关键词: 隧道工程；桩基加载；盾构隧道；竖向位移；Pasternak-Timoshenko梁模型；数值模拟

Abstract: With the increasing development intensity of urban subway overpasses, the structural safety of shield tunnels is becoming increasingly affected by adjacent pile foundations. Based on a practical engineering case, a method for calculating the vertical displacement of a Pasternak-Timoshenko beam coupling model under pile foundation loading was proposed. First, the additional vertical stress generated at the tunnel axis by pile-tip and pile-side loads was calculated by the Mindlin solution. Subsequently, the shield tunnel segments were equivalent to Timoshenko beams placed on a two parameter Pasternak foundation, and the analytical solution for vertical displacement was derived through Fourier series analysis. Parametric analyses on the beam length (30.0-60.0 m and infinite length) and load distribution width (6.0 m, 12.0 m) were carried out. And a three-dimensional finite element numerical model was used to compare and verify the theoretical model, based on which, the influence of beam length and load distribution width on tunnel settlement was further analyzed. The results show that the proposed theoretical model for calculating vertical displacement is reasonable. When the beam length is 60.0 m and the load width is 12.0 m, the ERMS and EMA between the analytical and numerical solutions are 0.474 mm and 0.471 mm, respectively. However, the analytical solution still underestimates the peak settlement by 0.560 mm and the influence width by 0.1D~ 0.2D.

Key words: tunnel engineering; pile foundation loading; shield tunnel; vertical displacement; Pasternak-Timoshenko beam model; numerical simulation