The focus of this paper is a discussion of a class of computational methods used to analyze discontinuous media, such as. geomaterials. Particular emphasis is directed toward a recently developed computational method based on finite element substructuring or domain decomposition techniques. As occurs naturally, a mass of fractured rock contains discrete rock blocks that interact along discrete fractures. Each rock block is modeled as a continuous elastic body. Intermittent contact between blocks is captured with slideline finite elements, based on a perturbed Lagrangian multiplier technique. The method is practical for implementation on multi-processing or parallel processing environments.


Ce paper se concernede sur la discussion d'un group de methodes de calcules utilisees pour l'analyse des milieux discontinues, comme les materiaux geologiques: Les methodes de calcule developpees recemment basees sur la decompesition des elements fin ou les techniques de decompesition d'une domaine sont particulièrment accentuees. Comme en nature, la masse du rocher fracture contient des does bloques du rocher discrète qui interagissent Ie long des fractures discretes. Chaque bloque du rocher est decrite comme un corps elastique continu. Le contact intermittent entre les bloques est capture par les elements fin glissant de cord, bases sur la technique de multiplicateur de Lagrangian perturbe. Ce methode est pratique pour implimentation sur les multiprocessors ou processeurs parallèles.


Im vorliegenden Bericht wird eine Gruppe von Berechnungsarten besprochen, um ein diskontinuierliches Medium zu analysieren, wie zum Beispiel Erdmaterialien. Der Schwerpunkt ist eine kuerslich entwickeite Berechnungsmethode, weiche auf einer Finiten Elementen Unterteilung basiert und eine Technik zur Bereichsaufteilung gibt. Aus in der Natur beobachtet man, dass serlkueftete Gesteine aus verschiedenen Gesteinsblocken bestehen, welche entlang diskreten Bruechen miteinan in Besiehung stehen. Jeder Gesteinsblock wird als kontinuierlicher elastischer Block modelliert. Die sporadischen Kontakte, welche zwischen den einzelnen Bloecken auftreten, werden mit speziellen Finiten Elementen modelliert, welche die Verschiebungsflaechen darstellen. Diese Finiten Elementen basieren auf einer abgewandeleten Lagranian Multiplikatoren Technik. Diese Methode eignet sich besonders fuer die Implementierung mit Parallelprozessoren und Mehrfachprozessoren.


There are many classes of important practical problems in mechanics in which it is imperative to account for the effects of physical discontinuities. This is particularly so in geomechanics, the mechanics of geological materials. Physical discontinuities are pervasive on virtually all scales in geomaterials and determine the load-deformation behavior, the strength, and the failure mechanisms of such materials. Such is the case with the interaction of grains and crystals that constitute soil and intact rock, joints or fractures in the bulk mass of rock, faults that generate earthquakes, and at an extreme scale the earth's tectonic plates. Computational methods for modeling discontinuous media are herein referred to as discontinuous deformation methods (DDM). The theory of several DDMs is the subject of discussion of this paper. In the next section the basic laws of mechanics that provide the foundation for DDMs are summarized. In the third section, the basis of the discrete element and discontinuous deformation analysis methods are summarized. In the forth section the theoretical basis for a new method is presented. Lastly, example results from the proposed method are presented.

Definition of Physically Discontinuous Media

Discontinuous media may be defined by considering a volume of space containing more than one body. A schematic representation of such a volume is show in fig. 1. Each discrete body within the volume is continuous in the sense that behavior of the body may be determined using the methods of continuum mechanics. Whether considered on a microscopic or a macroscopic scale, the physical feature that governs the load deformation behavior of the material within the volume of interest is the presence of surfaces bounding the bodies.

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