Seismic safety of underground structures is one of the main concerns in underground space exploitation.As the first step for dynamic seismic response analysis,the free vibration of long large cross-section underground structures is studied in the present paper.The general free transverse vibration motion equation of long large cross-section underground structure is derived with the comprehensive consideration of internal and external damping,effects of shear,cross-sectional rotational inertia and axial force,and a two-parameter soil model.In this way,Timoshenko's beam theory is extended.Two limit cases of free transverse vibration of underground structures are discussed.Parameter study shows that in general wave propagation velocities in structures increase with soil elastic parameters.However the influence of Winkler's parameter k-is significant while the effect of the second soil elastic parameter g-P is insignificant.The free vibration frequency of underground structures increases with relative wave number and soil elastic parameters.Unlike the influence of soil elastic parameters on wave propagation velocities,the influence of soil elastic parameters k-and g-P on the vibration frequency of underground structures have the same order;therefore the influence of the second soil parameter g-P on the free vibration of underground structures should not be neglected in dynamic seismic analysis of underground
