Abstract An analytical solution is recommended in this paper for time-dependent stress analysis of lined tunnels with a circular shape, regarding tunnel advancing rate. In previous works, it was assumed that the tunnel is excavated under an infinite advancing rate such that the progressing rate effect was neglected, the assumption which is not always true. However, this barrier is removed in this paper. The non-hydrostatic stress field is assumed as initial stress within rock mass. The concrete lining, and surrounding mass are supposed as isotropic homogenous materials, following elastic and viscoelastic constitutive models, respectively. The Burgers model is assumed to dominate viscoelastic behavior. The solution benefits from time discretization for both tunnel advancing rate, and rock support interaction, along with employing complex variable method. The solution presents a good agreement with COMSOL finite element software simulation for different advancing rates. It is found that there exist the progressing rate and time limits, which for higher values, the problem could be solved assuming instantaneous excavation of the hole.

中文翻译：

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考虑隧道推进速率影响的圆形衬砌隧道周围应力分量的时变分析

摘要 本文推荐了一种关于隧道推进速度的圆形衬砌隧道随时间应力分析的解析解。在以前的工作中，假设隧道是在无限前进速度下开挖的，从而忽略了前进速度的影响，但这种假设并不总是正确的。然而，这个障碍在本文中被消除了。非静水应力场被假定为岩体内的初始应力。混凝土衬砌和周围质量被假定为各向同性的均质材料，分别遵循弹性和粘弹性本构模型。假定 Burgers 模型支配粘弹性行为。该解决方案受益于隧道推进速度和岩石支护相互作用的时间离散化，同时采用复变量法。该解决方案与 COMSOL 有限元软件模拟对于不同的推进率表现出良好的一致性。发现存在进展速率和时间限制，对于更高的值，假设孔的瞬时开挖可以解决该问题。