Study On Derailment Probability Of Railway Vehicles On Bridges Shaken By Earthquake

With the rapid development of China's high-speed railways and the continuous improvement of the operating speed,the safety of vehicles on bridges has attracted great attention from researchers.In the nationally planned high-speed railway network,many railway lines are located in the high-frequency seismic regions,which requires the probability analysis of derailment of vehicle on the bridges shaken by earthquakes.However,due to the high cost of the simulation of the computer program,the statistical calculation of the probability of derailment is difficult to realize,making the calculation of the probability of derailment of vehicles on bridges shaken by earthquake a challenging task.In the classical Monte Carlo simulation method,the number of samples is inversely proportional to the failure probability,so for small failure probability events,a large number of samples is needed to obtain satisfactory accuracy.In order to improve the calculation efficiency,subset sampling simulation method and extreme value probability density evolution method are introduced into the probability analysis of derailment of vehicles on bridges shaken by earthquakes.The accuracy and efficiency of the two methods are compared,and the suggestion method for calculating the probability of derailment of vehicle on the bridges shaken by earthquakes is given.According to a specific engineering calculation example: Three different methods are used to calculate the derailment probability of a domestic high-speed train passing through a simply supported multi-span railway bridge at a speed of 180 km/h shaken by earthquake.The results show that compared with subset sampling method and classical Monte Carlo simulation method,the extreme value probability density evolution method has the highest efficiency,which verifies the rationality of the recommended algorithm.Finally,the effect of different bridge cycles on the probability of vehicle derailment on the bridges shaken by earthquake is discussed by using the proposed method.The following is the specific implementation process:Firstly,a single-degree-of-freedom oscillator under seismic excitation is taken as the validation model,and its boundary value-failure probability diagram is calculated by subset sampling simulation method and extreme value probability density evolution method.The calculation results are compared with classical Monte Carlo simulation method,which verifies the accuracy and efficiency of subset simulation method and extreme value probability density method.Comparing the computational efficiency of the two simulation methods,the proposed method for calculating the derailment probability of vehicle on bridges is given: the extreme value probability density evolution method.Then,three different methods are used to calculate the probability of derailment of a domestic high-speed train passing through a simple multi-span railway bridges at a speed of 180 km/h shaken by earthquake.Three simulation methods include classical Monte Carlo method,subset sampling simulation method and proposed extreme value probability density evolution method.The results show that: a.Under the conditions of the occurrence of random ground motion models developed by Atkinson and Silva,The derailment probability of domestic ordinary high-speed train passing a simple multi-span railway bridge at a speed of 180 km/h is calculated.b.Compared with subset sampling method and classical Monte Carlo simulation method,the extreme value probability density evolution method is the most efficient method in calculating the probability of vehicle derailment on bridges shaken by earthquake,which verifies the rationality of the proposed extreme value probability density method for calculating the probability of derailment of vehicle on bridges shaken by earthquake.Finally,the influence of different cycles of bridges on the probability of derailment of vehicles on bridges shaken by earthquake is discussed.It is found that the probability of derailment of vehicles decreases with the increase of cycles of bridge with the same operation speed,the reason of which is that the longer cycle of bridges,the lower amplitude of corresponding acceleration response spectrum and the lower derailment risk.