多点多维随机地震作用下高墩大跨桥梁动力反应分析

Dynamic response analysis of a high-pier and long-span bridge under multi-support and multi-component stochastic ground motions

为了克服传统Monte Carlo模拟方法由于高维随机变量所带来的巨大挑战,本文建议了一类空间相关多点多维(mD-nV)全非平稳地震动随机场的降维模拟方法,并结合概率密度演化理论,实现了多点多维随机地震作用下高墩大跨连续刚构桥动力反应精细化分析。首先,推导了基于相干函数矩阵的多点多维全非平稳地震动随机场本征正交分解模拟公式;然后,引入随机函数的约束形式,建立了多点多维全非平稳地震动随机场的降维模型;最后,以高墩大跨连续刚构桥为工程对象,采用动力时程分析并结合概率密度演化理论,实现了桥梁结构精细化动力反应分析。结果表明本文提出的降维模型具有较好的适用性,同时,高墩大跨刚构桥在多点多维地震作用下会引起桥墩在三方向的位移反应,因此,在进行结构抗震分析时,应充分考虑多点多维随机地震输入对结构动力反应与损伤失效机制的影响。

In order to overcome the great challenges brought by the conventional Monte Carlo simulation method with respect to the high-dimensional random variables, the dimension-reduction simulation method of spatially correlated multi-support and multi-component(mD-nV) non-stationary stochastic ground motion field is proposed. Combined with the probability density evolution theory, the refined dynamic response analysis of a high-pier and long-span continuous rigid frame bridge subjected to multi-support and multi-component stochastic ground motions is realized. Firstly, the proper orthogonal decomposition expression of multi-support and multi-component fully non-stationary seismic fields is derived based on the coherence function matrix. Then, by introducing the constraint form of random function, the dimension-reduction model of multi-support and multi-component non-stationary random earthquake field is established. Finally, taking a high-pier and long-span bridge as engineering object, the refined seismic response analysis of the bridge is conducted combining dynamic time-history analysis with probability density evolution theory. The results show that the dimension-reduction model proposed in this paper has good applicability. Meanwhile, the displacement responses of piers in three directions can be caused by multi-support and multi-component ground motion, of which the influence on structural dynamic response and damage failure mechanism should be fully considered.