Elastic continuum solution for tunneling effects on buried pipelines using Fourier expansion

This paper presents an analytical solution for the effect of tunneling-induced ground displacements on buried pipelines within an elastic continuum. The greenfield ground displacement is decomposed into an infinite series of trigonometric functions. The response of the soil and the pipeline to these trigonometric functions is then established and used to derive a solution for the global pipeline response using the superposition principle.

The approach is used first with the commonly used barrel load for interaction between the pipe and the soil, under the requirement for longitudinal soil-pipe compatibility. To avoid the a priori assumption of barrel load interaction forces, the solution is then extended to consider a more general interaction load pattern based on the requirement for cross-sectional compatibility (in addition to the longitudinal compatibility).

This is achieved by an additional Fourier series expansion describing the load variation along the pipe cross section. The cross-sectional Fourier expansion is solved as a minimization problem to achieve the compatibility. Previous solutions of the elastic continuum problem involved discretization along the pipeline (or the use of shape functions) with compatibility requirements at specific points, without any requirements for exact longitudinal and cross-sectional compatibility, as in the present solution.

The derived solutions are presented in a normalized manner and compared with previous solutions. Various aspects of the present and previous solutions are discussed and examined.