Experiences with the application of the coupled boundary element/finite element method to large scale industrial problems in rock and soil mechanics are presented. The applications range from problems in ttmnelling to the analysis of arch dams. Three case studies will be examined with respect to accuracy and efficiency. Efficiency is measured as time required to generate the mesh, computer time spent in the analysis and time spent for post-processing results. If available, comparison will be made with meshes involving finite elements only. The conclusion of the paper is that a coupled analysis offers a considerable reduction in time spent in the pre-processing/analysis/post-processing but does not result in any appreciable loss of accuracy.


The Boundary Element Method (BEM) offers considerable advantages in dealing with many problems in rock mechanics. Because infinite or semi-infinite domains can be dealt with a surface discretisation only, meshes tend to be much smaller and computation times shorter than with the Finite Element Method (FEM). With the BEM it is possible to consider an-isotropic material behaviour and via the multi-region method (Beer and Watson 1992) also inhomogeneous properties of the rock mass. However, if the analysis involves sequential excavation/construction and non-linear material behaviour, then special solution techniques have to be employed. One possibility is to combine the finite element method and boundary element methods. In such a combined analysis the infinite or semi-infinite rock mass is modelled very efficiently with the BEM whereas the sequential excavation and material nonlinear behaviour is modelled well with the FEM. Although the theoretical background of the coupled BEM/FEM method has been fairly well established (Beer and Watson 1992), the practical use of the method has not been widespread.

The purpose of this paper is to show on practical examples the considerable advantages that can be gained by applying the coupled method of analysis to a variety of problems in geomechanics ranging from tunnels to dams. The theoretical background to the coupled method has been explained in many publications (for a summary see for example Beer 1998) so details will not be repeated here. The method used in the following examples requires the computation of a stiffness matrix of the boundary element region only involving the nodes that are connected with finite elements. This scheme has the advantage that once the boundary element region has been solved (which usually takes most of the computer time) the simulation of sequential excavation and the non-linear iterations only involve the finite element region.

Three case studies will be presented:

§ Three-dimensional simulation of tunnel excavation.

§ Rock caverns for CERN facility.

§ Concrete arch dam with valley floor

For the first and the last we will show comparisons with meshes involving Finite Elements only. For the second example a finite element analysis would have been beyond the computer capabilities available. The analyses were performed with the BEFE code (Beer 1999) and clearly show the advantages that can be gained from a coupled approach.

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