Analytical Solution For Dual Time-dependent Chloride Diffusion In Concrete And Quantitative Durability Design Method Of Concrete Structure

In chloride environment,owing to effects associated with chloride ion ingress-induced diffusion etc.,the corrosion of steel reinforcement and the cracking of concrete cover result in the service life of the reinforced concrete structures cannot meet the design requirements.Therefore,it is an important prerequisite to analyze the chloride ion diffusion process accurately and develop the corresponding chloride ion diffusion model for the durability analysis and design of concrete structures.Analysis shows that the time-time-dependent of chloride diffusion coefficient and surface chloride concentration of concrete have important influence on the chloride ion diffusion process.In the meantime,the geometry of structures can also influence the chloride ion diffusion process and concentration accumulation of chloride ions in concrete.However,the accuracy and applicability of the existing analytical solution methods are limited,since them cannot take into account the comprehensive factors on the diffusion process and concentration distribution of chloride ions in concrete,including the time-dependent behavior of chloride diffusion coefficient and surface chloride concentration of concrete as weel as the geometry of structures,etc.The main objective of this study is to develop efficient and accurate analytical solutions for dual time-dependent chloride diffusion in rectangular cross section concrete and circular cross section concrete,which takes into account the time-dependent behavior of both surface chloride concentration of concrete and chloride diffusion coefficient.Then a quantitative durability design method of the concrete structure is proposed based on the analytical solutions for dual time-dependent chloride diffusion.The main contents are as follows:(1)The analytical dual time-dependent solutions for chloride diffusion in rectangular cross section concrete were developed,considering the time-dependent behavior of both surface chloride concentration of concrete and chloride diffusion coefficient.All of solving processes were based on the Fick's second law diffusion model in the three-dimensional Cartesian coordinate system and used variable substitution and the Duhamel's theorem.The proposed analytical solutions overcome the shortcomings of existing analytical solution methods that cannot take into account the comprehensive factors include the time-dependent behavior of chloride diffusion coefficient and surface chloride concentration of concrete,and the geometry of structures.By comparing the proposed analytical solutions with numerical analysis and field data,accuracy and applicability of the proposed analytical solutions were verified.Analytical results show that the time-dependent behavior of surface chloride concentration and chloride diffusion coefficient has a significant influence on chloride diffusion in concrete.Furthermore,the proposed analytical solutions are applicable for various kinds of time-dependent models of surface chloride concentration and multidimensional diffusion problems with high accuracy and efficiency.(2)The analytical dual time-dependent solutions for chloride diffusion in circular cross section concrete were developed,considering the time-dependent behavior of both chloride diffusion coefficient and surface chloride concentration of concrete.All of solving processes were based on the Fick's second law diffusion model in the three-dimensional cylindrical coordinate system and used variable substitution method,the separation variable method and the Duhamel's theorem.In contrast to numerical analysis,accuracy of the proposed analytical solutions were verified.Analysis results show that the proposed solutions are applicable for 2D and 3D diffusion analyse in circular cross section concrete as well as various kinds of time-dependent models of surface chloride concentration problems with high accuracy,which provide an effective way to analyze the chloride ions diffusion process in circular cross section concrete.(3)Based on the proposed analytical solutions for dual time-dependent chloride diffusion,the diffusion length compensation theory and the durability diffusion domain theory.The quantitative relationship between the design parameters of the durability of concrete structures and design life,critical chloride concentration,surface chloride concentration,thickness of the concrete cover is determined.A quantitative durability design method of the concrete structure is proposed,and the accuracy and adaptability of the method are verified by compare with the traditional durability design method.The proposed design method solves the problem that the traditional durability design method lacks of the quantitative durability design model and can not quantitatively calculate the defects of the durability design parameters.