B-bar based algorithm applied to meshfree numerical schemes to solve unconfined seepage problems through porous media

• Published in: International journal for numerical and analytical methods in geomechanics Vol. 40; no. 6; pp. 962 - 984
• Main Authors: Navas, Pedro, López-Querol, Susana, Yu, Rena C., Li, Bo
• Format: Journal Article
• Language: English
• Published: Bognor Regis Blackwell Publishing Ltd 25.04.2016; Wiley Subscription Services, Inc
• Subjects: Algorithms; Earth dams; free surface; Free surfaces; Joining; Mathematical analysis; Mathematical models; Maximum entropy; Media; meshfree; Meshless methods; Pore water; Porous media; Seepage; Soil columns; u − w formulation
• ISSN: 0363-9061; 1096-9853
• DOI: 10.1002/nag.2472

Summary The object of this work is to establish a meshfree framework for solving coupled, steady and transient problems for unconfined seepage through porous media. The Biot's equations are formulated in displacements (or u − w) assuming an elastic solid skeleton. The free surface location and its evolution in time are obtained by interpolation of pore water pressures throughout the domain. Shape functions based on the principle of local maximum entropy are chosen for the meshfree approximation schemes. In order to avoid the locking involved in the fluid phase of the porous media, a B‐bar based algorithm is devised to compute the average volumetric strain in a patch composed of various integration points. The efficiency of such an implementation for one phase problems is shown through the Benchmark problem, Cook's membrane loaded by a distributive shear load. The proposed methodology is firstly applied to various classical examples in unconfined steady seepage problems through earth dams, then to the dynamic consolidation of a soil column. The results obtained for both problems are quite satisfactory and demonstrate the feasibility of the proposed method in solving coupled problems in porous media. Copyright © 2015 John Wiley & Sons, Ltd.