## 4 Application: A Real Case
### Computational Results
From Figure 14, the curve has appeared inflection point and tends to converge, and it is thought when the number of iteration steps reaches the 7000 th step, SD/mean tends to converge, the difference between SD/mean of the 8000 th step, and SD/mean of the 7000 th step tends to zero. Therefore, it is thought that when the calculation reaches the 7000 th step, the iterative calculation would be terminated. To make the calculation convenient and consistent with the excavation of the roof, the 10,000 th step is also selected. Figure 14: The statistical results after the excavation of the first minelayer. (**a**) The relationship between SD/mean and the number of iterations after the excavation of the first minelayer; (**b**) The relationship between inter-step difference and the number of iterations after the excavation of the first minelayer. Figure 13: The Z-direction displacements after the excavation of the first minelayer. When the excavation of the first minelayer is completed and the iteration is terminated, the excavation of the second minelayer of the ore body is carried out. The Z-direction displacement after excavation of the second minelayer is shown in Figure 15, and the relationship between the number of iterations and the SD/mean values is shown in Figure 16a. The relationship between the difference of each adjacent two steps and the number of iterations is shown in Figure 16b. After completing the excavation of the second minelayer, Figure 15 shows that with increasing excavation depth, the sliding blocks on the south slope and the north slope gradually increase, but the sliding blocks on the north slope are still more. All the sliding blocks slide along the joint planes. From Figure 16, it is thought that when the iterative calculation reaches the 10,000 th step, the curve tends to converge, and the difference between the SD/mean of the 11,000 th step and the SD/mean of the 10,000 th step tends to zero. Therefore, it is thought that the iterative calculation would be terminated when another 10,000 steps are calculated. Figure 16: The statistical results after the excavation of the second minelayer. (**a**) The relationship between SD/mean and the number of iterations after the excavation of the second minelayer; (**b**) The relationship between inter-step difference and the number of iterations after the excavation of the second minelayer. Figure 15: The Z-direction displacements after the excavation of the second minelayer. The above excavation is divided into three times: the first excavation is the roof; the second excavation is the first layer of iron ore; and the third excavation is the second layer of iron ore. The results of the three excavations could verify the feasibility and applicability of the proposed energy-based method. However, with the increase in excavation layers, a large number of rock blocks would accumulate on the surface of the iron mine. The next excavation needs to first remove the sliding blocks, and then carry out the excavation of the underlying layers. In brief, according to the results of the above three excavations, it is thought that the proposed energy-based method in this paper is applicable to more jointed rock slopes that cannot determine the potential sliding surface before DEM modeling.