Penetration of Multi-Components De-icing Salts in Non-Saturated Concrete

在土木工程和结构工程中有许多实际问题可以用不同复杂程度的扩散方程来数学表征。除冰盐在混凝土结构中的渗透就是一个典型的例子。建议开发一个计算模型，将提供准确的长期预测多组分离子和水分渗透到大型混凝土结构。建立了一套完整的多组分输运过程的控制方程。考虑了离子之间、水分扩散与离子扩散之间以及离子与混凝土孔表面之间的耦合效应。将开发控制方程中所涉及的材料参数的多尺度模型。在细观尺度下的有效材料参数将基于微观结构的组成相来确定。具体的努力将被用来确定传输参数，使用高阶相关函数的数学形态学捕捉的多相微观结构的混凝土的空间分布的统计特征。将对混凝土中的渗透过程进行统计分析。将开发求解随机输运方程的数值算法，其中材料参数、初始条件和边界条件被认为是随机的。采用有限元模拟技术分析多组分除冰盐在大型混凝土结构中的渗透。本计画将提供数种数学形态学与统计分析的新方法。研究结果可以很容易地纳入结构分析程序，以模拟钢筋混凝土结构的长期性能，可用于大学，公共机构和私人公司的设计，施工，维护，管理和研究的公路和道路系统。这将有助于提高基础设施维护和管理的质量和效率。该项目还为土木工程专业的学生提供了一个独特的机会，学习数学系的分析和数值方法。另一方面，数学和统计学的学生将有机会将他们的知识应用于一个非常重要的实际问题，并对我国基础设施的运营和管理过程有一定的了解。来自科学和工程专业的研究生和本科生，特别是来自代表性不足群体的学生将被雇用参加拟议的工作。

There are many practical problems in civil engineering and structural engineering that can be mathematically characterized by diffusion equations of different degrees of complexity. Penetration of de-icing salts in concrete structures is a typical example. It is proposed to develop a computational model that will provide accurate long-term prediction for multi-components ionic and moisture penetrations into large-scale concrete structures. A complete set of governing equations for the multi-components transport processes will be established. Coupling effects between the ions, between moisture diffusion and ion diffusion, and between ions and the pore surfaces of concrete will be considered. Multi-scale models for the material parameters involved in the governing equations will be developed. The effective material parameters at meso-scale will be determined based on the constituent phases of the microstructure. Specific effort will be made to determine the transport parameters using high order correlation functions of mathematical morphology which capture statistical feature of spatial distribution of the multi-phase microstructure of concrete. Statistical analysis for the penetration processes in concrete will be performed. Numerical algorithms for solving the stochastic transport equations will be developed, in which the material parameters, initial condition, and boundary conditions are considered random. Finite element simulation techniques will be employed to analyze the penetration of multi-components de-icing salts in large-scale concrete structures. This project will provide several new methods in mathematical morphology and statistical analysis. The research findings can be readily incorporated into structural analysis programs to simulate long-term performance of reinforced concrete structures, which can be utilized by universities, public agencies and private companies for design, construction, maintenance, management, and research of highway and roadway systems. It will help to improve quality and efficiency of infrastructure maintenance and management. This project also provides a unique opportunity for the students in civil engineering to study analytical and numerical methods from the mathematics department. On the other hand, the students in mathematics and statistics will have an opportunity to apply their knowledge in a very important practical problem and have some insight on the operation and management process of our nation's infrastructure. Both graduate and undergraduate students from science and engineering majors, particularly students from underrepresented groups will be hired to participate on the proposed work.