Effect of tunnel diameter on ground vibrations generated by underground trains

A theoretical model has been developed of generating ground vibrations by underground trains travelling in idealised circular tunnels of finite diameter. By means of the reciprocity principle, the displacement field radiated by a point force applied to the bottom of the tunnel, i.e., the Green's function of the problem, has been derived in zero and first approximations versus tunnel diameter. This more precise Green's function has been applied to carry out calculations of railway-generated ground vibrations testing earlier developed methods. The results show that the velocities of generated low-frequency ground vibrations increase with the increase in tunnel diameter. It is also shown that zero approximation is accurate only at very low frequencies.