Dynamic consolidation problems in saturated soils solved through u–w formulation in a LME meshfree framework

Abstract

A meshfree numerical model, based on the principle of Local Maximum Entropy (LME), including a B-bar algorithm to avoid instabilities, is applied to solve axisymmetric consolidation problems in elastic saturated soils. This numerical scheme has been previously validated for purely elastic problems without water (mono phase), as well as for steady seepage in elastic porous media. Hereinafter, an implementation of the novel numerical method in the axisymmetric configuration is proposed, and the model is validated for well known theoretical problems of consolidation in saturated soils, under both static and dynamic conditions with available analytical solutions. The solutions obtained with the new methodology are compared with a finite element commercial software for a set of examples. After validated, solutions for dynamic radial consolidation and sinks, which have not been found elsewhere in the literature, are presented as a novelty. This new numerical approach is demonstrated to be feasible for this kind of problems in porous media, particularly for high frequency, dynamic problems, for which very few results have been found in the literature in spite of their high practical importance.

u–w formulation for dynamic problems in large deformation regime solved through an implicit meshfree scheme

“…Finally, once the method is tested, future research may employ it with different constitutive models in order to simulate different soils, depending on the different material properties. Also, it is required the assessment of the usage of different time integration schemes (see [29] and [1]) in order to improve the performance of the proposed methodology. The linearization will be stated for the weak form with respect to the reference configuration.…”

“…1.B, where the angular frequency ω is defined as 2π/T . This problem was first analytically solved by Zienkiewicz et al [44] in 1980s, and more recently by Navas et al using either implicit Eulerian method [29] or explicit Lagrangian schemes [28] employing LME shape functions.…”

Low‐order stabilized finite element for the full Biot formulation in soil mechanics at finite strain

“…The analysts also indicated that Π 1 values above 1e+2 were indicative of drained conditions and below 1e−2 of undrained conditions. Recently, Navas et al() using a meshfree method at large strain have observed that this zoning scheme is also valid for two‐dimensional problems.…”

Optimal transportation meshfree method in geotechnical engineering problems under large deformation regime

“…Such a problem has been solved by many authors (see the works of Simo and Rifai and Kasper and Taylor for details) and recently by Hughes et al through a B‐bar or F‐bar projection, by Hauret et al via diamond elements, and by Artioli et al employing assumed strain nodally integrated continuum element formulation for elastoplastic applications. Navas et al presented this problem with the first implementation of the B‐bar method with LME shape functions . In this case, neo‐Hookean nonlinear elasticity was employed.…”

“…Navas et al presented this problem with the first implementation of the B-bar method with LME shape functions. 5,6 In this case, neo-Hookean nonlinear elasticity was employed. The result seeks an asymptotic vertical displacement at the right upper corner (point P) in Figure 4A.…”