Research On Spatial Dynamic Effect Of Long-span Bridge And Running Safety Of Train During Strong Earthquakes

High-speed railways play a growing important role in solving traffic problem between major cities and promoting further economic and social development. In high-speed railway lines, more and more elevated bridges are adopted to reduce the influence of railway lines on the existing built environment. The number of trains running on a railway line is also increasing because of high speed. As a result, the probability that an earthquake occurs when a train is running over a bridge in earthquake-prone regions is much higher than before. Therefore, dynamic interaction analysis of train-bridge system under seismic ground motion becomes an important subject. Based on the existing research results in China and abroad, multilevel frameworks with the consideration of the characteristic of large-span and long extension bridges are established to analyze dynamic interaction of train-bridge system during earthquakes from the point of view of a large system. Corresponding computer simulation programs are worked out. The influences of input pattern, spatial variation of seismic ground motion and train speed on the train running safety are investigated.This research is sponsored by the National Natural Scientific Foundation of China (grant No.51078029). The main contents and research results are as follows:1) Seismic ground motion simulation with full consideration of the spatial variation.For long-extension and long-span bridges, the unconditional simulation approach based on the spectral representation is used to generate seismic acceleration time histories of bridge supports where only site characteristics is known. The conditional simulation approach on the basis of multivariate linear prediction theory is employed when the seismic acceleration time history of one support is provided. Generally, the bridge site is far from the epicenter, which means that the displacements, velocities and accelerations of the end of the record should be zero. Corresponding consistent earthquake record can be obtained from the accelerogram by using several methods.2) Input pattern of Seismic ground motionBased on the seismic excitation input in bridge aseismatic analysis and combined with coupled vibration characteristics of train-bridge system, the acceleration and displacement input patterns are compared in their characteristics, implementation methods and applicability. And the following conclusions can be drawn: Dynamic interaction analysis of train-bridge system during earthquakes focuses on the absolute motion, which is different from common bridge aseismatic analysis paying more attention to the relative motion.The displacement input pattern is applicable for all wheel-rail relations whereas the acceleration input pattern is only suited for linear case in consideration of the influence of the pseudo-static components.More modes of bridge vibration in mode superposition method should be taken into accout for the displacement input pattern.3) Multilevel frameworks for analyzing dynamic interaction of train-bridge system during earthquakesA simply-supported beam bridge is taken as a continuum which motion can be expressed by the differential equation. The vehicles are simplified into a series of sprung mass. Thus, a simplified framework with the consideration of multipoint seismic excitation and rail irregularities is established.On the basis of FE method and wheel-rail separation relationship, the framework for analyzing dynamic interaction between long-span bridges and high-speed train is presented, in which multi-support seismic excitation and the possible separation between wheels and rails are considered.4) Numerical solutionThe instability of RCM algorithm optimizing bandwidth in finite element analysis is solved by increasing the column height sum as a new criterion for node sequential arrange, on the base of considering layer and number of neighbor nodes as two old criterions. And the modified algorithm is applied in this research. The Newmark-βmethod with a simultaneous iteration approach is used to find the best solution for the nonlinear dynamic interaction, in which the initial iteration value can be acquired from known motions of the foregoing two interaction steps with the aid of the explicit integration expression. The above-mentioned schemes make the solution manageable under the condition of tiny time interval used in the analysis.The bridge and vehicle subsystems are simplified into spring-damping, sprung mass oscillators in vertical direction, respectively. The numerical stabilities of iterative schemes in solving dynamic interaction of train-bridge system are studied for different wheel-rail relations on the basis of the spectral radius theory. The virtual mass approach is proposed to avoid potential divergence5) Investigation of dynamic interaction of train-bridge system and possible separation between rails and wheels during earthquakeThe IEC3 high-speed train with eight cars running over a 3-span steel truss-arch bridge subject to earthquakes are taken as a case study. The following conclusions can be drawn from numerical results:The influence of spatial variation of seismic ground motion on dynamic response of coupled train-bridge system is great.The seismic response of train-bridge system may be seriously underestimated when using the acceleration input pattern due to the ignorance of the pseudo-static item.The separation number and duration time between rails and wheels are enlarged by non-uniform seismic ground motion. Moreover, the separation probability greatly increases with train speed.