# Safety Evaluation of Existing R.C. Buildings: Uncertainties Due to the Location of In Situ Tests
###### Abstract
Specifically, this paper investigates, through the case study of a typical reinforced concrete structure of the 1960s built in Italy, the probability that a safety assessment based on a pre-defined knowledge level and the value consequently assigned to the confidence factor can actually lead to the technician in charge obtaining a precautionary estimate of the building's capacity to resist seismic actions. To this end, the actual level of seismic safety of the building--evaluated by assuming perfect knowledge (never available in practice) of the mechanical properties of all the structural elements [12]--is compared with the safety level evaluated under the assumption that the tests were carried out, and thus that the mechanical properties were estimated, only for a small number of structural elements. In this case, as is usual, the safety index was assessed by introducing the elements' average strengths divided by a CF whose value was fixed according to the level of knowledge corresponding to the number of tests. For a given knowledge level, the probability distribution of the estimated safety level was evaluated in the paper by means of a Monte Carlo approach, which allows phenomena with significant uncertainties to be modelled by considering randomly generated scenarios and by evaluating the outcomes of the investigated model for each of them. In this way, the mean value of an output, its distribution, and its minimum or maximum values can be estimated. This method is used widely to evaluate the impact of risk and uncertainties in the prediction of outcomes. In the case examined here, the Monte Carlo method was applied to simulate a large set of alternative selections of the structural elements to be tested, with the same number of such elements randomly picked out, and by estimating the safety index of the building for each scenario. Moreover, to take into account that in real cases perfect knowledge of structural characteristics can never be attained, nine alternative realisations of the reference model--with equivalent statistical properties--were considered, and therefore a total number of \(9\times 10^{3}\) analyses were carried out for each one of the three knowledge levels prescribed by the codes. This procedure was intended to evaluate the effect on safety estimation uncertainty of different possible choices of structural element locations that, _ceteris paribus_, can be made by the technician in charge (denoted as the analyst in the following, according to [12]), even when the number of such tests is assumed to be constant. In this way, the paper deals with an intrinsic uncertainty in safety evaluation, starting from the observation that no strategy can assure that the different positions of the tests chosen by different analysts--even when they perform the same number of tests--will lead to unique \"best\" values of the average strengths of concrete and reinforcing steel. Thus, the paper explores how the unavoidable uncertainty of these values affects the evaluation of the safety index obtained by a given analyst (i.e., what the probability is for a given analyst of underestimating or overestimating the \"true\"--but never really knowable--safety index). The rest of the paper is organised in four parts: Section 2 describes the case study and the main assumptions of the performed analyses, Section 3 describes the numerical model implemented to assess building safety levels, Section 4 reports the statistical analyses and discusses the effects of the confidence factor values on the accuracy of the assessed vulnerability index, and Section 5 presents the conclusions.