Abstract Analytic solutions on twin tunnelling at great depth in viscoelastic geomaterial considering three-dimensional effects of tunnel faces are presented using the complex variable methods. According to the time interval between twin tunnel faces, the proposed solutions can be divided into two cases: A) newly constructing twin tunnels; and B) newly constructing single tunnel influencing an existing one. The analytic solutions can also consider sequential excavations and the mutual influence between twin tunnels. The three-dimensional effects of twin tunnel faces are transformed into equivalent plane-strain problems by introducing dimensionless coefficients. By means of a presented general case, the analytic solutions are verified via comparisons of both stresses and displacements with the numerical solution, in which a good agreement between these two solutions is observed. Subsequently, a parametric investigation is performed to study the influence of several parameters concerning twin tunnel geometry and excavation on stresses and displacements, together with the difference between Cases A and B. On the basis of the results, the analytic solutions provide quantitative insights into the essence of the three-dimensional effects of twin tunnel faces and would have certain values on the preliminary design stage of twin tunnels.

中文翻译：

---

考虑隧道掌子面三维效应的粘弹性岩土材料大深度双隧道复变解

摘要 使用复变量法给出了考虑隧道掌子面三维效应的大深度粘弹性土工材料双隧穿解析解。根据双隧道工作面之间的时间间隔，所提出的解决方案可分为两种情况：A）新建双隧道；B) 新建影响现有隧道的单一隧道。解析解还可以考虑顺序开挖和双隧道之间的相互影响。通过引入无量纲系数，将双隧道工作面的三维效应转化为等效平面应变问题。通过给出的一般情况，通过比较应力和位移与数值解来验证解析解，其中观察到这两种解决方案之间的良好一致性。随后，进行了参数调查，以研究与双隧道几何形状和开挖有关的几个参数对应力和位移的影响，以及案例 A 和 B 之间的差异。根据结果，解析解提供了对双隧道掌子面三维效应的本质，对双隧道初步设计阶段具有一定的价值。