Modal Analysis Methods for Validation of Vaulted Stone Masonry Models

Detailed three-dimensional finite element models are used in the assessment of masonry vaults and domes, in order to determine support reactions and stresses within the vault under various loading conditions. However, it is important to validate the models used on an existing structure by comparison of the results of the analysis to the response of the prototype. The problem of validating a structural model is particularly difficult for large-scale masonry vaults due to difficulties in access, and difficulties in loading the structure sufficiently to obtain a measurable response. Visual methods, such as investigation of cracks and comparing crack locations to tension zones in the model have been used with limited success; however, the lack of information on boundary conditions makes this method susceptible to error in structures with support settlements. Recently, modal testing has been proposed as a model validation procedure. In this procedure, the dynamic characteristics of the experimental model and the prototype can be compared. These comparisons may be simple comparisons of natural frequencies or much more complex determinations of mode shapes by methods of modal analysis. This paper reviews the application of modal analysis methods to masonry vault validation, and shows some specific examples, including detailed modal analysis tests done on the National Cathedral in Washington, DC, tests done on the Cathedral of St. John the Divine in New York City.