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This paper presents a computational framework for the numerical analysis of fluid-saturated porous media at large strains. The proposal relies, on one hand, on the Particle Finite Element Method (PFEM), known for its capability to tackle large deformations and rapid changing boundaries, and, on the other hand, on constitutive descriptions well-established in current geotechnical analyses (Darcy's law; Modified Cam Clay; Houlsby hyper-elasticity). An important feature of this kind of problem is that incompressibility may arise either from undrained conditions or as a consequence of material behavior; incompressibility may lead to volumetric locking of the low-order elements that are typically used in PFEM. In this work, two different three-field mixed formulations for the coupled hydro-mechanical problem are presented, in which either the effective pressure or the Jacobian are considered as nodal variables, in addition to the solid skeleton displacement and water pressure. Additionally, several mixed formulations are described for the simplified single-phase problem due to its formal similitude to the poromechanical case and its relevance in geotechnics, since it may approximate the saturated soil behavior under undrained conditions. In order to use equal order interpolants in displacements and scalar fields, stabilization techniques are used in the mass conservation equation of the biphasic medium and in the rest of scalar equations. Finally, all mixed formulations are assessed in some benchmark problems and their performances are compared. It is found that mixed formulations that have the Jacobian as a nodal variable perform better.

This paper describes a computational framework for the numerical analysis of quasi-static soilstructure insertion problems in water saturated media. The Particle Finite Element Method is used to solve the linear momentum and mass balance equations at large strains. Solid-fluid interaction is described by a simplified Biot formulation using pore pressure and skeleton displacements as basic field variables. The robustness and accuracy of the proposal is numerically demonstrated presenting results from two benchmark examples. The first one addresses the consolidation of a circular footing on a poroelastic soil. The second one is a parametric analysis of the cone penetration test (CPTu) in a material described by a Cam-clay hyperelastic model, in which the influence of permeability and contact roughness on test results is assessed.

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.

We describe the large strain implementation of an elasto-plastic model for structured soils into G-PFEM, a code developed for geotechnical simulations using the Particle Finite Element Method. The constitutive model is appropriate for naturally structured clays, cement-improved soils and soft rocks. Structure may result in brittle behavior even in contractive paths; as a result, localized failure modes are expected in most applications. To avoid the pathological mesh-dependence that may accompany strain localization, a nonlocal reformulation of the model is employed. The resulting constitutive model is incorporated into a numerical code by means of a local explicit stress integration technique. To ensure computability this is hosted within a more general Implicit-Explicit integration scheme (IMPLEX). The good performance of these techniques is illustrated by means of element tests and boundary value problems.

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We present an adaptive scheme for three-dimensional convection-diffusion problems discretized by the Finite Element Method. The adaptive scheme is based on a remeshing strategy that applies a maximum volume constraint to the elements of a reference mesh. The remeshing can increase or decrease drastically the size of the elements in a single step automatically. With this strategy, the mesh quality does not deteriorate; as a consequence, the number of iterations required to solve the system of linear equations using iterative algorithms is kept constant. Two examples of very different characteristics are presented in order to analyze the proposal for a wide range of situations. The first is a three-dimensional extension of the Smolarkiewicz problem and the second is a simplified version of a point source pollutant transport problem. The results show the flexibility of the proposal. An optimal remeshing frequency, from a computational cost and accuracy of the results point of view, can be defined for both kinds of problems.Peer ReviewedPostprint (author's final draft

Permeability is important in many geotechnical applications. The current CPTu practice to obtain permeability values relies on dissipation tests, which are frequently slow and only linked to permeability through compressibility measures. On-the-fly methods offer an alternative approach in which permeability is directly linked to CPTu penetration measurements. Several on-the-fly methods have been proposed and their applicability and relative advantages are not fully clear. Numerical effective stress simulation of CPTu testing is used here to explore in a simplified but realistic setting the relative merits of different on-the-fly methods. It is found that for partly drained materials the original simpler relation between cone metrics and normalized permeability works reasonably well. A continuous generalization of Elsworth and Lee method to the full permeability range is proposed, noting the connection to the backbone normalized pore pressure curve that describes the partly drained transition of cone penetration. The importance of an undrained limit beyond which the method produces large errors is stressed.