Study On Long Period Ground Motion Response And Damping Of Flexible Bridges Based On Response Spectrum Modification

At present,the seismic and seismic isolation design of bridges at home and abroad is mainly based on the analysis of ordinary ground motions,and the effects of long-period ground motions are often ignored.Long-period ground motion has a long duration,and the energy is concentrated in the low-frequency region,which has a severe impact on the seismic response of flexible bridges.Bridge code response spectra are mainly obtained from ordinary ground motion records and statistics,and the effects of long-period ground motions are not specifically considered,which are not applicable to flexible bridges.In addition,the pseudo-velocity response spectrum and relative displacement response spectrum of the code and actual ground motions have significant differences in the spectral characteristics of the long period,and the code response spectrum values are seriously distorted.Considering the effects of long-period ground motions and the shortcomings of the code response spectrum,this paper revises the long-period section of the bridge’s code response spectrum,and derives a modified response spectrum that is applicable to the seismic design of conventional and flexible bridges.In addition,this paper validates the response spectrum with actual flexible bridges and performs long-period seismic response and seismic mitigation analysis.The main research contents of this paper are as follows:(1)This paper selects various types of site strong earthquake records including long-period ground motions,and statistically obtains the actual average response spectrum.The code design response spectrum long-period segment is compared with the actual average response spectrum and fitted and revised.A formula for the modified response spectrum is proposed.The parameters of the long-period characteristic and critical period of the response spectrum are determined.(2)Considering that flexible bridges response are more sensitive to long-period ground motions,this paper takes two long-period structures of high-pier continuous rigid frame bridge and long-span hybrid girder cable-stayed bridge as engineering support.By establishing a CSiBridge dynamic analysis finite element model that performed separately code and modified response spectrum analysis,ordinary and long-period ground motion time history analysis,this paper calculates its seismic response and compare and verifies the reliability of the modified response spectrum.(3)Considering that the main pier of a high-pier continuous rigid frame bridge may enter the elastoplastic or plastic state under the E2 earthquake,the elastic seismic design theory is not applicable.In this paper,fiber plastic hinges are installed on the main pier of a high-pier continuous rigid frame bridge.The E2 earthquake elasto-plastic time history analysis is stimulated by ordinary and long-period ground motions,and bridge’s seismic performance is reasonably evaluated using the principle of ductility anti-earthquake.(4)Considering that long-span cable-stayed bridges tend to respond more strongly under long-period ground motion,this paper uses the Maxwell model to simulate viscous dampers for structural shock absorption analysis.By setting the working conditions of the damper parameters,this paper analyzes the long-period seismic response changes of cable-stayed bridges,and uses the damper parameters as optimization variables to establish the optimization objective function and response surface function to find the optimal parameter combination of the viscous damper to achieve the greatest shock absorption effect.Based on the above research and analysis,the main conclusions of this paper are as follows:(1)The modified response spectrum can better reflect the statistical law of the average response spectrum of the ground motion.Its long period is closest to the average value of the average response spectrum of the ground motion,and the modification effect is good.However,the code response spectrum of the long period is seriously distorted and too conservative.(2)The seismic response of the high-pier continuous rigid frame bridge and long-span hybrid girder cable-stayed bridge under the modified response spectrum is larger than that of the code response spectrum,and the seismic design is more conservative and safer.Compared with the long-period ground motion time history response,the maximum seismic response of the structure under the code response spectrum is smaller,while the maximum response value under the modified response spectrum reaches the maximum and is safer,which verifies the reliability of the modified response spectrum.At the same time,the modified response spectrum can provide a reference for the preliminary analysis of cable-stayed bridges,and it is easy to check with the time-history analysis results.(3)When plastic hinges are installed on the main piers of high-pier continuous rigid frame bridges,the maximum displacement of the main piers along the bridge and the maximum response of the bending moment are significantly reduced.The hysteresis effect of the cross section of the main pier is more obvious in the first working condition,and it is slight in the second working condition.However,the maximum bending moment of the main pier is less than the yielding bending moment and being still in an elastoplastic or slightly elastoplastic state,which indicates that the seismic performance of the bridge is good under ordinary and long-period ground motions.(4)The optimal parameters obtained from the optimization of the long-period seismic response viscous damper parameters of a cable-stayed bridge are C=1000 kN·(m/s)-0.5773 and α=0.5773.Under the excitation of long-period ground motion,the longitudinal displacements of the tower top and the beam end decreased by 81.6%and 94.6%,the shear force at the bottom of the tower increased by 94.5%,and the bending moment at the bottom of the tower decreased by 12.2%.At this time,the structural response is optimal.The innovations of this paper are as follows:(1)This paper proposes to take the frequency of long-period ground motion as a probability,and consider the factors of long-period ground motion to modify the long-period section of the bridge’s code design response spectrum,which can be applied to the seismic design of flexible bridges and provide a reference.(2)This paper proposes a linear interpolation modification method for the attenuation index of the long period of the response spectrum.(3)This paper proposes a method for adjusting the peak acceleration of long-period ground motion input,and introduces the parameter amplification factor αof the long-period spectral value of the long-period ground motion response spectrum,and statistically obtains the recommended interval of α value.