Keywords

1 Introduction

Within a certain thickness of soil layer from the ground surface to a certain depth, there will be full and strong weathering soil layers in the shallow layer. The surface rock and soil mass is generally loose in structure and poor in mechanical properties [1, 2] and the rock-mass deformation modulus is also decreased relative to Young's modulus [3]. In order to ensure the stability of the highway [4] and the railway track [5], the surface rock and soil mass needs to be removed before subgrade filling [6]. When the thickness of the surface rock and soil mass is not large, the removal method can be adopted [7, 8]. Otherwise, the foundation needs to be reinforced. For example, pile and borehole pressure grouting technique were adopted to reinforce the silty clay overlying the shallow-buried tunnel section, according to Zhong et al. [9], and then fill the subgrade of highway [10, 11]. If the surface rock and soil mass is not treated properly, the weak interlayer will form between the subgrade fill and the lower stable rock mass. Zhao et al. [12,13,14] proved that the existence of the weak interlayer will affect the integrity and creep failure model of the rock mass. During the operation of the project, the groundwater will seepage along the weak interlayer, further softening the rock and soil mass, which will lead to the instability of the subgrade fill, and then a landslide will occur, afterwards the weak interlayer becomes the sliding belt in the landslide [14,15,16].

As a commonly used landslide control and reinforcement measure, anti-slide piles are flexible in design, simple in construction and good in anti-sliding effect [17,18,19]. The selection of the anti-slide pile location is very important. The appropriate reinforcement location can not only give full play to the performance of the anti-slide pile [20], but also save the project cost, ensure the safety of the project, and achieve the optimal economic and technical ratio [21]. Therefore, the choice of its layout location is a very important issue in the scheme design [22]. For this reason, many researchers have conducted research and analysis on this issue using different research methods. Nian et al. [23] used the comparative analysis method to find that the optimal reinforcement location of the anti-slide pile is located in the middle of the slope; Tan et al. [24] thought of using energy analysis method to determine the best location for re-reinforcing slope with piles should be located in the lower slope. Li et al. [25] proposed a method based on the stress level distribution characteristics of the sliding zone and draw the following conclusions, that anti-slide piles should be placed in areas with higher stress levels in the sliding zone. Pan et al. [26] used the finite element software ABAQUS to analyze the stability of soil slope, the result shows that when the ratio of the distance from the pile to the toe to the horizontal distance of the toe is 0.6, the safety factor is the largest. Fang et al. [27] used the finite element strength reduction method to study the multi-slip belt slope, the anti-slide piles are always set in the middle and lower part of the slip zone. In addition, based on the relationship between slope deformation and slope stability. Yang et al. [28] proposed a method to determine the optimal reinforcement location of anti-sliding piles based on the slope deformation field, and found that the anti-sliding piles set up in places with large slope displacements have better reinforcement effects.

Although relevant research has been able to provide some reference opinions for engineering design, due to the diversity of landslide types, the occurrence of landslides and the location of landslides are quite different, resulting in large differences in the optimal reinforcement positions of anti-slide piles for different types of landslides. At present, the choice of the location of the landslide anti-slide pile is still based on experience in most cases, and there is no unified quantitative method. As a quantitative index that can describe the sliding mechanism of the landslide, the safety factor of the landslide point can describe the stability of different parts of the landslide, and it is widely used in the research of landslide stability [29]. However, there needs more research on the application of point safety factor in the design of landslide support structures. Taking a typical roadbed slope as an example, this paper discusses the guiding role of point safety factor distribution on the setting of anti-sliding piles for landslides, and provides suggestions for engineering design.

2 The Point Safety Factor

Generally, the instability sliding of a landslide begins locally, and the process from stabilization to instability is a process of asymptotic development, which can be described by sliding mechanism. After summarizing a large number of landslide cases, the engineering community has reduced the sliding mechanism of landslides to three categories: traction, translational, and pushing. The sliding mechanism classification describes the asymptotic failure process of landslide from local instability to overall sliding from a qualitative point of view, but this qualitative description method is relatively rough and is not easy to apply in engineering design. In order to quantitatively describe the sliding mechanism of landslides, Yang [29] proposed the concept of the point safety factor at landslide and derived the corresponding calculation formulas.

Using numerical methods to obtain the stress state, sliding surface normal vector and sliding direction of sliding belt elements, according to the theory of elasticity, the normal stress of the sliding belt element and the shear stress in the sliding direction can be obtained, and the point safety factor of the sliding belt element can be defined by Eq. 1,

$$ F_{{\text{E}}} = \frac{{\tau_{{\text{u}}} }}{\tau } = \frac{{c + \sigma_{{\text{n}}} \tan \phi }}{\tau } $$
(1)

In formula, \(c\) is the cohesion of the slip belt material, \(\phi\) is the internal friction angle of the slip belt material.

A weighted average of the area of the slip belt unit yields the overall safety factor for landslides in Eq. 2,

$$ F_{3d} = \frac{{\sum\limits_{i = 1}^{ne} {F_{{\text{E}}}^{i} S_{{\text{E}}}^{i} } }}{{\sum\limits_{i = 1}^{ne} {S_{{\text{E}}}^{i} } }} $$
(2)

In formula, \({\text{ne}}\) is the total number of slip belt units, \(F_{{\text{E}}}^{i}\) is the safety factor of unit i, \(S_{{\text{E}}}^{i}\) is the area of the slip belt represented by unit i.

For slope engineering, the potential sliding surface needs to be identified first. Yang et al. [30] believed that the strength reduction method was used to make the slope reach the limit equilibrium state, and the displacement contour of the potential sliding zone represents the potential sliding surface. According to this, the slope stress field can also be decomposed to obtain the normal stress and shear stress on the displacement isosurface, calculating the safety factor of the slope point and the overall safety factor according to formulas (1) and (2).

3 Layout of Anti-slide Pile for Landslide of the Subgrade Fill

3.1 General Situation of Roadbed Landslide Project

A highway in Yunnan Province was constructed and opened to traffic in December 2017, and the K32+780~K32+860 subgrade was built above the slope. The length of the filling slope is 80 m, the width is 12.75 m, the maximum filling height is 32.44 m, and the maximum center height is 15.45 m, which is located at the K32+840 section. On July 12, 2021, due to continuous rainfall, the subgrade suddenly underwent landslide, and the highway surface formed a pull crack. Since then, the landslide has continued to develop, and by August 20, the width of the highway crack has reached 24 cm, the hind edge of the landslide has been wrong by 53 cm, and the subgrade slope has been seriously damaged and needs to be remediated, as shown in Fig. 1.

Fig. 1
Two illustrations of a landslide on a highway surface with a steep pull crack, and its elevation model with pavement cracks above the landfill, along with its dimensions are traced. A scale reads elevation from 1280 to 1380 meters.

Subgrade plan (left) and subgrade profile (right)

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After on-site investigation and analysis, it was determined that the cause of the subgrade landslide was that the shallow loose soil on the original ground was not thoroughly cleaned during the subgrade filling construction, and a weak interlayer with an average thickness of about 1.0 m was formed between the subgrade filling and the lower rock layer. The groundwater formed by rainfall infiltrates downward along the weak interlayer, softening the weak interlayer and forming a landslide.

3.2 Computational Model and Parameters

Firstly, the landslide is numerically calculated and the distribution of point safety factor on the sliding surface is obtained [31]. According to the typical section of subgrade slope shown in Fig. 1, a numerical calculation model of subgrade slope is established. In order to reflect the control effect of the original highway on the stability of the subgrade slope, the overburden layer with thickness of 1.0 m was built. Accordingly, the calculation model consists of three materials, subgrade filling, original ground cover and underlying rock foundation. The unit width of the model is longitudinally stretched to form a quasi-three-dimensional calculation model, so as to obtain the spatial stress state of the slope body. The models are all discretized with hexahedral elements, and the element size is less than 0.4 m to improve the calculation accuracy. The divided model calculation grid is shown in Fig. 2.

Fig. 2
A 3 D mesh model of the elevation is divided into three zones. The default roadbed fill is on the top, the default original ground cover is at the center, and the default rock foundation is at the bottom.

Numerical computation model networks

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The finite difference software FLAC3D 6.0 is used for numerical calculation, and the yield criterion is the Mohr–Coulomb yield criterion. The calculation parameters are shown in Table 1.

Table 1 Rock mass calculation parameters
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3.3 Computational Model and Parameters

The displacement field of slope limit state before reinforcement is calculated as shown in Fig. 3. Among them, the range of 0.05–0.6 m contour line better shows the range and location of the potential instability slip zone of the slope body, which is consistent with the actual deformation cracks on site, as shown in Fig. 4. The potential slip zone consists of two sections, the front section develops along the overburden, and the rear section develops in the subgrade fill.

Fig. 3
A contour plot traces the zone displacement of an elevation in magnitudes. The default roadbed on the top has a higher displacement between 2.0000 E negative 02 and 1.7693 E negative 1, while the original ground cover and the rock foundation have zero magnitudes.

Displacement field in the ultimate state

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Fig. 4
A contour plot traces the point safety of an elevation calculated by a constant. A slope near the elevation model ranges from 1.0000 E positive 00 to 1.4099 E positive 00, while 3 vertical lines on the right read 1.4099 E positive 00. The remaining beds are plotted as grids.

Point safety factor distribution

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Fig. 5
A contour plot traces the zone displacement of anti-slide piles on the roads. The roadbed fill with a sharp square-shaped edge on the top has a higher displacement between 2.0000 E negative 03 and 1.0210 E negative 01, while the original ground cover and the rock foundation have zero magnitudes.

Anti-slide piles placed on the shoulder of the road (positionâ‘ ) calculate the results of the model

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Fig. 6
A contour plot traces the zone displacement of anti-slide piles on the primary platform. The roadbed fill with sharp edges on the top has a higher displacement between 3.0000 E negative 03 and 1.9613 E negative 02, while the original ground cover and the rock foundation have zero magnitudes.

Anti-slide pile calculation model results placed on a primary platform (positionâ‘¡)

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Fig. 7
A contour plot traces the zone displacement of anti-slide piles on the secondary platform. The roadbed fill with elevated edges on the top has a higher displacement between 3.0000 E negative 03 and 1.5156 E negative 02, while the original ground cover and the rock foundation have zero magnitudes.

Anti-slide pile calculation model results placed on a secondary platform (positionâ‘¢)

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The slope stress field in its natural state is introduced, and the safety factor of the slip belt point is calculated according to Eq. (1), and its distribution is shown in Fig. 4. Equation 2 calculates the overall safety factor of the slope is 1.217. It can be clearly seen from the distribution of the safety factor of the sliding belt points that the landslide presents an obvious composite sliding mechanism of front traction, rear pushing, and middle anti-sliding, which is consistent with the current development characteristics of landslides.

According to the distribution characteristics of the point safety factor on the sliding surface, the sliding surface can be divided into three sections with the design safety factor of 1.30 as the standard. Those are, the section less than 1.30 in the rear fill is the main sliding section, the section with the leading edge less than 1.30 is the traction section, and the section with the middle section greater than 1.30 is the anti-slip section. It can be seen that in the subgrade fill, the main sliding section has nearly penetrated the entire filling body, which is consistent with the poor slope stability. However, the central anti-slip section still exists, and the length is about 1/2 of the entire slip surface, which plays a good anti-slip effect, so that the slope of the roadbed has not yet occurred overall instability.

3.4 Reinforcement Location of Anti-slide Piles

According to the calculation results of the point safety factor, considering the stability of different positions of the slope, it is proposed to carry out the calculation and analysis of the pile in three positions. The three pile positions are located at the road shoulder (location①), the first-level platform (location②) and the second-level platform (location③), as shown in Fig. 4. In order to constrain the displacement of the pile head, a row of anchor cables is arranged at the pile head, and the form of a pile and an anchor support structure is adopted. The diameter of the anti-slip pile is 1.5 m × 2.0 m, the anchor cable tonnage is 500 kN, the angle between the anchor cable and the horizontal surface is 20°, and the anchorage length in rock is 8 m. The pile length is determined according to the different thickness of the slider at each pile position, and is determined according to the method that the length of the anchoring section and the free section is the same. In addition, in order to ensure the safety of the project, the anti-slip ability of the slider before the pile is not considered in the calculation, that is, the anti-slip pile is considered as cantilever pile.

3.5 Analysis of Reinforcement Effect of Different Pile Positions

The reinforcement effect evaluation method of anti-slip pile is as follows: (1) Establish a calculation model according to Figs. 5, 6 and 7, assign the corresponding model parameters, and calculate to the initial balance of the model. (2) The displacement of the model is cleared to zero, and the shear strength parameter is reduced according to formula (3). At the same time, a uniform load of 30 kPa is applied to the road surface to simulate the long-term traffic load. Recalculate formula (3) to balance, analyze the displacement field of the fill slope, and judge the quality of the pile position.

$$ \left\{ {\begin{array}{*{20}l} {{\text{c}}_{e} = \frac{c}{k}} \hfill \\ {\varphi _{{\text{e}}} = \arctan (\tan \varphi /k)} \hfill \\ \end{array} } \right. $$
(3)

In formula: Ce—cohesion of the reduced belt material.

φe—internal friction angle of the reduced belt material. The reduction coefficient k is taken as 1.3.

It can be seen from the calculation results shown in Figs. 5, 6 and 7 that due to the reinforcement of the anti-slide piles, the stability of the embankment slope can be guaranteed, and the overall instability and damage will not occur. However, there will be a certain degree of deformation of the subgrade, which is reflected in the vertical settlement and the horizontal displacement along the direction of the free surface, which is comprehensively reflected as the combined displacement of the filled subgrade. Therefore, in this paper, the combined displacement of the filled roadbed is used as the evaluation index of the reinforcement effect of the anti-slide pile. The calculation results are shown in Table 2.

Table 2 Comparison of supporting effect
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It can be seen that different pile positions have obvious effects on the reinforcement effect of the landslide.

  1. (1)

    Set anti-slide piles at the road shoulder, the cantilever section is long, about 20 m, and the maximum combined displacement is 10.2 mm; when the anti-sliding piles are set on the first-level slope, the maximum combined displacement is 8.2 mm; when the second-level slopes are set with anti-sliding piles, the cantilever section is shorter, but the maximum combined displacement reaches 15.2 mm.

  2. (2)

    The anti-sliding pile is set at the shoulder of the road (locationâ‘ ). Although the pile is located in the anti-sliding section of the sliding surface, the proportion of the anti-sliding section is only 1/3 of the sliding surface behind the pile, and most of the sliding surface points have a safety factor, less than 1.30. After the shear strength parameter of the sliding belt is reduced, the landslide is further unstable, which increases the landslide thrust of the anti-slide pile. In addition, the cantilever section of the anti-sliding pile is long and the lateral displacement is large, so the combined displacement of the sliding body behind the pile is obvious.

  3. (3)

    The anti-sliding pile is set at the first-level platform (locationâ‘¡), the pile is located in the anti-sliding section of the sliding surface, the proportion of the anti-sliding section is 3/5 of the sliding surface behind the pile, and the shear strength parameter of the sliding surface is folded. After the reduction, the point safety factor of the anti-slip section is still greater than 1.0, and it still has anti-slip capability. The anti-sliding ability of the anti-sliding pile and the anti-sliding section of the sliding surface is fully exerted, so the displacement of the slope body is relatively small.

  4. (4)

    The anti-sliding pile is set at the secondary platform (location③), although the pile length is very short (6.5 m), the potential instability section of the sliding surface is long. After the shear strength parameters of the sliding surface are reduced, the main sliding section of the trailing edge and the traction section of the leading edge will be unstable at the same time. Reinforcement effect of anti-slide piles.

  5. (5)

    In general, the reinforcement effect of anti-sliding piles at different positions depends on two aspects, one is the length of the pile, and the other is the proportion of the anti-sliding section behind the pile. The longer the pile length is, the more obvious the deformation of the sliding body behind the pile is. The larger the proportion of the anti-slip section, the more the anti-slip ability of the sliding belt can be fully exerted, and the better the reinforcement effect is. The proportion of the anti-sliding section of the sliding surface behind the pile is more important. In actual engineering, this can be the main basis to determine the pile location.

4 Conclusion

By applying the calculation method of the point safety factor of landslides and side slopes, the distribution of the point safety factor of the sliding surface in the landslide can be obtained, and the anti-sliding section of the landslide can be determined accordingly. The proportions of the anti-sliding sections of the three pile positions are 1/3, 3/5 and 1/2, respectively, and the maximum displacement of the sliding body after the shear strength parameters of the sliding surface are reduced are 10.2 mm, 8.2 mm and 15.2 mm, respectively.

The proportion of the anti-sliding section of the sliding surface behind the pile is an important factor affecting the reinforcement effect of the anti-sliding pile. In actual engineering, the selection of anti-sliding pile positions should be based on a combination of various engineering factors, make full use of the anti-sliding effect of the anti-sliding section of the sliding surface as much as possible, and increase the proportion of the anti-sliding section of the sliding surface behind the pile. The method in this paper provides a quantifiable standard for the selection of anti-slide pile positions and enriches the design theory of landslide support structures.