Nonlinear Static and Dynamic Analysis of Rocking Masonry Corners Using Rigid Macro-Block Modeling

Abstract

The corner failure is one of the most typical local mechanisms in masonry buildings vulnerable to earthquakes. The seismic assessment of this mechanism is poorly studied in the literature and in this paper it is addressed by means of both nonlinear static and dynamic analyses of rocking rigid blocks. The static approach is based on the displacement-based method and is aimed at predicting the onset of the 3D failure mechanism and its evolution through incremental kinematic analysis. This approach also considers the presence of a thrusting roof and the stabilizing contribution of frictional resistances exerted within interlocked walls. The capacity in terms of both forces and displacements is compared with the seismic demand through the construction of acceleration-displacement response spectra, with some originality. The nonlinear dynamic approach is based on the seminal Housner's work on rocking rigid blocks and considers the in°uence of transverse walls, roof overloads and outward thrust, all included in an updated equation of one-sided motion. In particular, the process of de¯ning an equivalent prismatic block, representative of the original corner geometry, is presented to convert the 3D dynamic problem into a 2D rocking motion. The wide suitability and advantage of such modeling approaches to assess the seismic response of rocking masonry structures with reference to spe-ci¯c limit states are demonstrated through a real case study, i.e. the collapse of a corner in a masonry school building during the 2016-2017 Central Italy seismic sequence. The compared results provide a good agreement of predictions in terms of both onset and overturning conditions, for which the static model appears to be more conservative than the dynamic one.

Experimental estimation of energy dissipation in rocking masonry walls restrained by an innovative seismic dissipator (LICORD)

“…The most common model for rocking masonry consists in a single degree of freedom (SDOF) system rocking about the two corner points (pivot points) on the ground. An additional horizontal restraint allows the simulation of transverse walls, vaults, arches or typical anti-seismic devices such as steel tie-rods (Giresini 2017;Argiento et al 2019;Casapulla et al 2019;Giresini et al 2019a). Often, steel tie-rods apply tensile concentrated forces during motion that could generate localized masonry failures, especially where the assumption of monolithic masonry is not adequate.…”

ONE-SIDED rocking analysis of corner mechanisms in masonry structures: Influence of geometry, energy dissipation, boundary conditions

“…The vulnerability of this mechanism is increased with the destabilizing contribution of the roof and the presence of openings near the edge. Other authors recently investigated this mechanism from experimental and analytical points of view and using non-linear static analysis procedures [16][17][18]. In this paper, the one-sided motion of a corner mechanism is investigated by analyzing it as single degree of freedom system with spring bed simulating the adjacent walls.…”

Out-of-Plane Seismic Response of Masonry Façades Using Discrete Macro-Element and Rigid Block Models

“…A compressive bed spring ( ) is considered in the onesided motion calculated as reported in [22], whereas an average tensile spring bed stiffness K , ′ has been assumed. This has been obtained by imposing and equivalence with a corresponding frictional macro-element model [26] for a displacement 1 corresponding to the end of the constant friction force ,1 in the capacity curve obtained from the kinematic analysis. The tensile spring bed stiffness K ,1…”

“…′ is the ratio of the corresponding frictional force with respect to the displacement times the thickness of the transverse walls , that is K ,1 ′ = ,1 / 1 [26]. The geometrical parameter Zg represents the height of the center of mass, R is the radius vector, h the equivalent block height,  the slenderness ratio of the block,  the masonry density, 0 the moment of inertia.…”