Numerical Simulation of Three-Dimensional Soil Arch Effect Between h-type Pile Based Discrete Element Method

: The h-type pile (hTP pile) is a complex anti-slip pile system, which connects the front pile and the 8 back pile through beams. When it is used in engineering, there is a complex soil arch effect between the soil 9 and the hTP pile, which makes the complex anti-slip mechanism. In this paper, the discrete element method 10 (PFC) is used to establish the hTP pile models, analyse the displacement and stress distribution law of the 11 soil body, investigate the spatial distribution and variation patterns of soil arches, this can provide a basis for 12 the design of hTP. The results indicate that the soil arch structure formed under the displacement between 13 hTPs can be divided into four stages: initial stage, development stage, overlapping stage and stable stage. 14 The development speed of the soil arch between the rear piles is slower than that of the soil arch between the 15 former piles. As the depth of the soil increases, the arch line of the soil arch gets closer to the rear pile; The 16 soil arch of the stress between hTPs can be divided into initial stage, development stage and stable stage. The 17 time step corresponding to the stable stage of the stress in the horizontal direction is equal to the sum of the 18 horizontal displacement generated by the overlapping stage and the stabilization stage. The stress of the soil 19 slope gradually decreases and extends from the surface to the bottom layer of the slope; Soil arches appear 20 on the rear side of both the front and rear piles at different anti-slip pile spacing, and they all tend to overlap. 21 The increase in pile spacing does not have a significant effect on theratio of soil arch height and soil arch 22 span, and the evolution of soil arch is similar between hTP at different pile spacing. All above can provide 23 reference for the application and design of hTPs.


Introduction
With the construction of infrastructure in western China, safety problems caused by landslides have become increasingly prominent (Runqiu, 2007;Alessandro, et al., 2022).To prevent the hazards caused by landslides, anti-slip piles have gradually become a common and effective support structure type in slope treatment (Zhou et al., 2014).For different geological characteristics and safety requirements, engineers have designed various forms of piles to enhance stability, such as ordinary anti-slip piles, anchor cable anti-slip piles and combined piles.However, most of piles are passive piles, which are greatly affected by the soil pressure around the piles (Beer and Wallays, 1972;Fan et al., 2019;Liu et al., 2021;Zhang et al., 2021).Therefore, it is of great significance to study and understand the interaction mechanism between pile and soil for engineering design.
The soil arch effect on the interaction between pile and soil has gradually become the focus and hot spot in engineering research since the existence of the soil arch effect was verified in the Trapdoor test (Terzaghi, 1943).Previous research results have found that the interaction between piles and soil can be judged by using the soil arch effect, the variation of soil arch between piles also tends to affect the slip arresting effect and structural safety of anti-slip piles (Wang and Zhou, 2017;Wu et al., 2017).In the current theoretical research, elastic-plastic theory and the non-linear Winkler theory have been introduced to analyze the deformation characteristics of soil between piles, and the calculation method of anti-slide pile is proposed from the elastic stage to the failure stage (Guo, 2009;Bouzid et al., 2013).Some scholars have further used the principle of pile-soil interaction to reveal the evolutionary rule of soil arches and concluded that the development of soil arches roughly goes through four stages: initial arch stage, maximum arch stage, loading recovery stage and limit stage (Robert and Sanping, 2002;Lu et al., 2010).In recent decades, various models have emerged to describe the shape of soil arches and their stress distribution, such as the model for the mechanical analysis of soil arch effects based on the assumption of vertical slip surfaces (Terzaghi, 1943), the model for the calculation of soil arch effects in two-dimensional wedges, the Hewlett & Randolph model (Hewlett and Randolph, 1988), the hemispherical crown model (Low et al., 1992), and the semi-circular arch model (Kempfert and Zaeske,1999).The development of computer technology has promoted rapid advances in numerical simulation technology.Many scholars have tried to study the interaction of soil arches between piles with the help of numerical simulation technology, and have made some progress.For example, the formation mechanism of soil arch was studied by using particle flow code, and it was found that the formation of soil arch mainly depends on the stress transfer of micro soil particles (Sun et al., 2011) Among the many influencing factors of the evolution mechanism of the soil arch effect between piles using finite element and finite difference methods, it was found that the pile spacing has a significant influence on the soil arch between piles.And when the pile spacing is too large, the poor stability of the soil arch can easily lead to the destruction of the soil between piles (Li et al., 2013;Li et al., 2015;Wang et al., 2017;He et al., 2018).In summary, there has been some research on the calculation principle, evolutionary process and influencing factors of soil arch of ordinary anti-slip piles.
However, when the landslide thrust is large, ordinary anti-slip piles can hardly meet the requirements of slope stability (Yu and He, 2010), and hTP can be used to better improve the stability of slops than ordinary anti-slip piles.For hTP, some scholars used model tests to compare the anti-slide effects of hTP, normal anti-slip piles, and portal anti-slip piles and anchor cable anti-slip piles, and found that hTP have more uniform stress distribution and less displacement at the top of the pile (Bo et al., 2017).In terms of indoor model tests, some scholars investigated the displacement of hTP tops at different spacings and found that the pile spacing would have a large effect on hTP (Li, 2018) In terms of numerical simulations, some scholars used the finite difference method to study the effect of anchorage depth and crossbeam width of hTP stress (Liu et al., 2018).For the engineering application of hTP, there is also currently targeted pile stress and displacement monitoring, but compared with the study of ordinary anti-slip piles, there is less research on hTP, and there is very little research on the soil arch between hTPs, and the existing research on hTP does not reflect the interaction between piles and soil very well.
Therefore, in this paper, the formation mechanism of soil arch between hTPs is investigated based on the numerical simulation method of particle flow code (PFC) in conjunction with the research results of soil arch effect of common anti-slip piles, and the influence of pile spacing on the evolution law of soil arch is analyzed to provide reference for the application and design of hTP.

Calculation principle
According to the soil arch theory analysis, soil arches exist behind both the front-rear piles of the hTP, and the soil arches of the front pile gradually penetrate into the interior of the soil arches of the rear pile, which causes fusion phenomenon between soil arches of the front-rear piles.As depicted in Fig. 1, the hTP is formed by connecting the front pile and the rear pile through the cross beam.

Soil arch force analysis
Assuming there is no shear and bending moments in the arch axis, the axial force F generated by the removal of the right half of the arch section acts on the point O. Establish the coordinate system as shown in Fig. 2, the equation of its arch axis is: For the bending moment at the foot of the arch at point A and according to the static equilibrium conditions it is obtained that: where T and R are the reaction forces generated at the foot of the arch and N is the horizontal axial force at the top section of the earth arch.
where  is the angle of friction between the pile and the soil.When s  ＞ ( the internal friction angle of the soil), taking tan s f  = .s  can be calculated by Eq. ( 7): tan arctan arctan where  and  are the shear stress and normal stress on the contact surface respectively; c and  are the cohesion and internal friction angle of the soil respectively, for the safety of calculation, take =0 c .
Substituting the expression for R , T into Eq.( 5): According to Eq. ( 8), the ratio between the arch height and arch span of the soil arch should be a constant value and an increase in the pile spacing does not affect the arch height to arch span ratio.Therefore, the research results of soil arching effect under specific pile spacing of anti-sliding piles are also applicable to soil arching effect under different pile spacings.

Three-dimensional discrete element model of the soil arch effect
Since the soil is a bulk medium and the hTP configuration is complex, this makes the soil pressure distribution and the soil arch effect mechanism complex.This paper adopts the method of coupling three-dimensional particle flow (soil mass) and solid unit (hTP) to analyze the soil arch effect of hTP.

Construction of Discrete Element Method Model
In the three-dimensional model, a contact bond is adopted for the bonding model between soil particles, and the boundary wall is used to restrain the soil movement.The bottom is subject to velocity constraints and the sides are normal constraints.The evolution of the soil arch in the hTP is studied by applying a certain velocity to the soil, as shown in Fig. 3.

Fig. 3. DEM numerical model of h-type pile
The pile adopts a linear elastic model.The size of fill area is 33m×39m×27m.The cross sections are 3m×3m.Set 3m=d, then the height of rear pile is hR=9.0d, the height of front pile is taken as hF=7.0d.The length of the crossbeam is taken as l=1.5d, and pile spacing is taken as S=4.0d.Considering the calculation efficiency, the particle size ranges from 0.28m to 0.4m, and the total number of model particles was 95801.For simplicity, the rear pile of hTP is referred as "R-Pile" and the front pile of hTP is referred as "F-Pile", and where not otherwise stated, displacements and stress in this paper are along the horizontal direction.

Calibration of the micro-scale parameters
The micro-scale parameters of the soil between the piles were calibrated using triaxial compressive tests, where the diameter and height of the triaxial specimen are 8m and 16m respectively, and the number of particles was 4363.Loading walls are set above and below the specimen to simulate the pressurisation process, and the side walls are restrained using wall units.
Some studies show that the contact bond model can well simulate the contact of soil particles (Zhang et al., 2021;Chen et al., 2021;Shi et al., 2022), so this contact model is adopted in this paper and stress-strain curves were obtained by applying 100, 200 and 300 kPa to the loading walls (Fig. 4).The parameters are listed in Table 1.

Deformation distribution of three-dimensional soil arches
Under the influence of the relative displacement between piles and soil, the soil arch effect gradually evolved into a phenomenon of soil stress redistribution.A constant horizontal velocity make the particles move gradually.However, the existence of anti-slip piles result in the particles in the process of movement must appear relative sliding, which further leads to stress changes.So the "soil arch structure" in the hTP can be analysed based on particle displacement deformation and stress changes.
The PFC 3D is used to study the soil arch effect.The soil particle balls are propelled to move horizontally at 0.1m/s along the negative X-axis in Fig. 3 to simulate the deformation effect of the landslide.The physical time of each time step was fixed as 5.4×10 -4 , and the displacement and stress under different time steps was used to analyze the change of soil arch effect, as shown in Fig. 5.

Horizontal deformation distribution
At 2000 time steps in Fig. 5(a), the soil arch generation is in the initial stage, the soil behind R-Pile and F-Pile is restrained by the pile.As the particle density of the soil behind the pile is greater than that of the soil in the pile, the soil deformation is locally reduced, which result in the soil constraint area gradually extends radially towards the middle of the slope.As the soil particles continue to move, by the 8000 time steps in Fig. 5(b), the soil arch is in a developmental stage and soil particles in the upper slope begins to stratify.The soil compacted area on the rear side of the R-Pile is radial and gradually becomes larger in extent, and a curved soil arch appears at the edge of the compacted area on the rear side of the two R-Pile.The soil particles of the lower slope body appear obviously stratified, and the soil arch appears obviously on the behind side of both F pile and R pile.Both soil arches exist in a certain thickness, and the stratification of the two soil arches is obvious.The displacement of the soil body on the free face is obviously larger than that of the soil body on the rear side of the soil arch.
As shown in Fig. 6, Yao Liang (Yao et al., 2014) also verified this phenomenon in physical model tests.The soil body behind the anti-slip pile after bearing the load, the soil arch effect will occur, the soil displacement on the back side of the soil arch is smaller, and the soil near the free face is more displaced and can even slip, At 16,000 time steps in Fig. 5 (Yao et al., 2014) As can be seen from Fig. 5 and Fig. 6, the development of the soil arch has roughly gone through four stages: initial stage, development stage, overlapping stage and stable stage.Compared with the R pile, the soil arch between the F piles develops faster.The displacement of the soil particles in the bottom layer A, middle layer B and upper layer C at the 2000 time steps, all appear to have two inflection points, as depicted in Fig. 7.The rear side of the R pile is often the place where the first displacement of each layer of soil particles appears at the inflection point, and the second displacement inflection point is located at 25 m.The appearance of the first inflection point indicates that at the initial stage, the antislip pile starts to form compression on the soil as the soil particles move; the appearance of the second inflection point may be related to the fact that the wall and the soil particles have a large contact force, which leads to a certain influence on the displacement of the soil particles.Combining the changes in displacement curves of the soil in each area under 8000 time steps and 16000 time steps in Fig. 7, it can be obtained that, as there is not much difference in the shape and interval of displacement curves of the soil arch between 8000 time steps and under 16000 time steps.At this time, the 8000 time steps are about the middle and late stages of the development of the earth arch, but the formation of soil arch in area C near the surface layer is obviously slower than the development of the soil arch in the middle and bottom layers.At 16000 time steps, the soil particles displacement curve shape changes less, but the overall displacement magnitude of each layer is found to change significantly, which indicates that the shape of the soil arch in the overlapping stage begins to stabilize.As the soil particles are given an overall velocity, they continue to produce displacement in each part while maintaining the shape of the soil arch.
As the time steps increase, the inflection point of the displacement curve of the soil particles in each area shows a tendency to move towards the pile side, and the slope of the inflection point gradually increases, which indicates that while the arch rise gradually decreases, the displacement difference between the soil particles inside and outside the arch line gradually increases.

Vertical deformation distribution
When the soil is subjected to external loads, under the action of stress redistribution, the soil will produce uneven displacement, which produces a soil arch effect.This inhomogeneous deformation does not only occur in the horizontal direction of a particular layer, but there are non-linear deformations in different horizontal displacements in different vertical regions.Although many scholars have used twodimensional simulations to study the soil arch effect, due to the spatial nature of the soil and soil arch, the two-dimensional simulations can only analyze the displacement in a certain horizontal region and cannot reflect the spatial deformation characteristics.Therefore, deformation monitoring in the vertical direction of the three-dimensional slope soil can better reflect the spatial nature of the soil arch effect.
In Fig. 8(a) and Fig. 8(b), it can be clearly seen that the displacement of the same horizontal layer of soil at different time steps along the depth direction of the soil body shows obvious arch, and the closer the soil particles to the soil arch line in the same layer of soil body, the smaller the displacement.With the increase of time steps, the displacement values at Profile-1 and Profile-2 both gradually increase, while the displacement arch values at Profile-3 show a gradually decreasing trend.Based on the overall change in values for Profile-1, 2 and 3, it can be seen that the displacement gradually decreases from the free face to the interior of the slope.
To further illustrate the vertical spatial characteristics of the displacement arch between the piles, displacement curves are plotted for the mid-section of the arch, as shown in Fig. 9.At 2000 time steps in the initial stage, the displacement of the middle and upper layers is approximately the same, and the displacement of the lower layers is significantly smaller than that of others layers.At 8000 time steps in the development stage, the displacement of the middle and upper layers is still much larger than that of the lower layers, but the peak displacement point starts to appear at 11.2m in the middle layer, and the value of the peak point is 0.35m.At 16000 time steps in the overlapping stage, the peak displacement point is still located near 11.2m in the middle layer, the value of the peak point increases to 0.56m, and the displacement difference between the middle layer and the upper layer increases further.It is inferred that this may be due to the existence of the crossbeam in the hTP, which causes the soil particles in contact with the crossbeam to be subjected to a certain frictional resistance, and the value of the frictional resistance is greater than the bond force between the soil particles.Due to the existence of the bond force between the soil particles causing the soil particles at the crossbeam to further influence the displacement of the surrounding soil particles.In this case, the displacement increases first and then decreases.
In the initial phase, the displacement curve in the middle section of Profile-2 has similar characteristics to the middle section of Profile-1.As the soil arch enters the development stage, the vertical displacement indicates a gradual decrease from the surface layer to the bottom layer.The rate of change of displacement is getting faster as judged by the slope of the curve.This indicates that the soil arch line from the surface, middle and then bottom layer is getting closer to the R-Pile pile body, and this tendency of proximity is getting faster with the increase of soil depth.The displacement in the middle section of Profile-3 is overall greater in the initial phase than in the development and overlapping stage, which is very different from the displacement curves in the middle section of Profile-1 and Profile-2.It is inferred that when the soil particles are first subjected to velocity, there is still a certain amount of pore space between the particles and the soil particles will produce a certain amount of displacement in the direction of the pile at this stage.As the time steps grow, the soil in this area will show a slight amount of displacement away from the pile body due to the effect of soil arch gradually occurs behind the R-Pile.

Horizontal Stress distribution
In order to obtain the horizontal stress of the slope, a measurement circle is used to monitor the stress change of soil particles in the strip area where A, B and C in Fig. 7(d) are located (as shown in Fig. 10).
In the Region-A area, the peak stress boundary is evident at 12m at any time steps, and the stresses in the soil particles at the free face are significantly lower, indicating that the number of soil bonds at the free face is lower compared to that of the soils at other locations.Combined with Fig. 11, it can be seen that during the process from 2000 time steps to 16000 time steps, the force chain from R-Pile to the location of F-Pile gradually becomes thinner and the force chain from F-Pile to the free face gradually disappears, which indicates that the presence of R-Pile at 11m causes the soil between the piles to be squeezed.At the same time, the soil arch formed by the squeezed soil between the piles is subjected to the pushing force from the soil on the back side, which leads to the appearance of the stress peak boundary line and makes the soil on the free face less stressed.In addition, the presence of the F-Pile further squeezes the soil around the pile, resulting in very low soil stresses in the 0-6m area.In the region of Region-B in the middle layer of the slope, the peak stress boundary appears near 11m at 2000 time steps, but as the running time step increases, the initial peak boundary starts to move away from the pile, and the initial boundary stabilizes near 16.5m after reaching 9000 time steps, which indicates that the soil arch generated by the R-Pile is gradually increasing in height as time gets longer.In Region-C, the maximum peak occurs mainly around 20m, but from 4500 time steps to 8000 time steps, there is a significant difference in stress distribution compared to the changes in Region-A and B during the same period.It can be inferred that when the soil arch formed by the topsoil is in the development stage, and the soil particles far away from the pile may have formed a relatively short new superimposed soil arch (Fig. 11(a)), which resulted in a change in stress in the topsoil located at 4500 time steps to 8000 time steps, but the superimposed soil arch was quickly destroyed as the running time step increased.
Region-A, B and C, before 2000 time steps, the stresses of soil particles at each location began to change and were at the initial stage of stress.As time steps increased, the stresses of soil particles continued to show large changes, with Region-A and Region-B stabilizing at 7000 time steps and Region-C stabilizing at 9000 time steps, which indicates that the soil arch under 2000-9000 time steps is in the development stage of stress change, but the development rate of soil arch stress at different depths may be different.After 9000 time steps, the stress of soil particles in each layer does not change significantly, and is in the stable stage of horizontal layer stress.From a comprehensive point of view, the horizontal layer stress values on the soil particles from the surface layer to the bottom layer of the slope show a trend from large to small, the peak of the horizontal layer stress shows a trend of gradually moving away from the free surface, and the horizontal layer stress values tend to be stable.

Vertical Stress distribution
The soil particles in the deformation monitoring zone shown in Fig. 8(d) in the first, second and third layers were monitored using measuring circles to obtain stress distributions and illustrated in Fig. 12(a), (b) and (c), respectively.The stresses in and around the pile at each time step of Profile-1 and Profile-2 are much greater than those at other locations, indicating that the soil arch transfers the bearing stresses to the foot of the arch.The width of the arch foot is greater than the width of the pile.However, the width of the arch decreases with the number of steps over time, falling to the width of the pile at 8000 steps.In Profile-3, the stresses do not change significantly at the locations where the piles are located, indicating that the effect of the soil arch created by the hTP on the stresses cannot be applied to the middle of the slope.At each time step, Profile-3 shows a clear characteristic which the stress gradually increases from the topsoil to the interior of the soil along the Z-direction.From 2000 time steps to 8000 time steps, Profile-1, 2 and 3 all show a sharp decrease in stress in the topsoil, presumably at the initial stage, the topsoil particles are influenced by the applied velocity and the existing and newly generated pores between the soil skeleton make the particles have space to move.The particles collide with each other very frequently, and as the running time increases, the pore space between the soil skeleton decreases and the particles tend to move more steadily.When the surface soil is less affected by the gravitational field, the stress in the surface soil decreases significantly, while the stress in the internal soil remains high.
At 2000 time steps, comparing the load distribution of Profile-1 and Profile-2, as shown in Fig. 12, the stress value of Profile-2 is greater than that of Profile-1, but after 8000 time steps, the stress value of Profile-2 is smaller than that of Profile-1.This may be due to the fact that at the initial stage of applying velocity to the soil particles, the R-Pile bears most of the soil thrust, and as the time step increases, the R-Pile transfers the force to the F-Pile and eventually makes the F-Pile carry a greater soil thrust than the R-Pile.The stress distribution and numerical magnitude of Profile-1, 2 and 3 did not change significantly from 8000 to 16000 time steps, indicating that the stresses along the vertical layer started to stabilise around 8000 time steps.
In order to further analyse the changes in the horizontal stresses as the time steps increase, the monitoring points behind and between the piles were monitored by measuring circles, and the pile-soil sharing ratios of 0.42:0.58,0.49:0.51and 0.44:0.55were obtained as shown in Fig. 13 before the soil body moved.As the running time step increases, the load of soil is continuously transferred to the piles.From Fig. 11(b), the pile-soil sharing ratio also gradually increases, the direction of the force chain at the back side of the piles also obviously orientated towards the piles.However, as the running time step continues to increase, the pile-soil sharing ratio begins to decrease slowly and eventually stabilizes.As the pile-soil sharing ratio increases and then decreases, the phenomenon is consistent with the existence and disappearance of the superimposed arch.It is assumed that the superimposed arch can transfer the overall stress of the soil on the back side of the arch to the pile through the original arch foot.With the increase in running time, the soil tends to stabilize and the stress on the soil particles starts to gradually decrease and stabilize.The superimposed arch also gradually disappears during this process, but as the soil arch does not transmit the stress perfectly, which leads to a gradual decrease in the stress stood by the pile and the pile to soil sharing ratio also gradually decreases and stabilizes.

Discussion
Pile spacing is of great significance to the study of soil arch effect.Therefore, the similarity of the evolution process of soil arches under different pile spacing is of great value.In the discrete element model, the horizontal displacements of the soil at the top and the middle of piles are obtained, where the maximum horizontal displacement value is ΔD, divided into 16 equal parts and differentiated by different colors, so as to plot the horizontal displacement of the soil at the top of B-Pile and Region-C in different pile spacing.As shown in Fig. 14, the red line is the soil arch at the back of R-Pile and the yellow dotted line is the soil arch at the back of F-Pile.When the anti-slip pile spacing continues to increase, the "soil arch structure" shows an obvious "parabolic" pattern under each working condition, and the soil arches behind the R-Pile and F-Pile show an obvious trend of overlap.
To further study the change of soil arch form under different pile spacing, it is assumed that the pile spacing is soil arch span with L and the soil arch rise as S. The statistics of the soil arch rise under each working condition were obtained as shown in Fig. 15, where the horizontal coordinate is the ratio of soil arch span to pile diameter and the vertical coordinate is the ratio of soil arch rise to pile diameter.According to Fig. 15, the rise of the soil arch increases linearly with the increase of the arch span, and the corresponding ΔS/ΔL in Fig. 15(a), (b) and (c) are 3.0, 2.3 and 2.8 respectively.The variation of ΔS/ΔL ratio under each working condition is relatively stable, which indicates that the rise of the soil arch is significantly affected by the increase of the anti-slip pile spacing.However, the shape of the soil arch does not change much, which is consistent with the theoretical calculations and analysis results in Part 2. The above study shows that the rise of the soil arch varies significantly with different anti-slip pile spacing, but ΔS/ΔL remains the same, and the evolutionary process is similar.

Conclusions
The discrete element method was introduced to create a landslide support model for hTP.The spatial soil arch effect of hTP was investigated to describe the distribution characteristics of the mechanical parameters of the soil in the pile.The main conclusions were including: (1) Between hTP, when the landslide medium is deformed horizontally, the soil goes through four stages of initial, development, overlapping and stable, with the soil arch between R-Pile developing at a slower rate than the soil arch between F-Pile.
(2) The soil arch line from the surface to the bottom layer is getting closer to the pile body behind the hTP, and this approaching trend becomes faster with the increase of the soil depth.The existence of hTP beams will affect the soil arch distribution of the soil on R-Pile and F-Pile.
(3) The soil arch stress between hTP in the horizontal direction goes through an initial stage, a development stage and stable stage.Where the stress stabilisation phase corresponds to the sum of the overlapping stage and the stable stage experienced by the horizontal displacement, from the surface layer to the subsoil of the slope, the horizontal layer stresses decrease gradually; The peak stresses of pile, the pile to soil sharing ratio and the stresses in the top soil layer all experience maximum values, when the arch footing width is at its maximum.
(4) Under different anti-slip pile spacing, the soil arch on the R-Pile and F-Pile will show fusion phenomenon, and the ratio of arch height and arch span under different anti-slip pile spacing is basically unchanged, which indicates that the evolution process of hTP is applicable to different pile spacing.

Fig
Fig. 2. Stress analysis of soil arch

Fig. 4 .
Fig. 4. The triaxial compressive simulation testTable 1 The mechanical parameters used in PFC3D simulations Effective modulus emod / MPa Stiffness ratio kratio Friction coefficient Density 80 3.0 0.5 1800 cb_strength tensile /Pa cb_strength shear /Pa Particles radius range Initial porosity 4×10 3 8×10 3 1.4 0.3 (c), the soil arch generation is in the overlapping stage, with the upper slope showing a significant soil arch; the soil arch on the rear side of the R-Pile on the lower slope disappears, and the soil arch on the rear side of the F-Pile does not change significantly.At 20,000 time steps in Fig. 5(d), the soil arch generation is in the stable stage, the upper and lower slope soil arch height and soil arch thickness are reduced, and the soil arch of the lower slope F pile and R pile are completely fused.

Fig. 7 .
Fig. 7. Horizontal displacement diagram (Displacement curves of soil particles in different areas): (a) Bottom Region-A (b) Middle Region-B (c) Upper Region-C (d) Soil monitoring area.

Fig. 12 .
Fig. 12. Horizontal stress distribution diagram under different profile: (a) profile-1, (b) profile-2, (c) profile-3, and the spatial positions of the Z and Y axes are identical to those of Z and Y in Fig. 7d.

Fig. 13 .
Fig. 13.Pile-soil sharing ratio: (a) Distribution of pile-soil load with time steps; (b),(c),(d) Changes in the share ratio of pilesoil at different points.

Fig. 15 .
Fig. 15.Arch height changes with different pile spacing: (a) Change of arch height at the top of R pile, (b) Change of side arch height behind R pile in C area, (c) Change of side arch height behind F pile in C area.