Macro-modeling of CFRP strengthening in U-shaped masonry walls under combined vertical and out-of-plane loads

Unreinforced masonry (URM) structures are a critical component of architectural heritage and remain widely used in residential buildings, particularly in developing regions. However, their vulnerability to seismic events necessitates effective retrofitting techniques to improve structural performance. Among various retrofitting methods, fiber-reinforced polymer (FRP) materials, particularly carbon-FRP (CFRP), have shown significant promise in enhancing the strength and ductility of masonry walls. While extensive research has been conducted on the retrofitting of rectangular URM walls, studies addressing the retrofitting performance of U-shaped walls under out-of-plane loading remain comparatively limited, despite their frequent occurrence in practice. Additionally, while vertical loads are known to influence structural behavior, their specific effects on the response of CFRP-retrofitted URM walls require further investigation. This paper presents a comprehensive numerical study investigating the out-of-plane behavior of U-shaped URM walls retrofitted with CFRP strips. A macro-modeling approach with nonlinear homogenized materials using the finite element method is employed to simulate different retrofit configurations, including horizontal, vertical, square mesh, diagonal strips, and fully covered wall faces. The effects of one-side versus both-side attachment, CFRP thickness, and varying vertical loads are also examined to identify optimal retrofitting strategies. Through a systematic evaluation of these variables, this study aims to provide deeper insights into their impact on ultimate wall strength while identifying cost-effective retrofitting solutions. To achieve this, a new parameter is introduced to quantitatively assess the cost-effectiveness of each retrofitting case. The results demonstrate that CFRP retrofitting significantly enhances the out-of-plane strength and overall structural response, with vertical load playing a critical role in modifying strength enhancement. Among the various configurations, the grid layout with extended horizontal strips attached to the side walls was found to provide the highest strength ratio while maintaining a favorable cost-effectiveness balance, making it the most efficient retrofitting strategy. The findings offer valuable insights into the design and application of CFRP-based retrofitting techniques, contributing to advancing knowledge in masonry strengthening and providing engineers and practitioners with data-driven guidance for selecting optimal retrofit strategies.