Hidden Markov Model Cracks Open the Secret Weak Zone Inside Coal Waste Concrete

Every year, the global coal industry dumps roughly 1.2 billion tons of coal gangue, a rocky by-product of mining and washing that piles up in sprawling waste heaps from Shanxi to Pennsylvania. Turning that waste into lightweight aggregate for concrete has long been touted as a circular-economy win, but engineers have struggled to answer a deceptively simple question: what actually happens at the microscopic boundary where the porous coal gangue particle meets the surrounding cement paste? A new study published in Case Studies in Construction Materials by Xingxin Zhao, Tao Wu, Ziyuan Wang, and Shicheng Fan of Chang’an University now delivers the most rigorous answer yet, combining an automated machine-learning detection algorithm with digital image correlation to trace how strength and cracking in coal gangue lightweight aggregate concrete are governed by its interfacial transition zone, the notoriously weak band of paste that surrounds every piece of aggregate.

The interfacial transition zone, or ITZ, is the cement industry’s version of a chain’s weakest link. In ordinary concrete, this porous, calcium hydroxide-rich region between aggregate and mortar is where damage typically begins. Measuring its thickness, however, has always been messy. The classic backscattered electron porosity-gradient method suffers from inconsistent grayscale thresholds that can shift results by 10 to 20 micrometers, while the calcium-to-silicon ratio approach depends on subjective judgments about where a plateau begins and ends. Existing automated tools, developed for normal-weight concrete, break down when confronted with the low calcium content and pore-induced signal noise characteristic of lightweight aggregates. The Chinese team’s solution, dubbed HMM-SF, chains together a Gaussian hidden Markov model and Sigmoid fitting to read elemental line scans from energy-dispersive X-ray spectroscopy and pinpoint interface boundaries without any human annotation at all.

The clever part of the algorithm lies in how it exploits chemistry. Among ten elements profiled across the interface, calcium turned out to be the ideal reference signal, because the cement paste is the only calcium-rich phase in the entire system: the Portland cement contains 57.04 percent calcium oxide, while the coal gangue aggregate shell holds just 3.37 percent and the core a mere 2.32 percent. That steep, well-directed gradient, combined with the relatively high signal-to-noise ratio of calcium’s characteristic X-ray line, gives the model a clean fingerprint to track. The workflow first identifies and interpolates across pores that would otherwise corrupt the signal, then uses a two-state hidden Markov model with Viterbi decoding to classify each measurement point as aggregate or mortar, fuses multi-element gradients to locate candidate boundaries, and finally fits Sigmoid curves to the calcium and calcium-to-silicon profiles, defining the ITZ as the interval between 10 percent and 90 percent of the elemental transition.

The validation exercise is a textbook demonstration of why each algorithmic component matters. In a five-level ablation experiment, a naive K-means clustering baseline catastrophically over-predicted 226 interfacial zones, achieving an F1 score of just 0.308. Swapping in a three-state hidden Markov model cut predictions to 76 but inflated the mean thickness to an implausible 105.4 micrometers, because treating the interface as a discrete state cannot capture its graded nature. Introducing Sigmoid fitting corrected the mean width to a physically sensible 41.6 micrometers, artifact filtering suppressed spurious detections, and the final multi-element gradient fusion lifted the complete model to a precision of 0.926, a recall of 0.969, and an F1 score of 0.947 against 65 manually annotated reference positions across 33 specimens.

With the tool validated, the researchers quantified 68 interfacial zones across eight mix proportions and discovered that their thicknesses follow a lognormal distribution with remarkable consistency. The global mean came out at 44.9 micrometers, the median at 27.5 micrometers, and the extremes ranged from 9.4 to 148.8 micrometers, a strongly right-skewed spread. A Kolmogorov-Smirnov test on pooled, group-centered residuals returned a p-value of 0.972, confirming that all eight mixtures share the same distributional shape parameter of 0.761, with only the location parameter shifting between mixes. Strikingly, even at the highest water-to-binder ratio and aggregate volume fraction tested, no abnormal interfacial thickening appeared, suggesting the porous coal gangue aggregate may actually help optimize the interface rather than degrade it.

That counterintuitive behavior traces back to the aggregate’s internal curing. Scanning electron microscopy revealed that cement particles and fly ash cenospheres embed themselves in the rough aggregate surface’s open pores, which range from 8 to 135 micrometers, anchoring calcium silicate hydrate gel that grows outward and interlocks with the paste. Unconnected pores act as tiny water reservoirs, absorbing and slowly releasing moisture that refines the interface and suppresses the growth of coarse, detrimental calcium hydroxide crystals. Connected macropores, by contrast, release moisture too quickly, locally raising the water-to-binder ratio and promoting excessive ettringite formation that increases interfacial porosity. The mix design variables left clear fingerprints: fly ash at 25 percent produced the densest interfaces, a water-to-binder ratio of 0.2 yielded the thinnest mean zone at 20.2 micrometers, and aggregate volume fraction showed a U-shaped optimum near 40 percent.

The cross-scale analysis delivered the study’s most commercially significant insight: interfacial thickness alone does not control strength. Within the fly ash series, mixes with 22.5 to 89.9 percent thicker mean zones lost only 6.8 to 13.0 percent of their compressive strength, while the water-to-binder ratio series showed strength dropping 18.3 percent despite a mere 8.5 percent thickening. The volumetric picture proved far more predictive. The ratio of interfacial zone volume to mortar volume correlated most strongly with 28-day compressive strength, with a Pearson coefficient of negative 0.766, and strength rose 33.0 percent as that ratio fell from 5.94 percent to 1.26 percent. The average mortar thickness between aggregates, which stretches from 1007 to 2447 micrometers across the mixes, correlated positively, because thicker mortar layers dissipate stress and lengthen crack paths. A power-law regression combining the three representative parameters achieved an R-squared of 0.858, though the authors caution that eight group-level observations make these exploratory relationships rather than universal laws.

Perhaps the most visually compelling results came from overlaying digital image correlation strain maps onto microstructural images of the loaded specimens. In normal-weight concrete, the interfacial zone consistently lit up first, entering the high-strain state from the 0.4 peak-displacement stage onward and confirming the classic ITZ-dominated damage nucleation described in the literature. In the coal gangue concrete, the three phases evolved almost synchronously, with inter-phase differences in high-strain area fraction as low as 1 to 5 percent at peak load. The team interprets this as a weak-phase competition mechanism: whichever of aggregate, interface, or mortar is locally weakest fails first and steers the damage direction, while the interface merely acts as a boundary condition reshaping the competition. Crack skeleton analysis reinforced the story, with 57.8 percent of total crack length running through the mortar and only 0.6 percent through the interface, and crack densities 18 to 41 percent lower than in normal-weight concrete across all three phases.

For a field racing to absorb mountains of coal mining waste into structural materials, the implications are twofold. Practically, the study points toward mix designs with roughly 25 percent fly ash replacement, water-to-binder ratios between 0.20 and 0.30, and aggregate volume fractions of 30 to 40 percent as the sweet spot where strength and interfacial quality align. Methodologically, the open-source HMM-SF algorithm, available on GitHub, offers the first objective, annotation-free route to quantifying interfacial zones in porous lightweight aggregate systems, removing a long-standing source of subjectivity that has plagued cross-scale modeling. The authors are careful to note the limits: the method assumes a monotonic elemental transition and would need recalibration for high-calcium aggregates, and the small interfacial area fraction of about 2 percent limits statistical resolution at the current imaging scale. Even so, by fusing hidden Markov statistics, sigmoid mathematics, and full-field strain imaging, the work transforms a fuzzy microscopic boundary into a measurable, predictable design variable, and brings carbon-saving coal gangue concrete one large step closer to code-worthy credibility.

Subject of Research: Automated identification of the interfacial transition zone in coal gangue lightweight aggregate concrete and its correlation with compressive strength and cracking behavior

Article Title: Interfacial transition zone in coal gangue lightweight aggregate concrete: Automated identification, strength correlation, and cracking behavior

Article References: Zhao, X., Wu, T., Wang, Z., & Fan, S. (2026). Interfacial transition zone in coal gangue lightweight aggregate concrete: Automated identification, strength correlation, and cracking behavior. Case Studies in Construction Materials, 25, Article e06581. https://doi.org/10.1016/j.cscm.2026.e06581

Image Credits: AI Generated

DOI: 10.1016/j.cscm.2026.e06581

Keywords: coal gangue, lightweight aggregate concrete, interfacial transition zone, hidden Markov model, EDS line scanning, digital image correlation, compressive strength, crack propagation, lognormal distribution, fly ash, internal curing, solid waste utilization