00/01289 Method and catalysts for the preparation of di-tertiary amines by the aminomethylation of nonconjugated dienes with synthesis gas and secondary amines

Abstract

This paper presents an effecient method of modelling faulted rock using the multiregion boundary element method. The boundary element method is ideally suited for modelling problems in rock mechanics because of the requirement to descretize surfaces only. This contrasts with the volume discretization needed for the finite element method, finite difference method and the distinct element method. The disadvantage of the boundary element method is that the rock mass is assumed to be isotropic and elastic. However, it is possible to model the non-linear behaviour on fault planes by using the concept of multiple regions and by connecting these regions via non-linear springs or Goodman type joint elements. The disadvantage of this method has been that joint stiffnesses have to be specified and that a great number of iterations are needed because the stiffness coefficient of a spring may change very rapidly from a very high value (for example when a joint is in compression) to a very low value (when a joint is in tension). This paper describes a novel method for the treatment of faults with the boundary element method which eliminates the need to specify joint stiffness parameters and which is able to model signi fault movement with very few iterations. The numerical scheme makes very effecient use of computer resources because the non-linear iterations only involve degrees of freedom at the interfaces. Examples of applications of the new model to practical problems in mining and geological engineering are given.