PSI - Issue 29

R. Gagliardo et al. / Procedia Structural Integrity 29 (2020) 48–54 R. Gagliardo, G. Terracciano, L. Cascini, F. Portioli, R. Landolfo/ Structural Integrity Procedia 00 (2019) 000 – 000

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1. Introduction The Architectural Cultura l Heritage must be protected aga inst na tural risks, not only seismic but a lso hydrogeological one. The issue of thevulnerability of masonry structures subjected to foundation movements is a still open topic in litera ture (Como (2015); Ochsendorf (2006); DeJong (2016)). A number of challenges exists in this research field. Among them, numerical and modelling approaches for the performance assessment of structures affected by settlement plays an important role. Various modelling approaches were a lready proposed in litera ture, some of them considering masonry as assemblage of discrete blocks (Baggio and Trovalusci (1998); Orduña and Lourenço (2005-1); Orduña andLourenço (2005-2); Bui andLimam(2012); Bui et a l. (2017); McInerney andDeJong (2015); Cascini et a l. (2020); Portioli and Cascini (2016); Portioli and Cascini (2017); Portioli (2020); Ga lassi et al. (2018-1); Ga lassi et a l. (2018-2); D’Altri et a l. ( 2019); Angelillo et a l. (2018); Di Carlo et al. (2018)) others like a continuum medium (de Felice and Malena (2019); Spada (2019); Milani et a l. (2016); Rossi et a l. (2016); Caliò et al. (2012); Caliò et a l. (2016); Giardina et a l. (2013); Giardina et a l. (2015); Giardina et a l. (2019); Reccia et a l. (2014); Alessandri et a l. (2015); Amorosi et a l. (2012);Amorosi et a l. (2014); Amorosi et a l. (2016); Lasciarrea et a l. (2019); Torres et a l. (2019); Drougkas et a l. (2019); Tubaldi et a l. (2018); Casalegnoet a l. (2013)). Applied element models were a lso introduced in litera ture for the performance assessment of masonry structure (Ma lomo et a l. (2019 -1); Ma lomo et a l. (2019-2)). The issue of the analyticalmodel for the collapse mechanism assessment of masonry types subjected to spreading support is a lso a high deba ted topic (Zampieri et a l. (2018); Zampieri et a l. (2019)). Comparisons betweendifferent numerical formulations devoted to theassessment of masonry structures subjected to settlements or spreading supportwere presented in Pepe et al. (2020-1), Pepe et al. (2020-2) and Landolfoet al. (2020). In this framework, this conference paper a ims a t assessing the structural response of masonry monumental church façades under settlement using a modelling stra tegy based on a discrete Rigid Block Limit Analysis (RBLA). The procedure analyzes structuremodelled as a collection of polyhedral rigid blocks assuming frictional contact interfaces with infinite compressive strength and zero tensile strength and neglecting the mortar contribution. The blocks interaction takes place at the interfaces, adopting a concave contact point formulation, where the internal forces are loca tedat the vertexes of the blocks and areessentially the normal force and the shear forces. The formulation involves both sliding and opening a t contact surfaces for the fa ilure conditions, assuming a cohesionless Coulomb fa ilure criterion. The casestudyof the monumental façade of the churchof theNatività della Beata VergineMaria in Bondeno (Italy) is investiga ted in this paper. A uniform foundation displacement is applied a t half of the model base a iming at the assessment of the crack pa ttern and structural behavior a t collapse. The va lue of the loss of the base reaction is associated to the activationof the failure mechanismcorresponding to the imposed settlement. The computational ability of thenumerical procedure is discussed in terms of CPUtime to solve themathematical problem andconvergence features. The paper is organized as follows: the rigid block model is described in section 2. Then, the case-study of the monumental church façade is presented andanalyzed in section3. Fina lly, the outputs are illustra tedandcompared. Nomenclature n k normal forcecomponent a t contact point k t 1k shear forcecomponent a t contact point k a long local coordinate axis 1 t 2k shear forcecomponent a t contact point k a long local coordinate axis 2 c vector of thecontact forces α load factor A equilibrium matrix of the rigid block model f D vector of dead loads f S vector of live loads μ friction coefficient ρ weight for unit volume