In this paper a new methodology to simulate saturated soils subjected to dynamic loadings under large deformation regime (locally up to 40\% in equivalent plastic strain) is presented. The coupling between solid and fluid phases is solved through the complete formulation of the Biot's equations. The additional novelty lies in the employment of an explicit time integration scheme of the u-w (solid displacement -- relative fluid displacement) formulation which enables us to take advantage of such explicit schemes. Shape functions based on the principle of maximum entropy implemented in the framework of Optimal Transportation Meshfree schemes are utilized to solve both elastic and plastic problems

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Summary This article presents a novel finite element formulation for the Biot equation using low‐order elements. Additionally, an extra degree of freedom is introduced to treat the volumetric locking steaming from the effective response of the medium; its balance equation is also stabilized. The accuracy of the proposed formulation is demonstrated by means of numerical analyses.

SUMMARYThe 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.

The objective of this work is twofold. First, we develop an eigensoftening algorithm to capture the gradual process of failure in materials with a softening behavior as an extension of the eigenerosion approach. Both methods are validated against the physical measurements in three-point bending tests of concrete with a drop-weight device, including impact and reaction forces, loading-line displacements as well as strain histories from gauges. The comparison shows that the eigenerosion algorithm significantly overestimates the tensile stresses and the strain peaks, while it captures the forces and crack pattern accurately. Predictions made by the proposed eigensoftening algorithm agree very well with experimental results in all aspects. Second, the energy evolution and partition in the beam predicted by the eigensoftening algorithm at various impact rates is analyzed to quantify the rate dependent fracture properties of concrete. It is demonstrated that, at impact loading conditions, the area below the reactiondeflection curve is much larger than the dissipated fracture energy.

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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.

Solving dynamic problems for fluid saturated porous media at large deformation regime is an interesting but complex issue. An implicit time integration scheme is herein developed within the framework of the u − w (solid displacement-relative fluid displacement) formulation for the Biot's equations. In particular, liquid water saturated porous media is considered and the linearization of the linear momentum equations taking into account all the inertia terms for both solid and fluid phases is for the first time presented. The spatial discretization is carried out through a meshfree method, in which the shape functions are based on the principle of local maximum entropy LME. The current methodology is firstly validated with the dynamic consolidation of a soil column and the plastic shear band formulation of a square domain loaded by a rigid footing. The feasibility of this new numerical approach for solving large deformation dynamic problems is finally demonstrated through the application to an embankment problem subjected to an earthquake.