Analytical solution and experimental validation for dual time-dependent chloride diffusion in concrete LuFeng Yang a , Qian Ma b , Bo Yu c,⇑ a Key Laboratory of Disaster Prevention and Structural Safety of China Ministry of Education, Guangxi University, Nanning 530004, China b School of Civil Engineering & Architecture, Guangxi University, Nanning 530004, China c Key Laboratory of Disaster Prevention and Structural Safety of China Ministry of Education, Guangxi Key Laboratory of Disaster Prevention and Engineering Safety, School of Civil Engineering and Architecture, Guangxi University, Nanning 530004, China highlights  A new analytical solution was developed for dual time-dependent chloride diffusion in concrete.  Influences of time-dependent behaviour of D and C s were investigated.  The proposed solution is applicable for various time-dependent models of surface chloride concentration with high accuracy. article info Article history: Received 29 April 2017 Received in revised form 6 October 2017 Accepted 30 November 2017 Keywords: Concrete Dual time-dependent diffusion Surface chloride concentration Chloride diffusion coefficient Analytical solution abstract An analytical solution for dual time-dependent chloride diffusion within concrete was developed by tak- ing into account the time-dependent behaviour of both surface chloride concentration and chloride dif- fusion coefficient. Firstly, the time-varying chloride diffusion coefficient was transformed into a constant one by introducing the equivalent diffusion time. Then an analytical solution for dual time-dependent chloride diffusion within concrete was presented based on the Duhamel’s theorem. Finally, the accuracy and applicability of the proposed analytical solution were validated by comparing with field data, exist- ing approximate analytical solutions and numerical results from finite element analysis. Analysis results show that the influence of time-dependent behaviour of chloride diffusion coefficient on the chloride concentration distribution within concrete is much larger than that of surface chloride concentration. Furthermore, the proposed solution is applicable for various kinds of (such as square-root, exponential, logarithmic and power-law, etc.) time-varying models of surface chloride concentration with high accuracy. Ó 2017 Elsevier Ltd. All rights reserved. 1. Introduction It has been widely recognized that chloride diffusion coefficient and surface chloride concentration of concrete are two important parameters for describing the diffusion process and concentration distribution of chloride ion within concrete. During the early per- iod, the analytical solution for the Fick’s second law of diffusion has been proposed by taking both the chloride diffusion coefficient and surface chloride concentration as constants [1], which is referred to as the analytical solution with dual constant parame- ters (ASDC). The ASDC is simple to implement and has been widely used in service life prediction [2,3] and durability analysis [4–6] of concrete structures. However, it was observed that the chloride diffusion coefficient usually decreases with the exposure period of concrete structure due to the hydration process of cement paste [7–9]. Based on this phenomenon, Mangat and Molloy [8], Maage et al. [9], DuraCrete [10] and Tang et al. [11] proposed several types of analytical solutions for chloride diffusion with time-varying chloride diffusion coefficient. However, above solutions ignore the time-dependent behaviour of surface chloride concentration of concrete (C s ). Due to the influences of material properties and environmental conditions of concrete structure, C s also exhibits obvious time-dependent behaviour. Several types of time-varying models including linear [12,13], square root [13,14], power-law [15], logarithmic [16,17] and exponential [18] functions have been adopted to describe the time-dependent behaviour of surface chlo- ride concentration. Moreover, Kassir et al. [18] proposed an analyt- ical solution for chlorine diffusion in concrete with time-varying https://doi.org/10.1016/j.conbuildmat.2017.11.176 0950-0618/Ó 2017 Elsevier Ltd. All rights reserved. ⇑ Corresponding author. E-mail addresses: lfyang@gxu.edu.cn (L.F. Yang), Ma_Qian@tju.edu.cn (Q. Ma), gxuyubo@gxu.edu.cn (B. Yu). Construction and Building Materials 161 (2018) 676–686 Contents lists available at ScienceDirect Construction and Building Materials journal homepage: www.elsevier.com/locate/conbuildmat