| Vertical stiffness is of great significance to ensure traffic safety and ride comfort on high-speed railway bridges.With the improvement of the design speed of the passenger wheel/rail traffic system,train-bridge coupled vibration responses are becoming ever more obvious,and the insufficient vertical stiffness may cause the problems such as the bridge deck slope over the limit,ride discomfort,and train derailment.There are still some problems,such as the limit standard of bridge stiffness with a speed above 350km/h is not specified in the“Code for Design on Railway Bridge and Culvert”,the coefficient of variation of train dynamic response is large under the action of random track irregularity,and the quantitative relationship between driving performance and bridge deformation is insufficient.Based on the ARMAX(Auto Regression and Moving Average with e Xogenous)surrogate model and considering the influence of random excitation,this thesis evaluates the vertical stiffness with the vertical acceleration of the car body at the comfort transcendence probability and puts forward a statistical analysis method of the vertical stiffness of railway bridges.The influence of different train and bridge factors on vertical stiffness is analyzed,and the limit value of vertical stiffness of a 400km/h high-speed railway bridge is suggested.The main research contents are as follows:(1)For the train-bridge coupled vertical system,the ARMAX surrogate model is used to replace the train-bridge coupled vibration equation to predict the train vertical acceleration.The MCS(Monte-Carlo simulation)calculation of the surrogate model is carried out and compared with the direct MCS calculation of the train-bridge coupled vibration system,to verify the accuracy and efficiency of the surrogate model.The results show that the efficiency of the surrogate model is about 3 orders of magnitude higher than that of the direct MCS calculation,and the accuracy can reach 99%,which shows the feasibility of the surrogate model in the small failure probability analysis of the train-bridge system.(2)Taking the vertical acceleration of the train body of 1.3m/s~2 as the ride comfort limit,the daily train operation pairs,line inspection cycle and track preventive grinding cycle are adopted to determine the comfort exceeding probability of 1/70000.The ARMAX surrogate model suitable for the decline of bridge stiffness is established,and the vertical acceleration of the car body at the comfort exceeding probability is calculated until it exceeds the limit.The bridge model with corresponding stiffness is loaded,and the vertical stiffness limit of the bridge is obtained.It has been verified that when the bridge stiffness decreases to the acceleration limit of the car body,the acceleration calculated by the surrogate model MCS has an error of less than 5%compared with the direct MCS calculation,and can be used to calculate the vertical deflection limit of the bridge and the rotation angle limit of the beam end under the influence of random excitation.(3)The lighter the vehicle axle load,the higher the vehicle speed and the larger the bridge span,the lower the vertical stiffness limit of the bridge(the limit is more strict).The bridge stiffness limit of the model with lower design speed is smaller than that of the model with higher design speed,and the limit value of the former decreases faster when the speed increases.The vertical stiffness of the bridge is not affected by the height of the pier and the length of the beam end.For the prestressed concrete simply supported beam bridge with a span of no more than 40m,the 400k/h high-speed train model is used to establish the relationship between the driving performance and the vertical stiffness of the bridge.Considering the influence of excitation randomness,it is suggested that the vertical deflection limit can be taken according to the extrapolated value L/1700(L is the bridge span),and the beam end angle limit can still be taken according to the existing provisions of the specification. |
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