| Curved bridges often suffer more serious damage in previous earthquake disaster reports due to its special mechanical characteristics.Many curved ramp bridges collapsed in Wenchuan earthquake,but the main bridges were almost complete.Therefore,there are still drawbacks in the design of curved girder bridges,which should be taken into consideration.This paper comprises of two parts: the first part is theoretical study and the other is application study.In the theoretical study,a 1D free-field time-domain algorithm based on the large mass method was derived as well as the new formula for calculating the equivalent load.In the application study,a seismic analysis method based on the separated foundation-bridge system model was proposed for the bridges adopting pile foundations,which had been implemented by a function framework in MATLAB.On the basis of the practical case,the seismic response of a curved bridge considering soil-structure interaction and spatial variability of ground motion was systematically studied by parameter analysis.The main work and achievements of this paper are as follows:1.A 1D free-field time-domain algorithm was derived based on the large mass method.The truncated boundary at the bottom of the free field is treated by the large mass method,so that the displacement response of the truncated boundary is consistent with the time history of the input displacement.The displacement solution of one-dimensional free field was extended to threedimensional free field,and the equivalent viscoelastic artificial boundary was introduced.A seismic response analysis method based on near-field foundation-bridge system model was proposed,and the corresponding auxiliary implementation program is compiled.Based on the substructure method of wave mechanics,a near-field foundation-bridge system model considering soil-structure dynamic interaction was established.The numerical results showed that the simulation method had good accuracy.2.Three typical analysis models of curved bridges were established,including the holistic model,p-y method model,fixed base model.Linear and non-linear seismic response analyses of curved bridges considering only traveling wave effect were performed.Seismic response patterns of curved bridges with different analysis models were studied.Advantages and disadvantages of each model and applicable conditions were evaluated.Suggestions were given for selecting appropriate seismic analysis models.3.Based on the trigonometric series method,the spatial multi-point correlation seismic time histories were generated,and the corresponding calculation program was compiled to generate different coherence degree seismic time histories.The seismic acceleration responses spectrum and displacement time histories under different coherence degree were compared.Based on the idea of substructure of wave theory and the generation method,a seismic response analysis method based on the separated near-field foundation-bridge system model was proposed,which provided an effective numerical method for addressing the coupling problem of soil-structure interaction and seismic spatial variation.4.The influence of spatial variability of ground motion on seismic response of a typical curved bridge with a curvature radius of 60 m in China was studied.Based on the proposed seismic analysis method in this paper,the seismic response patterns of the curved bridge under different apparent wave velocities,coherence and site conditions as well as under multi-dimensional and multi-point excitation were studied.In order to determine the unfavorable excitation angle of the curved bridge,the multi-angle analyses under horizontal bidirectional excitation were performed.By comparing and analyzing the results of the near-field foundation-bridge system model and the fixed foundation model,the influence patterns of parameter changes on seismic response of curved girder bridges was concluded,and comments for seismic design of curved bridges were also made. |
