The seismic vulnerability of a historical Basilica church located in Italy is studied by means of limit analysis and nonlinear finite element (FE) analysis. Attention is posed to the failure mechanisms involving the fa?ade of the church and its interaction with the lateral walls. In particular, the limit analysis and the nonlinear FE analysis provide an estimate of the load collapse multiplier of the failure mechanisms. Results obtained from both approaches are in agreement and can support the selection of possible retrofitting measures to decrease the vulnerability of the church under seismic loads. 1. Introduction Recent Italian seismic events, such as the Emilia (2012) and the L’Aquila earthquakes (2009), have demonstrated how churches are susceptible to damage when subjected to earthquake motions [1–3]. In fact, designed to withstand vertical loads, churches in general present slender walls, lack of horizontal structures, weak or nonexistent connections among structural elements, absence of effective tie-rods to absorb arch thrusts [4], and irregular stone texture. These aspects, added to poor material performance especially in tensile stress mode [5], are among the reasons for the structural collapses of historical monumental buildings when subjected to seismic forces. Cases of damaged or collapsed churches after earthquake events (sometimes also immediately after their renovations) are numerous. It is worthwhile to remember the collapse of St. Possidonio church (Italy) in 2012, the partial collapse of the church of Santiago in Lorca (Spain) in 2011, the collapse of the Catholic Cathedral of Port au Prince in Haiti in 2010 (right after its total restoration), and the partial collapse of the main church in St. Pietro di Coppito (Italy) in 2009, after consistent work of conservation. In the literature, the approaches employed to analyze the seismic behaviour of masonry structures can be summarized as follows: micromodeling approaches (see e.g., [6, 7]), macromodeling approaches (see e.g., [8]), multiscale approaches (see e.g., [9]), and full-scale approaches (see e.g., [10–14]). Among these methods, the most suitable to determine the seismic vulnerability of masonry buildings are the latters that correspond to limit analysis and nonlinear FE analysis [15, 16]. Both approaches aim at providing the value of the load that activates the failure mechanisms of the macroelements in which the church can be subdivided. In fact, the behavior at collapse of a masonry church under a seismic event is rarely global since several out-of-plane collapses of
References
[1]
G. Milani, “Lesson learned after the Emilia-Romagna, Italy, 20–29 May 2012 earthquakes: a limit analysis insight on three masonry churches,” Engineering Failure Analysis, 2013.
[2]
G. Brandonisio, G. Lucibello, E. Mele, and A. De Luca, “Damage and performance evaluation of masonry churches in the 2009 L’Aquila earthquake,” Engineering Failure Analysis, 2013.
[3]
P. B. Louren?o, A. Trujillo, N. Mendes, and L. F. Ramos, “Seismic performance of the St. George of the Latins church: lessons learned from studying masonry ruins,” Engineering Structures, vol. 40, pp. 501–518, 2012.
[4]
C. Gentilini, A. Marzani, and M. Mazzotti, “Nondestructive characterization of tie-rods by means of dynamic testing, added masses and genetic algorithms,” Journal of Sound and Vibration, vol. 332, no. 1, pp. 76–101, 2013.
[5]
C. Gentilini, E. Franzoni, S. Bandini, and L. Nobile, “Effect of salt crystallisation on the shear behaviour of masonry walls: an experimental study,” Construction and Building Materials, vol. 37, pp. 181–189, 2012.
[6]
G. Formica, V. Sansalone, and R. Casciaro, “A mixed solution strategy for the nonlinear analysis of brick masonry walls,” Computer Methods in Applied Mechanics and Engineering, vol. 191, no. 51-52, pp. 5847–5876, 2002.
[7]
R. Senthivel and P. B. Louren?o, “Finite element modelling of deformation characteristics of historical stone masonry shear walls,” Engineering Structures, vol. 31, no. 9, pp. 1930–1943, 2009.
[8]
I. Caliò, F. Cannizzaro, M. Marletta, and B. Pantò, “A discrete-element approach for the simulation of the seismic behavior of historical buildings,” in Proceedings of the 18th Italian Group of Computational Mechanics (GIMC '10), Siracusa, Italy, 2010.
[9]
S. Brasile, R. Casciaro, and G. Formica, “Multilevel approach for brick masonry walls—part I: a numerical strategy for the nonlinear analysis,” Computer Methods in Applied Mechanics and Engineering, vol. 196, no. 49-52, pp. 4934–4951, 2007.
[10]
G. C. Manos, V. J. Soulis, and A. Diagouma, “Numerical investigation of the behaviour of the church of Agia Triada, Drakotrypa, Greece,” Advances in Engineering Software, vol. 39, no. 4, pp. 284–300, 2008.
[11]
M. Betti and A. Vignoli, “Assessment of seismic resistance of a basilica-type church under earthquake loading: modelling and analysis,” Advances in Engineering Software, vol. 39, no. 4, pp. 258–283, 2008.
[12]
G. Castellazzi, S. de Miranda, and C. Mazzotti, “Finite element modelling tuned on experimental testing for the structural health assessment of an ancient masonry arch bridge,” Mathematical Problems in Engineering, vol. 2012, Article ID 495019, 18 pages, 2012.
[13]
G. Castellazzi, “Cultural heritage preservation: seismic assessment of a church fa?ade,” in Proceedings of the 3rd International Conference on Urban Sustainability, Cultural Sustainability, Green Development, Green Structures and Clean Cars (USCUDAR '12), Barcellona, Spain, 2012.
[14]
C. Mazzotti, S. de Miranda, G. Castellazzi, and F. Carrea, “Structural assessment of the railway masonry arch bridge crossing the Reno river in Bologna,” in Proceedings of the 6th International Conference on Bridge Maintenance, Safety and Management (IABMAS '12), Cernobbio, Italy, 2012.
[15]
A. De Luca, A. Giordano, and E. Mele, “A simplified procedure for assessing the seismic capacity of masonry arches,” Engineering Structures, vol. 26, no. 13, pp. 1915–1929, 2004.
[16]
E. Mele, A. De Luca, and A. Giordano, “Modelling and analysis of a basilica under earthquake loading,” Journal of Cultural Heritage, vol. 4, no. 4, pp. 355–367, 2003.
[17]
Hibbitt Karlsson & Sorensen Inc., Abaqus Theory Manual, 1998.
[18]
H. R. Lotfi and P. B. Shing, “An appraisal of smeared crack models for masonry shear wall analysis,” Computers & Structures, vol. 41, no. 3, pp. 413–425, 1991.
[19]
M. Dhanasekar and W. Haider, “Explicit finite element analysis of lightly reinforced masonry shear walls,” Computers & Structures, vol. 86, no. 1-2, pp. 15–26, 2008.
[20]
M. Brigante, A. Cozzo, G. Frunzio, and M. Fulgione, “Valutazione sperimentale delle tensioni in mu3 ratura di tufo giallo napoletano,” in Atti del II Convegno, Salerno, Italy, September 2003.
[21]
M. Betti and A. Vignoli, “Modelling and analysis of a Romanesque church under earthquake loading: assessment of seismic resistance,” Engineering Structures, vol. 30, no. 2, pp. 352–367, 2008.
[22]
J. Heyman, “The safety of masonry arches,” International Journal of Mechanical Sciences, vol. 11, no. 4, pp. 363–385, 1969.
[23]
P. Block, T. Ciblac, and J. Ochsendorf, “Real-time limit analysis of vaulted masonry buildings,” Computers & Structures, vol. 84, no. 29-30, pp. 1841–1852, 2006.
[24]
S.O. n. 30. G.U. n. 29, 4 Febbraio 2008, “D.M. del Ministero delle Infrastrutture e dei Trasporti 14 Gennaio 2008, Nuove Norme Tecniche per le Costruzioni,” Italy, 2008.
[25]
Min. II.TT.C.S.L.P., “Istruzioni per l'applicazione delle “Nuove norme tecniche per le costruzioni” di cui al decreto ministeriale 14 gennaio 2008. Circolare del 2/2/2009, n. 617 del Ministero delle Infrastrutture e dei Trasporti approvata dal Consiglio Superiore dei Lavori Pubblici, Suppl. ord. n. 27 alla G.U. del 26/02/2009 n. 47,” 2008.
[26]
S. V. Chaudhari and M. A. Chakrabarti, “Modeling of concrete for nonlinear analysis using finite element code ABAQUS,” International Journal of Computer Applications, vol. 44, no. 7, pp. 14–18, 2012.
[27]
C. Gentilini, G. Gottardi, L. Govoni, A. Mentani, and F. Ubertini, “Design of falling rock protection barriers using numerical models,” Engineering Structures, vol. 50, pp. 96–106, 2013.
[28]
M. A. Ramalho, A. Taliercio, A. Anzani, L. Binda, and E. Papa, “A numerical model for the description of the nonlinear behaviour of multi-leaf masonry walls,” Advances in Engineering Software, vol. 39, no. 4, pp. 249–257, 2008.
[29]
A. Giordano, E. Mele, and A. De Luca, “Modelling of historical masonry structures: comparison of different approaches through a case study,” Engineering Structures, vol. 24, no. 8, pp. 1057–1069, 2002.
[30]
L. Berto, A. Saetta, R. Scotta, and R. Vitaliani, “Failure mechanism of masonry prism loaded in axial compression: computational aspects,” Materials and Structures, vol. 38, no. 276, pp. 249–256, 2005.
[31]
J. M. Adam, A. Brencich, T. G. Hughes, and T. Jefferson, “Micromodelling of eccentrically loaded brickwork: study of masonry wallettes,” Engineering Structures, vol. 32, no. 5, pp. 1244–1251, 2010.
[32]
P. B. Louren?o and J. Pina-Henriques, “Validation of analytical and continuum numerical methods for estimating the compressive strength of masonry,” Computers & Structures, vol. 84, no. 29-30, pp. 1977–1989, 2006.
[33]
H. Derakhshan, M. Griffith, and J. Ingham, “Out-of-plane behavior of one-way spanning unreinforced masonry walls,” Journal of Engineering Mechanics, vol. 139, no. 4, pp. 409–417, 2013.
[34]
G. Cifani, A. Lemme, and S. Podesta, “Beni monumentali e terremoto,” DEI srl, Tipografia del Genio Civile, Roma, Italy, 2005.
[35]
M. Como and A. Grimaldi, “An unilateral model for the limit analysis of masonry walls,” in Unilateral Problems in Structural Analysis, Springer, London, UK, 4th edition, 1985.