Dynamic Response Of Bottom Floor Of Shallowly Buried Underground Structure Under Vertical Seismic Excitation

Duo to the development of aseismic theory of underground structures for the last several decades of and the rise of the underground structures, the understanding of many aseismic problems of underground structures has been improved remarkably. Despite the intensive researches in this area the systematic research of seismic response of the bottom floor of underground structures is still lacking.This paper studies the dynamic response of bottom floor of underground structures under vertical seismic excitation, analyzing the structure seismic capability of underground structure bottom floor. The main research results are as follows.(1) According to the D ’Alembert principle of dynamics, through the equilibrium analysis of the bottom floor infinitesimal element, dynamic equilibrium equation of bottom floor on Winkler foundation were derived. As to the boundary conditions of bottom floor of the structure, first the simply supported condition was considered, the floor vibration mode was determined. Based on the method of variable separation and the method of modal superposition, the analytical solution of displacements of bottom floor under vertical seismic excitation was determined. Then, substituting the calculation parameters, inputting the vertical seismic excitation, the author obtained the corresponding numerical solution of relative displacement of bottom floor of structure with foundation. At last, based on the data obtained previously, the internal force of bottom floor was obtained.(2) For the clamped boundary conditions of bottom floor, the structural vibration mode was determined. Because the exact analytical solution couldn’t be obtained, by using the Matlab in trial algorithm, its first three vibration mode was determined. By using the method of variable separation, the author determined the approximate analytical solutions of the bottom floor. Then, substituting the calculation parameters, inputting the vertical seismic excitation, the relative displacement and absolute displacement and internal force which the floor four edges clamped were found.(3) In practice, there is no ideal of simply supported and clamped conditions. The author thought that the side wall should be considered as rigidly connected to bottom floor, first determined the natural vibration modes, based on the trial algorithm to find out the first modal form. Then, the author obtained the relative displacement and absolute displacement and the internal force of bottom floor with consideration of the restriction of side wal s.(4) To determine the dynamic response of bottom floor on nonlinear Winkler foundation in the vertical seismic excitation, assume that its boundary conditions of four edges simply supported, the dynamic differential equation of bottom floor should be transformed into finite difference equation, to indicate displacement of each point on the floor. Based on the Matlab to solve the nonlinear finite difference equations, the author got the numerical solution. The displacement and force value of bottom floor of underground structure on nonlinear Winkler foundation is larger than the displacement and force value on Winkler foundation.