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全非平稳地震作用下地下空间结构随机反应及可靠度分析
引用本文:成梦辉,陈清军.全非平稳地震作用下地下空间结构随机反应及可靠度分析[J].上海力学,2020,41(2):308-318.
作者姓名:成梦辉  陈清军
作者单位:同济大学土木工程防灾国家重点实验室,上海200092
基金项目:国家自然科学基金;国家科技支撑计划;国家重点实验室建设项目计划
摘    要:为研究全非平稳地震作用下地下空间结构的随机地震反应特征及可靠度分析方法,本文基于非均匀调制演变随机过程,建立了一种同时考虑强度非平稳和频率非平稳的全非平稳随机地震动输入功率谱分析模型;利用频响函数和脉冲响应函数间的傅里叶变换关系,推导出了适用于地下空间结构随机反应分析的响应功率谱计算表达式,可结合有限元方法对全非平稳地震作用下地下空间结构进行随机反应分析.基于穿越过程为泊松过程假定,采用分部积分方法,进一步推导出了适用于首次超越破坏可靠度计算的互相关函数解析表达式.然后,本文以上海某两层三跨地铁车站为工程背景,建立土-地铁车站结构相互作用体系有限元模型,对全非平稳地震作用下地铁车站结构进行了随机反应分析和中柱可靠度分析.结果表明:在非均匀调制演变功率谱作用下,结构的响应功率谱也具有明显的演变特征;利用文中给出的互相关函数计算公式,可避开调制函数的数值微分,提高计算精度.

关 键 词:全非平稳地震作用  地下空间结构  土-结构相互作用  随机地震反应  可靠度分析  

Stochastic Responses and Reliability Analysis of Underground Space Structures Subjected to Fully Nonstationary Seismic Excitation
CHENG Menghui,CHEN Qingjun.Stochastic Responses and Reliability Analysis of Underground Space Structures Subjected to Fully Nonstationary Seismic Excitation[J].Chinese Quarterly Mechanics,2020,41(2):308-318.
Authors:CHENG Menghui  CHEN Qingjun
Abstract:In order to study the stochastic responses and reliability analysis method of underground space structures subjected to fully non-stationary seismic excitation, an input power spectrum analysis model with the consideration of both non-stationary characteristics of intensity and frequency was established based on the random process of non-uniform modulation evolution. By using the transformation relation between frequency response function and impulse response function, the mathematical expression of response power spectrum which is suitable for the random response analysis of underground space structure is derived. This expression can be combined with the finite element method to carry out the non-stationary random seismic response analysis of underground space structure. Meanwhile, based on the assumption that the crossing process is Poisson process, an analytical expression of cross-correlation function suitable for the calculation of the first passage failure reliability is further derived by using the integration by parts method. On this basis, taking a typical two-story and three-span subway station in Shanghai as an example, a three-dimensional finite element model of soil-subway station structure interaction system was established by ABAQUS software, and the fully non-stationary stochastic seismic response of the subway station structure and the reliability analysis of the mid-column were carried out. The results show that the structure response power spectrum also has obvious evolution characteristics under the action of non-uniform modulation evolution power spectrum. The calculation formula of cross correlation function derived in this paper avoids the numerical differentiation of modulation function and improves the calculation accuracy of cross correlation function.
Keywords:fully non-stationary seismic excitation  underground space structures  soil-structure interaction  stochastic seismic response  reliability analysis  
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