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 引用本文: 何超, 贾缘平, 周顺华. 隧道−地基−流体耦合系统动力响应的三维解析计算方法. 力学学报, 2023, 55(6): 1329-1341.
He Chao, Jia Yuanping, Zhou Shunhua. Three-dimensional analytical method for calculating vibrations of a coupled tunnel-soil-fluid system. Chinese Journal of Theoretical and Applied Mechanics, 2023, 55(6): 1329-1341.
 Citation: He Chao, Jia Yuanping, Zhou Shunhua. Three-dimensional analytical method for calculating vibrations of a coupled tunnel-soil-fluid system. Chinese Journal of Theoretical and Applied Mechanics, 2023, 55(6): 1329-1341.

## THREE-DIMENSIONAL ANALYTICAL METHOD FOR CALCULATING VIBRATIONS OF A COUPLED TUNNEL-SOIL-FLUID SYSTEM

• 摘要: 轨道交通隧道行车会引发地表或水中环境的振动, 从而对沿线居民或珍惜鱼类产生不良影响. 对此, 提出一种双洞隧道−地基−流体耦合系统动力响应的三维解析方法. 隧道和地基模拟为弹性介质, 空气或水模拟为理想流体介质, 利用时间和纵向坐标的双重傅里叶变换, 将时间−空间域内的三维动力问题转化为频域−波数域内求解. 利用波面转换和平移公式, 满足隧道、地基、流体及其交界面的边界条件, 实现动力耦合求解, 获得简谐载荷作用下双洞隧道−地基−流体系统动力响应的解析解. 通过与地基−流体耦合系统的动力基本解以及有限元−边界元耦合模型进行对比, 验证本文所提出方法的正确性. 对比分析单洞和双洞隧道内作用动力点源引起的地基、水以及地表空气的响应. 结果表明, 邻近隧道的存在会改变地基土中波动能量的分布, 进而改变水中或者空气中振动传播规律, 且邻近隧道的影响与载荷频率、观察点位置以及隧道间的相对位置关系密切相关. 当双洞隧道间距小于4倍隧道直径时, 隧道间的动力相互作用不可忽略. 研究成果可为隧道内行车引发的空气噪声以及水下振动传播特性研究和预测评估分析提供理论支撑.

Abstract: Train-induced vibrations from underground railway tunnels transmit to the ground surface or water, which may disturb adjacent residents or rare fish. This study presents a three-dimensional analytical method for calculating the dynamic response of the coupled tunnel-soil-fluid system. The twin tunnels and soils are simulated as the elastic solid, while the air or water is simulated as the ideal fluid medium. The three-dimensional dynamic problem in the time-space domain is transformed into the frequency-wavenumber domain by using the double Fourier transforms of time and longitudinal coordinates. The boundary conditions on the fluid-soil interface and the tunnel-soil interface are satisfied by introducing the transformation between the cylindrical waves and the plane waves and the transform between different cylindrical waves. The solution for dynamic response of the coupled tunnel-soil-fluid system under point loads is therefore derived. The accuracy of the proposed method is verified by comparing with the Green’s function and FE-BE model for a coupled soil-fluid system. The dynamic responses of soil, water, and air induced by point loads in a single tunnel and twin tunnels are compared and analyzed via two numerical cases. The results demonstrate that the existence of the adjacent tunnel can change the energy distribution of train-induced waves in the soil, thus affecting the propagation characteristics of waves in the water or in the air. The influence of the adjacent tunnel is highly dependent of the loading frequency, the observation position and the relative position between twin tunnels. When the distance between the two adjacent tunnels is less than four times of the diameter of the tunnel, the dynamic interaction between the twin tunnels play a relevant role in the response of the water or the air. This study can provide benefit for the evaluation of vibrations and radiated noise in air or water from underground railway tunnels.

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