Collaborative Research: Stochastic Nonlinear Dynamic Simulation for Prediction of Seismic Ground Motion

现有的预测地震地面运动及其相关不确定性的方法主要依赖于拟合已知地震和场地特征的记录运动（通常在地表）。然而，将这种获得的概率地震动应用于岩土工程问题，如自由场概率场地响应分析或概率土-结构相互作用分析，双重计算了土壤介质的不确定性和非线性。该项目的目标是开发一种新的基于物理的方法和相应的计算工具，通过(1)描述和量化未来地震事件中某一地点基岩运动的不确定性（右侧（RHS）不确定性），获得未来地震事件特定地点地面运动时程的完整概率描述（概率密度函数）；(2)表征和量化场地特定土壤性质的不确定性（左方（LHS）不确定性）；(3)在不确定土壤中传播不确定的基岩运动。获得特定地点地面运动时间历史的这种概率描述的能力不仅有助于准确评估任何民用基础设施对象的性能，而且有助于项目所有者、政策制定者和保险机构的关键决策过程。例如，如果预测的地面运动太不确定，那么项目所有者可能会问以下问题：可以采取什么步骤来减少这种不确定性？在回答这个问题时，还将演示评估RHS（源和路径）和LHS（土壤性质）不确定性参数对地震运动总体不确定性的相对贡献的过程。这将有助于项目所有者调动资源，以增加对不确定性的最重要贡献者的理解(来源？网站吗?路径？)，降低了知识的不确定性，进而降低了整体地震动的不确定性。此外，建议发展理论能力，通过力学控制方程系统地传播不同的不确定性来源，这将大大有利于经验建模界开发衰减模型，特别是针对数据有限或没有数据的地区（例如，美国东部）。即使对于美国西部，它也将有助于实证建模者更好地约束他们的模型。此外，所提出的技术还将为理解地面运动的空间变化及其相关的不确定性（协方差结构）提供见解，这是研究界重新关注的问题，特别是由于它们对生命线结构的抗震性能的影响。该项目将结合最先进的随机微积分和力学原理，开发一个基于有限元的随机计算框架，以在随机非线性非均质介质中传播随机波。据我们所知，这是第一次尝试在考虑LHS和RHS不确定性的随机空间中模拟波在非线性（弹塑性）非均质介质中的传播。由于材料特性和外力的不确定性存在于所有工程领域，因此本项目的影响将远远超出岩土工程领域。为了确保该项目的未来发展，高中科学和数学教师将通过暑期研讨会（通过RET补充）参与其中，以便他们将自己的经验传授给高中课堂。这里的目的是强调数学和物理在模拟物理现象（如地震）中的重要性，并在未来的工程师中播下早期的种子，以寻求在该领域的职业生涯。

Existing approaches for prediction of seismic ground motion and its associated uncertainties mostly rely on fitting to a recorded motion (usually at the surface) with known earthquake and site characteristics. However, application of such obtained probabilistic ground motion to geotechnical engineering problems, such as free-field probabilistic site response analysis or probabilistic soil-structure interaction analysis, double counts the uncertainties and non-linearities of the soil medium. The goal of this project is to develop a new, physics-based methodology and an attendant computational tool to obtain a complete probabilistic description (probability density function) of site-specific ground motion time-history for a future seismic event by (1) characterizing and quantifying uncertainties in bed-rock motion at a site during future seismic event (right hand side (RHS) uncertainty), (2) characterizing and quantifying uncertainties in site-specific soil properties (left hand side (LHS) uncertainty), and (3) propagating the uncertain bed-rock motion through the uncertain soil. The ability to obtain such probabilistic description of site-specific ground motion time history will not only help in accurately assessing performance of any civil infrastructure object, but also help in critical decision-making process by the project owners, policy makers, and insurance agencies. For example, if the predicted ground motion is too uncertain, then the project owner may ask the following question: what step can be taken to reduce that uncertainty? In answering that question, a process for evaluating the relative contributions of RHS (source and path) and LHS (soil properties) uncertain parameters to overall uncertainty in seismic motions will be demonstrated as well. This will assist the project owners in mobilizing resources for increase understanding of the most significant contributor of uncertainty (source? site? path?), reduce the knowledge uncertainty, and subsequently reduce the overall ground motion uncertainty. In addition, the proposed development of theoretical capability to systematically propagate different sources of uncertainties through the governing equation of mechanics will greatly benefit the empirical modeling community in developing attenuation models especially for the regions where there are limited or no data (for example, eastern United States). Even for western United States, it will help the empirical modelers in better constraining their models. Further, the proposed technique will also provide insight in understanding spatial variation of ground motion and its associated uncertainties (covariance structure), which are under renewed interest in the research community, especially due to their effects on seismic performances of lifeline structures. This project will combine the state-of-the-art stochastic calculus with the principles of mechanics in developing a finite element based stochastic computational framework to propagate random waves through random non--linear heterogeneous media. It, to best of our knowledge, is the first attempt to simulate wave propagation through nonlinear (elastic--plastic) heterogeneous medium in the stochastic space considering both LHS and RHS uncertainties. Since uncertainties in material properties and external forces are present in all fields of engineering, the impact of this project will be much wider than just in the area of geotechnical engineering. In order to ensure future of developments from this project, high school science and mathematics teachers will be involved (via RET supplement) through summer workshops so that they can transmit their experiences to high school classrooms. The objective here is to emphasize the importance of mathematics and physics in modeling physical phenomena such as earthquake and plant an early seed among the future engineers to seek a career in this field.