A three-phase model for predicting the effective chloride migration coefficient of ITZ in cement-based materials

Abstract

Specimens (water/cement ratio of 0 . 35) with various volume fractions (0, 0 . 1, 0 . 2, 0 . 3, 0 . 4 and 0 . 5) of fine aggregates were cast and tested to investigate the behaviour of the interfacial transition zone in mortar and the effect of the interfacial transition zone on the chloride migration coefficient. The double-inclusion method and Mori-Tanaka theory were used to predict the migration coefficient of three-phase composite materials, which are cement paste, interfacial transition zone and fine aggregate. There are two stages to calculate the overall migration coefficient of mortar. The first stage, the equivalent migration coefficient of fine aggregate and the interfacial transition zone, was calculated by Hori and Nemat-Nasser's double-inclusion model. The second stage, the equivalent migration coefficient, was used to calculate the overall migration coefficient of the mortar composite by Mori-Tanaka theory. A comparison was conducted between the theoretical and experimental data in this study. The results indicated that the migration coefficient of the interfacial transition zone is 1 . 5 to 10 times the migration coefficient of cement paste when an interfacial transition zone thickness of 20 to 30 ìm is assumed. NotationA specimen surface exposed to chloride ions (m 2 ) b experimental constant (mol/l) C chloride concentration (mol/l) C 0 initial chloride concentration in cathode cell (mol/l) E applied voltage (V) E Young's modulus of concrete F Faraday constant (F ¼ 96 500 J/(V mol)) k chloride migration rate (mol/(l s)) L thickness of specimen (m) M chloride migration coefficient (cm 2 /s) M a migration coefficient of fine aggregate (cm 2 /s) M c overall migration coefficient of the mortar composite (cm 2 /s) M e equivalent migration coefficient (cm 2 /s) M itz migration coefficient of interfacial transition zone (cm 2 /s) M m migration coefficient of cement paste (cm 2 /s) M s steady-state migration coefficient (cm 2 /s) R universal gas constant (R ¼ 8 . 314 J/(mol K)) S the component S 1111 of the Eshelby tensor for a single inclusion T absolute temperature (K) t elapsed time (h) V volume of solution in anodic cell (m 3 )

Prediction of chloride diffusion coefficients using multi-phase models

“…Figs. 10 and 11 show the detailed comparisons of the present analytical solutions with the numerical solutions obtained from the 2-D and 3-D models, and the experimental data obtained from the chloride migration tests in mortars (Yang and Weng 2013). It can be seen from the figures that in both the 2-D and 3-D cases the present predictions are in good agreement with the numerical data and/or experimental data.…”

“…Existing experimental data showed that the addition of aggregates and the corresponding ITZs generated surrounding the aggregates have significant influence on chloride penetration in concrete (Caré 2003, Delagrave et al 1997, Yang and Su 2002. To quantify the effect of aggregates and ITZs on the bulk diffusion coefficient of chloride ions in concrete, analytical and numerical prediction models have been developed by using the concepts of micro-scale and meso-scale modelling (Bentz and Garboczi 1991, Bourdette et al 1995, Byung and Seung 2004, Caré and Hervé 2004, Garboczi and Bentz 1997, Hobbs 1999, Shane et al 2000, Xi and Bazant 1999, Yang and Weng 2013, Ying et al 2013, Zheng et al 2012, Zheng and Zhou 2007. The popular analytical prediction models include the two-phase series and two-phase parallel models developed by Hobbs (Hobbs 1999), the two-phase spherical model developed by Xi and Bazant (Xi and Bazant 1999), and the n-phase spherical model developed by Caré and Hervé (Caré and Hervé 2004).…”

Aggregate Shape Effect on Multicomponent Ionic Electromigration in Concrete

“…For the cases of diffusion tests, the transport of ions in a saturated concrete is mainly driven by the concentration gradient of the species itself and can be described as Fick's first law, which is most utilised in the durability study of the cracked concrete (Abyaneh et al, 2013;Bentz & Garboczi, 1991;Bourdette et al, 1995;Caré, 2003;Caré & Hervé, 2004;Garboczi & Bentz, 1998;Jiang et al, 2013;Sun et al, 2011;Xiao et al, 2012;Yang & Weng, 2013;Ying et al, 2013;Zeng, 2007;Zheng et al, 2009Zheng et al, , 2012. When the electrostatic potential is involved such as in migration tests (Whiting, 1981;AASHTO T 277, 1983;ASTM C 1202ASTM C , 1994Tang & Nilsson, 1993a;NT-Build 492, 1999;AASHTO TP 64-03, 2003), the more significant driving force of ionic transport is the electrostatic potential gradient, in which case the flux of an ionic species can be expressed using the Nernst-Planck equation as follows:…”

“…Most of the existing multiphase models (Bentz & Garboczi, 1991;Bourdette et al, 1995;Caré, 2003;Caré & Hervé, 2004;Garboczi & Bentz, 1998;Jiang et al, 2013;Sun et al, 2011;Xiao et al, 2012;Yang & Weng, 2013;Ying et al, 2013;Zeng, 2007;Zheng et al, 2009) including previous work as well (Feng et al, 2016;Šavija et al, 2014), assumed circular or spherical aggregates for simplification. Figure 1 shows one of the 2-D concrete numerical models with the size of 50 mm × 50 mm.…”

“…As neither of the abovementioned method is appropriate to tackle the influences of individual components on chloride transport in concrete, finite element numerical models, originally developed for the stress analysis of concrete, have recently been applied to investigate the transport properties of concrete with multiple phases (Bentz & Garboczi, 1991;Bourdette, Ringot, & Ollivier, 1995;Caré, 2003;Caré & Hervé, 2004;Garboczi & Bentz, 1998;Jiang, Sun, & Wang, 2013;Li, Xia, & Lin, 2012;Sun, Zhang, Sun, Liu, & Wang, 2011;Xiao, Ying, & Shen, 2012;Yang & Weng, 2013;Ying, Xiao, Shen, & Bradford, 2013;Zeng, 2007;Zheng, Wong, & Buenfeld, 2009). By using this type of multiphase computational model, one can easily clarify and quantify the influence cause by different structure of concrete, i.e., inclusion aggregates, mortar/cement, and interfacial transition zones (ITZs), which cannot be fulfilled in 1-D analytical models.…”