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 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 (De
2) and index strength.
Figure 4 also shows the empirical equation that was used to determine the relationship between the index strength and log (De
2), y = 0.8181x + 0.1517, with R
2 = 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, 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 (De
2) and index strength for siltstone than that from the test findings, with an empirical equation of y = 38.731x − 118.66, as demonstrated by R
2 = 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. 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 (De
2) 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 R
2 = 0.9939. The findings of the tests for siltstone and coal show that sandstone’s R
2 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.
4.4. 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 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 (σ
1) sigma 1 and (σ
3) 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 (σ
1) sigma 1 and (σ
3) 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.