PSI - Issue 44

Stefano Bracchi et al. / Procedia Structural Integrity 44 (2023) 394–401 Stefano Bracchi et al. / Structural Integrity Procedia 00 (2022) 000 – 000

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Fig. 1c shows the effect of Bayesian updating on the distribution of mechanical properties. The prior distribution at KL2-A (dashed line) is updated based on the results of in-situ tests, which reduce the uncertainties, obtaining narrower posterior distributions (colored lines). The distributions of E are different between KL3-A-LOW-1 and KL3 A-LOW-2, due to the largest number of tests performed in the second case. Defining a posterior distribution with reduced dispersion, Bayesian updating is rewarding the larger knowledge obtained by the engineer by means of experimental tests. 4. Results of the analyses Fig. 2 shows the pushover curves obtained at KL1 and the distribution of critical peak ground acceleration (i.e. the minimum acceleration among all the analyses with different directions of seismic action and different force distribution) corresponding to the ultimate limit state. It is possible to notice the large dispersion of the results, due to the large uncertainties characterizing KL1. To calibrate partial safety factors, the lognormal distribution of the global displacement capacity associated with the critical analyses was calculated. The partial safety factors were then calculated as the ratio between the 50 th and 16 th percentile of the lognormal distribution, as: = 50 ℎ 16 ℎ (2) As regards KL2-A, pushover curves tend to have a lower dispersion with respect to KL1, due to the absence of the uncertainty on mortar quality. The lower dispersion is visible also in terms of acceleration capacity (Fig. 3). For KL2 B, the dispersion in the results is lower than KL2-A and characterized by larger values of acceleration capacity, consistently with the good quality of mortar assumed, as confirmed by the median value, which is larger than at KL2 A.

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Fig. 2. Pushover curves (a) and distributions of acceleration capacity corresponding to ULS (b) obtained from analyses at KL1.

At KL3-A-LOW-1, the engineer performs only two in-situ tests on a bad quality masonry; properties are hence assumed to belong to the lower third of the interval defined at KL2. Pushover curves tend to have a larger dispersion with respect to KL2-A, due to some models characterized by a different failure mechanism. This can be explained by the fact that several elements have similar shear and flexural strength and also a small variation in mechanical properties can vary the governing failure mechanism. The increase of dispersion is evident also when looking at the capacity in terms of peak ground acceleration (Fig. 4). In this case, the dispersion at KL3 due to the presence of different failure mechanisms cannot be reduced increasing the number of tests (KL3-A-LOW-2). Selecting an average masonry quality (KL3-A-CEN-1), it is evident how the dispersion is reducing. Also in this case, no reduction of uncertainties is evident when increasing the number of tests (KL3-A-CEN-2). Also selecting a good masonry quality (KL3-A-UPP-1), the dispersion reduces. At KL3-A-UPP-2, different failure mechanisms take