## 2 Why Strength Reduction for Large RC Structures?  
### FE and ANFE in the Field of Large RC Structures  
Figure 1 presents the powerhouse hydroelectric unit considered in this study. It is a RC structure characterized by complex geometry attributable to the hydraulic passage, and large members with thicknesses exceeding one meter. Typically, such large RC structures have low reinforcement ratios rarely exceeding 0.5%. The justification for employing sophisticated analyses tools such as ANFEA in assessing this structure, arises from the interplay of various factors: complex 3D geometry, tensile stresses and crack development at early age due to heat of hydration effects and mechanical restraint to rock foundation and size effect.  
Figure 1c displays a typical result from ANFEA for the semi-spiral case component of the powerhouse and for the critical short-circuit load case, schematically shown in Figure 1b. Despite the notably high magnitude of the short-circuit force F in this example (approximately 6000 kN, as detailed later), only a few elements exhibit cracking (coloured in red in Figure 1d), even though minimum reinforcement was provided in the model. This result is quite common in the field of mass hydraulic structures and can be attributed to three factors: (i) the contribution of the tensile strength of the concrete \(f_{i}^{\prime}\) (in the order of 2 to 4 MPa), which triggers the initiation of cracks; (ii) the contribution of the post-cracking energy of concrete after crack initiation and during crack propagation. This fracture energy, \(G_{F}\), in the order of 0.1 to 0.5 N.mm/mm\({}^{2}\) for mass concrete with coarse aggregates, would have important contribution in case of large concrete members due to the extensive cracked areas involved; (iii) the static redundancy of the structures also plays a crucial role by allowing redistribution of tensile stresses.  
Based on the authors' experience with ANFE, it is possible for a large RC structure to withstand external efforts solely through the contributions in tension and compression of concrete, without relying on any reinforcement. However, it becomes challenging to assert the adequacy of the structure's behavior in this scenario, as the contribution of concrete in tension is not guaranteed unless all the complex interactions at early age and very early age (tensile creep, heat of hydration effects, maturity development) are meticulously incorporated into the simulation.  
It can be inferred that assessing the actual demand on the reinforcement is not feasible using ANFEA, as it is somewhat _hidden by the tensile contribution of concrete_. In such cases, conventional linear elastic FE analyses may be used, and the demand on reinforcement can be evaluated after integrating stresses into sectional forces using available algorithms (e.g., [14]). However, this methodology becomes unusable when thermal effects are included in the FE model. High tensile sectional forces may arise due to temperature drops and to the large member size. These forces decrease instantaneously after initiation of the first crack and can be only be accurately considered within a non-linear computational framework.