Mechanical effects of tunneling on adjacent pipelines based on Galerkin solution and layered transfer matrix solution

The mechanical analysis of undercrossing tunneling on adjacent existing pipelines is an important challenge that geotechnical engineers may need to face when designing new excavation projects. A Galerkin solution and a layered transfer matrix solution for the tunnel–soil–pipeline interaction are given in order to compare the effects of soil stratifications on the pipeline behavior subjected to tunnel-induced soil movements. For the Galerkin solution, the soil is modeled by the modulus of subgrade reaction and the governing differential equations are converted to finite element equations using the Galerkin method. To take full consideration for non-homogeneous soil characteristics, a layered soil model is employed in the layered transfer matrix solution by applying the double Laplace transform and transfer matrix method. The differences between the two proposed solutions are verified with several examples including centrifuge modeling tests, finite difference numerical analysis and measured data in situ. Furthermore, the parametric analysis to existing pipelines in several representative layered soils in Shanghai is also carried out. The results discussed in this paper indicate that the Galerkin solution can estimate the pipeline mechanical behavior affected by tunneling in homogeneous soil with good precision. The layered transfer matrix solution is more suitable to simulate the soil stratifications on the pipeline behavior than the Galerkin solution.