Collaborative Research: A New Theory of 3D Particle Characterization

土壤等颗粒状材料在自然界中普遍存在，并广泛用作土木基础设施的工程材料（例如水坝，防洪堤，公路和铁路）。三维颗粒几何是从根本上了解颗粒材料在静态和动态载荷下的行为的关键信息。三维粒子几何由体积、表面积、大小和形状四个特征来表征，只有通过这四个特征之间的相互关系才能充分理解三维几何的特征。例如，对于随机矿物颗粒的体积与表面积之间的关系，人们的理解有限。这种关系显然也取决于粒子的形状（例如，具有相同体积的球体和椭球具有不同的表面积）。因此，这些特征之间的关系是全面解决三维粒子几何的四维方面的关键，这将使人们能够从根本上了解它们对颗粒材料行为的综合影响，并有助于更好地设计民用基础设施，以抵御地震等自然灾害。此外，该项目将通过与研究活动紧密结合，并利用3D打印和扫描技术的最新进展，开发本科课程的教育模块。研究小组将把教育模块纳入现有的岩土工程和材料工程本科课程。这一教育努力将为颗粒材料领域的知识发现、教与学的成功整合提供一种新的模式。该项目将基于一个新的、简单的公式开发一种新的理论，用于全面的3D粒子几何表征，该公式与定义3D粒子几何的参数相关。该公式通过将三维粒子形态表示为表面积、体积和大小的函数，揭示了四个粒子几何参数之间纠缠在一起的关系。该研究提出了三个研究假设来逐步检验这一新理论。该研究将(i)使用所研究的公式表征单个颗粒，（ii）表征颗粒群（即颗粒材料）与表面积和体积之间的幂律关系，以及（iii）进行测试，以调查使用新方法表征的几何信息与颗粒材料的各种机械性能之间的关系，包括膨胀率和强度。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

Granular materials such as soils are prevalent in nature and broadly used as engineering materials for civil infrastructure (e.g., in dams, levees, roads and railways). 3D particle geometry is a key piece of information to fundamentally understand the granular material behavior subjected to static and dynamic loadings. While the 3D particle geometry is characterized in terms of four features, i.e., volume, surface area, size and shape, the characteristics of the 3D geometry can only be fully understood through the interrelationships of these four features. For example, there is limited understanding of how volume is related to surface area for random mineral particles. This relationship clearly depends on the particle shape as well (e.g., a sphere and an ellipsoid with the same volume have different surface areas). The relationship between these features is therefore key to comprehensively address the four-dimensional aspects of 3D particle geometry, which will enable the fundamental understanding of their combined influence on the behavior of granular materials and will help to better design civil infrastructure against natural hazards such as earthquakes. In addition, this project will develop educational modules for undergraduate classes by closely integrating with the research activities and by using recent advances in 3D printing and scanning technologies. The research team will incorporate the education modules into existing undergraduate level courses in geotechnical and materials engineering. This educational effort will provide a new model for successfully integrating knowledge discovery, teaching and learning in the area of granular materials.This project will develop a new theory for comprehensive 3D particle geometry characterization based on a new, simple formula that correlates the parameters defining the 3D particle geometry. This formula unravels the intertwined relationships between the four particle geometry parameters by expressing the 3D particle morphology as a function of surface area, volume and size. The study develops three research hypotheses to test the new theory step-by-step. The research will (i) characterize individual particles using the researched formula, (ii) characterize particle groups (i.e., granular material) in association with a power law relationship between the surface area and volume, and (iii) perform testing to investigate the relationship between the characterized geometric information using the new approach and various mechanical properties of granular materials, including dilatancy and strength.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.