Collaborative Research: Characterization of Random Fields and their Impact on the Mechanics of Geosystems at Multiple Scales

在本研究中，通过使用精确的多尺度分层计算框架获得地系统的力学响应，明确地解释了土壤行为的多尺度性质。众所周知，颗粒介质（如沙子）的行为是在颗粒尺度上进行编码的，因此，在相关的感兴趣的尺度上扩大这种行为的方法？从颗粒尺度（~1mm）到场尺度（1m）？是获得更准确的土壤行为预测所必需的。在应变局部化、渗透或液化等极端条件下，经典的本构描述可能不再适用，多尺度分析尤为重要。几个未解决的问题说明了研究这种现象的重要性：在不同的尺度上，什么材料参数化是最合适的？准确的材料描述需要哪些相关的尺度？不确定性和不均匀性对场尺度行为的影响是什么？需要一个跨多个尺度的概率框架来回答这些问题，并一致地计算材料跨尺度的行为。以前所未有的方式，在多个尺度上开发了土壤孔隙度的概率模型，使用x射线计算机断层扫描的实验结果来研究毫米尺度下的空间相关性。从计算的角度来看，使用成熟的砂土模型演示了多尺度框架。在这种分层方法中，更准确的材料描述？在更精细的尺度上？只有在强烈的非均质性存在时才被追求，这种非均质性要么是物质的，要么是强加的（如变形）。分层方法是基于将宏观变形传递到更精细的尺度，然后返回更精确的平均应力。蒙特卡罗模拟以分层方式生成材料属性，以便在需要时获得细尺度材料数据，前提是先前模拟的粗尺度数据。这些建模方法将被开发，然后在几个参数和验证研究中使用，以深入了解多尺度效应重要的实际问题。多尺度建模为开发具有理想质量或特性的设计特定工程系统打开了大门，并将使科学家和工程师更好地理解复杂岩土系统行为中更精细尺度的作用。

In this research, the multi-scale nature of soil behavior is explicitly accounted for by obtaining the mechanical response of geosystems using an accurate multi-scale hierarchical computational framework. It is well known that the behavior of particulate media, such as sands, is encoded at the granular-scale and hence methods for up-scaling such behavior across relevant scales of interest?from granular-scale (~1mm) to field-scale (1m)?are needed to attain a more accurate prediction of soil behavior. Multi-scale analysis is especially important under extreme conditions such as strain localization, penetration or liquefaction, where the classical constitutive description may no longer apply. Several unanswered questions illustrate the importance of studying such phenomena: What material parameterizations are most appropriate at various scales? What are the relevant scales needed for an accurate material description? What are the impacts of uncertainties and inhomogeneities on field-scale behavior? A probabilistic framework across multiple scales is needed to answer these questions and to consistently compute the behavior of the material across scales. In an unprecedented fashion, probabilistic models for soil porosity are developed at multiple scales, using experimental results from X-Ray computed tomography to study spatial correlation down to the millimeter scale. From a computational standpoint, the multi-scale framework is demonstrated using well-established models for sands. In this hierarchical approach, a more accurate material description?at finer scales?is pursued only in the presence of strong inhomogeneities, either material or imposed (e.g. by deformations). The hierarchical approach is based on passing the macroscopic deformation down to the finer scale(s) and then returning more accurate, averaged stresses. Monte Carlo simulation is used to generate material properties in a hierarchical manner, so that fine scale material data can be obtained whenever necessary, conditional upon previously simulated coarse scale data. These modeling approaches will be developed and then used in several parametric and validation studies to bring insight to practical problems where multi-scale effects are important. Multi-scale modeling opens the door to develop design-specific engineering systems with desirable qualities or properties, and will allow scientists and engineers to better understand the role of finer scales on the behavior of complex geotechnical systems.