摘要
土与结构相互作用体系随机反应分析是地震工程领域中的前沿课题之一，地震动的三要素(持时、强度和频谱)都具有明显的随机性，把随机振动理论应用于土与结构相互作用体系地震反应分析的合理性是显而易见的。目前，关于土与结构相互作用体系随机反应分析的研究成果较少，与这一理论的先进性是很不相称的。本文详细地研究了土与结构相互作用体系随机地震反应分析方法，并对该方法的实际应用中的一些问题提出了作者的一些见解和处理方法。随机振动分析具有如下的特点：(1)随机振动反应得出的是响应的均值，它包含了大量时程曲线统计信息，比单一的时程曲线分析得出的结果更具有代表性和普遍性，(2)求出的最大值的均值较为直观，而不象时程分析那样繁琐。(3)随机振动反应输入的是功率谱，这实际上是从能量的角度来分析问题。
在结构动力时程分析方法和以随机振动理论为基础的概率设计理论日臻完善的现阶段，了解地震作用下结构体系动力反应全过程和具有概率统计意义上的土与结构相互作用体系地震响应不仅是可行的，而且也是非常必要的。开展这方面的研究对结构抗震设计及动力可靠度的研究都具有重要意义。
本文的研究内容如下：
为了对所研究的问题有一个全面的了解，第一章对土与结构相互作用问题作了简要概括，并确定了本文研究的内容，包括土与结构相互作用体系动力特性研究；基于反应谱的随机地震反应分析；基于地震动模型的随机响应分析；上部结构非线性对相互作用体系影响分析；地基二土分层特性和非线性特性以及基础埋深对相互作用体系随机响应影响分析。
土与结构相互作用体系随机地震反应分析首先考虑的是地震动的输入问题。第二章简要地介绍了随机地震动模型的几种表达方式，结合前人的研究成果和规范GB50011-2001对应的不同场地和烈度的有关数据，计算得到所需要的有关参数，并以此参数作为随机地震动输入为后续研究相互作用体系的随机反应分析提供依据。
土与结构相互作用体系随机反应分析要考虑的第二个问题是关于地基阻抗的确定，它是土与结构相互作用体系随机反应分析的基础性工作。第三章，据前人的研究成果，推导了计算地基阻抗的表达式，考虑了基础埋深、地基土分层特性以及地基土的非线性特性，并对地基阻抗表达式中的参数进行了确定。
土与结构相互作用体系自振特性是相互作用的基本问题，它是进行动力相互作用分析的基
础。结构体系的固有频率和阻尼对体系响应具有重要的影响。第四章建立了1--与结构相互作用体
系随机地震反应分析的方法—频响函数法。对土与结构相互作用体系的自振特性进行了系统的
研究。研究表明随着场地的变软，土与结构相互作用体系的周期与刚性地基假定计算的周期相比
变长;场地十二非线性特性和分层特性使相互作用体系的周期变长;基础的埋深对相互作用体系的
周期影响较小。
反应谱分析方法是目前抗震设计的一种重要方法，抗震设计者普遍接受了反应谱概念，认为
反应谱法可以更好地描述地震动及结构特性。迄今为止世界上大多数国家仍然把反应谱法作为抗
震设计的主要方法。第五章基于反应谱方法，根据反应谱与功率谱之间的关系，建立了土与结构
相互作用体系随机地震反应分析的反应谱方法，分别考虑地震动平稳过程和非平稳过程对相互作
用体系影响进行了随机地震反应分析。该方法与目前抗震规范的反应谱分析方法相协调。
地面运动具有明显的随机性，把地面运动作为随机过程描述是科学、合理的。第六章进行了
基于随机地震动模型的土与结构相互作用体系随机反应分析，地面输入运动为功率谱密度函数，
考虑地震动强度非平稳性和频谱非平稳性对相互作用系统的影响，根据线性时不变系统的动力特
性，利用脉冲响应函数与频响函数之间的关系，得到体系响应的统计量和随机响应演变谱，并对
地震动谱参数取不同值时对相互作用体系影响进行了详细的分析，迄今为止还没有人对此做过研
究。关于地震动频谱的非平稳性对土与结构相互作用体系的影响迄今为止也没有人做过研究。
在强震作用下，土与结构相互作用体系一般不再保持低频时的线弹性状态，也就是说结构体
系大都要进入非线性状态。第七章对土与结构相互作用非线性体系进行了随机地震反应分析，考
虑上部结构的非线性情况，把非线性结构系统等效线性化进行随机反应分析。
在强震作用下，不仅上部结构可能进入非线性状态，而地基土也可能进入非线性状态。第八
章同时考虑结构和地基土的非线性，对土与结构相互作用体系进行随机反应分析，同时还考虑基
础理置深度对相互作用体系的影响。通过分析表明，考虑土与结构相互作用体系的非线性特性，
体系的响应量明显增大，并通过实际结构震灾算例说明相互作用体系的非线性效应。第九章为结
论与展望。通过前面系统的研究，在对土与结构相互作用体系进行随机分析时，应考虑地震动强
度非平稳、频率非平稳和持时的影响。尽管本文对土与结构相互作用体系随机地震反应进行了系
统研究，由于土与结构相互作用体系问题的复杂性、地震动参数统计的局限性、地基阻抗函数确
定的困难性以及分析方法的
The stochastic response analysis of the soil-structure interaction system is one of advancing front subject. The three element factors (endurance time, intensity, frequency spectrum) of earthquake motion have obvious random characteristics, and the random vibration theory applied the stochastic response analysis of soil-structure interaction system is obvious ration. At the present time, the research achievement is few for random response analysis of soil-structure interaction system, and it is not matching about advancing of random vibration theory. The random response method for soil-structure interaction system is studied systematically at this dissertation, and the suggestions and treating methods about the practice application are proposed. The random seismic response analysis has characteristics: (1) it obtains mean value for random seismic response and includes large-tonnage time-dependent curve statistic information; (2) it is intuitive manner for mean value and not inconvenient as time-dependent met
hod; (3) it inputs power spectrum and analysis for the problem from power.
The time-dependent analysis method and random vibration theory method is gradual perfection and it is feasible and necessary to knows whole process for soil-structure interaction system and seismic response with statistic significance. It has important significance for seismic design and probability analysis.
Some main achievements of this dissertation are described as follows:
At chapter 1, a brief summary and a primary introduction is given to soil-structure interaction system and contents of research is given.
The first consideration is input problem of the earthquake motion for soil-structure interaction system. Some expresses of earthquake motion model are introduced, and calculation parameters for earthquake motion model using data of code GB0051-2001 are obtained at the chapter2, and it is base for the analysis of interaction system.
The second consideration is the compliance functions of foundation, and it is a basis work for soil-structure interaction system random response analysis. The chapter3 is a primary description of some foundation models, and deduces calculation formula of the compliance functions of foundation based on achievement of predecessors and the paramters of the compliance functions of foundation is determined.
The free vibration characteristics of soil-structure interaction system is basic problem of interaction system. It is the base of the dynamic interaction system analysis. The natural frequency and damping of interaction system has important effect to system response. At
the chapter4, the free vibration characteristics of soil-structure interaction system are studied, and the effects and some useful results are obtained.
The response spectrum method is a important method for seismic design, and seismic designers accepted the method generally, and they think that response spectrum method can describe characteristics of earthquake motion and structural system. At the chapter5, based on spectrum method, and the relation of power spectrum and response spectrum, the stochastic analysis method of soil-structure interaction system is established, and the effects of the stationary random process and the evolutionary random process of soil-structure interaction system response is considered. The method can match code GB0051-2001.
The ground motion has obviously stochastic, and it is described with the stochastic process method is science and ration. At the chapter6, based on random earthquake motion model, soil-structure interaction system stochastic response is studied, and input motion is power spectrum density function, and effects of frequency non-stationary characteristics and intensity non-stationary characteristics is considered. According to the time-invariant system with the hysteretic material damping and the transfer behavior of influence function and response function, the stationary and non-stationary mean square response and their spectral parameters are obtained. The effects of the spectr
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