“…Damage models have been used by several authors to study masonry structures under various loading conditions: walls under seismic loads (Callerio & Papa, 1998), (Maier, Papa, & Nappi, 1991), (Papa, 1995), (Toti, Gattulli, & Sacco, 2015), (Wawrzynek & Cincio, 2005) ; walls under a point shear load (Addessi, Marfia, & Sacco, A plastic nonlocal damage model, 2002), (Addessi & Sacco, A multi-scale enriched model for the analysis of masonry panels, 2012), (Berto, Saetta, Scotta, & Vitaliani, 2004), (Uva & Salerno, 2006), (Zucchini & Lourenço, A micro-mechanical homogenisation model for masonry: Application to shear walls, 2009); walls under in-plane vertical or horizontal loads (Greco, Leonett, Luciano, & Nevone Blasi, 2016), (Luciano & Sacco, 1997), (Massart, Peerlings, & Geers, 2004), (Quinteros, Oller, & Nallim, 2012), (Tesei & Ventura, 2016), (Zahra & Dhanasekar, 2016), (Zucchini & Lourenço, A coupled homogenisation-damage model for masonry cracking, 2004), (Zucchini & Lourenço, Mechanics of masonry in compression: Results from a homogenisation approach, 2007); vaults under different loads (Creazza, Matteazzi, Saetta, & Vitaliani, 2002), (Pelà , Cervera, & Roca, 2011), (Stablon, Sellier, Domede, Plu, & Dieleman, 2012); and bridges (Domède, 2006), (Domede, Sellier, & Stablon, 2013) ; among others. Most of the studies on masonry using damage models consider a wall subjected to in-plane loads or earthquake motions; the case of vaults (bridge or buried arches) is not commonly discussed.…”