Extending a Macro-Element Approach for the Modeling of 3D Masonry Structures Under Transient Dynamic Loading

Abstract

Masonry structures, particularly those used in developing countries and in historic buildings, typically consist of unreinforced masonry (URM) walls connected by timber or reinforced concrete elements. This study proposes enhancements to the existing two-dimensional (2D) deformable frame model (DFM) to enhance its ability in simulating masonry walls with a specific focus on accurately predicting the transient dynamic response of three-dimensional (3D) masonry structures while maintaining a minimal number of degrees of freedom (DOF). For the modeling of URM walls, the DFM framework employs elastic beams and diagonal struts with nonlinear constitutive behavior. Structural elements, such as reinforced concrete or timber reinforcements, are represented using conventional beam finite elements. This paper first reviewed the current DFM configuration, which primarily addresses the in-plane (IP) behavior of URM structures. It then introduced modifications tailored for 3D structural analysis. The reliability of the enhanced model was validated through two approaches. First, a modal analysis compared the results from the updated DFM with those from a reference 3D model based on cubic finite elements. Second, a shaking table experiment conducted on a half-scale masonry house was simulated. The findings demonstrate that, despite its limited number of DOF, the updated DFM effectively captures the main natural vibration modes. Furthermore, it shows the model’s ability to predict the nonlinear transient dynamic response of 3D masonry structures with accuracy and limited computational time.

Keywords

• 3D macro model
• finite element method
• unreinforced masonry
• modal analysis
• nonlinear transient dynamics analysis
• in-plane and out-of-plane loadings