# Safety Evaluation of Existing R.C. Buildings: Uncertainties Due to the Location of In Situ Tests
## 4 Effects of Uncertainties Related to Test Locations  
According to the Italian technical codes [1; 2], the seismic vulnerability assessment of an existing structure always requires the execution of in situ tests on the structural elements. Their number depends on the choice of the knowledge level, which in turn is related to the confidence factor (CF) (see Section 1) introduced to pass from the average values of test results to the design values of materials' strengths. All other factors being equal (the geometry of the building, the quantity and arrangement of the reinforcements, etc. ), as assumed in this paper, the design strength of concrete and steel, on the other hand, affect the safety level of the building provided by the structural analysis. However, even when the number of tests can be assumed as fixed (e.g., according to the indications of technical codes), the technician in charge may make alternative choices regarding the position of the tests. Therefore, for the same knowledge level, different analysts may estimate different mechanical properties for the same building. As a consequence, even if the numerical model developed to assess the response of the investigated structure and the confidence factor are the same with respect to any other characteristic of the building, different analysts may estimate different values of the seismic safety index because of the variation in the mean values of the concrete and steel strengths that each analyst assumed to be representative of the existing building on the basis of the available in situ tests. Mean values of concrete and steel strength can therefore be viewed as samples for a statistical analysis of the seismic safety index, as discussed below. The procedure here proposed is based on a Monte Carlo simulation to select the structural elements whose strengths are assumed to be measured in situ, with the aim of quantifying the uncertainty in the evaluated safety index as the location of the tests varies while keeping their number fixed. In detail, the probability distribution of the safety indexes evaluated by 100 different analysts was obtained, i.e., considering the mean values of concrete and steel strengths corresponding to 100 different combinations of test locations. To reduce the computational effort, however, for each given knowledge level, only 15 numerical FEM models were analysed, each one corresponding to a different combination of the mean strengths (\(f_{c}\) and \(f_{s}\)) virtually obtained by different analysts. As is usual in engineering practice, the obtained mean values were considered to be constant throughout the whole structure during the assessment of the safety index, which is different from the procedure (Section 3) for the evaluation of the actual index, where the knowledge of the local strength of each element was assumed and introduced in the model. The evaluated safety indexes for each \(f_{c}\), \(f_{s}\) pair are listed in Table 3 for knowledge level KL2 and a confidence factor (CFKL2) equal to 1.2 [2]. The safety indexes (\(\alpha_{KL2}\)) corresponding to other combinations of \(f_{c}\) and \(f_{s}\) may be obtained by fitting the obtained value by means of a polynomial law (see Figure 2). Similarly, Table 4 shows the safety indexes (\(\alpha_{KL1}\)) corresponding to knowledge level KL1 and CFKL1 = 1.35. At first the analyses with knowledge level KL2 are described below, assuming that no other information (e.g., results of tests during the building process) was available on the strength of materials. Under this hypothesis and with reference to the columns, i.e., the elements by which the safety level is conditioned in this case study (see Section 2), the Italian technical codes [1,2] suggest extended in situ testing that involves the testing of two samples of steel bars per storey and two concrete cores for each 300 m  
Figure 2: Polynomial surface (of order 3) fitting the values of the seismic safety indexes (\(\alpha_{KL2}\)) in Table 3 (black dots).