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The scaled boundary finite element method (SBFEM) is a semi-analyticalcomputational scheme, which is based on the characteristics of the finiteelement method (FEM) and combines the advantages of the boundary element method(BEM). This paper integrates the scaled boundary finite element method (SBFEM)and the polygonal mesh technique into a new approach to solving thesteady-state and transient seepage problems. The proposed method is implementedin Abaqus using a user-defined element (UEL). The detailed implementations ofthe procedure, defining the UEL element, updating the RHS and AMATRX, andsolving the stiffness/mass matrix by the eigenvalue decomposition arepresented. Several benchmark problems from seepage are solved to validate theproposed implementation. Results show that the polygonal element of PS-SBFEMhas a higher accuracy rate than the standard FEM element in the same elementsize. For the transient problems, the results between PS-SBFEM and the FEM arein excellent agreement. Furthermore, the PS-SBFEM with quadtree meshes shows agood effect for solving complex geometric in the seepage problem. Hence, theproposed method is robust accurate for solving the steady-state and transientseepage problems. The developed UEL source code and the associated input filescan be downloaded from https://github.com/yangyLab/PS-SBFEM.

A novel method in solving seepage problems implementation in Abaqus based on the polygonal scaled boundary finite element method