ABSTRACT:

The behaviour of blocky rock is modelled within the frame of Cosserat continuum theory. In a regular block structure, one can consider the influence of relative rotations between blocks by means of additional Cosserat rotations. The homogenisation procedure is presented and the constitutive parameters of the corresponding Cosserat continuum are derived for elastic behaviour of the joints. For dynamic loading the domain of validity of the Cosserat model is studied by comparing the dispersion functions of the discrete and the homogenised structure. It is obtained that for wave lengths greater than five times the size of the block, the ratio of these two functions is between 0.9 and 1.0

RESUME:

Le comportement des structures de blocs rocheux est modelise dans, Ie cadre de la theorie des milieux continus de Cosserat. Les rotations de Cosserat permettent de considerer l'influence des rotations relatives des blocs. On presente la methode d'homogeneisation et on determine les paramètres constitutifs du milieu equivalent de Cosserat pour un comportement elasiique des joints. Pour un chargement dynamique on evalue Ie domaine de validite du modèle de Cosserat en comparant les fonctions de dispersion de la structure discrète et de 1'1 structure homogeneisee. On a obtenu que pour des longueurs d'onde superieures à cinq fois la taille du bloc, Ie rapport de ces deux fonctions est compris entre 0.9 et 1.0.

ZUSAMMENFASSUNG:

Das verhalten von blockigem fels wird im Rahmen einer Cosserat theory modelliert. In einer regelmassigen Block Struktur laßt sich der Einfluß der relativ Verdrehungen zwischen Blöcken mit Hilfe zusatzlicher Cosserat Verdrehungen beruecksichtigen. Das Homogenisierungsverfahren wird dargestellt und die Konstitutiven Parameter des entsprechenden Cosserat Kontinuums werden fur den Fall elastischen Fugen Verhaltens abgeleited. Fuer den Fall dynamischer Belastung wird der Gueltigkeitsbereich des Cosserat Models durch Vergleich der Dispersionsfunktionen des diskreten mit der homogenisierten Struktur untersucht. Es folgt, daß das Verhaltnis der beiden Funktionen bei Wellenlangen größer fuenf mal der Block Lange zwischen 0.9 and 1.0 liegt.

1. INTRODUCTION

The numerical analysis of blocky structures is a straight-forward matter which can be dealt with (in most cases) using off the shelf discrete or finite element codes. In the latter case, special interface elements are needed in order to account for the unilateral kinematics of the rock joints. These discrete type analyses are very computer time intensive and, at least for periodic structures, one might argue that a homogenised continuum model would allow for a much more elegant and efficient solution (Muehlhaus, 1993). Averaging processes have been developed in order to describe the mechanical behaviour of inhomogeneous materials like jointed or layered rocks by considering an equivalent homogeneous continuum medium with averaged (effective) characteristics (Bakhalov and Panasenko, 1989). These methods are based on the asymptotic developments technique and the validity of the approximation is restricted to the case where the characteristic size of the recurrent cell of the periodic medium (e.g. block size or layer thickness) is small as compared to the characteristic size of the problem (e.g. the wavelength of the deformation field). In other words when the characteristic length of the macroscopic deformation pattern is smaller than a certain multiple of the characteristic fabric length of the material.

This content is only available via PDF.
You can access this article if you purchase or spend a download.