Apports des méthodes d'homogénéisation numériques à la classification des massifs rocheux fracturés

Abstract : The calculation method of the homogenized and anisotropic mechanical properties (elasticity tensor and resistance) of a rock mass using the finite element method, on a large scale, is first presented in this thesis.

The application of different types of numerical loading representing various compression and shear tests allows the determination of homogenized laws. These laws are deduced from the relations between the average stress and strain in a Representative Elementary Volume (REV). The different types of numerical loading (by prescribed stress or displacements) and their effects on the homogenized parameters are discussed.

A special attention is paid to the application of the theory of ellipsoidal elasticity of Saint Venant to the case of rock masses. This theory has several advantages. In particular, it allows the calculation of a three-dimensional (3D) elasticity tensor based on a plane (2D) calculations.
In addition to the method of determination of mechanical REV, a comparison with the size of the geometrical REV, which is easier to calculate, was elaborated. An approached analytical formula for the REV size is established for some non periodic rock masses according to the geometrical parameters of discontinuities.

The fundamental contribution of this thesis consists in establishing a mechanical classification of a family of rock masses. This classification is founded on the numerical homogenization methods that we propose. Then, a parametric study was carried out to determine the sensitivity of the results to the geometrical and mechanical parameters of the rock matrix and discontinuities. The homogenized mechanical parameters thus obtained constitute a useful data for the design and the study of different projects in rock masses (tunnels, slopes, dams foundations). The adjustment of some fundamental mechanical parameters (Young modulus, shear modulus) has led to the development of analytical expressions generalizing, for the cases of finite size fractures, the formulations of Amadei and Goodman [1981].

The development of this numerical classification has required the development and the validation of a powerful tool for numerical homogenization (HELEN) and, which is also easily usable in the case of other types of heterogeneous and anisotropic mediums (concrete, masonry...)

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Michel Chalhoub. Apports des méthodes d'homogénéisation numériques à la classification des massifs rocheux fracturés. Sciences de l'ingénieur [physics]. École Nationale Supérieure des Mines de Paris, 2006. Français. ⟨tel-00412033⟩

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