Difference solutions for responses of foundation-beams with arbitrary boundary conditions considering spatial soil variability and its applications

Abstract

This study proposes a comprehensive Vlasov foundation-Timoshenko beam model with arbitrary elastic boundary conditions by introducing the translational and rotational restraining springs. The difference solutions for the responses of the beam subjected to arbitrary distributed loads are strictly deduced considering spatial soil variability, thereby the reliability of that is validated via experimental data, closed-form analytical solutions and numerical simulation results. The results show that the proposed analytical model is applicable not only to homogeneous deposit and common boundary conditions, but also to heterogeneous deposits and arbitrary boundary conditions. In addition, the proposed V-T model is robust and universality since it can be degenerated into a V-E model, W-T model and W-E model, where “E” represents a Euler-Bernoulli beam and “W” represents the Winkler foundation model. Then the proposed model is employed to evaluate the longitudinal responses of an underlying shield tunnel induced by adjacent excavation. The complicated issues when the excavation is adjacent to the station are also thoroughly analyzed and discussed based on the proposed analytical model. Results indicate that the constraint of the station-tunnel junction on the shield tunnel could not be neglected when the excavation is close to the junction, and a flexible connection is beneficial to avoid the failure of the junction.