Study On Longitudinal Nonlinear Equivalent Stiffness Beam Model In The Joint Effect Of Shaft Force And Bending Moment Of Shield Tunnels

In recent years,the subway has developed rapidly at home and abroad,and more and more cities in China have begun to prepare to build the subway.As an important part of urban transportation,the safety of the structure design of the subway is very important.Scholars at home and abroad have done a lot of research on the subway shield tunnel.However,in the longitudinal analysis,there are still gaps in the theoretical research on the coupling of shaft force and bending moment,which need to be filled urgently.Based on the longitudinal equivalent stiffness beam model and the longitudinal nonlinear equivalent stiffness beam model,this paper studies the mechanical properties of the vertical vertical shield tunnel in the combination of shaft force and bending moment coupling,and the main results are as follows:(1)In this paper,the expression of the open amount of the shield tunnel is deduced.According to the vertical force and bending moment of the shield tunnel segment,the state of the tunnel is divided into three main modes.It is proved that the longitudinal equivalent stiffness beam model is a special case of the longitudinal nonlinear equivalent stiffness beam model at the N=0,Define 0)as the ratio of shaft force to bend moment to divide the three modes,which optimizes the model.(2)A method to solve the transcendence equation is proposed,which avoids the large amount of calculation required for iteration and has high precision.Based on the python language,the calculation procedure of the neutral axis angle,longitudinal equivalent bending stiffness and its efficiency,vertical equivalent pull stiffness,open amount and other parameters related to the performance of vertical nonlinear equivalent stiffness beam is written and analyzed.(3)Some assumptions and model characteristics of the model are analyzed by using FEA software.This paper discusses the effect of the number of tube rings on the numerical results when modeling calculations,and puts forward a method to eliminate the error of the number of rings on the results,which reduces the cost of calculation and improves the efficiency of calculation.Which verifies the validity of the theoretical model.(4)This paper analyzes the influence of the variation of the parameters of shield tunnel tubes and bolts on the parameter curves related to mechanics performance.An extremely precise fitting solution can be obtained without solving the transcendence equation.(5)Seismic examples are analyzed in FEA software,the change curve of 0)and open volume is obtained,This paper compares it with the theoretical solution of vertical nonlinear equivalent stiffness beam model and verifies the correctness of the theoretical solution.