The understanding of the diffusion process and mechanisms of harmful species (e.g. chlorides) in porous cementitious materials is important to control and improve the material durability under harsh environments. In this paper, fractal analysis on the pore structure of porous cementitious materials was conducted and involved in a diffusion model. Macro material geometric parameters were considered in the model to avoid the difficulties in the measurements of microscopic pore parameters. The deformations of porous cementitious materials under the uniaxial elastic loads were considered to correct the diffusion model. The stress-affected diffusivity was displayed in an elegant expression involving some macro material parameters (e.g. total porosity, elastic modulus of solid skeleton, Poisson ratio). Results show that the effective diffusivity is greatly influenced by the porosity and stress ratio. The uniaxial elastic loads decrease the pore areas but increase the lengths of the pore channels for mass diffusion, which eventually causes the decrease of the effective diffusivity. The plots of the relative diffusivity against the stress ratio follow linear forms. The developed fractal diffusion model may help better understand the diffusion process in complex porous cementitious materials under elastic loads. Going beyond this, the fractal diffusion model may provide a new tool to predict the diffusivity of porous building materials under complex mechanical and environmental loads.

中文翻译：

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多孔胶凝材料应力相关扩散的分形分析

了解多孔胶凝材料中有害物质（如氯化物）的扩散过程和机理对于控制和提高材料在恶劣环境下的耐久性很重要。在本文中，对多孔胶凝材料的孔隙结构进行了分形分析，并涉及扩散模型。模型中考虑了宏观材料几何参数，避免了微观孔隙参数测量的困难。考虑单轴弹性载荷作用下多孔胶凝材料的变形来修正扩散模型。应力影响的扩散率以一种涉及一些宏观材料参数（例如总孔隙率、固体骨架的弹性模量、泊松比）的优雅表达方式显示。结果表明，有效扩散率受孔隙率和应力比的影响很大。单轴弹性载荷减小了孔隙面积，但增加了用于质量扩散的孔隙通道长度，最终导致有效扩散率降低。相对扩散率与应力比的关系曲线遵循线性形式。所开发的分形扩散模型有助于更好地理解弹性载荷下复杂多孔胶凝材料的扩散过程。除此之外，分形扩散模型可以提供一种新的工具来预测多孔建筑材料在复杂的机械和环境载荷下的扩散率。最终导致有效扩散率降低。相对扩散率与应力比的关系曲线遵循线性形式。所开发的分形扩散模型有助于更好地理解弹性载荷下复杂多孔胶凝材料的扩散过程。除此之外，分形扩散模型可以提供一种新的工具来预测多孔建筑材料在复杂的机械和环境载荷下的扩散率。最终导致有效扩散率降低。相对扩散率与应力比的关系曲线遵循线性形式。所开发的分形扩散模型有助于更好地理解弹性载荷下复杂多孔胶凝材料的扩散过程。除此之外，分形扩散模型可以提供一种新的工具来预测多孔建筑材料在复杂的机械和环境载荷下的扩散率。