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Über dieses Buch

Numerical techniques for solving many problems in continuum mechanics have experienced a tremendous growth in the last twenty years due to the development of large high speed computers. In particular, geomechanical stress analysis can now be modelled within a more realistic context. In spite of the fact that many applications in geomechanics are still being carried out applying linear theories, soil and rock materials have been demonstrated experimentally to be physically nonlinear. Soils do not recover their initial state after removal of temporary loads and rock does not deform in proportion to the loads applied. The search for a unified theory to model the real response of these materials is impossible due to the complexities involved in each case. Realistic solutions in geomechanical analysis must be provided by considering that material properties vary from point to point, in addition to other significant features such as non-homogeneous media, in situ stress condition, type of loading, time effects and discontinuities. A possible alternative to tackle such a problem is to inttoduce some simplified assumptions which at least can provide an approximate solution in each case. The validity or accuracy of the final solution obtained is always dependent upon the approach adopted. As a consequence, the choice of a reliable theory for each particular problem is another difficult decision which should be 2 taken by the analyst in geomechanical stress analysis.

Inhaltsverzeichnis

Frontmatter

Chapter 1. Introduction

Abstract
Numerical techniques for solving many problems in continuum mechanics have experienced a tremendous growth in the last twenty years due to the development of large high speed computers. In particular, geomechanical stress analysis can now be modelled within a more realistic context.
W. S. Venturini

Chapter 2. Material Behaviour and Numerical Techniques

Abstract
Many stress analyses for geomechanical materials have been successfully carried out employing numerical techniques. Since the initial growth in electronic computer science in the sixties, the finite element method has been the most common technique to analyse stress distributions and deformation patterns in tunnel excavations, embankments, dams, building foundations and other geomechanical problems.
W. S. Venturini

Chapter 3. Boundary Integral Equations

Abstract
This chapter is concerned with the introduction of the basic integral equations for two-dimensional elastic linear material problems. It starts by briefly reviewing the partial differential equations for linear elastic material and introducing the necessary notations involved in the formulation. These governing equations are also extended to deal with problems in which initial stress and strain type loads are applied. Such kind of loads are not only important to take into account temperature or other similar loads, but also to model nonlinear material behaviour when used in conjunction with a well established successive elastic solution technique.
W. S. Venturini

Chapter 4. Boundary Integral Equations for Complete Plane Strain Problems

Abstract
In this chapter the general case of plane strain condition known as the “complete plane strain” (61, 62) is introduced into the boundary formulations. For this plane condition, displacements can develop in any direction; the only plane restriction that must be satisfied is that all displacement derivatives with reference to the third direction are equal to zero.
W. S. Venturini

Chapter 5. Boundary Element Method

Abstract
In this chapter a general procedure to obtain a numerical approach to solve the integral equations for plane (eqs. 3.3.5 and 3.3.7) and anti-plane (eqs. 4.3.15 and 4.4.1) cases previously formulated, is presented.
W. S. Venturini

Chapter 6. No-Tension Boundary Elements

Abstract
The boundary element equations presented in previous chapters are employed here to solve problems concerned with the theory of no-tension materials. The no-tension criterion appears to be one of the first departures from linear elastic theory used to model rock behaviour. In order to justify the choice of this criterion some aspects of rocks and rock masses are discussed, and the inability of these materials to sustain tensile stresses is emphasized in practical problems. The solution technique to be presented is achieved by an iterative process which consists of computing at each step an initial stress field to compensate the tensile stresses. The no-tension solution is shown to be obtained assuming a non-path dependent behaviour, therefore does not require any incremental process. An alternative solution considering path dependent behaviour is also presented.
W. S. Venturini

Chapter 7. Discontinuity Problems

Abstract
In this chapter alternative formulations to consider directionally orientated material weaknesses and slip or separation along discontinuities for rocks are presented. The chapter starts by introducing a model to study weakness in a particular direction within the context of continuum mechanics. In many schistous rock materials, shear and tensile strengths respectively parallel and orthogonal to schistosity are zero or very small in comparison to those of intact rocks (103). In order to model such material weaknesses the shear strength parallel to the schistosity is assumed to be governed by a simple Coulomb criterion of failure. Also the tensile stress in the direction orthogonal to the schistosity plane can be limited by the tensile strength value which is usually assumed to be zero.
W. S. Venturini

Chapter 8. Boundary Element Technique for Plasticity Problems

Abstract
In this chapter the boundary element formulation presented so far is adapted to solve problems concerned with the classical theory of plasticity. The chapter starts by reviewing the essential features of the one-dimensional elastoplastic analysis, followed by generalization of the plasticity concepts to continuum problems. Stress-strain relationships for post yield conditions are formulated for the boundary element technique. The procedure to compute the plastic solution is based on the initial stress process proposed by Zienkiewicz (42) for finite element formulation. The procedure has been implemented to handle four well established yield criteria (Mohr-Coulomb, Drucker-Prager, von Mises and Tresca).
W. S. Venturini

Chapter 9. Elasto/Viscoplastic Boundary Element Approach

Abstract
In this chapter a boundary element approach to deal with continuum problems involving viscous effects is presented. Basic concepts of time-dependent material behaviour, together with some rheological models used in geotechnical engineering, are introduced for one-dimensional cases. The Perzyna’s viscoplastic model is chosen to model viscoplastic behaviour. Based on this viscoplastic representation, the theory is extended to general continuum problems. The overlay concept borrowed from finite elements formulation (48,49) is also adopted here in order to model more complex time-dependent and plastic responses. As in finite elements, the technique can be also extended to solve problems with pure plastic behaviour. Finally, the applications presented in the last section of this chapter show the accuracy of the approach when it is used to model time-dependent behaviour or to simulate plastic responses with or without anisotropic effects.
W. S. Venturini

Chapter 10. Applications of the Nonlinear Boundary Elements Formulation

Abstract
In this chapter some geomechanical nonlinear problems are analysed using the boundary element technique presented in the previous chapters. For all examples the viscoplastic algorithm shown in chapter 9 is employed, even when only plastic solutions are analysed.
W. S. Venturini

Chapter 11. Conclusions

Abstract
The basic objective of this work was to develop numerical procedures for the boundary element method to analyse geotechnical problems of practical interest. Linear and nonlinear formulations such as no-tension, plasticity and others have been implemented to deal with a wide range of two-dimensional problems.
W. S. Venturini

Backmatter

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