Geometric Distortion-Informed Residual Deformation Estimation from Post-Earthquake Point Cloud Data

The interpretation of failure mechanisms in historic masonry vaults can benefit from the knowledge of residual displacement fields. This paper uses the recently developed π-ICP algorithm to generate these fields for the standing cross vault of St. George Sarilar Orthodox Church, which was severely damaged during the 2023 Kahramanmaraş earthquakes. π-ICP is used to conduct strain-energy-regularised non-rigid registration of a reference vault geometry to the post-earthquake point cloud. Different from previous applications, geometric distortion data from the supporting walls are used to impose boundary conditions on the registration. A novel noise-aware stopping criterion is also introduced to prevent overfitting. The mechanical plausibility of the inferred residual displacement field is evaluated through an independent finite‑element model of the vault subjected to similar boundary conditions. Despite the significant uncertainties involved in the modelling process, the simulations reproduce similar crack patterns and residual displacement fields. The results suggest that the extensive vault damage is primarily due to the support movements arising from the failures in one of the supporting walls and its foundations. The application highlights how the proposed workflow combining geometric distortion and π-ICP analyses can help derive new forensic insights from post-earthquake point cloud data.