为准确预测新建隧道上穿引起既有盾构隧道的纵向变形，首先，引入可以更加合理地模拟隧道-土体相互作用的Kerr地基模型，将既有隧道简化为Kerr地基上的Euler-Bernoulli梁； 其次，基于Mindlin解得到新建隧道开挖引起既有隧道轴线处的附加应力； 然后，基于有限差分法求得新建隧道上穿引起既有盾构隧道纵向变形解答；
最后，通过3个工程案例验证该方法的有效性，并对部分参数进行分析讨论。研究结果表明： 该方法较Winkler地基和Pasternak地基方法更能准确地预测新建隧道上穿引起既有盾构隧道的纵向变形。参数分析结果表明：
新建隧道直径的增加会同时增大既有隧道的隆起值和影响范围，而净距的增加会略微降低既有隧道的隆起值，但不会缩小既有隧道的影响范围。在实际工程中，当新建隧道以大断面或小净距上穿开挖时，应加强对既有盾构隧道的变形监测和保护。
To accurately predict the longitudinal deformation of
an existing shield tunnel caused by newlybuilt overcrossing tunnel, the
Kerr foundation model is introduced that can more reasonably simulate the
tunnelsoil interaction and the existing tunnel is
simplified as the EulerBernoulli beam on the Kerr
foundation. Then, based on the Mindlin solution, the additional stress
generated on the axis of the existing tunnel by the newlybuilt tunnel excavation is determined. Furthermore, based on the
finite difference method, the solution of longitudinal deformation of the
existing shield tunnel induced by the overcrossing of the newlybuilt tunnel is obtained. Finally, three engineering cases are used
to verify the effectiveness of the proposed method, and some parameters are
analyzed and discussed. The results show that the proposed method can predict
the longitudinal deformation of the existing shield tunnel induced by the new
tunnel overcrossing more accurately than predicted by the Winkler and Pasternak
foundation models. The results of the analytical parameters reveal that with
the increase in the newlybuilt tunnel′s diameter, the uplift value and influence range of the existing
tunnel increase simultaneously, while the increase in the clearance slightly
reduces the uplift value of the existing tunnel, but does not affect the
influence range of the existing tunnel. Thus, deformation monitoring and safety
measures should be adopted for the existing tunnels when a newlybuilt tunnel is crossing above with a large crosssection or small clearance.
