A practical and efficient numerical scheme for the analysis of steady state unconfined seepage flows

SUMMARY The scaled boundary finite-element method (SBFEM), a novel semi-analytical technique, is applied to the analysis of the confined and unconfined seepage flow. This method combines the advantages of the finite-element method and the boundary element method. In this method, only the boundary of the domain is discretized; no fundamental solution is required, and singularity problems can be modeled rigorously. Anisotropic and nonhomogeneous materials satisfying similarity are modeled without additional efforts. In this paper, SBFE equations and solution procedures for the analysis of seepage flow are outlined. The accuracy of the proposed method in modeling singularity problems is demonstrated by analyzing seepage flow under a concrete dam with a cutoff at heel. As only the boundary is discretized, the variable mesh technique is advisable for modeling unconfined seepage analyses. The accuracy, effectiveness, and efficiency of the method are demonstrated by modeling several unconfined seepage flow problems. Copyright © 2011 John Wiley & Sons, Ltd.

[1]  R. Borja,et al.  One the solution of elliptic free-boundary problems via Newton's method , 1991 .

[2]  Carlos Alberto Brebbia,et al.  Boundary elements applied to seepage problems in zoned anisotropic soils , 1979 .

[3]  Chongmin Song,et al.  A continued‐fraction‐based high‐order transmitting boundary for wave propagation in unbounded domains of arbitrary geometry , 2008, International Journal for Numerical Methods in Engineering.

[4]  Chandrakant S. Desai,et al.  Finite element residual schemes for unconfined flow , 1976 .

[5]  A. Leontiev,et al.  Mathematical programming approach for unconfined seepage flow problem , 2001 .

[6]  Chongmin Song,et al.  Development of a fundamental‐solution‐less boundary element method for exterior wave problems , 2006 .

[7]  K. Bathe,et al.  Finite element free surface seepage analysis without mesh iteration , 1979 .

[8]  J. Oden,et al.  Theory of variational inequalities with applications to problems of flow through porous media , 1980 .

[9]  Chongmin Song,et al.  A boundary condition in Padé series for frequency‐domain solution of wave propagation in unbounded domains , 2007 .

[10]  J. Wolf,et al.  The scaled boundary finite-element method – alias consistent infinitesimal finite element cell method – for diffusion , 1999 .

[11]  Yu-xin Jie,et al.  Seepage analysis based on boundary-fitted coordinate transformation method , 2004 .

[12]  Andrew Deeks,et al.  Potential flow around obstacles using the scaled boundary finite‐element method , 2003 .

[13]  S. P. Neuman,et al.  Finite Element Method of Analyzing Steady Seepage with a Free Surface , 1970 .

[14]  J. Prévost,et al.  Flow through porous media: A procedure for locating the free surface , 1987 .

[15]  Jean-Pierre Bardet,et al.  A practical method for solving free-surface seepage problems , 2002 .

[16]  Chongmin Song,et al.  Time‐harmonic response of non‐homogeneous elastic unbounded domains using the scaled boundary finite‐element method , 2006 .

[17]  Shiang-Woei Chyuan,et al.  Boundary element analysis and design in seepage problems using dual integral formulation , 1994 .