Finite Element Method (FEM) - Rock Mechanics Based on an Anisotropic Jointed Rock Model - page 230

The finite elements of which a computation section consists are connected with each
other, forming the finite element mesh (FE-mesh). Then, the linear equation system
including all elements of the FE-mesh is compiled. This is done by summing all the
contributions of all elements to the nodes that are contained in these elements. Then
the linear equation system of the entire system consisting of thousands of unknowns is
solved after the boundary conditions are introduced in the same manner as described
above for a single element. Clearly this can be economically conducted only with the aid
of powerful computers.
In a seepage flow analysis the piezometric heads in the nodes are the unknowns corre-
sponding to the displacements in a stress-strain analysis.
Fig. 10.3, for example, shows the FE-mesh for the stability analysis of a segmental
lining which is installed in tunnels driven by tunnel boring machines (Chapter 21). The
discretization of the computation section into finite elements has a decisive influence
on the accuracy of the results. The finer an element mesh the more accurately will the
calculated results generally correspond to the exact solution.
Figure 10.3 Finite element mesh (FE-mesh) of a machine driven tunnel with segmental lining
(Wittke et al. 2006)
The FE-mesh should be particularly fine in all those areas where large gradients of
stress and piezometric heads occur. For underground openings this is always the area
near the excavation. In Fig. 10.4 the discretization of the segmental lining and a longi-
tudinal joint are represented as details of the mesh shown in Fig. 10.3.