A three‐dimensional macroelement for modelling the in‐plane and out‐of‐plane response of masonry walls

Abstract

The seismic performance of unreinforced masonry buildings is commonly assessed using equivalent frame modelling. Its computational efficiency allows for a large number of analyses to be conducted, which are often required to account for epistemic and aleatoric uncertainties. To obtain a full description of the building response, in-plane and out-of-plane failure modes need to be considered, though previous elements for equivalent frame models of unreinforced masonry buildings only account for the in-plane response. This paper presents the formulation of a three-dimensional macroelement for modelling the dynamic in-plane and out-of-plane behaviour of masonry panels, which extends the approach of a previously developed macroelement to simulate the in-plane response. The proposed three-node, three-dimensional macroelement is implemented in the software OpenSees and describes the main features of the in-plane and out-of-plane behaviour of a masonry wall, including second-order geometrical effects and a coupled shear/flexural response. It also allows for the use of complex material models. The proposed element is used to simulate experimental results for in-plane shear-compression tests and out-of-plane free vibration tests of masonry panels. The implemented element, as well as the example models, is openly shared through the repository https://github.com/ eesd-epfl/OpenSees/wiki. K E Y W O R D S 3D macroelement, equivalent frame modelling, masonry, out-of-plane response, seismic analysis 1 | INTRODUCTION Unreinforced masonry buildings are among the most vulnerable under earthquake loading, and as such, are responsible for much of the economic and social impact of a seismic event. Because their seismic behaviour is heavily influenced by nonlinear phenomena, such as cracking or crushing, that is already apparent at moderate deformation levels, it is common to conduct nonlinear seismic analyses when assessing or even designing such buildings. To assist in this regard, several approaches have been proposed in the literature for modelling structural masonry, varying in the level of detail. In detailed micromodelling approaches, 1 the heterogeneity of the material is treated explicitly, whereas in simplified micromodels, joints are modelled by interface elements. 2,3 Less computationally expensive models include homogenised micromodels 4-6 and models in which damage is smeared into a continuum. 7-9 As an alternative to finite element modelling, discrete elements have been used for blocky structures, 10,11 accounting for the complex dynamics of interacting blocks. Although such modelling approaches comprise different levels of complexity and are, as a result,

Equivalent-Frame Modeling of Two Shaking Table Tests of Masonry Buildings Accounting for Their Out-Of-Plane Response

“…All masonry elements, both piers and spandrels, in the following analyses are modeled through the macroelement formulated in Vanin et al (2019) and presented in detail in Vanin (2019). Node regions between piers and spandrels are considered as rigid zones in which no deformation takes place.…”

“…The used elements can capture the in-plane and out-of-plane flexural response through three sectional models applied at the element ends and at the central section, which can reproduce the deformation modes shown in Figures 1A-C. Those sections are equipped with the section model presented in Vanin et al (2019), accounting for a no-tension material with limited compressive strength, modeling possible crushing at the section edges. The compressive behavior of the material is defined by a damage law which imposes no post-peak strength degradation and unloading to the origin.…”

“…Shear deformations in the out-of-plane direction, as well as torsional deformations, are modeled as linear elastic. Further details on the element formulation are presented in Vanin et al (2019) and Vanin (2019), to which the reader is referred. To capture the out-of-plane behavior of the element, a P − formulation is applied.…”

“…Models developed using forcebased elements (Raka et al, 2015;Siano et al, 2018;Peruch et al, 2019a,b) can potentially capture the out-of-plane response, although they have not yet been used in this context. One macroelement formulation explicitly developed for this is presented in Vanin et al (2019) and will be adopted herein. Moreover, these models require the explicit definition of modeling details that are neglected in standard in-plane equivalent-frame analyses, such as the possibly nonlinear behavior of all connections, including wall-to-wall connections at corners and floor-to-wall connections, or more generally, the nonlinear response of weak floors.…”

“…Moreover, these models require the explicit definition of modeling details that are neglected in standard in-plane equivalent-frame analyses, such as the possibly nonlinear behavior of all connections, including wall-to-wall connections at corners and floor-to-wall connections, or more generally, the nonlinear response of weak floors. In section 2, this paper presents the tools implemented in OpenSEES for developing a full three-dimensional equivalent frame model using the macroelement presented in Vanin et al (2019) and discusses the most relevant modeling choices and their effect on the numerical simulations. The analysis concentrates on the effect of out-ofplane mass that is not rigidly lumped to orthogonal walls on the modeling of roofs and gable elements as well as on the sensitivity of the response to the assumptions related to the behavior of connections (wall-wall and wall-slab connections) and the damping.…”