Unified egg ellipse critical threshold estimation for the deformation behavior of ultrahigh arch dams

•The deformation variation law is a direct indicator of dam overall stability.•A geometric center of an irregular deformation plane is proposed.•The unified egg-shaped ellipse equations are developed for ultrahigh arch dams.•The critical indexes are estimated considering the abnormal probabilities. This paper presents an innovative critical threshold estimation approach using unified egg-shaped ellipsoid modelling to study the deformation behavior of ultrahigh arch dams. First, the deformation variation law is regarded as a direct indicator of the overall stability and potential damage of ultrahigh arch dams based on comprehensively comparison with the results of theoretical calculations, experimental tests, numerical simulations and monitoring data. Subsequently, a novel geometric center of an irregular deformation plane constituted by all the deflection curves is proposed according to the measured distribution characteristics of the deformation spatial fields of the Xiaowan and Jinping I arch dams. Furthermore, unified egg-shaped ellipse equations are proposed to systematically identify the deformation critical attributes of Jinping I dam. Eventually, based on the peaks over threshold model, critical indexes are estimated considering the abnormal probabilities. The proposed methods are applied to Xiaowan dam as well. Results demonstrate that unified ellipsoid modelling can uniformly describe the abnormal features of the deformation behaviors of different ultrahigh arch dams, thereby the universal structural evolution characteristics to be understood in a wider range during their long-term operations.