# Shape Modelling and Volume Optimisation of Salt Caverns for Energy Storage
## 3 Results
### Effective Strains (ESs)  
In the initial period, the effective strains (ESs) showed a value from 0.6% to 0.4% in the bottom of caverns with an enlarged bottom and at the roof of caverns with an enlarged top (Figure 10A-D). In the five analysed withdrawal and injection periods, the distribution of ES in the cavern walls and surroundings was similar. In the withdrawal periods, the ESs were higher in comparison to the injection periods (Figure 10). The largest value of ES (red area) was indicated in caverns with a diameter of 120 m and sharp edges (Figure 10E,G,I,K). The area of these displacements was located in the bottom of caverns with an enlarged bottom and at the roof of caverns with an enlarged top. The highest value of ES in these caverns reached 7.0-10.0% (red and orange area locally) at the end of the first withdrawal period (Figure 10E,G) and 9.5% at the end of the first gas injection period (Figure 10M,O). A major increase was found at the end of the last withdrawal period (to 27.0%) (Figure 10L,K) and at the end of the first gas injection period (to 26.0%) (Figure 10O,X). However, these values of ES occurred locally (red area). The \"smoothing\" of the sharp edges to ss3 resulted in a decrease in ES (Figure 10F,H,J,L,N,P,R,W). Moreover, in the last injection and withdrawal periods, the value and distribution of the ES were the same for the cylindrical caverns and the caverns with a maximum initial diameter of 75 m and where ss2 and ss3 were below 2.5% (Figure 11).  
The difference in the value and distribution of ES between the injection and withdrawal period was less visible for caverns with a diameter of 75 m (Figure 11). In the last cycle of both withdrawal and injection periods, the ES reached 5.0-7.0% (light blue area) at the bottom and the roof of caverns with a diameter of 75 m and se (Figure 11D,G,M,P). In these groups, the distribution of the ES within the walls and surroundings of caverns with an enlarged bottom and top was the same. In the caverns with a maximum initial diameter of 120 m, the ESs were larger, and there were differences in their distribution between the enlarged-top and enlarged-bottom caverns (Figure 11).  
The cylindrical caverns showed better performance than the enlarged caverns (Figure 11). The largest ES reached 2.5% in the last withdrawal and injection period (Figure 11A-C,J-L). However, in caverns with a diameter of 75 m and with ss2 and ss3, the ES value and distribution were the same as in the cylindrical caverns (Figure 11).  
The ESs in caverns with a maximum initial diameter of 120 m were too large and involved a danger of plastic damage (Figure 10). ES values (lower than 3.0%) that involved no potential danger of plastic damage were registered in caverns with a maximum initial diameter of 75 m (Figure 11). The performed simulations indicated that the value and  
Figure 9: The displacements in the cylindrical caverns with se and ss3 for the first and last cycle (**A–H**).  
distribution of ESs were mainly affected by the cavern diameter. However, the \"smoothing\" of sharp edges influenced the value of ESs more than their distribution.  
Figure 10: The comparison of effective strain (ES) between enlarged-top and bottom caverns with a maximum initial diameter of 120 m (**A–W**).