# Safety Evaluation of Existing R.C. Buildings: Uncertainties Due to the Location of In Situ Tests
## 5 Conclusions  
In this paper, the case study of a framed reinforced concrete building designed to resist only gravitational and static loads, representative of a widespread typology of structures built in the 1960s in Italy, is examined. Indeed, buildings of this kind usually stand in seismic-prone zones, according to the current codes, and this requires improvements to their structural and building performances to guarantee acceptable levels of safety and habitability conditions. The actuality of this topic is also confirmed by the attention devoted by building codes to the analysis of existing buildings. These codes prescribe, among other procedures, the execution of experimental tests, the numbers of which depend on the desired knowledge level. Although this topic is still debated in the scientific literature [12; 13; 14; 15; 16], the Italian technical codes [1; 2] and the Eurocodes [4] prescribe the introduction of a confidence factor, based on the acquired knowledge level, in the assessment of seismic safety indexes, which serves to reduce the mean values of experimentally evaluated mechanical strengths of structural materials. It is worth noting that the positions in which the tests are performed depend on several factors, and, clearly, different analysts may choose different locations; consequently, they may assess different values of the mechanical properties and obtain different safety indexes. In the present paper, starting from the approach in [12], the case study of a residential r.c. building built in the 1960s in Italy is discussed with the aim of investigating the implications of the different choices that the technician in charge (the \"analyst\") can make regarding the structural elements to be tested for obtaining a prescribed level of knowledge. The case study of an r.c. building was examined, assuming, initially, perfect knowledge of the material mechanical properties of each structural element and, on this basis, evaluating the \"actual\" safety index. Then, numerical analyses were performed by considering the three knowledge levels prescribed by the building technical codes and, for each level, numerically simulating the acquisition of experimental strengths. In detail, a Monte Carlo approach was adopted to consider the effects of the different locations of the tests. A numerical simulation of \(10^{3}\) possible combinations of concrete and steel mechanical properties, as virtually assessed for each knowledge level suggested by the codes, was carried out, and the corresponding seismic safety indexes were evaluated by introducing the confidence factor suggested by technical codes for each knowledge level. To evaluate the capacity of the model assumed as a reference to describe the real structure, the same procedure was applied to nine different realisations of the same building, and thus a total number of 9x\(10^{3}\) combinations were analysed for each knowledge level. The analyses performed for the sample case show that the confidence factors corresponding to KL1 and KL2 [2] could effectively provide a precautionary assessment of the structural capacity of the building. With the level of knowledge KL2, in fact, for the analysed models (representative of nine alternative realisations of the reference model with equivalent statistical properties), almost all the analysts underestimated the actual building's structural capacity with an average probability of 92%. Thus, adopting a confidence factor CFKL2 = 1.2, the probability of overestimating the real structural capacity of the sample case discussed here was limited to about 8%, while for the level of knowledge KL1 (CFKL1 = 1.35), the probability of an unsafe evaluation became negligible. For the full-knowledge level, the safety index was instead overestimated when a value of CFKL3 = 1 was assumed, thus suggesting that the calibration of this parameter should not only depend on the number of available in situ tests but must consider their dispersion.