Dynamic response of existing tunnel under cylindrical unloading wave

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.