土—偏心结构相互作用地震反应参数分析与试验研究
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摘要
随着我国城市建设的快速发展,平面形式不规则的非对称建筑大量涌现,在地震过程中此类建筑由于所受惯性力作用与结构自身抗力不共线,因而会表现出平动与扭转耦联的变形特征。震害研究表明,地基条件对偏心结构振动特性有显著的影响,土与结构相互作用效应(SSI)会引起结构振动反应的增大。当前,各国抗震规范中给出的结构抗扭设计方法主要是基于刚性地基假定。由于考虑SSI效应后问题分析的复杂程度与计算规模大幅增加,给分析研究带来困难,尚不足以支撑抗震规范相关条文。为此,本文在综合国内外研究成果的基础上,提出了改进的分析模型和计算方法,以平衡分析精度和计算成本两方面需求,进而对各类参数影响规律进行系统地讨论,研究工作主要围绕以下几个方面进行:土-单层偏心结构体系的理论推导与参数分析;土-多层偏心结构体系平扭耦联参数分析;相互作用体系振动台试验设计与结果分析;土-偏心结构相互作用体系动力时程分析与规律验证。围绕上述问题,主要的创新工作及研究成果有:
(1)对偏心结构与土相互作用研究现状进行了系统的归纳和探讨,提出了基于分支模态法原理的分析方法,通过模态凝聚实现地基分支与结构分支间的相互耦合,完整考察地基土的质量、刚度和阻尼特性,模拟相互作用过程;研究工作从单层偏心结构(2DOF)情况出发,将地基多自由度因素蕴含于结构显式求解过程当中,推导了频域内结构平扭位移与变形传递函数表达式;对平扭耦联参数(扭平频率比Ω、结构偏心率B、结构偏心形式)和SSI效应参数(地基与结构刚度比、结构长细比)进行了系统的参数分析和影响规律研究;
(2)地基分支模型通常是由大量连续分布的实体单元(或平面单元)组成,计算规模较上部结构大得多。试算结果表明,地基主模态在全部地基振型中的分布极为分散,给有效地截取主模态截取范围带来困难。对此,本文提出在子结构层次应用Ritz向量法求解地基主模态问题,考察外部动荷载的空间分布与地基自身振动特性的对应关系,滤除对地基振动贡献较小的低阶振型。算例分析结果表明,Ritz向量法自振特性计算效率较传统模态向量有明显提高,适用于地基主模态分析与地震反应分析;
(3)在单层偏心结构研究的基础上,进而对多层偏心结构体系(五层)开展土—结构相互作用条件下的平扭耦联参数分析。研究理论由单层偏心情况发展而来,由于上部结构自由度数量已超过2个,无法给出结构振动反应的显示表达式,因而采用数值方法开展参数研究;研究工作主要针对刚度偏心体系(CRS)进行,对楼层偏心率B_i、广义扭平频率比Ω~′、偏心楼层分布、楼层相对偏心关系及地基刚度等参数进行了系统地分析,形成了多层偏心结构体系参数影响的规律性认识;
(4)以某单层框架结构为研究背景,缩尺为单层偏心结构模型,对其在刚性地基与相互作用条件下进行振动台试验研究;试验实施过程中对模型相似设计、模型土配制与土地动力学参数测试方法提出改进措施;获得了较为完整的实测数据,对相互作用体系与地基自振特性、偏心结构振动反应组成、偏心结构应变反应、以及偏心效应作用下的群桩与地基响应进行了系统的分析,为理论研究工作提供了参照;
(5)编制了基于Wilson-θ法原理的土-单层偏心结构体系直接积分法计算程序,同时,由傅立叶逆变换将频域内偏心结构平扭位移传递函数转换至时域,通过对比两组时程曲线结果,考察“强解耦”过程对分析精度的影响;考虑到SSI体系振动台试验条件与理论分析之间相差较大,从规律分析的角度出发,对比理论研究与试验实测数据,验证结构偏心率与地基条件因素对偏心结构体系平扭耦联反应的影响趋势。
With the rapid development of urbanization in China, more and more asymmetric buildings with irregular distribution in horizontal and vertical direction appeared. The seismic responses of such buildings are of torsionally coupled features typically. Previous earthquake damage investigations indicate that the vibration characteristic of eccentric structures can be notably altered by the flexibility of foundation soil, while the soil-structure interaction effect may enlarge the vibration response of super- structure. Since the complexity and computational scale will be increase significantly when incorporating the SSI effect into relative research. The provisions for structure eccentricity and torsion-resistant design in most design codes are based on fixed-base assumption, while the influence of SSI effect is not fully considered. Therefore, an analytical approach that retains the essential characteristics necessary for studying the torsionally coupled seismic response of eccentric structure built on flexible foundation with reasonable computational cost is presented in this dissertation.A series of innovative work has been done on the issue, the achievements and conclusions of which can be draw as follow:
(1) The research status of soil-eccentric structure interaction is classified and discussed. An analytical approach that retains all the essential characteristics for simulating the SSI effect is presented and formulated based on the branch mode theory. The superstructure and foundation branch are coupled through mode aggregation procedure. Parametric study of single-storey eccentric structure (2DOF) is firstly carried out by comparing the transfer function results of translational and torsional response, in which the DOFs of foundation soil are incorporated in the explicit solution of superstructure. The influence of torsional to translational frequency ratio, eccentricity ratio, eccentric form, height-to-base ratio and foundation flexibility are analyzed systematically.
(2) Since the foundation model usually consists of a large amount of continuous soild or plane elements, the computational scale is much higher than that of superstructure. Previous reaseraches indicate that the distribution of foundation modes is extremely scatted among all the modal analysis results, which makes it rather difficult to define the mode cut-off criterion. As a replacement of traditional modal vectors, Ritz vectors are employed in the solution of foundation mode which can filter the lower ranking mode of negligible contribution to the foundation vibration by taking the spatial distribution of external loading into consideration. The results of sample analysis show that Ritz vectors may significantly boost the solution efficiency of natural vibration, which is very suitable for the modal analysis and seismic analysis of foundation sub-structure.
(3) Based on the research of single-storey eccentric structure interaction system, the computational theory of multi-storey eccentric structures considering SSI effect is developed and formulated. Parametric analysis is carried out by numerical methods, since the number of DOF of superstructure exceed the limitation of explicit solution. The magnitude and rules of influence of parameters, such as floor eccentricity ratio, general ratio of torsional to translational frequency, relative stiffness of soil to structure, distribution of eccentric floor and relative eccentricity between floors, are analyzed and discussed comprehensively.
(4) Shaking table test for soil-pile-eccentric structure interaction system is carried out and compared with fixed base foundation test. During the preparatory stage, a series of improvement has been presented for model similitude design, fabrication of model soil and the dynamic performance test of soil material. The vibration characteristics of interaction system, constitution of eccentric super- structuctre response, acceleration and strain response, vibration response of group piles and foundation soil are measured and analyzed, which provides experimental reference to theoretical research.
(5) The direct integral program for soil-eccentric structure interaction system is established base on the Wilson-θalgorithm. The feasibility of the analytical approach developed in this paper is verified by comparing the time domain results derived by inverse fast Fourier transform procedure with the time-history curve of superstructure response obtained by direct integral program. Since the difference between shaking table test conditon of SSI system and theoretical assumption is not neglectable, the analytical results are compared for general rules, which proved the tendency of parameters influence of structure eccentricity and foundation flexibility on the torsionally-coupled response.
(1)对偏心结构与土相互作用研究现状进行了系统的归纳和探讨,提出了基于分支模态法原理的分析方法,通过模态凝聚实现地基分支与结构分支间的相互耦合,完整考察地基土的质量、刚度和阻尼特性,模拟相互作用过程;研究工作从单层偏心结构(2DOF)情况出发,将地基多自由度因素蕴含于结构显式求解过程当中,推导了频域内结构平扭位移与变形传递函数表达式;对平扭耦联参数(扭平频率比Ω、结构偏心率B、结构偏心形式)和SSI效应参数(地基与结构刚度比、结构长细比)进行了系统的参数分析和影响规律研究;
(2)地基分支模型通常是由大量连续分布的实体单元(或平面单元)组成,计算规模较上部结构大得多。试算结果表明,地基主模态在全部地基振型中的分布极为分散,给有效地截取主模态截取范围带来困难。对此,本文提出在子结构层次应用Ritz向量法求解地基主模态问题,考察外部动荷载的空间分布与地基自身振动特性的对应关系,滤除对地基振动贡献较小的低阶振型。算例分析结果表明,Ritz向量法自振特性计算效率较传统模态向量有明显提高,适用于地基主模态分析与地震反应分析;
(3)在单层偏心结构研究的基础上,进而对多层偏心结构体系(五层)开展土—结构相互作用条件下的平扭耦联参数分析。研究理论由单层偏心情况发展而来,由于上部结构自由度数量已超过2个,无法给出结构振动反应的显示表达式,因而采用数值方法开展参数研究;研究工作主要针对刚度偏心体系(CRS)进行,对楼层偏心率B_i、广义扭平频率比Ω~′、偏心楼层分布、楼层相对偏心关系及地基刚度等参数进行了系统地分析,形成了多层偏心结构体系参数影响的规律性认识;
(4)以某单层框架结构为研究背景,缩尺为单层偏心结构模型,对其在刚性地基与相互作用条件下进行振动台试验研究;试验实施过程中对模型相似设计、模型土配制与土地动力学参数测试方法提出改进措施;获得了较为完整的实测数据,对相互作用体系与地基自振特性、偏心结构振动反应组成、偏心结构应变反应、以及偏心效应作用下的群桩与地基响应进行了系统的分析,为理论研究工作提供了参照;
(5)编制了基于Wilson-θ法原理的土-单层偏心结构体系直接积分法计算程序,同时,由傅立叶逆变换将频域内偏心结构平扭位移传递函数转换至时域,通过对比两组时程曲线结果,考察“强解耦”过程对分析精度的影响;考虑到SSI体系振动台试验条件与理论分析之间相差较大,从规律分析的角度出发,对比理论研究与试验实测数据,验证结构偏心率与地基条件因素对偏心结构体系平扭耦联反应的影响趋势。
With the rapid development of urbanization in China, more and more asymmetric buildings with irregular distribution in horizontal and vertical direction appeared. The seismic responses of such buildings are of torsionally coupled features typically. Previous earthquake damage investigations indicate that the vibration characteristic of eccentric structures can be notably altered by the flexibility of foundation soil, while the soil-structure interaction effect may enlarge the vibration response of super- structure. Since the complexity and computational scale will be increase significantly when incorporating the SSI effect into relative research. The provisions for structure eccentricity and torsion-resistant design in most design codes are based on fixed-base assumption, while the influence of SSI effect is not fully considered. Therefore, an analytical approach that retains the essential characteristics necessary for studying the torsionally coupled seismic response of eccentric structure built on flexible foundation with reasonable computational cost is presented in this dissertation.A series of innovative work has been done on the issue, the achievements and conclusions of which can be draw as follow:
(1) The research status of soil-eccentric structure interaction is classified and discussed. An analytical approach that retains all the essential characteristics for simulating the SSI effect is presented and formulated based on the branch mode theory. The superstructure and foundation branch are coupled through mode aggregation procedure. Parametric study of single-storey eccentric structure (2DOF) is firstly carried out by comparing the transfer function results of translational and torsional response, in which the DOFs of foundation soil are incorporated in the explicit solution of superstructure. The influence of torsional to translational frequency ratio, eccentricity ratio, eccentric form, height-to-base ratio and foundation flexibility are analyzed systematically.
(2) Since the foundation model usually consists of a large amount of continuous soild or plane elements, the computational scale is much higher than that of superstructure. Previous reaseraches indicate that the distribution of foundation modes is extremely scatted among all the modal analysis results, which makes it rather difficult to define the mode cut-off criterion. As a replacement of traditional modal vectors, Ritz vectors are employed in the solution of foundation mode which can filter the lower ranking mode of negligible contribution to the foundation vibration by taking the spatial distribution of external loading into consideration. The results of sample analysis show that Ritz vectors may significantly boost the solution efficiency of natural vibration, which is very suitable for the modal analysis and seismic analysis of foundation sub-structure.
(3) Based on the research of single-storey eccentric structure interaction system, the computational theory of multi-storey eccentric structures considering SSI effect is developed and formulated. Parametric analysis is carried out by numerical methods, since the number of DOF of superstructure exceed the limitation of explicit solution. The magnitude and rules of influence of parameters, such as floor eccentricity ratio, general ratio of torsional to translational frequency, relative stiffness of soil to structure, distribution of eccentric floor and relative eccentricity between floors, are analyzed and discussed comprehensively.
(4) Shaking table test for soil-pile-eccentric structure interaction system is carried out and compared with fixed base foundation test. During the preparatory stage, a series of improvement has been presented for model similitude design, fabrication of model soil and the dynamic performance test of soil material. The vibration characteristics of interaction system, constitution of eccentric super- structuctre response, acceleration and strain response, vibration response of group piles and foundation soil are measured and analyzed, which provides experimental reference to theoretical research.
(5) The direct integral program for soil-eccentric structure interaction system is established base on the Wilson-θalgorithm. The feasibility of the analytical approach developed in this paper is verified by comparing the time domain results derived by inverse fast Fourier transform procedure with the time-history curve of superstructure response obtained by direct integral program. Since the difference between shaking table test conditon of SSI system and theoretical assumption is not neglectable, the analytical results are compared for general rules, which proved the tendency of parameters influence of structure eccentricity and foundation flexibility on the torsionally-coupled response.
引文
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