A method is presented for estimating the maximum bending moment for continuous ͑or rigidly jointed͒ pipelines affected by tunnel-induced ground movement. The estimation can be made based on the knowledge of tunnel and pipeline geometries, the stiffness of soil and pipeline, and tunnel-induced ground deformation at the pipeline level. The method takes account of soil nonlinearity by an equivalent linear approach, in which the stiffness of the soil is evaluated based on an average deviatoric strain developed along the pipeline. The approach is conservative and promises that the bending moment is not underestimated. The validity of the method as an upper bound approximation is evaluated against centrifuge test results.

An elastic continuum solution and a Winkler solution of the problem of tunnelling effects on existing pipelines are given. A comparison is made between an elastic continuum solution and a closed-form Winkler solution with Vesic subgrade modulus. Although applying the Vesic expression results in the same moments and displacements under external loading in a Winkler system and the elastic continuum, it is found that its use is not necessarily adequate for the problem of tunnelling effects on pipelines and may not be conservative owing to possible underestimation of bending moments. An alternative expression for the subgrade modulus is provided, resulting in similar maximum bending moments in the Winkler and elastic continuum systems.

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