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描述。除冰盐在混凝土结构中的渗透就是一个典型的例子。建议开发一种计算模型，为多组分离子和水分渗透到大型混凝土结构中提供准确的长期预测。将建立一套完整的多组分运输过程的控制方程。将考虑离子之间、水分扩散和离子扩散之间以及离子与混凝土孔表面之间的耦合效应。将建立控制方程中所涉及的材料参数的多尺度模型。细观尺度上的有效材料参数将基于微观结构的组成相来确定。利用数学形态学的高阶相关函数，捕捉混凝土多相微结构空间分布的统计特征，确定输运参数。将对混凝土的渗透过程进行统计分析。在考虑材料参数、初始条件和边界条件随机的情况下，发展了求解随机输运方程的数值算法。采用有限元模拟技术对多组分除冰盐在大型混凝土结构中的渗透进行了分析。该项目将在数学形态学和统计分析方面提供几种新的方法。研究成果可以很容易地整合到结构分析程序中，以模拟钢筋混凝土结构的长期性能，可供大学、公共机构和私营公司用于公路和道路系统的设计、施工、维护、管理和研究。这将有助于提高基础设施维护和管理的质量和效率。该项目也为土木工程专业的学生提供了一个从数学系学习分析和数值方法的独特机会。另一方面，数学和统计专业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行和管理过程有一些见解。来自理工科专业的研究生和本科生，特别是来自代表人数不足的群体的学生，都将被聘请参与拟议的工作。

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.