基于部分分层抽样的高墩桥梁随机地震响应分析

陈志强1,郑史雄1,丁自豪1,张金2

振动与冲击 ›› 2022, Vol. 41 ›› Issue (7) : 214-222.

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振动与冲击 ›› 2022, Vol. 41 ›› Issue (7) : 214-222.
论文

基于部分分层抽样的高墩桥梁随机地震响应分析

  • 陈志强1,郑史雄1,丁自豪1,张金2
作者信息 +

Random seismic response analysis of high-pier bridges based on partial stratified sampling

  • CHEN Zhiqiang1, ZHENG Shixiong1, DING Zihao1, ZHANG Jin2
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摘要

为了表征桥梁结构不确定性和随机参数相关性对桥梁结构抗震性能的影响,从概率角度对桥梁进行抗震性能分析,基于部分分层抽样原理建立了时-频非平稳地震作用下桥梁非线性随机地震响应分析方法。首先,基于地震动演化功率谱,采用谱表示方法生成非平稳地震动样本,并采用基于正交函数的思想对谱表示方法中的随机变量进行模拟,通过两个基本随机变量表征地震动的不确定性;然后,采用基于数论的部分分层抽样方法对地震动-结构随机变量抽样,从而对桥梁非线性随机地震响应进行模拟,减小桥梁随机地震响应分析中的抽样方差;最后,以一座实际高墩连续刚构桥为数值算例,对其进行了非线性随机地震响应分析,详细研究了桥梁结构不确定性和随机参数相关性对其地震可靠度的影响。研究结果表明:随机地震作用下,桥梁随机地震响应是典型的零均值非平稳随机过程,从地震动开始到结束,桥梁结构地震响应概率密度曲线存在由窄边宽,再由宽变窄的演化过程;随机地震作用下,桥梁结构关键响应的平均峰值因子存在一定差异,其通常在1.8到2.2之间变化;桥梁结构不确定性和随机参数相关性对高墩桥梁地震响应极值分布和地震可靠度的影响较为显著,忽略桥梁结构的不确定性和随机参数相关性将高估桥梁结构的地震可靠度。

Abstract

To characterize the influence of uncertainty and correlation of structural parameters on the seismic performance of bridge and analysis the seismic performance of bridge via probabilistic method, a nonlinear random seismic response analysis method of bridge under time-frequency non-stationary earthquake was developed based on partially stratified sampling. The non-stationary random seismic record samples were firstly generated based on the evolution power spectrum density of ground motions by using spectral representation method (SRM). The random variables involved into the SPR method were simulated by a random functions based method and the uncertainty of ground motions was characterized by two elementary random variables. Subsequently, the ground motion and structural uncertain parameters were sampled by using the number theory based partially stratified sampling method so as to simulate the nonlinear stochastic seismic response of bridge and also to reduce the sampling variance in the random seismic response analysis; Finally, a practical high-pier continuous rigid frame bridge is taken as an example, the nonlinear random seismic response analysis is carried out, and the influence of uncertainty and correlation of structural random parameters on its seismic reliability is studied in detail. The results indicate that the random seismic response of bridge under the stochastic seismic excitations is a typical non-stationary random process with zero mean. From the beginning to the end of ground motion excitation, the probability density curve of seismic response of bridge has the evolution process from narrow side to wide, and then from wide to narrow. The mean peak factors of critical responses of bridge structure vary from 1.8 to 2.2. The influence of uncertainty and correlation of structural parameters on the extreme value distribution and seismic reliability of high-pier bridges is significant. Ignoring the uncertainty and correlation of random parameters will significantly overestimate the seismic reliability of bridge.

关键词

非平稳 / 随机地震响应 / 极值分布 / 地震可靠度 / 部分分层抽样

Key words

non-stationary / random seismic response / extreme value distribution / seismic reliability / partially stratified sampling

引用本文

导出引用
陈志强1,郑史雄1,丁自豪1,张金2. 基于部分分层抽样的高墩桥梁随机地震响应分析[J]. 振动与冲击, 2022, 41(7): 214-222
CHEN Zhiqiang1, ZHENG Shixiong1, DING Zihao1, ZHANG Jin2. Random seismic response analysis of high-pier bridges based on partial stratified sampling[J]. Journal of Vibration and Shock, 2022, 41(7): 214-222

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