Numerical Investigation of Micromechanical Failure Evolution in Rocky High Slopes Under Multistage Excavation

Abstract

High rock slopes are extensively distributed in areas of major engineering constructions, such as transportation infrastructure, hydraulic projects, and mining operations. The stability and failure evolution mechanism during their multi-stage excavation process have consistently been a crucial research topic in geotechnical engineering. In this paper, a series of two-dimensional rock slope models, incorporating various combinations of slope height and slope angle, were established utilizing the Discrete Element Method (DEM) software PFC2D. This systematic investigation delves into the meso-mechanical response of the slopes during multi-stage excavation. The Parallel Bond Model (PBM) was employed to simulate the contact and fracture behavior between particles. Parameter calibration was performed to ensure that the simulation results align with the actual mechanical properties of the rock mass. The research primarily focuses on analyzing the evolution of displacement, the failure modes, and the changing characteristics of the force chain structure under different geometric conditions. The results indicate that as both the slope height and slope angle increase, the inter-particle deformation of the slope intensifies significantly, and the shear band progressively extends deeper into the slope mass. The failure mode transitions from shallow localized sliding to deep-seated overall failure. Prior to instability, the force chain system exhibits an evolutionary pattern characterized by “bundling–reconfiguration–fracturing,” serving as a critical indicator for characterizing the micro-scale failure mechanism of the slope body.

1. Introduction

High rock slopes are widely encountered in the construction of major infrastructure projects in mountainous areas, such as transportation routes, hydropower stations, and railways. Due to their great height, steep topography, and complex geological conditions, any instability can lead to severe engineering accidents and substantial economic losses, posing a significant threat to personnel safety and project operation [1]. Catastrophic landslides often result in severe infrastructure damage and economic losses, necessitating rigorous reinforcement measures such as pre-stressed anchor cables and anti-slide piles [2]. However, traditional design methods based on the limit equilibrium theory often oversimplify the complex evolution of rock discontinuities during these engineering interventions [3]. The stability of these slopes is often difficult to guarantee under intense external disturbances, such as construction excavation, seismic loading, and rainfall infiltration. The rock failure process typically initiates with localized instability and micro-crack propagation, progressively evolving into macroscopic sliding or collapse. The inherent discontinuity of the internal structure of high rock slopes contributes to the complexity of their overall mechanical response [4].

In high rock slope engineering, the multi-stage excavation process induces complex stress redistribution and dynamic evolution of internal discontinuities, making the instability mechanism difficult to predict and control [4]. Unlike instantaneous removal assumptions, multi-stage excavation is a progressive unloading process that induces significant stress path rotation and cumulative damage within the rock mass. This sequential disturbance often triggers transient instability that static analysis of the final geometry fails to capture. Existing research has conducted extensive numerical simulations and field monitoring studies focusing on the evolution of the slope stress field and deformation characteristics [5,6]. Among numerical methods, continuum approaches such as the Finite Element Method (FEM) and the Finite Difference Method (FDM) are widely used for slope stability analysis due to their ease of modeling and computational efficiency [7,8]. Numerical methods have been increasingly used in recent decades to determine the factor of safety (FoS) of slopes. Dawson et al. formalized the shear strength reduction (SSR) technique in finite element and finite difference analyses and showed that the numerically derived FoS is consistent with classical limit-equilibrium solutions while also providing deformation and failure information [9]. More recent studies further improve and extend the SSR approach, for example, by developing explicit finite element procedures for FoS evaluation [10] and by performing three-dimensional stability analyses of complex ridge slopes using strength reduction based on unified strength theory [11]. These works demonstrate that numerical modeling has become a robust tool for FoS assessment of soil and rock slopes and provide a methodological basis for the present study. However, these methods exhibit notable limitations when dealing with large deformations and fracture propagation in discontinuous structures like rock masses, making it difficult to capture meso-scale failure processes such as particle sliding and shear band evolution [12,13].

The Discrete Element Method (DEM) is a numerical simulation approach based on discontinuum mechanics. It overcomes the limitations of continuum models in describing material structure evolution and discontinuous failure. It is particularly suitable for simulating the meso-scale response of rock masses, including fracture evolution, micro-crack propagation, and force chain (fabric) re-configuration [14]. The Parallel Bond Model (PBM), proposed by Potyondy and Cundall, has effectively expanded the application of the Particle Flow Code (PFC) program in studying rock failure mechanisms [15]. In recent years, PFC has demonstrated good applicability and accuracy in addressing slope stability problems [16,17]. Previous studies have demonstrated the efficacy of DEM in capturing large-scale deformation and failure processes in rock slopes. For instance, Wang et al. successfully simulated the progressive failure of jointed rock slopes [18]. Scholtès and Donzé utilized DEM to analyze the effect of rock bridge damage on slope stability [19]. These works highlight the advantage of DEM in handling discontinuous media compared to continuum-based methods.

For the multi-stage excavation of high rock slopes, most existing studies focus on overall slope deformation analysis or on the simulation of a single working condition. Research that examines how slope stability evolves with changes in both slope height and slope angle is still relatively limited. Lisjak et al. summarized the advantages of DEM in rock failure modeling and pointed out that force chain re-configuration, localized stress concentration, and non-linear failure modes are key mechanisms distinguishing DEM from continuum models [20,21]. Research on the coupled effects of different geometric parameters on the slope failure mechanism is still insufficient, particularly in terms of understanding the evolution of slope stability during multi-stage excavation from a meso-mechanical perspective [16,22].

To address the above issues, this paper takes a typical high rock slope as the research object. The DEM software PFC2D(Version 6.0) is used to build several 2D meso-scale models with different combinations of geometric parameters (slope height and slope angle). These models are used to simulate the mechanical response and failure evolution of the slope during multi-stage excavation. By systematically comparing the displacement characteristics, force chain structures, failure modes, and shear band evolution under different height and angle conditions, the study reveals how key geometric parameters control slope instability and how they affect the failure mechanism in a non-linear way.

2. Model and Boundary Conditions

2.1. PFC Mechanical Constitutive Model

The numerical investigation was conducted using the commercial software Particle Flow Code (PFC2D, Version 6.0, Itasca Consulting Group, Minneapolis, MN, USA), a distinct implementation of the Discrete Element Method (DEM) originally conceptualized by Cundall and Strack [23]. Unlike continuum-based approaches (e.g., FEM) that treat rock masses as continuous media, DEM explicitly represents the material as an assembly of rigid particles. This feature makes it uniquely capable of simulating the transition from continuity to discontinuity, such as fracturing and block rotation, which is critical for high slope instability analysis [24].

Within the DEM framework, the choice of contact constitutive model dictates the macroscopic material behavior. The standard Linear Contact Model allows only force transmission and is limited to cohesionless granular materials like sand. To capture the mechanical behavior of cemented rock, specifically its tensile strength and resistance to rotation, the Parallel Bond Model (PBM) was selected. The PBM acts as a cementing material between particles, transmitting both forces and moments, thereby effectively reproducing the brittle fracture and shear band evolution characteristic of rock masses.

In the PFC2D program, the Linear Parallel Bond Model comprises two types of contact interfaces, as illustrated in Figure 1. The first contact interface (Figure 1a) represents a linear elastic bonded interface of finite size, characterizing the state where particles are bonded. Within this interface, the tensile strength element resists tension, the stiffness element governs particle deformation, and the cohesion and internal friction angle elements resist shear. The combined action of these elements endows the interface with the ability to resist moments.

When the forces or moments exceed the strength limits, the bond fails, and the parallel bond model degenerates into the linear model, which is the second contact interface (Figure 1b). The contact forces in the linear model primarily consist of linear forces and damping forces. Linear forces provide linear elastic (tensionless) and frictional behavior, generated by normal and tangential spring elements with constant stiffness. The damping force component provides viscous behavior, with viscosity controlled by the normal and tangential damping ratios. The linear model enforces slip by applying the Coulomb criterion to shear forces through a friction coefficient.

Unlike simple frictional contacts used for soil, this bond can transmit both force and moment, thereby simulating the rotational resistance of interlocked rock blocks. Under external loading, the formulas for calculating the force and moment transmitted by the parallel bond between particles are as follows:

$$\begin{array}{c}\begin{array}{c}\left\{\begin{array}{c}{F}_i^n={\bar{F}}_i^n+2\lambda R_i\left({\displaystyle \frac{\bar{E}}{L}}\right)\Delta {\delta }_i^n\\ F_i^s={\bar{F}}_i^s+2\lambda R_i\left({\displaystyle \frac{\bar{E}}{\bar{k}L}}\right)\Delta {\delta }_i^s\\ M_i^n={\bar{M}}_i^n+{\displaystyle \frac{2}{3}}{\lambda }^3{R}_i^3\left({\displaystyle \frac{\bar{E}}{L}}\right)\Delta {\theta }_i^n\end{array}\right.\end{array}\end{array}$$

(1)

The Stress States in the Parallel Bonds are Determined by

$$\begin{array}{c}\left\{\begin{array}{c}{\sigma }_i=-{\displaystyle \frac{F_i^n}{2\lambda R_i}}+{\displaystyle \frac{3\mid M_i^n\mid }{2{\lambda }^2{R}_i^2}}\\ {\tau }_i={\displaystyle \frac{\mid F_i^s\mid }{2\lambda R_i}}\end{array}\right.\end{array}$$

(2)

Parallel Bond Failure Conditions:

$$\begin{array}{c}\left\{\begin{array}{c}{\sigma }_i>{\sigma }_c\\ {\tau }_i>{\tau }_c=c-{\sigma }_i\tan \varphi \end{array}\right.\end{array}$$

(3)

${\bar{F}}_i^n$, ${\bar{F}}_i^s$, ${\bar{M}}_i^n$ are the normal contact force, shear contact force, and normal moment of the parallel bond at contact $i$ before the time-step update. $F_i^n$, $F_i^s$, $M_i^n$ are the normal contact force, shear contact force, and moment acting on the parallel bond at contact $i$. $\lambda$ is the parallel bond radius multiplier. $R_i$ is the parallel bond radius at contact $i$. $\bar{E}$, $\bar{k}$ are the parallel bond modulus and the stiffness ratio. ${\sigma }_i$, ${\tau }_i$ are the normal stress and shear stress of the parallel bond at contact $i$. ${\sigma }_c$, ${\tau }_c$ are the parallel bond tensile strength and shear strength, respectively. $c$, $\varphi$ are the parallel bond cohesion and internal friction angle.

These three sets of equations collectively form a complete “loading-response-failure” closed-loop for the parallel bond model. In slope stability analysis, they elucidate the mechanism of macroscopic phenomena from a microscopic perspective: external loads induce relative displacements and rotations between particles (Equation (1)), leading to stress concentration at the bonds (Equation (2)). When the stress reaches the material’s strength limit (Equation (3)), the bonds fracture, resulting in the reorganization of the force chain network. The exceedance of the tensile strength (${\sigma }_c$) corresponds to the initiation of tensile micro-cracks in the rock mass, while the triggering of the Mohr–Coulomb criterion corresponds to the formation and propagation of shear slip surfaces. The parameters $c$ and $\varphi$ enable the model to capture the dependency of rock mass strength on confining pressure, thereby allowing for a more realistic simulation of the failure evolution process from shallow tensile failure to deep-seated shear failure.

Upon fracture, the particles may still remain in contact, but the bond loses its tensile and shear strength, only allowing the transfer of contact forces via friction. This mechanism enables the particle system to naturally evolve cracks, shear bands, and changes in the force chain structure during the loading process. It constitutes the critical foundation for simulating the rock mass failure process at the meso-scale.

2.2. Model Geometry and Boundary Conditions

According to the Technical Code for Building Slope Engineering (GB 50330-2013), rock slopes with a height exceeding 30 m and soil slopes exceeding 15 m are defined as high slopes, requiring specialized investigation and design [25]. For this study, the set of slope height values were set to 30 m, 40 m, 50 m, and 60 m (with a constant slope angle of 45°), and the set of slope angle values were set to 35°, 45°, 55°, and 65° (with a constant slope height of 40 m). All working conditions were based on a unified modeling and loading methodology, with consistent material parameters maintained to ensure validity and comparability across different models.

Regarding boundary conditions, the model width was set at 1.5–2.0 times the slope height to simultaneously ensure numerical stability and control boundary effects, thereby minimizing boundary interference on the slope response. As shown in Figure 2, the particles at the model base were subjected to full constraints, the lateral boundaries were horizontally constrained, and the slope surface remained free. The initial equilibrium stress field was established using the gravity settling method. This involved applying the gravity load and gradually adjusting the particle contact network until a state of static equilibrium was achieved. This method helps to avoid imbalances caused by artificially applied initial stresses, enhancing the physical consistency of the simulation.

In the slope excavation process, a sequential multi-stage excavation method was adopted for the simulation. The depth of each excavation stage was set to approximately 10 m, with the target particle area being removed sequentially from top to bottom, starting at the slope crest. After each excavation stage, stress redistribution and particle motion calculations were performed. The next excavation stage was only initiated after the system reached a stable state. This process authentically reflects the stress adjustment and failure evolution mechanisms observed during actual engineering construction.

2.3. Parameter Calibration

The determination of micro-parameters in the Discrete Element Model includes parameters particle modulus, contact stiffness, bond strength, density, and friction coefficient. Although these parameters do not directly correspond to the constitutive parameters of a continuum medium, they collectively govern the macroscopic mechanical performance of the model.

Therefore, the core objective of parameter calibration is to ensure that the macroscopic response of the simulated rock mass under static loading conditions remains consistent with that of the actual rock mass material. In this study, the micro-parameters were iteratively adjusted based on a review of existing literature data, with some parameter values derived from previous experimental results and numerical studies on similar rock types. A series of numerical uniaxial compression tests were carried out in PFC2D. The particle normal and shear stiffness, bond strength, and friction coefficient were adjusted by trial and error so that the simulated stress–strain curves and peak strength agreed reasonably well with the target macroscopic properties. This calibration approach is generally consistent with existing micro-parameter calibration methods for rock PFC2D models [22,26,27,28], and the final parameter values fall within the ranges reported in the literature. The specific numerical values for each parameter are presented in

Table 1. Parameters of rock slopes.

Parameter	Value
Particle modulus (GPa)	2.4
Stiffness ratio	1.0
Particle tensile strength (MPa)	0.8
Particle cohesion (MPa)	1.0
Particle density (kg·m−3)	2350
Particle friction coefficient	0.5

.

The hydrogeological condition of the slope is assumed to be dry. Groundwater seepage and pore water pressure are not considered, and no hydraulic boundary conditions are applied. This simplification is adopted to control the number of variables and to isolate the influence of mechanical parameters and the excavation sequence on the displacement response. Within this framework, the model focuses on the dominant mechanical behavior of the rock slope under the considered engineering conditions.

3. Response Analysis During the Excavation Process

3.1. Response Analysis Methodology

In the PFC2D Discrete Element simulation process, to comprehensively elucidate the meso-scale failure evolution mechanism of high, steep rock slopes under multi-stage excavation conditions, this study systematically constructed a multi-scale response index extraction and analysis methodology based on several dimensions, including displacement response and force chain activity [29]. We further explored the physical significance of each index and its application value in identifying slope stability.

Displacement response, as one of the core parameters characterizing the macroscopic deformation behavior of the slope, is analyzed by extracting the cumulative displacement magnitude of individual particles throughout the simulation. Two-dimensional displacement contour maps are then constructed to intuitively illustrate the overall deformation pattern and localized strain concentration zones under different working conditions. The color distribution in the contour maps reflects the spatial heterogeneity of the deformation magnitude and can be utilized to identify the location of potential sliding surfaces and the dominant deformation zones. Further analysis of the displacement contour evolution process under varying combinations of slope height and angle helps to reveal the spatio-temporal path of deformation extent expansion and the instability characteristics corresponding to critical slope height or angle [30]. By comparing the density and directional changes in the isolines, areas of structural loosening and concentrated sliding can be identified, providing morphological evidence for the macroscopic failure trend [31].

At the particle mechanics level, to analyze the internal stress transmission paths and shear failure characteristics of the slope, this study extracted the force chain distribution maps at critical time steps during the simulation, based on the magnitude and orientation information of the normal contact forces between each contact pair. The directionality and connectivity characteristics of the force chains reflect the dynamic process of the internal friction mobilization mechanism and strength degradation behavior. Specifically, zones with dense, coarse force chains typically foreshadow the initial development of the shear band [32].

3.2. Analysis of Physical Response Characteristics Under Variations in Slope Height

To investigate the influence of varying slope height on the deformation behavior of rock slopes, four typical working conditions with a fixed slope angle of 45° were selected for comparative analysis, and the resulting displacement fields are illustrated in Figure 3. It can be distinctly observed that as the slope height increases, the overall slope displacement level exhibits a non-linear growth. Furthermore, the spatial distribution of the deformation zone shows a progressive expansion trend, extending from the toe towards the middle and upper parts of the slope mass.

As shown in Figure 3 and

Table 2. Displacement at Different Slope Heights.

Slope Height (m)	Crest Displacement (m)	Slope Toe Displacement (m)	Maximum Displacement (m)
30	0.047	0.022	0.058
40	0.059	0.043	0.064
50	0.078	0.076	0.083
60	0.094	0.091	0.102

, observation of the contour map distributions shows a clear pattern. As the slope height increases, the displacement response of the internal particles increases significantly. The deformation zone gradually expands. At the same time, the overall slope stability shows a clear downward trend.

For the 30 m slope, the displacement is mainly concentrated at the slope toe and in some local areas of the lower–middle slope face. The displacement isolines are relatively sparse and smooth (Figure 3a), indicating a stable toe-dominated deformation mode. This indicates that the slope is in a relatively stable state at this height. Only minor sliding occurs between shallow surface particles, and the overall structural integrity is basically preserved.

When the slope height is increased to 40 m, the displacement response of the slope becomes much stronger. The displacement zone expands rapidly upward from the original local area at the toe. A high-displacement band (yellow–red colors) appears in the middle–upper part of the slope face (Figure 3b). This shows that a potential shear-sliding path has formed inside the slope under stress redistribution.

When the slope height reaches 50 m, the red high-displacement zone is widely distributed in the displacement field. The shear-sliding band becomes more obvious (Figure 3c). It runs from the middle–upper part of the slope down to the toe. The maximum displacement increases to 0.08 m, and the displacement gradient becomes steep. This indicates strong relative sliding between particles. The slope mass is in a stage of intense non-linear deformation, and some local areas have already entered a state of plastic failure.

Under the condition of a 60 m slope height, the internal deformation of the slope reaches its maximum. The red high-displacement area almost covers the entire slope face. The maximum displacement exceeds 0.1 m, forming a typical through-going failure zone (Figure 3d). The sliding band cuts downward in an arcuate shape, characteristic of a deep-seated rotational failure. It shows typical failure features such as a clearly developed slip surface, strong strain concentration, and severe overall sliding. Comparing Figure 3a with Figure 3d, a distinct evolution in failure mode is observed. The 30 m slope (Figure 3a) exhibits a “toe-dominated shear mode,” where deformation is strictly confined to the slope foot. Conversely, the 60 m slope (Figure 3d) evolves into a “deep-seated rotational failure mode,” characterized by a circular arc sliding surface extending from the crest to the toe. This transition demonstrates that slope height does not merely scale the deformation magnitude but fundamentally alters the potential sliding mechanism.

In PFC, the force chains, as the core structure representing contact force transmission between particles, can clearly reflect the internal stress distribution state and potential failure paths within the rock mass. Force chain diagrams allow for the observation of stress concentration zones, dominant structural bands, and their evolution process, providing a micro-scale basis for analyzing the slope instability mechanism.

As shown in Figure 4, in terms of overall trends, the force chain structure within the slope changes systematically as the slope height increases. It evolves from a sparse distribution to a more centralized and continuous pattern. This indicates that the stress transmission path transforms from a “multi-point diffusion” mode to a “localized dominant concentration” mode.

For the 30 m slope, the internal force chains form a relatively uniform network composed of short chains. The overall structure is dense but does not show clear dominant stress paths. This suggests that the slope is still in a stable state. Inter-particle interactions are controlled mainly by static frictional contacts, and no large-scale shear sliding is observed.

When the slope height is 40 m, the force chain diagram shows a partially concentrated zone of thick chains (Figure 4b). This zone extends from the middle part of the slope face down to the toe. It indicates that some particles begin to exhibit directional stress transmission under excavation disturbance and gravity. The force chains display a certain preferred orientation. A rudimentary potential shear band gradually forms. This suggests that the slope mass is entering a stage of non-homogeneous stress redistribution. At the same time, the force chain density in the shallow surface layer decreases slightly. This indicates a reduction in effective contact forces between particles, which may be a precursor to shallow crack propagation.

When the slope height is 50 m, the internal stress redistribution becomes more pronounced. The force chain density decreases significantly on both sides of the main force chain concentration zone. Structurally, this forms a typical “stress corridor” pattern (Figure 4c). Particle interactions are now dominated by sliding contacts. This implies that internal frictional failure has occurred. The force chain system shows a typical tension–shear coupled pattern, and the potential failure zone exhibits preliminary continuity.

In the 60 m slope model, the force chain diagram presents a distinctly non-uniform banded distribution. The force chain density in the shallow part decreases further (Figure 4d, upper region), and local force chains even disappear. This suggests a severe weakening of inter-particle contact forces and the development of local debonding and sliding. At the slope toe, dense annular or radial force chain structures appear (Figure 4d, lower region). These structures indicate that particles have accumulated after sliding and subsidence and are bearing considerable reverse stresses.

In terms of evolution patterns, the increase in slope height not only intensifies the deformation in the surface layer, but also significantly changes the spatial position of the dominant deformation zone. From 30 m to 60 m, the high-displacement zone gradually migrates upward. It moves from the slope toe toward the middle and upper part of the slope face. This produces a clear spatial pattern of “upper loosening–middle shearing–lower accumulation.” It reflects an evolution of the rock mass failure mechanism from shear-dominated failure to shear–tensile coupled failure under the combined effects of high stress and stress relief.

This failure evolution process is consistent with the common three-stage instability mechanism of “shear–sliding–penetration” observed in rock slopes. It shows that once the slope height exceeds a critical value, the slope stability decreases rapidly. The instability mode changes from localized deformation to overall sliding. The influence of slope height on the displacement response of high and steep rock slopes is strongly non-linear. It is mainly expressed as intense stress concentration and sudden changes in the critical condition for failure.

3.3. Analysis of Physical Response Characteristics Under the Effect of Variations in Slope Angle

In the engineering of high, steep rock slopes, the slope face angle (or slope angle) is one of the critical geometric parameters influencing stability and deformation response. To investigate the influence of varying slope angle on the slope displacement behavior, numerical models of the slope were established using PFC with slope angles of 35°, 45°, 55° and 65°, and their corresponding response characteristics were subsequently analyzed.

As shown in Figure 5 and

Table 3. Displacement at Different Slope angles.

Slope Angles (°)	Crest Displacement (m)	Slope Toe Displacement (m)	Maximum Displacement (m)
35	0.049	0.031	0.060
45	0.053	0.035	0.062
55	0.059	0.048	0.218
65	0.063	0.064	0.425

, when the slope angle is 35°, the overall deformation is well controlled. Significant displacement only occurs at the slope crest (Figure 5a). The particles are arranged relatively densely, and the structural integrity of the slope remains intact.

When the slope angle increases to 45°, A clear displacement band appears in the surface layer (Figure 5b), representing a shallow raveling failure mode. It is mainly distributed at the crest and shoulder. This indicates that shallow particles slide and loosen along the slope face and form an initial detachment zone. The main driving factor is the increase in the downslope component of gravity.

At a slope angle of 55°, the high-displacement zone in the surface layer becomes larger. Localized accumulation and rock block falls occur (Figure 5c), indicating an abrupt expansion of the unstable zone. This reflects a shear failure and block spalling mechanism induced by the high slope angle. The displacement contour map clearly shows a trend of loosening of surface particles.

Under the 65° condition, a continuous red displacement band extends across almost the entire slope face (Figure 5d). The maximum displacement approaches 0.06 m. A large number of particles in the upper slope detach from the main structural body and show a typical surface detachment failure mode. At this angle, the sliding direction is almost parallel to the slope face, exhibiting a typical planar sliding mechanism. The particles exhibit a “lifting–sliding–accumulation” pattern, indicating that the slope is in a state of shallow instability.

Quantitative analysis of Table 3 reveals a critical non-linear threshold in the slope’s stability evolution. As the slope angle increases from 35° to 45°, the maximum displacement rises marginally (from 0.060 m to 0.062 m), indicating a linear accumulation phase. However, a distinct structural bifurcation occurs between 45° and 55°, where displacement surges by approximately 251% (reaching 0.218 m). This abrupt jump confirms the non-linear mutation characteristic of the failure mechanism, identifying 45–55° as the sensitive geometric range [33].

Furthermore, the displacement contours in Figure 5 visually capture the transition of failure modes: Figure 5b (45°) represents a shallow raveling mode, characterized by scattered localized loosening. In contrast, Figure 5c (55°) and 5d (65°) exhibit a clear planar sliding mode, where the shear band (red zone) aligns parallel to the slope face, consistent with the failure kinematics described by Hoek and Bray [34].

As shown in Figure 6, when the slope angle is relatively gentle (35–45°), the internal force chains of the slope show a “net-like and scattered” pattern (Figure 6a,b). The contact bonds between particles in the surface layer remain strong. The force chain structure is compact but not concentrated, and the overall stress transfer is in a diffused state.

When the slope angle increases to 55°, the contact structure of particles on the slope face shows a clear rotation. Many force chains begin to incline along the direction of the slope face. A dense band of oblique force chains appears (Figure 6c) in the middle–upper part of the slope face. This indicates that the surface stress path has been redirected due to the increased slope inclination.

When the slope angle is further increased to 65°, the evolution of the force chain structure as shown in Figure 6 becomes more drastic. Bond breakage occurs in the middle–upper part of the slope face, and the contact forces between particles disappear locally.

Compared with the response to changes in slope height, variations in slope angle mainly induce a more obvious shallow instability on the slope face. The resulting failure is localized, progressive in stages, and strongly fragmented. As the slope angle increases, the depth of the sliding surface does not increase significantly, but the sliding intensity rises sharply. After the slope angle exceeds 55°, the effective normal stress on shallow surface particles decreases, which weakens frictional resistance, while the shear stress increases rapidly. As a result, the shallow particle system changes from a “stable interlocking state” to a “sliding–separation” state.

Before a continuous sliding surface is fully formed, local failures first occur and then propagate to adjacent regions through inter-particle stress transfer. This is reflected in the continuous sliding and accumulation of local blocks. At the same time, as the structural integrity is destroyed, the displacement response gradually develops from local accumulation to overall participation of the slope mass.

4. Engineering Case Study

4.1. Engineering Overview

To facilitate a comparative analysis between the numerical simulation results and the actual engineering deformation behavior, this study is anchored by an analysis based on a real-world engineering project.

The selected typical slope is located within the expansion area of a mountainous transportation trunk line, featuring significant topographic relief and complex geological structures. The overall slope height is approximately 59 m. The rock mass is mainly composed of interbedded jointed sandstone and mudstone. Due to well-developed structural discontinuities and poor rock mass integrity, the site exhibits typical engineering characteristics of a high rock slope.

To maintain consistency between the numerical model and the actual engineering project, the geometric dimensions of the established model are essentially congruent with the measured slope. As shown in Figure 7, the placement of monitoring points at the slope toe (p1), slope face (p2), and slope shoulder (p3); also references the actual layout utilized in the field engineering setup. Blue represents highly weathered–moderately weathered siltstone, red represents highly weathered altered siltstone, and green represents moderately weathered–highly weathered altered siltstone.

The selection of rock mass mechanical parameters in the model is based on the on-site investigation results of the project, while being refined and corrected by referencing relevant domestic research literature. Regarding the boundary condition settings, rigid constraints are applied to the bottom and both sides of the model to reflect the actual fixed foundation and boundary impedance conditions. The initial stress field is established using gravity loading, and a self-weight balance step is performed before each stage of the excavation simulation, ensuring that the simulated excavation height is consistent with the construction sequence of the project.

4.2. Model Validation

To validate the predictive capability of the Discrete Element Model for the deformation response of rock slopes, the simulation results were comparatively analyzed against displacement data obtained from field engineering monitoring.

The measured data were acquired from a Global Navigation Satellite System (GNSS) displacement monitoring system. As shown in Figure 8, specifically utilizing monitoring points located at the lower part of the slope (DBC6-12-2-2), the middle slope (DBC6-12-4-2), and the slope crest (DBC6-12-6-1). Horizontal displacement variation data corresponding to different construction stages were collected from these points (Figure 9b).

Figure 9 illustrates the comparative results between the simulated particle displacement and the field-measured GNSS horizontal displacement. In terms of trend, the simulated displacement curves are generally consistent with the measured data, both exhibiting distinct staged growth characteristics: following the completion of each excavation stage, the displacement magnitude shows a stepwise (or ‘jump’) increase, subsequently entering a phase of slow growth. Notably, after the second excavation stage, the displacement at the lower and middle sections of the slope rapidly increases, reflecting the influence of stress redistribution and shear concentration. The response in the slope crest area is relatively lagged, but it also demonstrates significant cumulative displacement towards the later period of the third stage.

Quantitatively, the maximum simulated horizontal displacement is slightly higher than the measured value, with the maximum error not exceeding 18.6%. This discrepancy is primarily concentrated in the slope toe region. This deviation may be attributed to the possibility that the slip resistance (or shear impedance capacity) of certain structural discontinuities in the actual rock mass is higher than that stipulated in the model, or it may be influenced by the constraints of the field monitoring data update frequency.

From a quantitative perspective, the maximum deviation between the numerical displacements and the GNSS measurements is about 18.6%. This error mainly comes from several sources of uncertainty and model simplifications. First, in terms of geometry and boundary conditions, this study uses a two-dimensional PFC model and idealizes the slope topography and foundation constraints. The actual three-dimensional terrain is not fully represented, which causes errors in local stress transfer and displacement response. Second, the rock mass in the field is strongly heterogeneous and anisotropic, and the combinations of discontinuities are complex. In the numerical model, a layered homogeneous equivalent scheme is used, and not all structural planes and their shear resistance are explicitly modeled. This may lead to underestimation or overestimation of shear resistance at critical locations such as the slope toe. Third, the parameter calibration is based on existing laboratory tests and published data. However, there is no one-to-one correspondence between the micro-parameters in the discrete element model and the macroscopic mechanical properties, so some inversion uncertainty is unavoidable. In addition, the spatial distribution of GNSS monitoring points is limited, and the observed data are affected by sampling frequency, instrument accuracy, and installation conditions, which also introduce measurement errors.

Considering all of the above, for a high slope under multi-stage excavation and affected by many uncertainties, keeping the difference between simulated and measured displacements at about 20% can be regarded as acceptable in engineering practice. This level of accuracy is sufficient for identifying instability trends and for locating critical hazardous zones.

5. Conclusions

This paper utilized the PFC2D Discrete Element Method to construct a high rock slope model and, from a meso-scale perspective, elucidated the mechanism by which slope height and slope angle influence slope stability. The main conclusions are as follows:

As the slope height increases, the internal force chain structure of the slope transforms from discrete to continuous, and the stress concentration zone expands upward. Failure gradually evolves from localized shear at the slope toe to a through-going overall sliding mechanism initiated in the middle and upper sections. Conversely, an increase in slope angle intensifies the directionality of shear stress, driving the failure type to evolve from shallow surface loosening and sliding toward a shear-tensile coupled control mechanism. Under the combined effect of both parameters, the failure mechanism exhibits a progressive evolution pattern from “localized shear failure–shear-dominated sliding–shear-tensile coupled penetrating instability.”

A significant reduction in force chain density and an abrupt change in the dominant orientation occur in the slope toe and middle regions during the pre-failure stage, typically preceding the onset of overall particle sliding. This suggests that force chain parameters possess the capability to anticipate localized instability trends. This characteristic provides a theoretical basis for developing meso-scale early warning methods based on force chain identification, thereby expanding the analytical dimensions of slope stability assessment.

The particle displacement trends, sliding paths, and their temporal evolution patterns derived from the multi-stage excavation simulation exhibit a high degree of concordance with field-measured GNSS data, with errors controlled within a reasonable range. The model’s ability to accurately identify potential failure zones without explicitly modeling structural discontinuities validates its reliability in the analysis of high rock slopes, making it particularly applicable to high-risk slope projects predominantly controlled by complex joint development and discontinuous structures.

The limitations of this study include the use of a 2D model which simplifies the 3D topographic effects, and the simplification of the complex hydrological conditions. The maximum deviation of approximately 18.6% between the numerical and GNSS-measured displacements can be attributed to model idealizations, rock mass heterogeneity, parameter inversion uncertainty, and limitations of the monitoring system. Considering the complexity of a high rock slope under multi-stage excavation, a displacement difference on the order of 20% is acceptable in engineering practice. This accuracy is sufficient to capture the deformation pattern, identify instability trends, and delineate critical hazardous zones for slope stability evaluation.