Iterative solution of intersecting tunnels using the generalised Jacobi preconditioner

Abstract

This study presents settlement analyses of intersecting tunnels using the 3-D finite element method. This study demonstrates that the reinforcing or strengthening effects due to the presence of existing tunnel(s) are significant on the problem being investigated. Any existing tunnel prior to the new tunnelling has to be incorporated into analyses if more realistic assessments on the tunnelling impacts are required. This study also shows that when multiple closely spaced tunnels are constructed, the assumption that each tunnel behaves independently and the movements that would have occurred for each tunnel acting independently can be superimposed, is unlikely to provide good estimations. Note that the linear superposition technique has been commonly used in practice to reduce the complexity of very large problems that involve construction of multiple tunnels. Consequently, the entire problem has to be modelled and large-scale computing is unavoidable. The symmetric quasi-minimal residual method (SQMR) incorporating the generalised Jacobi (GJ) preconditioner is shown to be very economical in solving such large-scale finite element problems on personal computers. © 2006 Taylor & Francis Group.