Study On The Random Seismic Response Of Urban Underground Tunnels

With the rapid development of urban underground rail in recent years,the relevant seismic studies are becoming more and more important.However,the vertical seismic effects on tunnels have been less studied previously.After the 1995 Kobe Earthquake caused the worst damages to the subway stations in Kobe City,due to vertical earthquake excitation,people realize that the devastating vertical seismic action cannot be ignored.This paper presents a study on this topic based on a classical mass-damper-spring mathematical model.An analytical discrete model of urban underground tunnels subjected to vertical earthquake excitation is proposed herein by considering the first vertical vibration mode.Taking a light-rail project in Tianjin as an example,this study uses the proposed discrete model to analyze the displacement of tunnels and soils under vertical earthquake excitation.The soil displacement responses under stationary excitation and non-stationary excitation are analyzed with linear random vibration theory.This paper tries to find a method which can obtain the responses of tunnel structures under vertical earthquake excitation quickly and effectively.For this purpose,the main work is as follows:First,based on a mass-damper-spring model developed by Tamura and Okamoto,the mathematical formulas were improved according to the response characteristics of formation soil under the action of vertical earthquake.An analytical discrete model of urban underground tunnels subject to vertical earthquake excitation is proposed.It is proved that the model is feasible and accurate according to the results.Second,adopting the random vibration theory and virtual excitation method,the displacement and inner force responses of tunnels and soils in a project is analyzed.The behaviors of those responses are also studied.In order to verify the accuracy of the results obtained with the random vibration method,the finite element models with ABAQUS and MIDAS are also established to obtain the responses under vertical earthquake excitation.In addition,the CQC algorithm forms are used when adopting the virtual excitation method to solve a multi-degree-of-freedom(MDOF)system.The computation of this algorithm is very large.For the difficulty,this paper simplifies the computational implementation.The computational cost is greatly reduced.Finally,referring to the Duffing nonlinear system,a nonlinear system was applied to the mass-damper-spring model,and the effect of nonlinearity on the displacement responses of the system is analyzed.The analytical results show that the proposed discrete model can be used for vertical seismic analysis.And the computational cost is greatly reduced by using the proposed model and method.The results are in good agreement with the numerical simulation results.It can be seen from the analysis that the displacement responses under vertical earthquake excitation keep growing after seismic acceleration reaches its peak for a short duration and then they begin to decay.The relative displacement of the soil around tunnels can lead to huge shear stress and bending moment inside the tunnel.