Unconfined Seepage Analysis Using Moving Kriging Mesh-Free Method with Monte Carlo Integration

The unconfined seepage problem is a classic moving boundary problem, in which the position of phreatic surface is unknown at the beginning of solution and should be determined through iteration. Mesh-free methods are especially suitable for solving this problem. In this work, the moving Kriging mesh-free method with Monte Carlo integration is proposed. Additionally, a corresponding procedure for handling material discontinuity is presented, which extends the approach to inhomogeneous medium. The present method is a true mesh-free method, which does not require a mesh for either shape function construction or numerical integration. Another advantage of the present method is the convenient numerical implementation. Numerical examples show that the present method can achieve better convergence and higher accuracy with rational computation cost when compared with the original mesh-free method. The present method is also verified to be applicable in analyzing transient seepage through homogeneous and inhomogeneous media.

[1]  Farhang Daneshmand,et al.  Unconfined seepage analysis in earth dams using smoothed fixed grid finite element method , 2012 .

[2]  Franklin W. Schwartz,et al.  A grid generating algorithm for simulating a fluctuating water table boundary in heterogeneous unconfined aquifers , 1999 .

[3]  M. Buès,et al.  Numerical Efficiency Assessment of IB–LB Method for 3D Pore-Scale Modeling of Flow and Transport , 2015, Transport in Porous Media.

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

[5]  M. M. Toufigh,et al.  The solution of unconfined seepage problem using Natural Element Method (NEM) coupled with Genetic Algorithm (GA) , 2013 .

[6]  L. Tham,et al.  A new variational inequality formulation for seepage problems with free surfaces , 2005 .

[7]  The method of fundamental solutions for solving free boundary saturated seepage problem , 2011 .

[8]  Carmelo Gentile,et al.  A nonlinear programming analysis of unconfined steady‐state seepage , 1987 .

[9]  Mark A Fleming,et al.  Meshless methods: An overview and recent developments , 1996 .

[10]  L. Gu,et al.  Moving kriging interpolation and element‐free Galerkin method , 2003 .

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

[12]  D. G. Fredlund,et al.  Transient seepage model for saturated–unsaturated soil systems: a geotechnical engineering approach , 1987 .

[13]  Mark A Fleming,et al.  Smoothing and accelerated computations in the element free Galerkin method , 1996 .

[14]  M. Hashemi,et al.  Unsteady seepage analysis using local radial basis function-based differential quadrature method , 2011 .

[15]  Y. Jie,et al.  Simulated annealing based algorithm for node generation in seepage analysis with meshless method , 2012 .

[16]  Zuyu Chen,et al.  Seepage analysis based on the unified unsaturated soil theory , 2001 .

[17]  Makoto Nishigaki,et al.  FINITE ELEMENT ANALYSIS OF SATURATED-UNSATURATED SEEPAGE IN SOIL , 1977 .

[18]  Behzad Ataie-Ashtiani,et al.  Transient free-surface seepage in three-dimensional general anisotropic media by BEM , 2014 .

[19]  Jeng-Tzong Chen,et al.  Study of free-surface seepage problems using hypersingular equations , 2006 .

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

[21]  Baodong Dai,et al.  A meshless local moving Kriging method for two-dimensional solids , 2011, Appl. Math. Comput..

[22]  Mark A Fleming,et al.  Continuous meshless approximations for nonconvex bodies by diffraction and transparency , 1996 .

[23]  Ulrich Hornung,et al.  Evaluation of the Polubarinova-Kochina Formula for the Dam Problem , 1985 .

[24]  P. Frolkovic.  Application of level set method for groundwater flow with moving boundary , 2012 .

[25]  Y M Cheng,et al.  An efficient method for the free surface seepage flow problems , 1993 .

[26]  Masoud Darbandi,et al.  A moving‐mesh finite‐volume method to solve free‐surface seepage problem in arbitrary geometries , 2007 .

[27]  C. Desai,et al.  A residual flow procedure and application for free surface flow in porous media , 1983 .

[28]  L. Lam,et al.  Saturated-Unsaturated Transient Finite Element Seepage Model for Geotechnical Engineering , 1984 .

[29]  Feng Liu,et al.  Primal mixed solution to unconfined seepage flow in porous media with numerical manifold method , 2015 .

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

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

[32]  Nahidh Hamid Sharif,et al.  Adaptive ICT-Procedure for Non-linear Seepage Flows with Free Surface in Porous Media , 2002 .

[33]  T. Belytschko,et al.  Element‐free Galerkin methods , 1994 .

[34]  F. Daneshmand,et al.  Three dimensional smoothed fixed grid finite element method for the solution of unconfined seepage problems , 2013 .

[35]  A. Kacimov,et al.  Analytical Solutions for Steady Phreatic Flow Appearing/Re-emerging Toward/from a Bedrock/Caprock Isobaric Breach: The Polubarinova-Kochina–Numerov and Pavlovsky Problems Revisited , 2015, Transport in Porous Media.

[36]  Yu-xin Jie,et al.  Treatment of transitional element with the Monte Carlo method for FEM-based seepage analysis , 2013 .