Finite Elements

Abstract

In Chapter 5 we obtained the analytical solution for the plane strain problem of surface subsidence above a cut-and-cover tunnel. This, however, was only possible after introduction of significant simplifications into the problem formulation. In general, analytical solutions are available only for boundary value problems with simple geometry, boundary conditions and constitutive relationships. The majority of the realistic problems have to be solved numerically. Chapter 6 gives a very basic introduction into the most popular numerical approach—Finite Elements Method (FEM). Chapter 7 will explore an alternative approach—Finite Differences Method (FDM), which has advantages for solution of non-linear and unstable boundary value problems.