1. Introduction
In slope disaster management, the construction of retaining walls is one of the commonly used methods for slope disaster prevention. The pile–beam retaining wall, an improved version of the traditional retaining wall, is widely applied in slope reinforcement in mountainous areas due to its advantages such as good stability and strong anti-sliding capacity. The pile–beam retaining wall is mainly suitable for locations requiring high stability, a large bearing capacity, and excellent seismic performance, such as (1) areas with unstable soil, gentle terrain, or requiring significant earthmoving; (2) embankments on steep slopes, with riverbank erosion, with unstable overburden adjacent to existing lines, or on deep bedrock; and (3) locations with insufficient foundation-bearing capacity or inadequate foundation depth.
Qiao [
1] studied the optimal parameters (pile spacing, row spacing, and tie beam dimensions) of portal anti-slide piles to balance stability, structural deformation, and economic efficiency. Xia [
2] investigated the mechanical characteristics of pile–beam retaining walls under high-fill and soft-foundation conditions, including stress distribution, displacement, and deformation. Zhang [
3] analyzed the reinforcement effect of pile length parameters on backfill soil slopes reinforced by pile–beam retaining walls. Fu [
4] studied the settlement patterns of mountainous half-filled and half-cut widened subgrades reinforced with pile–beam retaining walls.
As early as the 1980s, pile–beam retaining walls were used in subgrade engineering. Li Haiping [
5] proposed a new type of buttressed pile–beam retaining wall. Their research results demonstrated that with the increase in support beam spacing, both the axial force in the support beams and the horizontal displacement at the top of the retaining piles increase, while the bending moment of the pile body shows minimal changes. When tie beams are installed, the horizontal displacement at the top of the retaining piles decreases, and the retaining piles generate significant counter-moment mutations at the tie beam locations. When pile foundations are adopted for the support beams, both the maximum bending moment of the retaining piles and the horizontal displacement at the top of the retaining piles are greater than those when strip foundations are used for the support beams. Zhao Qinghai [
6] innovatively proposed a pile–beam–counterfort tray retaining structure. The structure mainly consists of three parts: the counterfort tray retaining wall, the transfer beam, and the pile foundation. The upper counterfort tray retaining wall effectively narrows the embankment slope, the middle transfer beam transmits the upper loads to the lower pile foundation, and the lower pile foundation then transfers the loads to the bearing stratum. Yi Heng [
7] proposed a buttressed pile–beam retaining wall, but their designs were limited to simple working conditions and were not suitable for complex slope reinforcement scenarios. Li [
8] developed an EPS anti-slide pile composed of flexible EPS material. The frequency characteristics and dominant frequency band shift of EPS piles primarily occurred during the propagation phase following the main seismic acceleration. Under high seismic acceleration, both EPS piles and conventional piles exhibited certain degrees of deformation. The study employed EPS panels as damping layers to effectively buffer and dissipate slope deformation under seismic loading, with their damping performance closely related to seismic wave characteristics. Their test results demonstrated that the overall reduction in spectral displacement of EPS piles was significantly greater than that of conventional piles. Notably, the slip surface of the pile body showed high sensitivity to seismic action, making it a potential weak point in the seismic resistance of EPS piles. Luo [
9] proposed a novel drainage anti-slide pile (DASP) consisting of an upper hollow section with drainage holes and a lower solid section. However, these designs were not applicable to complex slope conditions. Sun [
10] discussed the stability of slopes reinforced with truncated piles and proposed a simplified numerical method based on the shear strength reduction method for analyzing slope stability.
Bao Jingjing et al. [
11] investigated the seismic performance of single-row anti-slide piles through combined FLAC3D numerical simulation and shaking-table tests. While the study successfully characterized the stress distribution and deformation patterns of piles under seismic loads, its simplified structural configuration (a single-row arrangement with a uniform cross-section) failed to capture the complex mechanical behavior of more sophisticated anti-slide systems. Their research particularly lacked an examination of structural complexities such as multi-row pile arrangements, variable cross-sections, or hybrid reinforcement systems, which are common in engineering practice. These limitations, coupled with the absence of parametric optimization, reduced the applicability of the findings to real-world seismic design scenarios. Huang Gucheng et al. [
12] elaborated on the earth pressure behind single-row pile–beam retaining walls, the beam structure, and the pile foundation structure, clarifying the design process of pile–beam retaining walls. Yu Wenjie [
13] further derived formulas for calculating the internal forces and displacements of double-row pile–beam retaining walls and validated these formulas using numerical simulations. Xia [
2] established a numerical model and found that the mechanical characteristics of three-row pile composite retaining walls, including the stress distribution, displacement, and deformation, were superior to those of single gravity retaining walls. Fu [
4] developed a finite element numerical model based on the translational and rotational tilt characteristics of pile–beam retaining walls during their service life, analyzing the impact of outward tilting on the settlement of widened subgrades.
In addition to the anti-slide pile–slope system, there is also the tunnel–slope system. In the tunnel–slope system, common relationships between tunnels and slopes include tunnels perpendicular to slopes [
14,
15], tunnels parallel to slopes [
16], two tunnels intersecting orthogonally within a slope [
17,
18], and tunnels obliquely intersecting slopes [
19]. Previous studies have primarily focused on the interaction between tunnels and slopes. Feng Haizhou et al. [
20] studied the seismic response of open-cut tunnels arranged longitudinally along anti-slide piles under the support of frame beams and anchor cable pile-slab walls, revealing the instability types of tunnel portal slopes under seismic action after rainfall. Zhong Zhanyong et al. [
21] proposed a large-span pile–beam retaining wall, allowing existing culverts to pass between two pile foundations, ensuring both the safe construction of culverts and the stability of railway subgrades.
However, research on the intersection of tunnels and slope anti-slide piles, such as the orthogonal or oblique intersection of mountain tunnels and slope anti-slide piles, remains limited. Additionally, there is insufficient research on the parametric analysis of buttressed pile–beam retaining walls, particularly their seismic performance under strong earthquakes. Therefore, this study proposes a new type of buttressed pile–beam retaining wall and takes the portal engineering of the Panzhihua Sunshine Tunnel’s left line, where anti-slide piles were removed, as an example. Using numerical methods, parametric analyses of the beam length, beam width, and retaining wall height were conducted to clarify the influence of these parameters on the reinforcement effect and mechanical performance of the buttressed pile–beam retaining wall, providing recommendations for its practical application.
4. Parameter Analysis and Discussion
In the design of the underpinning structure, particular attention should be paid to parameters such as the length and width of the transfer beam slab and the height of the retaining wall. Therefore, a parametric analysis was conducted to evaluate the seismic performance and reinforcement effectiveness of the buttressed pile–beam underpinning system based on project requirements. The entire parametric analysis process adopted the same load inputs and boundary conditions as those used in the standard verification model. The extreme values of each parameter analysis model during the seismic response were extracted for discussion. The numerical simulation conditions for the parametric study of the buttressed pile–beam retaining wall are illustrated in
Figure 12, and the influencing parameters are listed in
Table 5.
The parameter ranges were determined through integrated engineering practice and theoretical analysis: the pile length λ (0.5 D–2.0 D) covers scenarios from shallow sliding control (short piles) to penetrating potential slip surfaces (long piles); the pile width α (2.0 H–3.5 H) ensures minimum longitudinal stiffness (2.0 H for shear resistance) while coordinating bending capacity with beam height H; the height range H (0.4 L–1.0 L) adheres to anchorage requirements (0.4 L prevents overturning and 1.0 L enables full cross-sectional load transfer in anti-slide piles). Detailed values are provided in
Table 5.
To study the mechanical performance of the buttressed pile foundation beam retaining wall, the stress distribution at the top of the front and rear piles in the third group on the right side of the pile foundation and the stress distribution at the junction of the 13th anti-slide pile (from left to right) and the retaining wall were analyzed, as shown in
Figure 12.
4.1. Influence of Beam Slab Length
Figure 13 shows the displacement distribution at the slope crest, pile top, and buttress for different beam slab lengths. As shown in
Figure 13a, different beam slab widths do not change the distribution pattern of horizontal displacement at the slope crest and pile top. When the beam slab length increases from 0.5 D to 2.0 D, the displacement at the slope crest and pile top decreases from 1.85 mm ± 0.1 mm to 2.1 mm ± 0.1 mm, indicating that increasing the beam slab length has a minor effect on displacement. As shown in
Figure 13b, the transition point of pile top displacement between the reinforced and non-reinforced sections of the pile foundation beam retaining wall is quite noticeable. As shown in
Figure 13c, the beam slab length has a significant impact on the displacement of the buttressed pile foundation beam. In the case of a beam slab length 0.5 times the tunnel radius, due to the shorter beam slab length, the reinforcement length on the right side is insufficient, and the lack of support similar to buttress 21 on the left side causes the horizontal displacement to gradually increase from buttress rib 20 towards buttress rib 1, with the maximum horizontal displacement occurring on the far right, reaching 40.2 mm ± 1.0 mm. When the beam slab length increases to 1.0 D, the displacement of the retaining wall exhibits a symmetrical distribution with larger displacements in the middle and smaller displacements on both sides. As the beam slab length further increases, the reinforcement range of the anti-slide piles expands and the maximum horizontal displacement of the buttressed pile foundation beam retaining wall gradually shifts to the middle, showing a symmetrical distribution on both sides.
Figure 14 shows the stress distribution at the retaining wall for different beam slab lengths. The strain of the retaining wall increases nonlinearly with height. Taking the 0.5 D beam slab length as an example, the maximum stress at the top of the retaining wall is 2107.18 kPa ± 50 kPa, and the stress rapidly decreases to 1290.55 kPa ± 50 kPa at a height 0.5 m lower, showing a reduction of 38.7%. This indicates a sudden change at a height of 4 m, with a stress concentration at the top 0.5 m. Additionally, as the beam slab length increases, the stress on the retaining wall decreases slowly.
Table 6 shows the stress extremes at the top of the front and rear piles below the beam slab. As shown in
Table 2, different beam slab lengths have little effect on the stress difference between the front and rear piles.
4.2. Influence of Beam Slab Width
Figure 15 illustrates the distribution of extreme displacement values at the slope crest, pile top, and buttress for different widths of the transfer beam slab. As shown in
Figure 15a, when the width of the transfer beam slab increases from 2.0 H to 2.5 H, the extreme horizontal displacement at the slope crest decreases by nearly 5 mm ± 0.1 mm. However, the effectiveness of the slope support gradually diminishes with further increases in width. Additionally, the increase in width does not alter the distribution pattern of the horizontal displacement curves at the slope crest and pile top. As depicted in
Figure 15b, there is a clear distinction in the horizontal displacement at the pile top between slopes reinforced with buttressed pile–beam retaining walls and those without such reinforcement.
As shown in
Figure 15c, the influence of the transfer beam slab width on the reinforcement effect of the buttressed pile–beam retaining wall is primarily manifested through the soil-arching effect. The width of the transfer beam slab affects the clear spacing between the double-row piles beneath it, and this spacing controls the bearing capacity of the soil arch between the piles [
23]. As the pile spacing increases, the soil-arching effect becomes more pronounced, which enhances the anti-sliding capacity of the buttressed pile–beam retaining wall, thereby reducing the displacement of the anti-slide piles. While increasing the width of the transfer beam slab has a positive effect on the reinforcement of the buttressed retaining wall, it diminishes the positive impact on the displacement of the buttress.
Figure 16 shows the stress distribution at the retaining wall for different beam slab widths. The stress of the retaining wall increases nonlinearly with height. Taking the 2.0 H beam slab width as an example, the maximum stress at the top of the retaining wall reaches 2518.83 kPa ± 50 kPa and the stress rapidly decreases to 1752.625 kPa ± 50 kPa at a height 0.5 m lower, showing a reduction of 30%. A sudden change occurs at a height of 4 m, indicating a stress concentration at this location. As the beam slab width increases, the stress on the retaining wall decreases, but the rate of reduction is slower than that achieved by increasing the length of the transfer beam slab. When the width of the transfer beam slab increases from 2.0 H to 2.5 H, 3.0 H, and 3.5 H, the reduction rates of strain at the top of the retaining wall are 6.13%, 6.68%, and 8.07%, respectively. Correspondingly, the required concrete volume increases by 8.01%, 7.95%, and 8.53% when the width increases from 2.0 H to 2.5 H, 3.0 H, and 3.5 H. While the concrete volume increase rate remains roughly equal at each stage, the strain reduction rate gradually rises. This indicates that increasing the width of the transfer beam slab to reduce stress at the top of the retaining wall is more cost-effective than increasing the length of the transfer beam slab.
Table 7 presents the stress extremes of front and rear piles under varying transfer beam slab widths. The data reveal that beam slab width significantly affects the stress difference between front and rear piles. Notably, front pile stress shows minimal variation across configurations and consistently exceeds rear pile stress, demonstrating that the front pile and soil-arching effect dominate landslide resistance. This implies that increasing the beam slab width (and thus pile spacing) amplifies the deformation incompatibility in the buttressed pile-supported retaining wall system. Therefore, reducing the pile spacing and beam slab width appropriately can mitigate the pile stress imbalance.
4.3. Influence of Retaining Wall Height
Figure 17 illustrates the distribution of extreme displacement values at the slope crest, pile top, and buttress for different retaining wall heights. As shown in
Figure 17a, the influence of varying retaining wall heights on the distribution pattern of horizontal displacements at the slope crest and pile top is minimal. The horizontal displacements at both the pile top and slope crest reach their maximum values at the broken pile section. The displacement at the slope crest decreases nonlinearly as the retaining wall height increases.
As depicted in
Figure 17b, with the increase in retaining wall height, the displacement curve of the anti-slide piles within the retaining wall range changes from a downward convex curve with a larger curvature to one with a smaller curvature. This indicates that increasing the retaining wall height has a positive effect on the reinforcement of the anti-slide piles, making their displacements more consistent. Additionally, the extreme horizontal displacement of the anti-slide piles consistently occurs at piles numbered 11 and 12.
As shown in
Figure 17c, increasing the retaining wall height has a positive effect on the reinforcement of the buttressed retaining wall, but the rate of this positive effect decreases as the wall height increases. Theoretically, when the height of the retaining wall and the width of the transfer beam slab are equal, both at 13 m, forming an isosceles right triangle, the materials of the retaining wall and transfer beam slab can be utilized more efficiently. Equal lengths of the two perpendicular sides facilitate relatively uniform stress distribution, enhancing the supporting effect of the transfer beam slab and improving the stability and seismic performance of the retaining wall structure. This demonstrates that the height of the retaining wall significantly influences the overall stress distribution of the buttressed pile–beam retaining wall.
Figure 18 shows the stress distribution at the retaining wall for different retaining wall heights. The design height of the retaining wall affects the stress distribution pattern. When the design height of the retaining wall is less than 1.0 L, the maximum stress occurs at the top of the retaining wall; when the design height equals 1.0 L, the stress at the top of the retaining wall is the minimum.
As the design height of the retaining wall decreases below 1.0 L, the stress on the retaining wall decreases rapidly. When the design heights are 0.4 L, 0.6 L, 0.8 L, and 1.0 L, the strain at the top of the retaining wall decreases by 39.5%, 44.81%, and 52.43%, respectively; the corresponding increase in concrete volume is 14.3%, 12.51%, and 11.12%. The rate of stress reduction accelerates, while the incremental increase in concrete volume decreases, indicating that increasing the design height of the retaining wall can effectively reduce its stress.
Table 8 shows the stress extremes at the front and rear piles for different retaining wall heights. The retaining wall height has a significant effect on the stress difference between the front and rear piles. The higher the retaining wall height, the smaller the stress difference between the front and rear piles.
For different retaining wall heights, the stress on the front pile gradually decreases, and the stress on the front pile is always greater than that on the rear pile. When the retaining wall height increases from 0.4 L to 0.6 L, the stress on the rear pile increases while the stress on the front pile decreases; when the retaining wall height further increases to 0.8 L and 1.0 L, the stress on both the front and rear piles decreases. When the retaining wall height is small, the entire buttressed pile foundation beam retaining wall mainly relies on the pile foundation for anti-sliding force; when the retaining wall height is large, the anti-sliding capacity of the retaining wall itself increases, reducing its dependence on the pile foundation.
4.4. Selection Recommendations
In seismic zones, the impact of seismic forces on retaining structures is typically several times greater than that of static forces. Therefore, to fully consider the overall seismic performance and the influence during tunnel excavation, the Technical Code for Structural Safety Protection of Urban Rail Transit (CJJ/T 202-2013) specifies that for deep-buried mining method tunnels, the external operation influence zone remains a strongly affected area within the tunnel’s frontal and lateral 1.0b range (where b is the tunnel span) [
24]. Consequently, the minimum length of the transfer beam slab should be at least one times the tunnel width.
When the width of the transfer beam slab increases from 2.0 D to 2.5 D, 3.0 D, and 3.5 D, the corresponding increase in concrete volume is 8.01%, 7.95%, and 8.53%, respectively, indicating a linear increase in concrete usage. As the concrete volume increases, the reinforcement effect on the slope anti-slide piles gradually weakens and the stress difference between the front and rear piles becomes more pronounced. Therefore, the recommended width of the transfer beam slab is 3.0 times the height of the retaining wall. At this width, the displacements at the slope crest and pile top remain within controllable limits, the bearing capacity of the soil-arching effect is fully utilized, and both the front and rear piles can function effectively.
When the height of the retaining wall increases from 0.4 L to 0.6 L, 0.8 L, and 1.0 L, the corresponding increase in concrete volume is 14.3%, 12.51%, and 11.12%, respectively. As the concrete volume increases, the reinforcement effect on the slope anti-slide piles gradually weakens, and the stress difference between the front and rear piles becomes more pronounced. Considering the decreasing rate of concrete usage, the recommended height of the retaining wall is 0.6 times the cantilever length of the anti-slide pile. At this height, the displacements at the slope crest and pile top remain within controllable limits, and the stress distribution in the retaining wall is relatively uniform.
Taking into account the reinforcement effect [
25], structural stress characteristics, and economic efficiency of the buttressed pile–beam retaining wall under different parameters, the optimal parameters are determined as follows: the length of the transfer beam slab should be one times the tunnel diameter extended at the intersection of the tunnel and slope, the width of the transfer beam slab should be 3.0 times the height of the retaining wall, and the height of the retaining wall should be 0.6 times the cantilever length of the anti-slide pile. Additionally, referencing other studies [
1], it is recommended that the horizontal and longitudinal clear spacing of the piles be twice the pile diameter and the thickness of the transfer beam slab be two-thirds of the pile clear spacing.
4.5. Differences in Seismic Performance
The buttressed pile-supported beam-slab retaining wall demonstrates significant differences compared to conventional retaining walls through its “beam-slab–double-row piles–retaining wall” collaborative mechanism. While traditional retaining walls primarily rely on self-weight to balance earth pressure, exhibiting linear displacement distribution at the slope crest with limited adjustment capacity, the buttressed system forms a displacement buffer zone by extending the beam-slab length, resulting in a characteristic U-shaped displacement pattern with larger values at the center and smaller at both sides. Regarding pile stress behavior, conventional walls tend to show synchronous stress increases in both front and rear piles, whereas the new structure achieves dynamic equilibrium through active control of beam-slab width, utilizing soil-arching effects to increase stress in front piles while reducing stress in rear piles. Furthermore, the quantitative relationship between wall height and cantilever length of anti-slide piles provides more precise coordination between structural stability and displacement control compared to traditional empirical design approaches.
5. Conclusions
This study, based on the Panzhihua Sunshine Tunnel anti-slide pile project, analyzed the seismic performance and conducted a shaking-table test. Using numerical simulation methods, the parameters of the buttressed pile–beam retaining wall for reinforcing slope anti-slide piles were optimized. The influences of factors such as the thickness and width of the transfer beam slab and the height of the retaining wall on the displacement of the slope crest, pile top, stress distribution of the retaining wall, and stress difference between the front and rear piles were analyzed. The main conclusions are as follows:
(1) The time–history data of the pile top obtained from the numerical model correspond well with the data collected from the shaking-table test in terms of shape and peak values. The main frequency of the Fourier amplitude spectrum and the trend of peak earth pressure on the anti-slide piles were also well validated.
(2) Increasing the length of the transfer beam slab has a limited effect on reducing the extreme displacements of the slope crest, pile top, and tunnel. However, it significantly improves the displacement and stress state of the buttressed retaining wall, making the displacement and stress distribution more reasonable and uniform.
(3) Due to the soil-arching effect, increasing the width of the transfer beam slab effectively reduces the displacements at the slope crest and pile bottom. However, it leads to increased stress on the front piles and decreased stress on the rear piles, resulting in uneven stress distribution in the buttressed retaining wall.
(4) Increasing the height of the retaining wall enhances its stability and reduces the extreme displacements at the slope crest and pile top. However, it also leads to decreased stress on the front piles and increased stress on the rear piles.
(5) The optimal parameters for the buttressed pile–beam retaining wall under seismic conditions are as follows: the length of the transfer beam slab should be one times the tunnel diameter extended at the intersection of the tunnel and slope, the width of the transfer beam slab should be 3.0 times the height of the retaining wall, and the height of the retaining wall should be 0.6 times the cantilever length of the anti-slide pile. Additionally, the horizontal and longitudinal clear spacing of the piles should be twice the pile diameter and the thickness of the transfer beam slab should be two-thirds of the pile clear spacing.
(6) It should be noted that this study is based on typical geotechnical conditions in the Panzhihua region and specific seismic inputs, with the optimization scheme applicable to seismic designs of moderately to strongly weathered rock slopes or dense sand–gravel mixed strata. For projects with significantly different geological conditions or seismic characteristics, parameter adjustments should be made according to specific circumstances. Although increasing the beam-slab width and retaining wall height can improve seismic performance, it may also lead to uneven stress distribution in the structure. Therefore, reasonable dimension control during construction is necessary to avoid compromising overall structural stability. The research findings can provide a theoretical basis and optimization references for the seismic design of similar mountain tunnel and slope engineering projects.