The technique of various kinds of numerical analysis offered remarkable results to explication of many rock mechanical phenomena. These techniques regarded a rock stratum as a continuum body and solved the governing equation of continuum mechanics by using finite difference method, finite element method and/or others. Using numerical analysis based on continuum mechanics, however, the simulations of destruction phenomena caused by elastic waves and on the other hand, the elastic wave propagation which generated by fracturing events are quite difficult. In this paper, we express a rock stratum by a granular body model and develop a simulation technique can simulate both wave phenomena and destruction phenomena at once. The DEM (discrete element method) simulation results are compared with finite difference solutions of elastic wave equation. Furthermore, we simulate Hopkinson effect by this proposed method. Hopkinson effect is famous as a destruction phenomenon caused by elastic wave propagation.
ABRISS: In dieser Studie druecken wird eine Felsschicht durch ein Granularkörpermodell aus und entwickeln eine Simulationstechnik, die sowohl Wellenphanomene als auch Zerstörungsphanomene simulieren kann. Die Ergebnisse der Simulation mit DEM (Diskrete- Elemente-Methode) werden mit denen der Finit-Differenz-Lösung von Gleichungen elastischer Wellen verglichen. Desweiteren simulierten wir den Hopkinson-Effekt mit dieser vorgeschlagenen Methode. Der Hopkinson-Effekt ist als Zerstörungsphanomen beruehmt, verursacht durch Fortpflanzung elastischer Wellen.
Dans cette etude, nous exprimons un lit de roches par un modèle à corps granulaire et developpons une technique, permettant de simuler d'un coup le phenomène des ondes et le phe-nomène de destruction. Les resultats de la simulation DEM (methode d'elements discrets) sont compares aux solutions à difference finie de l'equation d'ondes elastiques. En outre, nous simulons l'effet d'Hopkinson par la methode proposee. L'effet d'Hopkinson est connu comme phenomène de destruction, cause par la propagation d'ondes elastiques.
In the numerical analysis for the geosciences, the governing equations are usually solved by the finite difference approximation, finite element method, and/or boundary element method based on the assumption that bedrocks can be modeled as a continuation medium. Therefore, even simulations for destruction phenomena are based on an assumption of a continuation body. For example, it is unsuitable for a simulation of the acoustic emission (A.E) wave propagation and the fracturing simultaneously. Recently, for such problems, the discontinuity dynamics model or a discrete particle model (Oda and Iwashita, 1999) has been investigated by many researchers.
In this paper, we investigated a simulation methodology for the elastic wave propagation from a viewpoint of discrete particle model (Toomey and Bean, 2000) and the distinct element method (DEM) (Cundall and Strack, 1979). In this approach, it assumes and treats a medium as a gathering of many particles and the simulation is not based on an elastic wave equation derived by the continuum mechanics. According to this methodology, the simulation study of A.E or earthquake wave propagation caused by the faulting which is a destruction phenomenon in the continuum media might become possible. We carried out a simulation study using DEM and compared with results of finite difference method, which solves an elastic wave equation.
