## 5 Applications
### Application 1: Spiral Case  
The spiral case is an example of a complex RC structure that has been rarely considered in literature. The normal load case for this structure involves full water pressurization, where the structure behaves as a pressure vessel. In this case, the load is mainly supported by and an internal steel liner containing the water (not shown in figures). The short-circuit load case considered is an accidental load case where the RC structure bears 100% of the load without the contribution of the steel liner. Large tangential loads \(F\) act simultaneously on each stator base (8 in total as shown in Figures 1b and 8a), creating a high torque on the RC structure, in the order of 300,000 kN.m. The short-circuit ultimate factored load case is: \(\lambda_{DL}DL+\lambda_{SC}SC\) where \(DL\) is the concrete dead load and \(SC\) are the 8 short circuit forces \(F\), each of 6000 kN. \(\lambda_{DL}=0.85\) is the dead load factor, and \(\lambda_{SC}=1.05\) is the short-circuit load factor. The mean compressive strength of concrete is 40 MPa and the mean yield strength of reinforcement is 400 MPa. The RC structure was designed to transfer the short-circuit loads to the spiral case foundation in two steps (Figure 9): (i) Step 1: from the stator support at level 1, to a lower level 2, using a combined system of struts and ties; (ii) Step 2: from level 2 to the foundation using a RC torsional resistance system. Figure 7: Example 3: RC tunnel section tested by [27]: (**a**) Geometry and loading; (**b**) Compressive stresses at failure; (**c**) Damage pattern at failure. A S&T model was used in step 1 (Figure 8c), composed of T1 and T2 reinforcement systems. T1 is required for a first downward deflection of the tangential and horizontal short-circuit forces. A 15 deg inclination angle with respect to horizontal was used from a rule of thumb in this industry, to set the inclination of S1 struts. This allowed to design the vertical T1 rebars which were welded to a horizontal steel plate located at level 1, as shown in Figure 9a. T2 is required for a second outward/downward deflection and consists of 12 horizontal continuous circumferential rebars as shown in Figures 8 and 9. A system T3 of vertical and horizontal circumferential rebars was designed to take in the global torsional effect, once the short-circuit struts reach the external wall of the spiral case (Figure 9a). The reinforcement was modeled (Figure 8b) and embedded into the spiral case concrete 3D solid elements. Both truss elements and surface elements were used for reinforcement, where surface elements allow to model two orthogonal layers of reinforcement. The SRDM methodology was performed in this first example, using reduced values of input parameters: \(\phi_{c}f^{\prime}_{c}\), \(\phi_{c}f^{\prime}_{t}\) for concrete and \(\phi_{s}f_{y}\) for reinforcement at the beginning of analysis (partial safety factors approach). Figure 10a shows the evolution of the kinetic over internal energy ratio during loading and reduction phases. It can be concluded that no failure occurred, and static equilibrium was reached at the end. This is confirmed by the results shown in Figure 11.  
Figure 8: Spiral case: (**a**) Geometry; (**b**) Embedded reinforcement; (**c**) S&T original design model for the short-circuit load case. Figure 10: Energy ratio (kinetic over internal) for: (**a**) spiral case example; (**b**) draft tube example. Figure 9: Spiral case: (**a**,**b**): original design concept (**c**,**d**): numerical results in terms of concrete compressive stresses at the end of strength reduction phase. Figure 11a compares stress in reinforcement before and after strength reduction (envelope of maximum stresses for both directions for surface elements). Figure 11c shows (in red) reinforcement elements that yielded at the end of the reduction phase. Except for the T1 elements, yielding was limited to localized areas in other sections. Stresses in concrete struts at the end of reduction phase were not critical as shown Figure 11b.