Out-of-plane behavior of masonry walls strengthened with full-length injected tie-rods

Key findings from this study

This research indicates that:

• Full-length injected tie-rods significantly increase out-of-plane capacity and post-peak stiffness without substantially changing initial structural stiffness.
• Optimal retrofitting configurations employ multiple rods at two different heights, with effectiveness plateauing beyond a threshold rod diameter.
• A modified kinematic analysis incorporating deformation-dependent steel behavior and selective rod mobilization predicts strengthened wall performance with approximately 7 percent average error relative to finite element simulations.

Overview

This study investigates the out-of-plane seismic behavior of unreinforced masonry walls retrofitted with full-length injected tie-rods through finite element modeling, parametric analysis, and a kinematic design approach. The research validates numerical frameworks against experimental data and develops practical analytical tools for predicting strengthened wall performance.

Methods and approach

Researchers constructed and validated finite element models against literature experimental data on unreinforced masonry walls. Two modeling strategies—solid-element and truss-element representations—were compared for accuracy and computational efficiency. Parametric analyses examined effects of rod quantity, placement height, and diameter on structural response. Dynamic simulations assessed drift control and failure timing under various excitations. A modified kinematic analysis method incorporated deformation-dependent steel contributions and empirical evidence regarding which tie-rods mobilize during out-of-plane loading.

Results

Finite element models accurately reproduced both the structural response of masonry walls and the bond mechanism of injected rods. Retrofitting with full-length tie-rods did not substantially alter initial stiffness but significantly improved out-of-plane capacity and post-peak stiffness. Multiple tie-rods positioned at two different heights and larger rod diameters proved most effective, though benefits plateaued beyond a threshold diameter. Dynamic simulations confirmed improved drift control and delayed failure across varied excitation patterns.

The modified kinematic analysis revealed that only front-wall rods aligned with out-of-plane loading contributed meaningfully to strengthened wall behavior. Corner integrity remained preserved and transverse-wall rods mobilized negligibly, observations corroborated by finite element evidence. The kinematic method predicted finite element results with approximately 7 percent average error, establishing its validity as a practical design tool.

Implications

The study provides both a validated numerical framework and an engineering-grade analytical method for designing full-length tie-rod retrofits in heritage masonry structures. The kinematic approach enables practitioners to predict strengthened wall performance without computationally intensive simulations, facilitating rapid design iteration and feasibility assessment.

The findings support full-length tie-rod installation as an effective strategy for mitigating out-of-plane seismic vulnerability in unreinforced masonry. The minimal visual impact of this technique, combined with demonstrated performance improvements and practical analytical tools, positions it as an attractive option for heritage preservation contexts where aesthetic constraints limit alternative strengthening approaches.

Scope and limitations

This summary is based on the study abstract and available metadata. It does not include a full analysis of the complete paper, supplementary materials, or underlying datasets unless explicitly stated. Findings should be interpreted in the context of the original publication.