A Fourier-based elastic continuum solution for jointed pipeline response to tunneling

This paper deals with the problem of tunneling effects on existing jointed pipelines. It extends a recently developed Fourier-based elastic continuum approach which has been applied to continuous pipelines. Unlike the continuous pipeline solution, in which the response in the spatial frequency domain is orthogonal (that is, each frequency response is independent of other frequencies), the joints lead to coupling between the spatial frequencies. Within the paper, closed form expressions are provided for the set of equations describing the coupling and interaction between the spatial frequencies. These expressions can directly be used to solve the global response of the jointed pipeline. The development is based on energy principles, and involves full cross-sectional as well as longitudinal compatibility, and hence may be regarded as more rigorous than previously published elastic continuum solutions which involve various assumptions regarding the distribution of interaction forces and discretization. The results of the suggested solution are compared against previous published, matrix based, solutions, where it is shown that the current method is well suited for the jointed pipeline problem. Finally, the condition of the more simplified Winkler system is addressed and various subgrade reaction models are discussed and compared with the more rigorous elastic continuum solution.