Assessing the stability of unreinforced masonry arches and vaults: a comparison of analytical and numerical strategies

ABSTRACT

Despite being accepted as a robust assessment of masonry stability, thrust line analysis (TLA) relies on assumptions that can lead to a conservative assessment of stability. This article aims to quantify the extent of these limitations through a comparison of TLA with discrete element modeling (DEM). Two studies are provided. The first study compares TLA with DEM (using fixed input parameters) in assessing the stability of unreinforced masonry arches, semi-circular barrel vaults, multi-ring arches, and groin vaults. The tests demonstrate the types of sliding failures overlooked by the safe theorem due to its assumption of infinite friction. Following these validations, the comparisons between 2D structures and 3D counterparts also give insight into the efficacy of the slicing method. The second study examines the effect of DEM input parameters on the DEM-predicted stability of the considered geometries. While material parameters had limited effect on the determination of stability, for each typology, joint friction angle had a unique impact on stability. These trends are graphically presented and demonstrate how t/R ratios alone are not sufficient to unequivocally confirm stability of the considered vaults. Overall, this research informs the extent of safety for using the geometry-based analysis tool, TLA, for analyzing masonry structures.

KEYWORDS:

• Arches
• discrete element modeling
• distinct element method
• graphic statics
• limit state analysis
• safe theorem
• thrust line analysis
• unreinforced masonry
• vaults

Acknowledgments

The authors would like to thank Anjali Mehrotra as well as Professors Axel Kilian, Matthew DeJong, Branko Glisic, and John Ochsendorf for their insightful contributions and feedback. Additionally, many thanks to Jim Hazzard, Principal Engineer and Software Manager from Itasca Consulting Group, and to the Itasca Education Partnership. The authors also thank the anonymous reviewer for the valuable feedback that allowed significant improvements of the manuscript.

Notes

¹ The general procedure of constructing the thrust line is adapted from Tutorial 3 found on Massachusetts Institute of Technology’s Interactive Thrust website (created by John Ochsendorf, Philippe Block, and Thierry Ciblac): http://web.mit.edu/masonry/interactiveThrust/tutorials/tutorial3.pdf.

² Selected scripts for the tests executed in this article may be accessed at http://github.com/demifang21.

Additional information

Funding

This material is based upon work supported by the National Science Foundation Graduate Research Fellowship Program under Grant No. DGE-1656466. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation. The bulk of this article originated from Demi Fang’s senior thesis at Princeton University, which was generously funded by the Lidow Fund at the School of Engineering and Applied Sciences.