Abstract This study focused on tunneling under challenging conditions, particularly with regard to the stress distribution and deformation in the humidity stress field. The swelling phenomenon during tunneling was treated as a quasi–humidity–mechanics coupled process, where the humidity diffusion and stress dilatancy were considered together to obtain the stress and deformation fields for tunnels crossing formations with high swelling potential. A solution to the nonstationary process of humidity transfer was derived according to Fick’s second law. First, the humidity distribution was obtained from the surrounding rock mass to determine the stress field. Then, a modified fractional viscoplastic model was developed to describe the whole creep process of soft rock swelling, as well as the damage and swelling deformation due to water immersion. Next, closed-form analytical solutions were derived for the displacement in the viscoplastic region, with more focus on the tunnel wall, based on a non-associated flow rule. The sensitivity of time-independent parameters was also analyzed. The solution was found to reasonably represent the tunnel convergence versus time when compared with the numerical simulation and monitoring data from the Nabetachiyama Tunnel.

中文翻译：

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一种用于预测膨胀岩中深埋隧道随时间位移的分数粘塑性模型

摘要 本研究的重点是在具有挑战性的条件下掘进，特别是湿度应力场中的应力分布和变形。隧道开挖过程中的膨胀现象被视为准-湿度-力学耦合过程，其中湿度扩散和应力剪胀一起考虑以获得隧道穿越具有高膨胀潜力的地层的应力和变形场。根据菲克第二定律推导出非平稳湿度传递过程的解决方案。首先，从围岩中获得湿度分布以确定应力场。然后，建立了改进的分数粘塑性模型来描述软岩膨胀的整个蠕变过程，以及由于浸水引起的破坏和膨胀变形。下一个，基于非关联流动规则，推导出粘塑性区域位移的封闭形式解析解，更多地关注隧道壁。还分析了与时间无关的参数的敏感性。与 Nabetachiyama 隧道的数值模拟和监测数据相比，发现该解决方案合理地代表了隧道收敛与时间的关系。