不规则起伏地基-隧道系统三维动力响应的半解析计算方法
SEMI-ANALYTICAL METHOD FOR THREE-DIMENSIONAL DYNAMIC RESPONSE OF IRREGULAR SOIL-TUNNEL COUPLED SYSTEM
-
摘要: 天然地基在形成过程中由于地质和环境的影响, 具有明显的不规则起伏特性, 其会直接影响轨道交通隧道行车振动在地基中的传播规律. 对此, 提出了一种不规则起伏地基-隧道系统三维动力响应的半解析计算方法. 地基和隧道均假设为沿纵向不变的弹性均匀介质, 通过时间和纵向坐标的双重傅里叶变换, 将时域-空间域三维动力问题转化为频域-波数域内求解. 将波数离散法和平面波展开法与边界积分方程结合, 建立求解不规则地基内复杂散射波场的联立方程组; 进一步利用波面转化公式, 满足隧道-土体界面的边界条件, 实现不规则地基与隧道的耦合求解, 获得简谐荷载作用下不规则地基-隧道系统三维动力响应的半解析解. 该方法可以适用于任意形状的起伏地形, 突破了既有理论方法将地表假设为水平边界的局限, 且仅需对地表不规则部分进行离散, 计算效率高. 通过对深圳地铁5号线一实际工程地质断面的案例分析, 结果表明不规则起伏地表会对位移响应产生显著影响, 且与荷载频率相关, 忽略地表的不规则特性会导致大约5 ~ 20 dB的预测误差. 研究成果可为轨道交通振动影响评估以及减振设计提供理论支撑.Abstract: Due to the influence of geology and environment during formation process, natural foundations have obvious irregular characteristics, which directly affects the vibration propagation in soil generated by rail transit load driving in the tunnel. In response, this article proposed a semi-analytical method for the three-dimensional dynamic responses of an irregular half-space-tunnel system. Both the soil and tunnel are assumed to be elastic and homogeneous media that remain constant along the longitudinal direction. By using a dual Fourier transform of time and longitudinal coordinates, the three-dimensional dynamic problem in the time-space domain is transformed into the frequency-wavenumber domain to solved. The wavenumber discretization method and plane wave expansion method are combined with boundary integral equations to establish a set of simultaneous equations for solving the complex scattered wavefield within the irregular half-space. Furthermore, utilizing the wave transformation method, the boundary conditions of the tunnel-soil interface are satisfied to coupling the irregular half-space and tunnel together, then the semi-analytical solution for the dynamic response from a tunnel in irregular half-space excited by a harmonic load is obtained. This method can handle arbitrarily shaped surfaces, which breaks the limitations of existing methods that assume the ground surface to be a horizontal boundary. Only the irregular parts of the surface need to be discretized, this method has high computational efficiency. Through conducted a real case study of Shenzhen Metro Line 5, the results indicate that irregularly ground surfaces have a significant impact on displacement responses and it is related to the load frequency. Neglecting the irregular characteristics of the ground surface can lead to a prediction error of approximately 5 to 20 dB. The research findings provide theoretical support for the vibration assessment and reduction design of rail transit system.
下载: