3.1. Method of Analyzing Anti-Slide Stability
A numerical simulation and analysis were conducted based on a typical slope case study [
13], utilizing the strength reduction method (SSRM). The Griffith method can yield a slope safety factor similar to traditional calculation methods. Compared to earlier approaches, the strength reduction method directly computes the sliding surface and safety factor of the slope, simplifying the otherwise complex process, and provides clear and intuitive results. This method has been widely accepted in engineering practice. The strength reduction method calculates the slope safety factor by determining the degree of strength reduction at the point when the slope soil reaches the critical state of failure. Specifically, the cohesion and internal friction angle of the slope soil is continuously reduced under unchanged external conditions until the slope fails. The reduction factor at this state is the slope’s safety factor [
14]. The formula for calculating the reduced shear strength parameters of the slope soil is as follows:
where
c and
ϕ represent the original shear strength parameters of the soil; cm and
ϕm represent the reduced shear strength parameters; and
Fr is the strength reduction factor.
In existing studies, there are three criteria for determining slope instability using the strength reduction method [
15]: the numerical simulation fails to converge; a continuous plastic zone forms through the slope; and a sudden increase in displacement occurs at a specific point on the slope surface. Each of these methods has its advantages and disadvantages: convergence in numerical simulations depends on various factors such as the calculation method and mesh division; the formation of a continuous plastic zone is difficult to evaluate objectively; and the selection of a characteristic point can influence the sudden displacement criterion. Some researchers compared results derived from these three criteria in practical cases and found them to be highly reliable and accurate [
16]. Therefore, this study combines the three criteria for a comprehensive analysis when determining the slope safety factor, ensuring an accurate evaluation of slope instability.
3.2. Stability Analysis of Unreinforced Slopes
Three characteristic points on the slope were selected to determine the onset of rapid displacement increase, as shown in
Figure 2: the slope toe (point A), the mid-slope (point B), and the slope crest (point C). The slope safety factor at the time of instability was confirmed through the FV1-U1 curve, as depicted in
Figure 3. The slope crest (C) and mid-slope (B) entered instability at a safety factor of FV1 = 1.172, while the slope toe (A) became unstable at FV1 = 1.181. Therefore, FV1 = 1.172 was selected as the critical safety factor corresponding to the onset of rapid displacement. This observation suggests that the slope crest and mid-slope are more prone to failure when instability occurs. When the numerical model failed to converge, the safety factor was FV1 = 1.201 (
Figure 4). When the plastic zone formed a continuous connection through the slope (
Figure 5), the safety factor was FV1 = 1.172, consistent with the value at which rapid displacement occurred. Therefore, the critical safety factor for slope failure in this typical model is FV1 = 1.172. Among the three evaluation methods, the safety factor obtained using the non-convergence criterion was higher, but it may not accurately reflect the actual instability conditions. Hence, relying solely on this method could be dangerous, and a combination of the other two methods should be used to assess slope instability accurately.
From
Figure 6 and
Figure 7, it can be seen that, when slope instability occurs, the type of landslide is a translational slide. After the upper soil becomes unstable, it slides downward along the slope, acting on the middle and lower parts of the soil, causing a progressive failure. The maximum horizontal displacement occurs at the bottom, accounting for 93.88% of the total displacement.
The final safety coefficient is 1.172, which is similar to the conventional calculated safety factor [
17], and the related literature [
18] stipulates that the stability safety coefficient of slopes at all levels should be greater than 1.35 under the general working condition, and the safety coefficient of the example is lower than that stipulated in the specification, which should be reinforced to make it meet the requirements.
3.3. C30 Concrete Anti-Slip Pile Reinforced Slope Stability Analysis
In most cases, the stability of slopes reinforced with anti-slide piles can be analyzed using 2D models, which offer high computational efficiency and good accuracy [
19]. However, to better analyze the location and degree of failure in anti-slide piles and simulate the slope conditions with the piles, this study employed a 3D numerical model. Considering that concrete anti-slide piles may undergo bending failure under lateral soil pressure and that linear elasticity is insufficient to accurately model the entire failure process, a plastic damage model for concrete was used.
Some researchers [
20] compared the bending capacity, economic efficiency, and construction duration of three different pile cross-sections and concluded that circular piles are more cost-effective, improve construction efficiency, and adapt better to varied terrain. This study focused on circular piles. A half-pile modeling approach was adopted to reinforce the unstable slope. The slope model remained unchanged, and the pile spacing was set equal to the slope model’s thickness (4 m). The boundary conditions of the slope also remained unchanged. The interaction between the piles and the slope soil was modeled as frictional contact, with normal contact defined as “hard” to transmit pressure, and a tangential friction coefficient of 0.3. The simulation consisted of two analysis steps: acquiring the initial geo stress and reducing the soil strength.
Previous studies often used idealized linear elastic models to simulate concrete anti-slide piles, but these models could not capture the plastic failure of concrete under sliding soil pressure, which affected the accuracy of the calculated slope safety factors after reinforcement [
21]. It was found that the damage eigenstructure model was used to reflect the softening nature of the piles during the reinforcement process and that the slope safety factor of the piles in the middle of the slope decreased after using the damage eigenstructure [
22]. Therefore, this study simulated the response of concrete anti-slide piles using the plastic damage model in ABAQUS. The input parameters for the C30 concrete used in the simulation are shown in
Table 2 and
Figure 8.
To investigate the influence of anti-slide pile location and length on the stability of reinforced slopes, nine calculation scenarios were designed. The ratio of the horizontal distance between the pile and the slope crest (a) to the horizontal distance of the slope (b) was used to represent the pile location. To account for location effects, values of a/b were set to 0.1, 0.3, 0.5, 0.7, and 0.9 for simulation. To examine the influence of pile length, the pile top’s vertical position relative to the slope was kept constant while the pile length was set to 15 m, 18 m, 21 m, 24 m, and 27 m. For the control groups, the pile length was set to 24 m, and a/b to 0.5.
Figure 9 and
Figure 10 show that, as the pile location changed, the maximum stabilizing effect on the slope occurred at a/b = 0.5, with a safety factor of FV1 = 1.45854. The arching effect between piles was strongest at this point, representing a 24.45% improvement over the unreinforced slope’s safety factor of 1.172 and meeting the required safety factor of 1.35. The tensile damage analysis revealed that, at a = 0.5 and a = 0.7, the peak tensile damage exceeded 0.8, indicating significant tensile failure. When varying the pile length, the best arching effect occurred with a pile length of 24 m, yielding a slope safety factor of FV1 = 1.47243 and a 25.63% improvement over the unreinforced slope. Among the five lengths tested, only the 15 m pile avoided significant tensile damage, while the remaining four experienced damage, with the largest damage occurring at 24 m.
3.3.1. Analysis of Pile Position Influence
As illustrated in
Figure 11a,b, the bending moments and shear forces experienced by the concrete anti-sliding piles vary with their positions. When a = 0.5, the anti-sliding pile experiences maximum bending moment and shear force, with the maximum bending moment reaching 1128 kN/m and the peak shear force being 299.9 kN. This result indicates that, when the anti-sliding pile is positioned in the middle of the slope, it bears the greatest shear and bending moments from the sliding soil mass, resulting in a pronounced arching effect, which enhances the stability of the slope. Conversely, at a = 0.1, the anti-sliding pile exhibits a negative bending moment, indicating the least effective arching effect and the poorest stability. For positions a = 0.3 and a = 0.7, the bending moments and shear forces are only slightly lower than those at a = 0.5. Thus, anti-sliding piles should be positioned centrally to maximize slope stability.
From
Figure 12a,b, it can be observed that, when the anti-sliding pile is subjected to the action of the sliding soil mass, both the soil stress F1 in front of the pile and the soil pressure F2 behind the pile initially rise before exhibiting a slight decline until a depth of 20 m. This behavior may be related to the detachment that occurs following the deformation of the concrete elements. However, when the pile depth exceeds 20 m, both F1 and F2 experience a sudden increase. The peak soil pressure F1 in front of the pile decreases with an increasing relative distance ratio a; thus, that is to say, the closer the anti-slip pile is to the lower position of the slope, the greater the landslide soil force it is subjected to. The soil pressure F2 behind the pile is minimized at a = 0.5 and a = 0.7, which are also the positions where the arching effect of the anti-sliding pile is most significant.
Slip-resistant piles play a role in slope stabilization by bridging the displacements of sliding and stabilizing soils and preventing the emergence of a soil-slip interface. The displacement of the anti-slip pile in the sliding soil body is large, and the displacement in the stable soil body is small, so the anti-slip pile bending moment occurs in the position where the sliding interface should have appeared, and the peak position of the bending moment, the magnitude of the shear force, the size of the pile front soil pressure, and the position of the sudden change in the soil pressure after the pile can be regarded as the position of the sliding interface and as the key design position of the pile cross-section and the pile body material.
The plastic damage analysis of anti-sliding piles at different positions, as shown in
Figure 13, indicates that, when a = 0.5 and a = 0.7, the tensile damage significantly exceeds the failure threshold of 0.8, resulting in pronounced bending and tensile failure. This finding correlates with the substantial arching effect observed, which significantly enhances the slope stability safety factor FV1. In other positions, no noticeable plastic damage occurs in the anti-sliding piles. During the process of stabilizing the slope, the concrete anti-sliding piles did not exhibit compressive damage, with all compressive damage values remaining below 0.1, indicating that they were in a safe compressive state.
3.3.2. Analysis of the Influence of Pile Length
The distribution of bending moments and shear forces of anti-sliding piles at different lengths concerning pile depth is illustrated in
Figure 14a,b. From the content of this figure, it can be observed that, when the length of the anti-sliding pile reaches 24 m, the maximum bending moment and shear force are achieved, with a maximum bending moment of 1207 kN/m and a maximum shear force of 311 kN. This finding indicates that, when
p = 24 m, the anti-sliding pile exerts the greatest earth arch effect to stabilize the sliding slope. The distribution of bending moments and shear forces under the action of sliding soil remains nearly consistent across different pile lengths.
As shown in
Figure 15a,b, compared to the soil pressure distribution of the pile when the position of the anti-sliding pile is altered, the distribution of soil pressures when changing the length of the anti-sliding pile exhibits a more pronounced correlation with pile length, primarily reflected in the back soil pressure. The peak value of the back soil pressure increases with the length of the anti-sliding pile. When
p = 15 m, there is no significant increase in back soil pressure; the pile is too short to reach the plastic zone of the soil slope, rendering it unable to stabilize the slope effectively.
From
Figure 16, it can be seen that, in the simulation calculations for five different lengths of anti-sliding piles, except for the case where
p = 15 m, the tensile plastic damage in anti-sliding piles exceeds the failure threshold of 0.8, indicating tensile failure. The damage areas are mainly concentrated within 10 m from the top of the anti-sliding pile, while no compressive damage occurs in the piles.
Based on the above calculations, it can be concluded that, when anti-sliding piles are constructed using conventional concrete materials to stabilize slopes, they are prone to bending failure in certain conditions due to insufficient bending strength and toughness, which may lead to failure in resisting the forces exerted by the slope soil. Currently, high-toughness cement-based materials exhibit superior bending toughness and strength, and their engineering applications have proven effective. However, there is limited research on applying these materials to the stabilization of slopes using anti-sliding piles. Most studies focus on enhancing the slope stability safety factor by adjusting pile spacing, length, and position, with few examining whether the anti-sliding piles themselves incur damage, especially bending failure. Therefore, this study aims to improve the bending toughness of the materials used in anti-sliding piles to enhance their stability against landslides.
3.4. Stability Analysis of Slope Reinforcement Using High-Toughness Concrete Anti-Sliding Piles
The physico-mechanical parameters of the materials measured in this study through tests such as axial compression are shown in
Table 3, which provides a theoretical basis for modeling the performance enhancement effect of the tunnel lining. These parameters include the following: the selection of good tensile and bending properties of the ratio for the lining of high-toughness cementitious composites of the principal parameters of this study, the obtained test stress–strain relationship is fitted, the calculation of the lining of high-toughness cementitious composites of the principal parameters of the calculation of the calibration of the lining of high-toughness cementitious composites of the principal parameters of
Figure 17, and its numerical simulation calculations for comparison of the effect of the application.
The simulation calculation scheme for the high-toughness anti-sliding piles was the same as that for conventional concrete anti-sliding piles. As shown in
Figure 18, with changes in the position and length of the anti-sliding piles, the variation pattern of the slope stability safety factor FV1 is consistent with that of conventional concrete anti-sliding piles. Considering the position of the anti-sliding piles, at a = 0.1 and a = 0.9, there is no significant improvement in FV1 for high-toughness anti-sliding piles compared to conventional concrete anti-sliding piles. In these two positions, improving the bending toughness of the anti-sliding pile materials does not enhance the slope’s safety performance. At a = 0.5, the slope stability safety factor FV1 reaches its maximum value of 1.54822, which is a 32.10% increase over the safety factor of 1.172 for the unreinforced slope, demonstrating a more pronounced improvement compared to conventional concrete anti-sliding piles. Furthermore, when considering the length of the anti-sliding piles, it was observed that the application of high-toughness anti-sliding piles significantly increases FV1 for different lengths, with the maximum safety factor reaching 1.55804 at
p = 24 m.
An analysis of the plastic damage in the high-toughness anti-sliding piles shown in
Figure 19 indicates that there is no tensile damage at a = 0.7, while tensile failure only occurs in four working conditions at the middle position of the slope.
3.4.1. Analysis of Pile Position Influence
As illustrated in
Figure 20a,b, the bending moment and shear force of high-toughness anti-sliding piles reach their maximum at a = 0.5, with the maximum bending moment of 1752 kN/m and the maximum shear force at 391.1 kN. This finding represents an increase of 35.61% and 30.41%, respectively, compared to conventional concrete piles, attributed to the superior tensile and flexural toughness of the high-toughness cement-based composite materials, enabling them to withstand greater bending moments and shear forces.
From
Figure 21a,b, it can be observed that, after changing the position of the anti-sliding piles, the soil pressures acting on the pile front (
F1) and pile back (
F2) for high-toughness anti-sliding piles show no significant difference in peak values compared to those of conventional concrete piles, and their variation patterns remain consistent. Specifically, the pile front soil pressure
F1 decreases as the relative distance ratio a increases.
3.4.2. Analysis of the Effect of Pile Length
Figure 22a,b illustrates the distribution of the bending moment and shear force under different lengths of ECC anti-sliding piles. At a pile length of
p = 24 m, the high-toughness anti-sliding piles exhibit the highest bending moment of 1793 kN/m and a maximum shear force of 392.8 kN, representing increases of 48.56% and 26.3%, respectively, compared to conventional concrete piles. This finding indicates that high-toughness anti-sliding piles can withstand larger bending moments and shear forces, facilitating the development of the soil arching effect.
As shown in
Figure 23a,b, after changing the length of the anti-sliding piles, the pile front soil pressure
F1 experiences a sharp peak increase at the pile base. At lengths of
p = 15 m and
p = 18 m, the pile back soil pressure
F2 does not show a sharp increase, possibly due to soil bending causing a gap, which prevents the pile from effectively stabilizing the soil.
From
Figure 24, it can be concluded that the high-toughness anti-sliding piles exhibit notable tensile failure when changing the length of the piles. Tensile plastic damage occurs only at the contact point of the sliding surface of the soil, with maximum tensile damage recorded at
p = 24 m at a value of 0.558, which is below the failure threshold of 0.8. The use of high-toughness cement-based composite materials significantly enhances the tensile toughness of the anti-sliding piles, thereby preventing bending failure.
3.5. Expansion of Design Methods to Cope with Different Soils
In this paper, only the applicability research and design optimization of high tenacity skid resistant piles in the soil parameters and slope dimensions under the actual condition of the dependent project are carried out, and the specific parameters of the optimized design and the stability enhancement effect are somewhat different in the face of different soil and slope dimensions. However, the superiority of anti-slip piles made of high-toughness concrete material and the method of obtaining the specific parameters of optimization design is the same, so we can use Isight software (version number: Isight 2023x) to carry out the DOE pre-optimization design of different material parameters and different soil sizes, take the minimization of slope displacement and the maximum tensile stress of anti-slip piles as the design objectives, derive the pile length, the relative distance ratio, the material parameters of the soil, and the slope gradient with the design objectives. The relationship between pile length, relative distance ratio, soil material parameters, slope gradient, and the design objective is determined, and a suitable approximation model type is selected for approximation modeling. Finally, a reasonable approximation formula is obtained to simplify its application; in the case of less than ideal simulation results, we can also use Isight to encapsulate the whole optimization design process and simplify the optimization design process in different application scenarios through parameterized modeling and DOE design optimization.