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摘 要
随着国家“海洋强国”战略的实施及海洋资源的不断开发，海上混凝土结构不断被兴建，严酷的服役条件对海上混凝土结构的耐久性和可靠性提出了更高的要求。混凝土等水泥基材料的宏观耐久性能与其微细观尺度结构特征密切相关，水泥基材料从流塑状态转变为凝结硬化状态主要归因于水泥浆体的水化反应，在此过程中，材料内部形成高度异质的微细观结构，直接决定了其宏观传输性能。传统的试验测试方法难以全面表征水泥浆体水化过程中微结构的演化以及服役过程中时变微结构引起的扩散性能变化，难以满足现代水泥基材料的研究和发展需求。因此，亟需开展更加先进的微观X射线计算机断层扫描（µXCT）实验，开发更加高效的数值模拟方法，以精确模拟和预测水泥浆体微观结构及传输性能的演化，从本质上把握其微观结构与传输性能间的内在关系。
本文围绕水泥浆体的水化及氯离子扩散模拟问题，开发了基于真实颗粒的水泥浆体微观结构精细化建模方法，开展了水泥浆体水化的µXCT扫描实验，并进一步提出了基于真实颗粒随机堆积结构和µXCT图像的连续水化模型及水泥浆体中氯离子扩散的多相格子Boltzmann模型。全文主要内容如下：
（1）三维颗粒形态多尺度表征和可控重构算法开发
基于μXCT图像，结合球谐函数和随机场理论，提出一种三维颗粒形态多尺度表征和可控重构算法。首先，对从μXCT图像中提取的635个三维真实颗粒的伸长度、扁度、凸度、球度、圆度和粗糙度进行了定量表征和统计分析，并建立了交互式“颗粒数据库”。随后，利用球谐函数将上述颗粒解析表示为连续极半径函数，并进一步将其分解为粗尺度、中尺度和细尺度的半径场，以捕捉不同尺度的颗粒形态特征。从分解的半径场中提取均值、标准差和自相关函数，通过随机场重构生成与真实颗粒具有相同统计信息的随机重构颗粒。通过定量对比真实颗粒和随机重构颗粒的形态指标，验证了所提出重构算法的有效性。
（2）基于真实颗粒的水泥浆体及混凝土精细化建模方法开发
基于从μXCT图像中提取的真实颗粒和动态物理引擎（Physics engine），分别提出了微观水泥浆体及细观混凝土的精细化建模方法。通过设定单向压实过程中水泥颗粒的碰撞边界，有效模拟水泥颗粒在水溶液中的分散悬浮结构，从而生成微观水泥浆体模型；此外，通过精确模拟混凝土浇筑过程中的振捣压实过程，从而生成满足设计级配、骨料分布更加均匀且体积分数更高的细观混凝土模型。
（3）基于真实颗粒的水泥浆体连续水化模型开发
基于内容（2）中生成的水泥浆体微观模型，建立了考虑复杂真实水泥颗粒形态的连续水化模型。通过球谐函数对真实水泥颗粒形态进行解析化表征，利用其球谐系数推导水泥颗粒的水化动力学方程，以及考虑温度、水灰比及不同尺寸颗粒间相互影响的水化速率控制方程。利用所开发的连续水化模型对水泥浆体水化过程中的微观结构演化进行模拟，揭示了不同养护温度和水灰比对水泥浆体整体微观结构、水化度、孔隙率和孔隙结构的影响机制。
（4）水泥浆体水化的μXCT扫描实验及基于图像的水化模拟
针对水灰比分别为0.4和0.6的两个水泥浆体试样，从水化1天到28天共进行7次连续µXCT扫描观测。通过对三维µXCT图像的处理和统计分析，探究了水泥浆体的微观结构演化过程。随后，结合内容（3）中开发的连续水化模型，将从首次扫描得到的μXCT图像中提取的未水化水泥颗粒作为模型输入，进一步建立了基于μXCT图像的连续水化模型。利用该模型对两个水泥浆体试样的水化过程进行了模拟，通过将模拟结果与μXCT图像序列在整体微观结构、水化度、孔隙率和孔隙结构方面进行直接对比，验证了模型的正确性。
（5）基于µXCT图像的水泥浆体氯离子扩散模拟
基于内容（4）中μXCT扫描实验获取的真实水泥浆体微观结构，建立了基于格子Boltzmann方法的水泥浆体多相氯离子扩散模型。利用该模型首先对固定浓度差下三维饱和通道中的氯离子扩散及包含并联、串联双扩散相介质中的氯离子扩散进行了模拟，模拟结果与解析解吻合良好，验证了模型的正确性。随后，考虑C-S-H凝胶内部氯离子扩散及双电层效应的影响，进一步模拟了水泥浆体中的氯离子扩散过程，揭示了C-S-H凝胶相对水泥浆体氯离子扩散系数的影响机制，以及水泥浆体氯离子扩散系数随其时变孔隙结构的变化规律。
关键词：水泥浆体；微观X射线计算断层扫描；水化模型；微观结构；氯离子扩散
ABSTRACT
With the proposal of the national strategy of "Maritime Power" and the continuous exploration and development of marine resources, marine concrete structures are continuously built, and the severe service conditions put forward higher requirements for the durability and reliability of the marine concrete structures. The macroscopic durability properties of cementitious materials are closely related to their micro- and meso-scale structural characteristics. The transformation of cementitious materials, such as concrete, from a fluid-plastic state to a set-hardened state is mainly attributed to the hydration reaction of the cement paste, during which a highly heterogeneous microstructure is formed internally, which directly determines its macroscopic transport properties. Traditional experimental test methods cannot fully characterise the microstructural evolution of the cement pastes and the changes in diffusion properties caused by time-varying microstructures, which is difficult to meet the research and development of modern cement materials. Therefore, it is highly desirable to carry out more advanced micro X-ray computed tomography (µXCT) experiments and develop more efficient numerical simulation methods to accurately simulate and predict the evolution of the microstructure and transport properties of cement pastes, and to essentially grasp the intrinsic relationship between their microstructure and transport properties.
Motivated by the above aim, this study conducted numerical research for modelling of hydration and chloride ion diffusion in cement pastes. In this study, a refined method for modelling the microstructure of cement pastes and a continuous hydration model based on real particles are first developed, followed by in-situ µXCT experiments on the hydration of cement pastes, and furthermore a continuous hydration model based on µXCT images and a lattice Boltzmann simulation method for chloride diffusion are proposed. The main content of this research is concluded as:
(1) Multiscale characterisation and controlled random reconstruction of 3D particle morphology.
Based on the μXCT images, the multiscale characterisation and controlled reconstruction algorithm of 3D particle morphology is proposed by combining the spherical harmonic function and random field theory. Firstly, the elongation, flatness, convexity, sphericity, roundness and roughness of 635 real particles extracted from μXCT images are quantitatively characterised and statistically analysed, and an interactive "real particle database" is established. Subsequently, the real particles extracted from μXCT images are analytically represented as continuous polar radius functions using spherical harmonic functions, and decomposed into coarse-, medium- and fine-scale radius fields to capture the morphological features of different scales. The mean, standard deviation and autocorrelation functions are extracted from the decomposed radius fields, and then reconstructed by a random field to generate randomly reconstructed particles that have the same statistical information as the real particles. The effectiveness of the proposed reconstruction algorithm is verified by quantitatively comparing the morphological indices of real particles and randomly reconstructed particles.
(2) Refined microscale and mesoscale model generation method for cement paste and concrete based on real cement particles.
Based on the real particles extracted from μXCT images and the dynamic physics engine, the refined microscale and mesoscale model generation method for cement paste and concrete are proposed, respectively. Through the collision margin of cement particles in the packing process, the dispersed suspension structure of cement particles in water solution is simulated by the unidirectional compaction to generate the microscale cement paste model; in addition, the mesoscale concrete model which meets the design grading, with a more homogeneous distribution and a higher volume fraction of aggregates, is effectively generated by the simulation of the vibration and compaction procedures in the process of concrete casting.
(3) Continuous hydration model for cement paste with real particles.
Based on the microscale model of cement paste generated in (2), a continuous hydration model considering the complex morphology of real cement particles is developed. In this model, the morphology of real cement particles is analytically characterized by the spherical harmonic function, and its spherical harmonic coefficients are used to derive the hydration kinetic equations of cement particles, as well as the rate-controlling equations considering the effects of temperatures, water-to-cement ratios, and the interactions between cement particles of different sizes. The developed continuous hydration model is used to simulate the microstructural evolution of the cement paste during hydration, revealing the mechanisms of the effects of different curing temperatures and water-to-cement ratios on the overall microstructure, degree of hydration, porosity and pore structure of the cement paste.
(4) µXCT tests and image-based hydration simulation of cement hydration.
For two cement paste specimens with water-to-cement ratios of 0.4 and 0.6, respectively, a total of seven consecutive µXCT scanning observations are carried out from 1 to 28 days of hydration. The microstructural evolution of the cement pastes is explored through the processing and statistical analysis of the 3D µXCT images. Subsequently, a continuous hydration model based on µXCT images is further developed by combining the continuous hydration model developed in (3) with the unhydrated cement particles extracted from the first scanned µXCT images as model input. The hydration process of the two cement paste specimens is simulated using the developed model, and the simulation results are directly compared with the μXCT image sequences in terms of overall microstructure, hydration, porosity and pore structure to validate the model.
(5) μXCT image-based simulation of chloride diffusion in cement pastes.
A lattice Boltzmann method-based multiphase chloride ion diffusion model for cement paste is developed based on the microstructure of the cement paste obtained from the μXCT scanning test in (4). The diffusion of chloride ions in a three-dimensional saturated channel and a medium containing parallel and series double diffusive phases at a fixed concentration difference is simulated, and the simulation results are in good agreement with the analytical solution, which verifies the correctness of the model. Subsequently, the chloride diffusion inside the cement paste is simulated by considering the influence of chloride diffusion inside the C-S-H gel and the electrical double layer effect, and the simulated results reveal the influence of the C-S-H gel on the chloride diffusion coefficient of the cement paste and the evolution mechanism of the chloride diffusion coefficient with the time-varying pore structure.
Key words: Cement paste; Micro X-ray computed tomography; Hydration model; Microstructure; Chloride diffusion
