# Investigation of Steep Waste Dump Slope Stability of Iron Ore Mine--A Case Study
## 3 Results and Discussion
### Experimental Findings  
Three direct shear tests were conducted on soil samples taken from three different locations of Waste Dump#1. The plots of the shear stress as a function of the shear displacement for various samples are presented in Figure 5.  
Figure 4: Discrete element modeling of the granular materials: (**a**) surrounding walls of the soil sample in the test, (**b**) PFC3D-based modeling of the soil sample in the direct shear test. From the data illustrated in Figure 5, a clear trend emerges in the relationship between shear stress and shear displacement of soil samples taken from Waste Dump#1. As shear stress increases, there is a corresponding increase in shear displacement. This trend is more obvious when the vertical stress is at 100 kPa, where the shear displacement shows significant sensitivity to changes in shear stress. However, as the vertical pressure grows beyond 100 kPa, the soil's sensitivity to shear stress begins to diminish. These observations show that the soil reacts less to shear stress changes under higher vertical stresses. Such a fact is mainly attributed to the increased compression of soil particles under higher pressures, which reduces their ability to move or displace relative to each other. In addition, it is observed that with the increase in vertical pressure, the total amount of shear displacement tends to decrease. This indicates that the ability of soil to displace is inversely proportional to the applied vertical pressure, representing a crucial feature in understanding the mechanical behavior of soil in the waste dump. The peaks or stable values observed in the shear stress-displacement curves could be rationally identified as the points representing the shear strength of the soil samples. Using this approach, the relationship between the shear strength of soil samples from three different locations in the Waste Dump#1 area under four vertical stresses (i.e., 100, 200, 300, and 400 kPa) can be determined, as demonstrated in Figure 6.  
It can be seen from Figure 6 that the shear strength of different samples almost exhibits a linear increase with the growth of the vertical stress. According to the relationship  
Figure 5: Shear stress–shear displacement curves for various soil samples under four levels of vertical loadings. curves, the cohesion and internal friction angle of the soil samples could be appropriately determined based on the statistical analysis of the fitted curves (i.e., by fitting appropriate linear lines of the form: \(\tau=c^{\prime}+\sigma^{\prime}\tan(\varphi^{\prime})\); Mohr-Coulomb's model). Based on this reasonably linear relationship between the shear strength and the vertical stress of the soil samples at the three locations where the samples were taken from Waste Dump#1, we can evaluate the cohesion (\(c^{\prime}\)) and internal friction angle (\(\varphi^{\prime}\)) of various samples, as illustrated via bar diagrams in Figures 7 and 8. In Figure 7a-c, the experimentally obtained cohesion values of various samples, their corresponding average values, and standard deviations (SDs) of these average values have been presented, respectively. As is seen, the average values for the three sampling locations are almost close to each other; however, their percentages of SDs are different such that the highest uniformity of the average cohesion values is detected for PTC-1-2, while PTC-1-3 exhibits the lowest uniformity of these data. In addition, the experimentally predicted internal friction angle for different samples, the corresponding average values obtained for the three sampling locations, and their SD values are provided in Figure 8a-c. The plotted results reveal that the average value of the internal friction angle gradually reduces as one goes from PTC-1-1 to PTC-1-2 and then to PTC-1-3; however, the variation rate is almost mild such that the corresponding average values of the internal friction angle obtained from the three sampling points are nearly close to each other.