# Numerical Parametric Studies on the Stress Distribution in Rocks around Underground Silo
## 6 Conclusions  
This article presented numerical parametric studies on the stress distribution in rocks around the underground silo for low- and intermediate-level radioactive waste disposal facilities in Korea. The 2D axial symmetric finite element model was used in this study, and a 3D finite element model was also used to verify the reliability of the 2D axial symmetric model. A finite element analysis of an analysis domain covering an underground silo and the surrounding rock mass was performed under three cases of differing ratios of in situ horizontal stress to vertical stress (Ko = 0.5, 1.0 and 2.0). Numerical results obtained through these analyses were presented and examined in detail for displacements, stresses, and safety factors associated with the excavation of an underground silo. To evaluate more accurately the stress state of the surrounding rock, a t-q plot showing the stress state in the octahedral plane was created, in addition to a p-q stress plot. The safety factor was also presented, using the stress value obtained through numerical analysis. The following conclusions arise from the numerical parametric study presented in this paper. 1. The numerical results of the 3D analysis were almost identical in every case to those of the 2D axial symmetric analysis, confirming the reliability of the 2D finite element model. 2. For the case of Ko = 0.5, the maximum displacement occurred in the vertical direction at the central point of the silo's bottom surface, since the in situ vertical stresses were twice as high as the in situ horizontal stresses. For the case of Ko = 2.0, on the other hand, the maximum displacement occurred in the radial direction at the mid-point of the cylindrical wall, since the in situ horizontal stresses are twice higher than the in situ vertical stresses. For the case of Ko = 1.0, where the in-situ stresses were hydrostatic, the maximum vertical displacement at the central point of the silo's bottom surface was somewhat higher than the radial displacement at the mid-point of the cylindrical wall. Figure 20: Safety factor distribution (Ko = 2.0). 3. For Ko = 0.5, all deviatoric stresses were somewhat below the lower-bound strength envelope in the triaxial extension mode. For Ko = 1.0, the deviatoric stress in the first element in line C5 reached the lower-bound strength in the triaxial extension mode. For Ko = 2.0, the deviatoric stresses in the first two elements in lines C5 and D6 were above the lower-bound strength envelope and the first element in line C5 almost reached the upper-bound shear strength in the triaxial compression mode. 4. For Ko = 0.5, the stress state was somewhat close to the triaxial compression mode at Location C, but was closer to the triaxial extension mode at Location D. The safety factors were 2.61 and 1.58 at Location C and D, respectively. For Ko = 1.0, the stress state was very close to the triaxial compression mode at Location C, but was very close to the deviatoric pure shear mode at Location D, with a Lode angel of \(-1.9^{\circ}\). The safety factors were 1.47 and 1.34 at Location C and D, respectively. For Ko = 2.0, the stress state at Location C was almost in the triaxial compression mode, reaching ultimate strength with a safety factor of 1.02. The stress state at Location D was also close to the triaxial compression mode, with a Lode angle of \(-20.9^{\circ}\), reaching ultimate strength with a safety factor of 1.08. Thus, the silo's storage wall may be subjected to the onset of shear failure at these regions. 5. It is better to compare the numerical results with in situ monitoring results. However, unfortunately, in situ monitoring results have not been reported anywhere. Any future data that is acquired should be compared with the results of this study. This study was initiated and designed by S.-H.K. ; the numerical simulations, data analysis, and writing of the paper were undertaken by K.-J.K. All authors have read and agreed to the published version of the manuscript.