Abstract: The authors investigate the influencing factors of the passive failure zone and the ultimate face support pressure ahead of the tunnel face during shield tunneling beneath existing pipelines in sandy soil layers. Numerical simulations are first conducted to evaluate the effect of the horizontal distance between the tunnel face and the existing pipeline on the development of the passive failure zone and the corresponding ultimate support pressure. Based on the critical conditions identified through simulation, a three-dimensional limit equilibrium model is proposed. This model, applicable to tunnel face behavior during vertical under-crossing of existing pipelines, comprises three components: an upper inverted frustum, the existing pipeline, and a lower logarithmic spiral wedge. A closed-form solution for calculating the ultimate passive support pressure is then derived. The model′s validity is confirmed by comparing theoretical predictions with numerical simulation results. The findings reveal that: (1) The impact on the failure mechanism and ultimate support pressure is most significant when the pipeline is located approximately one tunnel diameter ahead of the face. (2) The soil internal friction angle, pipeline burial depth, and tunnel-pipeline spacing markedly affect the passive support pressure. (3) With higher internal friction angles, the support pressure increases as the vertical clearance between the tunnel and pipeline grows. (4) With lower friction angles, the support pressure becomes much less sensitive to changes in vertical clearance.

Key words: shield tunnel, passive instability, ultimate support pressure, limit equilibrium method, under-crossing existing pipelines