Current status and prospects of calculation methods for dam and dike failures (Ⅱ)：Two-dimensional and three-dimensional mathematical models

SignificanceDam and dike failure, as one of the most frequent disaster events worldwide, exerts a profound impact on human production and daily life. Research on breach calculation methods is crucial for the assessment, prediction, and risk prevention of dam-break and dike-break floods. ProgressFrom a mathematical modeling perspective, this paper reviews and summarizes two-dimensional (2D) and three-dimensional (3D) computational models for breach development. The characteristics of common 2D and 3D mathematical models are summarized, and a comparative table of typical breach calculation methods is presented. Three representative 2D mathematical models are briefly introduced to facilitate comparative studies among researchers and to better understand the current development of dam-breach mathematical models. Furthermore, commonly used numerical computation techniques, commercial software, and open-source tools are summarized and compared. The current applications and future prospects of machine learning methods in breach calculation are also discussed, along with suggestions for future research directions and key priorities. Conclusion and ProspectOverall, existing studies on breach development mechanisms and numerical simulations still involve many simplifications and assumptions. Both 2D and 3D numerical methods are evolving toward more refined descriptions of breach development processes, but they require significant computational resources and time. Accurate and efficient full-process simulation of breach evolution is expected to remain an active research topic. Machine learning methods have gradually been applied to the prediction and analysis of breach development, and they are expected to extensively and in-depth applied in future relevant research.