Research On The Seismic Responses Of A Suspension Arch Bridge Considering Soil-structure Interaction

Bridge is one of the lifeline projects, and its seismic safety has always received significant attention. In order to satisfy the functions of traffic and the urban landscape, an abundant of irregular bridges with appealing design are constructed all around the world, however, the complexity of the seismic response is increased. The study of structural seismic response base on soil-structure interaction has always been a major technical challenge of bridge construction and security operation. Taking Tongtai Bridge which is a curved girder skew through suspension arch bridge with the world’s longest span in Zhangjiakou for a case study, the exhaustive research was conducted on the problems of soil-structure interaction, equivalent seismic input, selecting truncate modes and building damping matrix, which were encountered in the process of the seismic response analysis, and compared with the monitoring results. The following results were obtained:(1) Different input forms of single degree of freedom frame structure seismic analysis models were established and analyzed, in order to study the impact of soil-structure interaction on structural seismic response on the site type II. On this basis, based on the theory of two-step method, considering superstructure vibration which is affected by radiation damping of soil energy dissipation, a modified superstructure damping two-step method of equivalent seismic input calculation was proposed. The method is simple in computation and convenient for engineering applications.(2) In order to study the dynamic characteristics of Tongtai Bridge, the main girder and arch were divided by beam elements and the cables were divided by link elements, then the finite element model with ridge beam was built. Taking the displacement of the mid-span as constraint condition, the cable force was optimized. Afterwards, the modal analysis was performed, and the natural frequencies and the modes of the bridge were extracted. Then based on the mode superposition method, the contributions of single mode and different combinations of modes on structural displacements and base shear forces were investigated. Under three seismic excitations which were obtained by different soil sites, the effects of local modes, higher modes and modal truncation errors on the structural dynamic response were discussed from the transverse and horizontal directions. Moreover, mode contribution coefficients were compared with cumulative modes participating mass factors in deciding the number of participating modes to cause the mode truncation errors.(3) To construct the damping matrix of structures with closely-spaced natural frequencies, an optimization solution of Rayleigh damping coefficients was proposed, based on the seismic response spectrum theory and the completely quadratic combination (CQC) rule. Then, a constrained optimization method was further developed to enforce the arbitrary order mode damping ratio equal to the precise value by Lagrange multiplier method. The seismic response of Tongtai Bridge was analyzed to investigate the characteristics of the proposed method. Firstly, the solution stability of optimal Rayleigh damping coefficients was discussed. Secondly, the effects of the different combinations of optimal objective functions and constraint conditions on optimal reference frequencies and seismic response were compared, and the selection of constraints mode in constrained condition was also discussed. Numerical results show that the seismic response calculation error is smaller while the Rayleigh damping coefficients was obtained from CQC rather than the square root of sum square (SRSS) combination, and the constrained mode should be specified as the first order significant mode corresponding to structural seismic responses.(4) According to the structural characteristics of Tongtai Bridge, a comprehensive real-time automatic bridge health monitoring system was established, which contains environmental monitoring, static characteristics monitoring, dynamic characteristics monitoring, Weigh in Motion system and seismic response monitoring. During the bridge monitoring period, the signal of two earthquakes occurred in Hebei province was collected by seismic monitoring systems. The operational modal analysis of the bridge under environmental excitations was conducted, and the first three modes frequencies were identify. Compared to finite element results, the error is less than 5%, which proves that the finite element model is correct and the calculation results are reliable.(5) Considering foundation-soil-structure and pile-soil-structure interaction, the bridge finite element model was built. Comparing to the seismic response analysis of the bridge finite element model with rigid foundations, the necessity of considering soil-structure interaction is discussed, while processing seismic response analysis of suspension arch bridge on site type Ⅱ. On this basis, the seismic data from the monitoring system was applied to the seismic response analysis of the bridge. Comparing the numerical results to the measured bridge responses, it shows that the calculation results based on rigid foundation are smaller, which are not conducive to seismic safety, but the errors of the calculation results considering soil-structure interaction are less than 10%, which demonstrates the reasonable of the calculation method considering soil-structure interaction in this paper.