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The main challenge in the analysis of unconfined seepage flow is that the position of free surfaces is unknown a priori , which needs to be determined through a series of iterative processes. The numerical manifold method (NMM) is a promising method which uses a dual cover system consisting of both mathematical and physical covers. Compared with those traditional methods, NMM is characterized by meshing convenience, approximation accuracy, and being capable of coping with free boundary value problems. Unlike the traditional NMM where the material interface participates in cutting the mathematical cover while forming the physical cover, the physical patches in this study can contain the material interface. The new weight functions for such physical patches are constructed using the refraction law, followed by the application to the analysis of unconfined seepage flow problems. By comparing with analytical or reference solutions of some classic examples, it is validated that the proposed method can accurately locate the free surface, demonstrating its accuracy and convenience in solving unconfined seepage problems. [ABSTRACT FROM AUTHOR]