Dept. of Civil and Environmental Engineering, Matsue National College of Technology, Shimane, Japan
Graduate School of Environmental Science, Okayama University, Okayama, Japan.
Keywords: Mesh-free method, soil-water coupled problem, stabilization procedure
The development of numerical computation technologies has enabled a variety of engineering problems to be solved and has brought about remarkable progress in recent decades. Among the related findings, meshless and/or mesh-free methods in particular have been applied to some problems for which the usual finite element
method is ineffective in dealing with significant mesh distortion brought about by large deformations, crack growth, and moving discontinuities.
by means of EFGM (Modaressi et al., 1998)(Nogami et al., 2004)(Murakami et al., 2005)(Wang et al., 2006), the point/radial point interpolation method (PIM/RPIM) (Wang et al., 2001)(Wang et al., 2002), the local RPIM (Wang et al., 2005), RKPM (Chen et al., 2001)(Zhang et al., 2005), and the natural neighbor method (Cai et al., 2005), the transient response of saturated soil has been dealt with under cyclic loading by means of EFGM (Karim et al., 2002)(Sato et al., 2006), wave-induced seabed response and instability have been examined by EFGM (Wang et al., 2007) and RPIM (Wang et al., 2004), slip lines have been modeled by geological materials using EFGM (Rabczuk et al., 2006), and a Bayesian inverse analysis has been carried out in conjunction with the meshless local Petrov-Galerkin method (Sheu, 2006).
However, unless certain requirements are met in dealing with soil-water coupled problems for the finite element computation, based on the coupled formulation becoming ill-conditioned, numerical instabilities will occur (Chapelle et al., 1993). In order to overcome these weaknesses, several strategies have been proposed (Pastor et al., 1999). For example, as a necessary condition for stability, the interpolation degree of the displacement field must be higher than that of the pore pressure field. An alternative means of stabilization was also proposed based on the Simo-Rifai enhanced strain method which even allows an equal order of interpolation degree for both variables. However, these strategies are not directly applicable to meshless/mesh-free methods, because all the nodal points simultaneously have the same degree of freedom for both the displacement field and the pore pressure field, and no information between the element and the nodes can be utilized. The purpose of this paper is to present a stabilization methodology for the mesh-free analysis of soil-water coupled problems by incorporating the stabilizing term into the weak form. The following sections deal with descriptions of the formulation, including the stabilization term. In Section 3, two applications of the strategy to soil-water coupled problems are analyzed, one being the saturated soil column test appearing in Mira et al.(2003),to demonstrate the effectiveness of the strategy, and the other being the foundation behavior under displacement-controlled condition, for which the feasibility of theanalysis will be thoroughly discussed while