Theoretical method for an elastic infinite beam resting on a deformable foundation with a local subsidence

摘要

Local subsidence induced by underneath erosion or excavation is usually encountered by buried pipelines and tunnels, which in turn may cause distress to the existing pipelines and tunnels. A semi-analytical method is proposed for this kind of problem by simplifying the existing pipeline or tunnel as an elastic infinite Euler-Bernoulli beam and the ground as a deformable foundation with a local subsidence. The beam-foundation system is subject to a symmetrical distribution load. Closed-form solutions for the beam responses, including deflection and bending moment, are derived based on the elastic foundation beam theory by expanding the load expression as a Maclaurin series. The proposed method and solutions are validated by a series of 3D FEM numerical simulation and model test results. Sensitivity analyses are then carried out to investigate the influence of different parameters. The results show that the beam response is highly dependent on the length of local subsidence and the beam flexural rigidity. Moreover, comparations between the calculation results based on the Pasternak model and the Winkler model that can be degenerated from the former are also presented to illustrate the rationality of the proposed method in predicting the responses of the foundation beam in this typical problem.