Study On Damage Analysis And Ductility Optimization Of High-pier Long-span Continuous Rigid Frame Bridges Under Spatially Variable Ground Motions

A large number of infrastructures such as highways and railways have been constructed in the west of China in recent decades,where the high-pier long-span continuous rigid frame bridges are playing an important role in the transportation system.The dimensions of the continuous rigid frame bridges currently being designed and built are constantly setting new records and breaking them.However,most seismic design standards and methods for bridge structures do not take spatially variable ground motions into consideration,and they can barely match the large scale of construction for the high-pier long-span continuous rigid frame bridges.In addition most existing large rigid frame bridges have not experienced strong ground motions,so it is critical to study on the nonlinear dynamic performance and seismic capacity of these bridges subjected to multiple support excitations.The modified model for multi-support and multi-component spatially variable ground motions is developed based on discrete time-domain analysis.Damage analysis,incremental dynamic analysis and fragility analysis are conducted on the finite element models of high-pier long-span continuous rigid frame bridges.Furthermore,the failure mode and ductility optimization of the bridges under spatially variable ground motions are studied qualitatively and quantitatively.(1)The modified model for multi-support and multi-component spatially variable ground motions which takes the complex local site condition into account.The supports of the high-pier long-span continuous rigid frame bridges experience complicated variation of site features both vertically and longitudinally.To properly consider the local site effect on the ground surface motions owing to the soil layers upon the bedrock,the modified model for spatially variable ground motions is developed based on the transfer function for waves in discrete time domain.The reflection and transmission of up-going waves owing to the multiple soil layers on their propagation path are combined in the modified model.With only the physical characteristics of soils,such as the density,thickness and damping ratio adopted,the variation of amplitude and phase for the ground motions are represented with the transfer function in time domain,so that the local site effect is fully considered for the bedrock incident waves to the ground surface.The modified model of spatially variable ground motions can be widely applied to generate refined multiple support excitation for the seismic analysis of high-pier long-span continuous rigid frame bridges.(2)Damage analysis of high-pier long-span continuous rigid frame bridges with ground motion spatial variation and nonlinear effect considered.Nonlinear seismic analyses are conducted on the finite element model of a high-pier long-span continuous rigid frame bridge subjected to multiple groups of earthquake excitations from bedrock and ground surface.Studies on the relative displacement of piers,the internal force of the bridge deck and piers,the damage distribution and development of components and the whole structure demonstrate the failure mode of the high-pier long-span continuous rigid frame bridge.Results show that the tall piers with higher flexibility are more sensitive to the negative effect of ground motions.The rigid joints of piers and the deck,as well as the tie beams between the two legs of each tall pier,are the weak links for the seismic capacity of the bridge.The adverse impact of spatially variable ground motions with local site effect on the dynamic performance of high-pier long-span continuous rigid frame bridges cannot be neglected.Thus to ensure the conservative seismic demand for high-pier long-span continuous rigid frame bridges in dynamic analysis,the multiple support excitations can be replaced by the uniform excitation with the largest peak acceleration of them,where the site condition effect can be neglected such as on the plain.However for the high-pier long-span continuous rigid frame bridges located on complex site conditions such as valley and canyon sites,spatially variable ground motions with local site effect should be applied.(3)The influence of ground motion spatial variability on the ductility factor and fragility of high-pier long-span continuous rigid frame bridges,and correction coefficient for the seismic capacity of bridges subjected to multiple support excitations.The ultimate ductility factors and ductility demand ratios for the piers of large continuous rigid frame bridges are calculated using incremental dynamic analysis.Results show that the ductility capacity of double-limb thin-wall hollow piers is higher than single-limb piers with similar sizes.The ductility capacity of piers in transverse direction is higher than longitudinal direction.The advantage of tall piers in ductility capacity compared with short ones is more significant at the worse damage stages.Piers with larger height or located on soft soil sites are more sensitive to the spatial variability of ground motions.The ground motion spatial variability presents a greater influence on the seismic demand of piers in transverse direction than longitudinal direction.The upper fractile(mean plus one standard deviation)of the correction coefficient for spatially variable ground motions can be used as the amplification factor of seismic capacity for the bridges in the process of seismic design.This lead to a safety comparable with that of the uniform excitation case.The conventional synchronous design procedure thus can be corrected by increasing the ductility capacity.The fragility analysis of high-pier long-span continuous rigid frame bridges indicates that the structures present larger seismic demand in the transverse direction,while in the longitudinal direction,show higher sensitivity of failure probability especially at the complete damage stage subjected to spatially variable ground motions.(4)The ductility optimization for multi-span continuous rigid frame bridges based on equivalent seismic performance.There are certain conflicts between the seismic capacity and demand distribution pattern induced by the spatially variable ground motions.The optimization approach aims to eliminate the weak link of seismic capacity in the bridge,to improve the synchronous capability of anti-collapse for each pier and the seismic performance of the whole bridge system.The ultimate ductility factor is adopted as the capacity index to represent the capability of anti-collapse.The ductility capacity of each pier is optimally redistributed in accordance with the ductility demand pattern,through the adjustment of reinforcement ratio and section size for the piers.The iteration process is completed when the equivalent ductility capacity of each pier is convergent to the value of the target ductility capacity within a certain range of tolerance.The determination of optimization variable is related to the ratio of longitudinal reinforcement.Results show that the fragility curves at the complete damage state for piers of the optimal bridge model are remarkably closer compared with those of the original bridge model.Thus the discreteness of the failure probability for each pier is significantly reduced,the weak link of seismic performance is eliminated and the synchronous capability of anti-collapse is improved.The fragility analysis for the whole bridge systems indicate that the failure probabilities of the multi-span continuous rigid frame bridge at multiple damage stages are reduced using this ductility optimization method.It is proved that the seismic performance of the whole bridge is improved and the optimization objective is achieved.