# Shape Modelling and Volume Optimisation of Salt Caverns for Energy Storage
## 3 Results
### Displacements  
In the initial period, the largest displacements (23.8 cm) were indicated for the roof (red area) of the caverns with an enlarged top and diameter of 120 m (Figure 4A). The gradual \"smoothing\" of the sharp edges caused a reduction of the largest displacements in this area. The decrease in the cavern diameter corresponded to a decrease in the largest displacement value and area (Figure 4E-G). The largest displacements in the walls (14.0-16.0 cm) were found in the cavern with an enlarged bottom, sharp edges and an initial diameter of 120 m (Figure 4E). In the caverns with maximum initial diameters of 90 and 75 m, the area of the largest displacements was smaller and concentrated in the middle part of the caverns (Figure 4F,G). At the end of the first withdrawal period, the caverns with an enlarged bottom, a maximum initial diameter of 120 m, sharp edges and ss1 showed the largest displacements (138.44 cm) in the middle part and the surroundings (Figure 5A,B). The value of displacements reached 120.0-130 cm in the caverns with an enlarged top, maximum initial diameter of 120 m, sharp edges and ss1 for the displacements located over the roof of these caverns (Figure 5E,F). In the middle part of the caverns with an enlarged top, se and ss1 as well as with an enlarged bottom, ss2 and ss3, the largest displacements decreased to 100.0-110.0 cm (Figure 5C-F). A further decrease to 90.0-100.0 cm was found in caverns with an enlarged top, ss2 and ss3 (Figure 5G,H). The largest displacements in the caverns with an initial diameter of 90 and 75 m and sharp edges were 70.0 and 50.0 cm, respectively, and were  
Figure 4: The displacement value and distribution in simulated caverns; initial period: (**A–D**) enlarged top, (**E–G**) enlarged bottom, (**A–E**) maximum initial diameter of 120 m, (**F**) maximum initial diameter of 90 m, (**G**) maximum initial diameter of 75 m. se—sharp edges; ss—smoothing step. concentrated in the middle part of these caverns (Figure 5J,J). The caverns characterised by ss3 (Figure 5K,L) showed a lower value in the largest displacements from 70.0 cm (diameter: 90 m) to 60.0 cm (diameter: 75 m). At the end of the first injection period, the distribution of the largest displacements within the walls of the caverns was similar to the withdrawal period, but their value was lower (Figures 5 and 6). The largest displacements were registered in the walls of the cavern with an enlarged bottom (128.30 cm) and over the top of the cavern with an enlarged top (110.0 cm), both of which were characterised by an initial diameter of 120 m and se (Figure 6A,B). In this group of caverns (Figure 6A-D), the displacement value decreased with the smoothing steps. In comparison, the largest displacements in caverns with a maximum initial diameter of 75 m and se reached 50.0-60.0 cm in the enlarged-bottom caverns and 40.0-50.0 cm in the enlarged-top caverns (Figure 6E,F). In the caverns with ss3, the value amounted to 40.0-50.0 cm for caverns with an enlarged top and bottom (Figure 6G,H). However, the displacement value and distribution for caverns with a diameter of 90 m differed between caverns with an enlarged top and bottom (Figure 6I-L). The described trends continued in the following years, but the value of the largest displacements increased (at the end of the last withdrawal period) to 369.91 cm in the enlarged-bottom caverns with se and a maximum initial diameter of 120 m (Figure 7A) and to 300.0 cm in the enlarged-top caverns (Figure 7B). In comparison, the largest displacements in the caverns characterised by ss3 reached 225.0-275.0 cm (Figure 7C,D). The displacements in the caverns with se (Figure 7E,F) and a diameter of 75 m reached  
Figure 5: The displacement value and distribution in simulated caverns, first withdrawal period: (**A–D**), (**I–L**) enlarged bottom, (**E–H**) enlarged top, (**A–H**) maximum initial diameter of 120 m, (**I,K**) maximum initial diameter of 90 m, (**J,L**) maximum initial diameter of 75 m.  
150.0-175.0 cm.