Abstract: Arc collapse is a typical bank-scour hazard in the middle and lower reaches of the Yangtze River, characterized by sudden onset and substantial disaster risk. To reveal the staged development law of arc collapse from the perspective of flow-field dynamic evolution and to determine the hydrodynamic-geometric critical conditions governing scour-stage transitions, three-dimensional numerical simulations are performed for flow fields under different arc-shaped scour hole conditions using the SST-based detached-eddy simulation (DES). Based on the simulated flow-field characteristics, the evolutionary stages are classified into three categories. By combining datasets from generalized flume experiments of arc collapse, cavity-flow theory, and dimensional analysis, the critical geometric thresholds for stage transition are identified. The results indicate that: ① According to the flow-field features within the arc-shaped scour hole, the evolution of arc collapse can be divided into three successive stages: shear scour, vortex scour, and recirculation scour. These stages are governed by near-wall shear stress, vortex-induced sediment transport, and large-scale recirculation inside the arc-shaped scour hole, respectively. ②Two groups of dimensionless criteria for stage transition are constructed. By introducing a scale-correction term, a semi-empirical relationship applicable to both flume-scale and prototype-scale conditions is derived. For flume test cases, the critical width-depth ratio is approximately 10 for the transition from shear scour to vortex scour and around 2.5 for the transition from vortex scour to recirculation scour. The proposed criteria are suitable for qualitative identification of developmental stages of pocket-type arc collapse. The research outcomes provide theoretical support for hazard identification and riverbank protection against arc collapse in the middle and lower reaches of the Yangtze River.