Keywords: finite elements, 3D modeling, overlaid meshes, stabilized two-phase finite element formulations.

Three-dimensional finite element modeling is becoming more popular among practicing geotechnical engineers. This domain of design activity is indeed very complex and numerical modeling is usually the only possibility to deal with real world problems. While 2D finite element models and related software are widely accepted in daily practice, 3D models are still rarely used due to associated levels of complexity.

In the case of finite element software run on today's PCs, the size of the model (in terms of total number degrees of freedom) is always a crucial point, when making a model. Although automatic mesh generators may speedup geometric data generation, resulting meshes may exceed current computer resources.

Actually, low order enhanced bricks (BBAR or EAS type) are the most popular and very robust finite elements used in 3D applications. If we restrict the available class of low order finite elements to bricks only one may immediately notice that this constrained 3D meshing can be a difficult task.

The main goal of this paper is to present the actual capabilities of a 3D finite element system like Z_SOIL, designed for single processor PC platforms and oriented towards geotechnical engineering. The most important problems solved during its elaboration till current stage of development, with latest 3D options, are discussed.

Volumetric locking associated with nearly incompressible and dilatant elastoplasticity is discussed and two robust finite element formulations, namely BBAR [1] and EAS [2], applicable in particular to low order finite elements for a single phase continuum, are introduced first. Some modifications in the BBAR method in the context of plane strain applications are proposed and tested based on a simple patch test.

In the following sections of this paper, a short review of stabilized finite element formulations and related numerical examples for the problem of consolidation of two-phase continua are presented [3,4]. Two stabilized finite element formulations are proposed, which successfully eliminate the well known problem of strong spatial oscillations of pore pressure fields at the early stage of consolidation processes, and the "critical time" step limit is successfully eliminated, at low computational cost.

Simplifications in 3D modeling, by means of so-called overlaid meshes, are discussed next. The problem of numerical treatment of constraints is there of primary importance. Two possible approaches, Lagrange multipliers and penalty methods are discussed as a prelude to the overlaid meshes approach. The concept of overlaid meshes is shown to simplify and significantly reduce the size of 3D finite element models.

In the last part of the paper, a real world 3D tunneling problem in urban area is presented. All the details concerning generation of the 3D model are discussed and the versatility Z_SOIL.PC is demonstrated.

1

T. J. R. Hughes. "The finite element method. Linear Static and Dynamic Finite Element Analysis". Prentice Hall, Inc. A Division of Simon & Schuster, Englewood Cliffs, New Jersey 07632, 1987.

2

J. C. Simo and S. Rifai. "A class of mixed assumed strain methods and the method of incompatible modes". International Journal for Numerical Methods in Engineering, 29:1595-1638, 1990. doi:10.1002/nme.1620290802

3

A. Truty. A "Galerkin/least-squares finite element formulation for consolidation". International Journal for Numerical Methods in Engineering, 52:763-786, 2001. doi:10.1002/nme.224

4

Th. Zimmermann, S. Commend, A. Truty, and J.-L. Sarf. "Numerical simulations for dam constructions". In Proceedings of Computer Methods and Advances in Geomechanics, Desai et al. (ed), pages 1649-1654, Balkema, Rotterdam, 2001.

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