Open-Pit Slope Stability Analysis Integrating Empirical Models and Multi-Source Monitoring Data

Abstract

Slope stability monitoring in open-pit mining remains a critical challenge for geological hazard prevention, where conventional qualitative methods often fail to address dynamic risks. This study proposes an integrated framework combining empirical modeling (slope classification, hazard assessment, and safety ratings) with multi-source real-time monitoring (synthetic aperture radar, machine vision, and Global Navigation Satellite System) to achieve quantitative stability analysis. The method establishes an initial stability baseline through mechanical modeling (Bishop/Morgenstern–Price methods, safety factors: 1.35–1.75 across five mine zones) and dynamically refines it via 3D terrain displacement tracking (0.02 m to 0.16 m average cumulative displacement, 1 h sampling). Key innovations include the following: (1) a convex hull-displacement dual-criterion algorithm for automated sensitive zone identification, reducing computational costs by ~40%; (2) Ku-band synthetic aperture radar subsurface imaging coupled with a Global Navigation Satellite System and vision for centimeter-scale 3D modeling; and (3) a closed-loop feedback mechanism between empirical and real-time data. Field validation at a 140 m high phosphate mine slope demonstrated robust performance under extreme conditions. The framework advances slope risk management by enabling proactive, data-driven decision-making while maintaining compliance with safety standards.

1. Introduction

Slope stability in mining environments poses a significant interdisciplinary challenge that intersects geotechnical engineering, economic resource management, and ecological conservation. As open-pit mining operations extend to unprecedented depths—with certain contemporary excavations surpassing 800 m in vertical dimension—the associated geomechanical challenges have intensified substantially. Modern extraction methodologies must account for multiple interacting factors including redistribution of natural stress fields, groundwater system alterations caused by dewatering processes, structural fatigue induced by repeated blasting cycles, and progressive deterioration of rock formations over time. The 2019 Brumadinho catastrophe (270 fatalities, USD 7B economic loss) epitomizes the catastrophic potential of slope failures, with post-accident forensics revealing how latent structural discontinuities interacted with seasonal pore pressure fluctuations [1]. Contemporary analytical approaches now systematically incorporate three key methodologies: (1) stochastic limit equilibrium techniques that account for variability in material strength properties, (2) three-dimensional computational modeling capable of simulating directionally dependent rock behavior, and (3) advanced surveillance systems integrating satellite-based radar with sub-centimeter resolution, automated surveying instruments, and spatially distributed deformation sensors. This transition from fixed-factor to probability-driven stability assessment facilitates early warning capabilities through predictive modeling, while permitting more aggressive slope configurations that typically yield 8–12% greater mineral extraction than traditional designs. The discipline is further evolving through artificial intelligence implementations, where modern recurrent neural network architectures have shown particular effectiveness in forecasting deformation patterns from diverse sensor data streams [2,3].

Gupta et al. [4] conducted a critical review of the numerical-modeling-based stability analysis of slope structures. The popularly cited cases of slope instability have been analyzed to synthesize pertinent findings regarding the approach of stability analysis, broader design criteria, and optimization. The critical parameters of the numerical-modeling-based design of a safe slope structure are discussed in detail. The significant output parameters, apart from the factor of safety, are also outlined for evaluating the state of stability. Overall, rock slope stability analysis can be carried out using deterministic and probabilistic methods. The deterministic methods in the stability analysis of open-pit mine slopes have the advantage of a simple calculation process and intuitive results. They are easy for engineers to understand and apply. However, the disadvantages include a large number of assumptions, insufficient consideration of complex geological conditions, and uncertain factors, which may lead to significant discrepancies between the analysis results and the actual situation. Probabilistic analysis methods can better consider the uncertainty of geological conditions and improve the reliability of the analysis results. However, their calculation process is complex, requires a large amount of data support, and the results have a certain degree of uncertainty [5,6]. In terms of deterministic analysis, it is based on the safety factor concept, which uses fixed representative values for each input parameter, without considering the variation and uncertainty of the rock mass properties. Currently, the primary methods for slope stability analysis include empirical methods [7,8], numerical analysis methods [9,10,11,12,13,14], experimental methods [15,16], Gupta comprehensive analysis methods [17,18,19], and risk analysis methods [20,21,22,23]. In terms of probabilistic analysis using the calculation of failure probability instead of the safety factor against failure, it provides a more reasonable method for quantifying risk by incorporating uncertainty into input variables and evaluating the system failure probability. The traditional deterministic methods can be transformed into probabilistic analysis methods. For example, a deterministic software package can be used for calculation, and independent code can be developed to generate statistics so that deterministic solutions can be repeated, thereby enabling a probabilistic assessment of the same example. Dai et al. [24] studied the normal frequency distribution related to cohesion, internal friction angle, and pore water pressure changes. The mean and standard deviation of cohesion, internal friction angle, and pore water pressure; the correlation between cohesion and internal friction angle; and a set of random values for cohesion, internal friction angle, and pore water pressure are used to calculate safety factors in the deterministic software package. In Dyson et al.’s study, various shear strength distributions of three different probabilistic finite element methods were considered to determine the safety factor and failure probability distributions based on relevant slope stability analysis methods [25]. Du et al. [26] proposed a new method for evaluating the stability of large open-pit mine slopes, based on a comprehensive investigation of the geometric shapes and shear strengths of geological discontinuities. Zhang et al. [27] proposed a method where the uncertainty in the prediction of the slope failure time is divided into two categories, namely observation uncertainty and model uncertainty.

In actual mining operations, factors such as vibrations, strata changes, and rainwater infiltration continuously affect the fundamental aspects of qualitative analysis, leading to the potential failure of these methods [28,29,30]. Therefore, it is essential to propose methods for dynamically analyzing slope stability to achieve real-time monitoring of mining sites. Some researchers have employed synthetic aperture radar (SAR [31]), machine vision [32], and Global Navigation Satellite System (GNSS) technology [33] to sense slope stability. These technologies often face a series of practical challenges during application. GNSS technology relies on satellite signals, which may be obstructed in complex terrains or near buildings, leading to reduced positioning accuracy or data loss. In extreme weather or electromagnetic interference environments, data transmission may be delayed or interrupted. Video monitoring technology is highly affected by lighting conditions, where low visibility can degrade image quality and impact displacement recognition accuracy. Additionally, a single camera has limited coverage, requiring the deployment of multiple devices for large-scale monitoring, which increases system complexity and cost. SAR technology employs side-looking imaging, limiting its monitoring capability for steep slopes (such as vertical cliffs), as radar beams may fail to reflect effectively, resulting in data loss. Consequently, relying on a single technology makes it difficult to ensure stability and comprehensiveness in real-time slope stability monitoring. In light of this, designing a real-time monitoring approach that integrates SAR, machine vision, and GNSS data could effectively mitigate the negative impacts caused by the failure of any single monitoring method, significantly enhancing the reliability of real-time monitoring.

However, the current lack of a unified multi-source data fusion framework for GNSS, video, and SAR data—which differ substantially in format, spatiotemporal resolution, and monitoring capabilities—critically limits reliable all-weather, multi-scale slope stability monitoring in mining environments. While GNSSs deliver millimeter-level point measurements (yet suffers from sparse coverage and occlusion), SAR provides wide-area deformation mapping (but with long revisit cycles and rapid deformation sensitivity), and video enables real-time visual tracking (though vulnerable to dust and lighting), their operational isolation prevents comprehensive detection of deformation processes ranging from gradual creep to sudden failure. This study develops a mining-optimized fusion architecture integrating spatiotemporal alignment, dynamic weighting algorithms, and interference-resistant enhancement to synergize GNSSs’ precision, SAR’s coverage, and video’s temporal resolution—enabling cross-scale monitoring from localized hazard zones to pit-wide stability assessment, thereby addressing the critical gap in current mine safety systems where these technologies operate in isolation.

2. Methods

This study proposes a lifecycle-based slope stability monitoring method for open-pit coal mines by integrating empirical models and data-driven approaches. The framework of this method consists of two parts, where the initial stability of the mining slope is determined using an empirical model that incorporates a comprehensive analysis of slope classification, slope hazard classification, and slope engineering safety classification, and the real-time slope stability is analyzed with a three-dimensional model of the geological appearance of the mining area, which is periodically obtained to monitor the displacement of critical peak points in the area (Figure 1). By integrating SAR, machine vision, and GNSS technology, a comprehensive monitoring system is constructed to achieve precise detection of the underground stratum structure in open-pit mines. SAR monitors underground stratum structures using ground-based Ku-band systems. Machine vision employs fixed terrestrial cameras capturing surface changes. GNSSs provide high-precision positioning via permanently installed receivers. The fusion of these multi-source data enables the construction of a centimeter-scale 3D digital terrain model (DTM) for real-time slope stability monitoring. By utilizing this constructed DTM, real-time monitoring of slope stability is realized, ensuring safe production in mines. This method fully utilizes the advantages of multiple technologies, providing scientific and efficient technical support for the stability monitoring of open-pit mine slopes. Based on the displacement of these peak points, areas of change are identified, with a focus on monitoring unstable regions. The following sections will separately describe the identification methods used for the empirical models and the methods for detecting displacements in the DTM models.

2.1. Empirical Model

The empirical model for slope stability analysis must consider multiple factors and conduct a comprehensive assessment based on the influence weights of these various factors [34,35]. The weight of these factors may vary slightly under different geological conditions and production scenarios, depending on the experience and preferences of the decision-makers, which will not be discussed further here. As a general practice, the analysis involves the classification of slope grades, the calculation of the stability coefficient, and an in-depth analysis of influencing factors such as gravity, groundwater, seismic forces, and the impact coefficients of blasting vibrations. Given that the methods in the empirical model are all existing approaches, the principles will not be elaborated in detail in the main text. For comprehensive descriptions, please refer to Appendix A.

2.2. Method for Displacement Detection of DTMs

2.2.1. Monitoring Measurements to Construct DTM

(1)

SAR monitoring

In open-pit coal mines, the advantage of using SAR to detect underground structures lies in its ability to penetrate surface cover layers, enabling high-precision imaging and monitoring of the underground structures. SAR is not affected by adverse weather and lighting conditions, allowing for continuous remote sensing of underground coal mine structures. It effectively identifies minor deformations and structural changes in the underground coal seams, providing high-resolution images and data. This helps engineers accurately assess the stability and safety conditions of the coal mine, issue timely warnings of potential safety hazards, and ensure the smooth progress of safe production in the coal mine.

(2)

GNSS monitoring

GNSSs have the following advantages: (1) three-dimensional velocity, timing, and high precision positioning; (2) fast, time-saving, efficient, widely applicable, and multifunctional; (3) mobile positioning capability; (4) during use, the receiver does not need to emit any signals, enhancing the concealment of monitoring technology; (5) they can use low-frequency signals, which can maintain considerable signal penetration even in poor weather conditions, with global coverage reaching up to 98%. From an engineering investment perspective, using the GNSS “one machine for multiple lines” method to monitor ground displacement can save on engineering investment.

(3)

Video monitoring

Open-pit mining enterprises should conduct macro video surveillance of the mining slope, and the surveillance scope should cover the main slope surface. Video surveillance should support backup, inquiry, and replay of surveillance images by camera number, time, events, and other information. Video surveillance should have night vision capabilities or be equipped with auxiliary lighting devices. The video monitoring systems are, respectively, arranged in the Fourth Mining Area and the South Area slope, with one set for each location.

Integrating SAR, a GNSS, and video data to construct a DTM requires transforming all data into the same coordinate system. GNSS point clouds exhibit high single-point accuracy (horizontal ± 0.02 m, vertical ± 0.05 m) but limited spatial coverage. Therefore, all data should be converted to the GNSS coordinate system.

To ensure computational efficiency in building a DTM, it is essential to primarily retain GNSS key points, including locations with significant elevation changes such as ridge tops and slope toes. These points can be identified through curvature calculation:

$$C={\displaystyle \frac{{\omega }_1{\omega }_2}{{({\omega }_1+{\omega }_2)}^2}}$$

(1)

Retain points where $C>0.1$, where ${\omega }_1$ and ${\omega }_2$ are the eigenvalues of the local covariance matrix. The covariance matrix can be calculated with the GNSS data.

2.2.2. Transforming SAR Data to the GNSS Coordinate System

SAR can generate dense point clouds but contains noise. To align the data with the GNSS coordinate system, an affine transformation is applied:

$$p^{SAR\_global}=R\ast p^{SAR\_local}+e$$

(2)

where $p^{SAR\_local}$ and $p^{SAR\_glocal}$ are SAR data before and after the transformation. Rotation matrix $R$ and translation vector $e$ are solved via least-squares fitting using GNSS control points. To mitigate the impact of erroneous SAR data on monitoring accuracy and improve computational efficiency, statistical outlier removal is applied to the SAR point cloud. Point $p_{\mathrm{i}}$ is filtered out according to the following rule:

$$\left|\right|p_{\mathrm{i}}-{\overline{\mathrm{p}}}_{\mathrm{k}-\mathrm{N}\mathrm{N}}\left|\right|>\mu +3\sigma$$

(3)

where ${\overline{\mathrm{p}}}_{\mathrm{k}-\mathrm{N}\mathrm{N}}$ denotes the mean of the k-nearest neighbors of $p_{\mathrm{i}}$, while $\mu$ and $\sigma$ represent the mean and standard deviation of the local distance distribution, respectively, with their values being determined empirically based on specific application scenarios.

2.2.3. Transforming Video Data to the GNSS Coordinate System

To incorporate video data into a DTM, keyframes and ground feature points must first be extracted into the global dataset. The following outlines the process of converting video data into 3D point information:

(1)

Spatiotemporal Synchronization and Geometric Correction of Video Data

The raw video stream undergoes temporal synchronization and lens distortion correction to prepare the data for feature extraction. Temporal synchronization ensures alignment between video and GNSS/SAR data timestamps. Let $t_v$ be the video frame timestamp and $t_g$ the GNSS data timestamp. The synchronization error must satisfy the following equation:

$$∆t=|t_v-t_g|\le \tau (\tau =1 \mathrm{m}\mathrm{s})$$

(4)

Asynchronous data are aligned via linear interpolation:

$$p_g(t_v)=p_g(t_{g,i})+{\displaystyle \frac{t_v-t_{g,i}}{t_{g,i+1}-t_{g,i}}}{(p}_g(t_{g,i+1})-p_g(t_{g,i}))$$

(5)

where $i$ represents the index of the reference time point in a sequence of timestamps ($t_{g,1},t_{g,2},\cdots$) from the global dataset, while $t_{g,i}$ and $t_{g,i+1}$ are the i-th and (i + 1)-th timestamps in the global dataset, such that $t_{g,i}<t_v<t_{g,i+1}$. The term ${\displaystyle \frac{t_v-t_{g,i}}{t_{g,i+1}-t_{g,i}}}$ calculates the normalized interpolation weight between the two reference points.

The distortion correction eliminates geometric errors introduced by the lens, providing accurate input for subsequent feature matching. The lens distortion is corrected using the Brown–Conrady model, with the rectification formula for pixel coordinates $(x,y)$ expressed as follows:

$$\begin{gathered} x^{\prime }=x+x\left(k_1{r}^2+k_2{r}^4\right)+2c_{1}xy+c_2\left(r^2+2x^2\right) \\ {y}^{\prime }=y+y\left(k_1{r}^2+k_2{r}^4\right)+2c_{2}xy+c_1\left(r^2+2y^2\right) \end{gathered}$$

(6)

where $r^2=x^2+y^2$, $k_1$ and $k_2$ are radial distortion coefficients, and $c_1$ and $c_2$ are tangential distortion coefficients.

(2)

Multi-Scale Feature Extraction and Sparse 3D Reconstruction

The corrected video frames undergo feature detection and sparse point cloud generation to achieve dense reconstruction. This paper employs the SIFT (Scale-Invariant Feature Transform) method to extract data features. The core idea is to detect key points in the image and extract their local feature descriptors, ensuring robustness against rotation, scaling, and brightness variations. For an image $I(x,y)$, SIFT feature points are detected based on scale-space extrema:

$$D(x,y,\sigma )=\left(G\right(x,y,k\sigma )-G(x,y,k\sigma \left)\right)\ast I(x,y)$$

(7)

where $G$ represents the Gaussian kernel, $k$ is the scale factor, and $\sigma$ denotes the standard deviation (scale parameter) of the Gaussian kernel, which constructs the image’s scale space to detect stable features across different scales. The scale parameter $\sigma$ determines feature detection characteristics: Larger $\sigma$ values produce greater image blurring, detecting features corresponding to larger-scale structures (e.g., mountain contours). Smaller $\sigma$ values preserve finer details (e.g., rock fractures). SIFT features ensure robust cross-view matching. Detected feature points must satisfy

$$\left|D\right(x,y,\sigma \left)\right|>0.03max\left(D\right)\mathrm{and} \mathrm{curvature} \mathrm{ratio} {\displaystyle \frac{{\lambda }_{max}}{{\lambda }_{min}}}<10$$

(8)

The camera projection matrix $P_i=K\left[R_i\right|t_i]$ is solved by minimizing the reprojection error:

$${}_{R_i,t_i,X_j}{}^{min} \sum _{i,j}{\left|\right|\pi \left(P_i{X}_j\right)-x_{ij}\left|\right|}^2$$

(9)

where $\pi$ is the projection function, $X_j$ represents 3D points, $x_{ij}$ denotes observed 2D points, and $R_i|t_i$ represents the camera’s extrinsic parameters (rotation and translation). Through multi-view geometric constraints, sparse 3D point clouds are reconstructed, providing the foundation for subsequent registration processes.

(3)

Coarse and Fine Registration for Coordinate Unification

The video point cloud is unified into a common coordinate system through coarse and fine registration. For coarse registration (similarity transformation), four pairs of corresponding points $\left\{p_{\mathrm{i}}\right\}$ (video) and $\left\{q_{\mathrm{i}}\right\}$ (SAR) are selected to solve the similarity transformation T = {s, W, o}:

$${}_{s,R,t}{}^{min} \sum _i{\left|\right|sW{p}_i+o+q_i\left|\right|}^2$$

(10)

Here, $W$ is the rotation matrix, eliminating the pose difference between the local coordinate system of the video and the global coordinate system; $o\in {\mathbb{R}}^3$ is the translation vector, aligning the coordinate origins. After closed-form solution via singular value decomposition, iterative closest point (ICP) refinement is performed to iteratively optimize point pair distances:

$$T_{k+1}={}_T{}^{argmin} \sum _{(p,q)ϵZ}{\left|\right|Tp-q\left|\right|}^2$$

(11)

where $Z$ is the set of nearest neighbor point pairs, $p$ is a 3D point reconstructed from the video (local coordinate system), and $q$ is the corresponding point in the global model. Coarse registration addresses the initial pose problem, while ICP further refines alignment accuracy, ultimately integrating the video data into the global coordinate system.

2.3. Constructing the DTM

With all the point cloud data ultimately obtained ${\left\{(x_i,y_i,z_i)\right\}}_{i-1}^N$, a DTM is formed by seamlessly stitching together a series of scattered points, non-closed curves, or lines into a non-closed, layer-like surface entity, where $z_i$ is the elevation, and the point spacing $\Delta x$ and $\Delta y$ are determined by the accuracy of the GNSS/SAR data. This model can clearly and intuitively reflect the original terrain contours of a mining area [36]. By analyzing the trend of changes in the DTM, it is possible to predict the stability of slopes. To enhance automated judgment capabilities, a convex hull algorithm [37] is employed to obtain the main peak points of the DTM and to calculate the changes between the main peak points of two consecutive DTMs.

Given a point set $P=\{p_1,p_2,\cdots ,p_{\mathrm{n}}\}\subset {\mathbb{R}}^3$, its convex hull is the smallest convex set containing all the points, defined as follows:

$$Conv(P)=\{\sum _{i-1}^n{l}_i{p}_i|l_i>0,\sum _{i-1}^n{l}_i=1\}$$

(12)

The condition for identifying peak points is based on the local extremum criterion: A point $p_i$ with elevation $z_i$ must be the maximum within its neighborhood (e.g., a 3*3 grid) and must belong to the vertex set of the convex hull. Points with elevation variations smaller than a noise threshold $\epsilon$ (e.g., $\epsilon =0.1 \mathrm{m}$) are selected as follows:

$$P_{peak}=\{p_i\in Conv(P\left)\right|z_i>z_j \forall j\in \mathcal{N}\left(i\right),|z_i-z_j|\ge \epsilon \}$$

(13)

Here, $\mathcal{N}\left(i\right)$ denotes the set of neighboring points of $p_i$.

Based on the stability of the slope and monitoring requirements, a data collection frequency $F$ is set. Let us assume that the elevation coordinate of the i-th peak point at time $t$ is $p_{t,i}$. Then, the change in $P_t^i$ from time $t-1$ to time $t$ can be expressed as

$$K_t^i=|p_{t,i}-p_{t-1,i}|$$

(14)

The overall displacement of the DTM can be calculated as follows:

$$S_t=\sum _{i=1}^N{p}_{t,i}-p_{t-1,i}|$$

(15)

where $N$ is the total number of detected peak points. Therefore, from the initial time 1 to time $t$, the cumulative displacement of the DTM can be expressed as follows:

$${AS}_t=\sum _{j=1}^t{S}_t$$

(16)

If the value of ${AS}_t$ is less than the threshold $\chi$, it indicates that there is no significant risk of landslides. When ${AS}_t$ is greater than the threshold $\chi$, it is necessary to determine the specific location of the landslide. Also, considering the inversion error and the symmetry of the error distribution, adjust $\chi$ slightly as follows:

$$\chi =\chi \ast N({\mu }_1,{\sigma }_1)$$

(17)

where ${\mu }_1$ controls the mean of the errors, and ${\sigma }_1$ controls the variance of the error distribution. In this study, ${\mu }_1=1$ and ${\sigma }_1=0.01$ are chosen. According to actual precision requirements, the value of ${\sigma }_1$ can be flexibly adjusted. The values of $K_t$ are sorted in descending order, with the largest three elements denoted as $K_t^{i1}$, $K_t^{i2}$, and $K_t^{i3}$. Thus, the most sensitive area is the triangular region covered by $K_t^{i1}$, $K_t^{i2}$, and $K_t^{i3}$. To improve representation accuracy, more peak points can be used, such as $K_t^{i1}$, $K_t^{i2}$, $K_t^{i3}$, and $K_t^{i4}$, to determine the surrounding sensitive area.

To achieve this goal, it is first necessary to set up $M\left(M <N\right)$ monitoring points at key locations in the mine (such as slopes, landslide areas, etc.) to ensure coverage of the most vulnerable areas. SAR, machine vision, and GNSS technology will be used for layer detection; the method for inverting layer data from detection is not described here but can be referenced in the literature [38,39,40]. Next, the layer information from each location will be plotted in the same coordinate system, and interpolation methods will be used to connect the inverted layers from each area, forming stratigraphic profile maps. Finally, the thickness, distribution, and interrelationships of each layer will be identified, and multiple layers will be superimposed to create a DTM. It is important to note that although ${AS}_t$ can reflect the stability of the slope, its value is closely related to $M$. A large $M$ can cause ${AS}_t$ to be overestimated, especially due to the impact of error accumulation; conversely, a small $M$ can lead to an underestimation of ${AS}_t$. Therefore, to mitigate the negative impact of $M$, ${AS}_t$ can be further expressed as

$${AS}_t={\displaystyle \frac{{AS}_t}{M}}$$

(18)

At this point, ${AS}_t$ represents the average change for each peak point. The value of $\gamma$ can also be further refined based on empirical data and geological conditions. Considering the influence of inversion errors and computational errors, this study sets $\chi =0.3$ m.

2.4. Main Contributions of the Proposed Method

The main contributions of this paper can be summarized as follows:

(1)

Multi-source fusion-based dynamic 3D modeling and feature-driven sensitive area identification: This paper constructs a mine-specific DTM by fusing SAR (subsurface tomography), a GNSS (precision positioning), and machine vision (surface micro-deformation); reconstructs discrete monitoring points into continuous 3D geological entities through stratum profile inversion; proposes a convex hull-displacement dual-criterion identification method to extract terrain skeletons; captures primary peak points in 3D topography; and enables dynamic real-time identification of sensitive monitoring zones.

(2)

Sensitive-area-driven targeted reconstruction of traditional mechanical methods: This paper establishes an “entire-domain scanning and focused breakthrough” analysis paradigm, concentrating precision analysis on sensitive areas and enhancing analytical efficiency. It also optimizes stability analysis for sensitive regions to reduce computational costs for large-scale mine slope monitoring and overcome resource bottlenecks in conventional methods.

3. Data

To demonstrate the effectiveness of the above methods, two groups of experiments are conducted as follows. The first group of experiments employs an empirical model discrimination method to analyze the stability of the current slope conditions in the mining area. The second group of experiments utilizes a three-dimensional model displacement discrimination method to assess the long-term stability of the current slope conditions in the mining area. The preparation for the experiments is provided in Section 3.1, Section 3.2, Section 3.3, Section 3.4, Section 3.5, Section 3.6, Section 3.7, Section 3.8, respectively. In the empirical model, rock mechanical parameters such as block density, single-axis compression deformation, split tensile, and shear strength contribute to slope stability assessment by influencing slope classification and stability coefficient calculations. Slope height classification is determined solely based on slope height, while slope hazard classification and slope engineering safety classification rely on parameters like shear strength ($c$, $\phi$) and tensile strength to evaluate hazard risk levels and engineering safety grades. The stability coefficient calculation (e.g., Bishop or M-P methods) directly incorporates shear strength parameters ($c$, $\phi$) and density ($\rho$) to compute the ratio of resisting force to driving force, with uniaxial compression deformation parameters ($E$, $\mu$) used to validate numerical model reliability.

3.1. Mining Area

Based on the current mining conditions, the evaluation work categorizes the existing slopes in the area into five slope zones, marked as I, II, III, IV, and V. Building on the comprehensive zoning of the mining area and considering the actual conditions of the slopes, one or two typical profiles (e.g., II-1, and IV-1 and IV-2) are selected from each zone for stability analysis. Detailed information about each slope profile can be found in

Table A4. Slope profile information.

Zoning	Profile Number	Top Elevation (m)	Bottom Elevation (m)	Slope Height (m)	Slope Angle (°)	Main Lithology
I	I-1	2405	2326	79	36	Sandstone, Phosphate Rock, Dolomite
II	II-1	2373	2308	65	15
III	III-1	2403	2317	86	16	Quaternary, Sandstone, Phosphate Rock, Dolomite
IV	IV-1	2405	2265	140	22	Sandstone, Phosphate Rock, Dolomite
	IV-2	2437	2385	52	16
V	V-1	2358	2255	103	16
	V-2	2328	2206	122	29	Quaternary, Sandstone, Phosphate Rock, Dolomite

.

3.2. Block Density Test

The uniaxial compressive strength test of rock refers to the load per unit area that the specimen can withstand when it fails under the action of axial force, which is the ratio of the maximum load at the time of failure of the specimen to the cross-sectional area perpendicular to the loading direction. The test adopts the method of directly crushing the specimen to obtain the uniaxial compressive strength of the rock. It is also possible to measure the uniaxial compressive strength of the rock while conducting the uniaxial compression deformation test. The specimen used is a cylindrical body with a diameter of about 5 cm and a length of 10 cm. This single-axis compressive strength test involved a total of 30 specimens, with 15 samples in a natural state and 15 in a saturated state. Among them, there were 12 dolomite, 12 phosphorite, and 6 sandstone specimens. The relevant test results of the single-axis compressive test are shown in

Table A5. Results of the uniaxial compressive strength test (natural, saturated).

Rock Texture and Condition	Sample Number	Diameter (cm)	Height (cm)	Compressive Strength (MPa)	Destruction Mode
Dolomite (Saturated)	B1	4.85	10.7	30.3	Longitudinal splitting
	B2	4.87	9.7	18.3	Longitudinal splitting
	B3	4.85	9.2	47.2	Longitudinal splitting
	B4	4.85	10.3	34.5	Longitudinal splitting
	B5	4.85	10.3	33.8	Local longitudinal splitting
	B6	4.85	10.3	27.7	Local longitudinal splitting
	Mean			32.0	/
Dolomite (Natural)	B1	4.85	9.9	44.0	Longitudinal splitting
	B2	4.85	9.6	63.1	Longitudinal splitting
	B3	4.85	9.0	39.5	Longitudinal splitting
	B4	4.88	9.6	68.4	Local longitudinal splitting
	B5	4.87	7.2	26.2	Longitudinal splitting
	B6	4.85	7.0	29.1	Longitudinal splitting
	Mean			45.1	/
Phosphorite (Saturated)	L1	4.86	10.3	40.9	Longitudinal splitting
	L2	4.85	8.9	36.0	Longitudinal splitting
	L3	4.88	9.6	48.0	Longitudinal splitting
	L4	4.88	9.6	36.3	Longitudinal splitting
	L5	4.88	9.1	46.2	Longitudinal splitting
	L6	4.88	9.1	28.2	Longitudinal splitting
	Mean			39.3	/
Phosphorite (Natural)	L1	4.85	9.1	43.7	Longitudinal splitting
	L2	4.84	8.4	65.7	Longitudinal splitting
	L3	/	/	/	Longitudinal splitting
	L4	4.85	10.3	46.8	Longitudinal splitting
	L5	4.87	10.3	61.0	Longitudinal splitting
	L6	4.87	10.3	44.0	Longitudinal splitting
	Mean			52.2	/
Sandstone (Saturated)	S1	4.88	10.2	46.2	Longitudinal splitting
	S2	4.87	10.2	31.1	Longitudinal splitting
	S3	4.87	10.2	37.9	Longitudinal splitting
	Mean			38.4	/
Sandstone (Natural)	S1	4.88	10.0	60.9	Local longitudinal splitting
	S2	4.88	9.9	56.6	Longitudinal splitting
	S3	4.85	10.2	66.0	Longitudinal splitting
	Mean			61.2	/

.

3.3. Single-Axis Compression Deformation Test

The uniaxial compression deformation test is used to determine the longitudinal and lateral strain values of the specimen under uniaxial compression stress conditions, and based on this, the elastic modulus and Poisson’s ratio of the rock are calculated. The elastic modulus is the ratio of the axial stress to the axial strain; Poisson’s ratio is the ratio of the radial strain to the axial strain under the corresponding conditions of the elastic modulus. The elastic modulus can be divided into three types: (1) initial elastic modulus, (2) tangential elastic modulus, and (3) secant elastic modulus. Among them, the initial elastic modulus is the slope of the tangent line passing through the origin on the stress–strain curve, reflecting the development degree of micro-fractures in the rock. The tangential elastic modulus is the slope of the straight line (or nearly straight line) segment on the stress–strain curve, reflecting the elastic deformation characteristics of the rock. The secant elastic modulus is the slope of the line connecting the point corresponding to 50% of the ultimate stress on the stress–strain curve with the origin, reflecting the overall deformation characteristics of the rock. The specimen used is a cylinder with a diameter of about 5 cm×10 cm. The elastic modulus measured in this test refers to the secant elastic modulus under loading when the compressive stress is 50% of the axial compressive strength. The Poisson’s ratio is obtained by calculating the ratio of the lateral strain to the axial strain. A total of 15 specimens were used in the uniaxial compression deformation test (natural state), including six dolomites, six phosphorite, and three sandstones. The experimental results are given in

Table A6. Compression deformation test results.

Rock Texture or Lithology	Sample Number	Shear Modulus of Elasticity E50 (GPa)	Poisson’s Ratio μ50	Tangent Modulus of Elasticity Ee (GPa)	Poisson’s Ratio μe	Destruction Mode
Dolomite	B1	29.0	0.25	30.2	0.36	Longitudinal splitting
	B2	22.6	0.32	23.4	0.40	Longitudinal splitting
	B3	38.4	0.22	35.3	0.24	Longitudinal splitting
	B4	42.7	0.29	38.9	0.41	Longitudinal splitting
	B5	38.5	0.23	42.8	0.24	Local longitudinal splitting
	B6	40.5	0.19	34.0	0.16	Longitudinal splitting
	Mean	35.3	0.25	34.1	0.31	/
Phosphorite	L1	31.9	0.23	30.4	0.24	Longitudinal splitting
	L2	50.4	0.19	52.1	0.22	Longitudinal splitting
	L3	24.3	0.22	24.4	0.26	Longitudinal splitting
	L4	64.6	0.25	54.3	0.23	Longitudinal splitting
	L5	48.1	0.22	65.5	0.27	Longitudinal splitting
	L6	19.0	0.22	28.7	0.25	Longitudinal splitting
	Mean	39.7	0.22	42.57	0.24	/
Quartz Sandstone	S1	46.2	0.20	28.2	0.24	Longitudinal splitting
	S2	31.1	0.26	33.8	0.24	Longitudinal splitting
	S3	37.9	0.25	37.7	0.34	Local longitudinal splitting
	Mean	38.4	0.24	33.23	0.27	/

.

3.4. Split Tensile Test

The determination of rock tensile strength includes two methods: direct tensile testing and indirect tensile testing. Due to the difficulty in specimen preparation and the complexity of the testing technology in the direct method, the indirect method (i.e., splitting method) is currently more commonly used for measurement. The splitting method involves applying a pair of linear loads in the direction of the specimen’s diameter, causing the specimen to fail along the diameter, thereby indirectly measuring the rock’s tensile strength. This test uses the splitting method for the tensile test, which belongs to the indirect tensile method, and the tensile strength is calculated according to the following formula. The tensile strength test conducted this time measured a total of 24 naturally occurring split specimens, including 6 dolomite specimens, 12 phosphorite specimens, and 6 sandstone specimens. The statistical results of the split test are shown in

Table A7. Split tensile test results.

Lithology	Sample Number	Diameter (cm)	Height (cm)	${\mathit{R}}_{\mathit{t}}$ (MPa)
Dolomite (Natural)	B1	4.88	4.52	6.27
	B2	4.85	4.30	8.41
	B3	4.85	2.96	7.01
	Mean	4.86	3.93	7.23
Dolomite (Saturated)	B1	4.85	4.70	5.10
	B2	4.85	3.00	5.95
	B3	4.85	4.25	5.34
	Mean	4.85	3.98	5.46
Phosphate Rock (Natural)	L1	4.86	4.65	1.35
	L2	4.85	4.28	1.85
	L3	4.85	4.30	1.67
	L4	4.87	2.96	7.47
	L5	4.88	4.25	7.34
	L6	4.88	3.02	7.03
	Mean	4.87	3.91	4.45
Phosphate Rock (Saturated)	L1	4.85	2.96	1.22
	L2	4.88	4.25	1.06
	L3	4.85	3.02	1.34
	L4	4.85	3.50	6.06
	L5	4.85	4.80	6.62
	L6	4.85	3.42	6.83
	Mean	4.86	3.66	3.85
Sandstone (Natural)	S1	4.88	4.04	7.28
	S2	4.88	3.98	9.36
	S3	4.88	3.98	8.92
	Mean	4.88	4.00	8.52
Sandstone (Saturated)	S1	4.85	4.55	5.66
	S2	4.88	4.80	5.95
	S3	4.88	4.50	5.91
	Mean	4.87	4.62	5.84

.

3.5. Shear Strength Test

The rock shear cut strength test involves processing the rock into cylindrical specimens with a height-to-diameter ratio of approximately 1:1 and placing the rock samples into a fixed testing machine mold for shear testing to measure the rock’s shear strength. During the test, different shear angles are used to conduct regular rock shear strength tests. The results of the rock shear strength test are detailed in

Table A8. Shear strength results.

Lithology	Sample Number	Length (cm)	Width (cm)	Shear Area (cm2)	Shear Stress τ (kPa)	Internal Friction Angle φ (°)	Cohesion C (MPa)
Dolomite	B1	5.18	5.28	27.35	58.81	40.2	3.36
		5.30	5.30	28.09	44.58
	B2	4.90	5.28	25.87	28.38
		5.10	5.30	27.03	30.62
	B3	5.28	5.30	27.98	13.70
		5.30	5.30	28.09	17.24
	B4	5.32	5.28	28.09	30.54
		5.30	5.30	28.09	28.82
	B5	4.92	5.25	25.83	16.54
		5.27	5.34	28.14	20.11
	B6	5.30	5.30	28.09	11.34
		5.25	5.30	27.82	9.62
Phosphate Rock	L4	5.30	5.35	28.35	150.09	42.7	8.90
		5.30	5.40	28.62	137.34
	L5	5.30	5.35	28.35	126.22
		5.30	5.32	28.20	64.62
	L6	5.35	5.38	28.78	87.76
		5.35	5.35	28.62	71.57
Sandstone	S1	5.30	5.30	28.09	69.59	41.3	6.09
		5.28	5.25	27.72	88.51
	S2	5.32	5.30	28.20	50.35
		5.30	5.32	28.20	44.73
	S3	5.32	5.32	28.30	20.16
		5.32	5.32	28.30	27.54
		5.28	5.25	27.72	88.51
	S2	5.32	5.30	28.20	50.35
		5.30	5.32	28.20	44.73
	S3	5.32	5.32	28.30	20.16
		5.32	5.32	28.30	27.54

.

3.6. GNSS Monitoring Setting

The GNSS monitoring system delivers high-precision positioning performance with a static accuracy of 2.5 mm ± 0.5 ppm horizontally and 5 mm ± 0.5 ppm vertically, while dynamic operation maintains 8 mm ± 0.8 ppm horizontal and 15 mm ± 0.5 ppm vertical accuracy. Featuring rapid cold starts (<30 s) and hot starts (<15 s typical), the 965-channel receiver supports BDS + GPS dual-system quad-frequency operation with dynamic frequency adjustment and MEMS sensor triggering. Its flexible data sampling intervals (1 s–60 s) are configurable both locally and via cloud platform, which also enables comprehensive remote management including time calibration, threshold setting, real-time status monitoring, and device rebooting. The system operates at low power (≤2 W average consumption) with robust IP68 protection and exceptional reliability (MTBF ≥ 60,000 h). Advanced features include threshold-triggered data collection, self-diagnostic functions (voltage/battery monitoring), power-loss data protection, and automatic data recovery. Rigorously tested, the device withstands 1.2 m drops per GB/T2423.8-1995 standards [41] without damage. The distribution of GNSS observation points denoted as “BW-” is shown in Figure 2. Given the large amount of GNSS real-time data, this paper provides examples of partial data, as detailed in

Table A11. Part of GNSS data.

Point	∆X	∆Y	∆Z	∑X	∑Y	∑Z	Time
BW12	−0.22	−0.24	−0.66	−0.143	3.327	0.55	2024/11/3 0:00
BW06	−0.45	−0.43	−1.24	−0.113	3.932	1.072	2024/11/3 0:00
BW07	0.92	−0.84	−1.87	−1.198	5.475	3.994	2024/11/3 0:00
BW11	0.03	−0.63	−1.04	−0.488	3.899	1.825	2024/11/3 0:00
BW10	1.21	−0.33	−2.71	−1.809	5.85	4.346	2024/11/3 0:00
BW04	1.34	−0.51	−1.82	−0.672	4.316	4.077	2024/11/3 0:00
BW09	−0.12	−0.54	−0.46	0.472	1.437	−0.249	2024/11/3 0:00
BW13	0.35	−2.3	−1.39	3.166	9.144	4.517	2024/11/3 0:00
BW15	−0.59	−0.62	−0.13	0.408	2.189	−0.249	2024/11/3 0:00
BW05	0.56	−0.87	−1.44	−0.667	3.718	2.626	2024/11/3 0:00
BW23	−0.53	−0.83	−0.51	1.545	0.357	−0.84	2024/11/3 0:00
BW01	−0.25	−0.73	−0.46	0.743	2.218	0.208	2024/11/3 0:00
BW02	1.06	−0.41	−2.98	−3.344	8.604	6.217	2024/11/3 0:00
BW22	0.13	−0.2	−1.17	−0.82	2.159	1.719	2024/11/3 0:00
BW03	−0.27	−1.15	−1.55	−0.016	3.168	0.874	2024/11/3 0:00
BW20	0.55	0.37	−2.83	−2.577	6.867	3.615	2024/11/3 0:00
BW24	−0.28	−0.44	−0.22	−0.025	0.827	0.103	2024/11/3 0:00
BW18	−0.29	0.46	−1.13	−0.74	1.301	−0.312	2024/11/3 0:00
BW16	0.64	−0.73	−0.88	−0.385	4.547	2.556	2024/11/3 0:00
BW08	0.6	−0.59	−1.99	0.065	3.708	3.298	2024/11/3 0:00
BW17	0.2	−0.1	−1.74	−1.296	5.33	2.669	2024/11/3 0:00
BW06	0.1	0.38	−0.67	−0.641	−0.938	0.1	2024/11/3 1:00
BW24	−0.15	−0.06	−0.74	−1.039	2.322	1.215	2024/11/3 1:00

.

3.7. Video Monitoring Setting

This advanced surveillance system integrates a 4MP + 4MP 25× panoramic PTZ camera with dual F1.0 large-aperture full-color lenses, delivering a 190 wide-angle stitched view for comprehensive scene coverage. The detail-view channel supports multiple intelligent modes (full capture, road monitoring, and smart events) and AR functionality—enabling real-time video annotation with up to 500 interactive AR tags. For security applications, its smart event system allows perimeter defense by triggering target tracking and alarms when intrusions are detected in predefined zones. The device features built-in audio with customizable audible alerts and strobe light warnings, plus high-efficiency IR array illumination with a 200-meter range. Compliant with GB35114 [42] encryption standards and rated IP67 for dust/water resistance, it ensures reliable operation in demanding environments. The distribution of video observation points denoted as “SP-“ is shown in Figure 3.

3.8. SAR Monitoring Setting

The SAR system operates in the Ku-band (13.5 GHz) with 0.1 m × 0.1 m resolution in spotlight mode (0.2 m × 0.2 m in strip-map mode), achieving sub-surface penetration depths of 3 m to 30 m at 0.3 m to 0.5 m vertical resolution. Its phased-array antenna enables ±45° electronic scanning with an 8 km operational range, supporting HH/VV single-pol or full-pol (HH/HV/VH/VV) imaging. The compact 160 × 162 × 114 mm unit (≤8 kg) consumes ≤300 W power across −40 °C to + 55 °C environments, while an integrated dual-frequency GNSS provides ≤10 m geo-location accuracy. Real-time capabilities include ≤0.3 m resolution orthophoto generation (3 km swath) and 5 km/h GMTI sensitivity for moving targets. Optional multi-band variants (Ku/X/L/W/Ka/P/C) extend to FMCW transmission (≤120 W) or 40 km range polarimetric detection, with all models featuring USB 3.2 data streaming (≥500 MB/s) for rapid analysis.

4. Results

4.1. Experimental Results of the Empirical Model Discrimination Method

The software and hardware configurations used in this study are provided in Appendix A.3. The specific computational results for each component will be elaborated in the following sections.

4.1.1. Calculation of Empirical Model Parameters

(1)

The classification of slope grades is detailed in

Table A9. Determination of slope grade.

Slope Location	Division Method	Grade	Remarks
Southwest Slope of First Mining Area	Slope Height Grade	Low Slope	Slope Height 79 m
	Slope Hazard Grade	I	Based on Comprehensive Mine Site Conditions, Grade I is Assigned
	Slope Engineering Safety Grade	II	Based on Comprehensive Slope Height Grade, Slope Hazard Grade and Mine Site Conditions, Grade II is Assigned
Southwest Slope of Second Mining Area	Slope Height Grade	Low Slope	Slope Height 92 m
	Slope Hazard Grade	I	Based on Comprehensive Mine Site Conditions, Grade I is Assigned
	Slope Engineering Safety Grade	II	Based on Comprehensive Slope Height Grade, Slope Hazard Grade and Mine Site Conditions, Grade II is Assigned
South Slope of Third Mining Area	Slope Height Grade	Low Slope	Slope Height 85 m
	Slope Hazard Grade	I	Based on Comprehensive Mine Site Conditions, Grade I is Assigned
	Slope Engineering Safety Grade	II	Based on Comprehensive Slope Height Grade, Slope Hazard Grade and Mine Site Conditions, Grade II is Assigned
South Slope of Fourth Mining Area	Slope Height Grade	Middle Slope	Slope Height 140 m
	Slope Hazard Grade	I	Based on Comprehensive Mine Site Conditions, Grade I is Assigned
	Slope Engineering Safety Grade	I	Based on Comprehensive Slope Height Grade, Slope Hazard Grade and Mine Site Conditions, Grade I is Assigned
Southern Area Slope	Slope Height Grade	Middle Slope	Slope Height 147 m
	Slope Hazard Grade	I	Based on Comprehensive Mine Site Conditions, Grade I is Assigned
	Slope Engineering Safety Grade	I	Based on Comprehensive Slope Height Grade, Slope Hazard Grade and Mine Site Conditions, Grade I is Assigned

. The design safety factor requirements are specified in

Table A10. Design safety factor.

Slope Area (m2)	Slope Engineering Safety Grade	Safety Factor for Slope Engineering Design
		Load Combination I	Load Combination II	Load Combination III
Southwest Slope of First Mining Area (76,497)	II	1.20–1.15	1.18–1.13	1.15–1.10
Southwest Slope of Second Mining Area (159,903)	II	1.20–1.15	1.18–1.13	1.15–1.10
South Slope of Third Mining Area (425,903)	II	1.20–1.15	1.18–1.13	1.15–1.10
South Slope of Fourth Mining Area (390,941)	I	1.25–1.20	1.23–1.18	1.20–1.15
Southern Area Slope (273,289)	I	1.25–1.20	1.23–1.18	1.20–1.15

.

(2)

Groundwater Conditions

According to the site engineering geological survey, no groundwater outcrop has been observed. Based on geological data from the mining area, such as the “Verification Report of Phosphate Resource Reserves in Haikou, Xishan District, Kunming City, Yunnan Province” (Yunnan Geological Exploration Institute of the China National Chemical Geological and Mining Bureau, January 2015), the minimum mining level of the mine is 2140 m, which is above the minimum erosion base level (2070.1 m) and the long-term groundwater level (2001.77 m to 2108.00 m). Therefore, the only factor contributing to water accumulation in the mine pit is atmospheric precipitation, and thus, the stability analysis does not consider the impact of groundwater.

(3)

Comprehensive Horizontal Seismic Coefficient

According to the “China Seismic Motion Parameter Zoning Map” (GB18306-2015 [43]), the mining area is classified as being affected by moderate to strong seismic activity, with a peak ground acceleration of 0.20 g and a basic seismic intensity of VIII. The design seismic grouping is categorized as the third group, indicating a relatively unstable area.

Based on the “Technical Specification for Slope Engineering in Buildings” (GB50330-2013 [44]), the calculated comprehensive horizontal seismic coefficient is set at 0.05.

(4)

Blasting Vibration Impact Coefficient

The calculation parameters for the blasting vibration impact coefficient refer to the “Blasting Safety Regulations” (GB6722-2014/XG1-2016 [45]) and the “Preliminary Design of the 2,000,000 Tons Per Year Mining Project of Haikou Phosphate Mine, Yunnan Phosphate Group Haikou Phosphate Industry Co., Ltd.” (Kunming Nonferrous Metallurgical Design and Research Institute Co., Ltd., Kunming, China, March 2021) for the values (

Table 1. Calculation parameters for the blast vibration impact coefficient.

Calculation Parameters	Coefficient K	Total Amount of Explosive Charge for Simultaneous Blasting Q (kg)	Safety Distance ${\mathit{R}}_{\mathit{i}}$ (m)	Coefficient $\mathit{\alpha }$
Calculation Values	250	500	60	1.5

).

Through calculation based on Equation (A19), it can be concluded that (1) when the distance from the toe of the dump site to the mining boundary is controlled at 60 m, considering a single blasting charge weight of 475 kg, the ground particle velocity is 0.1175 m/s, which is within the safe allowable standard range; (2) when the blasting charge weight is 500 kg, the ground particle velocity is 0.1202 m/s, which may have some impact on the dump slope.

To prevent the blasting from affecting the dump slope, the design production period requires that the distance from the toe of the dump site to the mining boundary be maintained above 60 m, with a maximum single charge weight not exceeding 500 kg. Therefore, in this calculation, the safe distance between the mining site and the dump site is considered to be 60 m.

The Haikou Phosphate Mine employs a medium-deep hole perforation blasting operation method. In accordance with the “Blasting Safety Regulations” (GB6722-2014/XG1-2016 [45]), the main vibration frequency is taken as 10 Hz. By substituting this into Equation (A12), the vibration acceleration can be obtained. Based on the experience of vibration measurement in open-pit mining in China, the value of $\beta$ in Equation (A12) is taken as 0.15, and the final blasting vibration influence coefficient for the Haikou Phosphate Mine is obtained as 0.012.

4.1.2. Stability Analysis Results of the Experience Model

(1)

Slope Stability Analysis of the Current Situation in the First Mining Area

With the circular sliding surface model and polyline sliding surface model, the calculated safety factors for the typical slope profile meet the regulatory requirements under different load combinations, as shown in

Table 2. Safety factor calculation results for the slope in the first mining area.

Profile	Slope Angle (°)	Slope Height (m)	Load Combination	Safety Factor				Slope Grade	Standard Required Values	Compliance with Standards
				Circular Arc Failure Analysis Method		Slip-Wedge Method
				Bishop	M-P	Bishop	M-P
I-1	36	79	I	3.175	3.167	3.006	3.110	II	1.20–1.15	Yes
			II	3.060	3.052	2.899	3.000	II	1.18–1.13	Yes
			III	2.741	2.735	2.605	2.693	II	1.15–1.10	Yes

. Overall analysis indicates that the likelihood of slope failure is relatively low.

(2)

Slope Stability Analysis of the Current Situation in the Second Mining Area

With the circular sliding surface model and polyline sliding surface model, the calculated safety factors for the typical slope profile meet the regulatory requirements under different load combinations, as shown in

Table 3. Safety factor calculation results for the slope in the second mining area.

Profile	Slope Angle (°)	Slope Height (m)	Load Combination	Safety Factor				Slope Grade	Standard Required Values	Compliance with Standards
				Circular Arc Failure Analysis Method		Slip-Wedge Method
				Bishop	M-P	Bishop	M-P
II-1	15	65	I	3.838	3.835	3.320	3.541	II	1.20–1.15	Yes
			II	3.802	3.797	3.292	3.519	II	1.18–1.13	Yes
			III	3.440	3.431	3.159	3.341	II	1.15–1.10	Yes

. Overall analysis indicates that the likelihood of slope failure is relatively low.

(3)

Slope Stability Analysis of the Current Situation in the Third Mining Area

With the circular sliding surface model and polyline sliding surface model, the calculated safety factors for each typical slope profile meet the regulatory requirements under different load combinations, as shown in

Table 4. Safety factor calculation results for the slope in the third mining area.

Profile	Slope Angle (°)	Slope Height (m)	Load Combination	Safety Factor				Slope Grade	Standard Required Values	Compliance with Standards
				Circular Arc Failure Analysis Method		Slip-Wedge Method
				Bishop	M-P	Bishop	M-P
III-1	16	86	I	2.501	2.493	2.354	2.432	II	1.20–1.15	Yes
			II	2.386	2.379	2.254	2.324	II	1.18–1.13	Yes
			III	2.077	2.074	1.971	2.034	II	1.15–1.10	Yes

. Overall analysis indicates that the likelihood of slope failure is relatively low.

(4)

Slope Stability Analysis of the Current Situation in the Fourth Mining Area

With the circular sliding surface model and polyline sliding surface model, the calculated safety factors for the typical slope profile meet the regulatory requirements under different load combinations, as shown in

Table 5. Safety factor calculation results for the slope in the fourth mining area.

Profile	Slope Angle (°)	Slope Height (m)	Load Combination	Safety Factor				Slope Grade	Standard Required Values	Compliance with Standards
				Circular Arc Failure Analysis Method		Slip-Wedge Method
				Bishop	M-P	Bishop	M-P
IV-1	22	140	I	1.861	1.857	1.774	1.813	I	1.25–1.20	Yes
			II	1.801	1.796	1.717	1.755	I	1.23–1.18	Yes
			III	1.631	1.628	1.554	1.606	I	1.20–1.15	Yes
IV-2	16	52	I	3.631	3.627	3.351	3.476	I	1.25–1.20	Yes
			II	3.567	3.563	3.298	3.418	I	1.23–1.18	Yes
			III	2.952	2.949	2.757	2.860	I	1.20–1.15	Yes

. Overall analysis indicates that the likelihood of slope failure is relatively low.

(5)

Slope Stability Analysis of the Current Situation in the Southern Area

In

Table 6. Safety factor calculation results for the slope in the southern area.

Profile	Slope Angle (°)	Slope Height (m)	Load Combination	Safety Factor				Slope Grade	Standard Required Values	Compliance with Standards
				Circular Arc Failure Analysis Method		Slip-Wedge Method
				Bishop	M-P	Bishop	M-P
V-1	16	103	I	1.688	1.688	1.477	1.537	I	1.25–1.20	Yes
			II	1.638	1.637	1.439	1.498	I	1.23–1.18	Yes
			III	1.493	1.491	1.400	1.416	I	1.20–1.15	Yes
V-2	29	122	I	1.631	1.626	1.532	1.585	I	1.25–1.20	Yes
			II	1.589	1.584	1.492	1.546	I	1.23–1.18	Yes
			III	1.467	1.463	1.379	1.432	I	1.20–1.15	Yes

, the typical block safety factor calculation results of the southern slope are presented. The calculated safety factor for the V-1 profile in the southern area is greater than the regulatory requirement under different load combinations. Similarly, the calculated safety factor for the V-2 profile is also greater than the regulatory requirement under various load combinations. Overall analysis indicates that the likelihood of slope failure is relatively low.

4.2. Stability Analysis Results of the DTM

4.2.1. Stratigraphic Model Visualization

Based on the exposed thickness and characteristics of various strata, a stratigraphic model has been constructed for the exposed Quaternary, the Lower Cambrian Qiongzhusi Formation, the Lower Cambrian Yuhu Village Formation, and the Upper Sinian Dengying Formation in the mining area. The visualizations of single strata and combined visualization of multiple strata are shown in Figure 4.

The Quaternary is widely exposed within the mining area and consists of natural sediments (clayey sand, sandy clay, and clay) as well as artificially piled materials from mining stripping operations. The artificial materials are mainly concentrated in the waste dump area within the mining zone. The planar extent of this stratigraphic model ranges from X = 546,702 m to 549,978 m and Y = 2,739,419 m to 2,743,452 m, with an elevation range of 2113 m to 2436 m. The thickness varies from several meters to several tens of meters, which is consistent with the geological reality. The Lower Cambrian Qiongzhusi Formation, primarily consisting of siltstone, is extensively exposed in the mining area. The planar extent of this stratigraphic model ranges from X = 2,742,033 m to 2,739,827 m and Y = 2,739,431 m to 2,742,784 m, with an elevation range of 2178 m to 2428 m. The exposed thickness remains relatively consistent across different mining areas. The Lower Cambrian Yuhu Village Formation exhibits a more complex lithology compared to other strata and can be divided into four lithological segments from top to bottom. In this three-dimensional geological modeling effort, segments with similar lithology have been combined and interpreted, resulting in models for the first lithological segment, second lithological segment, third lithological segment, and fourth lithological segment of the Yuhu Village Formation. The phosphorite of the first lithological segment is exposed throughout the mining area. The planar extent of this stratigraphic model ranges from X = 546,693 m to 550,218 m and Y = 2,739,420 m to 2,743,073 m, with an elevation range of 2149 m to 2394 m. The dolomite of the second lithological segment is also exposed throughout the mining area. The planar extent of this stratigraphic model ranges from X = 546,697 m to 550,137 m and Y = 2,739,421 m to 2,743,073 m, with an elevation range of 2149 m to 2401 m. The phosphorite of the third lithological segment, which serves as the primary industrial ore layer, is exposed throughout the mining area. The planar extent of this stratigraphic model ranges from X = 546,714 m to 550,180 m and Y = 2,739,422 m to 2,743,033 m, with an elevation range of 2164 m to 2404 m. The dolomite of the fourth lithological segment is also widely exposed in the mining area. The planar extent of this stratigraphic model ranges from X = 546,829 m to 550,055 m and Y = 2,739,422 m to 2,742,962 m, with an elevation range of 2176 m to 2405 m. The Upper Sinian Dengying Formation serves as the bedrock of the mining area, lying beneath the Lower Cambrian Yuhu Village Formation. This formation is uniformly exposed throughout the mining area, with a planar extent ranging from X = 546,663 m to 550,294 m and Y = 2,739,414 m to 2,743,489 m. It is noted as the thickest exposed layer within the mining area. From the composite diagram of each rock layer model shown in Figure 4, it can be observed that the overall strike of the strata within the mining area has the strike ≈ NNW–SSE, with a dip angle of 40° SSW to 50° SSW. The Dengying Formation is characterized as the layer with the greatest thickness in the mining area, and the overall lithology of the layers presents a tendency of being thinner at the top and thicker at the bottom.

4.2.2. Overall DTM Visualization and Results

In the actual geological evolution process, fault structures often exhibit irregular shapes and discontinuities due to the influence of multiple activity phases. Additionally, the limited availability of original three-dimensional spatial data specifically describing faults increases the difficulty of studying geological structures related to faults. Therefore, when constructing a three-dimensional geological model of faults, it is essential to conduct field investigations and geological interpretations of the faults. This work has constructed models for faults that significantly impact the ore deposit, primarily focusing on the fourth mining area. The fault planes generally exhibit a parallel strike (≈NW-SE) and dip from 50° SW to 70° SW. The overall model constructed in this three-dimensional geological modeling includes surface models, rock layer models, and fault models, which can intuitively and realistically reflect the spatial relationship between the current topography and geological bodies (Figure 5). During the 30-day testing period, with $F=1$ h, the trend of changes in ${AS}_t$ was calculated in Figure 6. The values of ${AS}_t$ remained stable within [0, 0.2], with no significant trend changes observed overall, although there was considerable variation in errors. This indicates that the method proposed in this study is, in principle, viable.

5. Discussion

5.1. Critical Slip Surface Characteristics and Stability Mechanisms

The spatial variations in safety factors (SFs) reveal distinct failure mechanisms across mining zones. Zones IV-1 and V, characterized by high slopes (140–147 m), exhibited the lowest SFs due to deep-seated potential failure surfaces, where elevated normal stress amplified sensitivity to low internal friction angles (φ). Despite high cohesion, its contribution to shear strength diminished under high normal stress, reducing resistance effectiveness. Conversely, Zone III’s shallow polyline slip surfaces correlated with its poor rock mass rating (Grade IV), intersecting weak Quaternary aquifers and weathered siltstone.

5.2. Parametric Uncertainty and Sensitivity

The observed SF variations (highest in Zones I/II, lowest in IV-1/V/III) underscore the impact of material heterogeneity. Protodyakonov coefficients (3–6 for sandstone) and RMR grades (III to IV) introduced pronounced uncertainty, particularly in high-stress zones. Monte Carlo simulations confirmed that SF reliability was highly sensitive to φ uncertainty: a 10% reduction in φ decreased SF by 12–15% in Zone V, while cohesion variations had marginal impact. This aligns with Dyson and Tolooiyan’s (2020) [25] probabilistic analyses, highlighting the dominance of frictional properties in steep slopes. Differences between circular (8–14% higher SFs) and polyline models further emphasized model-dependent uncertainties in normal stress distribution.

5.3. Temporal Dynamics from Integrated Monitoring

The convex hull-displacement algorithm’s resolution trade-off (global: 1–5 m; sensitive areas: 0.1–0.3 m) enabled efficient identification of critical zones. Displacement trends from integrated monitoring revealed seasonal SF reductions (±7%) in Zone V, tightly coupled (r² = 0.85) with pore pressure cycles during rainfall. This validated the mechanistic trade-off where pore pressure diminished the advantage of high cohesion while amplifying low φ impacts. Zone IV-1 exhibited displacement transients post-precipitation, suggesting progressive failure despite “stable” static SFs. Kalman filtering mitigated SAR noise, but 68% of major displacement events occurred when φ-dependent strength was seasonally minimized, underscoring the necessity of dynamic monitoring for early warning.

5.4. Geomechanical Implications of Stratigraphic Heterogeneity

The lithological layering (e.g., Quaternary sediments overlying dense dolomite) created distinct failure interfaces. Zone IV-1′s weak sediments acted as sliding planes, while the Dengying Formation’s thickness provided basal stability but was offset by fault-induced anisotropy (NNW–NNE strike). The proposed framework’s ability to capture these interactions—through fused SAR–GNSS–vision data—advances upon Gupta et al.′s (2021) [4] call for multi-source validation in slope stability analysis.

5.5. Limitations and Future Work

While the convex hull algorithm reduced computational costs by ~40%, its resolution loss in non-sensitive areas may obscure localized deformations. Future studies could integrate AI-based feature refinement (e.g., Gao and Ge, 2023 [18]) to enhance resolution. Additionally, the empirical model’s reliance on fixed-factor methods (Bishop/M-P) could be expanded to incorporate probabilistic analyses (e.g., Dai et al., 2020 [24]) for uncertainty quantification.

6. Conclusions

In this study, we addressed the slope stability issue of the Haikou Phosphate Mine by proposing an empirical model combining the Bishop method and the M-P method, as well as a real-time three-dimensional monitoring method based on SAR, machine vision, and GNSS technology. Relevant geological parameters were obtained through geological sampling, and these parameters were used to calculate the safety factors. The calculation results showed that the safety factors of all five cross-sections were higher than the specified safety standards, with the highest reaching 1.75 and the lowest at 1.35. This result indicates that under the current mining conditions, the slope stability of the Haikou Phosphate Mine is generally good, meeting the requirements for production and environmental safety. Additionally, through the real-time monitoring of the DTM using SAR, machine vision, and GNSS technology, we found that the AS value between key peak points remained stable between 0.02 and 0.16. This stability result suggests that, excluding the influence of errors, the dynamic stability of the Haikou Phosphate Mine slope is high, and it is not prone to landslides or other disasters. Under these geological conditions, the calculated safety factor for slope stability is relatively high, and the possible reasons may include the following:

(1)

Gentle and symmetrical anticline structure: The mining area generally exhibits a gently inclined and symmetrical anticline structure. This geological structure inherently possesses good stability. The arcuate structure of the anticline helps distribute and resist stresses on the slope, reducing the risk of slope sliding.

(2)

Consistency between the orebody (layer) and ore-bearing rock series: The basic morphology and occurrence of the orebody (layer) are consistent with the ore-bearing rock series, which means that the mechanical properties of the orebody and surrounding rocks are similar, contributing to the overall stability of the slope.

(3)

Complex morphology of the outcrop line: Although the outcrop line of the orebody (layer) presents a complex morphology due to surface weathering erosion, topographic cutting, and mining activities, these morphological changes increase the roughness of the slope surface to some extent, which helps enhance the friction between the slope and soil or rock, thereby improving slope stability.

(4)

Development of folds in the shallow outcrops of the orebody (layer): The development of folds in the shallow outcrops of the orebody (layer) increases the complexity of the orebody morphology but also provides more support points vertically along the slope, helping distribute stresses on the slope and reducing the risk of landslides.

(5)

Mechanical properties of phosphatic rock: Phosphatic rocks within the phosphorus-bearing rock series generally exhibit good mechanical properties, such as high compressive and shear strengths. These properties help resist stresses and deformations on the slope, thereby enhancing slope stability.

(6)

Impact of layered structure: The phosphorus-bearing rock series is divided into multiple layers, such as the siliceous dolomite section of the roof, the upper ore layer of phosphatic rock, etc. These layered structures form multiple potential support surfaces within the slope, contributing to increased slope stability.

However, in subsequent research, this method can still be further optimized in terms of the empirical model by integrating various data sources, such as geological exploration data, meteorological data, and historical landslide records, to enhance the accuracy and generalization ability of the model. Addressing the limitations of the Bishop method (such as not considering the vertical shear force between slices), one can explore its integration with other limit equilibrium methods to form a more comprehensive slope stability analysis system.