A new stabilized enhanced strain element with equal order of interpolation for soil consolidation problems

Mira, Pablo; Pastor, M.; Li, T.; Liu, X.

doi:10.1016/s0045-7825(03)00416-x

Cited by 68 publications

(65 citation statements)

References 22 publications

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“…As for the Stokes problem, approximation spaces for the vector and the scalar fields, satisfying the LBB stability condition [9], can be used. This approach has been analyzed in [28,29,30] by Murad et al and by Mira et al [26] for the quasistatic Biot's model. However, these methods still present pressure oscillations, when very sharp boundary layers occur; see [13], where the Taylor-Hood method on the 1D Terzaghi problem has been evaluated.…”

Section: Discrete Formulationmentioning

confidence: 99%

Distributive smoothers in multigrid for problems with dominating grad–div operators

Gaspar

Gracia

Lisbona

et al. 2008

Numerical Linear Algebra App

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SUMMARYIn this paper we present efficient multigrid methods for systems of partial differential equations that are governed by a dominating grad-div operator. In particular, we show that distributive smoothing methods give multigrid convergence factors that are independent of problem parameters and of the mesh sizes in space and time. The applications range from model problems to secondary consolidation Biot's model. We focus on the smoothing issue, and mainly solve academic problems on Cartesian staggered grids.

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Section: Discrete Formulationmentioning

confidence: 99%

Distributive smoothers in multigrid for problems with dominating grad–div operators

Gaspar

Gracia

Lisbona

et al. 2008

Numerical Linear Algebra App

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“…The u−w formulation is employed herein (u and w denote, respectively, the absolute displacement of the solid phase and the relative displacement of the fluid phase). If linear approximation functions are used in the finite element scheme, compared to the more conventional u−p w formulation (p w denotes the pore water pressure), the u−w formulation gives stable solutions even for extremely low values of the soil permeability , and no stabilization algorithms are needed (Mira et al, 2003). In addition, while in u−p w formulation the relative flow acceleration is neglected, in u−w it is not, and therefore, more accurate solutions are obtained if the frequency of the input motion and/or the soil permeability are high (Zienkiewicz et al, 1980).…”

Section: Governing Equationsmentioning

confidence: 99%

Performance of heterogeneous earthfill dams under earthquakes: optimal location of the impervious core

López‐Querol

Moreta²

2008

Nat. Hazards Earth Syst. Sci.

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Abstract. Earthfill dams are man-made geostructures which may be especially damaged by seismic loadings, because the soil skeleton they are made of suffers remarkable modifications in its mechanical properties, as well as changes of pore water pressure and flow of this water inside their pores, when subjected to vibrations. The most extreme situation is the dam failure due to soil liquefaction. Coupled finite element numerical codes are a useful tool to assess the safety of these dams. In this paper the application of a fully coupled numerical model, previously developed and validated by the authors, to a set of theoretical cross sections of earthfill dams with impervious core, is presented. All these dams are same height and have the same volume of impervious material at the core. The influence of the core location inside the dam on its response against seismic loading is numerically explored. The dams are designed as strictly stable under static loads. As a result of this research, a design recommendation on the location of the impervious core is obtained for this type of earth dams, on the basis of the criteria of minor liquefaction risk, minor soil degradation during the earthquake and minor crest settlement.

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“…On the other hand, a stable formulation based on the Simo-Rifai enhanced strain element has been proposed as an alternative stabilization methodology even for the equal order interpolation in both displacements and pore pressures (Mira et al, 2003).…”

Section: The Role Of Interpolation Function Of the Efg For Computatiomentioning

confidence: 99%

Mesh-Free Method for Soil-Water Coupled Problem Within Finite Strain and Its Numerical Validity

Murakami

Setsuyasu

Arimoto

2005

SOILS AND FOUNDATIONS

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A formulation of the Element-Free Galerkin Method (EFG method), i.e., one of the mesh-free meshless methods developed in the field of computational mechanics for solving partial differential equations, is furnished for consolidation within finite strain and its validity for application to soil-water coupled problems is examined through a numerical analysis. The numerical strategy is constructed to solve a set of governing equations, e.g., the equilibrium for the nominal stress rate and the continuity of pore water, and the numerical discretization of the weakform of the governing equations leads to an updated Lagrangian scheme. The accuracy of the proposed numerical strategy is examined through an analysis of unconfined compression tests and simple shear tests under undrained and plane strain conditions through a comparison of stress paths integrated directly from the Cam-clay model within the framework of finite strain. It is also revealed that the particular type of weight function to be adopted in the moving least-squares (MLS) approximation, even in the same order, can determine the resultant shape functions of the EFG method for both the displacement and the pore water pressure field such that they are smoother than those of the usualFEM. The functions are advantageous in that they avoid spatial instability in the numerical solutions for pore water pressure under undrained conditions appearing in saturated soil column tests, where the shape function of the pore water pressure in the conventional FEM computation is adopted as a lower order than that of the displacement to remedy this type of numerical difficulty. To emphasize the applicability and the feasibility of the mesh-free computation, the consolidation phenomena are demonstrated in the analysis of a punch problem for a soft soil foundation which hasstress singularity under both ends of a rigid loading platen for the same problem which Yatomi et al. (1989) solved with FEM.

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A new stabilized enhanced strain element with equal order of interpolation for soil consolidation problems

Cited by 68 publications

References 22 publications

Distributive smoothers in multigrid for problems with dominating grad–div operators

Distributive smoothers in multigrid for problems with dominating grad–div operators

Performance of heterogeneous earthfill dams under earthquakes: optimal location of the impervious core

Mesh-Free Method for Soil-Water Coupled Problem Within Finite Strain and Its Numerical Validity

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