Estimation of Chloride Diffusivity in Hydrated Tricalcium Silicate Using a Hydration-Diffusion Integrated Method

Abstract

This study aims to develop a chloride diffusion simulation method that considers the hydration microstructure and pore solution properties during the hydration of tricalcium silicate (C₃S). The method combines the hydration simulation, thermodynamic calculation, and finite element analysis to examine the effects of pore solution, including effect of electrochemical potential, effect of chemical activity, and effect of mechanical interactions between ions, on the chloride effective diffusion coefficient of hydrated C₃S paste. The results indicate that the effect of electrochemical potential on chloride diffusion becomes stronger with increasing hydration age due to the increase in the content of hydrated calcium silicate; as the hydration age increases, the effect of chemical activity on chloride diffusion weakens when the number of diffusible elements decreases; the effect of mechanical interactions between ions on chloride diffusion decreases with the increase of hydration age.

References

[1] Touil B, Ghomari F, Khelidj A, et al.. Durability Assessment of the Oldest Concrete Structure in the Mediterranean Coastline: The Ghazaouet Harbour[J]. Marine Structures, 2022, 81: 103 121

[2] Kim J S, Chung S Y, Han T S, et al.. Correlation Between Microstructural Characteristics From Micro-CT of Foamed Concrete and Mechanical Behaviors Evaluated by Experiments and Simulations[J]. Cement and Concrete Composites, 2020, 112: 103 657

[3] Geng Z, She W, Zuo W, et al.. Layer-interface Properties in 3D Printed Concrete: Dual Hierarchical Structure and Micromechanical Characterization[J]. Cement and Concrete Research, 2020, 138: 106 220

[4] Ji Y S. Performance and Prediction of Reinforced Concrete in Full Service Life Due to Corrosion Damage Firsted, 2011, Beijing, China Railway Publishing House

[5] Patel R A, Phung Q T, Seetharam S C, et al.. Diffusivity of Saturated Ordinary Portland Cement-based Materials: A Critical Review of Experimental and Analytical Modelling Approaches[J]. Cement and Concrete Research, 2016, 90: 52-72

[6] Bourbatache K, Millet O, Aït-Mokhtar A, et al.. Modeling the Chlorides Transport in Cementitious Materials by Periodic Homogenization[J]. Transport in Porous Media, 2012, 94(1): 437-459

[7] Bourbatache K, Millet O, Aït-Mokhtar A. Ionic Transfer in Charged Porous Media. Periodic Homogenization and Parametric Study on 2D Microstructures[J]. International Journal of Heat and Mass Transfer, 2012, 55(21): 5 979-5 991

[8] Patel R A, Perko J, Jacques D, et al.. Effective Diffusivity of Cement Pastes From Virtual Microstructures: Role of Gel Porosity and Capillary Pore Percolation[J]. Construction and Building Materials, 2018, 165: 833-845

[9] Carrara P, De Lorenzis L, Bentz D P. Chloride Diffusivity in Hardened Cement Paste From Microscale Analyses and Accounting for Binding Effects[J]. Modelling and Simulation in Materials Science and Engineering, 2016, 24(6): 065 009

[10] Liu C, Zhang M Z. Effect of Curing Temperature on Hydration, Microstructure and Ionic Diffusivity of Fly Ash Blended Cement Paste: A Modelling Study[J]. Construction and Building Materials, 2021, 297: 123 834

[11] Liu L, Tao G H, Chen H S, et al.. Shape Effect of Cement Particles on the Ionic Diffusivity of Hardened Cement Paste—a Three-Dimensional Numerical Investigation[J]. Construction and Building Materials, 2020, 250: 118 736

[12] Tang L. Concentration Dependence of Diffusion and Migration of Chloride Ions: Part 1. Theoretical Considerations[J]. Cement and Concrete Research, 1999, 29(9): 1 463-1 468

[13] Tang L. Concentration Dependence of Diffusion and Migration of Chloride Ions: Part 2. Experimental Evaluations[J]. Cement and Concrete Research, 1999, 29(9): 1 469-1 474

[14] Chatterji S. Transportation of Ions Through Cement Based Materials. Part 3 Experimental Evidence for the Basic Equations and Some Important Deductions[J]. Cement and Concrete Research, 1994, 24(7): 1 229-1 236

[15] Johannesson B, Yamada K, Nilsson L O, et al.. Multi-Species Ionic Diffusion in Concrete with Account to Interaction between Ions in the Pore Solution and the Cement Hydrates[J]. Materials and Structures, 2007, 40(7): 651-665

[16] Zhang Y, Luzio G D, Alnaggar M. Coupled Multi-Physics Simulation of Chloride Diffusion in Saturated and Unsaturated Concrete[J]. Construction and Building Materials, 2021, 292: 123 394

[17] Sáez del Bosque I F, Martínez-Ramírez S, Blanco-Varela M T. FTIR Study of the Effect of Temperature and Nanosilica on the Nano Structure of C–S–H gel Formed by Hydrating Tricalcium Silicate[J]. Construction and Building Materials, 2014, 52: 314-323

[18] Thomas J J. A New Approach to Modeling the Nucleation and Growth Kinetics of Tricalcium Silicate Hydration[J]. Journal of the American Ceramic Society, 2007, 90(10): 3 282-3 288

[19] Juilland P, Gallucci E, Flatt R, et al.. Dissolution Theory Applied to the Induction Period in Alite Hydration[J]. Cement and Concrete Research, 2010, 40(6): 831-844

[20] Nicoleau L, Nonat A, Perrey D. The Di- and Tricalcium Silicate Dissolutions[J]. Cement and Concrete Research, 2013, 47: 14-30

[21] Naber C, Bellmann F, Sowoidnich T, et al.. Alite Dissolution and C-S-H Precipitation Rates During Hydration[J]. Cement and Concrete Research, 2019, 115: 283-293

[22] Bellmann F, Sowoidnich T, Ludwig H-M, et al.. Dissolution Rates During the Early Hydration of Tricalcium Silicate[J]. Cement and Concrete Research, 2015, 72: 108-116

[23] Zhang Z Q, Han F H, Yan P Y. Modelling the Dissolution and Precipitation Process of the Early Hydration of C₃S[J]. Cement and Concrete Research, 2020, 136: 106 174

[24] Wang X, Shen D, Wu S. Influence of Particle Internal Pores on Hydration Kinetics and Microstructure Development in Tricalcium Silicate Hydration[J]. Journal of Materials in Civil Engineering, 2021, 33(12): 04 021 335

[25] Thomas M D A, Bamforth P B. Modelling Chloride Diffusion in Concrete: Effect of Fly Ash and Slag[J]. Cement and Concrete Research, 1999, 29(4): 487-495

[26] Aguayo M, Yang P, Vance K, et al.. Electrically Driven Chloride Ion Transport in Blended Binder Concretes: Insights From Experiments and Numerical Simulations[J]. Cement and Concrete Research, 2014, 66: 1-10

[27] Sun G, Zhang J, Zhang L, et al.. M-T Scheme for Predicting Effective Diffusion Coefficient of Chloride Ions in Cement-based Materials[J]. Journal of Wuhan University of Technology-Materials Science Edition, 2020, 35(3): 520-527

[28] Yang C C, Su J K. Approximate Migration Coefficient of Interfacial Transition Zone and the Effect of Aggregate Content on the Migration Coefficient of Mortar[J]. Cement and Concrete Research, 2002, 32(10): 1 559-1 565

[29] Delagrave A, Bigas J P, Ollivier J P, et al.. Influence of the Interfacial Zone on the Chloride Diffusivity of Mortars[J]. Advanced Cement Based Materials, 1997, 5(3): 86-92

[30] Chen Y, Wu K, Xu L, et al.. Chloride Corrosion of Reinforced Calcium Aluminate Cement Mortar[J]. Journal of Wuhan University of Technology-Materials Science Edition, 2023, 38(1): 79-87

[31] Wilson W, Georget F, Scrivener K. Unravelling Chloride Transport/Microstructure Relationships for Blended-Cement Pastes with the Mini-Migration Method[J]. Cement and Concrete Research, 2021, 140: 106 264

[32] Wilson W, Gonthier J N, Georget F, et al.. Insights on Chemical and Physical Chloride Binding in Blended Cement Pastes[J]. Cement and Concrete Research, 2022, 156: 106 747

[33] Castellote M, Alonso C, Andrade C, et al.. Oxygen and Chloride Diffusion in Cement Pastes as a Validation of Chloride Diffusion Coefficients Obtained by Steady-State Migration Tests[J]. Cement and Concrete Research, 2001, 31(4): 621-625

[34] Costoya Fernández M M. Effect of Particle Size on the Hydration Kinetics and Microstructural Development of Tricalcium Silicate, 2008, Lausanne, EPFL

[35] Andrade C. Calculation of Chloride Diffusion Coefficients in Concrete From Ionic Migration Measurements[J]. Cement and Concrete Research, 1993, 23(3): 724-742

[36] Shen D, Wang X, Wu S. Determining Hydration Mechanisms for Initial Fall and Main Hydration Peak in Tricalcium Silicate Hydration using a Two-Scale Hydration Simulation Model[J]. Cement and Concrete Research, 2022, 156: 106 763

[37] Bentz D P. CEMHYD3D: A Three-Dimensional Cement Hydration and Microstructure Development Modeling Package. Version 3.0 Report 7232, 2005

[38] Shen D, Wang X. Simulation on Hydration of Tricalcium Silicate in Cement Clinker Firsted, 2023, Singapore, Springer Singapore

[39] Zhang M. Multiscale Lattice Boltzmann-Finite Element Modelling of Transport Properties in Cement-Based Materials, 2013, Delft, Delft University of Technology

[40] Bentz D, Garboczi E J. A Computer Model for the Diffusion and Binding of Chloride Ions in Cement Paste[R], 1993

[41] De Weerdt K, Colombo A, Coppola L, et al.. Impact of the Associated Cation on Chloride Binding of Portland Cement Paste[J]. Cement and Concrete Research, 2015, 68: 196-202

[42] Hirao H, Yamada K, Takahashi H, et al.. Chloride Binding of Cement Estimated by Binding Isotherms of Hydrates[J]. Journal of Advanced Concrete Technology, 2005, 3(1): 77-84

[43] Andrade C. Concepts on the Chloride Diffusion Coefficient[R]. Third RILEM workshop on Testing and Modelling the Chloride Ingress into Concrete, 2002

[44] Newman J. Electrochemical Systems, 1991 2nd ed New Jersey, Prentice-Hall, Englewood Cliffs

[45] Merkel B J, Planer-Friedrich B. Groundwater Geochemistry: A Practical Guide to Modeling of Natural and Contaminated Aquatic Systems, 2005 1st ed. Beijing, China University of Geosciences Press Translated by Y. Zhu, Y. Wang

[46] Parkhurst D. Description of Input and Examples for PHREEQC Version 3-A Computer Program for Speciation, Batch-Reaction, One-Dimensional Transport, and Inverse Geochemical Calculations, 2013, Denver, U.S. Geological Survey

[47] Charlton S R, Parkhurst D L. Modules Based on the Geochemical Model PHREEQC for Use in Scripting and Programming Languages[J]. Computers and Geosciences, 2011, 37(10): 1 653-1 663

[48] Zhou Z, Chen H, Li Z, et al.. Simulation of the Properties of MgO-Mg-fCl₂-H₂O System by Thermodynamic Method[J]. Cement and Concrete Research, 2015, 68: 105-111

[49] Vignes A. Diffusion in Binary Solutions: Variation of Diffusion Coefficient with Composition[J]. Industrial and Engineering Chemistry Fundamentals, 1966, 5(2): 189-199

[50] Wilke C R, Chang P. Correlation of Diffusion Coefficients in Dilute Solutions[J]. AIChE Journal, 1955, 1: 264-270

[51] Zhang T, Gjørv O E. Diffusion Behavior of Chloride Ions in Concrete[J]. Cement and Concrete Research, 1996, 26(6): 907-917

[52] Nicoleau L, Nonat A. A New View on the Kinetics of Tricalcium Silicate Hydration[J]. Cement and Concrete Research, 2016, 86: 1-11

[53] Sugiyama T, Ritthichauy W, Tsuji Y. Simultaneous Transport of Chloride and Calcium Ions in Hydrated Cement Systems[J]. Journal of Advanced Concrete Technology, 2003, 1(2): 127-138

[54] Tofts P S, Lloyd D, Clark C A, et al.. Test Liquids for Quantitative MRI Measurements of Self-Diffusion Coefficient in Vivo[J]. Magnetic Resonance in Medicine, 2000, 43(3): 368-374

[55] Garboczi E J, Bentz D P. Computer Simulation of the Diffusivity of Cement-Based Materials[J]. Journal of Materials Science, 1992, 27(8): 2 083-2 092

[56] Garboczi E J, Bentz D P. Modelling of the Microstructure and Transport Properties of Concrete[J]. Construction and Building Materials, 1996, 10(5): 293-300

[57] Joseph S, Bishnoi S, Van Balen K, et al.. Effect of the Densification of C–S–H on Hydration Kinetics of Tricalcium Silicate[J]. Journal of the American Ceramic Society, 2018, 101(6): 2438-2449

[58] Ma H Y, Hou D S, Liu J, et al.. Estimate the Relative Electrical Conductivity of C–S–H Gel From Experimental Results[J]. Construction and Building Materials, 2014, 71: 392-396

[59] Tao G. Multi-Scale Modeling on the Chloride Diffusion in Cement-Based Materials[D], 2020, Nanjing, Hohai University

[60] Poupard O, Ait-Mokhtar A, Dumargue P. Corrosion by Chlorides in Reinforced Concrete: Determination of Chloride Concentration Threshold by Impedance Spectroscopy[J]. Cement and Concrete Research, 2004, 34(6): 991-1 000

[61] Ngala V T, Page C L, Parrott L J, et al.. Diffusion in Cementitious Materials: II, Further Investigations of Chloride and Oxygen Diffusion in Well-Cured OPC and OPC/30%PFA Pastes[J]. Cement and Concrete Research, 1995, 25(4): 819-826

RIGHTS & PERMISSIONS

Wuhan University of Technology and Springer-Verlag GmbH Germany, Part of Springer Nature