# Shape Modelling and Volume Optimisation of Salt Caverns for Energy Storage
## 2 Three-Dimensional Numerical Model and Assessment Criteria  
### Experimental Verification of Cavern Shapes and Dimensions  
The evaluation of cavern shapes was based on numerical modelling and divided into two parts: the first part included the evaluation of three standard cavern shapes: cylindrical, enlarged top and enlarged bottom. The shape of enlarged caverns was based on a cylinder whose diameter in the roof of the bottom area was increased. The dimensions of examined caverns were adapted to the geological conditions of the Mechelinki salt deposit. Due to the fact that, in numerical simulations, sharp edges are prone to stress concentration [35, 36], the \"smoothing\" of sharp edges was performed in the second part. The \"smoothing\" was performed in three steps. In each step, a quadrant characterised by a different radius (10-30 m) was inscribed into the corners of a vertical cross section through the analysed cavern shapes (Figure 1). Consequently, the cavern shape evolved from a cylinder to a more complex shape. In the first step, the cavern shapes based on a cylinder with sharp edges were examined. In the next three steps, the edges were smoothed, and the radiuses of the quadrant were 10 (Step 1), 20 (Step 2), and 30 m (Step 3). Thus, four cases were considered: caverns with sharp edges (se) and smoothing steps 1 (ss1), 2 (ss2), and 3 (ss3). Finally, the analysed cavern shape consisted of a cylinder in the middle part and two hemispheres in the upper and lower part. As a result of smoothing, the maximal initial diameter that caverns had in the first step (Table 1) decreased, as did the cavern volume. The volume of the cavern from smoothing to Step 3 was about 84% of the cavern volume with sharp edges.  
Three shapes (cylindrical, enlarged top and enlarged bottom) varying in their maximum initial diameter with sharp edges and three \"smoothing\" steps for each shape (28 caverns in total) were analysed. The maximum initial diameter of the cylindrical shape was 60 m, and the height was 120 m. This cylindrical shape was validated as a base shape for further simulations. The base diameter and the height of the cavern were chosen based on the salt bed thickness and the most optimal proportions (H/D = 2/1). The base cavern diameter was enlarged in a roof or bottom of 60 m, 30 m and 15 m. As a result, caverns with an enlarged top or enlarged bottom and an initial diameter of 120 m, 90 m and 75 m were created (Table 1). The cavern height was constant for all simulated cavern shapes in consideration of the thickness of the rock salt layers in the Mechelinki salt deposit. The roof and bottom pillar thicknesses were set to 15 and 5 m, respectively. Therefore, the cavern diameter and edges were the key factors investigated. The volume of each simulated cavern was calculated (Table 1). All analysed shapes were regular in comparison to the complex shapes of real caverns or underground workings [21, 31]. These simulated shapes can form a basis for future cavern design.  
Figure 1: Smoothing steps achieved by inscribing the quadrant into the corner of the cavern’s vertical cross section: ss1—smoothing step 1, ss2—smoothing step 2, ss3—smoothing step 3.