Abstract When an underground tunnel is excavated suddenly in the high-stress rock mass, the unloading wave will generate from the tunnel boundary and propagate into the surrounding rock mass, which can induce strong dynamic vibrations and even damage to the adjacent existing tunnel. This study aims to investigate the dynamic response of existing tunnel induced by cylindrical unloading wave resulting from neighboring tunnel excavation. A two-dimensional mathematical physical model was first constructed based on the superposition principle of coupled static and dynamic loads, in order to derive the formulas for calculating the dynamic stress, velocity and displacement around existing tunnel induced by cylindrical unloading wave. A two-dimensional numerical model established by particle flow code (PFC) was then implemented to verify the theoretical analysis, and further to investigate the failure characteristics of existing tunnel under coupled static in situ stress and dynamic unloading wave. A series of parametric studies were conducted in the theoretical and numerical models to investigate the influence of unloading rate, unloading path, in situ stress and excavation radius on the dynamic response of existing tunnel. The results show that the unloading wave induced by tunnel excavation in high-stress rock mass can induce strong dynamic response in the surrounding rock mass of adjacent existing tunnel, and the increase of stress level and unloading rate will aggravate the dynamic effect. The peak value of velocity induced by nonlinear unloading is larger than that induced by linear unloading. In addition, the excavation-induced unloading wave can induce dynamic failures in the surrounding rock mass of existing tunnel under high in situ stress. Therefore, the unloading wave induced by adjacent tunnel excavation should be taken into consideration when evaluating the stability of deep tunnels.

中文翻译：

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圆柱卸荷波作用下既有隧道动力响应

摘要 地下隧道在高应力岩体中突然开挖时，卸荷波会从隧道边界产生并传播到围岩体中，引起强烈的动力振动，甚至对相邻既有隧道造成破坏。本研究旨在研究由邻近隧道开挖产生的圆柱形卸载波引起的现有隧道的动力响应。首次基于动静耦合叠加原理构建二维数学物理模型，推导出圆柱卸荷波引起既有隧道周围动应力、速度和位移的计算公式。然后通过粒子流代码（PFC）建立的二维数值模型对理论分析进行了验证，并进一步研究了静态地应力和动态卸载波耦合作用下既有隧道的破坏特征。在理论和数值模型中进行了一系列参数研究，研究卸载速率、卸载路径、地应力和开挖半径对既有隧道动力响应的影响。结果表明，高应力岩体隧道开挖引起的卸荷波会引起相邻既有隧道围岩的强烈动力响应，应力水平和卸荷速率的增加会加剧动力效应。非线性卸载引起的速度峰值大于线性卸载引起的速度峰值。此外，开挖引起的卸荷波会在高地应力下引起既有隧道围岩的动力破坏。因此，评价深部隧道稳定性时，应考虑相邻隧道开挖引起的卸荷波。