Pipe surge has always been an important topic in the study of embankment danger. At present, numerous studies have been conducted on pipe surge damage to embankment structures. Among them, the mathematical modeling approach is widely used in the study of seepage damage in embankment-based structures due to its accuracy, flexibility, and predictability. From the perspective of mathematical modeling, this paper summarizes the modeling methods, theoretical foundations, and applicable conditions of the pipe surge problem in embankment foundation structures based on the studies conducted by scholars at home and abroad. It aims to provide reference for other scholars to choose research methods in the process of researching the pipe surge problem in the future. At the same time, this paper summarizes the non-flooding dike foundation structure leakage disease risk detection technology and flood risk monitoring and treatment measures, and elaborates on their applicable conditions and advantages and disadvantages. It aims to provide reference for the prevention and treatment of pipe surge problems in actual projects.