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

Qi Meng,Lin-Hua Jiang,Chun-Jin Lin,Da Chen,Yan Zhang

doi:10.1155/2018/8085954

Qi Meng, Lin-Hua Jiang + Show 3 more

Open Access

https://doi.org/10.1155/2018/8085954

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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.

Highlights

It is well known that concrete structures exposed to the chloride environment, e.g., seawater and deicing salts, might be seriously damaged due to the chloride-induced corrosion of internal steel
Chemical/physical chloride binding by the hydration products reduces the free chloride concentration and retards the penetration of chloride to the level of the steel [23,24,25]. e discussion between free chloride and total chloride that which one can be responsible for the corrosion initiation is still existing [26,27,28,29]. us, free chloride is more used to evaluate the corrosion risk of reinforce concrete, while total chloride is collected and analyzed as a reference
(3) Compared with the traditional chloride transport model with the Dirichlet boundary condition, higher diffusion coefficient and surface chloride content are obtained by the Neumann boundary condition, which causes the penetration speed of chloride obtained from the proposed model with the Neumann boundary condition to be faster

Summary

Introduction

It is well known that concrete structures exposed to the chloride environment, e.g., seawater and deicing salts, might be seriously damaged due to the chloride-induced corrosion of internal steel. E actual transport of chloride is normally defined as zC/zt Dapp∇2C, where Dapp is the apparent diffusion coefficient generally obtained by the curve fitting of free chloride concentration with Fick’s second law [12, 33,34,35]. With the Dirichlet boundary condition, the surface chloride concentration of concrete is prescribed as a given value, e.g., chloride concentration of the external chloride environment. The Dirichlet condition might not be accurate especially in the zone of severe changes In this type of zone, the distribution of chloride concentration varies drastically that one cannot determine the exact value. E present research is organized as follows: first, the differential equation of nonstable transport of chloride with two different boundary conditions is summarized. According to relevant experimental results, 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

Description of Chloride Transport with Two Boundary Conditions

Experimental Validation

Results and Discussion

Conclusions