为准确预测新建隧道上穿作用下既有盾构隧道的隆起位移，考虑土体的天然成层性，提出成层地基中新建隧道上穿作用下盾构隧道纵向位移的解析解答。首先，分析盾构隧道与周围土体的相互作用，构建盾构隧道与土体的整体耦合平衡方程。其次，基于Mindlin解求得新建隧道开挖卸荷作用下下部成层地基土的隆起位移，结合耦合平衡方程得到盾构隧道的纵向位移解。最后，与3个上穿工程实测数据进行对比，对相关参数进行分析。结果表明： 1）当既有隧道下部地基分层性不明显，前人基于弹性地基梁的预测方法与本文方法均能较好预测下部隧道的隆起位移； 2）当地层具有明显分层时，所提方法预测结果与实测结果具有较好的一致性； 3）增大新建隧道直径将导致既有盾构隧道隆起位移的增加和隆起范围的增大； 4）减小新建隧道与下卧隧道之间的穿越净距将导致下部盾构隧道的隆起值增加； 5）既有盾构隧道位于上软下硬地层之上时，其隆起范围小于上硬下软地层，但其隆起量大于上硬下软地层。
In this study, considering the natural stratification
of the stratum, an analytical solution for the longitudinal displacement of a
shield tunnel associated with an overcrossing tunneling in layered soils is
proposed. The proposed solution can accurately predict the heave of the
existing shield tunnel due to the overcrossing tunneling. First, the
interaction between the shield tunnel and surrounding soil is analyzed and the
overall coupling equilibrium equation between them is established. Second,
based on Mindlin′s solution, the uplift displacement of the underlying layered soils
due to unloading pressure induced by the excavation of a new tunnel is
obtained. Moreover, the longitudinal displacement of the shield tunnel is
obtained by combining with the overall coupling equilibrium equation. Finally,
the results obtained using the proposed method are compared with the
measurement data from three overcrossing projects, and the related parameters
are analyzed. The results indicate the following: (1) Previous prediction
methods based on elastic foundation beams and the proposed method
satisfactorily predict the tunnel heave in the case of minimal stratification
of the ground beneath the existing tunnel. (2) The predicted results from the
proposed method concur with the measurements in the case of remarkable
stratification of the ground. (3) Increasing the tunnel diameter will increase
the uplift displacement and widen the range of the tunnel heave. (4) Reducing
the clearance between the new tunnel and the existing tunnel increases the
tunnel heave. (5) When the existing tunnel is located on the upper soft and
lower hard strata, its uplift range is smaller but its uplift magnitude is
greater than that of the upper hard and lower soft strata.
