Characterised by their elegance and structural efficiency, masonry arches prevalent in historical buildings are often susceptible to severe damage under earthquake actions. Seismic assessment of masonry structures, with their curved horizontal components, requires precise numerical tools capable of capturing the complex geometries involved. Within the OpenSees framework, we employ equivalent frame models (EFM) for their low computational demand and demonstrated robustness. However, elements dedicated to the precise modelling of arches remain limited. To address this gap, we introduce an arch macro-element, which simulates arches as assemblies of 2D discrete rigid blocks (voussoirs), thereby enabling the identification of local collapse mechanisms. Nonlinear interactions occur at contact points along the interface corners, where tensile strength is assumed to be zero and compressive strength is considered infinite. The model incorporates the Coulomb failure criterion without cohesion to simulate potential failures through sliding and opening at the interfaces of voussoirs. Based on a variational rigid-block modelling approach, the method uses an optimisation-based algorithm to calculate displacements and forces. Requiring fewer material properties for masonry, it reduces uncertainty in simulations of historical structures. Full integration within a beam-like element ensures compatibility with other OpenSees components. Validation is performed using an experimental campaign from the literature, involving an arch on buttresses tested on a shake table. By combining the benefits of rigid block modelling with the equivalent frame approach, this element aims to contribute to the reliable seismic assessment of heritage structures while also supporting the identification of optimal retrofit solutions in line with conservation recommendations.

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Modelling Masonry Arches Using Rigid Block Programming within the OpenSees Framework

  • Ivana Božulić,
  • Qianqing Wang,
  • Francesco Vanin,
  • Katrin Beyer

摘要

Characterised by their elegance and structural efficiency, masonry arches prevalent in historical buildings are often susceptible to severe damage under earthquake actions. Seismic assessment of masonry structures, with their curved horizontal components, requires precise numerical tools capable of capturing the complex geometries involved. Within the OpenSees framework, we employ equivalent frame models (EFM) for their low computational demand and demonstrated robustness. However, elements dedicated to the precise modelling of arches remain limited. To address this gap, we introduce an arch macro-element, which simulates arches as assemblies of 2D discrete rigid blocks (voussoirs), thereby enabling the identification of local collapse mechanisms. Nonlinear interactions occur at contact points along the interface corners, where tensile strength is assumed to be zero and compressive strength is considered infinite. The model incorporates the Coulomb failure criterion without cohesion to simulate potential failures through sliding and opening at the interfaces of voussoirs. Based on a variational rigid-block modelling approach, the method uses an optimisation-based algorithm to calculate displacements and forces. Requiring fewer material properties for masonry, it reduces uncertainty in simulations of historical structures. Full integration within a beam-like element ensures compatibility with other OpenSees components. Validation is performed using an experimental campaign from the literature, involving an arch on buttresses tested on a shake table. By combining the benefits of rigid block modelling with the equivalent frame approach, this element aims to contribute to the reliable seismic assessment of heritage structures while also supporting the identification of optimal retrofit solutions in line with conservation recommendations.