The paper presents an efficient method of analysing the sequential construction of a tunnel in an an-isotropic rock mass under a complex stress state. It will be shown that the effort in generating the mesh and the computing time is an order of magnitude smaller than for an equivalent finite element analysis. Since the results are not affected by the finite element shape functions introduced inside the domain, the resulting stress distribution is also more accurate.


The numerical simulation of the construction of a tunnel in an anisotropic rock mass in mountain regions requires a three-dimensional analysis since this would be the only way to consider a complex surface topology and general conditions of anisotropy. In many simulations carried out the finite element method (FEM) is used where a sub-domain if the infinite rock mass is divided into solid elements. However, even with modern software the effort in the preparation of the mesh (especially if branching tunnels are involved) and in carrying out the analysis substantial. Also the artificial boundary conditions applied at the boundary of the sub-domain may influence results. An alternative to the FEM is the boundary element method (BEM). In this method only surfaces need to be defined and infinite domains may be considered without truncation. The results of BEM analyses have also been found to be more accurate than FEM analyses because variation of displacements inside the rock mass solutions are obtained which satisfy the equations of equilibrium and compatibility exactly. The widespread use of the BEM has been hampered by the inability of the method to handle sequential excavation and construction and by the lack of efficient software that could handle elasto- and visco-plastic rock mass behaviour. However these restrictions are being removed so that the BEM will become a very attractive alternative to the FEM for tunnel analysis. In this paper we will show an application rack multi-region BEM to the sequential excavation of a tunnel driven through an an-isotropic rock mass on a slope.


The theory of the BEM has been presented previously by Beer (1992) and good introductory text books (see for example Beer (2001)) are available. Here we will only summarise the method used to simulate sequential excavation/construction and visco-plasticity. 3.2 Fundamental solutions An essential ingredient of the BEM is a fundamental solution of the differential equations that govern the problem. For elastic and isotropic domains the solution first presented by Kelvin (Thomson, 1848) is used. In many cases the rock mass has a distinct an-isotropy that has to be considered. In most cases however we deal with an orthotropic behaviour, that is the material properties are different in two orthogonal directions. In this case the derivation of the fundamental solution is more complex. In a method suggested by Watson (2002) a numerical solution is obtained. This solution can be divided into one part that only depends on the direction of r the other on the distance r.

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