The Role of LEM in Mine Slope Safety: A Pre- and Post-Blast Perspective

Abstract

Slopes are formed as a result of mining operations. These slopes are classified as artificial slopes. Improper planning of slopes can lead to instability and potentially trigger landslides. PT. Allied Indo Coal Jaya employs the open-pit mining method in its coal mining operations. Slopes are naturally formed in open-pit mines. Additionally, PT. Allied Indo Coal Jaya utilizes blasting for rock demolition. Therefore, it is crucial to assess the impact of blasting activities on slope stability. This study investigates the influence of blasting on slope stability in coal mines using the limit equilibrium method (LEM). The study evaluates the effects of factors such as ground vibration, blast distance, and blast hole count on the factor of safety (FoS) of slopes. The limit equilibrium method (Fellenius, Bishop, Janbu, Spencer, and Morgenstern-Price) is employed to determine the factor of safety. The factor of safety is modeled using RocScience SLIDE version 6.0 in this study. The factor of safety (FoS) is defined as the ratio of the stabilizing force to the destabilizing force acting on the slope. This study also models the influence of ground vibration, distance, and total number of blast holes on the factor-of-safety (FoS) value. The results indicate that the slope remains stable both pre- and post-blasting, with an overall FoS value greater than 1 for the five slopes examined using various limit equilibrium method (LEM) techniques. However, the FoS value decreased prior to blasting due to the impact of ground vibration and blast distance. It is evident that the ground vibration (PPA) increases with the number of blast holes. The amount of ground vibration decreases as the number of blast holes increases. An increased number of blast holes leads to a decrease in the FoS value. The observed decline in slope FoS values and the increase in PPAs is attributable to the growing number of blast holes. The type of explosive, along with its power and rate of detonation, influences the amount of energy produced, which in turn affects the degree of ground vibration. The findings indicate that the slopes remain stable (FoS > 1) both before and after blasting, although blasting slightly reduces the FoS. The study reveals that as the number of blast holes increases, both ground vibration (PPA) and the reduction in FoS increase, underscoring the effects of explosive power and detonation rate on slope stability.

1. Introduction

Landslides, one of the world’s most dangerous natural disasters, cause significant property damage and loss of life. Landslides pose a significant threat in many regions due to their immense potential for devastation, which is often underestimated [1]. Slopes, whether artificial or natural, are formed by mining operations. Improper planning can lead to instability [2]. Typically, when a slope fails, an analysis is conducted to determine the cause of failure. In most cases, landslide assessments are carried out after the failure has occurred [3]. To minimize rock extraction, the final slope of an open-pit mine is typically excavated to the steepest possible angle. Many modern rock engineering projects, such as open-pit mines, railroads, road cuttings, and dams, depend on these studies. Factors influencing slope stability, particularly shear strength parameters, can be difficult to identify and quantify, complicating the characterization of slope failures [4]. Slope stability remains a major challenge for engineers and workers in the fields of soil and rock science. There is significant disagreement among scientists regarding the most accurate method for calculating slope stability [5].

Blasting is a widely used method in mining operations, particularly for extracting minerals and other materials. Blasting breaks down hard materials into smaller sizes, facilitating transportation and processing. It produces materials of specific sizes, which is crucial for subsequent processing steps. Efficiency can be improved by setting specific fragment sizes. Blasting-induced vibrations may affect slope stability, and these vibrations may increase driving forces, potentially leading to landslides. One of the factors influencing the factor of safety (FoS) and slope stability is the vibration parameter from blasting. In blasting activities, blocks prone to falling, sliding, toppling, or rotating, which may cause production impairments, must be considered in the slope stability analysis of open-pit mines [6].

The blasting action during production causes minimal damage to the surrounding rock [7]. Geological and geotechnical investigations are conducted prior to blasting to identify potential hazards that could compromise slope stability. Pre-blast assessments enable better planning regarding the site, type of explosives, and blasting methods to be used. Pre- and post-blasting evaluations strengthen the foundation for factor-of-safety (FoS) change analysis and help identify potential slope stability issues. This phase is critical in proactive slope management; it is aimed at preventing accidents and ensuring the safety of blasting activities. Careful monitoring and assessment of changes in factors of safety (FoS) resulting from blasting can preserve slope stability and reduce the risk of accidents.

Stability can be affected by several factors related to the blasting pattern, including the number and distribution of holes, hole spacing, diameter and depth of the holes, blast interval, type and properties of explosives, and geological and soil or rock conditions. The rock mass in the vicinity of the blasting area is subjected to repeated blasting, inducing shear and tensile stresses. This weakens the rock mass and undermines the slope’s stability [8]. Regarding blast distance, the area near the explosion’s center is likely to experience the most structural damage [9]. Blasting energy from larger charges may increase the thrust force on the slope, reducing the safety factor. A high RQD value indicates high-quality rock, which can improve slope stability. In contrast, a low RQD value indicates a high degree of discontinuity, potentially compromising stability. A decrease in strength due to the opening or shearing of new or enlarged cracks and joints is referred to as induced damage in the rock mass [10].

Slope stability analysis is a static or dynamic procedure, either analytical or numerical, used to assess slope stability and identify the causes of slope movement or failure [2]. Several primary and widely recognized techniques for analyzing slope stability include the numerical approach, conventional methods, and limit equilibrium methodology [11]. Slope stability is currently assessed using techniques based on the theory of limit equilibrium [12]. The limit equilibrium method (LEM) is one of the most traditional and fundamental analytical techniques for slope stability assessments, owing to its ease of use, low formulation complexity, and short analysis times [13]. The stability of a slope against potential failure or landslides is determined by its factor of safety (FoS). It is defined as the ratio of the available shear strength of the soil and rock to the shear stress required to cause failure [14]. The probability that a safety factor less than one (FoS < 1) indicates instability can be used to express the findings of this two-dimensional limit equilibrium analysis. The rock mass under study remains stable under static or pseudo-static conditions if (FoS > 1) [15].

A more detailed explanation of the underlying assumptions and concepts of each limit equilibrium method (LEM) technique can be found in long-term steady-state analytical studies, which yielded comparable factor-of-safety (FoS) values of 1.92 using the LEM and 1.89 with the stress-based finite element method (FEM). Both models produce identical slip circles, resulting in comparable stress distributions. As a result, comparable FoS values are obtained [16]. A key distinction between the limit equilibrium method (LEM) and the finite element method (FEM) is the formation of local minimum failure surfaces in the LEM. The study suggests that the most effective way to assess slope stability in a multi-layered formation is to combine the FEM with the LEM [17].

Due to its efficiency in conducting rapid and straightforward evaluations, the industry has adopted the limit equilibrium method (LEM) as the standard [18]. A mathematical model based on limit equilibrium analysis has been developed to predict the behavior of slow-moving narrow-tillage tools in cohesive and frictional materials [19]. By modeling soil behavior using the limit equilibrium method, specific assumptions were made, allowing geotechnical problems to be addressed based on these assumptions. FoS values were determined by comparing the forces acting to slide down a surface with those opposing the slide, assuming that a slip circle forms on the surface [20]. In addition to advancing understanding of quarry slope stability, our research provides practical recommendations for improving the efficiency and safety of mining operations [21]. The primary objective of this study is to employ the limit equilibrium method (Fellenius, Bishop, Janbu, Spencer, and Morgenstern-Price) to assess the impact of ground vibration from blasting on the stability of the mine slope at PT. Allied Indo Coal Jaya. In addition to comparing the results of five methods, this study models the influence of ground vibration, distance, and total number of blast holes on the FoS value.

2. Geographical and Geological Setting

2.1. Geographical Setting

An open-pit mine is used by the coal mining business PT. Allied Indo Coal Jaya. On 4 April 2010, PT. Allied Indo Coal Jaya, which covers 327.40 Ha, was granted a mining business license. PT. Allied Indo Coal Jaya’s mining site is situated in Sawahlunto City, Talawi Regency, West Sumatra Province, Indonesia (Figure 1). The IUP area of PT. Allied Indo Coal Jaya is situated at 00° 35′ 34″–00° 36′ 59″ South and 100° 46′ 48″–100° 48′ 47″ East on a geographic map. The observation slope is located at an elevation of 341 m above sea level. The study area’s topography is predominantly characterized by low to steep hills, with slope angles ranging from 5° to 30°. In contrast, the slope angle in flat areas ranges from 0° to 4°. The slope of the hill ranges from 140 to 500 m above sea level. At an elevation of 500 m, the highest point of the eastern slope forms a limestone hill. The hills generally feature steep slopes, with angles ranging from 30° to 50°. The observation slope, with a height of 67 m and a slope angle of 64 degrees, is located on the central-western slope, both before and after blasting.

2.2. Geological Setting

PT. Allied Indo Coal Jaya is located in the Ombilin Basin. The Ombilin Basin, an intra-mountain basin, was formed by complex bedrock block faults near the end of the Pre-Tertiary period. The basin was formed by the active horizontal movement of the Silungkang fault, which runs parallel to the Sumatran fault system. The basin has a base of Pre-Tertiary rocks and is filled with deposits dating to the Tertiary era, with a thickness of approximately 4600 m and covering an area of about 1500 km². The Tertiary series consists of six formations: the Brani Formation, Sangkarewang Formation, Sawahlunto Formation, Sawahtambang Formation, Ombilin Formation, and Ranau Formation. The PT. Allied Indo Coal Jaya is situated in the Ombilin Formation, according to Figure 2.

The Ombilin Formation consists of members from both the upper and lower formations. PT. Allied Indo Coal Jaya is located in the Ombilin Basin, particularly in the Ombilin Formation, which was formed during the Tertiary period, primarily between the Eocene and Miocene epochs. This formation comprises several key rock units, including the following:

• Clastic sedimentary rocks, including sandstone, claystone, and siltstone, are the dominant components of these formations, formed in a deltaic to fluvial deposition environment.
• Coal: This formation is notable for its relatively thick coal seam, formed over periods of geological time as organic materials accumulated in a swampy environment.
• Minor volcanic units: Small layers of volcanic rock are deposited during volcanic eruptions.

Sandstone, coal, and siltstone from the Ombilin Formation are the dominant geological formations in the Allied Indo Coal Jaya region. This represents a comprehensive analysis of the local rock properties, given as follows:

• Sandstone: The sandstone in this area ranges from fine to coarse and is primarily composed of quartz. Clay minerals indicate prior weathering activities, and ancient river currents influenced the sedimentation patterns observed in the rock strata.
• Coal: The Ombilin Formation contains sub-bituminous to bituminous coal with medium to high carbon content. These coals exhibit good calorific values, as demonstrated by proximal and ultimate analyses, which are crucial for meeting energy sector demands.
• Siltstone: The varying thicknesses of siltstone strata, which serve as overburden rocks, are critical to mine stability and the risk of landslides.

The distribution patterns of coal are influenced by the faults and folds within the region’s geological structure. One of the primary faults affecting the mining process is the Ombilin Fault, which displaces the coal seam. Moreover, this region is a key mining target due to the presence of anticline and syncline folds, which concentrate coal deposits. As groundwater in these regions tends to follow faults and porous rock layers, mine planning must account for potential water seepage, as it may affect slope stability and mining operations.

The Sawahlunto Formation consists of coal, muddy shale, siltstone, and brownish ash shale with quartz sandstone interbeds. Shales commonly consist of mudstone or carbonaceous material. The sandstone exhibits a point-bar sequence, characterized by upward, cross, and laminated bedding, with a distinct erosional base. Occasionally, the coal seams contain embedded gray siltstones. Coal is often dispersed and surrounded by other rock layers. Sandstone, on the other hand, often forms lenticular shapes. Sandstone and coal are more commonly found in the Parambahan area, near the Tungkar Plateau.

The Sawahtambang Formation consists of interspersed and thick sandstone layers. Shale and siltstone are locally formed within these strata. Sandstone properties include angular, hard, massive texture, ranging from fine-grained to very coarse, with quartz conglomerates and pebble-sized fragments, and it varies in color from light gray to brown. Lithologically, PT. Allied Indo Coal Jaya consists of four rock types: siltstone, sandstone, claystone, and coal.

3. Materials and Methods

3.1. Laboratory Testing

Laboratory tests were conducted to evaluate the physical and mechanical properties of rocks. The physical properties include the determination of rock density, which is measured in three forms: natural density, dry density, and saturated density. The mechanical properties are assessed by testing the shear strength of the rock. In this study, siltstone is the rock tested, with five rock samples corresponding to the five slopes under analysis. The ISRM 2007 [22] Standard forms the basis for the standards used in the preparation and testing of rock density. Rocks were tested for shear strength in accordance with ASTM D 3080–11 [23]. Three samples were used to determine the normal and shear stress values for each slope. In total, 15 samples were used for the rock shear strength test.

The samples were taken from the inner field in the form of boulders. As shown in Figure 3a, a hand tool is used to prepare the sample during its initial stage. The sample, shaped like a core, was extracted using a core drill. As shown in Figure 3b, the top and bottom of the core sample are trimmed using a cutting machine in accordance with the test requirements. As shown in Figure 3c, the weight of each sample is determined by rock density testing using a digital scale. A direct shear test apparatus, shown in Figure 3d, is used to measure the cohesion and internal friction angle of rock samples in the laboratory. All test equipment used in the experiments was calibrated prior to use.

3.2. Limit Equilibrium Methods

This approach minimizes unknown forces (such as reactions, stable portions of rock masses, or forces between blocks, particularly the shear forces acting on the previously determined avalanche surface) and can be described by equilibrium equations for one or more blocks assumed to be undeformed. In this study, slope modeling is conducted using RocScience SLIDE version 6.0. The slope safety factor model is presented using five methods, namely the Fellenius method, the Bishop method, the Janbu method, the Spencer method, and the Morgenstern-Price method.

• Fellenius Method

The Fellenius approach results in a linear safety factor equation, making it the simplest of the slice methods. Using this technique, the potential sliding mass is divided into sub-vertical slices [11]. Several slices exist in the sliding mass above the failure surface [24]. These forces are typically negligible as they are parallel to the bases of each slice.

$$\mathrm{F}=(\mathrm{W} ✲ \mathrm{c}\mathrm{o}\mathrm{s}(\mathrm{\alpha }) ✲ \mathrm{t}\mathrm{a}\mathrm{n}(\mathrm{\phi })+\mathrm{c}\mathrm{L})/(\mathrm{W} ✲ \mathrm{s}\mathrm{i}\mathrm{n}(\mathrm{\alpha }\left)\right)$$

(1)

where W, L, and c are the cohesion forces. The effective angle of internal friction is represented by φ, whereas the angle formed by the tangent to the horizontal and the center of each slice’s base is represented by α. F is the force.

• Bishop Method

This method assumes that a normal or horizontal force is adequate to determine the forces between the slices, while ignoring the shear forces between them. When the surface type is circular and the failure surfaces are determined using the grid search method, the Bishop method is applied [25].

$$\mathrm{S}\mathrm{F}=(\mathrm{R}\mathrm{F}/\mathrm{D}\mathrm{F}) ✲ \mathrm{c}\mathrm{A}+(\mathrm{W} ✲ \mathrm{c}\mathrm{o}\mathrm{s}(\mathrm{\psi }\mathrm{p})-\mathrm{u}-\mathrm{v} ✲ \mathrm{s}\mathrm{i}\mathrm{n}(\mathrm{\psi }\mathrm{p}\left)\right) ✲ \mathrm{t}\mathrm{a}\mathrm{n}\left(\mathrm{\phi }\right)$$

(2)

where RF denotes the response force and SF denotes the shear force. DF represents the distance between the response force and the shear force calculation point. c represents the cohesion of the slip plane. A represents the area that slides. W represents the bulk of rock above the slip plane. Ψp represents the angle formed by the load and the horizontal axis. u represents the horizontal displacement, while v represents the vertical displacement.

• Janbu Method

This technique calculates the force between the slices by applying a correction factor. The vertical component of the interslice forces is assumed to depend on the numerical approximation of the moment equilibrium differential equation in the Janbu method [26]. Cohesion, the deep shear angle, and the failure surface are associated with this correction factor.

$$\mathrm{N}\mathrm{\gamma }=1.3(\mathrm{\gamma }/\mathrm{c}) ✲ \left(\mathrm{t}\mathrm{a}\mathrm{n}\right(\mathrm{\phi })+0.5) ✲ {(1-\mathrm{s}\mathrm{i}\mathrm{n}(\mathrm{\phi }\left)\right)}^2$$

(3)

where Nγ represents the bearing capacity factor of the cohesionless material. γ represents the unit weight of the soil. c represents the cohesion of the material, while φ represents its internal friction angle.

• Spencer Method

Additionally, this approach assumes that a relationship always exists between the shear force and the normal force between the slices. The failure surface may pass through slices determined piecewise and discretized by a predetermined number of points, with interslice forces acting at an unspecified angle [27].

$$\mathrm{N}\mathrm{\gamma }=1.3(\mathrm{\gamma }/\mathrm{c}) ✲ \left(\mathrm{t}\mathrm{a}\mathrm{n}\right(.5) ✲ {(1-\mathrm{s}\mathrm{i}\mathrm{n}(\mathrm{\phi }\left)\right)}^2 ✲ (1+0.2 ✲ (\mathrm{B}/\mathrm{D}))$$

(4)

where Nγ represents the bearing capacity factor of the cohesionless material. γ represents the unit weight of rock or soil. c represents the cohesion of the material, while φ represents its internal friction angle. B represents the width of the foundation. D represents the depth of the foundation.

• Morgenstern-Price Method

This technique defines the direction of the force between the slices by assuming an arbitrary mathematical function [28].

$$\mathrm{N}\mathrm{\gamma }=1.3(\mathrm{\gamma }/\mathrm{c}) ✲ \left(\mathrm{t}\mathrm{a}\mathrm{n}\right(\mathrm{\phi })+0.5) ✲ {(1-\mathrm{s}\mathrm{i}\mathrm{n}(\mathrm{\phi }\left)\right)}^2 ✲ (1+0.2 ✲ (\mathrm{B}/\mathrm{D}\left)\right)✲(1+0.1 ✲ (\mathrm{D}/\mathrm{B}\left)\right)$$

(5)

where Nγ represents the bearing capacity factor of the cohesionless material. γ represents the unit weight of rock or soil. c is the material’s cohesion. φ represents the internal friction angle of the material. B represents the width of the foundation. D represents the depth of the foundation.

4. Results and Discussion

Table 1. Siltstone rock density test results.

Code	Natural Density (gr/cm3)	Dry Density (gr/cm3)	Saturated Density (gr/cm3)
S1	2.609	2.597	2.644
S2	2.467	2.244	2.519
S3	2.336	2.044	2.443
S4	2.301	2.240	2.387
S5	2.207	2.105	2.269
SD	0.157	0.214	0.141
Average	2.384	2.246	2.452
Min	2.207	2.044	2.269
Max	2.609	2.597	2.644

presents the results of evaluating the natural density, dry density, and saturated density of five rock samples from each slope used to examine the physical characteristics of siltstone rocks. Among the five slope samples, the average natural density was 2.384 gr/cm³. The average dry density value was 2.246 g/cm³. Meanwhile, the average saturated density value was 2.452 g/cm³. The natural density of the five rock samples ranges from 2.207 to 2.609 g/cm³, with a standard deviation of 0.157. The dry density ranges from 2.044 to 2.597 g/cm³, with a standard deviation of 0.214. Conversely, the saturation density of the sample ranges from 2.269 to 2.644 g/cm³, with a standard deviation of 0.141. Siltstone with higher porosity has more voids, resulting in lower density. The mineral content of siltstone can influence its density. For instance, the density of siltstone increases with the proportion of denser minerals, such as quartz. The degree of cementation between silt grains also influences density. Siltstone with higher cementation levels will have greater density. Dense rocks on slopes are generally more stable because dense rocks create more friction on the underlying rock, reducing the likelihood of landslides. In slope stability studies, the relationship between density and other rock or soil characteristics is crucial. Understanding these relationships can reduce the likelihood of accidents, inform the development of safety measures, and improve predictions about slope stability. Risk management in mining and construction projects requires a data-driven approach that encompasses all of these factors.

Table 2. Siltstone rock shear strength test results.

Code	Normal Stress (kPa)	Shear Stress (kPa)	Cohesion (kPa)	Internal Friction Angle (Degree)
S1	437	414	73.77	45.71
	873	742
	1310	1309
S2	448	425	72.99	45.65
	883	752
	1332	1328
S3	459	447	54.89	45.29
	894	774
	1355	1350
S4	426	414	61.27	45.89
	872	767
	1322	1338
S5	537	525	70.17	46.00
	983	878
	1544	1560
SD	390.13	404.44	8.22	0.27
Average	911.67	868.20	66.62	45.71
Min	426.00	414.00	54.89	45.29
Max	1544.00	1560.00	73.77	46.00

presents the rock shear strength test findings. Samples S1, S2, S3, S4, and S5 were collected from every rock that makes up the slope. For every sample that was analyzed, values for normal stress and shear stress were determined.

As shown in Figure 4, each normal and shear stress in the plot is represented by a regression line. The average normal stress value for the five samples was 911.67 kPa. The typical stress value range for the five samples was 426 kPa to 1544 kPa. The average shear stress value was 868.20 kPa, within a range of 414–1560 kPa. The average cohesion value was 66.62 kPa, with a standard deviation of 8.22. The cohesion range of the five rock samples comprising the slope is 54.89–73.77 kPa. The average internal friction angle was 45.71 kPa, with a standard deviation of 0.27. The internal friction angle ranged from 45.29 to 46 kPa. The regression equation yielded the cohesion and internal friction angle values for each of the five rock samples comprising the slope, as shown in Figure 4a–e. The mechanical characteristics of siltstone can also be influenced by the distribution of its grain sizes. Finer-grained siltstone may have greater cohesion and a lower internal friction angle compared to coarser-grained siltstone. The degree of cementation between grains can also influence the mechanical characteristics of siltstone. Higher cementation levels typically result in higher cohesion and internal friction angles. The strength characteristics of siltstone can be impacted by its porosity. Higher porosity can result in reduced cohesion and internal friction angles.

The cohesion value and deep shear angle for Slope 1, as shown in Figure 4a, are c = 73.77 kPa and φ = 45.71°). Similarly, as shown in Figure 4b, φ = 45.65° and c = 72.99 kPa are found on Slope 2. Slope 3 has φ = 45.29° and c = 54.89 kPa. On Slope 4, c = 61.27 kPa and φ = 45.89° were observed. Similarly, c = 70.17 kPa and φ = 46° are found for Slope 5. Slope 1, with c = 73.77 kPa, has the greatest cohesion value among the five slopes. Meanwhile, Slope 4 has the greatest internal friction angle, φ = 45.89°. Particularly at low normal loads, the cohesion value contributes to the overall shear strength of the rock. In contrast, the high normal stress is primarily influenced by the deep shear angle. On slopes, rocks with high cohesion are typically more stable. Avalanches are less likely due to the rock’s increased resistance to shear pressures from strong particle connections. The greater the shear force the rock can withstand before a landslide occurs, the larger the deep shear angle. This suggests that rocks with larger deep shear angles are more stable on slopes.

Five slope samples were evaluated. The rocks, which are siltstone, cover the entire hillside. The siltstone boulders in the field are remnants of the overburden from coal mining. Blasting operations for overburden stripping are currently underway at PT. Allied Indo Coal Jaya. As shown in Figure 5a, Slope 1 has a slope of 64° and a slope height of 67 m. As shown in Figure 5b, Slope 2 has a slope of 59° and a slope height of 72 m. As shown in Figure 5c, Slope 3 has a slope of 64° and a slope height of 55 m. As shown in Figure 5d, Slope 4 has a slope of 64° and a slope height of 50 m. As shown in Figure 5e, Slope 5 has a slope of 64° and a slope height of 45 m. As shown in Figure 6, every slope that has been modeled has a slope of 64° and a slope height of 67 m. However, depending on the test results of each slope (from Slope 1 to Slope 5), the material properties based on the mechanical and physical testing are input. An increase in the φ value indicates higher soil resistance to friction, thereby suggesting a more stable slope. As the value of c increases, the tensile strength between slope stability and soil grains also increases [29]. It is crucial to consider the risks associated with the uncertainty in determining the rock’s strength properties, specifically the internal friction angle and cohesion [12].

In addition to causing excessive vibration and detensioning (decrease in stress) within the rock mass, a poor blasting profile can severely affect the stability of the mass. In this study, Figure 5 provides a preliminary indication that excessive vibration can impact the surrounding slopes. Strong vibrations can induce new cracks or exacerbate existing ones, ultimately weakening the strength and stability of the slope. In the field, explosives primarily damage the rock and its compressive strength parameters; when the shock wave exceeds the rock’s strength limit, the slope may collapse [30].

The explosive used in the mining activities of PT. Allied Indo Coal Jaya is Ammonium Nitrate Fuel Oil (ANFO). This explosive consists of 94.3% Ammonium Nitrate and 5.7% Fuel Oil. ANFO is commonly used in the mining industry due to its efficiency. The velocity of detonation (VoD) or the detonation velocity of ANFO is 3000 m/s. ANFO is the most practical and cost-effective method for acquiring rock and energy resources [31]. As the ANFO load increases, so does the pressure and vibration [32].

Figure 7 It provides an explanation of the blasting source and the vibration measurement’s location. STA-1, which is located at latitude coordinates 0°36′4.65″ S and longitude coordinate 100°48′16.07″ E, represents the location of explosion 1. The separation between STA-1 and the measurement point is 411.69 m. STA-2 is located 388.42 m away at latitude coordinates 0°36′3.84″ S and longitude coordinates 100°48′18.04″ E. STA-3 is located 379.64 m away at latitude coordinates 0°36′8.32″ S and longitude coordinates 100°48′28.55″ E. STA-4 is situated 500.30 m away at latitude coordinates 0°36′8.75″ S and longitude coordinates 100°48′27.19″ E. STA-5 is located 392.19 m away at latitude coordinates 0°36′8.95″ S and longitude coordinates 100°48′18.43″ E.

Table 3. Measurement of vibration due to blasting.

Code	Distance (m)	Total Holes	Actual PPV (mm/s)			SD	Frequency (Hz)	Actual PVS (mm/s)	PPA (g)
			Vertical	Longitudinal	Transverse
STA 1	411.69	210	0.018	0.008	0.016	72.805	3.455	0.255	0.016
STA 2	388.42	145	0.014	0.017	0.015	62.85	11.276	0.267	0.017
STA 3	379.64	120	0.014	0.013	0.021	70.242	7.671	0.28	0.013
STA 4	500.3	150	0.011	0.021	0.018	87.533	5.933	0.3	0.021
STA 5	392.19	260	0.068	0.06	0.059	65.879	13.51	1.081	0.06
SD	49.403	56.965	0.024	0.021	0.019	9.567	4.045	0.361	0.020
Average	414.448	177	0.025	0.024	0.026	71.862	8.369	0.437	0.025
Min	379.64	120	0.011	0.008	0.015	62.85	3.455	0.255	0.013
Max	500.3	260	0.068	0.06	0.059	87.533	13.51	1.081	0.06

explains that STA-4, which is 500.3 m away from the explosion’s source, is the location that is farthest from it. At STA-3, the closest measurement to the explosion source was made, at a distance of 379.64 m. In the meantime, STA-5 had 260 blast holes overall, which was the highest number. With only 120 holes, the STA-3 explosion has the fewest blast holes out of the five blasting activities. STA-5 had the highest PPA value ever measured, at 0.06 g. In the meantime, STA-3 had the lowest PPA value, which was 0.013 g. This number suggests that the vibration value produced increases with the number of blast holes used. Conversely, the vibration value generated decreases with increasing blast hole numbers. This designates the explosives’ use. The five blasting locations produce an average vibration of 0.025 g.

The results of applying the Fellenius approach to calculate slope safety parameters prior to blasting operations are shown in Figure 8. The slope modeled using the natural density value represents the slope under natural conditions. The lowest FoS value from the five-slope model is observed in Slope 4, which has a value of 3.246, as shown in Figure 8c. Meanwhile, Slope 5 exhibited the highest FoS value of 4.051, as shown in Figure 8e. As shown in Figure 9a–e, all slopes that experienced vibrations due to blasting exhibit a lower safety factor post-blasting. The FoS value of Slope 1 decreased from 3.711 to 3.614. The FoS value of Slope 2 decreased from 3.832 to 3.730. The FoS value of Slope 3 decreased from 3.246 to 3.180. The FoS value of Slope 4 decreased from 3.563 to 3.443. The FoS value of Slope 5 decreased from 4.051 to 3.689. Slope 5 experienced the largest drop in safety factor among the five slopes, with a difference of 0.362. This is consistent with the extensive use of blast holes on Slope 5.

Table 4. Results of slope factor of safety values for pre-blasting activities.

Code	Slope Condition	Factor of Safety (FoS) Pre-Blasting
		Fellenius	Bishop	Janbu	Spencer	Morgenstern-Price
S1	Natural	3.711	3.549	3.982	8.674	8.146
	Dry	3.723	3.56	3.997	8.181	7.968
	Saturated	3.676	3.517	3.939	8.059	7.786
S2	Natural	3.832	3.659	4.127	8.981	8.241
	Dry	4.105	3.912	4.533	9.167	8.673
	Saturated	3.775	3.607	4.059	8.314	7.739
S3	Natural	3.246	3.125	3.434	7.405	6.614
	Dry	3.562	3.411	3.81	7.787	7.789
	Saturated	3.149	3.038	3.319	6.734	5.560
S4	Natural	3.563	3.416	3.802	7.762	7.603
	Dry	3.631	3.478	3.883	8.419	7.937
	Saturated	3.472	3.334	3.694	7.602	7.528
S5	Natural	4.051	3.861	4.387	9.007	8.524
	Dry	4.193	3.993	4.637	9.952	8.872
	Saturated	3.971	3.788	4.289	9.338	8.568
SD		0.296	0.271	0.370	0.845	0.841
Average		3.711	3.550	3.993	8.359	7.837
Min		3.149	3.038	3.319	6.734	5.560
Max		4.193	3.993	4.637	9.952	8.872

displays the FoS values for the five methods examined prior to blasting. Meanwhile,

Table 5. Results of slope factor of safety values for post-blasting activities.

Code	Slope Condition	Factor of Safety (FoS) Post-Blasting
		Fellenius	Bishop	Janbu	Spencer	Morgenstern-Price
S1	Natural	3.614	3.461	3.859	6.227	6.769
	Dry	3.626	3.472	3.873	6.490	6.795
	Saturated	3.580	3.430	3.818	6.158	6.363
S2	Natural	3.730	3.566	4.000	6.726	6.809
	Dry	3.994	3.812	4.321	7.611	7.603
	Saturated	3.674	3.515	3.930	6.348	6.159
S3	Natural	3.180	3.065	3.349	5.789	5.316
	Dry	3.489	3.345	3.718	6.825	6.827
	Saturated	3.085	2.980	3.237	5.395	5.643
S4	Natural	3.443	3.307	3.647	5.344	6.117
	Dry	3.509	3.367	3.727	5.079	6.252
	Saturated	3.356	3.228	3.544	5.074	5.940
S5	Natural	3.689	3.535	3.923	4.049	4.808
	Dry	3.817	3.655	4.081	4.275	4.972
	Saturated	3.617	3.467	3.835	3.962	4.393
SD		0.233	0.213	0.274	1.078	0.886
Average		3.560	3.414	3.791	5.690	6.051
Min		3.085	2.980	3.237	3.962	4.393
Max		3.994	3.812	4.321	7.611	7.603

shows the FoS values following blasting for each of the five methods. The slopes remain in a stable state both pre- and post-blasting, as indicated by the overall FoS values, which exceed 1, for the five slopes examined using various LEM techniques. However, after the impact of ground vibrations caused by blasting, the FoS value prior to blasting (Table 4) decreased. Ground vibration generally increases with the number of blast holes used. Excessive ground vibration can disrupt material grain bonds, leading to loosening and a decrease in the material’s shear strength. Vibrations may produce fractures that weaken the slope structure by creating fissures in the rock mass. Vibration can increase pore water pressure in the material, reducing the rock’s effective strength. In conclusion, the increased number of blast holes can lower the slope’s FoS value and increase the likelihood of landslides.

The purple line in Figure 10 indicates that the FoS value obtained using the Spencer method is the highest among the five methods. Meanwhile, the Bishop method (shown by the red line) has the lowest FoS value. Figure 11 displays the FoS value after blasting. The Morgenstern-Price method yields the highest FoS value (shown by the green line). However, certain samples, such as samples 6 and 7, have FoS values lower than those determined using the Spencer method. Nevertheless, the value generally exceeds those of the alternative methods. Meanwhile, the Bishop method has the lowest FoS value after blasting. The same applies prior to blasting (red line). Compared to other methods, the Bishop method consistently yields a lower factor-of-safety (FoS) value. Numerous factors, including the type of method, the properties of the rock, the geometry of the slope, the geological structure, and the groundwater conditions, significantly impact the FoS value produced by each method.

The relationship between PPA (g), FoS, and distance (m) is demonstrated using the thin-plate spline method and the interpolation method. As illustrated in Figure 12, the recorded ground vibration increases with distance. Conversely, the recorded ground vibration decreases as the measuring distance from the source increases. Increased ground vibration reduces the slope’s FoS rating. The FoS decreases as the PPA value increases. Conversely, a lower PPA value corresponds to an increase in FoS. A bar graph illustrating the range of the ground vibration contour values is shown in the legend. Vibration intensity increases with the extent of yellowing, and the value rises correspondingly. As the vibration contour value increases, the gradation becomes more pronounced, turning dark blue.

Figure 13 shows how PPA, FoS, and total blast holes are related to each other. The PPA value (g) interval is explained by the bar graph on the legend. Evidently, the value of the ensuing ground vibration (PPA) increases with the number of blast holes. However, the amount of ground vibration generated decreases with the number of holes in the blasting. More holes in the explosion have an effect on the FoS value decreasing. Accordingly, the impact of declining slope FoS values and increasing PPAs is due to the increasing number of blast holes.

The total energy released during blasting increases with the number of blast holes used. This may result in wider and more powerful vibrations. Generally, vibration intensity decreases as the distance from the explosion site increases. Vibrational energy diminishes as distance increases due to the propagation of vibration waves. The risk of vibration-induced damage can be reduced if the structure or slope is located at a safe distance from the blast site. However, if the distance is too close, the vibrations may cause landslides, collapses, or fissures. The type of explosive, including its power and detonation rate, influences the amount of energy produced and is one of several parameters affecting the degree of ground vibration. The recorded vibration amplitude decreases as the distance from the explosion site to the measurement point increases. Ground vibrations are also influenced by geological factors; the characteristics of the surrounding rocks and soil determine how far the vibrations propagate. The vibration is also influenced by the blasting pattern, which depends on the order and duration of the blast hole activation. A limitation of this study is the lack of discussion on slope modeling considering the groundwater level conditions. The absence of monitoring well data hampers the description of piezometric line data for slopes. Additionally, the slope material properties discussed in this study are homogeneous for siltstone. The inclusion of data on the coal seam would improve the completeness of the slope modeling. Geomechanical classifications, including Rock Mass Rating (RMR), Q-System, GSI (Geological Strength Index), and Hoek-Brown Classification, are used to evaluate field parameter values and reverse analysis. A limitation of this study is that the slope model was created using data from field measurements of the slope’s dimensions and laboratory tests of rock properties, without field validation through geomechanical classification. Therefore, it is anticipated that future research will incorporate reverse analysis into the computation.

5. Conclusions

Several factors affect slope stability. These factors include slope geometry, material conditions and types, rainfall, humidity, vegetation, loads exerted on slopes, gravitational forces, geological conditions and rock structures, water pressure in the soil, and human activities. The human activity emphasized in this study is blasting. Blasting can eliminate the cohesive force in soil or rock layers, particularly if it fragments the material, as seen in mining operations. Additionally, blasting vibrations can propagate across blasting areas and slopes. If not properly managed, these shock waves can cause instability by displacing soil or creating gaps in deeper layers. These tremors can trigger landslides, particularly on slopes that are already near the stability threshold. According to the overall FoS value for the five slopes examined using various LEM techniques, the slope remains stable both before and after blasting, with a value greater than 1. However, after the impact of blasting on ground vibration, the FoS value before blasting decreased. Ground vibration generally increases with the number of blast holes used. This indicates that the FoS value obtained using the Spencer approach is the highest among the five methods. Meanwhile, the Bishop method yields the lowest FoS value. After blasting, the Morgenstern-Price approach yields the highest FoS value. However, certain samples, such as samples 6 and 7, have a lower FoS value than that determined using the Spencer approach. Still, the FoS value generally exceeds those obtained by alternative methods. Meanwhile, the Bishop approach yields the lowest FoS value after blasting. The same holds true before blasting. Compared to other methods, the Bishop method consistently yields a lower factor-of-safety (FoS) value. Numerous factors, including the procedure type, rock properties, slope geometry, geological structure, and groundwater conditions, significantly impact the FoS value produced by a method.

The distance from the blast source significantly impacts vibration, as the intensity of vibration decreases with increasing distance from the source. Even with an increased blasting distance, the resulting vibrations grow with the amount of energy released. At certain distances, vibration strength can be reduced by employing more controlled blasting techniques (e.g., gradual blasting or adjusting the type of explosive). Seismic wave energy propagates more readily to the surface, so surface blasting typically produces stronger vibrations than subsurface blasting. The recorded ground vibration increases as the distance from the source increases. Conversely, recorded ground vibration decreases with increasing measuring distance from the vibration source. Increased ground vibration reduces the slope’s FoS value. The FoS decreases as the PPA value increases. Conversely, a lower PPA value corresponds to a higher FoS. Clearly, the resulting ground vibration (PPA) increases with the number of blast holes. However, the amount of ground vibration generated decreases as the number of blast holes increases. More blast holes in the explosion lead to a decrease in the FoS value. Therefore, the decrease in slope FoS values and the increase in PPAs are due to the rising number of blast holes. The type of explosive, whose power and detonation rate influence the amount of energy released, is one of several factors affecting ground vibration intensity. The recorded vibration amplitude decreases as the distance from the explosion site to the measurement point increases. Ground vibrations are also affected by geological factors; the characteristics of the rocks and soil surrounding the explosion site determine how far the vibrations propagate. Vibration is also affected by the blasting pattern. The vibration pattern generated depends on the order and duration of blast hole activation. The findings indicate that the slopes remain stable (FoS > 1) before and after blasting, though blasting slightly lowers the FoS. The study shows that as the number of blast holes increases, both ground vibration (PPA) and FoS reduction increase, highlighting the impact of explosive power and detonation rate on slope stability. Further research emphasizes the importance of delay intervals between blast holes to minimize vibration levels and maintain slope stability. Planning the optimal slope angle and shape, along with using delay blasting techniques to minimize vibration peaks that could affect the FoS, are two practical suggestions.