A Study On Random Vibration Method For Inelastic Analysis Of Long-Span Bridges Under Non-uniform Seismic Excitations

With the rapid development of society and economy,large-span bridges have been widely used in China.China is a country with frequent earthquakes,and the safety of bridges under earthquakes is crucial.As the ground motion is inherently random,it is more reasonable to use the random vibration method to carry out seismic analysis of long-span bridge structures.In the past two decades,many random vibration methods have been applied to the seismic analysis of long-span bridge structures,and some remarkable research results have been achieved.However,most of these random vibration methods are time-consuming or not easy for engineers to understand,which limit these methods expanding to practical engineering.In the seismic random vibration analysis of long-span bridges,the problems of non-uniform seismic excitation and inelastic seismic analysis are hot and difficult to solve,and the traditional random vibration methods can not solve these problems well.This paper is devoted to develop an efficient and accurate time-domain explicit method for seismic random vibration analysis,which can provide an effective approach for the elastic and inelastic random vibration analysis of long-span bridges under non-uniform seismic excitation.On this basis,the research on seismic fragility analysis of long-span bridges is further carried out,and an efficient seismic fragility analysis method is proposed,which can provide an effective calculation tool for reasonable evaluating the seismic capacity of long-span bridges.The work in this dissertation is described as follows:(1)A literature review is carried out for linear and nonlinear random vibration methods,and the research statuses of non-uniform seismic excitation,structural inelastic and seismic fragility of large-span bridge structures are presented.(2)The explicit time-domain method is proposed for elastic random vibration analysis of long-span bridges under non-uniform seismic excitation.Based on the relative motion method,the time-domain explicit expressions of structural dynamic responses under non-uniform seismic excitation are derived.Then the explicit time-domain method(ETDM)is proposed under non-uniform seismic excitation,by which the statistical moments of structural responses can be quickly obtained.Meanwhile,the efficient Monte-Carlo simulation(MCS)based on ETDM is proposed,by which more comprehensive statistical information can be further obtained such as the mean peak value of structural response under non-uniform seismic excitation,and the structural dynamic reliability analysis can be carried out effectively.Taking a suspension bridge as a practical example,the random vibration analysis of the bridge under longitudinal non-uniform seismic excitations is conducted in the present study,and then the effectiveness of the proposed method is verified.The traveling-wave effect,the incoherence effect and the local site effect on the standard deviations and mean peak values of critical responses and structural seismic dynamic reliability are studied,respectively.(3)The efficient MCS based on ETDM with dimension-reduced iteration scheme is proposed for the inelastic random vibration analysis of long-span bridges under non-uniform seismic excitation.For the long-span bridge structure with local nonlinearities,the time-domain explicit expressions of structural seismic responses are derived based on the quasi-linear equation of motion of the structural system.Then,with the advantage of the dimension-reduced representation of the explicit expressions,the ETDM with dimension-reduced iteration scheme is proposed,where only those degrees of freedom associated with inelastic elements need to be solved through iteration process,leading to significant improvement of the computation efficiency for inelastic time-history analysis.Combined with MCS,the efficient MCS based on ETDM with dimension-reduced iteration scheme is proposed for inelastic random vibration analysis of long-span bridges under non-uniform seismic excitations.A continuous rigid frame bridge and a suspension bridge are taken as the practical examples to verify the feasibility of the proposed method.(4)The lognormal mixture model method is proposed for seismic fragility analysis of long-span bridges.The seismic demand samples are efficiently obtained through ETDM with dimension-reduced iteration scheme,and the probability distribution of the structural seismic demand is obtained by using the lognormal mixture model.Then,an efficient and accurate seismic fragility analysis method is proposed for long-span bridge structures.The new method can avoid the calculation error caused by many assumptions of the cloud approach,and can also overcome the problem of large sample size when the direct Monte Carlo simulation used in the case of low failure probability.A suspension bridge is taken as a practical example to verify the high accuracy and efficiency of the proposed method in seismic fragility analysis of long-span bridges.The results show that,the above series of methods based on explicit time-domain solution can effectively solve the problems of the elastic and inelastic response analysis of long-span bridges under non-uniform random seismic excitations,and seismic fragility analysis.And they have ideal computational accuracy and efficiency.