硅酸盐学报

混凝土裂缝的微生物自修复与氯离子扩散不同时序耦合过程数值模拟

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邹凯 , 王立成

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): 602-610

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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) : 602 -610

混凝土裂缝的微生物自修复与氯离子扩散不同时序耦合过程数值模拟

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邹凯, 王立成

作者信息

大连理工大学海岸与海洋工程全国重点实验室，辽宁大连 116024

通讯作者:

王立成（1975—），男，博士，教授。

作者简介:

邹凯（1993—），男，博士研究生。

Numerical Simulation of Temporal Coupling Between Microbially Induced Crack Self-Healing and Chloride Diffusion in Concrete

Kai ZOU, Licheng WANG

Affiliations

State Key Laboratory of Coastal and Offshore Engineering, Dalian University of Technology, Dalian 116024, Liaoning, China

Corresponding Author:

WANG Licheng (1975-), male, Ph.D., Professor. E-mail: wanglich@dlut.edu.cn

ZOU Kai (1993-), male, Doctoral candidate. E-mail: zoukai812@gmail.com

出版时间: 2026-02-20 doi: 10.14062/j.issn.0454-5648.20250219

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摘要

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为揭示混凝土裂缝的微生物自修复对Cl^-扩散速度的抑制机制，提出了包含裂缝闭合和Cl^-扩散的多时序耦合数值模拟方法。基于开裂微生物试件格构网络模型，分别建立了裂缝自修复和Cl^-扩散数值模块，并通过裂缝宽度-物质扩散系数关系模型实现了模块间的耦合作用。通过预测宽度为0.4 mm砂浆裂缝的闭合时间验证了模型的可行性。数值模拟结果表明，微生物自修复可显著降低试件中裂缝的渗透性，对Cl^-扩散速度的抑制效果沿裂缝深度呈下降趋势，试件浅层区域（0～0.5 mm）的Cl^-扩散系数可恢复至未开裂时的量值水平；裂缝持续动态扩展会降低微生物的自修复效果，裂缝尖端Cl^-浓度由10 d时的0.0062% （质量分数）增至73 d的0.1396%。

关键词

微生物自修复 / 氯离子扩散 / 裂缝 / 混凝土 / 耦合时序

Abstract

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Introduction

Chloride-induced corrosion of steel reinforcement can severely damage the reinforced concrete in marine and saline environments, specifically accelerating steel depassivation, electrochemical corrosion, and structural weakening. To deal with these challenges, the microbially induced calcium carbonate precipitation (MICP) technique emerges as a promising self-healing solution for concrete. The existing experimental investigations are predominantly limited to post-healing strength recovery and durability enhancement. However, the chloride ingress mechanism under working conditions remains insufficiently explored, particularly regarding the temporal coupling between crack closure and crack propagation process. Furthermore, a dual inhibitory effect induced by crack closure is also identified, which simultaneously impedes chloride penetration and restricts the transport of healing agents (e.g., urea, calcium sources). In this work, two numerical modules were proposed. The crack self-healing behavior as well as chloride diffusion process were simulated by a lattice network model. The inter-module coupling was implemented by a diffusion coefficient model dependent on crack width. The inhibition effect of crack healing on chloride diffusion within microbial sample was quantitively analyzed by the proposed model.

Methods

A lattice network model discretized by Voronoi diagram was adopted to simulate the diffusion of self-healing component (i.e., urea) and chloride in microbial samples. The governing equation for urea hydrolysis kinetics could follow Fick's second law with an extended term of ureolysis rate. The calculated mass of calcium carbonate was obtained from urea concentration profiles and then used to iteratively update crack healing ratios. Based on this foundation, chloride diffusion was subsequently simulated by means of the dynamically adjusted diffusion coefficients that could correspond to the changing crack widths. For numerical implementation, a cylindrical microbial mortar specimen (φ 30.0 mm×50.0 mm) containing a parallel crack (20.0 mm×0.4 mm) was modeled. To systematically evaluate the chloride inhibition effects of MICP and reproduce the chloride concentration distribution under temporal coupling issues, three working conditions were defined, i.e., post-healing chloride diffusion (PHD), simultaneous healing-diffusion (SHD), and sustained cracking with healing-diffusion (SCHD).

Results and discussion

During the early healing period (i.e., 10 d and 30 d), no significant variation in urea concentration distribution appears within cracks. This is generally believed to originate from the dynamic equilibrium between urea supply and mineralization consumption during the initial healing stage. However, after 73 d healing, a sharp decline in urea concentration occurs in the 0-0.5 mm region near the crack surface. The MICP-driven crack closure is likely a primary mechanism for the inhibition of chloride diffusion. The results of crack healing ratio and diffusion coefficient along crack depth show that the increase in crack healing ratio within the 0-5.0 mm range results in a reduced diffusion coefficient. At 73 d, cracks within the 0-1.0 mm range reach the 0.08 mm threshold defined in diffusion coefficient versus crack width model, leading to a linearly decreased diffusion coefficient as crack closure develops. In the 0-0.5 mm region, the numerical results of crack healing ratio ranging from 96.2% to 99.9% indicate that the surface crack is nearly closed. The MICP-based crack healing is able to inhibit the ingress of Cl^-. Under the PHD condition at 10, 30, and 73 d, a stepwise decline in Cl^- concentration distribution occurs along the crack depth, even for the Ref group at 73 d. Within the 0-5.0 mm range, MICP-induced crack healing causes a rapid decrease in Cl^- concentration reduction, and this range corresponds to the predefined mineralization reaction zone. For the zone ranging from 5.0-20.0 mm, the concentration gradient gradually flattens, which is attributed to accelerated Cl- replenishment facilitated by high diffusion coefficients. At depths of exceeding 20.0 mm, the migration of Cl^- from the crack region to the concrete matrix leads to an abrupt reduction in diffusion coefficient, steepening the concentration gradient. The results of quantitative analysis reveal that after 73 d healing, Cl^- concentrations at 10 mm and 20 mm depths are reduced by 47.65% and 58.29%, respectively, compared to the Ref group. The sustained cracking also compromises the healing efficacy and hence elevates Cl^- concentration. At the initial healing stage, the SHD group exhibits significantly higher Cl^- concentrations than other groups due to wider cracks and lower healing ratios. As healing progresses, Cl^- concentration under SHD condition gradually approaches that in PHD group. Despite the smaller initial crack width for SCHD condition, the sustained cracking greatly increases the diffusion coefficient in crack. At the crack tip (i.e., 20.0 mm depth), Cl^- concentration in SCHD group increases from 0.0062% at 10 d to 0.1396% at 73 d, exceeding the final concentration in SHD group (0.1131%) by 123.49%.

Conclusions

This work proposed a numerical framework via integrating crack healing and chloride diffusion modules to address the experimental limitations in analyzing temporally coupled processes of sample cracking, microbial self-healing activation, and chloride ingress. The permeability of cracked microbial sample was significantly inhibited by MICP-driven crack closure. Under the PHD condition, Cl^- concentration distribution exhibited a progressive attenuation along the crack depth, with reductions of 47.65%(i.e., 10.0 mm) and 58.29% (i.e., 20.0 mm) compared to the Ref condition. Moreover, in shallow surface regions (0-0.5 mm), the chloride diffusion coefficient was restored to levels comparable to intact matrices. However, the sustained cracking could have a compromise microbial self-healing efficacy. Under the SCHD condition, Cl^- concentration at the crack tip increased from 0.0062 wt%(10 d) to 0.1396% (73 d). These results demonstrated that the MICP technique could be suitable for non-structural cracks induced by environmental stresses.

Key words

microbial self-healing / chloride diffusion / crack / concrete / temporal coupling

引用本文

邹凯, 王立成. 混凝土裂缝的微生物自修复与氯离子扩散不同时序耦合过程数值模拟. 硅酸盐学报, 2026 , 54 (2) : 602 -610 . DOI: 10.14062/j.issn.0454-5648.20250219

Kai ZOU, Licheng WANG. Numerical Simulation of Temporal Coupling Between Microbially Induced Crack Self-Healing and Chloride Diffusion in Concrete[J]. Journal of the Chinese Ceramic Society, 2026 , 54 (2) : 602 -610 . DOI: 10.14062/j.issn.0454-5648.20250219

基金

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辽宁省自然科学基金(2020-MS-100)
辽宁省“兴辽英才计划”项目(XLYC2211006)

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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.0454-5648.20250219

接收时间：2025-03-27
首发时间：2026-10-27
出版时间：2026-02-20

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出版历史

收稿日期：2025-03-27
修回日期：2025-04-23

基金

辽宁省自然科学基金(2020-MS-100)

辽宁省“兴辽英才计划”项目(XLYC2211006)

作者信息

大连理工大学海岸与海洋工程全国重点实验室，辽宁大连 116024

通讯作者:

王立成（1975—），男，博士，教授。

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https://castjournals.cast.org.cn/joweb/gsyxb/CN/10.14062/j.issn.0454-5648.20250219

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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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