Analysis of Influence Factors of Anti-Slide Pile with Prestressed Anchor Cable Based on Bearing and Deformation Characteristics of Pile Body

Abstract

In order to deeply study the mechanism of prestressed anchor anti-slide pile, an indoor model experimental device was developed, and a finite difference and particle flow numerical analysis model of slope anchor cable anti-slide pile was established based on the reinforcement project of prestressed anchor cable anti-slide pile in a mountain road slope. Based on the analysis of the force and displacement characteristics of the anti-slide pile, the influence of the prestress of the anchor cable, the inclination angle of the anchor cable, the width and column spacing of the anti-slide pile and the inclination angle of the landslide, the height and nature of the filling soil on the force and deformation characteristics of the pile are discussed, and some design parameters are optimized. Results show that the larger the prestress of the anchor cable, the smaller the displacement of the pile body, but the excessive stress is not conducive to the safety of the pile body. The optimal tension should be 50–70% of the designed tension of the anchor cable. With the increase in the inclination angle of the anchor cable, the displacement of the pile decreases first and then increases, and there is an optimal inclination angle of the anchor cable. In the double row piles, with the increase in pile spacing, the front row piles gradually change from supporting the soil between the double row piles to supporting the sliding body with the back row piles, and the double row piles are plum-shaped. When the pile spacing is 2.5 times the pile diameter, the force of the front and rear piles is the most reasonable. In the process of soil arching evolution, the influence of cohesion on the soil arching effect is greater than that of the internal friction angle.

1. Introduction

With the need for the construction and layout of China’s road network, highways, railways and other infrastructure will inevitably cross the high and steep slopes of mountainous areas. Due to the hydraulic effect of expansive soil and the attenuation of soil shear strength in the sliding zone, slope failure often occurs in unpredictable locations, and landslide complexes may cause large-scale damage [1,2,3]. In order to prevent the sliding failure of the slope, sometimes it is necessary to take reinforcement measures for some special road sections, but unreasonable support methods not only cannot guarantee the safety of the slope, but may even cause greater economic losses and casualties [4,5,6,7,8]. Therefore, it is very important to select reasonable support methods and design parameters to ensure the safety of slope reinforcement engineering and reduce the investment of engineering construction. Among them, prestressed anchor cable anti-slide piles have become the preferred method in high and steep slope landslide treatment engineering because of their good anti-slide effect, fast construction speed and low environmental pollution [9,10,11,12,13].

The primary goal of slope reinforcement management is to ensure the stability of the slope engineering. Therefore, the current research on prestressed anchor cable anti-slide piles mostly focuses on the stability analysis before and after slope reinforcement. Such as that by Ausilio [14], this paper discusses the anti-slide pile influence on slope stability, and a method for determining the optimal pile position of anti-slide pile is proposed; Lei Wenjie [15] carried out a numerical simulation of the anti-slide pile reinforcement project, and discussed the influence of pile position on the slope safety factor, position and shape of the most dangerous sliding surface. Although there are many research results on the influence of pile position, pile length, pile spacing and other factors on the anti-slide stability of the slope, there are relatively few research results on the design optimization of anti-slide piles [16]. By constructing a three-dimensional numerical analysis model, Zhang Sifeng [17] studied the influence law of anti-slide pile section shape, anchorage depth and other factors on the reinforcement effect of anti-slide pile. In addition, the current anti-slide pile design mostly adopts the transfer coefficient method to first determine the design landslide thrust acting on the pile, and to analyze the stress characteristics of the loaded section and embedded section of the pile according to the cantilever beam and elastic foundation beam models [18]. However, in fact, the current design method has difficulty in fully reflecting the coupling effect of the slope anchor cable anti-slide pile system [19,20]. In addition, there is also a big lack of theoretical verification of some existing engineering experience.

Based on the engineering practice of slope reinforcement with prestressed anchor cable anti-slide piles in a mountainous highway in Shandong Province, and based on the indoor model test method, this paper establishes FLAC3D and PFC2D numerical analysis models. From the macro and micro aspects, the influence of design parameters, such as anchor cable tension, anchor cable inclination, double row anti-slide pile arrangement and row spacing, on the force and displacement of the pile body is studied from multiple angles. Based on this, some design parameters are optimized. The research results can provide theoretical guidance for the design and application of similar joint-retaining structures.

2. Materials and Methods

2.1. Laboratory Test Plan

The slope anti-slide pile model device was independently designed and manufactured. According to the similarity principle, the indoor model test was carried out. The stress values of soil between piles and anti-slide pile body were measured by static strain gauge. According to the test results, the influence of different anti-slide pile width and column spacing, landslide inclination and fill properties on the soil arching effect were obtained.

In this paper, the design model box was assembled by supporting columns, a bearing, a soil retaining plate on both sides, a slope toe soil retaining plate and two slope soil retaining plates. The assembled model box was not closed on the top and one side, and the box bottom was a designed inclination angle (30° or 45°; two optional inclination angles). The appearance size of the model box was 680 mm × 400 mm × 500 mm, and the similarity ratio was 1:100. The model box was made of 3 mm thick iron material. The assembled model box profile (Figure 1a) and the installation diagram (Figure 1b) are as follows:

This experiment design included three kinds of anti-slide pile widths, for 40 mm, 32 mm and 27 mm, respectively; the test aggregates for simulating the surrounding soil were mixed dry subgrade soil and Fujian Pingtan standard sand. The soil was screened with a 2.36 mm sieve. The particle gradation is shown in

Table 1. Test aggregate gradation.

Grain diameter (mm)	>4.75	2.36~4.75	1.18~2.36	0.6~1.18	0.3~0.6	0.15~0.3	<0.15
Proportion	1%	5%	10%	22%	40%	18%	4%

. The screening of soil is shown in Figure 2a, and the mixing soil is shown in Figure 2b.

After the installation of the device was completed, the soil aggregate was poured into the space several times, and the earth pressure box was buried in layers while the aggregate was poured. The seven earth pressure boxes were buried in the design position, and the aggregate was statically pressed and this was repeated many times until the design height was reached. The bottom soil retaining plate was removed to cause the aggregate to fall off under the action of gravity until the aggregate balance around the anti-slide pile reached equilibrium and no longer moved. The static strain gauge was used to collect the earth pressure value and analyze the obtained data. The layout scheme of the resistance earth pressure box (diameter 25 mm, height 7 mm, maximum range 40 kpa), layout scheme and supporting of DH-3816 static strain gauge and related software are shown in the figure below (Figure 3).

In order to prevent other factors from interfering with the test results, the aggregate was fully compacted during the test, the loading plate was placed horizontally on the top of the aggregate, the weight was placed on the loading plate as the constant load, and the position of the model box was fixed to prevent the model box from moving.

2.2. Finite Difference Method Numerical Simulation Testing Scheme

To make up for the shortcomings of the research parameters and response laws in the indoor model test, this paper, which is based on practical engineering and a numerical simulation method, used a finite difference method of combined retaining structure to study the influencing factors on the stress and deformation. This numerical simulation analysis was based on a landslide treatment project in a mountain area of Jinan City, Shandong Province. The front edge of the slope is highway and civil facilities. In order to ensure the normal road width and the safety of people’s lives and property, the sliding body was formed after vertical excavation. On a vertical slope with a height of 10 m, the main reinforcement measures were in the form of prestressed anchor cable anti-slide piles. According to the above engineering practice, the numerical analysis model was divided into slope and bedrock [21], and the length of the model was 20 m. The ground line with a gradient inclination subgrade direction and a slope of 18° was considered in the model. The front of the slope was excavated into a vertical slope with a height of 10 m according to the design requirements. The size of the model after excavation is shown in Figure 4a. The soil constitutive model adopts the Mohr–Columb plastic yield criterion. In the calculation, the physical and mechanical parameters of rock and soil mass provided by the engineering design unit and determined according to the engineering analogy method are shown in

Table 2. Physical and mechanical parameters of slope form.

	Parameter	Cohesive Force c /kPa	Angle of Internal Friction/°	Shear Modulus /MPa	The Bulk Modulus /MPa
Geotechnical Engineering
Slope		30	30	50	30
The bedrock		1 × 103	40	1.2 × 103	2 × 103

. Except from the fact that the free surface was adopted for the free face of the model, normal constraints were adopted on the left, right and back of the slope model, as well as around and at the bottom of the bedrock. Through applying the gravity field to the initial model, the slope initial displacement field of the slope was obtained as shown in Figure 4b. It can be seen from the figure that the maximum displacement of the slope was more than 10 m, which cannot be stable under the action of gravity, and it was necessary to take reinforcement measures.

Considering the height of the slope and the amount of sliding body, the combined reinforcement measures of prestressed anchor cable and anti-sliding pile were adopted in the project. As a result of the anti-slide pile elastic modulus and strength were much larger than the slope, the linear elastic model was used in the numerical simulation, and the anti-slide pile shear and bulk modulus were both 5 Gpa. According to the design documents, the numerical analysis of certain anti-slide pile length showed it to be 15 m, and the embedded section was 1/3 of the pile length. In order to simplify the calculation, the fix command is used to limit the displacement of the pile in the length of the pile embedded section. The pile center distance was 6 m, and the pile body was a rectangular section of 2 m × 2 m; the anti-slide pile layout scheme is shown in Figure 5a. For a detailed analysis of the pile–soil interaction process, the paper selected 15 units on the anti-slide pile node as a late monitoring point analysis (see Figure 5b). In the numerical analysis, the prestressed anchor cable was simulated by the cable element in the FLAC program, and its anchorage segment with the interaction between the space rock and soil mass spring bond-slip unit to simulate [22], which can vividly reflect the action law of the prestressed anchor cable in the rock and soil mass. In the calculation, three prestressed anchor cables were arranged, and the external anchor heads were located at 2/15 of the three anti-slide piles from the pile top. The length of anchor cables was 17 m, of which the free section was 12.5 m long and the inclination angle was 15°. In addition, in order to consider the interaction between the pile and the surrounding rock and soil, the contact interface was set to reflect the interaction characteristics. The mechanical parameters of the contact surface were determined by referring to the relevant literature [23], as shown in

Table 3. Model interface parameter Table.

	Parameter	Cohesive Force /Pa	Angle of Internal Friction /°	The Tangential Stiffness /kN·m−1	The Normal Stiffness /kN·m−1
Contact Surface
Slope and anti-slide pile		—	30	1 × 107	1 × 107
The bedrock and the anti-slide pile		1 × 103	37	1 × 107	1 × 107

.

2.3. Granular Flow Numerical Simulation Testing Scheme

In order to deeply analyze the change in soil arch form and internal stress of the slope soil when the relative displacement of soil between piles occurs, and to explore the load transfer law when soil moves, this paper uses PFC2D5.0 software to establish a two-dimensional numerical analysis model of slope particle flow. It is assumed that the soil displacement only occurs in the free face direction, and the pile displacement is ignored. The design size of the model is 7.5 m × 6.0 m, the cross-sectional size of the three anti-slide piles are 1.0 m × 1.0 m, and the pile spacing is 2.5 m. According to the rules of normal distribution, the density of soil particles filled in the model is 2600 kg/m³, and the parameters of soil particles are shown in

Table 4. Slope particle flow model parameter list.

Name	The Coefficient of Friction μ	The Normal Stiffness Kn/(N/m)	Shear Stiffness Ks/(N/m)	Particle Radius (mm)
Wall	0	6 × 107	6 × 107	-
Anti-slide pile	1.0	6 × 107	6 × 107	-
Soil particles	0.8	5 × 106	5 × 106	7~10

. After the model reaches the initial balance, the ‘ wall ‘ on the lower side of the model was deleted to form a free face. In order to simulate the horizontal movement process of soil particles, gravity was applied to soil particles. The model was calculated under the action of gravity, and the displacement and stress of soil particles were monitored by setting a measuring circle. The slope particle flow model is shown in Figure 6.

3. Results

3.1. Influence of Pile Width and Pile Spacing on Soil Arching Effect and Stress of Anti-Slide Pile

3.1.1. Influence of Pile Width of Single Row Pile on Soil Arching Effect and Stress of Anti-Slide Pile

In this section, the evolution law of the soil arching effect and the force characteristics of anti-slide pile body under different pile widths are analyzed by means of indoor model test. The dry subgrade soil and Fujian Pingtan standard sand were mixed in a certain proportion as the selected aggregate. The 45° inclination landslide is selected. The section widths of three kinds of piles are 27 mm, 32 mm and 40 mm, respectively, the pile thickness is 3 mm, the clear distance between piles is 6 cm, and the fill height is 35 cm.

When anti-slide piles with a pile width of 27 mm were used to reinforce the slope, the earth pressure measured by No. 1~7 earth pressure boxes in the soil with time were as shown in Figure 7. It can be seen from the figure shows that No. 1, No. 3, No. 5 soil pressure boxes were larger than No. 2, No. 4, No. 6 earth pressure value, and the values of No. 1~6 earth pressure boxes were greater than those measured by No. 7 earth pressure box, which indicates that the stress characteristics of the earth arch are that the earth pressure value gradually decreases from the arch foot to the central axis of the arch, and the earth pressure value between piles reaches the minimum at the central axis of the arch. In addition, the variation law of each earth pressure cell value with the shedding time shows the same law; that is, it increases first with the extension of loading time, and then decreases after reaching the peak value. The analysis shows that with the movement of the loading plate, the pile soil particles embedded between crowded degree increased, resulting in the enhancement of the indirect contact force of soil particles, and the soil arch effect gradually reached the maximum. At this time, it is the ultimate bearing state of the soil arch, but at this time, the soil arch cannot completely offset the upper load. After the soil arch is destroyed, the soil overflowed from the pile, and the earth pressure decreases.

Figure 8a shows the numerical variation curve of earth pressure of No. 1 earth pressure box under different pile widths. It can be seen that with the increase in pile width, the maximum earth pressure of pile width 40 mm is, respectively, 17.3% and 22.1% higher than that of pile width 32 mm and pile width 27 mm. With the increase in pile width, the soil pressure between piles increases, the soil arch effect increases gradually, and the ultimate bearing capacity of the soil arch increases. However, the height of the soil arch measured directly is 21 mm, 22 mm and 22 mm, respectively, when the pile width is 27 mm, 32 mm and 40 mm, and the height of the soil arch does not change much.

Figure 8b is the curve of the force change of the anti-slide pile when the pile spacing is 6 cm and the pile section width is 27 mm, 32 mm and 40 mm. It can be seen from the figure that the maximum soil pressure of pile body with pile width of 40 mm is, respectively, 24.1% and 31.9% higher than that of pile widths of 32 mm and 27 mm. The pile width is proportional to the force on the pile. The reason for this phenomenon is that when the width of the pile body is increased, the soil arching effect and the ultimate bearing capacity of the soil arch between the piles are enhanced, so that the earth pressure transmitted from the load to the anti-slide pile through the soil arch is increased, and the pile body is increased.

To sum up, the larger the width of the pile cross section, the stronger the ultimate bearing capacity of the soil arch, the more stable the soil arch formed, and the soil pressure transmitted by the soil arch to the anti-slide pile increases, so that the anti-sliding effect of anti-slide pile is better, which is advantageous to the slope stability.

3.1.2. Influence of Double Row Pile Spacing on Soil Arching Effect and Stress of Anti-Slide Pile Body

In this section, three kinds of clear pile spacing are designed, which are 2 cm, 4 cm and 6 cm, respectively. The aggregate is mixed dry subgrade soil and Fujian Pingtan sand. The landslide adopts a 45° inclination angle, the fill height is 35 cm, and the section width of anti-slide pile is 40 mm. The anti-slide pile is set by plum blossom pile arrangement, and the dead load is applied at the top of the aggregate. The variation curve of earth pressure with shedding time is shown in Figure 9a,b.

Figure 9a,b shows that with the increase in row spacing between piles, the soil arching effect formed by the front row piles gradually increases and the rear row piles show a decreasing trend. This is because the larger the pile spacing, the weaker the anti-sliding effect of the back row piles on the soil, and the more the sliding thrust of the soil is transmitted to the front row piles, so that the thrust of the front row pile is increased, and the earth pressure behind the pile is increased.

Figure 9c shows the stress-sharing ratio curve of the front and rear rows of anti-slide piles with the change in pile row spacing. It can be found that with the increase in pile row spacing, the proportion of front row piles gradually increases, and the force borne by rear row piles gradually decreases. For every 1 cm increase in pile spacing, the average change in the proportion of front and rear piles is 4.2%. That is to say, with the increase in pile row spacing, the role of front row piles gradually changes from supporting the soil between double row piles to supporting the sliding body together with rear row piles. In practical engineering, the front row piles are generally used as auxiliary piles; that is, the sharing ratio of the front row piles should be lower than that of the back row piles. Therefore, with the increase in pile spacing, the anti-sliding effect of the back row piles and the soil arching effect formed by them are gradually weakened, and the soil arching effect formed by the front row piles is gradually enhanced, but the stress of the front row piles is increased, which can easily cause instability.

3.2. Influence of Landslide Inclination on Soil Arching Effect and Stress of Anti-Slide Pile

It is generally believed that the greater the inclination of the landslide, the greater the sliding thrust of the soil mass, and the soil mass slides under the action of the sliding thrust. However, due to the obstruction of the anti-slide pile, the displacement behind the pile and the soil mass between the piles lose synchronization, so that the soil mass between the piles forms soil arching. The action of soil arching can prevent the soil from flowing out of the pile and transfer the earth pressure to the anti-slide pile in the form of arch axial force. The force transmission mechanism of the soil arching effect is shown in Figure 10.

In this paper, two kinds of landslide inclination angles of 30° and 45° are designed for test. The same volume of soil is poured into the model box, the width of the anti-slide pile is 40 mm, and the net distance between the piles is 6 cm. In order to ensure a certain initial quality of the reinforced soil, the soil only falls off under the action of self-weight until the soil arch is formed and stabilized, so as to obtain the final earth pressure inside the soil arch. Figure 11a,b show the earth pressure values measured by No. 1~7 earth pressure boxes under 30° and 45° landslide inclination, respectively.

It can be seen from Figure 11a,b that all earth pressure data in the 45° landslide inclination test are significantly greater than the earth pressure with 30° inclination; the earth pressure of the 45° landslide at the same buried position at the vault position is greater than the 30° landslide earth pressure, indicating that the soil arch height of 45° landslide is lower; the soil pressure of the 30° landslide and 45° landslide is −13.18 kPa and −20.61 kPa, respectively. The soil pressure of the 45° landslide is 56.4% higher than that of the 30° landslide, indicating that the pile body is more stressed when the 45° landslide occurs. This shows that increasing the inclination angle of the landslide will strengthen the bearing capacity of the soil arch, and finally increase the thrust transmitted by the soil to the anti-slide pile. For the anti-slide piles of the same size and arrangement, the smaller the angle of the landslide, and the supporting system is more secure [24].

In conclusion, the analysis shows that under the same reinforcement scheme, the smaller the landslide inclination is, the more conducive to slope stability and the smaller the stress on the pile body. In practical engineering, the landslide thrust can be reduced by reducing the original ground slope to increase the anti-overturning safety factor of the pile.

3.3. Influence of Filling Properties on Soil Arching Effect and Stress of Anti-Slide Pile

The soil arching effect is that the soil in the range of soil arching is stabilized by interlocking and squeezing each other, and the sliding thrust is transmitted to the anti-slide pile at the arch foot in the form of arch axial force. The shear capacity of the soil arch reflects the strength of the soil arching effect, and the shear strength of soil mainly depends on the internal friction angle and cohesion. It is generally believed that the internal friction angle of soil affects the biting force produced by the mutual embedding and extrusion between soil particles [25,26]. The greater the biting force, the stronger the bearing capacity of the soil arch. In this paper, from the internal friction angle and cohesion of fill, the influence of the soil arching effect and pile force is analyzed when the internal friction angle and cohesion change synergistically.

Based on the aggregates shown in Table 1, two kinds of mixed aggregates of dry subgrade soil and Fujian Pingtan sand were tested. The particle gradation under three working conditions is shown in

Table 5. Grain diameter proportion Table.

	Grain Diameter	>4.75	2.36~4.75	1.18~2.36	0.6~1.18	0.3~0.6	0.15~0.3	<0.15
Proportion
condition 1		2%	10%	15%	30%	20%	15%	8%
condition 2		1%	5%	10%	22%	40%	18%	4%
condition 3		1%	1%	6%	10%	55%	25%	2%

. The higher the content of Fujian Pingtan sand in the filler, the larger the internal friction angle and the lower the cohesion. The content of subgrade soil in condition 1 is the highest, while the content of Fujian Pingtan sand in condition 3 is the most; that is, according to the friction angle, the order is condition 1 < condition 2 < condition 3, and according to the cohesion, the order is condition 1 > condition 2 > condition 3.

The load is applied on the top of the aggregate, and the soil is destroyed after shedding. The analysis of the data of No. 1 earth pressure gauge in the whole process, and its change curve with the shedding time are shown in Figure 12a. It can be seen from the figure that the peak earth pressure decreases in the order of condition 1, condition 2 and condition 3; the peak earth pressure of working condition 1 is, respectively, 12.2% and 31.5% higher than that of working condition 2 and working condition 3, which indicates that the ultimate bearing capacity of the soil arch decreases gradually; and under the same load, condition 1 has a longer time to resist soil damage. The above phenomena show that when the internal friction angle and cohesion of the soil work together, the soil arching effect gradually increases with the decrease in the internal friction angle or the increase in cohesion in the soil. In the process of soil arching evolution, compared with the influence of friction angle and cohesion on the soil arching effect, cohesion occupies a dominant position.

Figure 12b is a numerical histogram of the maximum stress value of the pile body under three working conditions. The maximum soil pressure of pile body under condition 1 is, respectively, 10.5% and 19.7% higher than that under condition 2 and condition 3. It can be found that the stress condition of the pile body is consistent with the law of earth pressure between piles, which is dominated by cohesion and decreases with the decrease in cohesion. This shows that with the increase in soil cohesion, the soil arching effect is enhanced, and the thrust of the load transmitted to the anti-slide pile through the soil arching is increased, which can give full play to the anti-slide ability of the anti-slide pile. This shows that with the increase in soil cohesion, the soil arching effect is enhanced, and the thrust of the load transmitted to the anti-slide pile through the soil arching is increased, which can give full play to the anti-slide ability of the anti-slide pile.

Based on the above analysis, although the soil arching effect increases with the increase in internal friction angle and cohesion, the cohesion of filler has a greater impact on the soil arching effect than the internal friction angle, and the influence on the sliding thrust transmitted by the anti-slide pile is more significant.

4. Discussion

4.1. Anchor Cable Tension and Tension Angle Impact Analysis

4.1.1. Anchor Cable Tension Impact Analysis

In order to analyze the influence of anchor cable tension on the stress of anti-slide pile and slope stability, based on a FLAC3D numerical calculation model, the displacement curve along the anti-slide pile body under different tension is obtained by changing the size of anchor cable tension, as shown in Figure 13a.

It can be seen from the Figure that the displacement of the cantilever pile basically increases linearly from bottom to top. The maximum displacement occurs at the pile top, and the displacement exceeds 50 mm, and, at this time, the maximum displacement of the slope body is 152 mm. Although the existing specification for the cantilever pile top horizontal displacement limit value is not clearly defined, excessive displacement will obviously put forward higher requirements on the bending strength of the anti-slide pile, so as to increase the pile cross-sectional area of the anti-slide pile and reinforcement ratio. With the application of anchor cable tension, the force on the pile body tends to be reasonable, and the displacement of the pile body decreases significantly. Compared with the application of 800 kN anchor cable tension, the maximum horizontal displacement of the original cantilever pile body reduced by about 64%. It is worth mentioning that when the prestress increases to 1200 kN, the pile body has a reverse displacement in the direction of the sliding body. This phenomenon reflects the fundamental difference between the prestressed anchor cable anti-slide pile and the cantilever anti-slide pile in the force characteristics. It also shows that the application of prestressed anchor cable is more beneficial to slope stability. A similar conclusion can be obtained from the curve of the shear stress of the free section of the pile body with the prestress of the anchor cable shown in Figure 13b.

It can be seen from Figure 13b that the shear stress concentration phenomenon occurs at the bottom of the free section of the cantilever pile, and the shear stress of the pile body is significantly higher than that of the prestressed anchor cable anti-slide pile. This is mainly because the cantilever anti-slide pile bears the sliding force of the slope by relying on the embedded section, which leads to the stress concentration phenomenon at the bottom of the free section of the pile body. With the application of anchor cable tension, the combined action system of prestressed anchor cable and anti-slide pile forms a simply supported beam stress structure, so that the stress concentration at the bottom of the free section of the pile body gradually disappears, and the shear stress at the anchor head outside the anchor cable gradually increases. The setting of anchor cable improves the stress distribution of anti-slide pile and is more conducive to the safety of the pile body.

Table 6. Slope, anti-slide pile displacement and stress characteristic value.

Prestress of Anchor Cable /kN	Biggest Displacement of the Pile Body /mm	Slope with the Maximal Displacement /mm	The Maximum Shear Stress at Anchorage Point /kPa	At the Bottom of the Pile Free Period of Maximum Shear Stress /kPa
0	50.53	152.24	\	3762.74
800	18.4	121.68	608.85	1465.5
1000	3.8	121.27	546.3	1151.37
1200	0.84	120.77	516.43	1108.71
1400	5.54	117.83	633.5	871.9
1600	10.76	113.21	702.54	598.66
1800	16.79	108.92	789.72	288.17

lists the maximum displacement of the slope and pile body and the maximum shear stress of the pile body when the tensile force of the anchor cable is 0, 800, 1000, 1200, 1400, 1600 and 1800 kN, respectively. The maximum displacement of the slope body refers to the maximum displacement of each part of the soil obtained by model calculation after stability, which is caused by the gushing phenomenon of the soil between the piles. It can be seen from the Table 6 that when the prestress of the anchor cable is increased, the shear stress near the anchorage point increases, while the shear stress at the pile bottom decreases, and the maximum shear stress at the anchorage point decreases first and then increases with the increase in prestress. When the tension of the anchor cable is less than or equal to 1000 kN, although the shear stress and horizontal displacement of pile body are significantly improved compared with cantilever pile, the shear stress of the pile body is still large.

When the tension of the anchor cable is greater than 1600 kN, the position of the maximum shear stress is transferred from the bottom of the free section to the anchor head outside the anchor cable. When the prestress value is 1600 kN and 1800 kN, although the maximum stress of the pile body is obviously reduced, the moving distance of the pile body to the slope direction is large, which is bound to increase the passive earth pressure of the anti-slide pile, which is not conducive to the stability of the pile body. When the tension of the anchor cable is between 1200 kN and 1600 kN, the displacement of the pile body is smaller and the stress distribution is more balanced.

In addition, when the tensile force is 1400 kN, the difference between the maximum positive and negative shear stress at the anchorage point of the pile body and the bottom of the free section is about 27% of the maximum shear stress at this time, and the maximum displacement of the pile body is only 5.5 mm, which is far less than the general elastic deformation range of the prestressed anchor cable [27]. The requirement of 3 cm, the tensile force 1400 kN is also the most appropriate prestress design value of the project.

If the tensile force of anchor cable is too small, it cannot effectively reduce the pile bending moment, and if it is too large, it may fail because the deformation of the slope exceeds the elastic range due to the sliding of the slope in the later stage. Therefore, it is appropriate to set the anchor cable tension to 50–70% of its design tensile force [27]. The optimal tension determined in this project study is 1400 kN, which is located in the range of 50–70% of the design tensile force.

4.1.2. Influence of Anchor Cable Angle on Force and Deformation of Pile Body

Based on a FLAC3D numerical calculation model, seven numerical models of the angle between the prestressed anchor cable and the horizontal plane are constructed, which are 15°, 20°, 25°, 30°, 32.5°, 35° and 40°. Through calculation and analysis, the displacement curve of the free section of pile body under different inclination angles of anchor cable is obtained as shown in Figure 14, and the corresponding maximum force and deformation of pile body are shown in

Table 7. Different angles corresponding to the maximum stress and displacement of pile body.

Anchor Cable Angle	Displacement of Pile Top /mm	The Maximum Shear Stress at Anchorage Point /kPa
15°	0.93	−690.19
20°	0.83	−621.02
25°	0.69	−554.75
30°	0.29	−486.28
32.5°	0.1	−402.79
35°	−0.2	−412.85
40°	−0.22	−438.65

.

It can be seen from Figure 14 that with the increase in anchor cable inclination, the displacement in the middle of the free section of the pile body decreases first and then increases. When the anchor cable inclination is 32.5°, the displacement of the pile body is the smallest. However, if the inclination angle of the anchor cable is too large, the embedded angle between the pile top and the soil will become smaller, and the pile deformation will occur at the top of the soil-squeezing pile. After that, with the increase in the inclination angle of the anchor cable, the displacement of the pile body to the free surface gradually increases. In addition, when the inclination of the anchor cable increases, the displacement of the pile top to the free surface gradually increases, and the reverse bending phenomenon at the pile top becomes more and more obvious. At the same time, according to Table 7, with the increase in anchor cable inclination, the maximum shear stress and displacement of the pile top at the anchor point decrease first and then increase. When the anchor cable inclination is 32.5°, the maximum shear stress and displacement of the pile top show the minimum value; that is, under this anchor cable inclination, the maximum shear stress at the anchor point of pile body and the displacement at the middle and top of pile body are the minimum values. Therefore, choosing a reasonable anchor cable inclination of prestressed anchor cable has significant engineering application value for reducing the stress and deformation of the combined retaining structure.

4.2. Analysis on the Influence of Arrangement form and Row Spacing of Double Row Anti-Slide Piles

4.2.1. Influence of Arrangement of Double Row Anti-Slide Piles on Soil Stress between Piles

Based on a PFC2D program, this section carries out numerical simulation research on three common pile layout forms; namely parallel pile layout, plum blossom type and partially interval pile layout, designed based on these two pile layout methods. Since the safety and convenience of construction are not guaranteed when the pile diameter is less than 2 times, a connecting beam should be installed when the spacing is greater than 6 times the pile diameter. Therefore, the spacing between the front and rear rows of piles should be 2–6 times the pile diameter [28,29,30,31]. The size of the rectangular section anti-slide pile set in this section is 1 m × 1 m, the row spacing and column spacing are 2.5 times the pile diameter. The numerical calculation model of partially spaced pile is shown in Figure 15, and the circle in the figure is the measurement circle.

In this paper, the soil stress between piles under 20,000, 30,000, 40,000 and 60,000 time steps are monitored, respectively, and the evolution law of the soil arching effect under different pile layout conditions is obtained, as shown in Figure 16a–d.

It can be seen that under the condition of rectangular pile arrangement, the X-direction stress and the thickness of soil arch gradually increase with the increase in time, and the soil arch moves from the back row pile to the front row pile. When the plum blossom pile is arranged, the X-direction stress at 20,000 time step is much larger than the soil X-direction stress between rectangular piles at the same time step, indicating that the soil arch is formed faster when the plum blossom pile is arranged. In addition, it can be seen from the Figure that the X-direction stress value of the plum blossom cloth pile is much larger than the X-direction stress value of the rectangular and interval piles, and the former is about 2.8 times that of the latter two, which indicates that the soil arching in the case of plum blossom cloth pile is more stable. The interval pile takes into account the characteristics of both rectangular and plum blossom pile. The soil arch is formed quickly but the soil stress between piles is small, indicating that the formed soil arch is not as stable as the plum blossom pile.

Figure 16d shows the X-direction stress fluctuation range measured by the measuring circle. It can be seen that the thickness of the soil arch under the form of the rectangular pile layout is much smaller than that in the other two forms, indicating that the spatial effect of rectangular pile layout is the worst, and the soil arch effect between the front and rear piles is not strong. The soil arch thickness of the spacing piles is the largest, but the stress level of the soil arch is lower, and the bearing capacity of the soil arch is lower than that of plum blossom piles, which can also be reflected from the contact diagram of soil particles between piles under different pile layout forms in Figure 17a–c. The denser and thicker the black line in the figure indicates that the contact force of soil particles is greater, which also indicates that the compactness of the soil is higher here. It can be seen from the figure that the indirect contact force of soil particles of the plum blossom pile arrangement is the largest, which also shows that the soil arch formed is the most stable. Compared with the soil arch formed by the rear piles in Figure 17a–c, it is found that the soil contact force fails to penetrate when the rectangular and interval piles are arranged, while the contact force can be penetrated when the plum blossom type piles are arranged, which is consistent with the X-direction stress monitored by the measuring circles No. 20~25 measurement circle in Figure 15. In conclusion, the plum blossom pile arrangement can not only increase the stability of the soil arch formed by the front anti-slide piles, but also assist the rear pile to form a stable soil arch.

4.2.2. Influence of Different Row Spacing on Soil Stress between Piles under Double Row Anti-Slide Piles

In this section, the influence of different row spacing of plum blossom piles on soil stress between piles is numerically analyzed, and the established numerical analysis model is shown in Figure 18a. Design 1.5, 2.0, 2.5, 3.0 and 3.5 times of pile diameter are designed as row spacing, and the influence of pile row spacing on double row anti-slide piles is analyzed mainly from the reinforcement effect of front row piles. The contact diagram of soil particles obtained after 60,000 steps of model operation is shown in Figure 18b–f.

It can be seen from the figure that with the increase in pile row spacing, the soil contact force behind the front row piles gradually increases; that is, the slope thrust shared by the front row piles gradually increases. Moreover, the normal stress behind the front row piles increases at an average rate of 8.9% after 2.0 times the pile diameter pile row spacing. The soil arch is formed within a certain distance behind the pile. In order to give full play to the bearing capacity of the soil arch, it is necessary to appropriately increase the pile row spacing to provide sufficient formation space for the soil arch. When the row spacing reaches 3.5 times the pile diameter, the front row piles have formed a stable soil arch. However, according to the existing engineering experience, the front piles are mainly used to support the landslide thrust between the front and rear piles, and should be used as auxiliary piles, and the thrust ratio shared by the front and rear anti-slide piles should be 3.5:6.5. With the increase in pile row spacing, the front row piles are gradually used as the main piles, which is obviously unreasonable. According to the analysis of the soil stress data between the front and rear rows of anti-slide piles (as shown in

Table 8. Value of normal stress behind pile.

Pile Row Spacing	Normal Stress behind Front Pile/KPa	Normal Stress behind Rear Pile/KPa	Stress Ratio of Front Row and Rear Row
1.5 times pile diameter	−20.765	−59.100	2.6:7.4
2.0 times pile diameter	−20.467	−47.756	3.0:7.0
2.5 times pile diameter	−22.369	−38.088	3.7:6.3
3.0 times pile diameter	−24.082	−17.439	5.8:4.2
3.5 times pile diameter	−26.440	−5.263	8.3:1.7

), it can be seen that when the pile row spacing is 2.5 times the pile diameter, it is the closest to the ideal thrust ratio. If the row spacing is too large or too small, the stress on the pile body will be unreasonable, and the pile row spacing is too small, which is not conducive to construction [32].

5. Conclusions

Based on engineering practice, this paper constructs a three-dimensional numerical analysis model of slope-anchor cable anti-slide pile by using FLAC3D numerical simulation software, and an indoor model experimental device was developed independently. The influence of the prestress of the anchor cable, the inclination angle of the anchor cable, the width and spacing of the anti-slide pile, and the inclination angle of the landslide on the stress and deformation of the pile are studied. The main conclusions are as follows:

(1) In a single row of piles, the larger the width of the pile section, the greater the ultimate bearing capacity of the soil arch formed, the stronger the soil arch effect, and the greater the thrust transmitted to the pile body of the anti-slide pile. In the double row piles, the row spacing is increased, the sliding thrust is redistributed, the effect of the back row anti-slide piles is weakened, the thrust of the front row piles is increased, and the front row piles gradually change from supporting the soil between the double row piles to supporting the sliding body together with the back row piles.

(2) Under the same reinforcement scheme, the smaller the inclination angle of the landslide, the more favorable to slope stability and the smaller the stress on the pile body. With the increase in cohesion and internal friction angle, the soil arching effect shows an increasing trend, but the influence of cohesion on the soil arching effect is greater than that of internal friction angle.

(3) Compared with cantilever anti-slide pile, prestressed anchor cable anti-slide pile improves the stress distribution of the pile body and is more conducive to the safety of the pile body. However, excessive tensile force is not conducive to the stress of pile body. It is appropriate to select 50~70% of the design tension of anchor cable.

(4) There is an optimal value of the inclination angle of the anchor cable on the anti-slide pile. At this angle, the maximum shear stress at the anchorage points of the pile body and the displacement at the middle and top of the pile body are the smallest. Therefore, seeking a reasonable inclination angle of prestressed anchor cable has a significant impact on reducing the stress and deformation of the combined retaining structure.

(5) Under the working condition of double row piles, the pile layout mode affects the distribution of stress between piles. Compared with the rectangular pile layout and interval pile layout, the plum blossom pile layout can give full play to the spatial advantages, form a more stable soil arch, and is more conducive to the stability of slope. When the double row piles are arranged in plum blossom shape, the pile row spacing is 2.5 times the pile diameter, which is the closest to the ideal thrust ratio.