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

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.