A methodology is presented for the back-analysis of convergence measurements in deep tunnels to determine the constitutive parameters of the surrounding rock mass. Since increasing deformations and stresses with time are due to both the face advance and the time-dependent behavior of the ground, the two effects must be considered during the excavations. To that end, an analytical solution assuming an unlined circular tunnel excavated in a homogeneous isotropic ground under an initial isotropic stress field and assuming a fractional viscoelastic plastic behavior is developed. A second closed-form solution is also derived assuming an instantaneous excavation. Additionally, combining the developed analytical solution that takes into account the progressive face advance and an empirical approach, convergences are back-analyzed based on a least-squares optimization method to calibrate the constitutive parameters of the ground. The presented methodology aims to characterize the long-term behavior of tunnels and offers the advantage of being directly applicable during the excavation phase as soon as convergence measurements are available. Finally, the method is illustrated by two case studies related to the Fréjus road tunnel and the Saint-Martin-la-Porte access gallery (SMP2).

中文翻译：

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考虑工作面前进和时间相关行为的解析解，用于各向同性初始应力状态下深圆形隧道收敛测量的反分析


提出了一种对深部隧道收敛测量进行反分析以确定围岩体本构参数的方法。由于随时间增加的变形和应力是由于工作面推进和地面随时间变化的行为造成的，因此在开挖过程中必须考虑这两种影响。为此，开发了一种解析解，假设在初始各向同性应力场下在均匀各向同性地面中开挖无衬砌圆形隧道，并假设分数粘弹性塑性行为。假设瞬时挖掘，还得出了第二个封闭式解。此外，结合所开发的考虑渐进面前进的解析解和经验方法，基于最小二乘优化方法对收敛性进行反分析，以校准地面的本构参数。所提出的方法旨在表征隧道的长期行为，并具有一旦收敛测量可用即可在开挖阶段直接应用的优点。最后，通过与弗雷瑞斯公路隧道和圣马丁拉波特通道 (SMP2) 相关的两个案例研究来说明该方法。