Stochastic Methods for Seismic Engineering Applications

该项目的目标是(1)将地震分析的变异性方法推广到土的边界快速度矩阵与无界区域相关联的情况，以及(2)建立一组土的非线性本构方程。这将使评估土体本构特性的变化对地震动效应的影响，从而对土-(嵌)结构体系在这种地震动作用下的响应的影响成为可能。这些结果将通过蒙特卡罗模拟得到验证。描述高阶统计近似公式的代数复杂性将在数字计算机中通过与人工智能程序密切相关的符号处理语言来处理。将探索统计相关性的最终结果的自动顺序改进。将努力开发一种计算机代码，在有限元分析的框架内实施适当的随机等效线性化方法，以实现这一目标。还将努力制定分析大纲，说明如何将变异性分析和非线性反应分析结合起来。本项目将寻求充分扩展随机方法在地震工程中的适用性，以便合理地处理这些问题中固有的随机性和不确定性。

The objectives of this project are (1) to extend the variability methods of seismic analysis to situations where the soil boundary swiftness matrix is associated with an unbounded region, and (2) to develop a set of nonlinear constitutive equations for the soil. This will make it possible to evaluate the effects of variation in the soil constitutive properties on the seismic ground motions and hence on the response of soil-(embedded) structure systems subjected to such ground motions. These results will be verified against Monte Carlo simulations. The algebraic complexities of the formulae depicting the higher-order statistical approximations will be handled in a digital computer by symbolic manipulation languages germane to artificial intelligence procedures. Automated sequential refinements of the final results of the statistical correlations will be explored. A major effort will be expended to develop a computer code which implements an appropriate stochastic equivalent linearization method within the framework of a finite element analysis to achieve this objective. Efforts will also be made to develop analytical outlines as to how the variability and nonlinear response analyses can be combined. This project will seek to fully extend the applicability of stochastic methods in earthquake engineering so that the inherent randomness and uncertainty existing in these problems can be rationally dealt with.