# A Comparative Study between Polyline and Straight Line Arrangements of Antislide Piles Based on Soil Arching Effect

Authors: Xue-gang Dai; A. Fa-you; Peng Zhang; Shi-qun Yan
Journal: Advances in Civil Engineering
 (2022)

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## Abstract

Considering the limitations of terrain and engineering expenses, antislide piles are sometimes arranged in polylines. Studies show that this arrangement adversely affects the mechanical characteristics of antislide piles. However, there is no in-deep understanding of this issue and the structural design and calculation method of this arrangement have not been discussed in relevant standards. Aiming at resolving this shortcoming, the polylines pile arrangement is studied in this article to provide a scientific basis for designing and calculating antislide piles. To this end, the cantilever pile is taken as the research background, and the soil arching effect between piles is taken as the research object. Then the performances of the single-row polyline pile layout and straight line pile layout are analyzed in the Dawanjiang landslide and the results are verified from the aspects of the landslide reinforcement and the influence on the antislide pile structure. The obtained results show that the polyline pile layout is disadvantageous to the safety of the antislide pile structure, and the soil arch between piles under the polyline pile layout condition is not uniform. Meanwhile, it is found that as the polyline pile layout angle increases, the stress concentration appears at the “inflection point.” Under this circumstance, the soil arch between piles is not uniform, and the stress concentration intensifies.


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## Body

## 1. Introduction

Pile is a civil engineering structure with a long history, which has been used for more than 14,000 years. With the development of science and technology, piles have been made of cast-iron sheets, steel, cement, concrete, and reinforced concrete [1–3]. With the rapid development of engineering construction, pile foundation has been widely used in housing construction, bridge wharf, and managing geological disasters. Recently, numerous investigations have been carried out on the design theory, construction technology, testing technology, and application of piles in diverse applications [4–6].Landslide is one of the most catastrophic natural geological disasters in the world. The study of landslide formation and prevention methods has attracted many scholars worldwide [7, 8]. In this regard, antislide piles have notable antislide characteristics, low sewage works, flexible arrangement, convenient construction, and good treatment effect. Accordingly, investigating the antislide pile has become a research hotspot. A review of the literature indicates that numerous investigations have been carried out on antislide piles from different aspects. However, most investigations have been focused on the bearing mechanism of antislide piles [9–11] and developing modified design and calculation methods [12, 13]. Studies show that the plane layout of an antislide pile, including the position of the pile and the distance between the piles, significantly affects the pile performance and stability of the structure. Li et al. [14] developed an interval model for stabilizing piles based on the friction soil arching effect. Moreover, Li et al. [15] proposed a simplified analytical model to analyze double-row pile stabilized slopes. Liu et al. [16] improved the plane layout of stabilizing piles based on the piecewise function expression of the irregular driving force. Zhang et al. [17, 18] proposed a method to calculate the maximum and minimum pile spacing considering the soil arching effect and interactions between multilayered sliding masses. Li et al. [19] developed a mechanical model of the soil arch to investigate interactions between piles and slope and optimize the pile spacing. Regarding the plane layout of antislide piles, a straight line arrangement is mainly adopted to ensure the antisliding effect, where the piles are arranged perpendicular to the landslide thrust direction. However, due to the limitations of terrain conditions and engineering investment in actual engineering, the antislide piles are sometimes arranged in polylines as well. The biggest feature of polyline layout is that the antislide piles are distributed in polylines on the plane. That is, some antislide piles are arranged perpendicular to the landslide thrust direction, while the other part of the piles is arranged obliquely to the landslide thrust direction Figure 1. Currently, although polyline layout is commonly used in landslide control, its kinetic mechanism is unclear, and the design and computational methods for pile structures have not been explained in relevant regulations. Hence, mechanism research is required to investigate the overall antisliding and soil arching effects of polyline layout, as well as its influence on the internal force distribution of antislide pile bodies.Figure 1
Schematic of polyline pile arrangement (made by the authors).As a major index reflecting the antisliding effect of piles, the soil arching effect refers to the stress redistribution caused by the heterogeneous displacement of soil under the pile-soil interaction. By transferring the landslide thrust to the antislide piles via the cohesion between soil bodies, it can fully exploit the soil shear strength to enhance the antisliding effect [20]. The discovery of the “granary effect” in 1884 by Roberts [21] marks the earliest research on the soil arching effect. Since 1943, when Terzaghi, a famous geomechanical scientist, confirmed the presence of the soil arching effect through the “Trapdoor test” [22], scholars around the world have paid attention to the research concerning the soil arching effect, achieving fruitful outcomes. Wang et al. [23] studied the soil arching in slopes. Furthermore, Zhang et al. [24–26] studied landslides in the reinforced soil arch by antisliding piles. Bosscheret al. [27, 28] studied the soil arch in Sandy. Deb et al. [29, 30] established a soil arch model. Moreover, numerous indoor model tests [31–33] and numerical simulations [34–36] have been carried out to investigate soil arching. However, none of the extant studies has involved the soil arching effect under polyline pile arrangement, which is worthy of further research. Analyzing the above statements, it can be noted that the design of polyline pile arrangement is a very topical issue. Therefore, the purpose of this study is to provide a corresponding scientific basis for the design of the polyline arrangements of antislide piles, and to achieve this, it is necessary to solve the following tasks:(1)
Studying the soil arching effect under polyline pile arrangement. And studying the evolution characteristics differences of soil arching effect in straight lines from those arranged in polylines.(2)
Revealing the risks of the polyline arrangements of antislide piles.


## 2. Soil Arch Calculation Model

### 2.1. Basic Hypotheses

Soil arching effect is a 3D space problem with complex stress relationships, which is caused by the heterogeneous displacement between soil particles under the action of landslide thrust. During analysis in this study, the soil arching effect is transformed into a plane strain problem and the following hypotheses are made:(1)
The thrust of landslide behind piles is a uniform load, where the resistance of soil in front of piles and the lateral pressure of soil are disregarded;(2)
The influences of arch thickness and soil self-weight are disregarded, and the soil arch is a single line type;(3)
The soil arching problem is assumed as a plane strain problem, and the arch shape variation with depth is disregarded.


### 2.2. Equation for Reasonable Arch Axis

Reasonable axis of soil arch means that when the soil arching effect is optimal, the structure and shape of soil arch are inevitably in the most reasonable stress state, which is called the reasonable arch axis in structural mechanics. There is no bending moment or shear force on any section on the reasonable arch axis, where only the axial force exists.As is clear from the force diagram of soil arch in Figure2, the force F on the arch back is a uniform load, b denotes the width of each antislide pile, L denotes the net distance between piles, px,py, ph and pvrepresent the end reactions of piles to the soil arch in the X and Y directions, and f is the soil arch vector height. Since the bending moment at any point on the reasonable arch axis equation is 0, the balance equation is established for the moment at arbitrary point N as follows:(1)F2x2−Pxy+Pyx=0.Figure 2
Force diagram of soil arch [37].
(a)(b)According to the force balance in theX direction:(2)Pv=Px.According to the force balance in theY direction:(3)py=L2F.By taking the moment at pointO, the balance equations are established as follows:(4)F8L2−F4L2+Pxf=0Px=F8L2.Accordingly, the equation for soil arch axis is given as follows:(5)y=4fxL−xL2.At any pointM on the axis of symmetrical soil arches, the vertical support force is Fx, the horizontal thrust is px=F/8L2, and the resultant force O is given as follows:(6)O=FL2+64x2f28f.The azimuth angleα of soil arch line is expressed as follows:(7)a=tan−18fFxFL2=tan−18fxL2=tan−1dydx.It is clear from Equation (7) that the resultant force O at any point is precisely the axial force. According to Equation (7), the resultant force O at any point is the increasing function of x. That is, the minimum axial force at the arch crown is L2/8fF, and the maximum axial force at the arch foot is FLL2+16f2/8f. Hence, on the premise of the abovementioned hypotheses, failure of soil arch occurs initially at the foot position.


## 2.1. Basic Hypotheses

Soil arching effect is a 3D space problem with complex stress relationships, which is caused by the heterogeneous displacement between soil particles under the action of landslide thrust. During analysis in this study, the soil arching effect is transformed into a plane strain problem and the following hypotheses are made:(1)
The thrust of landslide behind piles is a uniform load, where the resistance of soil in front of piles and the lateral pressure of soil are disregarded;(2)
The influences of arch thickness and soil self-weight are disregarded, and the soil arch is a single line type;(3)
The soil arching problem is assumed as a plane strain problem, and the arch shape variation with depth is disregarded.


## 2.2. Equation for Reasonable Arch Axis

Reasonable axis of soil arch means that when the soil arching effect is optimal, the structure and shape of soil arch are inevitably in the most reasonable stress state, which is called the reasonable arch axis in structural mechanics. There is no bending moment or shear force on any section on the reasonable arch axis, where only the axial force exists.As is clear from the force diagram of soil arch in Figure2, the force F on the arch back is a uniform load, b denotes the width of each antislide pile, L denotes the net distance between piles, px,py, ph and pvrepresent the end reactions of piles to the soil arch in the X and Y directions, and f is the soil arch vector height. Since the bending moment at any point on the reasonable arch axis equation is 0, the balance equation is established for the moment at arbitrary point N as follows:(1)F2x2−Pxy+Pyx=0.Figure 2
Force diagram of soil arch [37].
(a)(b)According to the force balance in theX direction:(2)Pv=Px.According to the force balance in theY direction:(3)py=L2F.By taking the moment at pointO, the balance equations are established as follows:(4)F8L2−F4L2+Pxf=0Px=F8L2.Accordingly, the equation for soil arch axis is given as follows:(5)y=4fxL−xL2.At any pointM on the axis of symmetrical soil arches, the vertical support force is Fx, the horizontal thrust is px=F/8L2, and the resultant force O is given as follows:(6)O=FL2+64x2f28f.The azimuth angleα of soil arch line is expressed as follows:(7)a=tan−18fFxFL2=tan−18fxL2=tan−1dydx.It is clear from Equation (7) that the resultant force O at any point is precisely the axial force. According to Equation (7), the resultant force O at any point is the increasing function of x. That is, the minimum axial force at the arch crown is L2/8fF, and the maximum axial force at the arch foot is FLL2+16f2/8f. Hence, on the premise of the abovementioned hypotheses, failure of soil arch occurs initially at the foot position.


## 3. Comparative Analysis of Soil Arching Effect Simulations

Formation of soil arching effect is attributed to the principal stress migration, in which the soil body transfers the landslide thrust to the nearby area of pile periphery soil by relying on the shear strength between soil particles under the pile-soil interaction. Thus, the strength of soil arching effect can be determined by the deflection degree of stress between soil particles. Stronger soil arching effect indicates greater deflection of principal stress and a more obvious decrease of landslide thrust along the negative direction of theY-axis (landslide thrust direction). Unlike the ordinary arch structure, the soil arch is a stress arch generated inside the soil body. Its action and nonaction zones have the same medium, making it difficult to determine a clear boundary. Meanwhile, given the coincidence of the intersection point between the reasonable axis and midspan symmetry plane of soil arch with the stress peak point in the X direction, the straight line distance from this point to the rear of antislide piles along the Y direction is precisely the vector height of soil arch. Thus, the change in soil arching effect range can be analyzed based on the variation of arch vector height. Besides, the extrusion strength between soil particles is determined according to the size of X-directional principal stress on the midspan symmetry plane of soil arch. Greater value of X indicates stronger soil extrusion effect and higher arch strength. In summary, during the analysis of soil arching effect in this study, the principal stress distribution isogram in the Y direction, and the X- and Y-directional principal stress distribution curves on the midspan symmetry plane of soil arch are mainly analyzed, in order to compare the evolution of soil arching effect under straight line layout versus that under polyline layout.In this section, fast lagrangian analysis of continua in 3 dimensions (FLAC3D) software, which is a powerful tool to perform geotechnical analyses of soil, rock, groundwater, constructs, and ground support [38, 39] is applied to carry out numerical analyses. Studies show that FlAC3D software has remarkable advantages. First, it uses the “mixed discrete method” to simulate plastic failure and plastic flow. It is worth noting that this method is more accurate than the “discrete integration method,” which is usually used in the finite element method. Second, even though the simulated system is static, the dynamic equations of motion should be solved, which makes FLAC3D have no numerical obstacles in simulating the physically unstable process. Last, it adopts an explicit solution scheme. Therefore, the explicit solution takes almost the same time to obtain the nonlinear stress-strain relation as the linear constitutive relation, while the implicit solution takes a long time to solve a nonlinear problem. Meanwhile, there is no need to store the stiffness matrix so multielement structures can be solved with less memory capacity. Therefore, it is feasible to simulate large deformations because there is no stiffness matrix to be modified. Accordingly, the FLAC3D software is selected in the present study to analyze the problem.During numerical analysis, a geological model of an ideal landslide is built based on FLAC3D while ignoring the changes in surface configuration. Figure3 displays the typical section of the homogeneous soil landslide. To eliminate the influence of boundary conditions, the model boundary before the piles is extended to 20 m, while that behind the piles is extended to 30 m during modeling. The self-weight load is primarily considered in the calculation herein, and unidirectional constrained boundaries are adopted on the two sides and bottom of the model. Regarding the soil constitutive model, the Mohr–Coulomb plasticity model following Mohr–Coulomb yield criterion is adopted, while the elastoplastic model is employed for the antislide piles and retaining plates. Table 1 details the computational parameters.Figure 3
Schematic of a typical cross-section of ideal landslide (made by the authors).Table 1
Physicomechanical parameters of materials.
Model materialElastic modulus E (GPa)Poisson’s ratioμInternal friction angleφ (°)Cohesion C (kPa)Soil body0.020.251517Antislide pile300.2——Retaining plate0.30.2——


### 3.1. Numerical Simulation of Straight Line Pile Arrangement

#### 3.1.1. Modeling

Figure4 depicts the ideal model for a straight line layout of piles, which is 64.4 m long, 40 m wide, and 14 m high. The slide body has a thickness of 6 m. The model is divided into 277,344 meshes, and a total of 9 antislide piles are set up, with a length of 10 m, where the anchoring section is 6 m below the pile top. The pile cross section is 2 m long, 1.5 m wide, and the pile spacing is 6 m. Retaining plates are provided behind the antislide piles, which are 6 m long, 6 m wide and 0.5 m thick. For the model, its right side is the positive direction of the X-axis, its rear side is the positive direction of the Y-axis, and its top side is the positive direction of the Z-axis.Figure 4
Model of straight line pile arrangement.During the investigation of soil arching effect, the action zone of the 5 antislide piles in the middle is selected for the study. The corresponding soil arches are the 3# soil arch between 3#–4# piles, the 4# soil arch between 4#–5# piles, the 5# soil arch between 5#–6# piles, and the 6# soil arch between 6#–7# piles. Disregarding the changes in soil arches in the vertical direction, the horizontal section atZ = 8 m is taken for analysis.


#### 3.1.2. Analysis of Simulation Results

Figures5 and 6 separately display the displacement and principal stress isoline maps in the Y direction under a straight line layout of piles. By analyzing the displacement and stress distribution of soil behind the piles, we can determine whether the soil arching effect occurs, and can reflect the deflection of landslide thrust and the action range of soil arches. It is clear from Figure 5 that the displacement of soil between the piles is significantly larger than that of soil behind the piles. That is, heterogeneous displacement is present between the particles of the slide body. In Figure 6, the Y-directional principal stress at the arch midspan decreases gradually from the back to the front of the piles, while the stress value on the back side of the piles increases gradually. This indicates that the Y-directional principal stress along the landslide thrust direction is deflected to both sides and concentrated near the back of the piles. Based on the formation conditions and mechanism of soil arches, it can be determined that the soil arching effect already occurs under the straight line layout. Besides, according to the principal displacement and stress distribution in the figure, under the straight line layout, the action ranges of 3#, 4#, 5#, and 6# soil arches are basically identical. The closer the principal stress to the sheet-pile wall vicinity, the more obvious the stress deflection, which is manifested as the greater isoline density on the stress isoline map. Contrastively, as the distance from the wall increases, the isoline density gradually decreases, the thickness of the isobaric zone increases, and the abrupt stress change becomes unobvious. This indicates that the farther away from the sheet-pile wall, the weaker the soil arching effect.Figure 5
Displacement isoline map in theY direction.Figure 6
Principal stress isoline map in theY direction.Figures7, and 8 separately depict the Y- and X-directional principal stress distributions on the midspan symmetry plane of soil arches under the straight line pile arrangement. As is clear, the forces and action ranges are basically identical for the 3#, 4#, 5#, and 6# soil arches. In Figure 7 the Y-directional principal stress decreases most obviously in the X = 0.5–4.9 m region, and in Figure 8, the X-directional principal stress also reaches its peak in this region, suggesting that this region is the range of soil arching effect. Besides, it is clear from Figure 7 that at X = 1.95 m, the principal stress value peaks, that is, the vector heights of soil arches are all 1.95 m.Figure 7
Y-directional principal stress curve at midspan of soil arch.Figure 8
X-directional principal stress curve at midspan of soil arch.In summary, the soil arching effect can be produced when the piles are arranged in straight lines, which weakens gradually along the direction against the antislide piles. Meanwhile, the forces and action ranges are basically identical for the 1#, 2#, 3#, and 4# soil arches. This suggests that under a straight line layout, the landslide thrust is uniformly distributed at various positions, and the antislide sheet-pile walls evenly share the load, which is beneficial to the safety of sheet-pile wall structure.


### 3.2. Numerical Simulation of Polyline Pile Arrangement

#### 3.2.1. Modeling

To investigate the evolution characteristics of soil arching effect under the polyline arrangement of piles, a model of polyline pile layout is built (Figure9), with which the numerical simulation analysis is performed on the soil arching effect between piles. Compared to the afore-described straight line layout, the parameters of the polyline pile layout model remain unchanged except for the adjusted layout angle of the antislide piles. On the basis of a straight line layout, a “section orthogonal to thrust” is arranged for the antislide piles on the right of 5# pile, which serves as the inflection point. This section is consistent with that under the straight line layout. Meanwhile, the part on the left of 5# pile is a “section oblique to thrust,” which is overall arranged by rotating at a certain angle with the central point of 5# pile as the circle center. The antislide piles in this section are obliquely intersected with the landslide thrust. In this study, models of 10°, 20°, and 30° polyline pile layouts are separately built. Figure 9 displays the model of 10° polyline pile arrangement.Figure 9
Model of 10° polyline pile arrangement.


#### 3.2.2. Analysis of Simulation Results

For the convenience of analysis, during the investigation of the soil arching effect under polyline pile arrangement, the soil arches are classified into those on the “section oblique to thrust” and those on the “section orthogonal to thrust.” The 3# and 4# soil arches are on the “section oblique to thrust,” whereas the 5# and 6# soil arches are on the “section orthogonal to thrust.” Besides, the 5# arch is also called the “inflection point” soil arch, since it is very close to the inflection point.Figure10 illustrates the isoline maps of Y-directional principal stresses under the 10°, 20°, and 30° polyline pile arrangements, while Figure 11 presents the comparisons among Y-directional principal stress curves at the midspan under the straight line and 10°, 20°, and 30° polyline pile arrangements. As is clear, the Y-directional principal stress values of soil arches at the midspan gradually decrease from the back to the front of piles, while the stress values on the back side of piles gradually increase. There are clear trajectories of principal stress deflection, indicating that the soil arching effect is exerted. However, unlike the case of straight line layout, under the polyline pile arrangement at the same angles, the Y-directional principal stresses of both 3# and 4# soil arches decrease, while those of both 5# and 6# soil arches increase, especially for the 5# arch. That is, when the piles are arranged in polylines, the soil pressures at the arch crown within the “section oblique to thrust” decrease, while those within the “section orthogonal to thrust” increase. Such an increase is most evident for the soil arch at the inflection point. Moreover, with the increasing angle of polyline pile layout, the Y-directional principal stress at the “inflection point” increases more evidently. Meanwhile, the principal stresses in the Y direction also differ by the angle of polyline pile layout. Specifically, with the increase in such angle, the isoline density of Y-directional principal stress gradually decreases, the thickness of the isobaric zone gradually thickens, and the progressive decrease of stress is unobvious, suggesting the gradual weakening of soil arching effect.Figure 10
Comparisons among principal stress isoline maps in theY direction, (a) 10° polyline pile arrangement, (b) 20° polyline pile arrangement, and (c) 30° polyline pile arrangement.
(a)(b)(c)Figure 11
Comparisons among principal stress curves in theY direction.
(a)(b)(c)(d)Table2 lists the peak statistics for the Y-directional principal stresses of soil arches at various pile layout angles, whereas Figure 12 depicts the variations of Y-directional principal stresses of soil arches at various pile layout angles. As is clear, with the increase in the angle of polyline pile arrangement, the Y-directional principal stresses on the midspan symmetry planes of 3# and 4# soil arches decrease continuously, while those of 5# and 6# soil arches increase continuously. In addition, with the increase in the angle of polyline pile arrangement, the Y-directional principal stress peaks at the midspan of 3# and 4# arches move backward to varying degrees, suggesting that the range of soil arching effect shifts away from the antislide piles. Meanwhile, as displayed by the variation curves of Y-directional principal stresses, the inscribed slopes of the curves are gradually decreasing, indicating the weakening of the soil arching effect. The Y-directional principal stress peaks at the midspan of 5# soil arch move forward to varying degrees with the increase in the pile layout angle, suggesting the diminishing range of soil arching effect. Regarding the changes in the stress curves, the inscribed slopes of the curves increase, the abrupt changes of Y-directional principal stresses are obvious, and the soil arching effect is enhanced. Regarding the Y-directional principal stress distribution of 6# soil arch, the Y-directional principal stress at the arch crown somewhat increases under polyline pile arrangement, despite a smaller increase than that of the 5# soil arch. The peak point position for 6# arch is consistent with that under a straight line arrangement, and the soil arching effect and its range of action are fundamentally unchanged.Table 2
Peak statistics for the Y-directional principal stresses of soil arches.
Pile layout angleY-directional principal stress peak (kPa)Peak position3# soil arch4# soil arch5# soil arch6# soil arch3# soil arch4# soil arch5# soil arch6# soil archStraight line layout6.116.116.116.114.94.94.94.910° layout6.16.096.576.144.85.14.44.920° layout65.967.016.175.25.34.34.930° layout5.925.87.376.225.85.54.34.9Figure 12
Variation curves of Y-directional principal stresses of soil arches at various pile layout angles.
(a)(b)(c)(d)Table3 lists the peak and vector height statistics for the X-directional principal stresses of soil arches, whereas Figures 13 and 14 separately depict the X-directional principal stress distributions of different soil arches under polyline pile arrangement and the X-directional principal stress variations of soil arches at different pile layout angles. According to Figure 13, under polyline pile arrangement, the principal stresses in the X direction are overall large in the middle and small on two sides, and maximum principal stress in the X direction is noted at the 5# soil arch. Suggestively, the extrusion effect between soil particles becomes stronger as the distance to the inflection point becomes closer, and the stress concentration becomes obvious, which is detrimental to the structural safety of the antislide pile at the inflection point.Table 3
Peak and vector height statistics for the X-directional principal stresses of soil arches.
Pile layout angleX-directional principal stress peak (kPa)Vector height (m)3# soil arch4# soil arch5# soil arch6# soil arch3# soil arch4# soil arch5# soil arch6# soil archStraight line layout5.55.55.55.51.951.951.951.9510° layout6.927.297.736.142.172.331.461.9520° layout7.37.78.47.262.272.241.461.9530° layout8.48.89.417.272.252.560.971.95Figure 13
Comparisons among principal stress curves in theX direction.
(a)(b)(c)(d)Figure 14
X-directional principal stress curves on the midspan symmetry planes of soil arches under polyline pile arrangements.
(a)(b)(c)(d)It is clear from Figure14 that with the increase in pile layout angle, the X-directional principal stresses at the midspan of 3#, 4#, 5#, and 6# soil arches increase continuously, indicating that under polyline pile arrangement, the extrusion effect between soil particles is enhanced with the increasing layout angle, and the stress concentration becomes ever obvious, which is detrimental to the structural safety of antislide piles. Based on the vector height changes of soil arches, the soil arch vector heights show uneven distribution under polyline layout when compared to the straight line layout, with those on the “section oblique to thrust” greater than those on the “section orthogonal to thrust.” That is, the 3# and 4# soil arches exhibit larger action ranges than the 5# and 6# soil arches, showing agreement with the Y-directional principal stress distributions in Figure 11.


## 3.1. Numerical Simulation of Straight Line Pile Arrangement

### 3.1.1. Modeling

Figure4 depicts the ideal model for a straight line layout of piles, which is 64.4 m long, 40 m wide, and 14 m high. The slide body has a thickness of 6 m. The model is divided into 277,344 meshes, and a total of 9 antislide piles are set up, with a length of 10 m, where the anchoring section is 6 m below the pile top. The pile cross section is 2 m long, 1.5 m wide, and the pile spacing is 6 m. Retaining plates are provided behind the antislide piles, which are 6 m long, 6 m wide and 0.5 m thick. For the model, its right side is the positive direction of the X-axis, its rear side is the positive direction of the Y-axis, and its top side is the positive direction of the Z-axis.Figure 4
Model of straight line pile arrangement.During the investigation of soil arching effect, the action zone of the 5 antislide piles in the middle is selected for the study. The corresponding soil arches are the 3# soil arch between 3#–4# piles, the 4# soil arch between 4#–5# piles, the 5# soil arch between 5#–6# piles, and the 6# soil arch between 6#–7# piles. Disregarding the changes in soil arches in the vertical direction, the horizontal section atZ = 8 m is taken for analysis.


### 3.1.2. Analysis of Simulation Results

Figures5 and 6 separately display the displacement and principal stress isoline maps in the Y direction under a straight line layout of piles. By analyzing the displacement and stress distribution of soil behind the piles, we can determine whether the soil arching effect occurs, and can reflect the deflection of landslide thrust and the action range of soil arches. It is clear from Figure 5 that the displacement of soil between the piles is significantly larger than that of soil behind the piles. That is, heterogeneous displacement is present between the particles of the slide body. In Figure 6, the Y-directional principal stress at the arch midspan decreases gradually from the back to the front of the piles, while the stress value on the back side of the piles increases gradually. This indicates that the Y-directional principal stress along the landslide thrust direction is deflected to both sides and concentrated near the back of the piles. Based on the formation conditions and mechanism of soil arches, it can be determined that the soil arching effect already occurs under the straight line layout. Besides, according to the principal displacement and stress distribution in the figure, under the straight line layout, the action ranges of 3#, 4#, 5#, and 6# soil arches are basically identical. The closer the principal stress to the sheet-pile wall vicinity, the more obvious the stress deflection, which is manifested as the greater isoline density on the stress isoline map. Contrastively, as the distance from the wall increases, the isoline density gradually decreases, the thickness of the isobaric zone increases, and the abrupt stress change becomes unobvious. This indicates that the farther away from the sheet-pile wall, the weaker the soil arching effect.Figure 5
Displacement isoline map in theY direction.Figure 6
Principal stress isoline map in theY direction.Figures7, and 8 separately depict the Y- and X-directional principal stress distributions on the midspan symmetry plane of soil arches under the straight line pile arrangement. As is clear, the forces and action ranges are basically identical for the 3#, 4#, 5#, and 6# soil arches. In Figure 7 the Y-directional principal stress decreases most obviously in the X = 0.5–4.9 m region, and in Figure 8, the X-directional principal stress also reaches its peak in this region, suggesting that this region is the range of soil arching effect. Besides, it is clear from Figure 7 that at X = 1.95 m, the principal stress value peaks, that is, the vector heights of soil arches are all 1.95 m.Figure 7
Y-directional principal stress curve at midspan of soil arch.Figure 8
X-directional principal stress curve at midspan of soil arch.In summary, the soil arching effect can be produced when the piles are arranged in straight lines, which weakens gradually along the direction against the antislide piles. Meanwhile, the forces and action ranges are basically identical for the 1#, 2#, 3#, and 4# soil arches. This suggests that under a straight line layout, the landslide thrust is uniformly distributed at various positions, and the antislide sheet-pile walls evenly share the load, which is beneficial to the safety of sheet-pile wall structure.


## 3.1.1. Modeling

Figure4 depicts the ideal model for a straight line layout of piles, which is 64.4 m long, 40 m wide, and 14 m high. The slide body has a thickness of 6 m. The model is divided into 277,344 meshes, and a total of 9 antislide piles are set up, with a length of 10 m, where the anchoring section is 6 m below the pile top. The pile cross section is 2 m long, 1.5 m wide, and the pile spacing is 6 m. Retaining plates are provided behind the antislide piles, which are 6 m long, 6 m wide and 0.5 m thick. For the model, its right side is the positive direction of the X-axis, its rear side is the positive direction of the Y-axis, and its top side is the positive direction of the Z-axis.Figure 4
Model of straight line pile arrangement.During the investigation of soil arching effect, the action zone of the 5 antislide piles in the middle is selected for the study. The corresponding soil arches are the 3# soil arch between 3#–4# piles, the 4# soil arch between 4#–5# piles, the 5# soil arch between 5#–6# piles, and the 6# soil arch between 6#–7# piles. Disregarding the changes in soil arches in the vertical direction, the horizontal section atZ = 8 m is taken for analysis.


## 3.1.2. Analysis of Simulation Results

Figures5 and 6 separately display the displacement and principal stress isoline maps in the Y direction under a straight line layout of piles. By analyzing the displacement and stress distribution of soil behind the piles, we can determine whether the soil arching effect occurs, and can reflect the deflection of landslide thrust and the action range of soil arches. It is clear from Figure 5 that the displacement of soil between the piles is significantly larger than that of soil behind the piles. That is, heterogeneous displacement is present between the particles of the slide body. In Figure 6, the Y-directional principal stress at the arch midspan decreases gradually from the back to the front of the piles, while the stress value on the back side of the piles increases gradually. This indicates that the Y-directional principal stress along the landslide thrust direction is deflected to both sides and concentrated near the back of the piles. Based on the formation conditions and mechanism of soil arches, it can be determined that the soil arching effect already occurs under the straight line layout. Besides, according to the principal displacement and stress distribution in the figure, under the straight line layout, the action ranges of 3#, 4#, 5#, and 6# soil arches are basically identical. The closer the principal stress to the sheet-pile wall vicinity, the more obvious the stress deflection, which is manifested as the greater isoline density on the stress isoline map. Contrastively, as the distance from the wall increases, the isoline density gradually decreases, the thickness of the isobaric zone increases, and the abrupt stress change becomes unobvious. This indicates that the farther away from the sheet-pile wall, the weaker the soil arching effect.Figure 5
Displacement isoline map in theY direction.Figure 6
Principal stress isoline map in theY direction.Figures7, and 8 separately depict the Y- and X-directional principal stress distributions on the midspan symmetry plane of soil arches under the straight line pile arrangement. As is clear, the forces and action ranges are basically identical for the 3#, 4#, 5#, and 6# soil arches. In Figure 7 the Y-directional principal stress decreases most obviously in the X = 0.5–4.9 m region, and in Figure 8, the X-directional principal stress also reaches its peak in this region, suggesting that this region is the range of soil arching effect. Besides, it is clear from Figure 7 that at X = 1.95 m, the principal stress value peaks, that is, the vector heights of soil arches are all 1.95 m.Figure 7
Y-directional principal stress curve at midspan of soil arch.Figure 8
X-directional principal stress curve at midspan of soil arch.In summary, the soil arching effect can be produced when the piles are arranged in straight lines, which weakens gradually along the direction against the antislide piles. Meanwhile, the forces and action ranges are basically identical for the 1#, 2#, 3#, and 4# soil arches. This suggests that under a straight line layout, the landslide thrust is uniformly distributed at various positions, and the antislide sheet-pile walls evenly share the load, which is beneficial to the safety of sheet-pile wall structure.


## 3.2. Numerical Simulation of Polyline Pile Arrangement

### 3.2.1. Modeling

To investigate the evolution characteristics of soil arching effect under the polyline arrangement of piles, a model of polyline pile layout is built (Figure9), with which the numerical simulation analysis is performed on the soil arching effect between piles. Compared to the afore-described straight line layout, the parameters of the polyline pile layout model remain unchanged except for the adjusted layout angle of the antislide piles. On the basis of a straight line layout, a “section orthogonal to thrust” is arranged for the antislide piles on the right of 5# pile, which serves as the inflection point. This section is consistent with that under the straight line layout. Meanwhile, the part on the left of 5# pile is a “section oblique to thrust,” which is overall arranged by rotating at a certain angle with the central point of 5# pile as the circle center. The antislide piles in this section are obliquely intersected with the landslide thrust. In this study, models of 10°, 20°, and 30° polyline pile layouts are separately built. Figure 9 displays the model of 10° polyline pile arrangement.Figure 9
Model of 10° polyline pile arrangement.


### 3.2.2. Analysis of Simulation Results

For the convenience of analysis, during the investigation of the soil arching effect under polyline pile arrangement, the soil arches are classified into those on the “section oblique to thrust” and those on the “section orthogonal to thrust.” The 3# and 4# soil arches are on the “section oblique to thrust,” whereas the 5# and 6# soil arches are on the “section orthogonal to thrust.” Besides, the 5# arch is also called the “inflection point” soil arch, since it is very close to the inflection point.Figure10 illustrates the isoline maps of Y-directional principal stresses under the 10°, 20°, and 30° polyline pile arrangements, while Figure 11 presents the comparisons among Y-directional principal stress curves at the midspan under the straight line and 10°, 20°, and 30° polyline pile arrangements. As is clear, the Y-directional principal stress values of soil arches at the midspan gradually decrease from the back to the front of piles, while the stress values on the back side of piles gradually increase. There are clear trajectories of principal stress deflection, indicating that the soil arching effect is exerted. However, unlike the case of straight line layout, under the polyline pile arrangement at the same angles, the Y-directional principal stresses of both 3# and 4# soil arches decrease, while those of both 5# and 6# soil arches increase, especially for the 5# arch. That is, when the piles are arranged in polylines, the soil pressures at the arch crown within the “section oblique to thrust” decrease, while those within the “section orthogonal to thrust” increase. Such an increase is most evident for the soil arch at the inflection point. Moreover, with the increasing angle of polyline pile layout, the Y-directional principal stress at the “inflection point” increases more evidently. Meanwhile, the principal stresses in the Y direction also differ by the angle of polyline pile layout. Specifically, with the increase in such angle, the isoline density of Y-directional principal stress gradually decreases, the thickness of the isobaric zone gradually thickens, and the progressive decrease of stress is unobvious, suggesting the gradual weakening of soil arching effect.Figure 10
Comparisons among principal stress isoline maps in theY direction, (a) 10° polyline pile arrangement, (b) 20° polyline pile arrangement, and (c) 30° polyline pile arrangement.
(a)(b)(c)Figure 11
Comparisons among principal stress curves in theY direction.
(a)(b)(c)(d)Table2 lists the peak statistics for the Y-directional principal stresses of soil arches at various pile layout angles, whereas Figure 12 depicts the variations of Y-directional principal stresses of soil arches at various pile layout angles. As is clear, with the increase in the angle of polyline pile arrangement, the Y-directional principal stresses on the midspan symmetry planes of 3# and 4# soil arches decrease continuously, while those of 5# and 6# soil arches increase continuously. In addition, with the increase in the angle of polyline pile arrangement, the Y-directional principal stress peaks at the midspan of 3# and 4# arches move backward to varying degrees, suggesting that the range of soil arching effect shifts away from the antislide piles. Meanwhile, as displayed by the variation curves of Y-directional principal stresses, the inscribed slopes of the curves are gradually decreasing, indicating the weakening of the soil arching effect. The Y-directional principal stress peaks at the midspan of 5# soil arch move forward to varying degrees with the increase in the pile layout angle, suggesting the diminishing range of soil arching effect. Regarding the changes in the stress curves, the inscribed slopes of the curves increase, the abrupt changes of Y-directional principal stresses are obvious, and the soil arching effect is enhanced. Regarding the Y-directional principal stress distribution of 6# soil arch, the Y-directional principal stress at the arch crown somewhat increases under polyline pile arrangement, despite a smaller increase than that of the 5# soil arch. The peak point position for 6# arch is consistent with that under a straight line arrangement, and the soil arching effect and its range of action are fundamentally unchanged.Table 2
Peak statistics for the Y-directional principal stresses of soil arches.
Pile layout angleY-directional principal stress peak (kPa)Peak position3# soil arch4# soil arch5# soil arch6# soil arch3# soil arch4# soil arch5# soil arch6# soil archStraight line layout6.116.116.116.114.94.94.94.910° layout6.16.096.576.144.85.14.44.920° layout65.967.016.175.25.34.34.930° layout5.925.87.376.225.85.54.34.9Figure 12
Variation curves of Y-directional principal stresses of soil arches at various pile layout angles.
(a)(b)(c)(d)Table3 lists the peak and vector height statistics for the X-directional principal stresses of soil arches, whereas Figures 13 and 14 separately depict the X-directional principal stress distributions of different soil arches under polyline pile arrangement and the X-directional principal stress variations of soil arches at different pile layout angles. According to Figure 13, under polyline pile arrangement, the principal stresses in the X direction are overall large in the middle and small on two sides, and maximum principal stress in the X direction is noted at the 5# soil arch. Suggestively, the extrusion effect between soil particles becomes stronger as the distance to the inflection point becomes closer, and the stress concentration becomes obvious, which is detrimental to the structural safety of the antislide pile at the inflection point.Table 3
Peak and vector height statistics for the X-directional principal stresses of soil arches.
Pile layout angleX-directional principal stress peak (kPa)Vector height (m)3# soil arch4# soil arch5# soil arch6# soil arch3# soil arch4# soil arch5# soil arch6# soil archStraight line layout5.55.55.55.51.951.951.951.9510° layout6.927.297.736.142.172.331.461.9520° layout7.37.78.47.262.272.241.461.9530° layout8.48.89.417.272.252.560.971.95Figure 13
Comparisons among principal stress curves in theX direction.
(a)(b)(c)(d)Figure 14
X-directional principal stress curves on the midspan symmetry planes of soil arches under polyline pile arrangements.
(a)(b)(c)(d)It is clear from Figure14 that with the increase in pile layout angle, the X-directional principal stresses at the midspan of 3#, 4#, 5#, and 6# soil arches increase continuously, indicating that under polyline pile arrangement, the extrusion effect between soil particles is enhanced with the increasing layout angle, and the stress concentration becomes ever obvious, which is detrimental to the structural safety of antislide piles. Based on the vector height changes of soil arches, the soil arch vector heights show uneven distribution under polyline layout when compared to the straight line layout, with those on the “section oblique to thrust” greater than those on the “section orthogonal to thrust.” That is, the 3# and 4# soil arches exhibit larger action ranges than the 5# and 6# soil arches, showing agreement with the Y-directional principal stress distributions in Figure 11.


## 3.2.1. Modeling

To investigate the evolution characteristics of soil arching effect under the polyline arrangement of piles, a model of polyline pile layout is built (Figure9), with which the numerical simulation analysis is performed on the soil arching effect between piles. Compared to the afore-described straight line layout, the parameters of the polyline pile layout model remain unchanged except for the adjusted layout angle of the antislide piles. On the basis of a straight line layout, a “section orthogonal to thrust” is arranged for the antislide piles on the right of 5# pile, which serves as the inflection point. This section is consistent with that under the straight line layout. Meanwhile, the part on the left of 5# pile is a “section oblique to thrust,” which is overall arranged by rotating at a certain angle with the central point of 5# pile as the circle center. The antislide piles in this section are obliquely intersected with the landslide thrust. In this study, models of 10°, 20°, and 30° polyline pile layouts are separately built. Figure 9 displays the model of 10° polyline pile arrangement.Figure 9
Model of 10° polyline pile arrangement.


## 3.2.2. Analysis of Simulation Results

For the convenience of analysis, during the investigation of the soil arching effect under polyline pile arrangement, the soil arches are classified into those on the “section oblique to thrust” and those on the “section orthogonal to thrust.” The 3# and 4# soil arches are on the “section oblique to thrust,” whereas the 5# and 6# soil arches are on the “section orthogonal to thrust.” Besides, the 5# arch is also called the “inflection point” soil arch, since it is very close to the inflection point.Figure10 illustrates the isoline maps of Y-directional principal stresses under the 10°, 20°, and 30° polyline pile arrangements, while Figure 11 presents the comparisons among Y-directional principal stress curves at the midspan under the straight line and 10°, 20°, and 30° polyline pile arrangements. As is clear, the Y-directional principal stress values of soil arches at the midspan gradually decrease from the back to the front of piles, while the stress values on the back side of piles gradually increase. There are clear trajectories of principal stress deflection, indicating that the soil arching effect is exerted. However, unlike the case of straight line layout, under the polyline pile arrangement at the same angles, the Y-directional principal stresses of both 3# and 4# soil arches decrease, while those of both 5# and 6# soil arches increase, especially for the 5# arch. That is, when the piles are arranged in polylines, the soil pressures at the arch crown within the “section oblique to thrust” decrease, while those within the “section orthogonal to thrust” increase. Such an increase is most evident for the soil arch at the inflection point. Moreover, with the increasing angle of polyline pile layout, the Y-directional principal stress at the “inflection point” increases more evidently. Meanwhile, the principal stresses in the Y direction also differ by the angle of polyline pile layout. Specifically, with the increase in such angle, the isoline density of Y-directional principal stress gradually decreases, the thickness of the isobaric zone gradually thickens, and the progressive decrease of stress is unobvious, suggesting the gradual weakening of soil arching effect.Figure 10
Comparisons among principal stress isoline maps in theY direction, (a) 10° polyline pile arrangement, (b) 20° polyline pile arrangement, and (c) 30° polyline pile arrangement.
(a)(b)(c)Figure 11
Comparisons among principal stress curves in theY direction.
(a)(b)(c)(d)Table2 lists the peak statistics for the Y-directional principal stresses of soil arches at various pile layout angles, whereas Figure 12 depicts the variations of Y-directional principal stresses of soil arches at various pile layout angles. As is clear, with the increase in the angle of polyline pile arrangement, the Y-directional principal stresses on the midspan symmetry planes of 3# and 4# soil arches decrease continuously, while those of 5# and 6# soil arches increase continuously. In addition, with the increase in the angle of polyline pile arrangement, the Y-directional principal stress peaks at the midspan of 3# and 4# arches move backward to varying degrees, suggesting that the range of soil arching effect shifts away from the antislide piles. Meanwhile, as displayed by the variation curves of Y-directional principal stresses, the inscribed slopes of the curves are gradually decreasing, indicating the weakening of the soil arching effect. The Y-directional principal stress peaks at the midspan of 5# soil arch move forward to varying degrees with the increase in the pile layout angle, suggesting the diminishing range of soil arching effect. Regarding the changes in the stress curves, the inscribed slopes of the curves increase, the abrupt changes of Y-directional principal stresses are obvious, and the soil arching effect is enhanced. Regarding the Y-directional principal stress distribution of 6# soil arch, the Y-directional principal stress at the arch crown somewhat increases under polyline pile arrangement, despite a smaller increase than that of the 5# soil arch. The peak point position for 6# arch is consistent with that under a straight line arrangement, and the soil arching effect and its range of action are fundamentally unchanged.Table 2
Peak statistics for the Y-directional principal stresses of soil arches.
Pile layout angleY-directional principal stress peak (kPa)Peak position3# soil arch4# soil arch5# soil arch6# soil arch3# soil arch4# soil arch5# soil arch6# soil archStraight line layout6.116.116.116.114.94.94.94.910° layout6.16.096.576.144.85.14.44.920° layout65.967.016.175.25.34.34.930° layout5.925.87.376.225.85.54.34.9Figure 12
Variation curves of Y-directional principal stresses of soil arches at various pile layout angles.
(a)(b)(c)(d)Table3 lists the peak and vector height statistics for the X-directional principal stresses of soil arches, whereas Figures 13 and 14 separately depict the X-directional principal stress distributions of different soil arches under polyline pile arrangement and the X-directional principal stress variations of soil arches at different pile layout angles. According to Figure 13, under polyline pile arrangement, the principal stresses in the X direction are overall large in the middle and small on two sides, and maximum principal stress in the X direction is noted at the 5# soil arch. Suggestively, the extrusion effect between soil particles becomes stronger as the distance to the inflection point becomes closer, and the stress concentration becomes obvious, which is detrimental to the structural safety of the antislide pile at the inflection point.Table 3
Peak and vector height statistics for the X-directional principal stresses of soil arches.
Pile layout angleX-directional principal stress peak (kPa)Vector height (m)3# soil arch4# soil arch5# soil arch6# soil arch3# soil arch4# soil arch5# soil arch6# soil archStraight line layout5.55.55.55.51.951.951.951.9510° layout6.927.297.736.142.172.331.461.9520° layout7.37.78.47.262.272.241.461.9530° layout8.48.89.417.272.252.560.971.95Figure 13
Comparisons among principal stress curves in theX direction.
(a)(b)(c)(d)Figure 14
X-directional principal stress curves on the midspan symmetry planes of soil arches under polyline pile arrangements.
(a)(b)(c)(d)It is clear from Figure14 that with the increase in pile layout angle, the X-directional principal stresses at the midspan of 3#, 4#, 5#, and 6# soil arches increase continuously, indicating that under polyline pile arrangement, the extrusion effect between soil particles is enhanced with the increasing layout angle, and the stress concentration becomes ever obvious, which is detrimental to the structural safety of antislide piles. Based on the vector height changes of soil arches, the soil arch vector heights show uneven distribution under polyline layout when compared to the straight line layout, with those on the “section oblique to thrust” greater than those on the “section orthogonal to thrust.” That is, the 3# and 4# soil arches exhibit larger action ranges than the 5# and 6# soil arches, showing agreement with the Y-directional principal stress distributions in Figure 11.


## 4. Analysis of a Typical Landslide Case

The Dawanjiang landslide is located in the southwest of the Dawanjiang formation in Banxing village, Mengding town, Gengma county, with a distribution elevation range of 461–475 m. The landslide exhibits a “gentle-steep-gentle” stepped landform longitudinally. The trailing and leading edges are rather gentle, with slopes of 2–8°, while at the landslide position, the slopes are relatively steep, which vary from 15° to 45°. The landslide has a main sliding direction of 176°, and an arched plane shape. Approximately, its average length is 50 m, average width is 60 m, overall area is 3,000 m2, average thickness is 5 m, and overall volume 1.5 × 104 m3. As a small shallow-layer soil landslide, it directly threatens the safety of 9 households (45 people) and 12 buildings in Dawanjiang village Figure 15.Figure 15
Aerial view of the Dawanjiang landslide.Borehole exposure results show that the soil exposed in the landslide site is mainly Quaternary loose deposits, which, from top to bottom, are the Quaternary artificial layer (Q4ml), the Quaternary diluvial layer (Q4dl), and the Quaternary alluvial-proluvial layer (Q4al + pl). Lithologically, the soil comprises clay and silty clay, with strong hydrophilicity. After the surface water seeps along the soil body, it easily forms a saturated water weakness belt with low shear strength within a certain depth. The underlying bedrock in the landslide site is the limestone of lower Permian Yongde formation (P1y), which is not exposed on the surface.Tensile cracks L1 with good continuity and maximum widths of 2–10 cm are formed around the trailing edge of the landslide, which is locally dislocated to form 0.1–1.0 m rear wall of the landslide Figure16. Meanwhile, bulging cracks L2 with good continuity are formed on the leading edge of the landslide Figure 17. Field investigation finds that the landslide has a clear boundary between its east and west sides.Figure 16
Trailing edge boundary of the landslide.Figure 17
Leading edge bulging of the landslide.The Dawanjiang landslide is a soil landslide Figure18. According to the sliding surface exposed by the boreholes, the stability coefficient of the landslide is calculated by the transfer coefficient method. The relevant parameters are: weights of slide body (1) Natural weight: 18.2 kN/m3; (2) Saturated weight: 19.0 kN/m3. Table 4 lists the values and calculations of geotechnical parameters.Figure 18
Engineering geological profile of the landslide.Table 4
Physicomechanical parameters of landslide and stability calculations.
Calculation conditionShear strength index(kN/m) overall sliding force(kN/m) overall sliding resistanceStability factorNaturalSaturatedC (kPa)φ (º)C (kPa)φ (º)Natural92.5478.6535.331.12Natural + rainstorm82.5501.41461.230.92As revealed by the stability calculations, the safety factor of the landslide under natural conditions is 1.12, and the landslide is in a basically stable state. Under natural + rainstorm conditions, the landslide has a stability factor of 0.92, which is in an unstable state and requires management.Regarding the landslide control scheme, support with antislide piles is adopted. The antislide piles were arranged in a straight line and in a polyline for comparative analysis. Under a straight line layout, the piles are arranged at the leading edge of the landslide, while under a polyline layout, the piles are arranged according to the terrain lines. Since the sliding surface of the landslide is 5-6 m in depth, the length of antislide piles is set at 9 m. The length of the anchoring section is 1/3 of the pile length, and the pile spacing is set at 5 m. Figure19displays the plan layout of the antisliding piles. Based on the actual terrain changes, the backfill back pressure is involved in both the straight line and polyline pile layouts, albeit with differences in their quantity.Figure 19
Plane layout of antislide piles arranged in a straight line and in a polyline.During calculation, the parameters of antislide piles are described as follows: the cross-sectional area = 3 m2, the elastic modulus E = 20 GPa, the Poisson’s ratio = 0.2, the X-axis polar moment of inertia = 7, the Y-axis polar moment of inertia = 5, the Z-axis polar moment of inertia = 3, the stiffness on unit length of shear coupling spring Ks = 1 × 108 kN/m, the cohesive force on unit length of shear coupling spring = 2 × 104 kPa, the internal friction angle on unit length of shear coupling spring = 15°, the stiffness on unit length of normal coupling spring Ks = 1 × 108 kN/m, the cohesive force on unit length of normal coupling spring = 2 × 104 kPa, and the internal friction angle on unit length of normal coupling spring = 15°.


### 4.1. Analysis of Landslide Displacement

Figures20 and 21 separately present the landslide displacement nephogram under the straight line and polyline pile arrangements. In terms of displacement field distribution, the straight line layout can effectively prevent the downward sliding of landslide since the antislide piles are arranged at the leading edge, where the displacement of soil in front of piles is basically 0. Contrastively, in the case of polyline pile layout, although the antislide piles can prevent the downward sliding of soil behind piles since they are arranged along the terrain lines, the soil in front of piles in the polyline layout zone is still at the downward sliding risk.Figure 20
Displacement nephogram under polyline pile reinforcement.Figure 21
Displacement nephogram under straight line pile reinforcement.


### 4.2. Analysis of Landslide Plastic Zone

During the calculation with Mohr–Coulomb plasticity model in FLAC3D, if the stress in the unit body reaches the Mohr–Coulomb yield criterion, this area will be damaged or be a potential damage area, which is defined as the plastic zone. Depending on the failure mechanism, the plastic zone can be divided into the shear failure zone and the tensile failure zone. During the calculation, some areas may have entered the failure state, and then retreated due to the stress redistribution, which is marked as shear-p or tension-p on the plastic zone diagram. Meanwhile, on the diagram of area currently in a failure state, this is marked as shear-n or tension-n, so the analysis of the plastic zone is based primarily on the distribution area of shear-n and tension-n. The larger the plastic zone area, the larger the failure area of landslide, and vice versa. For the convenience of analysis, the color of the areas, which had entered the failure state but later retreated with the progress of calculation, is adjusted to the same color as the background meshes.Figures22 and 23 separately depict the plastic zone distributions of the landslide under the straight line and polyline pile layouts. Comparison between the two figures reveals that in the case of polyline layout, both the tensile and shear failure zones of the landslide are larger than those under the straight line layout. For the site of soil before piles, in particular, the shear failure area of soil body is significantly larger than that under a straight line layout.Figure 22
Plastic zone distribution under straight line layout.Figure 23
Plastic zone distribution under polyline layout.


### 4.3. Comparative Analysis of Internal Force Distribution of Piles

Figures24 and 25 separately display the bending moment and shear force distribution nephodiagram of antislide piles under straight line pile arrangement. Clearly, in the case of straight line layout, the antislide piles have a maximum bending moment of 1484.8 kN m and a maximum shear force of about 330 kN. The bending moment and shear force distributions at various pile positions are relatively uniform.Figure 24
Pile bending moment distribution under straight line layout.Figure 25
Pile shear force distribution under straight line layout.Figures26 and 27 separately present the bending moment and shear force distribution nephogram of antislide piles under polyline pile arrangement. Clearly, both the pile bending moments and shear forces increase, whose distributions are nonuniform. The maximum bending moment is 2,215.9.4 kN m, whereas the maximum shear force is 492.4 kN, showing markedly larger values than those under a straight line layout. Based on these, it can be confirmed that when the antislide piles of identical size are used to reinforce the same landslide, the polyline layout poses a greater risk to the pile’s structural safety.Figure 26
Pile bending moment distribution under polyline layout.Figure 27
Pile shear force distribution under polyline layout.


## 4.1. Analysis of Landslide Displacement

Figures20 and 21 separately present the landslide displacement nephogram under the straight line and polyline pile arrangements. In terms of displacement field distribution, the straight line layout can effectively prevent the downward sliding of landslide since the antislide piles are arranged at the leading edge, where the displacement of soil in front of piles is basically 0. Contrastively, in the case of polyline pile layout, although the antislide piles can prevent the downward sliding of soil behind piles since they are arranged along the terrain lines, the soil in front of piles in the polyline layout zone is still at the downward sliding risk.Figure 20
Displacement nephogram under polyline pile reinforcement.Figure 21
Displacement nephogram under straight line pile reinforcement.


## 4.2. Analysis of Landslide Plastic Zone

During the calculation with Mohr–Coulomb plasticity model in FLAC3D, if the stress in the unit body reaches the Mohr–Coulomb yield criterion, this area will be damaged or be a potential damage area, which is defined as the plastic zone. Depending on the failure mechanism, the plastic zone can be divided into the shear failure zone and the tensile failure zone. During the calculation, some areas may have entered the failure state, and then retreated due to the stress redistribution, which is marked as shear-p or tension-p on the plastic zone diagram. Meanwhile, on the diagram of area currently in a failure state, this is marked as shear-n or tension-n, so the analysis of the plastic zone is based primarily on the distribution area of shear-n and tension-n. The larger the plastic zone area, the larger the failure area of landslide, and vice versa. For the convenience of analysis, the color of the areas, which had entered the failure state but later retreated with the progress of calculation, is adjusted to the same color as the background meshes.Figures22 and 23 separately depict the plastic zone distributions of the landslide under the straight line and polyline pile layouts. Comparison between the two figures reveals that in the case of polyline layout, both the tensile and shear failure zones of the landslide are larger than those under the straight line layout. For the site of soil before piles, in particular, the shear failure area of soil body is significantly larger than that under a straight line layout.Figure 22
Plastic zone distribution under straight line layout.Figure 23
Plastic zone distribution under polyline layout.


## 4.3. Comparative Analysis of Internal Force Distribution of Piles

Figures24 and 25 separately display the bending moment and shear force distribution nephodiagram of antislide piles under straight line pile arrangement. Clearly, in the case of straight line layout, the antislide piles have a maximum bending moment of 1484.8 kN m and a maximum shear force of about 330 kN. The bending moment and shear force distributions at various pile positions are relatively uniform.Figure 24
Pile bending moment distribution under straight line layout.Figure 25
Pile shear force distribution under straight line layout.Figures26 and 27 separately present the bending moment and shear force distribution nephogram of antislide piles under polyline pile arrangement. Clearly, both the pile bending moments and shear forces increase, whose distributions are nonuniform. The maximum bending moment is 2,215.9.4 kN m, whereas the maximum shear force is 492.4 kN, showing markedly larger values than those under a straight line layout. Based on these, it can be confirmed that when the antislide piles of identical size are used to reinforce the same landslide, the polyline layout poses a greater risk to the pile’s structural safety.Figure 26
Pile bending moment distribution under polyline layout.Figure 27
Pile shear force distribution under polyline layout.


## 5. Conclusions

Through numerical simulation, this study comparatively analysis the soil arching effect characteristics of cantilever antislide piles arranged in straight lines versus polylines. In the typical case of the Dawanjiang landslide, the differences between a polyline and straight line pile layouts are verified, as well as their impacts on landslide control and the pile structure. The main conclusions are drawn as follows:(1)
Under straight line arrangement of piles, the soil arching effect gradually weakens along the direction away from the antislide piles, and the forces and action range of soil arches at various pile positions are basically identical. This indicates that under a straight line layout, the landslide thrust is uniformly distributed at various positions, and the antislide sheet-pile walls evenly share the load, which is beneficial to the structural safety of the walls.(2)
In the case of polyline pile arrangement, the soil pressures at the apex of soil arches within the “section oblique to thrust” decrease, while those within the “section orthogonal to thrust” increase. Such an increase is most evident for the soil arch at the inflection point. Moreover, with the increasing angle of polyline pile layout, the principal stress at the “inflection point” increases ever more evident, which is detrimental to the structural safety of the antislide sheet-pile wall at the inflection point.(3)
The polyline pile layout has a weakening effect on the soil arching evolution in the “section orthogonal to thrust,” which though attenuates with the increasing distance. This is manifested mainly in the reduced range of soil arching effect at the “inflection point,” and the significantly increased principal stress at the arch apex. After being far away from the “inflection point,” the range of soil arching effect in the “section orthogonal to thrust” increases gradually, while the principal stress shows relative decreases until it recovers to the same value as that under the straight line layout.(4)
The structural forces of antislide piles arranged in straight lines differ markedly from those arranged in polylines. Under a straight line layout, the bending moment and shear force distributions at various pile positions are relatively uniform. Contrastively, under polyline layout, both the bending moments and shear forces of the antislide piles increase, whose distributions are nonuniform. Suggestively, when piles of identical size are used to reinforce the same landslide, the polyline pile layout poses a greater risk to the pile’s structural safety.



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*Source: 3352337-2022-10-14.xml*