Large scale three-dimensional finite element analysis of underground construction

Abstract

This paper discusses the possibility of using three-dimensional finite element analyses to analyse and design underground construction works. Two common problems associated with three-dimensional analyses mean very large memory requirement and long computing times. To overcome these problems, the Authors outline some recent developments in iterative solution algorithm which can lead to large savings in memory and time. It is shown that these iterative methods offer viable and faster alternatives to Gaussian elimination approach for solving very large finite element equations in geotechnical engineering, such as those arising from three-dimensional analyses, with significantly reduced memory requirement. The convergence characteristics of ill-conditioned coupled-flow problems can be improved by using a generalized Jacobi preconditioner. Drained problems can be efficiently solved using the preconditioned conjugate gradient method with the standard Jacobi preconditioner. On the other hand, undrained problems are better solved as "nearly-impermeable" consolidation problems, using quasi-minimal residual method with the generalized Jacobi preconditioner. The advantages of iterative methods increase with the size of the problem. For very large problems, the speed-up can be very significant. The applicability of iterative methods is illustrated by the study of a tunneling project involving earth pressure balance machine. The details of face pressure application, tunnel convergence around shield and lining installation were modeled. The results show that large-scale three-dimensional analyses with iterative solution cannot only be implemented on relatively modest computation platforms with reasonable turnaround times, but they are also able to illuminate ground mechanisms which cannot be reflected by two-dimensional analyses. © 2006 Taylor & Francis Group.