Issue 50

M. Godio et alii, Frattura ed Integrità Strutturale, 50 (2019) 194-208; DOI: 10.3221/IGF-ESIS.50.17 197 Figure 1 : Acceleration profile components of cracked URM walls subjected to out-of-plane relative top and bottom support motion: (a) component generated by the overall support motion; (b) component provided by the relative motion between the top and bottom supports; (c) component engendered by the inertia forces of the two rocking macro-blocks. Since in the experimental tests the out-of-plane walls are excited at their base, usually the overall support motion corresponds to the motion applied at the wall base and the diaphragm flexibility is concentrated at the wall top support. In that case, the trapezoidal acceleration profile of the support, i.e. the components (a)+(b) of the acceleration, can experience variation of the acceleration at the top of the wall only [15]. The URM walls tested in this study undergo generic out-of-plane relative support motions where both the top and the bottom supports can move. W ALL MODEL he numerical model used in this study consists of a discrete element model of an URM wall of unitary length spanning vertically between the top and the bottom supports (Fig. 2). The model is built by means of the commercial software UDEC 6.0 [12] and is the same model previously used and validated by Godio and Beyer [32]. In what follows, the model is briefly recalled. As a novelty, in this study the displacement histories applied to the wall top and bottom supports are different, as illustrated in Fig. 2. The discrete element model falls within the class of simplified micro-models for masonry, according to which each masonry unit has an effective height h b that is equivalent to the nominal unit height plus the mortar joint thickness (Fig. 2). The numerical model used in this study consists of a 2.8 m-high masonry wall made up of 14 units of effective height 0.2 m each, laying on a 0.6 x 0.3 m² discrete element representing the bottom wall support and in contact with a 0.5 x 0.1 m² discrete element representing the top wall support. This top block exerts a permanent, or dead, load of 0.88 kN. In addition, a vertical stress σ v is applied to the top support. The axial force, or overburden, O is the resultant of the vertical stress plus the dead load. Each masonry unit is modelled as an element of infinite stiffness and strength [12]. The wall deformation is therefore included in the constitutive law used for contact. As in [32], a Coulomb slip model with integration over the contact area is adopted as joint material model [12]. The elastic joint stiffness coefficients are calculated as [10,32] w n b w,e m ff E t k h t  n s k k 2(1 ν)   (3) where E m is the elastic modulus of masonry and ν is its Poisson’s ratio. The joints are also characterised by a tensile strength f t , a cohesion c, a friction angle φ, and a dilatation angle ψ. The masonry units have rounded corners [12]. Contact between the units consequently occurs over an effective thickness t w,eff defined as w,eff w b t t 2r   (4) with r b the radius of the rounded corner of the units. Contact is discretised in such a way that 10 contact points are placed across the effective wall thickness [32], which enables a realistic simulation of the contact forces exchanged by the blocks during the wall bending and rocking [35,36]. The parametric study carried out in this paper aims at studying the influence u T ( t ) u B ( t ) .. .. u T ( t ) u B ( t ) ( a ) ( b ) ( c ) T