Numerical simulation study on the embedding depth of anti slip piles in fully weathered granite landslides

Taking the reinforcement project of the fully weathered granite landslide in Fanling as the research object, this study establishes a numerical slope model with anti-slide pile reinforcement, the most common means in slope reinforcement engineering, while considering the pile-soil interaction. Using the strength reduction method, the effects of different anti-slide pile embedment depth on the stability of the reinforced slope are discussed. The research results indicate the following findings. (1) The embedment depth is negatively correlated with the slope displacement. (2) When the embedment depth is more excellent than 7m, the slope Factor of safety is 2.032>2.0, which meets engineering safety requirements. (3) According to the changes in displacement and the factor of safety, the stress analyses of the pile body and the economic factors, the optimal embedment depth for the Fanling landslide are determined as 8 m. The results afford certain application and promotion values by providing theoretical references and technical guidance for similar anti-slide pile reinforced slope projects.


Introduction
The theoretical design and construction technology of anti-slide piles has become increasingly mature.However, in terms of engineering practice, there are still several problems in the current research of anti-slide piles: firstly, the mechanism of pile-soil interaction is not clear, and there is much subjective randomness in the simplified calculation process; Second, the design parameters and schemes such as pile spacing, embedded depth, section size, etc. are empirical and conservative, which makes the economic applicability of reinforcement Engineering economics low.
Scholars have researched these two issues.One of the research objectives is to analyze the stability of the pile slope after anti-slide pile reinforcement, obtain the stability limit solution, and evaluate the reinforcement effect; The second is to calculate the internal force of the pile body, derive various applicable, accurate and straightforward calculation formulas, and provide a reference for engineering optimization design.Limit Balance theory is the most widely used theoretical analysis method.Relevant scholars have given applicable limit solutions and stability evaluation methods.In the analysis of failure modes and stress distribution, factors such as dimensionless anchoring ratio [1], cross-sectional shape [2], uncertainty of rock mass parameters [3], and stress distribution [4] have been successively considered.For internal force calculation, according to different types of anti-slide piles, transfer matrix algorithm [5], M-method [6], a three-segment method [7], simplified Bishop method and transfer coefficient method [8], Structural mechanics force method and double parameter method [9] are successively used to calculate the displacement and internal force of anti-slide pile structures.In addition, relevant scholars have also considered different influencing factors in the calculation of interior details, such as the actual distribution of resistance [10], the practical influence range of embedding [11], the continuity of internal forces and deformation [12], and the height of soil arch [13].
In the existing anti-slide pile slope reinforcement engineering cases, most focus on homogeneous soil slopes and layered soil slopes, while there needs to be more research on weathered rock layered slopes.In previous studies, the author conducted physical model experiments [14] and numerical simulations [15] on the triggering mechanism of the fully weathered granite landslide in Fanling.This article is a follow-up study and takes the anti-slide pile reinforcement project of the fully weathered granite landslide in Fanling as the research object, conducts numerical simulation analysis on the "pile soil" system, and optimizes the pile length, embedded depth, and pile spacing of the anti-slide piles in this project.

Summary of landslide reinforcement engineering
The Fanling slope is located in the Laoshan Scenic Area in eastern China.Affected by heavy rainfall, a landslide occurred in August 2020 [16].Reinforcement treatment began in 2022.The anti-slide pile of the Fanling landslide is set on the upper side of the 212 provincial roads, with its axis approximately 12m away from the local highway.This section uses anti-slide piles and anchor cables to prevent sliding, with one pile and one anchor.The cross-section of the anti-slide pile is 2.0m × 2.6m, with a pile length of 22.4-24m and a pile center distance of 6m.The pile body is poured with C30 concrete.Each pile is connected by a cross beam at the top, with a rectangular cross-section between the piles, with a height of 1.0m and a width of 0.5m.In this paper, firstly, the strength reduction method is used to study the influence of the length and spacing of an anti-slide pile on the stability of its reinforced weathered rock slope and the shear force and bending moment of the anti-slide pile.

Modeling
Based on existing data and layout location, a typical 3D anti-slide pile reinforced slope model is established based on ABAQUS (figure 1).The establishment of anti-slide piles uses the tensile function in ABAQUS to generate separate components and assemble them.The friction surface between the piles and soil is used, and the standard and tangential contact characteristics are both Penalty (penalty contact).Three anti-slide piles were placed in the middle of the slope to study better the impact of pile spacing on the reinforcement effect and avoid single pile effects.Change the length of the pile body and the distance between piles and conduct classification discussions.The material parameters are shown in table 1.In the "pile-soil" system simulation, the strength reduction method based on the displacement criterion is used to reduce rock and soil mass parameters to the unstable stage before failure and calculate the slope's Factor of safety (Fs).The process is shown in figure 2. Based on the actual situation of the project, two influencing factors, namely the embedded depth (pile length) and pile spacing, are selected for optimization research on anti-sliding piles.A total of five sets of different embedding depths and five different pile spacing were set up, and nine collections of working conditions were simulated (table 2).   3. When the embedding depth is less than 7m, i.e., the embedding percentage is less than 30.4%, a small displacement will occur at the pile foundation.This is because the anchoring section of the pile is too short, and the torque of the bearing layer below the anchoring point is too low, resulting in displacement at the pile bottom, which cannot fully exert the anti-slide effect based on the stiffness of the pile body.The horizontal and vertical displacement results of extracting the maximum displacement point of the slope are shown in figure 4 (a).As the length of the pile's embedded section increases, the slope's horizontal and vertical displacement decreases, which can enhance the reinforcement effect by increasing the embedded depth.When the embedding depth increases from 5m to 9m, the percentage of embedding length rises from 23.8% to 36%.For each 1m increase in pile length, the maximum horizontal displacement of the slope decreases by 0.213cm, 0.115cm, 0.046cm, 0.028cm, and the maximum vertical displacement decreases by 0.085cm, 0.057cm, 0.032cm, and 0.013cm.When the embedding depth increases from 5m to 7m (the embedding percentage increases from 23.8% to 30.4%), the response amplitude of slope displacement change is relatively large.It can be seen that when the embedded depth is more excellent than 7m, the reduction in horizontal and vertical displacement of the slope is relatively small.Therefore, the slope is believed to have already achieved a good reinforcement effect.It can be determined that the optimal embedding depth should be greater than 7m, and the optimal embedding percentage should be more significant than 30.4%.

Slope stability.
The results of the transient plastic deformation zone of the slope obtained at different embedding depths are shown in figure 5.The development of the plastic deformation zone shows a significant weakening in the anti-slide pile area.The sliding surface of the landslide, also known as the ultimate fracture surface, is divided into two parts by the pile body.The fracture surface at the rear edge of the landslide is well-developed.When the embedding depth increases from 5m to 6m, the anti-slide pile undergoes displacement at the bottom of the pile due to insufficient embedding depth and anchoring force, and the plastic strain of the slope decreases by 0.132 × 10 -3 .Therefore, the plastic pressure slightly increases when the embedding depth reaches 7m.In comparison, when the embedding depth increases from 7m to 9m, the plastic strain decreases, achieving an excellent anchoring effect.The horizontal and vertical displacement results of the extracted slope Factor of safety are shown in figure 4 (b).The safety factor is 1.961, 2.011, 2.032, 2.054 and 2.067 when the pile spacing increases from 5m to 9m.When the pile embedment depth is 7-9m, the Factor of safety change curve is relatively gentle, and when it is less than 7m, the Factor of safety loss is more.When the embedment depth is more excellent than 7m, the slope Factor of safety is 2.032>2.0,which meets engineering safety requirements.

Force law of pile body.
The anti-slide pile body's bearing capacity and the degree of deformation generated are limited.When the internal force or displacement of the pile body exceeds the limit value, the plastic strain will occur until failure.When optimizing the design of anti-slide piles, attention should be paid to their impact on slope stability and the stability of the anti-slide piles themselves.The stress and horizontal displacement cloud map results of the anti-slide pile body obtained at different embedding depths are shown in figure 6 and figure 7.As shown in figure 6, due to a sudden change in the support reaction at the embedded point of the anti-slide pile at the interface of the sliding bed, the internal force of the anti-slide pile undergoes a sudden change.As shown in figure 7, the anti-slide pile achieves the maximum displacement value at the pile head.The maximum displacement of the antislide pile head can reach 2.38cm under different pile spacing conditions.However, when the embedded depth is less than 8m, there is always a significant vertical displacement at the bottom of the anti-slide pile, affecting the anti-slide pile's reinforcement effect.The horizontal displacement of the pile top gradually becomes the same after the embedded depth exceeds 7m.As previously known, when lf ≤ 7m, the lateral displacement of the anti-slide pile decreases, but the anti-slide pile cannot be fully anchored.When lf ≥ 8m, the anti-slide pile fully arrives, and the deformation of the pile body increases.The more significant sliding force it bears causes the displacement of the pile head to be more critical.On this basis, the internal force and bending moment of the anti-sliding pile with different embedded lengths were analyzed, as shown in figure 8.When the simulated embedding depth of the anti-slide pile is 5-6 m, the stress on the anti-slide pile body is highly uneven.The maximum shear stress on the local part of the embedded section of the anti-slide pile is -11026.67kN and -9890.61kN, which far exceeds the maximum shear stress values of the implanted area of 3207.67 kN and 3363.33 kN, which is unfavorable for the stability of the anti-slide pile.If the embedded end of the anti-slide pile is less than 7m and the embedded length is less than 30.4% of the total length of the pile, the embedded depth is not enough to generate adequate bearing capacity to resist the sliding force, resulting in excessive peak shear force on the pile body.The reaction force before the anti-slide pile increases with the deepening of the embedding depth and reaches the maximum height at the embedding point and the shear force and bending moment it bears also increase.When the embedded depth is 7m, the proportion of embedded length reaches 30.4%, and the anti-slide performance is improved.The sliding force it bears is improved, and the shear force and bending moment carried by the embedded section of the anti-slide pile increase and become positive.The peak shear force delivered by the embedded area reaches -6940kN, and the peak bending moment gets 24146.67kN•m.Due to the short length of the embedded section of the anti-slide pile, the demand for anchor force at the bottom of the pile is too high, resulting in an excessive internal force on the embedded section of the pile, The force on the pile body is also uneven, and the anti-slide pile is easily damaged by shear.
When the embedded depth is 8-9m, the proportion of embedded length is more significant than 33.3%, and the sliding force borne by the anti-slide pile is increasing.The shear force and bending moment gradually increase in the embedded section of the pile body, and the anti-slide performance of the anti-slide pile is becoming more robust, while the peak shear force of the embedded part is decreasing, indicating that the pile body is uniformly stressed and more stable.If the length of the embedded part of the anti-slide pile is continuously increased, the pile body can bear all the sliding force of the rear slope at this time.If the embedded component is continually increased, the shear bending moment of the pile body will remain unchanged, with little change in force.Still, it can slightly improve the contribution of landslide safety because the Factor of safety of the landslide will be slightly improved.In conclusion, based on the analysis of displacement change, Factor of safety change, pile shear force and bending moment, and considering economic factors, it can be judged that the optimal embedding depth of an anti-slide pile is 8m, accounting for 33.3% of the pile length.

Conclusion
This article uses the reinforcement project of the fully weathered granite landslide in Fanling to establish a numerical model of pile-soil interaction.The numerical model includes five types of pile spacing (5, 6, 7, 8, 9m).Based on the strength reduction method, the effects of the length of anti-slip piles on slope stability, pile shear force, bending moment were studied.The main conclusions are as follows: The slope's horizontal and vertical displacement decrease with the embedment depth increase.
From the displacement change, the change of Factor of safety, the force analysis of the pile body and economic factors, the optimal embedment depth is 8m, accounting for 33.3% of the length of the pile body.The Factor of safety of the slope is 2.032>2.0,which meets engineering safety requirements.

Figure 1 .
Figure 1.Schematic diagram of anti-slide pile reinforcement slope model.

Figure 2 .
Figure 2. Flow chart of strength reduction method.

Figure 4 .
Figure 4. (a) Horizontal and vertical displacement diagram of slope under different embedded depths.(b) Slope safety factor diagram under different embedded depths.

Figure 8 .
Figure 8.The force law of pile body under different embedded depth conditions.(a) pile shear force; (b) bending moment.