A local radial point interpolation method for dissipation process of excess pore water pressure

Abstract

Purpose

Develop a local radial point interpolation method (LRPIM) to analyze the dissipation process of excess pore water pressure in porous media and verify its numerical capability.

Design/methodology/approach

Terzaghi's consolidation theory is used to describe the dissipation process. A local residual form is formulated over only a sub‐domain. This form is spatially discretized by radial point interpolation method (RPIM) with basis of multiquadrics (MQ) and thin‐plate spline (TPS), and temporally discretized by finite difference method. One‐dimensional (1D) and two‐dimensional consolidation problems are numerically analyzed.

Findings

The LRPIM is suitable, efficient and accurate to simulate this dissipation process. The shape parameters, q=1.03, R=0.1 for MQ and η=4.001 for TPS, are still valid.

Research limitations/implications

The asymmetric system matrix in LRPIM spends more resources in storage and CPU time.

Practical implications

Local residual form requires no background mesh, thus being a truly meshless method. This provides a fast and practical algorithm for engineering computation.

Originality/value

This paper provides a simple, accurate and fast numerical algorithm for the dissipation process of excess pore water pressure, largely simplifies data preparation, shows that the shape parameters from solid mechanics are also suitable for the dissipation process.

Citation

Wang, J.G., Yan, L. and Liu, G.R. (2005), "A local radial point interpolation method for dissipation process of excess pore water pressure", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 15 No. 6, pp. 567-587. https://doi.org/10.1108/09615530510601468