Abstract: In view of the influence of rectangular foundation pit excavation on the deformation of underlying tunnel, based on Mindlin’s classical solution, the formula to calculate the additional stress at the tunnel due to the excavation of foundation pits was derived, considering the influence of the residual stress at the bottom of the pit and the effect of the retaining pile. For the shield tunnel with buried depth more than 1.5 times the outer diameter of the tunnel, a spring layer was added onto the upper part of Pasternak model to consider the constraint of the overlying soil layer on the tunnel, and the deflection differential equation of foundation beam was established. The finite difference method was used to discretize the tunnel into independent node elements, so as to solve the longitudinal vertical displacement and horizontal displacement of the tunnel. Finally, it was compared with the tunnel deformation data obtained by finite element numerical simulation and engineering measurement. The research shows that: when the interaction between deeply-buried shield tunnel and soil is considered, compared with Pasternak model method, the proposed method can better reflect the real mechanical behavior between the two, and the obtained analytical solution is closer to the numerical solution, and its agreement with the measured value is also higher, which proves the rationality and superiority of the proposed method. In addition, the proposed method saves a lot of modeling work and can be used to preliminarily evaluate the influence of excavation of foundation pits on the longitudinal deformation of the underlying shield tunnel in the design.

Key words: tunnel engineering; excavation of foundation pits; shield tunnel; Mindlin solution; Pasternak model; longitudinal deformation

摘要： 针对矩形基坑开挖对下卧隧道变形影响这类课题，基于Mindlin经典解，考虑了坑底残余应力及围护桩效应的影响，推导了基坑开挖卸荷作用在隧道处附加应力的计算公式。对于埋深超过1.5倍隧道外径的盾构隧道，通过在Pasternak模型上部增加一层弹簧层来考虑上覆土层对隧道的约束作用，建立起地基梁的挠度微分方程。采用有限差分的方法把隧道离散为独立的节点单元，从而求解出隧道纵向的竖向位移和水平位移，最后与有限元数值模拟、工程实测得到的隧道变形数据对比分析。研究表明：在考虑深埋盾构隧道与土体的相互作用时，相对于Pasternak模型方法，笔者方法更能反映两者之间真实的力学行为，得到的解析解更接近于数值解，与实测值吻合度也较高，证明了方法的合理性和优越性；另外，笔者方法省去了大量的建模工作，在设计方案时能够用于初步评估基坑开挖引起下卧盾构隧道纵向变形的影响。

关键词: 隧道工程；基坑开挖；盾构隧道；Mindlin解；Pasternak模型；纵向变形