A new modeling framework can now predict how and when concrete heals itself, bringing measurable precision to microbial self-healing materials and advancing durability forecasting for next-generation infrastructure.
Study: Full-cycle prediction of crack healing in self-healing concrete using generalized polynomial chaos expansion. Image Credit: Viacheslav Zhedankov/Shutterstock.com
A recent paper in Communications Engineering presents a polynomial chaos expansion (PCE)-based multidimensional prediction framework that quantifies internal crack healing in self-healing cement-based materials across the entire repair cycle.
Rather than assessing healing at isolated time points, the approach captures the full temporal evolution of damage and recovery.
Why Microbial Self-Healing Concrete
Microbial self-healing concrete is designed to repair cracks autonomously. Microorganisms embedded within the concrete matrix remain dormant until cracking occurs. When exposed to moisture and oxygen, their metabolic activity triggers calcium carbonate precipitation, sealing cracks from within.
The result is a material that can improve structural stability, extend service life, and reduce maintenance demands while also offering environmental benefits by limiting repair-related resource use. For infrastructure exposed to aggressive environments, this capability is especially valuable.
The Modeling Challenge
Despite its promise, microbial self-healing concrete presents a complex modeling problem.
Healing performance depends on multiple interacting variables, and early-stage repair behavior is highly variable. Traditional polynomial chaos expansion (PCE) methods model uncertainty using orthogonal polynomial series tied to predefined probability distributions, typically Gaussian.
In practice, however, experimental data from self-healing systems often deviate from ideal Gaussian assumptions. That mismatch limits predictive reliability. To address this, researchers developed a generalized PCE (gPCE) framework capable of accommodating arbitrary input distributions, allowing the model to reflect real-world variability more accurately.
Building a Full-Cycle Prediction Framework
The research team began by constructing a foundational statistical database identifying the key factors that influence healing behavior. Using this dataset, they developed a first-order PCE surrogate model to describe the temporal evolution of crack repair from early-stage fluctuations to later nonlinear saturation.
Initial validation revealed a common issue: strong accuracy loss during early healing stages due to high stochastic variability.
To strengthen performance, the researchers applied Sobol sensitivity analysis and functional relevance-based dimensionality reduction. Less influential predictors were removed, improving model robustness while reducing computational complexity.
To further enhance flexibility, the team introduced Kernel Density Estimation (KDE) to construct an arbitrary-distribution PCE (aPCE) framework. This allowed adaptive generation of orthogonal polynomial bases directly from non-parametric input distributions. The result was a unified full-cycle model, replacing separate age-specific prediction models with a single distribution-adaptive framework.
Experimental Design
Self-healing mortar specimens were prepared using fine aggregate, ordinary Portland cement, a specialized healing agent, a high-range water-reducing agent, and water.
The healing agent incorporated Bacillus mucilaginosus within a core-shell structure alongside calcium nitrite and sodium aluminate. To evaluate internal crack healing, the team used a multidimensional testing setup that included an industrial camera system, a custom-designed apparatus, a NELD-RUL530 device, and an HC-U81 ultrasonic tester.
After 14 days of curing, specimens were cracked using a universal testing machine at a loading rate of 0.10–0.20 kN/second, targeting a uniform 1 mm crack width. A 12-hour wet–dry cycle simulated service conditions. Artificial seawater was prepared following ASTM D1141 standards, and all tests were conducted at 25 ± 2 °C.
This structured approach ensured that the modeling framework was grounded in controlled, repeatable experimental data.
What the Results Showed
The framework demonstrated strong predictive reliability, even at healing ages not explicitly included in model training. Extrapolative validation confirmed robustness throughout the full healing cycle.
Healing behavior showed clear temporal dependence. Surface healing approached approximately 97 % by 28 days, while internal recovery progressed more gradually. Water permeability resistance closely tracked surface crack closure, highlighting the importance of early-stage surface sealing for durability performance.
Sobol sensitivity analysis revealed shifting parameter influence over time. During the early stages, the crack water seepage repair rate (k) contributed most significantly. By 28 days, the crack anti-chloride repair rate (m) became the dominant parameter.
Model refinement produced substantial gains in predictive accuracy. The original five-dimensional first-order PCE model was reduced to a three-dimensional second-order model, improving 7-day prediction accuracy (R2 increased from 0.5236 to 0.8536) while cutting complexity by more than 50 %. By 28 days, R2 reached 0.9523.
The arbitrary-distribution PCE (aPCE) model further reduced error, achieving a root mean square error of 0.5297 and lowering maximum prediction errors by 42.3 % compared to Gaussian-based models.
Perhaps most importantly, the study distinguishes between age-specific Gaussian modeling and pooled non-parametric distribution modeling used in the unified full-cycle framework. This shift enables a more realistic, distribution-adaptive prediction strategy rather than static, time-sliced analysis.
A Step Toward Predictable Self-Healing Infrastructure
This study demonstrates that microbial self-healing concrete can be modeled with meaningful precision across its entire healing lifecycle.
By addressing stochastic variability, particularly in early-stage repair, the proposed framework strengthens confidence in performance forecasting and service-life prediction.
As self-healing materials gain traction in infrastructure applications, reliable predictive tools will be essential for design standards, lifecycle planning, and durability optimization.
Journal Reference
Fu, C. et al. (2026). Full-cycle prediction of crack healing in self-healing concrete using generalized polynomial chaos expansion. Communications Engineering. DOI: 10.1038/s44172-026-00608-5, https://www.nature.com/articles/s44172-026-00608-5
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