GNGTS 2019 - Atti del 38° Convegno Nazionale

430 GNGTS 2019 S essione 2.2 The vulnerability of each analysed mechanism has been evaluated by using multi-linear regressions, in which the response, d , representing the occurred damage, and the considered v explanatory variables, x , accounting for the vulnerability modifiers, are fitted by a linear formulation, according to: d = m 1 x 1 + m 2 x 2 + … + m n x n + b + e (1) where x 1 represents the MCS intensity measure univocally assigned to each church location and referred to one of the two main shocks; x 2 , x 3 , … x v are the vulnerability modifiers considered for each mechanism; m 1 , m 2 , … m v are the obtained regression coefficients; b is the intercept and e is the error term. The influence of each vulnerability modifier is considered assigning them a score between 0 and 1 as indicator of either the absence or presence of a characteristic and its effectiveness. A modifier reducing the vulnerability, such as an earthquake-resistant element, will score close to 0 if effective and 1 if ineffective or absent. Amodifier increasing the vulnerability will score close to 1 if present and 0 if absent or negligible. Two statistical procedures, namely the Stepwise and the Best Subsets (Draper and Smith 1998), were used to determine the variables that generated the most efficient predictive model: the Stepwise selection method, that consists in inserting variables in turn until the regression equation involves a p -value below the selected threshold, and the Best Subsets procedure, that selects the subset of parameters that optimise an objective criterion, such as having the largest coefficient of determination. The two procedures used allow to identify those parameters that can be neglected, while providing both a better damage prediction and the possibility of a faster territorial-scale vulnerability assessment. Although not included in the current Italian form, poormasonry qualitywas found to be crucial for at least twenty mechanisms. It is also important to highlight that the presence of poor masonry can lead to wall disintegration (Fig. 1), before a rigid-body mechanism can be activated. In the case at hand, this phenomenon was observed in 21% of the activated mechanisms. Therefore, masonry performance is crucial and the investigation of its mortar is recommended (Liberatore et al., 2016). Other very relevant modifiers are connections, between intersecting walls or between walls and horizontal structures, which influence twelve regressions. On the contrary, despite is widely known that tie rods help to reduce the overturning of the walls (Giresini et al., 2018), they seem to play a negligible role, probably due to the predominance of other modifiers such as connections. It was also found that buttresses only slightly influenced the predicted damage, but their presence was detected only in about 15% of the investigated churches. Large slenderness noticeably influenced the two mechanisms associated with the presence of dome and belfry (#14 and #28). Other parameters, such as large openings (whose combined length exceeds 1/3 of the wall length), heterogeneous materials (assigned in case of reed-mat vaults for mechanism #8 and when two adjacent structural elements are made of different masonry types), asymmetry conditions (e.g., due to eccentricity of a projection with respect to the underlying masonry, or due to juxtaposition of a new extension) and the presence of vertical-stacked-bond vaults, are relevant for specific mechanisms. Fig. 1 - Example of poor quality masonry causing wall disintegration: San Lorenzo Martire (Cossito, Amatrice).