Introducing tunnel kinematic constraints into an elastic continuum formulation of tunnel–soil–pipeline interaction

Abstract

This paper presents a new formulation of the problem of tunnelling effects on pipelines, which incorporates the tunnel kinematic constraints in the tunnel–soil–pipeline interaction analysis. This ‘constrained continuum formulation’ can be considered an extension of the original ‘two-stage’ elastic-continuum method, which traditionally neglects the mutual influence of the pipeline on the tunnel and vice versa. The new approach retains the advantage of using the greenfield condition as an input, but it allows closed-form consideration of the stiffening effect of the tunnel on the soil domain. The paper details the formulation and then provides an investigation into the effect of varying fixities: namely, both as ‘wished-in-place’ tunnels and as evolving, advancing constraints, with the tunnel ‘construction’. Normalised solutions are presented and compared with the previous formulation. In general, the addition of tunnel constraints leads to a stiffer soil action, and thus higher bending stressing in the pipeline; modelling of the tunnel kinematic constraint is conservative. The question of when such analysis is desired is discussed, concluding with a simple-to-use inequality suitable for design.