Predicting shotcrete degradation in hot environments using response surface modeling

Deep beneath the Earth’s surface, where temperatures routinely climb past 60 degrees Celsius and humidity can soak the very rock walls of a tunnel, the concrete that keeps miners and infrastructure safe is quietly falling apart. Now, a new study has revealed exactly when and why that deterioration becomes most dangerous, and the answer is not simply “the hotter, the worse.” Instead, researchers report that the worst damage occurs at a devious middle ground of temperature and humidity — a sweet spot of destruction where moisture feeds harmful chemical reactions and drying shrinkage simultaneously, creating a perfect storm of internal stress inside the material.

The research, led by Yu Zhang, Mingzhe An, Yue Wang, and Gang Huang and published in the journal Results in Engineering, focuses on shotcrete, the spray-applied concrete that serves as the primary support lining in tunnels, mines, and countless underground structures worldwide. Unlike ordinary concrete that is poured into molds, shotcrete is pneumatically projected onto rock surfaces at high velocity, mixed with large doses of alkali-free accelerators that make it set within minutes. That flash-setting behavior is precisely what makes it both an engineering marvel and, as the new findings suggest, uniquely vulnerable to geothermal environments.

Underground projects frequently encounter severe geothermal conditions stemming from complex geological structures and rock formations. Engineers generally divide these environments into two categories: dry-heat settings with low humidity, typically found in intact rock masses where heat moves by conduction, and wet-heat settings with high humidity, where fractures allow hot groundwater to permeate. Field statistics cited in the study show that while virgin rock temperatures in many mines remain below 60 degrees Celsius, temperatures in long, deeply buried tunnels often hover around that mark. Rock surface temperatures can reach as high as 80 degrees Celsius in dry conditions and approach 90 degrees Celsius in humid environments — conditions hot enough to fundamentally alter the chemistry of cement-based materials.

At those temperatures, the microscopic architecture of shotcrete begins to unravel. Elevated temperatures drive internal moisture migration and evaporation, which can hinder the ultimate degree of cement hydration. High heat does accelerate early hydration kinetics, producing rapid early strength gains, but it often comes at a hidden cost: hydration products clump together into coarse aggregations, and a dense shell forms around unhydrated cement grains, blocking further reaction and leaving a heterogeneous microstructure riddled with localized weak zones. For shotcrete, the problem is compounded by its primary hydration product, ettringite — known to mineralogists as AFt — which is thermodynamically unstable at elevated temperatures and prone to transformation, setting the stage for severe microstructural damage.

But the team behind the new study suspected something more subtle was going on. Most previous research had examined shotcrete under extreme humidity conditions — bone-dry or fully saturated. The researchers hypothesized that intermediate humidity levels might actually trigger a more detrimental mechanism, described vividly as a “tug-of-war” inside the material. At moderate humidity, there is enough moisture to fuel harmful expansive phase transformations, including the potential for abnormal ettringite growth, while the same conditions still drive significant drying shrinkage. The result is a synergistic peak of internal stresses that neither extreme can match. Testing that hypothesis required a systematic way to quantify degradation across a continuous range of coupled thermal-hygral conditions — a problem the team solved with an unlikely statistical weapon.

Enter Response Surface Methodology, or RSM, a statistical technique that fits empirical mathematical models to experimental data, most often used in materials science to optimize concrete mix designs — balancing sustainable additives in self-compacting concrete, for example, or tuning eco-friendly grouts made from waste materials. The researchers flipped the script: rather than using RSM to maximize strength, they adapted it for risk assessment, modeling deterioration trajectories and pinpointing the precise temperature and humidity thresholds where performance collapse is most severe. They structured their experiments with a Central Composite Design and captured the nonlinear interplay of temperature and relative humidity through a second-order polynomial regression model containing linear, quadratic, and interaction terms.

The experimental program was deliberately comprehensive. The team tested shotcrete made from Ordinary Portland Cement of grade P·O 42.5, granite-derived manufactured sand, crushed granite coarse aggregate graded from 5 to 10 millimeters, a polycarboxylate superplasticizer with a 25 percent water-reduction rate, and an aluminum sulfate-based alkali-free liquid accelerator with a solid content of 57 percent — the ingredient responsible for the material’s rapid setting. Evaluations were performed at 28 days, the standard age for engineering design and quality acceptance, and combined non-destructive testing with destructive mechanical tests. Ultrasonic Pulse Velocity, or UPV, served as a non-destructive window into the material’s interior: because sound waves travel more slowly through cracks and pores, a drop in pulse velocity is a reliable early-warning signal of internal degradation long before visible damage appears.

The measurements were then cross-validated against direct microstructural evidence, including morphological analysis and pore structure characterization, establishing a verification system in which the statistical predictions and the physical damage signatures corroborate one another. This triangulation matters for practical engineering: it means the regression equations are not merely statistical curve-fitting exercises but are anchored in the actual chemical and physical mechanisms of thermal damage. The researchers also implemented a strategy based on the Desirability function — a standard tool of RSM optimization — but inverted its purpose, deploying it to hunt down, rather than avoid, the environmental conditions responsible for maximum degradation.

The findings carry immediate safety implications. Shotcrete degradation does not unfold slowly over decades; it compromises the material’s resistance to rock deformation and spalling during construction and early service, the very stages when workers are most exposed. A support layer that loses stiffness and strength in a hot, moderately humid tunnel can fail while the tunnel is still being excavated. By identifying the most adverse combinations of temperature and humidity, the new models give engineers a quantitative theoretical basis for performance assessment and structural integrity management — allowing them to predict, before a single spray of concrete is applied, how a given underground environment will chew through the lining over time.

The work also fills a genuine methodological gap. Earlier studies had investigated the influence of temperature or humidity on shotcrete performance, and some had explored their combined effects, but those investigations generally relied on discrete experimental observations without a continuous mathematical framework to quantify nonlinear interactive behavior. By converting scattered data points into continuous response surfaces, the study transforms what was previously a patchwork of case-by-case findings into a predictive tool. The authors say the approach provides targeted theoretical guidance and robust solutions for performance prediction and risk mitigation in harsh geothermal engineering applications, and the framework could readily be extended to other cement-based materials facing coupled environmental stresses.

For the growing global fleet of deep tunnels, geothermal power installations, and mines reaching ever greater depths, the message is clear: the environment that surrounds underground concrete is not just a background condition but an active agent of degradation, and its most destructive mode thrives in the middle ground. As infrastructure pushes deeper into the Earth’s heat, knowing exactly where that tipping point lies — and being able to compute it before construction begins — may prove as important to underground safety as the concrete itself. The study stands as a striking example of how a statistical tool built for optimizing recipes can be turned into a weapon for predicting failure, and how sometimes the most dangerous conditions are not the extremes, but everything in between.