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基于非局部结构导数的水化过程分析中的应用

Study on the Hydration Process of Fresh Cement Paste based on the Non-local Structural Derivative

  • 摘要: 新拌水泥浆体(Fresh Cement Paste,FCP)广泛应用于建筑工程及3D打印等领域,其性能优化对提升建筑结构的施工质量与耐久性具有重要意义。然而,目前针对水泥浆体早期水化过程中颗粒扩散行为的动力学建模仍较为缺乏,亟需发展新的理论工具以揭示其复杂演化机制。本研究基于Riemann-Liouville型非局部结构导数理论,建立了一种能够准确表征新拌水泥浆体水化过程的特快扩散模型。采用有限差分法得到模型的数值解,其对应的均方位移(MSD)可以看作结构函数的积分形式。为了验证模型的准确性,选用Mittag-Leffler函数作为结构函数,结合非线性最小二乘法拟合FCP水化过程中0 s~8 s和0 s~18 s的MSD实验数据,并与分形导数反常扩散模型和以指数函数为结构函数的非局部结构导数模型进行对比分析。结果表明,非局部结构导数特快扩散模型能够更精准有效地模拟水泥颗粒的特快扩散行为。该模型为深入理解FCP在早期水化过程中的黏弹性演变微观机制提供了新的理论视角,也为混凝土材料性能的预测与过程控制提供了有效的数学工具,具有重要的理论价值与工程应用前景。

     

    Abstract: Fresh cement paste (FCP) is widely used in construction engineering and 3D printing. Optimizing its performance is crucial for improving the construction quality and durability of building structures. However, there is still a lack of kinetic models for the particle diffusion behavior during the early hydration process of cement paste, necessitating the development of new theoretical tools to reveal its complex evolution mechanisms. This study establishes an ultrafast diffusion model based on the Riemann-Liouville non-local structural derivative theory to accurately characterize the hydration process of FCP. The numerical solution of the model is obtained using the finite difference method, and the corresponding mean square displacement (MSD) can be regarded as an integral form of the structural function. To validate the model, the Mittag-Leffler function is selected as the structural function, and nonlinear least-squares fitting is applied to the experimental MSD data of FCP hydration from 0 s~8 s and 0 s~18 s. A comparative analysis is conducted with the fractal derivative anomalous diffusion model and the non-local structural derivative model employing an exponential structural function. The results demonstrate that the non-local structural derivative ultrafast diffusion model can more accurately and effectively simulate the ultrafast diffusion behavior of cement particles. The model provides a new theoretical perspective for understanding the micromechanisms of viscoelastic evolution during the early hydration of FCP, as well as an effective mathematical tool for predicting and controlling the performance of concrete materials, showing significant theoretical value and engineering application prospects.

     

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