PSI - Issue 44

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

395

2

Stefano Bracchi et al. / Structural Integrity Procedia 00 (2022) 000 – 000

1. Introduction The current version of Eurocode 8 (EN1998-3, 2005, EC8) faces the problem of building knowledge by introducing discrete knowledge levels (KLs), with associated values of a confidence factor (CF), to be applied as reduction factor of material strengths. Several works (e.g. Franchin et al. 2010; Tondelli et al. 2012) pointed out the limitations of this approach for different types of buildings and in particular for unreinforced masonry (URM) buildings. The code indeed does not directly address several sources of uncertainties (e.g. Rota et al. 2014; Bracchi et al. 2015) and it does not differentiate the approach based on the different analysis methods. Also, in case of nonlinear static analysis, the reduction of material strengths does not usually correspond to a consistent reduction of the building displacement capacity. The draft of the new Eurocode 8 (EN1998-3, 2021), currently under review, proposes a new approach for accounting for building knowledge in case of nonlinear static analysis, based on partial safety factors to be applied to the lateral displacement capacity of the building. However, at least when referring to URM buildings, the proposed methodology needs to be properly validated by specific studies. Furthermore, proposed values of the partial safety factors appear to be significantly large (1.7-1.9), without resulting from a proper calibration. Therefore, this work aims at studying the consistency of this assessment procedure, by verifying that an increase of knowledge actually implies a reduction in the uncertainties on the seismic assessment and by providing a probabilistic framework for the calibration of partial safety factors ’ values . To this aim, the work proposes a procedure, accounting for the possible choices of an engineer in charge of the assessment, and considering all the KLs. At each KL, various structures with different sets of mechanical properties are considered, by sampling each mechanical parameter from suitably defined probability distributions and properly accounting for correlation between material properties and structural members. Nonlinear static analyses are then performed using the TREMURI software (Lagomarsino et al. 2013), adopting multi-linear constitutive laws for piers and spandrels (Cattari and Lagomarsino 2013). Performing the seismic assessment of each structure, it is possible to derive distributions of displacement capacity of the building, from which values of partial safety factors can be calculated. In this procedure, epistemic uncertainties are accounted for, varying the width of the intervals on which marginal distributions of mechanical properties are defined, based on the knowledge level selected by the engineer assessing the considered structure. The interval of values on which marginal distributions are defined is significantly larger at KL1, whereas its width reduces at KL2 and KL3 when information on the quality of mortar is present. At KL3, EC8 proposes the application of a Bayesian updating approach (Bracchi et al. 2016), allowing to define posterior distributions of material properties, accounting for the results of experimental tests performed. 2. Seismic assessment of existing URM buildings according to the draft of the new EC8 The draft of the new EC8 introduces three Knowledge Levels (KL1, KL2, KL3), accounting for the epistemic uncertainty involved in the seismic assessment process. In particular, EC8 defines three different categories of knowledge, related to geometry (Knowledge Level of Geometry, KLG), construction details (Knowledge Level of Construction Details, KLD) and materials (Knowledge Level of Material, KLM). At each of these categories of knowledge, a minimum (KLG1, KLD1, KLM1), average (KLG2, KLD2, KLM2) and maximum (KLG3, KLD3, KLM3) level of knowledge is associated. To attain a specific KL, it is possible to perform investigations or experimental tests with a specified degree of completeness: limited, extended and exhaustive. Knowledge of material properties represents the most important source of uncertainty of those previously mentioned. To identify values of material properties, the engineer can select a masonry typology among the ones proposed by EC8. For each typology, EC8 provides an interval of variation of material properties, with the associated normal distribution. Mechanical parameters considered in this table are compressive strength of masonry f m , tensile strength associated with diagonal cracking f t , initial shear strength f v0 , Young’s modulus E , shear modulus G and specific weight w . Values in the table refer to bad quality masonry, with weak mortar and lack of transversal connections among the leaves. In the majority of the cases, the engineer is able of identifying the correct masonry typology based on visual survey of the surface of the walls, sometimes with more thorough local investigations. However, this identification is not always straightforward, especially in case of stone masonry (Bracchi et al. 2016).