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The deformation of the overlying pipeline caused by the soil tunnel excavation cannot be ignored in the case of the small spacing between the pipeline and the tunnel. Based on the rigid bar method, the pipeline-soil interaction model was established, with the simply supported beam as the basic system, and the loads acting on the pipeline by the soil are considered to be linearly distributed. Calculation methods for continuous and discontinuous pipeline deformations were established. The results calculated by the proposed method agree well with the experimental data of centrifuge tests and field data. Parametric study on the effect of the volume loss (η = 1%, 2%,3 %), rotational stiffness (β 0  = 4.47 × 10 6 N⋅m/rad, 4.47 × 10 8 N⋅m/rad, 4.47 × 10 10 N⋅m/rad), ratio of pipeline section length to inflection point of soil settlement curve (L/i s  = 0.5, 1.0, 1.5, 2.0) and soil elastic modulus (E = 10 MPa, 30 MPa, 50 MPa) on the deflection and joint rotation angle of the discontinuous pipeline were carried out. Results show that: (1) the maximum pipeline deflection and the maximum rotation angle of the joint increase as η increases and decrease as β 0 increases; (2) in the "odd" case, the maximum pipeline deflection and the maximum rotation angle of the joint first increase and then decrease as L/i s increases, reaching a peak at L/i s  = 1.5, while in the "even" case, the maximum pipeline deflection decreases as L/i s increases and the maximum rotation angle of the joint first increases and then decreases as L/i s increases; (3) in the "odd" case, the maximum pipeline deflection and the maximum angle of rotation of the joint decrease as E increases, while the opposite trend is observed in the "even" case. Additionally, the maximum pipeline deflection and the maximum rotation angle of the joint are always greater in the "odd" case than that in the "even" case., (© 2023. Springer Nature Limited.)

The existing tunnel construction causes stratum deformation, which in turn leads to additional deformation and internal force of the overlying pipeline, thus increasing the risk of pipeline accidents. Then, how to correctly calculate the deformation and internal force of pipeline is the key to pipeline safety evaluation. To this end, this study firstly used the Pasternak foundation beam model to simulate the interaction of pipeline and soil, and divided the pipeline into the void area (i.e., pipeline-soil detachment) and the coordination area (i.e., pipeline-soil is always deformed together) between pipeline and soil. The differential equation of pipeline deflection for the void area and the coordination area were established respectively, and the solutions of pipeline deflection, the internal force of pipeline and the width of pipeline-soil void area were presented. Subsequently, the accuracy of the proposed method was verified by comparing with the available model and field test data, and it is found that the calculation results are too conservative without considering the pipeline-soil voiding phenomenon. Finally, the detailed parametric analysis was conducted. The results show that the pipeline deflection decreases with the increase of the pipeline-tunnel spacing between pipeline and tunnel, the pipeline bending stiffness and the soil elastic modulus, but increases with the increase of the formation loss rate, and the width of pipeline-soil void area increases with the increase of the pipeline-tunnel spacing, the pipeline bending stiffness and the soil elastic modulus., (© 2023. The Author(s).)