Tilting plane tests on a small-scale masonry cross vault: Experimental results and numerical simulations through a heterogeneous approach G. Milani a , M. Rossi b , C. Calderini b,⇑ , S. Lagomarsino b a Department of Architecture, Built Environment and Construction Engineering (A.B.C.), Technical University of Milan, Piazza Leonardo da Vinci 32, 20133 Milan, Italy b Department of Civil, Chemical and Environmental Engineering (DICCA), Via Montallegro 1, 16145 Genoa, University of Genoa, Italy article info Article history: Received 12 August 2015 Revised 21 March 2016 Accepted 11 May 2016 Keywords: Masonry cross vaults Discrete non-linear FEM Collapse load prediction Seismic mechanisms Experimental simulation abstract The seismic response of masonry vaults is discussed by presenting the results of an experimental campaign on a small-scale model and their numerical simulation though a heterogeneous full 3D non-linear Finite Element (FE) approach. The model relies into a discretization of the blocks by means of few rigid-infinitely resistant parallelepiped elements interacting by means of planar four-noded inter- faces, where all the deformation (elastic and inelastic) occurs. In the framework of a heterogeneous approach, two typologies of interfaces are present, namely internal brick–brick interfaces, here assumed elastic, and mortar joints with zero thickness, behaving as a frictional (Mohr–Coulomb) material with infinite strength in compression and almost vanishing tensile strength. The model is incremental, non- linear elasto-plastic and exhibits softening at mortar interfaces. Each load step is solved by means of mathematical programming, i.e. through the formulation of a suitable constrained minimization problem where the objective function is represented by the energy of the mechanical system. The experimental and numerical results are compared and discussed in terms of both collapse mechanisms and force/dis- placement capacity. Ó 2016 Elsevier Ltd. All rights reserved. 1. Introduction The disasters caused by past and recent earthquakes on both monumental and ordinary buildings of historical centers have induced the researchers to investigate their seismic behavior. Most of the research works were focused on studying the seismic response of masonry vertical structures, while less efforts were addressed to the analysis of horizontal structural elements, gener- ally constituted by timber floors or masonry vaults. These latter elements, in particular, have been little studied, especially in the context of historical buildings [1,2]. However, they have a relevant role in the seismic preservation of heritage buildings. On the one hand, working as horizontal diaphragms, their behavior signifi- cantly affect the overall response of the building in terms of strength and stiffness; on the other hand, their collapse may cause casualties and cultural losses (related to the presence of frescos or attached decorative elements). Despite the importance of the problem, at present there is still a lack of knowledge in understanding the 3D behavior of vaults because of its complexity. In published literature, many studies on different modeling strategies for masonry vaults were done. Most of them have been oriented to the analysis of vaults under static forces, either by extending the classic theory of limit analysis of arches to spatial structures [3–9] or adopting non-linear contin- uum [10–14] or discrete models developed in the framework of the Finite Element method [12–17]. However, only few of them are specifically addressed to the seismic analysis, and still less are focused on understanding vaults behavior in the context of the seismic response of the whole building [18,19]. A further effective tool of analysis consists in experimental investigations that aim to better understand the three-dimensional behavior of vaults and to provide suitable data to verify the reliability of theoretical models to simulate their response, e.g. [20–22]. An extensive literature review and classification of analytical and numerical modeling techniques, as well as experimental evidences, is given in [23]. In this paper, the attention is focused on the investigation of a heterogeneous non-linear FE code, developed by the first author of this paper, in predicting the seismic behavior of vaults. In partic- ular, the response of the vault when subjected to horizontal forces proportional to their mass and to differential displacements at the abutments is analysed. Its capability is verified based on the results of a new set of experimental tests on a 1:5 small scale model of a cross vault carried out by the other three authors and described in Section 2. The numerical model, fully described in Section 3, relies into a discretization of masonry material in rigid infinitely resistant eight-node elements, while mortar joints are lumped into http://dx.doi.org/10.1016/j.engstruct.2016.05.017 0141-0296/Ó 2016 Elsevier Ltd. All rights reserved. ⇑ Corresponding author. Tel.: +39 010 3536514; fax: +39 010 3532534. E-mail address: chiara.calderini@unige.it (C. Calderini). Engineering Structures 123 (2016) 300–312 Contents lists available at ScienceDirect Engineering Structures journal homepage: www.elsevier.com/locate/engstruct