the plate anchor gradually transfers outwards. This results in the variation of the soil force with distance. The variation range of the values in the upper and lower fourth rows of measuring circles is minimal, indicating that the plate anchor load is not transmitted to this depth and is beyond the function range of the plate anchor.Figure 24
Rotation variation of particle above the plate.Figure 25
Rotation variation of particle below the plate.


### 4.3. Orientation Variation of Soil Particles in Different Surface Shapes

Soil particles are not perfectly round but complex non-round clusters. To study the orientation variation of soil particles in different surface shapes, three different combinations of elliptical particles, H-type (particles mainly distributed in the horizontal direction), V-type (particles mainly distributed in the vertical axis direction), and R-type (particles distributed within the range of 0°∼360°), were chosen in this paper, as shown in Figure26. The three types of particles can exhibit distinctive directional characteristics and represent common Earth materials.Figure 26
Three types of particles with different shapes. (a) H-type particles. (b) V-type particles. (c) R-type particles.
(a)(b)(c)Through the numerical simulation of the elliptic particles, the evolution of the orientation of the particles under the influence of horizontal loads was analyzed, including the variation of long-axis orientation and contact normal direction orientation. The development and change in the long-axis orientation of the particles reflect the rearrangement of particles and the evolution of structural anisotropy after loading. These are essential fabric parameters to describe the microstructural changes of the soil during loading. Contact normal direction orientation is the distribution and quantity of particle contact, which directly affects the transmission of the contact force and stability of the structure. The evolution law of meso-fabric anisotropy during soil changes is expressed quantitatively.The mathematical expression for the long axis orientation is:(1)Oθ=1+αΡCOS2θ−θ2π.Type:Oθ is the percentage of particles falling in the long axis of the total number of particles. αΡ is the directional anisotropy coefficient of the grain along the long axis, and its value mainly reflects the degree of anisotropy. θΡ is the main direction of particle orientation along the long axis.The mathematical expression of contact normal is:(2)Eθ=1+αCOS2θ−θ2π.Type:Eθ is the percentage of the number of contact points falling in the contact normal direction of the total number of contact points. α is the contact normal anisotropy coefficient, and its value mainly reflects the strength of the anisotropy degree. θα is the main direction of contact normal. The long-axis orientation and contact normal direction orientation between the elliptic particles were obtained through the simulation, and the wind rose diagram was fitted.Figure27 shows the directional evolution law of the long axis orientation of the three types of particles before and after loading. Before loading, the H-and V-type particles have obvious initial orientation. The H-type particles of the long axis direction are mainly oriented 0° and 180° (horizontal direction). The V-type particles of the long axis direction are mainly concentrated in the approximate 90° direction (vertical direction), while the R-type particles did not have an obvious orientation compared to the other two particles. The long axis of the V-type particles are mostly horizontal before loading and changed slightly after loading, deflecting and evolving along the direction of 150° clockwise. The proportion of the long-axis falling in the direction of 150° increased, and the rose pattern changed from the original thin shape to a slight bulge in the middle quarter. The H-type particles also exhibit a similar situation, changing from vertical to 60°. R-type particles also rotated but in the opposite direction, moving counterclockwise.Figure 27
Long axis orientation evolution before and after loading. (a) H-type particles before loading. (b) H-type particles after loading. (c) V-type particles before loading. (d) V-type particles after loading. (e) R-type particles before loading. (f) R-type particles after loading.
(a)(b)(c)(d)(e)(f)It can be concluded that the plate anchor is displaced under a horizontal load, and the elliptic soil particles also rotate under the influence of the displacement of the anchor plate. The long axis direction of the particles also changed. The changing angle of the long axis is consistent with the axial displacement direction of the plate anchor. The random orientation of the long axis determines if the particle itself stabilizes under the action of gravity. The plate anchor played a minor role, and gravity became the main factor causing the change of its long axis direction.Contact normal orientation analysis is an extension of the coordination number. The coordination number represents the change in contact number, and contact normal orientation represents the variation of the contact direction. Figure28 shows the directional evolution of the contact directions of the three types of particles before and after loading. Before loading, H-type particles and V-type particles have an apparent initial orientation in the contact direction, while R-type particles do not. After loading, the number of contacts between H-type particles in the normal direction of the main direction decreases significantly. The original contact direction mainly ranges from 0° to 30°, and after loading, the particle orientation ranges from 80° to 100°. H-type particles gradually shifted from transverse to vertical. The V-type particles deflected from the range of 80° to 100° to 70° to 110° and gradually became inclined. There is no noticeable change in the R-type particles with loading and no optimal direction. It can be concluded that, under the action of a horizontal load, the displacement movement of the plate anchor affects the elliptic particles and causes them to rotate, and decreases the contact normal angle.Figure 28
Contact normal orientation evolution before and after loading. (a) H-type particles before loading. (b) H-type particles after loading. (c) V-type particles before loading. (d) V-type particles after loading. (e) R-type particles before loading. (f) R-type particles after loading.
(a)(b)(c)(d)(e)(f)


## 4.1. Stress of Soil Particles

When the vertical plate anchor is subjected to a horizontal load, it dramatically influences the surrounding soil. In this paper, the axial stress and shear stress were analyzed, and the research scope was within the range of the four rows of measuring circles above and below the plate anchor (as shown in Figure11). The average stress values obtained from each row of measuring circles were monitored and extracted for comparative analysis.Figures14 and 15 show the change of contact stress between soil particles before and after loading, respectively. Thicker the black lines in the figure indicate more significant contact stress between the particles.Figure 14
Contact stress before loading.Figure 15
Contact stress after loading.Before loading, the contact stress between particles is mainly distributed under the plate anchor. After loading, the contact stress between soil particles under the anchor plate increases, and significant contact stress also appears above the plate anchor caused by the friction between the plate anchor and soil particles and compaction of the nearby soil. However, the contact stress between soil particles behind the anchor plate decreases significantly, indicating that with the movement of the anchor plate, the front soil is gradually compacted, while a certain gap forms in the rear. The nearby soil particles fill in the gap, and the compactness decreases. The contact between the soil decreases. Overall, in such projects, sufficient compaction should be ensured before prestressing the anchor plate to reduce the displacement caused by the anchor plate, reduce the disturbance to the soil behind the anchor plate, and improve the overall stability.Figures16 and 17 show the mean soil stress in the x-direction monitored by the four rows of measuring circles above and below the plate anchor. During the whole loading process, the average x-direction soil stress above and below the anchor is negative, indicating that the soil within this range is under pressure from the anchor. The average absolute value of the stress in the x-direction obtained by the following four rows of measuring circles is generally more significant than that obtained by the above four rows of measuring circles. Among the above measuring circles, the closer the distance to the plate anchor, the greater the value, indicating that the external load spreads outward along the radial direction of the plate anchor body. Among the average stress obtained by the following four rows of measuring circles, the value measured by the next row of measuring circles near the plate anchor is the largest, indicating that the plate anchor greatly influences this area.Figure 16
Upper average soil stress in thex-direction.Figure 17
Lower average soil stress in thex-direction.Figures18 and 19 show the average shear stress of the soil obtained from the four rows of measuring circles above and below the plate anchor, respectively. Overall, the average shear stress is greater near the plate and decreases with distance. With an increase in the time step, the average shear stress increases rapidly, then decreases slightly, and finally gradually stabilizes. The stress of the upper soil decreases after reaching its maximum value, and the value stabilizes after falling to a certain extent. However, the lower soil stress continuously increases, and the reduction is no longer evident after reaching its maximum value. The results show that the soil particles move and change the internal stress due to the plate anchor’s influence when compressed by the plate anchor load. The particles resist the shear force from the plate anchor. Due to the limited space, the shear resistance of the soil under the anchor continues to increase until it reaches equilibrium with the anchor. However, the soil particles above the anchor continue to move after the shear stress reaches its maximum value, decreasing the average shear stress and the phenomenon of decline.Figure 18
Average shear stress of upper soil.Figure 19
Average shear stress of lower soil.


## 4.2. Microscopic Parameters of Soil Particles

Soil is a granular material, and the variation of its microscopic parameters affects the properties of the soil. In this section, the bearing characteristics of the plate anchor and the evolution law of the soil particles are studied by analyzing the porosity, coordination number, and rotation of the soil particles.Figures20 and 21 show the soil porosity variation obtained from the four rows of measuring circles above and below the plate anchor. When a horizontal load is applied to the plate anchor, the average porosity of the measured circles decreases both above and below the anchor. The law of the four rows of measuring circles above the plate anchor is the same as that in the x-direction stress of the soil above the plate anchor. The variation rule of the average porosity obtained from each row of measured circles below the anchor is from the upper soil section. Furthermore, porosity was the least at the deepest values (fourth row), similar to the x-direction stress at the same position. The above trends show that the porosity variation between soil particles is closely related to the x-direction stress variation, which is affected by the plate anchor and the depth of the position; the influence of the dead weight stress is indispensable.Figure 20
The porosity of upper soil particles change with increased load.Figure 21
The porosity of the lower soil particles change with increased load.The particle coordination number is the degree of contact between soil particles and is a way to reflect the variation of force transmission between particles. It also represents the variation process of particles subjected to a horizontal load. A coordination value of 3 is the minimum index to maintain a stable state between two-dimensional circular particles.Figures22 and 23 show the soil particle coordination number variations obtained from the four rows of measuring circles above and below the plate anchor, respectively. The average coordination values obtained from the fourth row vary little, indicating that the force exerted by the horizontal load on the plate anchor is dispersed in the transmission process by the depth of the fourth row. The overall direct influence range is within three rows, here about 1.2 m.Figure 22
Coordination number above the plate.Figure 23
Coordination number below the plate.Also, the mean coordination number variation is closely related to the time step. The measured average coordination number curve fluctuated in the first 10,000 steps, decreasing first and then increasing. However, after the 10,000th time step, the variation of the average coordination number decreased, and the degree of fluctuation of the curve decreased and stabilized. The average coordination number in the four rows of the lower part of the anchor was greater than that in the upper part of the anchor. This is because the particles below the anchor are in closer contact due to gravity acting on the particles.When the plate anchor is loaded, the average coordination number of the first row of measured circles above the plate anchor varied greatly, decreasing rapidly from 3.17 to below 3, indicating that the particles are in a chaotic and unstable state and could no longer resist the external tension load. With an increase in time, the average coordination number gradually increased and finally stabilized, indicating that the load on the soil near the plate anchor is redistributed and stabilized once again. The first row below the anchor has the same variation trend as the previous row, but it is overall more stable. The minimum value of the coordination number in the next row is greater than 3, indicating no severe instability among particles within this range. The overall variation value ranges between 3.0 and 3.6, which also verifies the influence of the dead particle weight.Particle rotation is the particle rotation value over time under an external load. In this model, the change of rotation quantity reflects the shear change between soil particles and the anchor plate. A larger particle rotation indicates a more substantial shear effect of the anchor plate.Figures24 and 25 show the rotation variation of the soil particles obtained from the four rows of measuring circles above and below the plate anchor, respectively. With the increase in the time step, the rotation obtained by each row of measured circles first increases and then stabilizes, indicating that the external load’s influence gradually decreases. With a continued external load, particle rotation mainly occurs within the range of the first and second rows of measuring circles, and the rotation angle has a nonlinear relationship with the running time step. In the radial direction along the bolt body, the rotation variation gradually decreases, and the values measured in the first, second, and fourth rows were greater than those in the third and fourth rows, indicating that with an increase in radial distance from the plate body, the influence of the external load gradually decreases. The values measured in the third row of the upper and lower measuring circles are larger than those in the second row, indicating that the soil further from the plate anchor is initially less affected when a load is applied. With the redistribution of the overall force on the model, the force on the soil near the plate anchor gradually transfers outwards. This results in the variation of the soil force with distance. The variation range of the values in the upper and lower fourth rows of measuring circles is minimal, indicating that the plate anchor load is not transmitted to this depth and is beyond the function range of the plate anchor.Figure 24
Rotation variation of particle above the plate.Figure 25
Rotation variation of particle below the plate.


## 4.3. Orientation Variation of Soil Particles in Different Surface Shapes

Soil particles are not perfectly round but complex non-round clusters. To study the orientation variation of soil particles in different surface shapes, three different combinations of elliptical particles, H-type (particles mainly distributed in the horizontal direction), V-type (particles mainly distributed in the vertical axis direction), and R-type (particles distributed within the range of 0°∼360°), were chosen in this paper, as shown in Figure26. The three types of particles can exhibit distinctive directional characteristics and represent common Earth materials.Figure 26
Three types of particles with different shapes. (a) H-type particles. (b) V-type particles. (c) R-type particles.
(a)(b)(c)Through the numerical simulation of the elliptic particles, the evolution of the orientation of the particles under the influence of horizontal loads was analyzed, including the variation of long-axis orientation and contact normal direction orientation. The development and change in the long-axis orientation of the particles reflect the rearrangement of particles and the evolution of structural anisotropy after loading. These are essential fabric parameters to describe the microstructural changes of the soil during loading. Contact normal direction orientation is the distribution and quantity of particle contact, which directly affects the transmission of the contact force and stability of the structure. The evolution law of meso-fabric anisotropy during soil changes is expressed quantitatively.The mathematical expression for the long axis orientation is:(1)Oθ=1+αΡCOS2θ−θ2π.Type:Oθ is the percentage of particles falling in the long axis of the total number of particles. αΡ is the directional anisotropy coefficient of the grain along the long axis, and its value mainly reflects the degree of anisotropy. θΡ is the main direction of particle orientation along the long axis.The mathematical expression of contact normal is:(2)Eθ=1+αCOS2θ−θ2π.Type:Eθ is the percentage of the number of contact points falling in the contact normal direction of the total number of contact points. α is the contact normal anisotropy coefficient, and its value mainly reflects the strength of the anisotropy degree. θα is the main direction of contact normal. The long-axis orientation and contact normal direction orientation between the elliptic particles were obtained through the simulation, and the wind rose diagram was fitted.Figure27 shows the directional evolution law of the long axis orientation of the three types of particles before and after loading. Before loading, the H-and V-type particles have obvious initial orientation. The H-type particles of the long axis direction are mainly oriented 0° and 180° (horizontal direction). The V-type particles of the long axis direction are mainly concentrated in the approximate 90° direction (vertical direction), while the R-type particles did not have an obvious orientation compared to the other two particles. The long axis of the V-type particles are mostly horizontal before loading and changed slightly after loading, deflecting and evolving along the direction of 150° clockwise. The proportion of the long-axis falling in the direction of 150° increased, and the rose pattern changed from the original thin shape to a slight bulge in the middle quarter. The H-type particles also exhibit a similar situation, changing from vertical to 60°. R-type particles also rotated but in the opposite direction, moving counterclockwise.Figure 27
Long axis orientation evolution before and after loading. (a) H-type particles before loading. (b) H-type particles after loading. (c) V-type particles before loading. (d) V-type particles after loading. (e) R-type particles before loading. (f) R-type particles after loading.
(a)(b)(c)(d)(e)(f)It can be concluded that the plate anchor is displaced under a horizontal load, and the elliptic soil particles also rotate under the influence of the displacement of the anchor plate. The long axis direction of the particles also changed. The changing angle of the long axis is consistent with the axial displacement direction of the plate anchor. The random orientation of the long axis determines if the particle itself stabilizes under the action of gravity. The plate anchor played a minor role, and gravity became the main factor causing the change of its long axis direction.Contact normal orientation analysis is an extension of the coordination number. The coordination number represents the change in contact number, and contact normal orientation represents the variation of the contact direction. Figure28 shows the directional evolution of the contact directions of the three types of particles before and after loading. Before loading, H-type particles and V-type particles have an apparent initial orientation in the contact direction, while R-type particles do not. After loading, the number of contacts between H-type particles in the normal direction of the main direction decreases significantly. The original contact direction mainly ranges from 0° to 30°, and after loading, the particle orientation ranges from 80° to 100°. H-type particles gradually shifted from transverse to vertical. The V-type particles deflected from the range of 80° to 100° to 70° to 110° and gradually became inclined. There is no noticeable change in the R-type particles with loading and no optimal direction. It can be concluded that, under the action of a horizontal load, the displacement movement of the plate anchor affects the elliptic particles and causes them to rotate, and decreases the contact normal angle.Figure 28
Contact normal orientation evolution before and after loading. (a) H-type particles before loading. (b) H-type particles after loading. (c) V-type particles before loading. (d) V-type particles after loading. (e) R-type particles before loading. (f) R-type particles after loading.
(a)(b)(c)(d)(e)(f)


## 5. Conclusions

This paper investigated the bearing behavior of horizontally loaded vertical plate anchors from a macroscope and microscope perspective. The results are as follows:(1)
When the anchor is subjected to a horizontal load, the anchor plate compresses the soil in front of it, moving the soil vertically away from the anchor. The soil behind the anchor plate also is displaced and moves towards the anchor plate.(2)
The soil near the anchor plate is mainly under pressure from the anchor plate. The pressure in front of the anchor plate is significant, regardless of the axial or shear stresses. The plate anchor affects the soil stress state and is related to the dead weight stress caused by the burial depth.(3)
The change trend of porosity reflects the change of axial stress. The soil near the anchor has a greater stress effect, while the soil far away from the anchor has a smaller impact. Particle coordination number reflects the change of contact number between particles. After the bolt is loaded, the soil particles close to the bolt are highly active and in a chaotic and unstable state, unable to resist the external tension load. Particle rotation is an important meso-physical quantity reflecting the shear evolution process of the interface between soil and anchor body. Under external load, particle rotation mainly occurs in the range of the first and second row of measuring circles, and the rotation Angle has a nonlinear relationship with the running time step under load.(4)
Under the influence of the displacement of the anchor bolt, the elliptic particles move and rotate, and the long axis orientation of the particles also changes, and the angle of change is consistent with the axial displacement direction of the anchor bolt. The displacement motion of bolt affects the contact normal direction of elliptic particles, which makes them rotate. However, not only the deflection angle is changed, but the contact normal angle also decreases. The long axis orientation and contact normal of the three elliptic particle types vary. The particles with a long axis distributed in the horizontal direction are the most stable, while those with a long axis distributed in the vertical direction are the most unstable.(5)
The anchor plate with large size is subjected to larger pressure and has obvious influence on soil displacement. The force of anchor plate increases first and then decreases, and the soil force is redistributed.



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*Source: 7371229-2022-06-10.xml*