硅酸盐学报

基于非平衡热力学的混凝土多离子耦合传输电化学模型

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石松 ¹ , 肖祥文 ¹ , 朱兴吉 ² , 刘齐民 ¹

硅酸盐学报 | 混凝土耐久性机理表征与预测方法专题—研究论文 2026,54(2): 666-675

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硅酸盐学报 |混凝土耐久性机理表征与预测方法专题—研究论文 2026 , 54 (2) : 666 -675

基于非平衡热力学的混凝土多离子耦合传输电化学模型

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石松¹, 肖祥文¹, 朱兴吉², 刘齐民¹

作者信息

^1．武汉理工大学土木工程与建筑学院，武汉 430070

^2．江汉大学精细爆破全国重点实验室，武汉 430056

通讯作者:

刘齐民（1988—），男，副研究员。

作者简介:

石松（2000—），男，硕士研究生。

Non-Equilibrium Thermodynamics-Based Electrochemical Model for Multi-Ion Coupled Transport in Concrete

Song SHI¹, Xiangwen XIAO¹, Xingji ZHU², Qimin LIU¹

Affiliations

^1.School of Civil Engineering and Architecture, Wuhan University of Technology, Wuhan 430070, China

^2.State Key Laboratory of Precision Blasting, Jianghan University, Wuhan 430056, China

Corresponding Author:

LIU Qimin (1988-), male, Ph.D., Associate Professor. E-mail: liuqm@whut.edu.cn

SHI Song (2000-), male, Master candidate. E-mail: songshi@whut.edu.cn

出版时间: 2026-02-20 doi: 10.14062/j.issn.0454-5648.20250339

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摘要

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氯离子侵蚀是导致混凝土性能劣化的关键因素之一，其过程涉及复杂的电化学相互作用与传输-反应耦合机制。本工作基于非平衡热力学原理，结合质量守恒和麦克斯韦方程，建立了多离子传输-反应耦合的电化学模型。不同于传统的离子传输模型，该模型充分考虑水化产物与各离子间的溶解沉淀反应，计算域涵盖外界溶液、多相混凝土以及溶液-混凝土界面，可定量描述混凝土表面处各离子浓度的动态变化过程。通过对比试验数据，验证了模型的准确性和可靠性。在此基础上，通过系统的参数分析，探明了扩散系数、骨料粒径、界面过渡区（ITZ）厚度及外加电场等对氯离子传输的影响机制。结果表明：扩散系数和电场对溶液-混凝土体系中的各离子浓度影响显著，而骨料粒径和ITZ厚度的影响相对有限；离子浓度在溶液-混凝土界面处发生突变现象，证实了外界溶液域的作用。研究成果为混凝土结构耐久性设计及性能优化提供理论依据。

关键词

氯离子侵蚀 / 多相混凝土 / 骨料分布 / 多离子

Abstract

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Introduction

As one of the most widely used engineering materials in modern infrastructure, concrete is prone to premature deterioration under chloride-rich conditions such as marine environments and deicing salt exposure, which severely compromises the service life of structures. The ingress of chloride ions involves complex physicochemical processes, including dissolution and precipitation of minerals, adsorption and transport of ions, chemical reactions among ions, and the self-induced electric field generated arising from ionic interactions. Moreover, concrete is inherently a heterogeneous multiphase material, which comprises the cement paste, aggregates, and interfacial transition zone (ITZ) phases. Traditional experimental methods are often time-consuming and difficult to quantitively characterize the coupling mechanism between the electric and chemical fields. Alternatively, various theoretical models at different length scales for concrete durability were developed based on the assumption of fixed concentration at the concrete surface, while their predictive results contradict the experimental findings, where the ion concentration is dynamically changed at the concrete surface. Herein, this work introduces a non-equilibrium thermodynamics-based electrochemical model for multi-ion coupled transport in exterior solution, interior concrete, and their interface. The model enables to capture the dynamically change in ion concentration at the concrete surface. The model is numerically solved by finite element method and validated with several experimental results, where good agreements are achieved. Afterwards, the model is employed to investigate the impacts of initial diffusion coefficients, aggregate particle size, ITZ thickness, and external electric fields on the chloride ion transport behavior, the evolutions of mineral amounts and electric potential.

Methods

Based on non-equilibrium thermodynamics, an electrochemical model at mesoscale level is developed to simulate chloride-induced degradation in concrete. The model starts from the derivation of reaction rates for chemical reactions between the minerals and mobile ions, where the forward and backward reactions are fully considered to reflect the real scenario. The diffusion of multi-ions is governed by the conservation law of mass and the electric polarization is achieved based on Gauss's theorem. The constitutive relations are derived based on the second law of thermodynamics. Regarding the free energy density, it is formulated with consideration of mixing and polarization effects. For direct calculation of ion concentrations at the concrete surface, the computational domains include the exterior ionic solution, interior concrete, and their interface. By setting the appropriate boundary and initial conditions, the model is then implemented into the finite element software. Afterwards, the effect of solution domain size is investigated on the ion concentration, where a optimum solution domain size is finalized via the balance of computational accuracy and cost. For ensuring the accuracy of the developed model, it is validated with experimental data in open literature, where satisfactory agreements are achieved. After that, the effects of initial diffusion coefficient, aggregate size, ITZ thickness, and external electric fields are carried out on the transport of multi-ions, the dissolution of minerals, and the electric field evolution.

Results and Discussion

The diffusion of Cl^- ion is required to span different spatial domains, for example from the exterior solution to solution-concrete interface, and then the interior concrete. Due to the difference in diffusion coefficients between the solution and the concrete, the ion concentration exhibits a sharp discontinuity at the solution-concrete interface zone. Moreover, the ion concentration at the concrete surface is dynamically changed with time, which is consistent with the experimental findings. Additionally, it is found that the ingress depth increases obviously with increasing diffusion coefficient, and the concentration distribution profile is significantly varied for different kinds of mobile ions. Under the condition of a constant aggregate volume fraction, the aggregate particle size and the ITZ thickness have a limited effect on Cl^- transport. It is because that the ITZ generally fails to form a connected network within the concrete, preventing the establishment of continuous fast diffusion pathways at the mesoscale. With the increase of the applied electric field, Cl^- continuously accumulates at the concrete interface and migrates more rapidly into the interior concrete. Compared with a 2 V electric field, when the applied electric field is increased to 6 V, the penetration depth of Cl^- increases by about 40%.

Conclusions

A non-equilibrium thermodynamics-based electrochemical model has been developed theoretically to capture chloride transport and reactions within concrete. The model reveals that chloride ingress is driven by diffusion coefficient, weakly affected by aggregate size and ITZ thickness, and significantly accelerated by the external electric fields. A sharp variation of ion concentration is found at the concrete-solution interface, and the ion concentration at the interface is dynamically changed. The model framework is derived based on the constitutive theory of non-equilibrium thermodynamics, offering a rigorous physical foundation. It is conventionally extended to couple stress, temperature, or moisture field, thereby simulating ion transport process and multi-field coupled degradation behaviors under complex environments, such as salt-freeze cycles and stress-corrosion conditions. This work may also provide a theoretical guidance for design and optimization of concrete durability.

Key words

chloride ion ingress / multi-phase concrete / aggregate distribution / multi-ions

引用本文

石松, 肖祥文, 朱兴吉, 刘齐民. 基于非平衡热力学的混凝土多离子耦合传输电化学模型. 硅酸盐学报, 2026 , 54 (2) : 666 -675 . DOI: 10.14062/j.issn.0454-5648.20250339

Song SHI, Xiangwen XIAO, Xingji ZHU, Qimin LIU. Non-Equilibrium Thermodynamics-Based Electrochemical Model for Multi-Ion Coupled Transport in Concrete[J]. Journal of the Chinese Ceramic Society, 2026 , 54 (2) : 666 -675 . DOI: 10.14062/j.issn.0454-5648.20250339

基金

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湖北省自然科学基金(2025AFB579)

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2026年第54卷第2期

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文章信息

doi: 10.14062/j.issn.0454-5648.20250339

接收时间：2025-04-29
首发时间：2026-10-27
出版时间：2026-02-20

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收稿日期：2025-04-29
修回日期：2025-05-30

基金

湖北省自然科学基金(2025AFB579)

作者信息

^1．武汉理工大学土木工程与建筑学院，武汉 430070

^2．江汉大学精细爆破全国重点实验室，武汉 430056

通讯作者:

刘齐民（1988—），男，副研究员。

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2种不同金属材料的力学参数

科 Family	属数 Number of genus	种数 Number of species	占总种数比例 Percentage of total species (%)	属 Genus	种数 Number of species	占总种数比例 Percentage of total species (%)
鹅膏菌科Amanitaceae	2	11	5.26	鹅膏菌属 Amanita	10	4.78
小菇科 Mycenaceae	2	12	5.74	丝盖伞属 Inocybe	5	2.39
多孔菌科 Polyporaceae	8	14	6.70	蜡蘑属 Laccaria	5	2.39
红菇科 Russulaceae	3	23	11.00	小皮伞属 Marasmius	6	2.87
				小菇属 Mycena	11	5.26
				光柄菇属 Pluteus	5	2.39
				红菇属 Russula	17	8.13
				栓菌属 Trametes	5	2.39

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