Finite Element Modeling for Stability Assessment of Sedimentary Rock Slopes

Abstract

To prevent landslides, the slope is a crucial component that needs to be evaluated. Mining activities produce slopes, both natural slopes and artificial slopes, and if a slope is not designed properly, its stability will be adversely affected. The purpose of this study is to determine the stability of a slope supported by sedimentary rocks as the constituent material of the slope. Data processing is carried out using the RS2 Version 11 software and finite element methods (FEMs) by considering the value of the strength reduction factor (SRF) and maximum displacement of the slope. The results obtained for stage 1 show that a maximum displacement of 0 m was obtained, along with a critical value of SRF = 1. A maximum displacement of 0.2 m was obtained in stage 2, with a critical SRF of 1.25. In stage 3, 0.2 m was the highest attained displacement, and the critical SRF was 1.26. A maximum displacement of 0.4 m and a critical SRF of 1.31 were found in stage 4. The maximum displacement in stage 5 was 0.8 m, while the critical SRF was 1.34, and the critical SRF in stage 6 was 1.35, while the maximum displacement was 0.8 m. Finally, the maximum displacement in stage 7 was 1.6 m, while the critical SRF was 1.36. A general pattern emerged from the results of stages 1 through 7. Specifically, the maximum permitted displacement value increased with the critical value of SRF. As the slope moved, it also became more stable, with a big critical SRF. If a slope’s deformation exceeds 1.6 m, it will collapse at a safety factor of 1.36. Furthermore, the contour level showed that the factor of safety (FoS) falls between 1.4 and 4.2. Additionally, as sigma 1 and 3 increase, the resulting FoS value increases as well.

1. Introduction

Slopes can be divided into two types: artificial slopes and natural slopes. The ability of a slope to tolerate or experience movement is influenced by its stability. An artificial slope is an incline or decline in the ground that is created by humans for various purposes. Unlike natural slopes formed by geological processes, artificial slopes are intentionally constructed to meet specific needs. Various techniques are used to estimate the stability of slopes, and each has its benefits and drawbacks [1]. Slope stability, and the causes of slope movement or failure, can be analyzed and determined using a static or dynamic, analytical or numerical process called slope stability analysis. When a situation requires a balance in forces or moments, a stability analysis can provide the solution. Slope stability is defined as the ratio, represented as a safety factor, between shear strength and shear stress [2].

Moreover, these activities disturb and harm the exposed failure surface of the soil mass and rock. The use of effective numerical simulation technology for landslide disaster evaluation and prediction is thus essential to guarantee the sustainable development of both nature and humankind. By doing this, we can considerably reduce the detrimental effects of landslides and successfully prevent bad effects [3]. A crucial factor that must be taken into account when examining slope stability is its impact on the choice of mechanical characteristics for the rock strata that make up the slope [4].

A failure risk analysis is the process of determining the probability of landslides and the potential losses they cause. This analysis is important in areas prone to landslides, such as steep slopes, areas with high rainfall, and areas with high geological activity. Geotechnical engineers primarily base their design decisions on the factor of safety calculations in the majority of slope stability analysis scenarios. The reliability between the factor of safety and the precision of geotechnical input data makes it an invaluable tool for estimating the distance between a slope and failure [5]. Various methods have been developed to guarantee slope stability and to stop sliding [6]. To interpret the findings of the physical model testing, this study employed finite element numerical modeling [7]. The approach to a slope stability analysis that is most commonly utilized is the finite element method (FEM). The main benefit of FEM over other methods is that it does not require any assumptions regarding the location of the failure surface and the slope’s forward progress.

Shear strength reduction (SRR) is a method or concept that uses the FEM model of the slope as a starting point and gradually reduces the shear strength of a material by a safety factor until the deformation becomes unmanageable [8]. The comparison of the force that propels movement with the force that resists it is called the factor of safety (FoS) [9]. For slope materials, the SSR approach as given in the literature assumes the Mohr–Coulomb strength [10]. The material qualities of the slope, the method by which the safety factor is computed to influence slope stability, and the definition of slope failure are the three main study variables that impact a stability analysis. Sedimentary rocks are used in such a study. Sedimentary rocks are a type of rock that is formed as a result of the deposition and compaction of loose materials on the Earth’s surface. The assignment of an adequate constitutive model of strata is a crucial and significant stage in numerical modeling [11]. The failure conditions are then examined under various stress reduction factor (SRF) scenarios with varying rock parameters. A software that is frequently used in the fields of engineering geology, geotechnical engineering, and mining engineering to ensure that surface and underground structures are properly planned, evaluated, and supported is RS2 [12]. RS2 Version 11 is a two-dimensional software for displacement and stress analyses that blends the contour element and finite element analysis methods [13,14].

This study can serve as a guide and suggestive measure to prevent landslides by analyzing slopes, which are often composed of sedimentary rocks. In addition to this, by obtaining a thorough understanding of the slope conditions, preventive actions can be carried out following a slope simulation to prevent landslides.

2. Geographical and Geological Setting

2.1. Geographical Setting

The mining business license area CV. Bara Mitra Kencana covers a 49.61-hectare area and is geographically positioned at a latitude of 00°37′08.22″–00°36′58.36″ south and at a longitude of 100°47′18.39″–100°46′48.10″ east. The administrative center is located in Tanah Kuning, Batu Tanjung Village, Talawi District, Sawahlunto City, Indonesia, while the mine is located at a distance of approximately 117 km from Sawahlunto City, in Padang City. The BMK14 slopes, which have a strongly wavy topography and a pattern of dendritic flow from the youngest to oldest phases, were used as the study region. The kinds of rocks that are present in this region also influence its morphological shape, in addition to its geological features. The study region is situated at a height of approximately 268 m above sea level (Figure 1).

2.2. Geology Setting

The Lower Ombilin Formation (Tmol) has quartz sandstones with mica arcase inserts, quartz conglomerates, clay shales, and coal. The research area is part of this formation. Both the oldest and youngest rocks were discovered at the research site, with the most common intrusive rock in this area being granite. The rocks range in color from granite to quartz monzonite, with white specks scattered throughout their gray-white color. The local people use these textured rocks, which are often phaneritic to porphyritic and regionally worn, as a building material. Diorite stone is trace-textured and locally cracked and has a dark gray to greenish-gray color with black patches. These rocks have a microlithic foundation and is made up of mafic and felspar minerals. Claystones, conglomerates, marl with sandstone inserts, and tuff sandstones with fossilized limestone comprise the upper unit of the Ombilin Formation. This rock unit dates back to the early Miocene. CV. Bara Mitra Kencana belongs to the Ombilin Formation (Figure 2). The Sangkarewang Formation is composed of locally angled coarse andesite breccia and dark brown to blackish marl flakes that are interbedded with arcose sandstones. A hard conglomerate with several sandstone inclusions makes up the Brani Formation.

3. Method

3.1. Point Load Index Test

ASTM D5731-16 [15] and ISRM 2007 [16] are the standards for point load index testing [17]. The sample that was utilized was an irregular sample. An irregular sample is a test sample that has an irregular shape. During irregular testing of samples at point load, we must keep in mind a D/W ratio of 1.0–1.4. D/W is the ratio of the diameter (D) to the width (W) in mm of the rock sample tested in this point load index test. Six coal samples, six siltstone samples, and six sandstone samples were employed in this experiment. The quantities of samples used in the tests are representative of the area. Point load index testing was conducted using the type 32-D0550 Type CONTROLS instrument. This study examined the correlation between three different rocks’ index strengths and De². The index strength (Is) in a point load test is a measure of the rock’s strength, acquired by applying increasingly concentrated stress through a certain device to a rock specimen until the rock fractures. The unit for index strength (Is) is MPa (Megapascals). The comparable core diameter is De in this context and is a standard diameter (usually 50 mm) that is used to compare the findings from the point load tests. De contributes to a consistent interpretation of the test findings because the size of rock cores can vary. The strength index is used in numerical simulations as an input parameter for the strength of the rocks that make up the slope.

3.2. Shear Strength Test

The guidelines for shear strength testing, ASTM D 5607–08 [18] and ISRM 2007 [17], were followed [19]. The type of sample used was a standard core sample, and three samples of coal, three samples of siltstone, and three samples of sandstone were used. Changes in the shear stress and normal stress were noted using the shear strength test. Each sample’s internal friction angle and cohesion value were determined using three tests. To prevent uncontrolled failure and excessive sample displacement, the sample was sheared at a constant speed of 0.5 mm/min during the direct shear test [20].

3.3. Finite Element Method

Using the RS2 Version 11 software, the strength reduction factor (SRF) was analyzed and the maximum displacement of the slopes was determined. When a material’s shear strength on the sliding surface is insufficient to withstand the shear loads, the slope breaks. Therefore, a metric is used to assess the stability of the slopes: the factor of safety. The slope is stable for FoS values larger than 1 but unstable for values less than 1 [10]. The factor of safety for slope failure after a shear failure is easily computed, as follows:

$$FoS={\displaystyle \frac{\tau }{{\tau }_f}}$$

(1)

where $\tau$ is the slope material’s shear strength, which can be calculated using the Mohr–Coulomb criteria, as follows:

$$\tau =C+{\sigma }_n tan \phi$$

(2)

where ${\tau }_f$ represents the sliding surface’s shear stress, calculated as follows:

$${\tau }_f=C_f+{\sigma }_n tan {\phi }_f$$

(3)

where C_f and ${\phi }_f$, the factored shear strength parameters, are as follows:

$$C_f={\displaystyle \frac{C}{SRF}}$$

(4)

$${\phi }_f={tan}^{-1}\left({\displaystyle \frac{tan\phi }{SRF}}\right)$$

(5)

where

• τ = the shear stress of the material (kPa);
• τ_f = the shear stress of the sliding surface (kPa);
• C = the cohesion of the material (kPa);
• C_f = the cohesion of the sliding surface (kPa);
• σ_n = the normal stress (kPa);
• φ = the internal friction angle of the material (degrees);
• φ_f = the internal friction angle of the sliding surface (degrees).

The strength reduction factor is denoted by SRF. This technique is named the shear strength reduction method. Finding the FoS value that leads to the slope’s failure is crucial to achieving the right SRF [1]. A critical SRF reflects the FoS (factor of safety). The slope is in a critical condition when FoS = 1, the slope is in a stable condition when FoS > 1, and the slope is in an unstable condition when FoS < 1.

4. Results and Discussion

4.1. Point Load Index Testing

Some irregular samples used for the point load index test are shown in Figure 3. Three different kinds of rocks were used for the tests. The sample was made up of six coal samples, six siltstone samples, and six sandstone samples.

Table 1. Point load index test results for coal.

Code	D (mm)	W (mm)	De2 (mm)	log De2	Is (MPa)
S-1	38.16	41.80	2031.96	3.31	2.84
S-2	25.27	29.81	959.62	2.98	2.60
S-3	44.36	49.29	2785.36	3.44	2.93
S-4	34.10	38.14	1656.78	3.22	2.78
S-5	42.24	46.74	2515.03	3.40	2.95
S-6	45.37	50.30	2907.15	3.46	3.02
SD	7.61	7.81	746.20	0.18	0.15
Average	38.25	42.68	2142.65	3.30	2.85
Min	25.27	29.81	959.62	2.98	2.60
Max	45.37	50.30	2907.15	3.46	3.02

displays the findings of the point load index tests conducted on coal.

In Table 1, the index strength has an average value of 2.85 MPa, a minimum value of 2.60 MPa, a maximum value of 3.02 MPa, and a standard deviation of 0.15. In general, coal samples are categorized as soft and readily fractured rocks, with an average value of 2.85 MPa. Figure 4. Relationship between Is and log (De2) in coal. illustrates the relationship between log (De²) and index strength.

Figure 4 also shows the empirical equation that was used to determine the relationship between the index strength and log (De²), y = 0.8181x + 0.1517, with R² = 0.971. The graph indicates a strong correlation between the distance between the conus values and index strength.

The results of the point load index test for siltstone rocks are shown in

Table 2. Point load index test results for siltstone.

Code	D (mm)	W (mm)	De2 (mm)	log De2	Is (MPa)
Sil-1	32.23	36.11	1482.58	3.17	4.61
Sil-2	36.18	39.57	1823.75	3.26	7.73
Sil-3	33.04	36.36	1530.36	3.18	4.60
Sil-4	35.17	38.31	1716.39	3.23	6.52
Sil-5	34.53	38.05	1673.72	3.22	5.57
Sil-6	37.19	40.58	1922.51	3.28	8.83
SD	1.87	1.75	168.17	0.04	1.72
Average	34.72	38.16	1691.55	3.23	6.31
Min	32.23	36.11	1482.58	3.17	4.60
Max	37.19	40.58	1922.51	3.28	8.83

, obtained by testing six samples with an average index strength value of 6.31 MPa, a minimum value of 4.60 MPa, a maximum value of 8.83 MPa, and a standard deviation of 1.72. Out of the three types of rocks that were examined, the findings of the siltstone test are stronger than those of the coal test, and the average Is of sandstone is higher than that of the other two types of rocks.

From Figure 5, a stronger correlation can be seen between log (De²) and index strength for siltstone than that from the test findings, with an empirical equation of y = 38.731x − 118.66, as demonstrated by R² = 0.9517. Both factors are thought to have a very strong correlation.

An average value of 3.66, a minimum value of 3.32, a maximum value of 3.92, and a standard deviation value of 0.22 were found in

Table 3. Point load index test results for sandstone.

Code	D (mm)	W (mm)	De2 (mm)	log De2	Is (MPa)
San-1	35.14	42.40	1898.01	3.28	3.51
San-2	36.28	43.52	2011.34	3.30	3.63
San-3	38.33	47.28	2308.59	3.36	3.82
San-4	34.41	39.37	1725.76	3.24	3.32
San-5	37.53	46.04	2201.12	3.34	3.77
San-6	39.34	48.29	2420.04	3.38	3.92
SD	1.90	3.35	262.55	0.06	0.22
Average	36.84	44.48	2094.14	3.32	3.66
Min	34.41	39.37	1725.76	3.24	3.32
Max	39.34	48.29	2420.04	3.38	3.92

. According to the test results, sandstone has a compressive strength rating that is higher than coal’s but lower than siltstone’s.

The relationship between index strength and log (De²) in sandstone is depicted in Figure 6, where a strong correlation is found, with the empirical equation y = 4.0194x − 9.6762, as indicated by R² = 0.9939. The findings of the tests for siltstone and coal show that sandstone’s R² value is more significant than those of the other two rocks, perhaps as a result of the precise D/W ratio modification during test preparation.

4.2. Rock Shear Strength Testing

The results from testing the shear strength of coal, siltstone, and sandstone are shown in

Table 4. Results of the rock shear strength test.

Code	σn (kPa)	τ (kPa)	φ (Degree)	c (kPa)
Co-1	0.20	10.92	53.84	8.92
Co-2	0.40	14.84
Co-3	0.61	12.88
Sil-1	0.20	12.88	48.52	8.04
Sil-2	0.40	18.76
Sil-3	0.60	24.64
San-1	0.20	14.84	49.25	8.59
San-2	0.40	22.68
San-3	0.60	24.65

: values for cohesion, internal friction angle, shear stress, and normal stress. Coal, siltstone, and sandstone are denoted by the letters Co, Sil, and San, respectively. In the RS2 Version 11 software, the cohesion parameters and internal friction angles were used as input parameters.

4.3. Physical Properties

Laboratory tests of the physical characteristics of the three types of rocks yielded the following average specific mass values: coal = 1133.83 kg/m³, siltstone = 2207.67 kg/m³, and sandstone = 2387.83 kg/m³. Of the three types of rocks, sandstone had the highest specific mass, while coal had the lowest specific mass (

Table 5. Results of the physical property test for coal, siltstone, and sandstone.

Rock Type/#	Coal	Siltstone	Sandstone
	ρ (kg/m3)	ρ (kg/m3)	ρ (kg/m3)
1	1134	2207	2388
2	1135	2208	2389
3	1134	2207	2387
4	1133	2209	2388
5	1134	2208	2386
6	1133	2207	2389
SD	0.75	0.82	1.17
Average	1133.83	2207.67	2387.83
Min	1133	2207	2386
Max	1135	2209	2389

).

4.4. Critical SRF and Maximum Displacement

The material properties and RS2 Version 11 processing results for stages 1, 2, and 3 are shown in Figure 7. The three layers are shown in three different colors to represent the different materials. The sandstone layer is presented in color, the siltstone layer is gray, while the coal layer is black. The slope model dimensions are as follows: bench angle slope = 31 degrees; total height of the slope = 41 m; bench height = 29 m; bench width = 35 m; and crest width = 25 m. The elevation and thickness of each layer were matched to the three layers during input. The most common elastic type is the isotropic type, where the functional parameters remain constant in all directions. The isotropic elastic type in this study has a Young’s modulus of 20,000 kPa and a Poisson ratio of 0.3. Plastic was chosen as a parameter, and the peak and residue parameters are the same. The model was also extended with piezometric lines to show the groundwater levels on the slopes. Normal-to-boundary was chosen as the orientation type to make the normal distribution load perpendicular to the sloped border, with a 55 kPa distribution load. Additionally, an earthquake factor of 0.3 g was input in the direction of the slope and in the horizontal direction for the seismic loading section. In the slope stability analyses, this seismic coefficient value was utilized as an input parameter for the earthquake load [21]. Six noded triangles, or six triangular corner points, were used in the mesh configuration, making it a uniform mesh type. The more meshes that are created to complement each rock mass, the more precise the results will be. Stage 1 in Figure 7 produced a maximum displacement of 0 m and a critical value of SRF = 1. Stage 2 produced a maximum displacement of 0.2 m and a critical SRF of 1.25. Stage 3 produced a maximum displacement of 0.2 m and a critical SRF of 1.26. Stages 2 and 3 exhibited the highest maximum displacements; the maximum obtained displacement increased with critical SRF value. A critical SRF = 1 means critical slope conditions and is indicated by a displacement value = 0. Starting from stages 2 and 3, the slope is said to be stable because the critical SRF or FoS value is >1.

The crucial SRF and maximum displacement values for stages 4, 5, 6, and 7 are displayed in Figure 8. With a maximum displacement of 0.4 m, a critical SRF of 1.31 was attained in stage 4. The critical SRF in stage 5 was 1.34, with a maximum displacement of 0.8 m. The critical SRF for stage 6 was 1.35, and the maximum displacement was 0.8 m. The critical SRF in stage 7 was 1.36, with a maximum displacement of 1.6 m. One recurring pattern in the stage 4–7 data is that the maximum permitted displacement value increased with the critical value of SRF. Based on Figure 8, the change in the contour gradation area (total displacement) decreased with increasing SRF critical value. A slope with a big critical SRF is considered to be more stable in terms of movement. Stages 4, 5, 6, and 7 describe a slope in a stable condition as the critical SRF or FoS value is >1. Deformation, or maximum displacement, is the maximum amount of movement that is allowed in the field and considered safe before signs of landslides are seen.

The strength reduction factor and maximum total displacement are related, as shown in Figure 9. The red line indicates the failed-to-converge zone, and the blue line shows the converged zone distribution value. The dotted line at 1.36 is the maximum safe SRF limit. The maximum displacement is at 1.6 m if the convergence zone meeting point is drawn vertically towards the x-axis. It follows that the slope will collapse at a safety factor of 1.36 if the deformation is more than 1.6 m.

The top layer that constitutes the slope is the sandstone layer. This stratum is rather close to the top and is up to 5 m thick. The distributions of the values for (σ1) sigma 1 and (σ3) sigma 3 in the sandstone layer are shown in Figure 10. Points A through J show the locations of ten observation points. The values obtained for sigma 1 and sigma 3 are smaller than those found in the coal and sandstone seams, as can be shown from their distributions.

Table 6. Safety factors in the sandstone, coal, and siltstone layers.

Point	Sandstone			Coal			Siltstone
	σ1 (kPa)	σ3 (kPa)	FoS	σ1 (kPa)	σ3 (kPa)	FoS	σ1 (kPa)	σ3 (kPa)	FoS
A	112.50	20.00	1.53	487.50	280.00	3.74	712.50	420.00	3.90
B	112.50	40.00	2.23	450.00	240.00	3.33	675.00	400.00	3.94
C	150.00	40.00	1.81	450.00	200.00	2.64	675.00	380.00	3.61
D	112.50	40.00	2.23	450.00	180.00	2.37	675.00	360.00	3.31
E	112.50	20.00	1.53	450.00	180.00	2.37	637.50	360.00	3.63
F	75.00	20.00	1.89	412.50	160.00	2.30	600.00	320.00	3.32
G	37.50	0.00	1.24	375.00	120.00	1.98	562.50	300.00	3.32
H	75.00	20.00	1.89	300.00	100.00	2.05	487.50	240.00	2.98
I	75.00	20.00	1.89	262.50	80.00	1.93	375.00	200.00	3.34
J	37.50	0.00	1.24	112.50	40.00	2.23	262.50	140.00	3.36
SD	36.23	14.76	0.36	117.26	73.91	0.60	148.38	91.99	0.30
Average	90.00	22.00	1.75	375.00	158.00	2.49	566.25	312.00	3.47
Min	37.50	0.00	1.24	112.50	40.00	1.93	262.50	140.00	2.98
Max	150.00	40.00	2.23	487.50	280.00	3.74	712.50	420.00	3.94

yielded an average FoS value of 1.75 for the sandstone layer. The FoS standard deviation is 0.36, with a minimum value of 1.24 and a maximum value of 2.23. Compared with the other two types of rock layers, the sandstone layer has a lower average FoS value. The sigma 1 and sigma 3 values, which are often lower than those of the other two types of rock layers, have an impact on the FoS value.

The distributions of the (σ₁) sigma 1 and (σ₃) sigma 3 values in the coal layer are displayed in Figure 11. The coal seams show an approximately 15-degree slope and have a thickness of 4 m in the field. The values of sigma 1 and sigma 3 in the coal seams are found to be larger than those in the sandstone seams. The combination of surface parameter values and layer value parameters in the center, namely coal, is what causes these phenomena. The value of the safety factor attained in the coal seam is likewise greater than the value in the sandstone seam; thus, naturally, larger sigma 1 and sigma 3 values will also have an impact on the safety factor.

The average FoS value for the coal layer in Table 6 is 2.49. The FoS values range from 1.93, as the minimum, to 3.74, as the maximum. On the other hand, the FoS standard deviation is 3.74. When compared with the value of the sandstone FoS, the average value of the coal FoS is higher. The lowest layer that makes up the slope is the siltstone layer. The coal seam is beneath this seam. The distributions of the values for (σ₁) sigma 1 and (σ₃) sigma 3 in the siltstone layer are depicted in Figure 12. Compared with the two levels above, both values evidently have the highest values. The siltstone layer’s safety factor is shown in Table 6. The FEM model’s parameters between the layers show that the maximum main pressure (sigma 1) and minimum main pressure (sigma 3) values in soft rocks (coal) are typically lower than those in hard rocks (sandstone and siltstone). A weaker rock structure, a lower cohesive strength, and a lower shear resistance are some of the causes. Bear in mind that several variables can affect the values of sigma 1 and sigma 3 in soft rocks, including the kind of soft rock, the geological environment, and the existence of external loads.

Considering the FoS values at every observation point (Figure 13), the sandstone layer has the highest FoS value, as shown in the graph with the pink bars. The coal seam has the second-highest FoS, also indicated in the pink bar graph. However, the sandstone layer—represented by the yellow bar graph—has the lowest FoS value. Point B has the highest FoS. Measuring FoS = 3.94, this occurs in the sandstone stratum. Table 6 shows that the sandstone layer has the lowest FoS value, with FoS = 1.24.

The correlation between the sigma 1, sigma 3, and FoS values is plotted in Figure 14. The contour level indicates that the FoS ranges from 1.4 to 4.2. The resulting FoS value for each point (Figure 13) rises in tandem with the increases in sigma 1 and sigma 3 values. Generally speaking, a greater FoS value and a lower sigma 3 make the slope more stable because a lower sigma 3 reduces the resulting shear stress while a larger sigma 1 raises the maximum shear resistance. It is crucial to remember that many variables affect the slope’s stability, and the link between sigma 1, sigma 3, and FoS is just one of them. The kind of soil, the state of the groundwater, and the existence of human-made constructions on the hillsides are other variables to take into account.

5. Conclusions

A critical SRF = 1 in stage 1 means a critical slope condition. Starting from stage 2 and stage 3, the slope is said to be stable because the critical SRF or FoS value is >1. A slope with a big critical SRF is considered to be more stable in terms of movement. Stages 4, 5, 6, and 7 describe a slope in a stable condition as the critical SRF or FoS value is >1. For stage 1, a maximum displacement of 0 m was obtained, along with a critical value of SRF = 1. A maximum displacement of 0.2 m was obtained in stage 2, with a critical SRF of 1.25. In stage 3, the highest attained displacement was 0.2 m, and the critical SRF was 1.26. A maximum displacement of 0.4 m and a critical SRF of 1.31 were found in stage 4. The maximum displacement in stage 5 was 0.8 m, while the critical SRF was 1.34. The maximum displacement was 0.8 m in stage 6, and the critical SRF was 1.35. Finally, the maximum displacement in stage 7 was 1.6 m, while the critical SRF was 1.36. A general pattern emerged from the results of stages 1 through 7. Specifically, the maximum permitted displacement value increased with the critical value of SRF. As the slope moved, it became more stable, with a big critical SRF. If a slope’s deformation exceeds 1.6 m, it will collapse at a safety factor of 1.36. The contour level also indicates that the FoS ranges from 1.4 to 4.2.

The FEM model’s parameters between the layers show that the maximum main pressure (sigma 1) and minimum main pressure (sigma 3) values in soft rocks (coal) are typically lower than those in hard rocks (sandstone and siltstone). A weaker rock structure, a lower cohesive strength, and a lower shear resistance are some of the causes. Bear in mind that several variables can affect the values of sigma 1 and sigma 3 in soft rocks, including the kind of soft rock, the geological environment, and the existence of external loads. The resulting FoS value will rise in tandem with increases in the sigma 1 and sigma 3 values. Generally speaking, a greater FoS value and a lower sigma 3 will make the slope more stable because a lower sigma 3 reduces the resulting shear stress while a larger sigma 1 raises the maximum shear resistance. It is crucial to remember that many variables affect the slope’s stability, and the link between sigma 1, sigma 3, and FoS is just one of them. The kind of soil, the state of the groundwater, and the existence of human-made constructions on the hillsides are other variables to take into account.