Numerical Simulation Study on the Spacing of Landslide Anti-slip Piles Based on Strength Reduction Method

In landslide control engineering, anti-slip piles are the most commonly used means. This article established a numerical model of the interaction between fully weathered granite landslides and anti-slip piles based on the strength reduction method. Firstly, five pile-soil interaction models with different pile spacing were established using Abaqus software, and individual components were generated and assembled using the stretching function. The friction surface is used between the pile and soil, and the normal and tangential contact characteristics are both Penalties. Secondly, the strength reduction method based on displacement criteria is used to reduce the rock and soil parameters to the unstable stage before failure, while calculating the slope safety factor. Then, the influence of anti-slip pile spacing on slope stability, pile shear force, bending moment, and soil arch effect are studied. The strength reduction method and pile-soil interaction model used in this article can effectively avoid single pile effects and have high accuracy in characterizing soil arching effects. The results afford certain application and promotion values by providing theoretical references and technical guidance for similar anti-slide pile reinforced slope projects.


Introduction
Anti-slide piles have the characteristics of flexible pile placement and good reinforcement effect and are the most commonly used means in slope reinforcement engineering.Its mechanism is based on the interaction between piles and soil, transferring the thrust of the slope to the formation, combining the anchoring force and passive pressure of the building to achieve the effect of reinforcing the slope.
Strength reduction is the effective used numerical simulation method for analyzing pile-soil interaction.Related scholars have conducted numerical simulation research, exploring the deformation and failure characteristics of slopes [1], stress distribution [2], deformation response law [3], and other anti-slide pile mechanisms.They have also studied the effects of changes in structural parameters such as pile spacing [4], pile cross-sectional size [5], and anchor length [6] on structural performance.For example, Zhang et al. [7] established a reliability analysis model for landslide systems and explored the influence of pile parameters on the system's reliability index and stability coefficient.In addition, load calculation and transmission mechanism [8], pile damage situation [9], pile top connection method [10], and overall reliability [11] are also considered.

Numerical Simulation Modeling
The Huiling landslide is in Laoshan District, Qingdao City, Shandong Province, China.The area has a high degree of weathering and is a typical fully weathered granite landslide [12].In August 2020, under the influence of rainfall, the landslide was damaged [13].In 2022, the landslide will be treated with antislip piles, with a cross-section of 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 [14].Using Abaqus software, establish a numerical model based on the prototype landslide size (Figure 1).To avoid the single pile effect and better study the influence of pile spacing on the reinforcement effect, three anti-slip piles were installed on the landslide.The strength reduction method is based on displacement changes as a criterion, reducing the rock and soil parameters to the unstable stage before failure, and calculating the slope safety factor (Figure 2).This simulation set 5 different pile spacing (5,6,7,8,9 m).Other parameters are fixed, including the pile length of 23 m, the embedded depth of 7 m, and the interface size of 2.5 × 2.5 m.

Slope Displacement
The displacement response results of the slope obtained under different pile spacing are shown in Fig. 3.The results of the maximum displacement point of the slope are extracted as shown in Fig. 4 (a).As the spacing between piles increases, the displacement of the slope increases, which weakens the effectiveness of reinforcement.The pile spacing increased from 5m to 9m.For each 1m increase, the maximum displacement (horizontal) increased by 0.024cm, 0.032cm, 0.118cm, 0.294cm, and the maximum displacement (vertical) increased by 0.023cm, 0.028cm, 0.047cm, and 0.127cm, respectively.When the pile spacing rises to more than 7m, the response amplitude of slope displacement changes significantly increases.when the pile spacing is more significant than 7.5m, the slope's horizontal and vertical displacement is relatively substantial.It can be preliminarily determined that the optimal pile spacing should be less than 7.5m.

Slope Stability
Under different pile spacing, the results of the transient plastic deformation zone of the slope obtained are shown in Fig. 5, and the displacement results of the slope Safety factor taken are shown in Fig. 4 (b).The existence of piles effectively intercepts the development of plastic deformation.When the spacing increases from 5m to 9m, the plastic deformation of the slope increases by 0.413 for every 1m increase in pile spacing × 10 -3 , 0.003 × 10 -3 , 0.009 × 10 -3 , 0.049 × 10 -3 .The increment is relatively large at 8-9m.Its Safety factor is 2.054, 2.034, 2.012, 1.975 and 1.903 when the pile spacing increases from 5m to 9m; When the pile spacing is 5-7m, the change curve of safety factor is relatively flat; When it is more excellent than 7m, the loss of Safety factor is more, and the change curve tends to be dull.
Considering the change of Safety factor and displacement, the optimal pile spacing is 7m, and the slope Safety factor is 2.012, which meets the engineering safety requirements.

Force Law of Pile Body
The stress and displacement (horizontal) cloud map results of the anti-slide pile body obtained under different pile spacing are shown in Fig. 6 and Fig. 7.The internal force of the anti-slide pile undergoes a sudden change due to the sudden change in the support reaction force at the interface of the sliding bed and the embedded point of the anti-slide pile.The pile achieves the maximum displacement value at the top of the pile.Under different spacing arrangements, the maximum value can be 2.4cm, equivalent to 1% of the full length of the single pile cross-section.However, it should be pointed out that when the spacing is more excellent than 7m, the deformation of the pile body gradually tends to be consistent.When the spacing is less than 6m, the lateral displacement of the pile top is minimal, which is due to the relatively small sliding force of the slope.After the spacing exceeds 6m, due to the greater sliding force borne, the displacement of the pile top is slightly increased.In contrast, the internal force of the pile remains almost unchanged.Therefore, the displacement of the pile top tends to be the same after the spacing is greater than 6m.On this basis, the internal force and bending moment values were obtained, and curve analysis was conducted on them.As shown in Fig. 8, the ultimate internal force value increases with the increase of the spacing.When S=5m, the shear force on the pile is the smallest because the pile is too close to produce a coupling effect, and the pile positions on both sides share the soil pressure on the middle pile.But after S>6m, there is almost no change in the peak internal force.This is because as the spacing is smaller, the settlement pressure borne by the soil-arch on the side is less, and the corresponding internal force is lower, resulting in lower soil pressure on the pile side.The larger the spacing, the greater the soil arch bears the settlement pressure, therefore, the corresponding internal force.However, the arching-soil effect will weaken after the spacing exceeds the threshold (S>8 m in this article).The pile will only bear the settlement pressure of the soil around the pile.The peak internal force will also decrease and tend to stabilize.Although the slope is more stable when S=6m than when S=8m and the Safety factor is higher, the peak bending moment when S=8m is 96.51% when S=6m, and the peak shear force when S=6 is 96.49% when S=8.However, due to the similar internal force distribution in both cases and the significant engineering cost advantage when S=8m, the support effect at a pile spacing of about 7 is more advantageous.When S>6m, the difference in the shear force curve is minimal because the pile's shear force increases rapidly 50% (10 m) below the pile top, rather than the same shear force at different pile spacing.As a result, the difference in shear force between the shallow layer of the pile top and body is minimal, showing some "overlapping" characteristics.At a distance of about 10 meters from the top, there was a sudden change in the internal force of the body due to the sudden increase in the support reaction force of the anti-slide pile at the rock soil interface.The finite element numerical simulation considers the continuum assumption, so the strain of the rock and soil is consistent at the rock-soil interface.According to Hooke's law, the stress values on the rock-soil interface are quite different under the elastic modulus with significant differences.As a result, the external force borne by the rock between the two interfaces increases sharply.Therefore, when designing anti-slide piles, local reinforcement treatment is necessary.

Distribution Law of Arching Soil Effect
The soil between piles can provide an excellent anti-slide effect for the slope.The principle is that the ground between piles undergoes an arching soil effect, which refers to arch stress regulation formed in the soil due to uneven soil deformation.To ensure the stability of the ground between piles, the reasonable spacing between pile groups should be able to utilize the arching soil effect between piles fully.In the simulation process, the displacement (horizontal) of the soil between piles can to some extent, reflect the soil arch shape and distribution law between pile groups.Extract the full horizontal displacement cloud map of the pile part of the reinforcement model to study the soil-arching effect distribution law between piles under different pile spacing.When S=5m, the arrangement is dense, and the pile body is too close, resulting in a coupling effect.The pile positions on both sides share the soil pressure borne by the middle pile body, so the displacement value of the central pile position is smaller than that of the two sides, and the pile body is not fully utilized.Therefore, the optimal pile spacing should be considered at least 6m.When S=6-7m, the layout is relatively dense, and the soil between the piles forms a clear arch (green area).The soilarch effect occurs, and the soil displacement at the rear edge of the anti-slide pile (light green space) is effectively limited.Within this range, the slope's safety factor will fluctuate less with the increase of pile group spacing.When S＞7m, the restricted soil around the anti-slide pile (in the light green area) begins to creep towards the side as the soil arch curvature between the piles decreases.At this point, due to the arching soil effect between piles, although the soil remains stable, the soil displacement limited by the support behind the pile is greater than that of the unsupported part behind the pile.At this time, the Safety factor of the slope is reduced to 2.012.When S=8-9m, the arching soil effect between piles begins to decrease, the soil arching height increases and the arc-shaped trace begins to appear with straight edges, transforming into a triangular-like shape.At the same time, the Safety factor of the slope decreases to 1.975.When S＞9m, the arching soil effect between the piles is significantly weakened, and the soil restricted by the retaining behind the pile is drained by the anti-slide pile, resulting in a large displacement.The anti-slide effect of the pile group begins to change to the single pile effect, and the Safety factor of the slope is reduced to 1.903.
The spacing is inversely proportional to the range of soil limited by their rear support.When the spacing reaches 7-8m, the soil displacement between piles shows a significant upward trend, indicating that piles can only effectively limit the displacement of the slope at the rear edge of the piles.After the arrangement of piles, the soil at the rear edge is first restricted, and the displacement is hindered.Then, the ground between the piles is driven to displacement under the sliding force of the slope.The soil is squeezed, staggered, and continuously tightened in the distance, and finally, the soil arch effect occurs, forming an arched mechanical trace of the soil.The soil-arching effect occurs at the back of the pile, which restricts the ground and extends from the back to the pile, ultimately forming an arch.The curvature of the soil arch trace between piles decreases continuously with the increase of the spacing until it disappears.In conclusion, based on displacement change, Safety factor change, stress analysis of pile body, stress analysis of soil arch and economic factors, the optimal pile spacing can be determined as 7~7.5m.

Conclusion
This article uses the strength reduction method to establish a numerical model of landslide anti-slip pile interaction and studies the influence of anti-slip pile spacing on slope stability, pile shear force, bending moment, and soil arch effect.The main conclusions are as follows: (1) A pile-soil interaction model was established using Abaqus software, and individual components were generated and assembled using the stretching function.The friction surface is used between the pile and soil, and the normal and tangential contact characteristics are both Penalties.This model effectively avoids the single pile effect and has high accuracy.
(2) In the simulation of the pile-soil system, the strength reduction method based on displacement criteria is used to reduce the rock and soil parameters to the unstable stage before failure, while calculating the slope safety factor.This method can effectively characterize the soil arching effect.
(3) The numerical simulation method used in this project is not only suitable for weathered granite slopes, but also for soil slopes, and can be effectively applied in landslide prevention and control engineering.

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