Research on Stability of Transmission Tower Slopes with Different Slope Ratios Under Rainfall Conditions and Reinforcement Effects of Anti-Slide Piles

Abstract

With the extensive construction of high-voltage power grid projects in complex mountainous terrains, rainfall-induced slope instability poses a significant threat to the safety of transmission tower foundations. This study focuses on a power transmission and transformation project in Huizhou City, Guangdong Province. Using MIDAS GTS NX 2019 (v1.2), an unsaturated seepage-mechanics coupling model was established to systematically investigate the influence of slope ratios (1:0.75, 1:1, and 1:1.25) on slope stability under rainfall conditions and the reinforcement effects of anti-slide piles. The results demonstrate that slope ratios significantly govern slope responses. For steep slopes (1:0.75), post-rainfall matrix suction loss reached 43.2%, peak displacement attained 74.49 mm, and the safety factor decreased by 12.5%. In contrast, gentle slopes (1:1.25) exhibited superior stability. Anti-slide piles effectively controlled displacement growth (≤9.15%), but pile bending moments increased markedly with steeper slope ratios, accompanied by a notable expansion of the plastic zone at the slope toe. The study reveals a destabilization mechanism characterized by “seepage–strength degradation–displacement synergy” and recommends engineering practices adopting slope ratios of 1:1–1:1.25, combined with anti-slide piles (spacing ≤ 1.5 m) and dynamic drainage measures. These findings provide critical guidance for the design of transmission tower slopes in mountainous regions.

1. Introduction

In recent years, China’s high-voltage power grid infrastructure has undergone significant expansion, with cumulative investments surpassing 150 billion yuan. However, a considerable portion of the planned transmission lines traverses mountainous and hilly regions, where complex terrain and extreme weather conditions synergistically amplify engineering risks. A representative example is the power transmission project in Huizhou City, Guangdong Province, where overhead lines span denuded residual hill landforms characterized by substantial elevation variations (ranging from 4.13 m to 144.55 m, with a total relief of 140.42 m) and slope gradients of 10–30°. Situated within South China’s heavy rainfall zone, this region faces escalating threats from rainfall-induced landslides, which increasingly jeopardize the stability of transmission tower foundations [1,2,3]. A concern further exacerbated by global climate change. Consequently, quantifying the influence of intense rainfall infiltration on the mechanical response of anti-slide pile foundations has emerged as a pivotal technical challenge in safeguarding power grid reliability.

Anti-slide piles are widely regarded as the optimal support structure for power transmission tower foundations on slopes due to their structural simplicity, high stiffness, and strong adaptability to complex terrain. Given the necessity of constructing high-voltage transmission lines across hilly regions, a significant number of tower foundations must be built on potentially unstable slopes, making their stability critical for ensuring power grid safety [4,5]. However, most existing studies focus on slope stability under non-rainfall conditions, neglecting the dynamic effects of rainfall infiltration on the pile-soil system. Moreover, research under rainfall conditions remains limited.

Natural soils are typically unsaturated, and rainfall infiltration increases their moisture content, reducing matric suction and leading to soil softening. This change in soil properties significantly impacts the structural integrity of transmission tower foundations. To address this gap, this study employs finite element numerical simulations to investigate the vertical settlement and horizontal displacement behavior of anti-slide piles under rainfall infiltration. Additionally, the mechanical response and deformation characteristics of anti-slide pile foundations are analyzed, with particular attention to the effects of varying slope gradients.

An orthogonal experimental design is adopted to examine the influence of anti-slide pile placement and slope ratio on stability patterns under simulated rainfall conditions [6,7]. By monitoring slope displacement and recording bending moment variations in the piles, the interaction mechanism between the foundation and surrounding soil is elucidated. The findings provide valuable insights for the design and implementation of anti-slide pile foundations in transmission tower projects, offering practical guidance for related research and engineering applications.

Current research in the field of geotechnical engineering has primarily focused on the analysis of slope stability under rainfall conditions and the performance of pile foundations, with studies examining the impacts of rainfall patterns and soil types on slope stability. Investigations have been conducted by controlling rainfall volume, intensity, and duration to understand the infiltration and stability changes in slopes. For instance, the influence of Singapore’s changing rainfall patterns on slope stability has been explored [8,9,10], as well as the effects of rainfall duration on soil pressure and arching effects in pile foundations [11,12,13]. Additionally, the stability of pile foundations under the combined effects of earthquakes and rainfall has been analyzed using Abaqus 2018 finite element software [14,15]. Given the potentially catastrophic consequences of pile foundation failure in transmission towers, the layout of pile foundations is crucial for the load-bearing performance of transmission tower foundations.

Pile foundations, known for their simple structure and high load-bearing capacity, are a common choice for transmission tower foundations [16,17,18]. Properly spaced piles can create an arching effect in the soil, enhancing the load-bearing capacity of the foundation. Studies have shown that the arching effect is negatively correlated with the ratio of pile spacing to pile diameter [19,20]. Other research has used numerical analysis to investigate the impact of different pile spacing and diameter ratios on soil arching effects, while vibration table tests have been conducted to study the influence of pile spacing on soil deformation characteristics, dynamic soil pressure, and pile internal force distribution [21,22]. The reinforcement effects of polymer piles under rainfall conditions have also been examined, as well as the cyclic effects and dynamic responses of pile foundations under vertical cyclic compressive loading through single-pile model tests [23,24]. Despite extensive research on pile foundation load-bearing performance, the impact of different slope ratios on pile foundation load-bearing performance remains unclear.

In the field of geotechnical engineering, research on the bearing performance of pile foundations currently mainly employs two methods: indoor scaled model tests and in-situ tests. Indoor scaled model tests have the advantages of being convenient, economical, and controllable. However, they involve a significant degree of simplification of actual conditions. In situ tests can better study the force conditions of pile foundations in actual projects, but they are difficult to conduct, costly, and unable to effectively investigate the influence of different variables on the bearing performance of pile foundations. Therefore, with the development of computer technology, numerical analysis methods have gradually become mainstream. The finite element numerical analysis method was first used to calculate the safety factor of slopes, making complex slope problems more intuitively solvable [25]. Scholars have continuously improved rainfall infiltration algorithms to enhance computational accuracy in recent years. For instance, some studies have proposed new formulas for calculating the safety factor of 3D stepped slopes in non-uniform unsaturated soil [26,27], while others have established three-dimensional slope models based on the strength reduction and stepwise loading finite element method, considering the interaction between anti-slide piles and soil, to obtain more accurate results [28,29].

This study employs finite element numerical simulation to investigate the stability of pile foundations used as transmission tower bases under rainfall conditions, addressing existing research gaps and providing scientific support for engineering practice. Transmission towers are inevitably constructed on slopes, and the stability of these slopes is crucial for the safe operation of the towers. Slope instability can lead to tower collapse, resulting in severe power accidents and economic losses. Therefore, researching slope stability is of significant practical importance for ensuring the safe operation of transmission towers. Although previous studies have examined slope stability and pile foundations under rainfall, few have systematically compared different slope ratios for transmission tower foundations. The combined effects of rainfall infiltration, anti-slide piles, and varied slope geometries—especially under intense rainfall typical of South China—remain underexplored. This study fills these gaps using unsaturated seepage–mechanics coupled finite element simulations to assess how different slope ratios (1:0.75, 1:1, and 1:1.25) affect slope stability and anti-slide pile reinforcement. The results deepen understanding of slope-pile system responses and provide practical guidance for the safe design of transmission tower foundations in rainfall-prone areas.

2. Finite Element Modelling of Rainfall Infiltration on Slopes

2.1. Model Building

The selection of the research tool for this study was based on the Midas GTS NX 2019 (v1.2), a program capable of supporting static/dynamic analysis, seepage/cementation analysis and slope stability analysis. The present study is concerned with the rainfall conditions of the slope model. In order to define the geotechnical materials, the program utilizes the Bishop equivalent effective stress formula as the basis for calculating effective stress in unsaturated soils. In the call of the function, it is only necessary to take into account the formula for the fit experience coefficient.

In this analysis, the coefficient of permeability of water in the soil is referenced to the computational equation proposed by Alonso E [30], characterizing the relationship between the coefficient of permeability and matrix suction:

$$k_w={\displaystyle \frac{a_w{k}_{ws}}{a_w+{\left[\begin{array}{c}{b}_w\left(u_a-u_w\right)\end{array}\right]}^{c_w}}}$$

(1)

where $k_w$ is the permeability coefficient; $k_{ws }$ is the Saturated permeability coefficient of the soil; and $a_w,{ b}_w,{\mathrm{a}\mathrm{n}\mathrm{d} c}_w$ are the Constant parameters.

In the transient analysis of finite element simulation, the soil body undergoes a transition from unsaturated to saturated, and the software must set the corresponding unsaturated characteristic function for the soil body in the calculation. Should this characteristic be overlooked, the software will revert to the initial state of the soil body as saturated. This will result in the inability to carry out the seepage analysis based on time change. Furthermore, the calculation process is likely to result in the system reporting an error. The calculation of inaccurate results will be the consequence of forced convergence. In this paper, the Van Genuchten independent unsaturated characteristic function, as incorporated within the MIDAS GTS NX 2019(v1.2) framework, is employed in the finite element analysis, which is manifested as a soil-water characteristic curve. The latter is a function model that aims to delineate the quantitative relationship between the volumetric water content of the soil body and the suction force of the matrix. The Van Genuchten model was developed by the Dutch scholar Michiel Van Genuchten [31] in 1980, following a substantial number of studies that demonstrated the superior fitting effect of the V-G model for both coarse and clayey soils. Its specific expression is as follows:

$$\theta ={\theta }_r+{\displaystyle \frac{{\theta }_s-{\theta }_r}{{\left[1+{\left(\alpha \cdot h\right)}^n\right]}^m}}$$

(2)

where $h$ is the Negative head pressure; ${\theta }_s$ is the Saturated moisture content; ${\theta }_r$ is the Residual moisture content; and $\alpha , m, \mathrm{a}\mathrm{n}\mathrm{d} n$ are the Fit parameters.

The permeability parameters of the granite residual soils used in this study are shown in

Table 1. V-G model correlation coefficient values.

Function	Function Type	Coefficient Value
Unsaturated Characteristic Function	Independent Functions	-
Types of Permeability Functions	Van Genuchten	$\alpha$ = 0.8, $n$ = 1.18, $m$ = 0.68
Type of Water Content Function	Van Genuchten	${\theta }_r$ = 0.07, ${\theta }_s$ = 0.47, $\alpha$ = 0.8, $n$ = 1.18, $m$ = 0.68

:

It is important to note that given MIDAS GTS NX 2019 (v1.2) incorporates a built-in Van Genuchten unsaturated characteristic function, only the empirical coefficients for fitting the formulae need to be taken into account when calling it. The soil–water characteristic curve Van Genuchten is demonstrated in Figure 1 and Figure 2:

This study investigates the influence of rainfall infiltration on slope stability under different slope ratios by analyzing three slope configurations with ratios of 1:0.75, 1:1, and 1:1.25. All three slope models share identical geometric dimensions: a total horizontal length of 120 m, slope height of 45 m, slope width of 60 m, and foundation depth of 15 m. The two-dimensional wireframe models of these three slope configurations are presented in Figure 3.

The CAD wireframe of the aforementioned slope is imported into the MIDAS.GTS.NX software to form a 2D wireframe. A check is then performed on the 2D wireframe to ascertain the presence of any duplicate line segments. Subsequently, a surface is generated from the 2D wireframe, and the 2D surface is extended along the y-axis for planar stretching, thus forming a 3D model. Following this, a Boolean operation is carried out for the foundation and slope. Finally, the final intersection is built into a 3D solid model, as illustrated in Figure 4.

2.2. Material Property Configuration and Mesh Generation

In this study, three slope ratios (1:0.75, 1:1, 1:1.25) were established for the purpose of calculation, and the fundamental physico-mechanical parameters of the soil layer and the anti-slip piles were ascertained on the basis of the relevant investigation results and field samples for the indoor tests, as illustrated in

Table 2. Basic Physical Parameters of Soil.

Material Type	Constitutive Model	Elastic Modulus E (MPa)	Poisson’s Ratio ν	Volumetric Weight γ (kN/m)	Initial Void Ratio e0	Cohesion c (kPa)	Internal Friction Angle φ (°)
Granite Residue	M-C	50	0.3	18	0.5	26	37
Skid Pile	Elasticity	33500	0.2	25	/	/	/

below. The anti-slide piles primarily serve as rigid supports, effectively restricting the slope’s horizontal displacement and sliding tendencies. In this study, the piles were designed to operate within normal working conditions without reaching yield or failure states. Accordingly, adopting an elastic constitutive model accurately represents their mechanical behavior. Furthermore, the elastic model provides high computational efficiency, which is especially beneficial for large-scale numerical simulations. This approach is particularly advantageous when assessing the overall stability of slopes under rainfall conditions, as it substantially reduces computational complexity.

To account for the more detailed mechanical responses at lower slope angles, the mesh was progressively refined as the slope ratio increased. Specifically, the 1:0.75 slope model used 10,564 nodes and 7047 elements; the 1:1 model used 11,004 nodes and 9360 elements; and the 1:1.25 model used 11,648 nodes and 10,207 elements. As shown in Figure 5. Finer meshes were applied, especially near the slope surface and potential slip zones, to better capture the gradual changes in mechanical behavior caused by slope angle variation. This approach refers to the relevant literature [32].

2.3. Boundary Conditions and Loading

The numerical simulation considered gravitational forces as the sole external loading under natural conditions, with the gravity load systematically applied to the entire slope model. To properly constrain the computational domain while allowing for realistic deformation patterns, the following kinematic boundary conditions were implemented: (i) lateral displacement constraints (x-direction) on both side boundaries, (ii) longitudinal constraints (y-direction) on the front and rear boundaries, and (iii) full fixation (x–y directions) at the base interface. The ground surface remained unconstrained to permit free deformation. The hydrogeological boundary conditions were carefully defined to represent field conditions: the slope–foundation interface served as the reference datum for initial hydraulic head distribution, while rainfall infiltration was modeled as a time-dependent surface flux boundary with corresponding seepage face activation to simulate unsaturated flow processes. This comprehensive boundary condition setup, illustrated in Figure 6, ensures proper representation of both mechanical and hydrological behaviors in the coupled analysis.

2.4. Rainfall Condition Configuration

China’s current rainfall classification standard is based on 24 h cumulative precipitation amounts, with rainfall categories defined in

Table 3. Rainfall Intensity Classification Standard.

Rainfall Type	Light	Moderate	Heavy	Torrential	Severe Torrential	Extreme Torrential
24 h Rainfall (mm)	≤10	10~25	25~50	50~80	80~120	≥120

.

The present study principally considers the effect of differing slope ratios on slope stability under conditions of rainfall infiltration with constant rainfall intensity and duration.

Huizhou City, situated within the Guangdong Province, is subject to a subtropical monsoon humid climate characterized by a protracted rainy season that persists throughout the year. This climate is marked by substantial rainfall, including heavy torrential downpours, as illustrated in

Table 4. Rainfall conditions.

Slope Type	Rainfall Intensity	Rainfall Duration
1:0.75	50 mm/d	12 h/24 h
1:1	50 mm/d	12 h/24 h
1:1.25	50 mm/d	12 h/24 h

.

3. Finite Element Analysis of Slope Infiltration Results

3.1. Pore Water Pressure Analysis

Pore water pressure is a critical parameter for characterizing soil seepage and stability. This study analyzed the response characteristics of slopes with different gradients under a 24 h stepped rainfall pattern (12 h per cycle) using numerical simulations. The results show (Figure 7, Figure 8 and Figure 9) that for slope models with gradients of 1:0.75, 1:1, and 1:1.25, the maximum pore water pressures after 12 h were 147.687, 147.877, and 148.096 kPa, respectively. After 24 h, these values increased to 148.076, 148.375, and 148.737 kPa, respectively. Meanwhile, the extreme values of negative pressure zones showed a decreasing trend as the rainfall duration extended, with corresponding reductions of 5.0, 4.4, and 3.6 kPa, respectively.

These data reveal a dual evolution pattern: (1) The peak pore water pressure is positively correlated with rainfall duration, with an average increase of 0.38% across all models after 24 h; (2) Under the same rainfall duration, for every 0.25 increase in slope gradient (from 1:0.75 to 1:1.25), the peak pressure increases by 0.14% to 0.44%. This characteristic is attributed to the enhanced seepage effect caused by the shortened seepage path of the slope and the accumulation of pore water pressure due to the contraction of the unsaturated zone, which is consistent with the laws of soil seepage [33].

3.2. Displacement Field Analysis

Rainfall infiltration significantly alters the hydraulic regime of slope soils, manifesting in three principal aspects: elevation of pore water pressure, enhancement of saturation degree, and reduction of matric suction. These hydraulic modifications directly initiate displacement evolution, thereby compromising slope stability. Displacement monitoring data revealed pronounced spatial heterogeneity in deformation patterns, with the x-direction displacement exhibiting notably predominant magnitudes (approximately one order higher than those in y- and z-directions), justifying our focused investigation on x-directional responses. Figure 10 illustrates the slip surface distribution and x-direction maximum displacement nephograms for slopes with three distinct ratios (1:0.75, 1:1, and 1:1.25) under 24 h rainfall intensity of 50 mm/d.

Displacement analysis of slopes with varying ratios after 24 h rainfall infiltration revealed a critical correlation: As the slope ratio increased from 1:1.25 (gentle slope) to 1:0.75 (steep slope), the maximum sliding displacement escalated significantly from 13.37 mm to 74.49 mm, accompanied by progressive migration of slip surfaces from the toe (0.78 m) toward the crest (16.58 m). This phenomenon is attributed to dual mechanisms: On one hand, steeper slopes (smaller ratio values) accelerate infiltration rates, inducing pronounced matric suction dissipation that amplifies global displacements. On the other hand, gentler slopes (1:1.25 ratio) develop localized pore water pressure concentrations at the toe (water table elevation exceeding ground level by 0.5–1.2 m), which redirects plastic failure zones toward lower slope regions. These findings quantitatively demonstrate that slope ratios govern rainfall-induced stability through their decisive control over both seepage field redistribution and plastic zone evolution.

3.3. Safety Factor Analysis

The safety factor, serving as the pivotal evaluation index for slope stability, is defined as the ratio of anti-sliding moment to sliding moment (or anti-sliding force to sliding force) along potential slip surfaces. In accordance with Article 5.2.3 of GB50330-2013 Technical Code for Building Slope Engineering [34], the stability status of slopes adopts a four-grade classification system as specified in

Table 5. Classification Criteria for Slope Stability Status.

Safety Factor	Fs < 1.00	1.00 ≤ Fs < 1.05	1.05 ≤ Fs < 1.15	Fs > 1.15
Slope Stability Status	Unstable	Marginally Stable	Basically Stable	Stable

.

Numerical simulations based on the Strength Reduction Method were conducted to evaluate the stability of slopes with three distinct ratios (1:0.75, 1:1, and 1:1.25) under 24 h rainfall conditions at an intensity of 50 mm/d. The safety factor contour plots, obtained through finite element calculations, are illustrated in Figure 11, Figure 12 and Figure 13.

A comparative analysis was conducted on the stability responses of slopes with three distinct ratios (1:0.75, 1:1, and 1:1.25) under natural and rainfall conditions (50 mm/d for 24 h). The results demonstrate that under natural conditions, the safety factors for slopes with ratios 1:0.75, 1:1, and 1:1.25 were 1.225, 1.264, and 1.298, respectively. Following rainfall infiltration, these values decreased to 1.096, 1.106, and 1.127, corresponding to reduction rates of 10.5–12.5%. Rainfall-induced effects markedly amplified plastic strain, triggering a 22–30% expansion of critical slip surfaces and elevating x-direction displacements to 3.2–4.8 times those observed under natural conditions. Notably, the maximum rate of safety factor variation occurred within the slope ratio range of 1:1 to 1:1.25, indicating heightened sensitivity to rainfall infiltration within this gradient interval.

Further analysis revealed that the slope with a ratio of 1:0.75 exhibited the most pronounced stability degradation: its matric suction loss reached 43.2%, peak x-direction displacement attained 74.49 mm, and safety factor reduction rate (12.5%) ranked highest among the three slope ratios. This phenomenon elucidates the intrinsic mechanism whereby slope ratios govern stability by modulating infiltration dynamics—larger slope ratios (e.g., 1:0.75) amplify hydraulic gradients, accelerating rainwater infiltration and soil softening processes, thereby exacerbating deformation and stability deterioration. These findings establish a theoretical foundation for designing protective measures in rainfall-prone slope engineering.

4. Slope Reinforced with Anti-Slide Piles Under Rainfall Conditions

4.1. Anti-Slide Pile Reinforcement Design Theory

This study investigates the influence of rainfall infiltration on the stability of anti-slide pile-reinforced slopes with varying ratios (1:0.75, 1:1, and 1:1.25) by selecting a representative reinforcement configuration where piles are positioned along the slope central axis (pile location ratio Lx/L = 0.5). Under coupled effects of slope geometry and 24 h rainfall (50 mm/d), the evolution of reinforcement efficacy was systematically analyzed. Anti-slide piles stabilize slopes through three synergistic mechanisms: (1) transferring sliding forces to stable strata via pile rigidity; (2) optimizing pile spacing to activate soil arching effects, forming stress-arch structures between piles; and (3) constraining displacement development to mitigate deformation. The pile spacing design, based on soil arching theory, was calculated using the formula proposed by Zhao et al. [35]. Equation (3) ensures the theoretical validity and engineering applicability:

$$L={\displaystyle \frac{cb\left(1+sin\phi \right)\left(5-3sin\phi \right)}{4qcos\alpha cos\phi \left(1-sin\phi \right)}}+b$$

(3)

where:

$c$—Cohesion of the soil behind the piles;

$\phi$—Internal friction angle of the soil behind the piles;

$b$—Width of the pile;

$q$—Distributed line load of the soil behind the pile;

$\alpha$—Slope angle.

In the numerical simulation, rectangular anti-slide piles with dimensions of 15 m in length and 1.0 m in width were implemented to reinforce the slope, aligning with the study area’s geological conditions and engineering requirements. Based on the aforementioned formula, the net spacing between adjacent piles was determined as 1.5 m. The analysis was conducted using MIDAS GTS NX 2019(v1.2) software, incorporating a coupled seepage-stress interaction model for pile-soil systems. A hyperbolic contact model was adopted to simulate interfacial behavior between piles and soil, where interface elements characterized relative displacements at material boundaries. These elements were defined by two critical parameters: normal stiffness modulus (Kn) and shear stiffness modulus (Kt). The values of these interfacial parameters were derived from established empirical formulas, expressed as follows:

$$K_n={\displaystyle \frac{RE\left(1-{\nu }_i\right)}{t_v\left(1+\nu \right)\left(1-2{\nu }_i\right)}}$$

(4)

$$K_t={\displaystyle \frac{R}{2t_v\left(1+\nu \right)}}$$

(5)

where:

${\nu }_i$—Poisson’s ratio of the interface;

$\nu$—Poisson’s ratio of the soil;

$t_v$—Virtual thickness parameter;

$E$—Elastic modulus of the soil;

$R$—Strength reduction factor.

In MIDAS GTS NX 2019 (v1.2), the normal stiffness modulus (Kn) and shear stiffness modulus (Kt) of the pile-soil interface are automatically calculated by the software by inputting the virtual thickness parameter (tv) and strength reduction factor (R). Additionally, the pile end element configuration incorporates both pile end bearing capacity and spring stiffness, with specific parameter values detailed in

Table 6. Parameter values of pile element and pile end element.

	Pile Element	Pile Tip Element
Normal Stiffness Modulus Kn (kN/m3)	500,000	/
Shear Stiffness Modulus Kt (kN/m3)	200,000	/
Pile Tip Bearing Capacity (kN)	/	8000
Pile Tip Spring Stiffness (kN/m)	/	31,616

.

4.2. Effect of Rainfall on Horizontal Displacement of Slopes with Varying Ratios

Figure 14 illustrates the characteristics of horizontal displacement variations in slopes with different ratios before and after rainfall. The analysis indicates that the mid-lower slope regions consistently exhibit the maximum horizontal displacements, with magnitudes diminishing radially outward. Post-rainfall, all slopes demonstrated increased horizontal displacements: a 9.15% increase for the 1:0.75 slope, 1.8% for 1:1, and 3.52% for 1:1.25. This phenomenon primarily stems from the dual effects of shear strength reduction and increased driving forces induced by rainwater infiltration. Notably, despite the displacement amplification, the limited magnitude of increases (below 10%) suggests that anti-slide piles effectively restrained excessive rainfall-induced displacements, significantly enhancing slope stability under wet conditions.

4.3. Effect of Rainfall on Plastic Strain in Slopes with Varying Ratios

As shown in Figure 15, the distribution characteristics of plastic strain in slopes with varying ratios under anti-slide pile reinforcement are illustrated for both pre- and post-rainfall conditions. Regardless of rainfall exposure, plastic strains, in all cases, predominantly concentrated in the toe region and adjacent potential slip surfaces, aligning with the stress concentration and shear deformation patterns inherent to slope instability. The toe region, being a critical stress concentration zone, initiates yielding and plastic deformation in soils, followed by progressive propagation of plastic zones along potential slip surfaces toward the slope interior—indicating a shear-driven sliding failure mechanism.

By comparing the distribution of plastic strain before and after rainfall for the same slope ratio, it can be seen that the maximum plastic strain values have increased to varying degrees after rainfall. Specifically, in the model with a slope ratio of 1:0.75, the maximum plastic strain increased from 2.09 before rainfall to 2.27, a rise of 8.6%. For the model with a slope ratio of 1:1, the maximum plastic strain slightly increased from 2.43 to 2.45, a rise of 0.8%. In the model with a slope ratio of 1:1.25, the maximum plastic strain rose from 5.51 to 5.59, an increase of 1.4%. In addition, the scope of plastic strain influence generally expanded after rainfall and showed a tendency to extend toward the upper part of the slope body.

The results demonstrate that rainfall infiltration significantly exacerbates plastic deformation and compromises the overall stability of slopes. This phenomenon is attributed to the shear strength degradation and enhanced driving forces caused by soil saturation and increased self-weight, which collectively lower the yield threshold of soils, thereby inducing larger irreversible deformations under external loading. Plastic strains predominantly concentrate in the slope toe and potential slip surface regions—precisely the critical load-bearing zones where anti-slide piles function to resist sliding thrust and constrain failure progression. Although anti-slide piles effectively mitigate further deformation development, adjacent soils—particularly in the compression zone ahead of piles and shear zones along pile sides—still exhibit pronounced plastic strains due to localized stress concentration.

4.4. Influence of Rainfall on the Bending Moment of Anti-Slide Piles for Different Slope Ratios

Figure 16 illustrates the contour distribution of bending moments along anti-slide piles under varying slope ratios and rainfall conditions. The results demonstrate that the maximum bending moment occurs at specific depths for each slope ratio: approximately 9 m for the 1:0.75 slope ratio, 8 m for 1:1, and 6 m for 1:1.25, with values rapidly diminishing toward the pile tip. Overall, the bending moment distribution exhibits a consistent pattern across all slope ratios and rainfall scenarios, characterized by lower values at the upper and lower sections and a mid-depth peak, aligning with the mechanical behavior of anti-slide piles as flexural members resisting lateral soil thrust.

Notably, post-rainfall conditions amplify maximum bending moments compared to pre-rainfall states, indicating reduced slope stability and increased loading on piles due to infiltration effects. Furthermore, steeper slopes (1:0.75 and 1:1) consistently exhibit higher peak bending moments than the gentler 1:1.25 slope ratio both before and after rainfall. This trend quantitatively confirms that steeper slopes impose greater thrust demands on anti-slide piles, necessitating enhanced reinforcement designs for slopes with smaller ratios (e.g., 1:0.75) in rainfall-prone regions.

Anti-slide piles located along the central axis of the slope were selected, and the bending moment data of each node were systematically extracted to plot the distribution curves of the pile bending moment, as shown in Figure 17. The comparative analysis shows that the steeper the slope (the greater the slope ratio), the higher the bending moment experienced by the pile. This finding is consistent with the theoretical understanding that steeper slopes have a higher potential for landslides and exert greater lateral thrust on the piles.

Under the influence of rainfall, the maximum bending moment increase rates for piles in slopes with different ratios were 0.7% (for a slope ratio of 1:0.75), 0.3% (for 1:1), and 0.1% (for 1:1.25). This reveals that systems with smaller slope ratios (gentler slopes) inherently possess greater stability, are less sensitive to rainfall disturbances, and experience more limited additional load increments due to rainfall. This indicates that gentler slopes have better natural drainage properties, which can effectively reduce the adverse effects of rainwater on soil stability and, consequently, the additional load demands on the pile-bearing capacity caused by rainfall. This conclusion provides important theoretical support for the optimized design of anti-slide piles in slope areas sensitive to rainfall.

4.5. Analysis of Anti-Slide Pile Displacement Under Rainfall Infiltration

As shown in

Table 7. Horizontal Displacement of Anti-Slide Pile Top and Bottom.

Slope Ratio	Pile Head Displacement (mm)	Pile Toe Displacement (mm)
1:0.75	0.36	0.01
1:1	1.48	0.026
1:1.25	1.64	0.03

, the horizontal displacements of the pile top and pile bottom under rainfall conditions are presented. For all three slope ratios, the horizontal displacement of the pile bottom is close to 0, at 0.01 mm, 0.026 mm, and 0.03 mm, respectively, indicating that the pile bottom is essentially fixed. In contrast, the maximum horizontal displacement occurs at the pile top, measuring 0.36 mm, 1.48 mm, and 1.64 mm for the different slope ratios. This indicates that the pile body undergoes deformation dominated by bending and inclination under the thrust of the soil, with the upper part of the pile bearing the primary load. Further analysis reveals that the horizontal displacement of the pile top increases with the slope ratio but at a decreasing rate. Using the slope ratio of 1:0.75 as a reference, the pile top displacement increases by 1.12 mm when the ratio increases to 1:1, and by only 0.16 mm when the ratio increases to 1:1.25. This suggests that the steeper the slope, the greater the thrust on the anti-slide pile, but the incremental increase in thrust tends to stabilize.

The overall deformation of the pile is relatively small. When the slope ratio is 1:1, the maximum horizontal displacement at the pile top increases to 1.48 mm, indicating a significant increase in thrust. For the 1:1.25 slope ratio, the maximum horizontal displacement at the pile top reaches 1.64 mm. Although this is close to the displacement observed at the 1:1 slope ratio, the potential sliding surface is larger, and the volume of soil is greater, resulting in an increased thrust on the pile. These results are clearly demonstrated in Figure 18.

The thrust experienced by the anti-slide pile is closely related to the potential sliding area around it. Slopes with ratios of 1:1 and 1:1.25 are more prone to forming extensive potential sliding surfaces after rainfall infiltration. When the soil strength is weakened by rainwater, the soil mass can slide along this surface, exerting a significant thrust on the pile. Steeper slopes are more susceptible to instability compared to gentler slopes and are characterized by more sudden and impactful failures. Therefore, they require priority monitoring and early warning measures. These findings provide important references for optimizing the design of anti-slide piles.

5. Summary and Discussion

This study, through an unsaturated seepage-mechanics coupling model, has revealed the stability patterns of mountainous transmission tower slopes under rainfall infiltration with different slope ratios (1:0.75 to 1:1.25) and the reinforcement mechanisms of anti-slide piles:

(1) Slope Ratio Effect: The steep slope (1:0.75) has a significantly higher rate of matric suction loss (43.2%) and peak displacement (74.49 mm) compared to the gentle slope, with a safety factor reduction of up to 12.5%. The slope ratio range of 1:1 to 1:1.25 is identified as the optimal interval for stability, which can reduce the risk of sudden slippage. Steeper slopes not only increase the downslope gravity component but also accelerate rainfall infiltration and pore water pressure buildup, leading to faster loss of matric suction and reduced soil strength. In contrast, gentler slopes slow these processes, contributing to greater overall stability.

(2) Anti-Slide Pile Efficiency: The piles effectively suppress displacement growth (≤9.15%), but the bending moment of the pile increases significantly with steeper slopes (e.g., for a slope ratio of 1:1.25, the pile top displacement is 1.64 mm). This suggests the need for optimized pile positioning and stiffness matching.

(3) Instability Mechanism: Rainfall drives the accumulation of pore water pressure (peak value of 148.74 kPa) and the softening of unsaturated soil (cohesion reduction of 26 kPa), promoting the expansion of the plastic zone towards the slope toe. This study has unveiled the “seepage–strength attenuation–displacement synergy” degradation pathway.

For the first time, this study quantified the regulatory effect of slope ratio on the unsaturated seepage field and revealed the nonlinear characteristics of the safety factor with varying slope ratios, providing a new method for risk assessment of complex terrain slopes.

This research provides important engineering guidance: It is recommended in practical applications to prioritize slope ratios of 1:1 to 1:1.25 for improved safety and economy and to install anti-slide piles within the plastic zone at the slope toe (with pile spacing ≤ 1.5 m) alongside dynamic drainage and real-time pore pressure monitoring. These measures can significantly enhance the operational safety of transmission tower foundations in complex mountainous terrains.

However, the present study is subject to certain limitations arising from the sole reliance on numerical analysis. The models adopted are based on assumptions of homogeneous soil and constant, idealized rainfall conditions and have not yet been validated by physical model tests or monitored real cases. Such simplifications may affect the applicability of the findings to highly heterogeneous or dynamically evolving field conditions. The generalizability of the results should therefore be carefully considered, especially when dealing with sites exhibiting strong stratigraphic variability or subject to extreme or rapidly changing rainfall events.

In future research, it is essential to conduct field experiments or centrifuge model tests for validation, to incorporate more complex, non-homogeneous stratigraphic conditions and dynamic meteorological data, and to further investigate the synergistic reinforcement mechanism between vegetation root systems and anti-slide piles. Such studies will help establish a more robust and practical disaster prevention and control system for transmission tower slopes in diverse environmental settings.