Although advanced modeling techniques such as the finite element method (FEM) have been used successfully in dynamic site response analysis, the high computational expense has hindered the incorporation of input parameter uncertainty in such analysis. Thus, when the variation of the peak ground acceleration (PGA) at the ground surface, which is the outcome of the site response analysis, has to be evaluated in the face of uncertainty, a surrogate model such as Response Surface Method (RSM) model is often used in lieu of the FEM model. In this paper, the RSM surrogate model was implemented in the context of seismic site response analysis to evaluate the variation (or uncertainty) of the PGA due to the propagation of input parameter uncertainty. The engineering implication of the variation of the surface PGA is significant as this knowledge is required for such tasks as reliability analysis of soil liquefaction and probabilistic seismic risk analysis. To derive the RSM model specifically for a site response analysis, a parametric study of the dynamic site responses using FEM code ABAQUS with the modified Davidenkov soil constitutive model implemented as a user-defined material subroutine is first conducted. The input parameters, including the soil profile, soil properties, and input ground motion, in a typical dynamic site response analysis are then characterized and screened for their suitability to be included in the RSM model. For a given site response problem in the face of uncertainty, representative “samples” are taken for site response analysis using ABAQUS, and the analyses are carried out and finally the response surface is constructed using the outcomes of the ABAQUS numerical experimentations. The accuracy of the developed RSM model is then validated using the results of ABAQUS on cases not used in the development of the RSM model. Once the RSM model is deemed satisfactory, the reliability-based formulation for evaluating the mean and standard deviation of the surface PGA is established. Example is provided to illustrate the RSM approach for dynamic site response analysis in the face of input parameter uncertainty.

中文翻译：

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不确定性下的动态场地响应分析——一种基于响应面法的方法

尽管有限元法 (FEM) 等先进的建模技术已成功用于动态场地响应分析，但高昂的计算费用阻碍了将输入参数不确定性纳入此类分析。因此，当地面上峰值地面加速度 (PGA) 的变化（即场地响应分析的结果）必须在面对不确定性时进行评估时，可以使用响应面法 (RSM) 模型等替代模型常用于代替 FEM 模型。在本文中，RSM 代理模型在地震现场响应分析的背景下实施，以评估由于输入参数不确定性的传播而导致的 PGA 变化（或不确定性）。地表 PGA 变化的工程意义非常重要，因为这些知识对于诸如土壤液化的可靠性分析和概率地震风险分析等任务是必需的。为了获得专门用于场地响应分析的 RSM 模型，首先使用 FEM 代码 ABAQUS 和作为用户定义材料子程序实现的修正 Davidenkov 土壤本构模型对动态场地响应进行参数研究。然后对典型动态场地响应分析中的输入参数（包括土壤剖面、土壤特性和输入地面运动）进行表征并筛选它们是否适合包含在 RSM 模型中。对于面临不确定性的给定场地响应问题，使用 ABAQUS 抽取具有代表性的“样本”进行场地响应分析，并进行分析，最后使用 ABAQUS 数值实验的结果构建响应面。然后使用 ABAQUS 对 RSM 模型开发中未使用的案例的结果验证开发的 RSM 模型的准确性。一旦认为 RSM 模型令人满意，就建立了用于评估表面 PGA 平均值和标准偏差的基于可靠性的公式。提供了一个例子来说明面对输入参数不确定性的动态场地响应分析的 RSM 方法。一旦认为 RSM 模型令人满意，就建立了用于评估表面 PGA 平均值和标准偏差的基于可靠性的公式。提供了一个例子来说明面对输入参数不确定性的动态场地响应分析的 RSM 方法。一旦认为 RSM 模型令人满意，就建立了用于评估表面 PGA 平均值和标准偏差的基于可靠性的公式。提供了一个例子来说明面对输入参数不确定性的动态场地响应分析的 RSM 方法。