A Discrete Element for Modeling Masonry Vaults

Abstract

The assessment of the seismic response of historical masonry buildings represents a subject of considerable importance but, at the same time, of very difficult task. Refined finite element numerical models, able to predict the non-linear dynamic mechanical behavior and the degradation of the masonry media, require sophisticated constitutive law and a huge computational cost that makes these methods nowadays not suitable for practical application. In the past many authors developed simplified or alternative methodologies that, with a reduced computational effort, should be able to provide numerical results that can be considered sufficiently accurate for engineering practice purposes. However most of these methods are based on simplified hypotheses that make these approaches inappropriate for monumental buildings. In this paper a three dimensional discrete element model, able to predict the nonlinear behaviour of masonry shell elements, is presented as an extension of a previously introduced spatial discrete-element conceived for the simulation of both the in-plane and the out-of-plane behavior of masonry plane elements. The new macro-element enriches a larger computational framework, based on macro-element approach, devoted to the numerical simulation of the seismic behaviour of historical masonry structures.

FRP-Reinforced Masonry Structures: Numerical Modeling by Means of a New Discrete Element Approach

“…The spatial element is able to catch the out of plane behavior of plane walls but is not suitable to model structures with a curved geometry, such as vaults and domes. In order to overcome this limit the model was further upgraded to obtain a shell macro-element characterized by an irregular geometry , variable thickness along the element and skew interfaces [9], [10], Figure 1c. The calibration procedures, concerning the mechanical properties of the links, were properly extended in order to account for the more complicated geometry of the element, but keeping the same general philosophy.…”

“…The proposed new element is consistent with a discrete macroelement able to simulate the nonlinear response of masonry curved structures [9], [10] within a wider macro-modelling strategy originally introduced to simulate the in-plane nonlinear response of masonry walls [11]. The new nonlinear flat element, able to simulate the presence of FRP strips, interacts with the masonry support by means of a new discrete interface for the masonry-FRP interaction, able to simulate the delamination phenomena both by normal pure opening (mode I) and by shear bond-slip (mode II).…”

Multi-Directional Seismic Assessment of Historical Masonry Buildings by Means of Macro-Element Modelling: Application to a Building Damaged during the L’Aquila Earthquake (Italy)

“…In the numerical model the structural transformations and the recent seismic retrofits provided to the building have been considered. The main aim of the retrofitting interventions made in the 1990s was to prevent the major causes of collapse in masonry The discrete element conceived to model shell masonry elements [27,28,37] represents an extension of the rectangular element and is constituted by an articulated quadrilateral whose geometry is not regular in order to allow the meshing of a generic curved surface with macro-elements (Figure 10c). Each macro-element is still characterized by four rigid edges whose orientation and dimension are associated to the shape of the element and to the thickness of the portion of modelled masonry that is represented.…”

“…To this aim, an innovative discrete element, introduced by Caliò et al [19], is used. This model, in the original formulation, was conceived for the simulation of the nonlinear in-plane behaviour of unreinforced masonry walls suitable for building with "box behaviour" and then upgraded for modelling infilled frame structures [20][21][22][23] and monumental masonry buildings [25][26][27][28] in which a complex interaction between in-plane and out-of-plane behaviour is observed.…”

“…Since the building was subjected to a localized partial collapse of secondary elements (a frescoed mirror vault located in one of the two main halls of the palace), an additional detailed local model of the room was implemented considering a more advanced model accounting for the out-of-plane masonry behaviour [25,26], also in the presence of curved elements [27,28].…”