2018•Advances in Materials Science and EngineeringOpen access

Modeling of Chloride Distribution in Cement‐Based Materials with Neumann Boundary Condition

Qi Meng, Yan Zhang, Chunjin Lin, Linhua Jiang, Da Chen

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Abstract

The nonstable transport of chloride in cement‐based materials, including diffusion, convection, and chloride binding, is described as a general form of Fick’s law. Inspired by the heat transport of concrete, the second boundary condition called the Neumann boundary condition is considered in the chloride transport of concrete. The theoretical deduction of one‐dimensional chloride distribution with the Neumann boundary condition is performed, while a virtual boundary is introduced to carry out the approximate treatment. Finally, the comparison between the general Dirichlet boundary condition and the present Neumann boundary condition and the influence of the thickness of the virtual boundary as well as the influence of the water‐cement ratio (w/c) are discussed.

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The nonstable transport of chloride in cement‐based materials, including diffusion, convection, and chloride binding, is described as a general form of Fick’s law. Inspired by the heat transport of concrete, the second boundary condition called the Neumann boundary condition is considered in the chloride transport of concrete. The theoretical deduction of one‐dimensional chloride distribution with the Neumann boundary condition is performed, while a virtual boundary is introduced to carry out the approximate treatment. Finally, the comparison between the general Dirichlet boundary condition and the present Neumann boundary condition and the influence of the thickness of the virtual boundary as well as the influence of the water‐cement ratio (w/c) are discussed.

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Available abstract

The nonstable transport of chloride in cement‐based materials, including diffusion, convection, and chloride binding, is described as a general form of Fick’s law. Inspired by the heat transport of concrete, the second boundary condition called the Neumann boundary condition is considered in the chloride transport of concrete. The theoretical deduction of one‐dimensional chloride distribution with the Neumann boundary condition is performed, while a virtual boundary is introduced to carry out the approximate treatment. Finally, the comparison between the general Dirichlet boundary condition and the present Neumann boundary condition and the influence of the thickness of the virtual boundary as well as the influence of the water‐cement ratio (w/c) are discussed.

Key concepts: Neumann boundary condition, Chloride, Boundary value problem, Robin boundary condition, Materials science, Cauchy boundary condition, Boundary (topology), Mixed boundary condition

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