Our archaeoseismological studies of the ruins of a medieval Christian temple located at the foot of Kilisa-Kaya Mountain in the southeast of the Crimean Peninsula have shown that the building structures have obvious traces of significant seismic damages: tilts, shifts, and rotations of both entire building elements and individual stone blocks or their packages. Extended subvertical interblock cracks break the walls of the temple to their entire residual height. Oblique cracks that occur under conditions of longitudinal compression cut elongated building blocks. The stone pavement of the temple is also damaged: there are depressions in it. Judging by the fact that the temple was repaired, and sections of the repaired walls were also deformed, the structure was affected by two seismic events. The last of them left traces in the apse and the northern portal. Seismic oscillations spread in the sublatitudinal direction. The damage caused by this earthquake apparently includes shifts and tilts of brickwork in the submeridionally oriented walls, as well as the loss of domed and arched parts of the building. The first earthquake led to the appearance of deformations (shifts) in the walls of the sublatitudinal strike, after which the temple was repaired. The second seismic event, apparently, led to the formation of a landslide in the upper reaches of the dry creek in the valley of which the temple was located. The lake formed above the dam once broke through the barrier, and a mudslide passed down the valley. The mudflow material filled the interior of the temple and formed sediments around the building. Mudslide deposits covered and preserved the walls of the temple, as well as deformations in them for hundreds of years. Judging by the severity of the damage to the religious building, built with special quality, the intensity of seismic oscillations during both seismic events was at least VIII points. The exact dates of the construction of the temple and the earthquakes still need to be clarified, for which further research of the monument is necessary. Since its construction is tentatively dated from the second half of the 12th century to the first half of the 13th century, the first earthquake occurred after the specified date. It is known that the temple was almost completely buried under a layer of soil by the end of the 18th century. Accordingly, the second seismic event can be dated to this time.

In seismic finite element analysis of saturated soils, the challenges primarily reside in liquefaction and the large deformation of soil induced by strong earthquakes. Traditional updated Lagrangian methods may result in severe mesh distortion after updating the spatial configuration of nodes. To address this issue, this study develops an r adaptive approach based on a solid - fluid coupling finite element method (FEM) platform to mitigate mesh distortion problems. This technique optimizes mesh nodes without altering the overall topology, thereby maintaining mesh integrity. However, enhancing mesh accuracy comes at the expense of increased computational costs. To alleviate high computational expenses, this study couples two types of adaptive time stepping techniques, based on mixed error and displacement history curvature, with mesh adaptation. Through verification on two typical dynamic liquefaction models of saturated soil on embankment and subway station, this technique effectively balances the relationship between computational accuracy and costs.