Slope Deformation Mechanisms and Stability Assessment under Varied Conditions in an Iron Mine Waste Dump

Abstract

The instability of geological slopes in mining environments poses a significant challenge to the safety and efficiency of operations. Waste Dump#2 at the Ziluoyi Iron Mine in China is a notable case study that highlights the challenges associated with sizable base slopes and large step heights. To address hidden hazards in the mine and the above issues, an inclusive investigation is carried out to examine the physical and mechanical properties of the soil–rock slope through indoor testing and analyze the deformation mechanisms of the slope using numerical simulations, taking various factors into account. The study reveals that the stability of Waste Dump#2 is deeply affected by weight, groundwater conditions, earthquake loading, and rainfall. To this end, the cohesion and internal friction parameters of the soil–rock slope are first determined through direct shear tests, which show a cohesion of 6.215 kPa at the top of the slope and an internal friction angle of 34.12°. By adopting GEO-SLOPE, 3D Mine, and AutoCAD software, stability calculations of the slope are performed, which give stability coefficients of 1.547 under normal conditions, 1.276 in rainfall, and 1.352 in seismic conditions. These results meet safety standards and ensure the safe and efficient operation of the mine.

1. Introduction

With the continued expansion of open-pit mining operations, excavation depths have gradually deepened, leading to the creation of many distinct topographical features in the form of excavations in mining sites. These excavations continue up to several hundred meters in terms of the slope height of the mine. The existence of such mining slopes poses significant challenges, as their excessive deformations can lead to slope instability and, in extreme cases, geological disasters, which remarkably affect the safety and economic aspects of mining operations [1].

Slope stability analyses mainly use quantitative and qualitative approaches [2], because both aspects affect slope stability. Qualitative analysis requires a comprehensive assessment of the various factors influencing slope instability, allowing rapid assessment of slope stability and future trends. Qualitative factors include aspects such as the failure pattern exhibited by the slope, structural characteristics of rock and soil mass, joint conditions, rock properties, groundwater, and qualitative classification of rock and soil mass [3]. Commonly, quantitative methods rely on precise mathematical or numerical models, including limit equilibrium, finite element, finite difference, and discrete element approaches. The geomechanical and geological factors associated with the quantitative analyses include parameters such as rock cohesion, internal friction angles, slope height, pore water pressure, slope angle, and unit weight of rock and soil, among others [4,5]. The limit equilibrium method (LEM) is often employed in quantitative analysis because it provides a convenient approach to calculating slope safety factors using available data. The LEM is a simple but potentially powerful approach, whose reliability depends on how the input data implemented in the modeling have been derived and selected, as well as the way in which the LEM analysis is employed [6]. However, it should be noted that despite the widespread acceptance of the LEM as the theoretical basis for various assumptions underlying analytical theories and methods, slope stability analyses do not consistently yield the same results in terms of accuracy [7,8]. The choice of slope stability analysis methods depends on several factors such as the level of detail required, data availability, and available resources. In general, a combination of quantitative and qualitative factors is employed for the slope stability analysis, providing a more comprehensive assessment [9,10].

Until now, many research works have been devoted to addressing the challenge of mine slope stability. For instance, Yuan et al. [11] used the finite element method as well as the discrete element method to analyze the stability of three distinct rock slopes and determine the safety factor of the slope section. Rui [12] introduced a computer-based approach for stability analysis of complex soil slopes. A C++ language code was developed to perform stability analysis of complex soil slopes, which led to a gradual enhancement of the accuracy of slope calculations. Yu et al. [13] proposed a numerical simulation approach to evaluate the stability of roadway slopes via ADINA finite element analysis software. The analysis of calculated results revealed that the approach employed to assess slope stability was both simpler and more reasonable in determining highway slope stability. Sun et al. [14] developed a comprehensive fuzzy assessment and analysis model of slope stability and determined its classification index. The obtained results indicated that the model can evaluate regional slope stability and the evaluation results are reasonable. Yin et al. [15] used a combination of numerical simulation, slope ratio method, and other methods to evaluate slope stability, especially for artificial slopes that combine soil and rock. Xie et al. [16] employed Midas GTS 3D software, a finite element-based package, to construct an appropriate complex 3D geological model of slope topography, internal fault, and weak slope structural plane. By taking specific treatments, they were able to overcome the complex geological modeling of the slope such that the software calculation results were reasonably realistic and could provide a useful reference for slope engineering. Guo et al. [17] analyzed the primary factors affecting the stability of the open slope and established the GM (1, N) model based on the Xingshan open-pit design and provided an effective approach to evaluate the stability of the open-pit slope. Guanhua [18] assessed the stability coefficient of stepped slopes in inhomogeneous and anisotropic soils based on the limit analysis methodology as well as the strength reduction method and showed a noticeable effect of the ratio of slope width to slope height (B/H) on the slope stability. Li et al. [19] proposed a simplified method considering the inhomogeneous shear strength of the soil to evaluate slope stability, complementing the existing evaluations of undrained and unreinforced clay slopes. Huang et al. [20] developed a novel methodology to evaluate the three-dimensional stability of frame beam anchor plate (FBAP)-reinforced unsaturated soil slopes, which exhibited a noteworthy improvement in slope stability of about 29–52% using FBAP. Shu et al. [21] proposed a three-dimensional approach that was fully capable of considering the spatial variations of soil properties. The developed approach relied on the plastic limit analysis upper-bound theorem. The obtained results emphasized the substantial influence of nonstationarity and coefficient of shear strength variation on the slope damage width, while also highlighting the linkage among the failure mechanisms, slope inclination, and soil strength.

In addition, Li et al. [22] investigated the stress distribution, strain characteristics, and stability of a 30 m loess slope with a 45° inclination subjected to the action of a power transmission tower. Their findings highlighted that the stability is essentially influenced by factors such as the initial stress state, elastic modulus, Poisson’s ratio, strength, and shape, as well as the structure and load conditions. Ma et al. [23] implemented the finite difference approach and the unified strength theory to analyze the influence of intermediate principal stress on slope stability. The results revealed that the effect of intermediate principal stress on the slope stability in the presence of the joint flow and non-joint flow conditions was equivalent. Zhang et al. [24] considered five slope models with different slope shapes and performed the time-history analysis based on the Newmark scheme to assess the seismic stability of the established slope models with various amplitudes. The results indicated that the orders of seismic stability of slopes with different shapes subjected to identical amplitudes were almost broken line slope, concave slope, linear slope, broken line slope, and convex slope from high to low. Gasmo et al. [25] implemented a numerical model to study the effect of rainfall intensity on slope infiltration and the consequential effect on slope stability, indicating that the infiltration was the highest at the top of the slope. Wang et al. [26] developed a three-dimensional slope stress calculation model and examined the effect of seepage and tailings pressure on slope stability. The results showed that tailings pressure increases the safety factor of the slope stability, while seepage incorporates into the reduction of its safety factor. Liu et al. [27] established a bedding rock slope model by FLAC3D and evaluated its dynamic stability via the quasi-static method, dynamic time history method, and dynamic strength reduction method. The achieved results indicated that the slope stability lessens with the increase in the rock layer inclination and slope angle. Jiang and Zhang [28] utilized the strength reduction method to adjust the elastic parameters to calculate the slope stability. The numerical results indicate that adjusting the elastic parameters has little effect on the stability, but the influence on the slope displacement is more apparent. Xu and Yang [29] calculated the three-dimensional static and seismic stability of a heterogeneous soil slope based on the limit analysis method and the results showed that the triangular distribution pattern had the best effect on strengthening the slope stability followed by the uniform distribution pattern and upwardly strong triangular distribution pattern. Kang et al. [30] employed the generalized Hoek-Brown criterion to evaluate the slope stability of the Chaarat gold mine project, and the results showed that the slope stability is mostly affected by the change of the geological strength index related to the scale effect. Zhao and Jia [31] deeply investigated the change law of the safety factor of slope stability subjected to fluctuating water level conditions, and the results showed that the safety factor of slope stability increases with the rise of water level. Wang et al. [32] introduced the transient saturation-unsaturated seepage states to the finite element-based model to examine the effect of rainfall intensity on slope stability. The achieved results from the research indicated that the intensity of rainfall has little effect on slope stability within 6 h after the rainfall. If the rainfall intensity becomes low, the slope safety factor would be relatively high and vice versa. By combining the finite element method and the shear strength reduction method, Yang [33] proceeded with examining the effect of the initial gravity field on the slope stability analysis as a function of slope height, slope angle, and soil bulk density. The calculation results revealed that the initial gravity field has a great impact on the slope displacement and shear stress, but it almost exhibits no relationship with the slope height, slope angle, or soil bulk density and thereby has little effect on the slope stability safety factor.

Most of the above-mentioned research works were limited to two-dimensional analyses. To generalize the investigation of the problem, Han et al. [34] proposed a slope stability methodology for anisotropic and heterogeneous slopes in the presence of three-dimensional loading conditions according to the upper bound theorem of the limit analysis method, and the results showed that this method is suitable for pure cohesive soil treatment and frictional cohesive soil, isotropic and anisotropic, homogeneous and heterogeneous, loaded and unloaded. Xiao et al. [35] developed a numerical model for slope stability analysis via Midas/GTS to examine the changing trend of loose bulk accumulation on the base slope safety factor, indicating that the upper and lower slopes change respectively. The simulation results compared the effect of slope deformation with the upper slope safety factor. The deformation of the slope also led to the reduction of the slope safety factor, which is more obvious. Sun et al. [36] established a novel slope analysis model (Y-slope W) to assess the stability of the reservoir slope in the presence of the water-rock coupling effect, and the results showed that the fluctuation of the reservoir water level has a remarkable influence on the slope stability, and rapid drawdown is the most unfavorable conditions for slope stability. Rajabian and Shukla [37] established an analytical expression based on the friction circle method by which the safety factor of anchor-reinforced slopes can be predicted via Taylor stability diagrams. A comparison between the factor of safety estimated by the Taylor diagrams and that of the limit equilibrium method using SLIDE indicated a reasonably good agreement between them. Zou et al. [38] applied particle swarm optimization (PSO) as a method for inverting the mechanical parameters of the bank slope. Subsequently, a real-time stability analysis approach was developed to provide high accuracy using constant observed displacements. The results indicated that the PSO effectively retrieves mechanical factors and predicts slope stability in real-time via a combination of observed displacements and numerical simulations.

The body of knowledge in this field has shown that slope instability usually occurs in specific geological contexts and is often caused by various factors, including heavy rainfall and seismic activity. For example, rainfall is able to affect factors such as soil suction, groundwater levels, soil strength, and surface erosion, as well as the interactions among the slope, vegetation, and atmosphere to rule and control the stress-strain state in the slope [39], which ultimately contribute to slope instability. Likewise, the forces generated by the earthquake loading are able to cause landslides [40,41]. In light of these challenges, our study focuses on developing a comprehensive methodology to examine the stability of deep open-pit mine slopes under various conditions, including normal circumstances, rainfall events, and seismic scenarios. Our approach involves integrating the limit equilibrium analysis method with GeoStudio 2021.4, 3D Mine 2023.06, and AutoCAD 2020 software. The accuracy of these calculations is critical in reducing slope failures, which is capable of resulting in noticeable costs and safety risks. A case study conducted on the Waste Dump#2 of Ziluoyi Iron Mine serves as a practical application of our approach. Through this case study, we performed a detailed stability analysis of a Waste Dump#2 slope, elucidated the instability mechanism, and identified the key influencing factors. Furthermore, our research attempts to fill the current gap in slope stability analysis by providing a comprehensive method that considers the influence of geological and environmental factors.

2. Experiments and Methods

The mining method of Ziluoyi Iron Mine of Xinjiang Congling Energy Co., Ltd. follows an open-pit approach. The slope height of the existing station varies in the range of 100 and 200 m, while there are two abandoned waste dumps, each between 100 and 200 m high. In addition, the eastern dry selection station waste dump has a height of 78 m. To proactively mitigate safety risks and prevent incidents that could jeopardize the well-being of teams and mining enterprises, we conducted a stability analysis for Waste Dump#2 (see Figure 1). This analysis was carried out with the aim of clarifying the instability mechanisms and factors affecting the slope stability, thereby ensuring the safe and efficient operation of the mine.

In the inner part of the mining area, the layer structure and hydrogeological conditions are simple, and the hydrologic type in this area is mainly characterized by deep bedrock fracture water. The surface lithology is mostly gravel and bedrock, affected by topography and landform. Atmospheric precipitation and other main recharge cannot constitute the formation conditions of groundwater, and no groundwater was found during the investigation.

A section for our analysis was considered along the direction of material discharge within Waste Dump#2, which provides the profile shape illustrated in Figure 1. The height of the slope is 159 m, with an average slope angle of 30° and an average base angle of 25°.

2.1. Sampling Preparation and Pretesting

Evaluation of both the soil mechanical properties and the strength parameters serves as a basis for establishing effective slope control measures. To determine the strength of the soil in the slope under study and to obtain a comprehensive understanding of the mechanical properties of the soil in Waste Dump#2, representative soil samples were collected at the site. After that, various mechanical properties, including the shear strength, internal friction angle, and cohesion, were evaluated through laboratory tests.

Both the surface disturbance and in-depth soil sampling approaches were employed to collect samples. The samples were collected from the location shown in Figure 2a, i.e., the bottom and top of Waste Dump#2 (No. PTC-2-1). After collecting the samples, each soil sample was quickly sealed with plastic film and labeled with the necessary details, including the soil layer position, sample serial number, sampling location, and depth.

Soil samples were set aside for particle analysis, while the rest were sieved using a 5 mm sieve. The obtained results for the particle size distribution of both the dry and wet soil samples taken from the bottom and top of Waste Dump#2 are demonstrated in Figure 3. Additionally, our further analyses on the dry and wet samples led to the following results for the percentage values of gravel, sand, silt, and clay for the bottom and top samples taken, as presented in

Table 1. Percentages of various main ingredients of soil in the tested samples.

Samples from Waste Dump#2	Gravel (2 mm–76.2 mm)		Sand (0.075 mm–2 mm)		Silt and Clay (<0.075 mm)
	Wash Sieving (%)	Dry Sieving (%)	Wash Sieving (%)	Dry Sieving (%)	Wash Sieving (%)	Dry Sieving (%)
Bottom	33.5	41.3	53.2	57.7	13.8	1.5
Top	43.7	75.8	46.3	24.7	10.7	0.8

.

In addition, some samples sieved through a 2 mm sieve were selected for direct shear testing, as indicated in Figure 2b.

2.2. Experimental Procedure

The experimental approach employed in the present investigation includes direct shear tests, as presented in Figure 2c. A representative air-dried sample, passed through a sieve with a 2 mm hole, exhibited a mass of 1200 g. The amount of air-dried sand required for each sample was measured based on the specific dry density, with an accuracy of 0.1 g. Four samples were selected for each group of tests, and shear tests were performed in the presence of vertical pressures of 100, 200, 300, and 400 kPa, respectively. The test was carried out by starting the stopwatch and performing shear at a speed of 0.8 mm/min to 1.2 mm/min. The runner rotated at a constant speed of 4 to 6 rpm. The samples were subjected to shear damage within 3 to 5 min as the shear deformation reached 4 mm. If the shear stress reading continued to increase, the shear deformation would reach 6 mm with each turn of the wheel. The load sensor or dynamometer reading was measured along with the vertical displacement reading if needed until the shear failure occurred. The shear stress and shear displacement for each sample can be calculated by utilizing Equations (1) and (2):

$$\tau =CR,$$

(1)

$$\Delta L=\Delta L^{\prime }\left(n-R\right).$$

(2)

$\tau$—shear stress (unit: kPa);

$\Delta L$—shear displacement (unit: 0.01 mm);

$C$—calibration coefficient of the measuring force of the ring (unit: kPa/0.01 mm);

$R$—the measuring force ring micrometer reading (unit: 0.01 mm);

$\Delta L’$—the shear displacement of the rotating wheel to turn a revolution (unit: 0.001 mm);

$n$—the number of revolutions of the rotating wheel.

By plotting the τ − ∆L relationship curve, the peak value or stable value on the curve of shear stress (τ) as a function of the shear displacement (ΔL) is selected as the shear strength of soil (${\tau }_f$).

By depicting the τ − σ relationship curve, the cohesion (c) and the internal friction angle (φ) are obtained according to the τ − σ relation curve.

The experimental instruments and pieces of equipment for sample testing are provided in

Table 2. Experimental instruments and pieces of equipment.

Instrument	Model and Main Parameter	Manufacturer
New Standard Soil Sieve	N.A.	China Beijing Zhongjiao Jianyi Technology Development Co., Ltd.
Electronic Balance	BSA224S	China Shenzhen Xinlangpu Electronic Technology Co., Ltd.
Strain-controlled Straight Shears (Quadruple Shears)	ZJ	China Nanjing Soil Instrument Factory Co., Ltd.

.

2.3. Theoretical Foundation

The waste dump classification criteria are detailed in

Table 3. Classification of waste dumps in terms of volume and height [42].

Waste Dump Grade	Total Volume of a Single Waste Dump (×104 m3)	Stacking Height (m)
Level 1	V ≥ 10,000	H ≥ 150
Level 2	2000 ≤ V < 10,000	100 ≤ H < 150
Level 3	500 ≤ V < 2000	50 ≤ H < 100
Level 4	V < 500	H < 50

(“Standard for waste dump design of nonferrous metal mines” (China National Standard, GB50421-2018)) [42], which presents the waste grading scale. In cases where the main slope of the waste dump exceeded 24°, the waste grade was set at a higher level. In evaluating the stability of the waste dump slope, three distinct working conditions were considered, as depicted in Figure 4.

In the present investigation, a limit equilibrium analysis was meticulously conducted to assess the slope stability. For a simple circular sliding surface, the fundamental principle of such a concept in conjunction with the Bishop–Morgenstern approach is briefly outlined later (see Figure 5).

Assuming that the whole slope is a homogeneous medium and the shear strength obeys the Mohr–Coulomb criterion:

$${\tau }_f=c’+\sigma ’\tan \phi ’,$$

(3)

where $c’$ represents the effective cohesion of the medium, $\phi ’$ is the effective internal friction angle of the medium, and $\sigma ’$ denotes the effective normal stress on the shear surface.

In the case of considering a circular sliding surface, the safety factor associated with each arc can be simply calculated as follows. Let us divide the sliding body into N vertical bars, assuming that there are no interaction forces between each two adjacent bars [43]. According to the equilibrium scheme used for the arc plane (hereinafter referred to as the equilibrium of forces), we employ Bishop’s simplified method of slices based on the Morgenstern approach, the so-called Bishop–Morgenstern (B-M) solution [38], to assess the factor of safety of the waste dump slope. By this virtue, the factor of safety for circular sliding surfaces can be readily calculated as:

$$F_s=\frac{M_r}{M_0}=\frac{{{\displaystyle \sum }}_{i=1}^N\left(c^{\prime }\mathsf{\Delta }{L}_i+\left(W_i\cos {\alpha }_i-u_i\mathsf{\Delta }{L}_i\right)\tan {\phi }^{\prime } \right)}{{{\displaystyle \sum }}_{i=1}^N{W}_i\sin {\alpha }_i},$$

(4)

where $\mathsf{\Delta }{L}_i$ represents the arc length of the shear surface of the i-th block,$W_i$ is the weight of the i-th block, u_i is the pore pressure of the i-th block,${\alpha }_i$ denotes the angle between the shear surface of the i-th block and the horizontal surface, M_r is the resistance moment, and M_o denotes the overturning moment.

The above explanations aim to provide a simple pictorial vision of our numerical analysis of safety factors of slopes with circular sliding surfaces. However, to investigate slope stability for general sliding surfaces (i.e., non-circular) and arrive at more rational results, we also utilize the Morgenstern–Price (M–P) method whose wide analytical formulations and corresponding details have been not provided here for the purpose of conciseness.

2.4. Software Selection

This study has been conducted by using a combination of GEO-SLOPE, 3D Mine, and AutoCAD software to assess slope stability. The specific calculation steps are illustrated in Figure 6.

To establish safety and stability standards, the determination takes into account the waste dump grade and the calculated working conditions. Under normal conditions, general safety and stability standards for waste dumps should follow the guidelines specified in

Table 4. Safety factor reserve standard for various grades [42].

Waste Dump Grade	Safety Factor Reserve Standard
Level 1	1.25~1.30
Level 2	1.20~1.25
Level 3	1.15~1.20
Level 4	1.15
Notes: Under rainfall conditions, the integral safety standard of the waste dump can be reduced by 0.05 based on the provisions of this code table, but the minimum safety factor shall not be less than 1.10. Under seismic conditions, the integral safety standard of the waste dump can be reduced by 0.05~0.10 based on the provisions of this code table, but the minimum safety factor shall not be less than 1.10.

(“Standard for waste dump design of nonferrous metal mines” (China National Standard, GB50421-2018)) [42].

A general discussion on the failure process of the slopes with granular materials, including temporal and spatial failures, has been now provided in Appendix A and Appendix B.

3. Results and Discussion

3.1. Direct Shear Test Results

Soil samples for the direct shear test were selected from the top of the slope of Waste Dump#2. Comparative tests were performed on various samples in the presence of various vertical pressures. To this end, 12 representative soil samples were selected and divided into three groups (specified by PTC-2-1-1, PTC-2-1-2, and PTC-2-1-3), and four samples were taken from each group. The shear tests of various soil groups were performed under vertical pressures of 100, 200, 300, and 400 kPa.

Figure 7 and Figure 8 illustrate the τ − ∆L and the τ-σ relationship curves obtained by direct shear test and numerical simulation, respectively. From the τ − ∆L relationship curves, it can be seen that the shear strength of different samples changes slightly with the increase of vertical pressure in the initial stage of loading. With continuous loading, especially at the end of the loading period, the shear strength of the specimen increases obviously with the growth of the vertical pressure. According to the τ-σ relationship plots, it can be seen that the stress–strain curves measured by each sample have similar change laws and all of them vary linearly. According to the direct shear test results, the cohesion of Waste Dump#2 is in the range of 4.15–7.40 kPa, and the internal friction angle is placed in the interval of 31.20°–36.95°.

The slope stratigraphy consists of quartz schist and discharged material and is reported as calculated using the RMR engineering rock evaluation method and the Hoek–Brown criterion. The finalized quartz schist has a bulk density of 26.0 kN/m³, cohesion of 530 kPa, and an internal friction angle of 15.0°. The discharged material has a bulk dry density of 11.23 kN/m³, an average cohesive force of 6.215 kPa, and an average angle of internal friction of 34.12°.

In addition, the average natural moisture content and the specific gravity of the materials of Waste Dump#2 from the performed tests are obtained as: w = 0.34 and Gs = 2.247. Therefore, the void ratio can be calculated as e = 0.963, and the wet and saturated unit weights can be rationally estimated by: $\gamma ={\gamma }_d\left(1+w\right)=11.23\left(1+0.34\right)=15.048$ kN/m³ and ${\gamma }_{sat}={\gamma }_d+\left(\frac{e}{1+e}\right){\gamma }_w=11.23+\left(\frac{0.963}{1+0.963}\right)\times 9.81=16.043$ kN/m³.

3.2. Evaluation of the Waste Dump Slope Stability

Let us consider Waste Dump#2 with a height of 159 m; the slope angle is 25°, and the degree of waste dump is Level 1. In accordance with the requirements of the standard specifications, the reserve safety factor is 1.25–1.30.

The main assumptions utilized in the stability analysis of the problem, which somehow reflects the limitations of the present study, are as follows:

• The discharge material (in our case study, Ziluoyi Iron Mine, Waste Dump#2) is both homogenous and isotropic.
• No sizeable cracks exist in the body of the discharge material.
• In the mechanical modeling of the problem, the quartz schist medium underneath the discharge material is assumed to be rigid.
• The strength of the material and the mechanical behavior of the discharge material are mainly modeled based on the Mohr–Coulomb criterion (see Equation (4)).
• The failure surface fully occurs in the discharge material, which has a lower strength than the underlying quartz schist.
• Three distinct conditions (i.e., normal, rainfall, and seismic conditions) have been considered in the stability analysis of the understudied slope and their potential interactions have been not taken into account.

The previously created two-dimensional profiles were imported into the GeoStudio software using AutoCAD, the relevant parameters were assigned to each rock layer, and the input and output of the slip surface were artificially considered to perform calculations and judge the stability of the slope.

We assume that the consisting materials of the slop are homogeneous and thereby, under steady-state conditions, the equation of water surface (H) can be expressed as: ${\nabla }^{2}H=0$. By imposing the appropriate boundary conditions at the top and bottom of the slope according to the considering rainfall, considering the groundwater surface at the bottom of the slope as the appropriate value of H at the bottom, we can easily arrive at the water profile under rainfall conditions. To analyze the water surface, we perform an analysis via GeoStudio. To examine the pseudo-static analysis of slope stability under rainfall conditions, we used B-P and M-P approaches in conjunction with the following relation to assess the slope stability of the understudied Waste Dump#2 [44]:

$$F_{rot}^{est}=A_{est}{\left[\frac{c’}{\gamma H\tan \phi ’}-\frac{{\gamma }_w{h}_p\tan {\phi }^{\prime }}{\gamma H\tan {\phi }^{\prime }}+\zeta \frac{{\gamma }_w{h}_c^{*}\tan {\phi }^b}{\gamma H\tan {\phi }^{\prime }}\right]}^{B_{est}}\tan {\phi }^{\prime }+\frac{\tan {\phi }^{\prime }}{\tan \beta },$$

(5)

where the values of A_est and B_est introduced in this relation have been defined in Ref. [44] and displayed with more details in the following section.

We perform a pseudo-static analysis to consider the effect of seismic loading on the potential stability. It should be noted that for rotational failure of the slope in the presence of seismic loading based on the pseudo-static approach, we have used the B–M and M–P methods in conjunction with the following formula to examine slope stability for unsaturated soil slopes (see Ref. [44]):

$$F_{dyn}^{rot}=A_{est}\left[1-\frac{k_h\tan \beta }{k_h+\tan \beta }\frac{60}{\beta }\right]{\left[\frac{c^{\prime }+{\gamma }_w{h}_c\tan {\phi }^b}{\gamma H\tan \phi ’}\right]}^{B_{est}}\tan {\phi }^{\prime }+\frac{1-k_h\tan \beta }{k_h+\tan \beta }\tan \phi ’,$$

(6)

where K_h represents the horizontal pseudo-static seismic coefficient.

In addition, the values of A_est and B_est can be determined from the following relations:

$$A_{est}=10.50\exp \left(-0.009\beta \right),$$

(7)

$$B_{est}=\{\begin{array}{c}0.72-3.5\times {10}^{-5}{\beta }^2+0.0031\beta ; if 0\le \frac{c’}{\gamma H\tan \phi ’}\le 1\\ 0.83-2.2\times {10}^{-5}{\beta }^2+0.0026\beta ; if 1<\frac{c’}{\gamma H\tan \phi ’}\le 3\end{array}$$

(8)

where β signifies the slope angle.

The 2000 seismic ground motion zonation map of China [45], as illustrated in Figure 9, exhibits seven levels. These are: (i) <0.05 g, (ii) 0.05 g, (iii) 0.10 g, (iv) 0.15 g, (v) 0.20 g, (vi) 0.30 g, and (vii) >0.40 g, according to the seismic peak ground acceleration (PGA) in each region and the 10% of probability of exceedance in the class (medium hard) site over 50 years.

According to the map provided in Figure 9, the PGA of the understudied site is 0.20 g. It is worth mentioning that the process of selecting an appropriate seismic coefficient is the most crucial and difficult aspect of a pseudo-static stability analysis. In theory, the values of seismic coefficients depend on the measurement of the amplitude of the inertial force that is induced in the slope by the dynamic forces generated during an earthquake. However, since soil slopes are not rigid and the peak acceleration generated during an earthquake lasts for a very short period of time, seismic coefficients used in practice generally correspond to acceleration values well below the predicted peak ground accelerations (as pointed out by Kramer [46]). Nevertheless, the choice of coefficients used in the slope stability analysis is very subjective and lacks a clear rationale.

Hynes-Griffin and Franklin [47] recommended that K_h = 0.5 × PHA, where PHA stands for the peak horizontal acceleration of the earthquake in g’s, while Corps of Engineers [48] suggested K_h = 0.1 for major earthquakes and K_h = 0.15 for great ones. Further, an investigation by Marcuson and Franklin [49] displayed the reasonable value for K_h places in the range of [PHA/3, PHA/2]. For a factor of safety values of the slope greater than 1.15, Seed [50] examined the stability of granular-based slopes and suggested the interval of [0.1–0.2] for K_h.

Based on the above research works, herein we considered the average value of the proposed interval for K_h by Marcuson and Franklin [49], namely K_h = 0.586×PHA and considering PHA = PGA/g, arriving at K_h = 0.117 by considering PHA = PGA/g. In addition, with regard to the rank of the seismic zone of the understudied location, 5 out of 7, almost indicating a major earthquake. As explained above, the suggested K_h by the Corps of Engineers [48] for earthquake levels ranging from major to great is K_h = 0.1–0.15; hence, for our study case, choosing a value closer to 0.1 would be a rational consideration. Based on these two clarifications, herein we have considered K_h = 0.12 as the coefficient of horizontal pseudo-static seismic load.

Using GEO-SLOPE 2021.4 based on the B–M and M–P methods through analyzing various sliding surfaces, the obtained safety factors’ cloud map of various slip surfaces under seismic conditions (pseudo-static seismic loading) based on the above value of K_h is presented in Figure 10.

As is seen from Figure 10, through recalculating the safety factor of the slope under seismic conditions, we can arrive at the critical value of SF = 1.352 amongst various values for different surfaces. As is seen, the predicted safety factor for the Waste Dump#2 slope under seismic conditions is about 12.6% lower than that under normal conditions, but both of them satisfy the minimum values of safety factors of “Waste Dump Grade Level 1” (i.e., 1.25~1.3) according to Table 4.

The above-provided graphs are also available for natural and rainfall conditions, which yielded SF = 1.547 and SF = 1.276, but for the sake of brevity, the corresponding graphs have been not presented here.

As illustrated in Figure 11a–c, the critical factors of safety (SFs) of Waste Dump#2 were obtained as 1.547 under normal conditions, 1.276 under rainfall conditions, and 1.352 under seismic conditions, all of which conform to the safety standard.

As our investigations were centered around the case study of Ziluoyi Iron Mine’s Waste Dump#2, we did not conduct a direct comparison study on the predicted results relevant to slope stability analysis. However, we carried out thorough indoor tests and utilized the measured geotechnical and geomechanical data to make a more accurate prediction of slope failure and stability.

3.3. Slope Problems and Control Measures

3.3.1. Disaster Prevention and Control Measures of Waste Dump#2

By examining the progressive failure mode of the slope, it was found that the slope of Waste Dump#2 in Ziluoyi Iron Mine can be essentially affected by weight, groundwater, seismicity, and rainfall, and thereby reasonable disaster prevention and suitable control measures should be provided.

• Timely mapping of the zone of sliding deformation cracks in the waste dump to master the extent of the deformation area is required. The monitoring points are set in the deformation zone to more effectively capture the deformation state of the slope. If sliding deformation appears to increase, the production operations in the deformation zone must be stopped immediately and personnel and equipment must be evacuated to a safe place.
• The top of the waste dump and safety platform is set with a 3% inward reverse slope to prevent the sloping roof from collapsing during the discharge process, which would cause personnel and vehicles to roll off. The design of the waste dump unloading platform is set up about 10 m away from the edge of the safety mine truck. The mining truck is made of piles of waste rock, and the height of the staff is 1/2 the height of the wheel platform of the vehicle.
• The cracks caused by subsidence and deformation of the waste dump should be filled and compacted in time to prevent the penetration of a large amount of rainwater and the stability of the slope. Low-lying areas formed by compaction or water should be filled in time to prevent rainwater accumulation and infiltration to form landslides.

3.3.2. Providing Instructions for Slope Displacement Monitoring of Waste Dump#2

The mine safety facility design report pointed out the need to monitor the horizontal and vertical displacement of the slope to rationally understand the slope stability. The existing mine slope monitoring approach is the traditional geodetic method and the main monitoring tool is a GTS-102 n-type total station.

Horizontal displacement observation adopts a triangulation method for observation, and the plane control grid (triangulation grid) is first established in the measurement area. The triangular grid consists of several working base points in the measurement area, and the displacement observation points around the pit are set and connected according to the spacing required by the specifications. In observation, we utilized a steel ruler or infrared range finder to measure the starting edge of the triangle along the control grid (baseline), and the total station was employed to observe the interior angle of the triangle according to the accuracy of the fourth triangular precision observation. The displacement of any point can be calculated by internally organizing the results of external observations. The base point of work on the site is determined according to the rock stability of the mining slope.

Vertical monitoring reference networks and horizontal displacement monitoring reference networks are effectively adopted for synchronized observation. The measurement of vertical settlement should be designed as a closed-level network precision measurement using the triangular elevation measurement method. The main aims are to increase the number of measurements and to optimize the leveling method to enhance the observation accuracy. The project performs external observations, as well as internal calculations and analyses based on the second-level measurement standard. Combined with the data measured by the horizontal displacement monitoring network, in order to ensure the validity and accuracy of the observation data, this allows use to observe whether the data is stable in time.

After the establishment of the vertical monitoring point, monitoring is carried out during the production period once a week, and the monitoring is encrypted if there is any abnormality in the variables. At the end of each monitoring period, monitoring records are made and if there is any abnormality, the main person should be informed immediately.

In summary, the slope monitoring tools available in the mine are single and the monitoring data are one-sided.

The slope stability of the waste dump should be monitored using a global navigation satellite system (GNSS) and real aperture radar (RAR) among others for slope surface displacements.

The working principles of RAR and GNSS are schematically presented in Figure 12.

RAR is a set of intelligent systems used to monitor slope stability in open-pit mines. It continuously and repeatedly covers a large area of the slope by transmitting high-frequency electromagnetic waves through a large dish antenna to obtain information about the displacement as well as the rate of change of the rock body in time series and 3D dynamic cloud maps that can be captured in real time. Through the 3D dynamic cloud map, the abnormal deformation area can be directly and quickly identified. The whole deformation process of the slope rock body can be dynamically tracked and monitored, and the non-contact, long-distance, wide-area, full-time, and high-precision space–time measurements can be made to achieve the purpose of accurately predicting and forecasting the geologic hazards such as slice gangs and landslides, ensuring safe production at open-pit mines.

The GNSS slope detection system mainly works through the satellite positioning system to perform comprehensive monitoring of the slope of the open-pit mine, and the system is capable of performing real-time monitoring of the monitoring points with the help of internet technology, high-precision satellite navigation, pseudo-dynamic algorithms, and other technologies in practical application. After the detailed knowledge and examination of the surrounding environment of the open-pit mine, several distinct monitoring points are set up according to the displacement monitoring network on the slope of the open-pit mine. After making sure that the monitoring points are able to realize the output of the original data of the satellite navigation, the output data information is transmitted to the data processing and control server through the wireless network. Through the server, the data changes are transformed and presented in the form of three-dimensional coordinate changes, thus real-time monitoring and management of slope monitoring points are appropriately realized.

The main advantages of the GNSS slope monitoring system in open-pit mine slope monitoring are reflected in the following aspects: First, the monitoring function can be realized without the need to pass between each GNSS station, which reduces the time and energy consumed by relevant personnel moving the station and substantially improves the application effect of the GNSS slope detection system in complex environments. Second, the GNSS system is capable of receiving data from more than 30 satellites simultaneously, ensuring the accuracy of detection results even in various harsh environmental conditions. Third, the GNSS slope monitoring system is also able to realize data acquisition, transmission, storage, interpretation, and other functions in a practical application, which is able to ensure the accuracy of the monitoring results and automate the system operation.

4. Conclusions

This study dealt with complex aspects of waste dump slope behavior in the context of an open-pit mine. The investigation essentially led to several insights into the progressive failure mode, temporal evolution, and spatial evolution of the understudied waste dump slope. Waste Dump#2, which is located at a height of 159 m and has a slope angle of 25°, is classified as Level 1 according to the waste dump grading standard outlined in GB50421-2018 “Standard for waste dump design of nonferrous metal mines” [42]. This classification is critical to determine the reserve standard of the safety factor, which according to the standard requirements is in the range of 1.25–1.30. Through an in-depth analysis of the slope behavior and slope stability analysis, the crucial obtained results can be summarized as follows:

• The direct shear tests on soil samples from Waste Dump#2 provided valuable visions into its geotechnical properties. The cohesion range was obtained in an interval of 4.15–7.40 kPa, with an internal friction angle between 31.20° and 36.95°. The average of these values, resulting in a cohesion of 6.215 kPa and an internal friction angle of 34.12°, were effectively employed in the complementary analyses.
• The slope stability assessment was carried out through numerical simulations involving various environmental conditions, including normal, rainfall, and seismic scenarios, using appropriate software and formulations in the existing literature. The results were reassuring because the actual slope stability factor of Waste Dump#2 acted upon by normal conditions was measured to be 1.547. In the presence of rainfall, this factor slightly decreased to 1.276, which is still within the safety standard. Even under seismic conditions, the slope remained stable with a safety factor of 1.352, indicating its resilience against external forces.
• Understanding the progressive failure behavior of waste dump slopes in open-pit coal mines and implementing appropriate control measures is also critical to ensure the safety of personnel, equipment, and the environment. The insights and recommendations presented in this study significantly help to improve risk management and prevent possible disasters in open-pit mining operations.

Stability analysis in geotechnical engineering is crucial for preventing unwanted consequences such as soil erosion, landslides, and other natural disasters. With the latest advancements in dataset collection as well as machine learning (ML) and artificial intelligence (AI) algorithms [51,52,53,54,55,56,57], geotechnical engineers can appropriately control these tools to enhance their slope stability optimally [58,59]. These innovative technologies allow engineers to collect and analyze large amounts of data and make more accurate predictions about the potential risks associated with a given slope in an optimal manner. As a result, the use of AI- and ML-based algorithms and dataset collection as an essential part of modern geotechnical engineering optimal practices is highly recommended for near-future research works.