地表移动荷载对既有地下隧洞动力影响解析研究

为获得地表移动荷载对地下隧洞的动力影响,首次给出了地表移动荷载作用下半空间隧洞动力响应解析解。地表移动荷载采用移动简谐荷载模拟,含隧洞半空间地基通过各向同性弹性介质模拟。基于弹性地基控制方程在直角坐标系和柱坐标系下基本解及平面与柱面波函数波形转换,结合地基表面和隧洞柱面施加边界条件,在频域中求得移动荷载下半空间弹性地基与隧洞解析解答,并结合快速Fourier逆变换求得隧洞时域动力响应。利用本解析模型,可计算获得地面移动荷载引起的地下隧洞振动影响,通过与已有研究对比,对本模型正确性进行验证。计算分析了不同荷载移动速度与隧洞埋深下,隧洞表面位移、加速度和地基中动应力响应。研究表明,随着荷载移动速度增加,隧道拱顶地基中动应力与振动加速度均显著增加。地基中动应力随隧道埋深增加迅速衰减,隧洞加速度随埋深衰减相对较慢,但当隧洞埋深超过某一临界深度时,隧洞振动可低于我国规范规定限值。在低速范围,隧洞临界深度随荷载速度线性增加,但当荷载速度超过一定值,隧洞临界深度随着荷载速度呈指数型增长。

Analytical investigation of dynamic impact of moving surface loads on underground tunnel

To investigate the influences of the moving surface loads on the underground tunnel, an analytical solution for calculating vibrations from a circular tunnel buried in a half-space due to moving surface loads is firstly given. The surface load is represented by a moving harmonic point load, and the half-space with a circular hole is visco-elastic. The analytical solution is obtained in the frequency domain based on the fundamental solutions of governing equation for elastic ground in Cartesian and cylindrical coordinate systems. Also, the transformations between the plane wave functions and the cylindrical wave functions and the surface boundary conditions should be used. Then the response in the time domain is obtained by the inverse Fourier transform. The influences of moving surface loads on the vibration of underground tunnel can be investigated by using the analytical model. The displacement and acceleration of the tunnel and the dynamic stress response in the ground under different load velocities and tunnel buried depth are analyzed. The results show that both the dynamic stress and the acceleration responses above the vault of the tunnel increase significantly as the moving speed of the load increases. The dynamic stresses decay rapidly as the buried depth of the tunnel increases, while the acceleration responses decay relatively slowly. When the buried depth of the tunnel increases to the critical depth, the vibration level of the tunnel can meet the requirements of Chinese specification. The critical tunnel buried depth increases linearly with the moving speed of loads at the low speed range, while when the speed exceeds 100 km/h, the critical tunnel buried depth increases exponentially with the increase of load speed.