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.