1. Introduction
The mountainous areas of Southwest China have the characteristics of valley deep-cutting, a large topographic gradient, and complex geological structures, where the numerous high and steep slopes are important potential factors that breed geological disasters and threaten the safety of engineering construction. With the development of infrastructure in mountainous areas in this region, the construction of bridges across valleys has gradually increased. Usually, the bridge foundations of a cross-river bridge are mostly in the form of pile foundations and are located on the high and steep slopes on both sides of the canyon, which brings the enormous engineering load and has a significant impact on the stability of the bridge foundation bank slope. Especially when the bank slopes are developed with fracture zones and toppling deformation development, the combined action of bridge loads and changes in reservoir water levels can cause complex failure modes occurring on slopes. At present, traditional slope stability analysis and evaluation methods find it difficult to meet the evaluation requirements for such bank slopes with complex geological structures and the influence of engineering loads, and there is no recognized and reasonably stable evaluation method.
In recent years, many scholars have conducted relevant research on the stability of the slopes of bridge foundations from different perspectives. Song, Fei, and Ye studied the deformation characteristics, evolution laws, failure mechanisms, potential instability ranges, etc., of different slopes affected by bridge foundations or bridge loads through different numerical simulation methods [
1,
2,
3]. Through on-site geotechnical tests, bridge foundation model simulation tests and on-site monitoring data, the impact of bridge foundations on slope stability was characterized and relevant theories for analyzing the stability of bridge foundation slopes were proposed [
4,
5,
6,
7,
8].
Also, the development of toppling deformation in many rock slopes causes instability cases, with related studies on the deformation modes and mechanisms of toppling rock masses. Haider and Ning analyzed the evolutionary process of the failure of the toppling slopes through numerical simulation [
9,
10]. Through centrifugal model tests and similarity tests, some scholars have studied the deformation processes, failure mechanisms, and evolution stages of different types of toppling slopes [
11,
12,
13,
14]. Differential settlement at the base of each rock column, a circular shear failure in the continuous mass and the relation of the blocks of the toppling rock mass and the slope geometry were considered to investigate and determine the mechanism of the sliding and toppling [
15,
16]. There are also related studies to conduct more convenient and high-speed stability analysis of toppling failure using the fictitious horizontal acceleration technique, simplified semi-distinct element algorithm, and step-by-step analytical solutions [
17,
18,
19].
However, there is little research on the failure mechanism and stability analysis of rock bank slopes with toppling deformation development affected by bridge loads. Dai et al. revealed the deformation and failure mechanism and stability control elements of toppling layered rock slopes under bridge loads, evaluated the stability using the limit equilibrium method and vector sum method, and analyzed the expansion law of the plastic zone using the strength reduction method [
20]. Huang et al. determined the degree of toppling deformation, explored the failure mode, summarized the stress–strain characteristics through numerical simulation results, and revealed the evolution process of the toppling deformation body [
21].
Additionally, rock slopes with fault and fracture zones are widely distributed and there are many studies on related issues. Azarfar et al. used numerical simulation and laboratory measurements to analyze the sensitivity of the stability and faults of rock slopes at different scales [
22]. Liu et al. studied the instability mechanism of composite strata slopes with faults and weak layers and analyzed the stress field and damage zone evolution using the finite element strength reduction method [
23]. Mehdi provided an empirical relationship for rock slope stability assessment with numerous micro-faults and fracture development [
24]. Kumar collected and tested undisturbed soil samples from landslide areas with fracture zones developed and used different methods to conduct dynamic and static analysis of the slope stability [
25]. Due to the characteristic of the fracture zones, such as the low bearing capacity, poor deformation resistance, poor permeability, etc., serious treatments are urgently needed. The spatial structure inside the slopes is complex, and the existence of fractured zones can cause damage to the stability of the slope [
26]. Some scholars selected different treatment methods for slopes with fault fracture zones to prevent slope instability from the perspectives of the occurrence, location, and geometric relationship with slopes [
27,
28,
29,
30].
Based on the content of the literature review, it can be concluded that some studies only simplified the geological structures of slope numerical analysis models or analyzed the results of two- or three-dimensional numerical simulations, leading to the uncertainty of the analysis results and errors between the analysis results and the true state. The stability of slopes in most studies is only influenced by a single factor, such as toppling rock masses, fault fracture zones, or changes in reservoir water levels, which makes it difficult to reflect the complex deformation and failure mechanisms of the slope with complex terrain and geological structures.
The object of this study is a high and steep bank slope of bridge foundations with a complex geological structure, which has the development of fault fracture zones and toppling deformation, while toppling deformation and fault fracture zones are common geological structures worldwide, and the special mechanical properties can accelerate the failure and deformation of slopes. The object is also influenced by the combined effects of bridge foundation loads and reservoir water fluctuations. This study is of great significance in exploring the effects of fault fracture zones on slope stability, evaluating the stability of toppling rock bank slopes, analyzing the deformation and failure mechanisms of slopes of bridge foundations, ensuring the safe construction and normal operation of bridge engineering in canyon areas and providing experiences of the selection of the layout of the bridge foundations in similar engineering geological conditions and environments. In addition, the research ideas can provide references for similar projects and an effective tool for the establishment of a stability evaluation model for the toppling bank slopes with fracture zones developed under engineering loads.
Therefore, based on the existing research and the complexity and particularity of the research object, the main objectives of the paper are as follows:
Based on the geological structure of the bank slope, establish a geological model that is consistent with the real geological conditions, select a reasonable method for applying bridge loads, and establish an effective numerical analysis model for the bank slope based on the limit equilibrium method and discrete element method.
Based on engineering geological analysis methods and the special properties of fault fracture zones, analyze the potential failure modes and deformation mechanisms of bank slopes under the influence of external factors.
Based on numerical analysis results and analysis of the deformation and failure mechanism of the bank slope, summarize the incentive mechanisms of bridge loads and reservoir water on the deformation and failure of the bank slope, and propose a comprehensive evaluation method for the stability of the toppling bank slope with the development of fault fracture zones under diverse influencing factors.
5. Discussion
5.1. Mechanism of the Deformation and Failure of the Toppling Bank Slope with Fault Fracture Zones Developed under the Action of Bridge Loads and Reservoir Water
5.1.1. Incentive Mechanism of Bridge Loads and Reservoir Water on the Deformation and Failure of the Bank Slope
There are many weathering cracks and unloading cracks on the toppling bank slope. Such joints are special and their adverse distribution will affect the stability of the bank slope, leading to the deformation and failure of the bank slope. The horizontal and vertical loads of the bridge foundations are transmitted to the bedrock on the bank slope during the operation of the bridge, while stress is transferred to the rock mass through the joints. The continuously stress increase causes local damage to the rock mass under the bridge foundations where the plastic zones form. Also, as soon as the bridge loads are applied to the upper bank slope, the sliding force along the potential failure surfaces increases, which not only increases the compression of the rock mass at the lower slope but also further expands the tensile cracks formed via toppling deformation on the rock mass and promotes the cracks to the deeper part at the upper bank slope.
Due to the influence of the existence of the fault fracture zones and toppling deformation, the integrity of the rock mass on the surface of the bank slope is extremely loose and shows strong permeability, allowing reservoir water and rainfall to infiltrate into the rock and soil of the bank slope in a short period of time. After the reservoir impoundment, the groundwater level on the bank slope significantly increases, with the speed of lifting in the middle and upper parts of the bank slopes being lower than that in the lower parts. Under the influence of the penetration within the bank slope, the dynamic erosion of the river near and below the water level of the bank slope is accelerated. Also, due to the infiltration of water, the change in the pore water pressure and a decrease in the effective stress weakens the sliding-resistance capability of the bank slope with the change in the water content of the rock and soil mass on the bank slope, leading to decreased in the strength, physical and chemical properties. Local deformation and instability may occur under the effects of water pressure and seepage. Meanwhile, the increase in the pore water pressure causes deformation of the joints in the lower part of the bank slope, resulting in the change in the opening and closing states of the joints, which affects the seepage in joints and changes the stress state of the bank slope further.
Therefore, the lower bank slope undergoes deformation due to the changes in the seepage field caused by the water level variations of the Lancang River, leading to the formation of plastic zones at the foot of the bank slope and providing development potential and deformation space for the further bending, tension-fracture and toppling deformation of the loose toppling rock mass in the upper part. Meanwhile, the loose mass on the shallow part of the bank slope that undergoes deformation under the bridge loads and the infiltration force caused by rainfall can continue deforming to the free face. With the development of the plastic zones at the foot of the slope upwards, the stability of the bank slope reduces. As soon as the connection of the plastic zones under the bridge foundation and the bank slope foot is achieved, the instability of the bank slope forms, threatening the operation of the reservoir and the bridge.
5.1.2. Influence of Bridge Loads and Reservoir Water on the Deformation of Toppling Rock Mass
The further toppling deformation of the rock mass on the bank slope is influenced by the lower rock mass of the bank slope, which is closely related to the structure of the slope rock mass. The bank slope in this study is a reverse slope, with a steep slope and a rock dip angle greater than 40°. Under gravity, the rock mass undergoes bending deformation toward the free face. The tension cracks form on the tension side of the rock layer. When the tensile stress on the bending side of the rock mass is greater than its tensile strength, the rock mass fractures. When the sliding surface formed with the through fractures respectively caused by the action of reservoir water and bridge loads in the rock mass of the lower and upper part of the bank slope, the toppling failure occurs along the area with the highest shear stress. Therefore, bending tensile failure is the main failure mode of the toppling rock mass on the bank slopes. The tensile strength of the rock mass is much lower than the compressive strength, so that the occurrence of bending tensile fracture failure depends on whether the tensile fracture points are able to form on the tensile side of the rock mass under the action of the rock mass’s self-weight, which leads to the fact that the tensile strength of the rock mass can be used as the judgment standard for bending tensile fracture failure.
Under the gravity of the rock mass, the vertical force and bending moment can cause the formation of bending deformation and tensile stress in the rock layer. Due to the relatively tight fit of the rock layers in the toppling rock mass on the bank slope, the cantilever beam model can be used as the mechanical model to analyze the development and failure mode of the bank slope toppling deformation (
Figure 17).
Assuming that a single rock layer can be treated as a single cantilever beam, the values of the shear strength (c, φ) of the interlayer are the same and the normal stress and shear stress are uniformly distributed, take a single unit point on the tensile side of the rock layer for the stress state analysis. In the natural state, the rock masses in the different toppling deformation zones remain stable, and the tensile fracture points of the rock layers in the medium or weak toppling deformation zones have not yet formed or are not clearly developed, failing to form a continuous failure surface. The reservoir impoundment reduces the overall anti-sliding ability of the bank slope, while the stress () of the compressive side reduces and the stress () of the tensile side increases in the cantilever beams in the lower bank slope under the action of seepage force, accelerating the formation of tension cracks and increasing the deflection of the cantilever beams. Similarly, under the influence of bridge loads and rainfall infiltration, the failure of the upper cantilever beam and the formation of tension cracks are also accelerated. Therefore, the action of bridge loads and reservoir water changes the stress state of the tensile fracture points, increases the bending moment on the tension side, accelerating the deformation and failure speed of the bending and tensile cracking and increasing the displacement of the slope between the bridge foundations and the water level and the connection of the plastic zones.
5.1.3. Influence of Fault Fracture Zones on the Stability of the Toppling Bank Slope
The fault fracture zones have the ability of hydraulic conductivity and serve as advantageous channels for rainwater infiltration, which increases the permeability of the bank slope. Rainfall infiltrates through the cracks on the slope surface and the fractured zones. The fractured rock mass near the slope surface is preferentially saturated, while accelerating the uplift of the underground water on the bank slope. The matric suction decreases with the increase in the water content as the state of the fractured rock mass near the slope surface turns into the saturated state. The connections between the particles are loose and the local connection mode changes, causing a rapid decrease in the mechanical properties of the fault mud along the direction of the fractures after being softened by hydration. Therefore, at the moment the deformation of the rock mass in the upper bank slope passes through the fault fracture zones, further dislocation occurs on the rock masses of the hanging wall and footwall of the fault fracture zones, making the displacement of the fault fracture zones more pronounced.
The phenomena of shear, tensile, and torsional deformation and the development of cracks happen on the rock masses of the hanging wall and footwall of the fault fracture zones. Meanwhile, the mechanical properties of the fault breccia and fault mud are poor. This causes the significant difference between the rock mass on the bank slope and the fault fracture zones, indicating that the fault fracture zones are weak interlayers of the bank slope. The deformation of the fault fracture zones is obvious, and the displacement of the rock mass on the bank slope exhibits inconsistency with that on fracture zones. The dip direction of the fault fracture zones is opposite to that of the bank slope, resulting in the complexity of the interaction between the weak interlayers and rock mass. When the rock mass on the bank slope breaks along the maximum bending points, stress concentration is generated in the upper part of the fault fracture zones, causing further deformation and strengthening of tensile stress in the fault fracture zones. The original cracks within the zones continue to expand and extend into the slope. When the sliding force caused by the weight of the rock mass and the bridge loads is greater than the shear resistance of the fault fracture zones, stress concentration occurs at the contact surface of the fractured rock mass and toppling rock mass. The sliding rock mass compresses the upper boundary of the fault fracture zones, causing displacement and further dislocation of the fractured rock mass. The increase in the deformation of the rock mass on the upper bank slope promotes the deformation of the fault fracture zones, leading to a deeper sliding body on the bank slope. When the ratio of the power caused by loads to that consumed by the compression and displacement of the sliding body along the sliding surface formed within the penetrating plastic zone is greater than 1, the bank slope will undergo deformation, instability and failure.
5.2. Determination of the Optimal Bridge Scheme
Based on the incentive mechanism of the bridge loads and reservoir water on the deformation and failure of the toppling bank slope with fault fracture zones developed, the layout of the bridge foundations is selected by combining the numerical simulation results and engineering geological conditions comprehensively.
The stability of the bank slope is influenced by the geological structure of the bank slope. The fracture zones, as the weak interlayers in the bank slope, have a significant impact on the stability due to its development position, width, attitude, and mechanics properties of the fractured rock mass. Therefore, the spatial relationship between the loading positions of the bridge and the fracture zones should be considered. In addition, the integrity of the rock mass is affected by toppling deformation, weathering, and unloading, with the development of joints and cracks in the rock mass (especially in the extremely strong toppling deformation zone A) leading the rock mass quality as another major factor affecting the burial depth of the bridge foundations. At the same time, the rock mass at the lower bank slope is also influenced by factors such as the dynamic erosion, seepage, and softening of the reservoir water, which is damaged first and provides space for the deformation of the upper bank slope. Therefore, the bridge foundations should be far away from the river and the main pier should been buried in extremely strong toppling areas as little as possible while meeting the foundation-bearing capacity and considering the limitations on the deformation of the upper rock mass.
- 2.
Calculation Results of the Stability Numerical Evaluation Model
According to the numerical simulation results of the evaluation model for the bank slope stability, it can be concluded that if the Slip 1 and Slip 4 are damaged, it will directly affect the main pier in Scheme 1. In contrast, although the stability of Slip 4 in Scheme 2 cannot meet the safety requirements, the fact that the distance between the rear edge and the main pier cap of 50 m poses a smaller threat to the main pier. Also, under all the working conditions of Scheme 2, the failure ranges are more concentrated, and the stability coefficients is greater than that of Scheme 1.
Therefore, the layout of the bridge foundations should follow Scheme 2.
5.3. Limitations of the Stability Numerical Evaluation Model
In order to study the stability of the bank slope, the two- and three-dimensional stability numerical evaluation model discrete element method was used to understand the mechanism of the deformation and failure. However, the limitations of the model also show as the following:
In the numerical simulation calculations, the bridge loads are applied by adding the static loads of the bridge structures in the position of the bridge foundations, but there is no comparison between the difference between the equivalent concentrated force or equivalent surface force and dynamic load on the simulation results.
Due to one of the research objectives being the stability of the bank slope under bridge loads, except for the selection of the bridge foundations layout based on the simulation result, we did not underscore its relevance to bridge safety and engineering design such as the bridge design, construction, and maintenance.
This study mainly discusses the effects of bridge loads and reservoir water on the fault fracture zones developed on the stability of the bank slope through the evaluation model, while there are other factors affecting the stability without consideration, which may cause differences between the results and actual conditions.
The geotechnical parameters in the paper refer to relevant engineering and simulation parameters in the region, and the rationality is verified by comparing the calculation results with qualitative analysis. However, it is inadequate in the analysis of parameters, which can be further addressed via indoor testing or simulation experiments.
Based on these limitations, the future research directions can be drawn as follows. Study the influence of the bridge load application methods on the bank slope stability; improve the simulation method and supplement the content of safety simulation for the upper bridge structures; conduct indoor tests or simulation experiments to further calibrate the key parameters required for numerical simulation; and change the position of the bottom surface of the foundations at different parts of the toppling deformation zones to study the effect on the development of toppling deformation.