Study On Multi-dimensional Seismic Isolation And Mitigation For High Speed Railway Viaduct Considering Train-bridge Coupling Effects

China has the longest mileage of high speed railways around the world,meanwhile,several earthquake zones are spread all over the country.Therefore,it is meaningful to conduct the seismic analysis of high speed railway viaduct systems.Researchers have widely studied the train-bridge coupling effects as well as the earthquake resistance of bridges,nevertheless,they were mostly treated as two separated subjects.The dynamic behaviors of bearings in high speed railway viaduct systems under earthquakes remain to be further studied.The present work focuses on the seismic analysis of a train-wheel-bridge-support/bearing(TWBS)coupled system.The main contents of the present work are listed as follows.(1)A nonlinear bearing model with high precision is establishedA detachable multi-dimensional seismic isolation and mitigation bearing is designed and manufactured.In order to capture the nonlinear behaviors of the bearing,the HFDZ model for the horizontal direction and the VFDZ model for the vertical direction are formed by introducing additional coefficients into the basic Fractional Derivative Zener(FDZ)model.Experimental verification shows that the bearing model achieves high precision.(2)A state-space method to calculate the bearing model in time domain is proposedA state-space method to solve the generalized fractional differential equation is established,which is then used to calculate the nonlinear bearing model in time domain.This method requires to store and calculate the past state vectors,leading to an increasing memory consumption that will gradually lower the computation speed.The analysis reveals that the remote past data have a low impact on the current calculation,thus,a cut-off value for the using number of the past state vectors is determined by setting a reasonable changing rate limit for the state vectors’ weighting coefficients.It has been verified that this approach could largely speed up the simulation while maintaining an acceptable precision.(3)The real-time dynamic response calculation of structures with bearings is realized based on the subsystem methodDynamic responses of structures installed with bearings are calculated by using the subsystem method,which treats the structures and bearings as two separated subsystems,and then calculate the corresponding state-space equations individually.Two simplified systems are studied for verification purpose:(1)linear framework-bearing system;(2)simplified trainbridge-bearing system.In the linear framework-bearing system,at first,the FDZ model is adopted for the bearing,and the subsystem method is verified by comparing with the frequency domain method.And then,both the FDZ and HFDZ models are used to model the bearing.The system responses using these two models show much differences,thus,there is a practical significance to adopt more precise bearing model.In the simplified train-bridge-bearing model,the state-space equation about the modal coordinates is built based on the principle of modal decomposition for the bridge subsystem.In this way,the number of degrees-of-freedom is sharply decreased,therefore the computing efficiency is improved.For the bearing subsystem,the input must be displacement due to the parallel mechanism of the bearing,however,to couple with the bridge subsystem,only the bearing subsystem with force input can be formed if no action is taken.To address this problem,an extra mass block is put between the bridge and bearing.Owing to the dynamics of the mass block,the bridge subsystem with displacement input can be established.The realization of the simplified train-bridge-bearing system provides a theoretical basis for the building and analysis of the TWBS system.(4)An elaborate TWBS system is established and its dynamic behaviors are thoroughly studiedThe subsystem method is used to establish the TWBS system,where the nonlinear contact between the wheel and rail,track irregularity,non-uniform earthquake excitation,etc.are taken into account.Based on an actual engineering structure,an illustrative example of the TWBS system which contains three bridge spans and four train cars is built.The system dynamic behaviors and the bearing effects under three excitation scenarios are thoroughly studied and discussed: train-induced excitation only,earthquake excitation only,train-induced and earthquake excitations.The main observation is that under the earthquake excitation,the bearing is able to reduce the bridge response,whereas,it can conversely magnify the train response,especially when the train speed is low.This conclusion could aid in the design of bearings implemented in high speed railway viaducts,as it suggests that there is a requirement to find a balance considering the bearing’s beneficial effects for the bridge responses,and adverse effects for the running safety and comfort of the train.The main innovations of the present work are listed below.(1)A detachable multi-dimensional seismic isolation and mitigation bearing is designed.A nonlinear bearing model is proposed based on FDZ model.The proposed model is capable to precisely describe the bearing’s frequency-/amplitude-dependencies and the slow stabilization phenomenon in horizontal direction,as well as the frequency-dependency and stress stiffening in vertical direction.(2)A state-space method to calculate the nonlinear bearing model in time domain is proposed.By combing it with the subsystem method,a generalized method to solve the dynamic responses of systems with elements govern by fractional derivative models is established.(3)An efficient and highly modularized/parameterized TWBS system is established in Simulink based on the subsystem method.The system dynamic behaviors and the bearing effects are thoroughly studied through an illustrative example built from an actual engineering structure.