In reinforced concrete (RC) structures exposed to chloride salt environments, the internal pore system provides pathways for chloride ion transport. Chloride ions that penetrate the concrete induce reinforcement corrosion and subsequent expansion, thus leading to concrete cracking. The newly formed cracks further accelerate chloride penetration and exacerbate structural deterioration. Numerical approaches provide an effective way for analyzing these coupled processes. However, conventional methods such as the finite element method, the extended finite element method, and the phase-field method are based on local theories, which makes it difficult to accurately capture displacement discontinuities during crack evolution. Consequently, the quantitative prediction of crack length and width remains a considerable challenge. Moreover, despite the development of numerous models, the most existing approaches are limited to individual physical processes and cannot fully represent their interactions. To address these limitations and investigate the corrosion-induced cracking behavior of concrete, it is essential to establish a coupled model of chloride diffusion and corrosion-induced cracking, enabling the quantitative prediction of the length and width of internal corrosion-induced cracks.

In this study, a diffusion–mechanics coupled lattice Boltzmann–peridynamic (LB–PD) model was proposed to simulate corrosion-induced cracking in concrete during chloride ion diffusion. A generation–placement method was employed to construct the concrete meso-structure, incorporating aggregates, mortar, and the interfacial transition zone (ITZ). Chloride ion transport within cracked concrete was simulated by using the lattice Boltzmann method (LBM), where cross-scale transport between the concrete matrix and ITZ was achieved via adjusting the LBM particle distribution functions. Meanwhile, corrosion-induced cracks at different scales were captured via categorizing the bonds in the peridynamic (PD) model into three distinct types, namely mortar bonds, aggregate bonds, and ITZ bonds. The processes both were accomplished without the need for additional mesh refinement. A stress-based PD bond failure criterion was further established based on the Peridynamic differential operator (PDDO). To accurately characterize the crack morphology, the Zhang–Suen thinning algorithm was introduced to extract the skeleton of corrosion cracks, and the crack length and width were quantitatively evaluated based on the crack skeleton.

The proposed LB–PD model is employed to simulate corrosion-induced cracking in concrete cover for specimens containing single and three reinforcing bars. In the single-reinforcement case, the simulations are conducted with and without considering the coupling between chloride diffusion and reinforcement corrosion. The results indicate that the coupling significantly accelerates crack propagation, although the crack initiation time remains largely unaffected. Cracks initiate predominantly around the reinforcement and extend outward along ITZ between aggregates and the matrix, highlighting a key role of microstructural heterogeneity in controlling crack paths.

For the specimen with three reinforcements, cracks similarly initiate near the reinforcements and propagate to form a network of primary and secondary cracks. The simulations reveal that the spatial distribution of aggregates affects crack evolution. The regions with sparse aggregate distribution exhibit a faster crack growth and a more severe reinforcement corrosion, whereas denser aggregate arrangements constrain crack propagation and reduce corrosion severity. This heterogeneity also leads to a non-uniform chloride concentration on reinforcement surfaces, further affecting the initiation and development of corrosion-induced cracks.

The results demonstrated that the proposed model could effectively capture the coupled processes of chloride transport and reinforcement corrosion, reproducing the multi-scale evolution of cracks in reinforced concrete. The model also provided insights into the interactions between microstructural features, chloride diffusion, and mechanical cracking, which were critical for understanding the degradation mechanisms of concrete structures under chloride attack. Cross-scale simulation of chloride transport and corrosion-induced cracking could be achieved without detailed modeling of ITZ, indicating a good adaptability of the model. Furthermore, the Zhang–Suen thinning algorithm was employed to extract crack skeletons, enabling a quantitative prediction of crack length and width. The simulations also confirmed the dual restraining effect of aggregates on both crack propagation and chloride diffusion, providing a mesoscopic-level explanation for reinforcement corrosion and crack initiation mechanisms. Noted that the current model could consider only chloride diffusion and did not account for multi-ion interactions or associated chemical reactions. Future work could extend the model to a diffusion–chemical–mechanical multi-physics framework to more accurately evaluate the durability of concrete structures and optimize protective strategies.

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.

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).

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%.

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.