The research team, led by Ala Ameryan, Mansour Ghalehnovi and Mohsen Rashki, tackled a problem that has haunted reliability engineers for decades: the sheer computational expense of evaluating a performance function. In realistic engineering settings, each evaluation may require running a full finite element model of a structure, a calculation that can take minutes or hours on high-performance computers. The gold standard, Monte Carlo Simulation, demands millions of such evaluations to reliably estimate a small failure probability, making it utterly impractical for real-world design work. Alternative approaches such as the First Order Reliability Method, known as FORM, are cheap but stumble badly when the boundary between safety and failure is strongly curved or irregular, sometimes failing outright to locate the critical design point.

The new method builds on two earlier lines of research. The first is the Kriging surrogate model, a statistical technique borrowed from geostatistics that constructs a probabilistic approximation of an expensive function. Kriging has a remarkable property: it not only predicts the value of the function at any point but also quantifies its own uncertainty, reporting a variance that signals how much it trusts each prediction. The second ingredient is active learning, embodied in the well-known AK-MCS method. Instead of blindly sampling the expensive function everywhere, AK-MCS uses a so-called U-learning function to hunt for the sample points where the surrogate is most uncertain about whether the structure is safe or failed. Each such point is evaluated with the true model and added to the training set, so the surrogate grows smarter precisely where it matters most: along the limit state surface that separates survival from collapse.

AK-MCS alone, however, struggles with rare events. When the failure probability is extremely small, the Monte Carlo candidate pool must be enormous, and the surrogate must classify millions of points. The authors’ solution was to fuse this active learning machinery with the First Order Control Variates Method, or FOCM, a technique they had previously developed for high-dimensional, highly nonlinear problems. FOCM works by locating the most probable failure point, linearizing the performance function around it, and then using the control variates principle to correct the bias introduced by that linearization. The correction factor, denoted lambda, is estimated by a modest simulation and multiplies the first-order failure probability to recover the true value. Crucially, FOCM is largely insensitive to the dimensionality of the problem, a property that most surrogate methods lack.

The mathematical elegance of AK-FOCM lies in how the two components divide the labor. The active learning Kriging model concentrates computational effort on the narrow, critical band around the limit state surface, aggressively filtering out the vast safe and failed regions where classification is trivial. Once the surrogate has converged, FOCM takes over: the design point is refined, the performance function is linearized without ever computing explicit partial derivatives, and a correction factor absorbs the truncation error. The authors justify a key simplification, the decoupling of a statistical weighting term from the failure indicators, using the concentration of measure phenomenon in high-dimensional spaces, which guarantees that the residual error shrinks as the number of random variables grows. For rare events, an n-sigma scaling trick artificially inflates the failure probability to a measurable level and then maps it back analytically, sidestepping the statistical wall that defeats ordinary Monte Carlo.

The validation campaign was extensive, spanning twenty mathematical and engineering benchmark problems. In the first test, a two-dimensional exponential function so nonlinear that both FORM and AK-MCS failed completely, AK-FOCM delivered a reliability index of 3.99 against the Monte Carlo reference of 4.01, an error of just half a percent, using only 89 function evaluations. The original FOCM needed 1,818 evaluations for comparable accuracy, meaning the new integration cut the computational cost by 95.1 percent. In a second, severely nonlinear example with exponentially distributed variables, AK-FOCM reached the correct answer with 63 evaluations, roughly 22 percent of what FOCM required, while AK-MCS produced an error three times larger.

The method then faced genuine engineering challenges. A conical shell structure loaded by compression and bending, whose dominant failure mode is buckling, was analyzed with six random variables following lognormal, normal and Gumbel distributions. Monte Carlo demanded one hundred million samples; AK-FOCM matched the reference reliability index of 4.79 with only 115 function calls, whereas AK-MCS failed to converge even with twenty times more initial samples. A fourth case study examined the static strength of an automobile front axle beam, an I-section component carrying the entire weight of the vehicle’s front end. Here AK-FOCM again reproduced the Monte Carlo reliability index of 2.06 with 92 evaluations, outperforming FOCM’s 123 calls while matching its accuracy.

Because surrogate methods involve random initial sampling, the team also ran a rigorous statistical robustness analysis. Thirty independent runs of the hardest nonlinear example produced a mean reliability index of 2.514 with a coefficient of variation below one percent, demonstrating that the method is remarkably insensitive to the luck of the initial sample draw. Sensitivity tests showed that varying the initial training set size from 10 to 30 points changed the final answer by less than half a percent, and enlarging the Monte Carlo candidate pool beyond a critical threshold drove the variance of the estimate essentially to zero. Boxplots of the required function calls across repeated runs showed not only a lower median cost for AK-FOCM but also tighter variability, indicating predictable, stable performance rather than occasional lucky runs.

The authors are candid about the boundaries of their framework. If the initial design of experiments completely misses a small, isolated failure region, the active learning loop could converge prematurely and underestimate risk. Severely discontinuous or highly oscillatory performance functions may violate the assumption that the linearization error can be fully compensated by the correction factor. And although FOCM itself tolerates high dimensions, the Kriging surrogate remains vulnerable to the curse of dimensionality, so problems with thousands of random variables would still degrade its fidelity and inflate its overhead. The method has so far been tested on static structural problems, and the authors call for future comparisons against emerging deep learning-based reliability frameworks and validation on full-scale, time-variant dynamic finite element models.

Even with those caveats, the implications for engineering practice are substantial. Reliability analysis has long been trapped in a trade-off between methods that are accurate but unaffordable and methods that are affordable but fragile. By coupling a self-aware surrogate that learns where to look with a dimensionally robust variance-reduction core, AK-FOCM offers a way to estimate the probability of catastrophic rare events at a fraction of the traditional cost. For designers of critical infrastructure, vehicles and aerospace structures, that could mean running reliability checks routinely during design rather than as a final, expensive afterthought, ultimately translating abstract probability mathematics into safer buildings, safer cars and safer machines in the physical world.

Subject of Research: A hybrid active learning Kriging and first order control variates method for efficient structural reliability analysis of rare failure events

Article Title: AK-FOCM: Integration of active learning Kriging with first order control variates reliability method

Article References: Ameryan, A., Ghalehnovi, M., & Rashki, M. (2026). AK-FOCM: Integration of active learning Kriging with first order control variates reliability method. Results in Engineering, 32, Article 113197. https://doi.org/10.1016/j.rineng.2026.113197

Image Credits: AI Generated

DOI: 10.1016/j.rineng.2026.113197

Keywords: structural reliability, AK-FOCM, active learning, Kriging, Monte Carlo simulation, control variates, failure probability, surrogate modeling, finite element analysis, FORM, rare events, computational efficiency

The research, led by Phani Prasanthi together with B. Raghu Kumar, U. Koteswara Rao, and T. Srinag, presents an integrated framework that weaves together three complementary strands of investigation: physical tensile testing, finite element simulation, and Arrhenius-based kinetic modeling. The goal was not simply to measure how carbon fiber-reinforced polymer composites weaken under heat, but to build a predictive pipeline that can forecast both strength loss and service life across a wide range of operating temperatures, including conditions that were never directly tested in the laboratory.

The experimental backbone of the study consisted of tensile tests conducted at four temperatures: room temperature, 50 degrees Celsius, 80 degrees Celsius, and 100 degrees Celsius. These are not exotic conditions. Components under an aircraft hood, near engine bays, or in sun-exposed automotive structures routinely experience thermal environments in this range, which makes the findings directly relevant to real-world design decisions. The tests were designed to capture the thermo-mechanical behavior of the composites as the polymer matrix that binds the carbon fibers together begins to soften and degrade.

The results were striking. Compared with room-temperature performance, tensile strength fell by 33.33 percent at 50 degrees Celsius, by 61.92 percent at 80 degrees Celsius, and by 57.94 percent at 100 degrees Celsius. The non-monotonic pattern, in which the drop at 100 degrees Celsius was slightly smaller than at 80 degrees Celsius, underscores how complex the underlying degradation mechanisms can be. The polymer matrix is the weak link in this story: carbon fibers themselves retain their strength at these temperatures, but the epoxy or similar resin surrounding them loses stiffness and load-transfer capability as thermal energy disrupts its molecular network. Once the matrix can no longer grip the fibers effectively or transfer stress between them, the composite as a whole fails far below its nominal capacity.

What makes the new work more than another set of measurements is the second pillar of the framework: finite element simulation. The team built numerical models of the tensile tests and calibrated them against the experimental data. The simulations tracked the experiments closely, with prediction errors below 5 percent at room temperature and at 50 degrees Celsius. That level of agreement matters because it establishes the model as trustworthy enough to extrapolate. Having validated the simulation against real data at the lower temperatures, the researchers then used it to predict tensile behavior all the way up to 200 degrees Celsius, a regime where direct testing becomes more difficult and more expensive.

This experimental-to-numerical handoff is a pattern increasingly common in materials engineering, and it addresses a genuine bottleneck. Physical testing at every temperature of interest would demand dozens of specimens, environmental chambers, and weeks of laboratory time. A validated simulation, by contrast, can sweep through a temperature range in hours and flag the conditions that deserve closer experimental scrutiny. In safety-critical fields such as aerospace, where certification authorities demand evidence rather than intuition, a simulation that has been anchored to experimental reality provides exactly the kind of defensible evidence that design reviews require.

The third pillar pushes the work from static prediction into the realm of lifetime forecasting. The researchers employed an Arrhenius kinetic model, a mathematical approach with roots in chemical kinetics that describes how reaction rates accelerate exponentially with temperature. Originally developed to characterize the temperature dependence of chemical reactions, Arrhenius modeling has become a standard tool for predicting the thermal aging and degradation of polymers. In this study, the team used it to establish a quantitative relationship between thermal degradation kinetics and the degradation of tensile strength, effectively linking the speed of molecular-level damage to the macroscopic property that engineers care about most.

The practical payoff of that link is service life prediction. By fitting the kinetic model to the strength data, the framework can estimate how long a composite component will retain adequate strength when held at a given elevated temperature, rather than merely reporting a single strength value measured after an arbitrary exposure. This is the kind of information that maintenance planners and structural designers actually need: not just how strong the material is today, but how strong it will be after years of service in a hot environment. The authors position the integrated framework as a reliable and efficient methodology for predicting tensile strength degradation and service life across a wide range of operating temperatures, supporting both design and long-term reliability assessment in high-temperature applications.

The broader context makes the contribution timely. Carbon fiber composites are expanding into new territory, from wind turbine blades that bake in the sun for decades to electric vehicle battery enclosures that must survive thermal excursions, and the literature has documented repeated concerns about elevated-temperature performance. Previous studies have examined temperature effects on composite mechanics, aging and durability, and failure mechanisms under combined thermal and mechanical loads, but comprehensive frameworks that unite experiment, simulation, and kinetic lifetime modeling in a single validated pipeline remain comparatively rare. The new study also connects to a wider engineering tradition: damage mechanisms and life assessment of high-temperature components have been studied in metals for decades, and this work extends similar predictive logic to polymer-matrix composites.

There are, of course, boundaries to what the study claims. The data availability statement notes that no datasets were generated or analyzed beyond the study itself, and the reported predictions above 100 degrees Celsius rest on simulation and kinetic extrapolation rather than direct measurement, which is precisely why the validation at lower temperatures was so important. The non-monotonic strength behavior between 80 and 100 degrees Celsius also hints that matrix-dominated failure mechanisms may shift with temperature, a nuance that future experimental work could probe further. Still, the framework’s architecture is deliberately modular: as new experimental data arrives, the finite element model and the Arrhenius parameters can be refined, tightening the predictions over time. For an industry that increasingly stakes safety and performance on materials whose weakest ingredient is the polymer holding them together, a tool that turns scattered test data into a continuous, temperature-resolved map of strength and lifespan is a meaningful step forward. It transforms a question that once required a laboratory and a calendar into a calculation that can be run before the first part is ever manufactured.

Subject of Research: Temperature-dependent tensile behavior and service life prediction of carbon fiber-reinforced polymer composites

Article Title: An integrated experimental–numerical–kinetic framework for predicting the tensile behavior of carbon fiber reinforced composites at different temperatures

Article References: Prasanthi, P., Kumar, B. R., Rao, U. K., & Srinag, T. (2026). An integrated experimental–numerical–kinetic framework for predicting the tensile behavior of carbon fiber reinforced composites at different temperatures. Polymer Bulletin, 83(12), Article 673. https://doi.org/10.1007/s00289-026-06709-7

Image Credits: AI Generated

DOI: 10.1007/s00289-026-06709-7

Keywords: carbon fiber composites, tensile strength, finite element analysis, Arrhenius model, thermal degradation, service life prediction, polymer matrix, elevated temperature, CFRP, aerospace materials, structural reliability, integrated

The physical heart of the framework is a corrosion-fatigue deterioration model built on decades of established fracture mechanics. Fatigue cracks at welded joints are represented as semi-elliptical surface flaws, characterized by a depth that grows through the plate thickness and a half-length that spreads along the surface. The stress intensity factor range at both the deepest point and the surface intersection of the crack is computed with the Newman-Raju formulation, one of the most widely trusted equations in fatigue assessment. Crack growth per loading cycle then follows the Paris law, the classic power-law relationship between growth rate and stress intensity, refined by the Walker correction to capture the strong influence of stress ratio. This last detail matters enormously for welds, because tensile residual stresses left behind by welding can push the effective stress ratio near the crack tip toward unity, meaning nearly the entire loading cycle drives the crack forward.

What makes the model genuinely a corrosion-fatigue model rather than a simple fatigue calculation is its explicit coupling of environmental degradation with crack propagation. Corrosion depth evolves over time following a power-law relation governed by a corrosion coefficient and exponent, continuously reducing the effective plate thickness. As the plate thins, the geometric correction factors and stress intensity factors change, accelerating crack growth. On top of that geometric effect, an environmental amplification factor multiplies the Paris coefficient, representing the direct chemical acceleration of cracking in aggressive media. In verification simulations, the consequences were striking: an identical welded detail predicted to survive 14.645 million cycles in air lasted only 7.344 million cycles under corrosion-fatigue conditions, a life reduction of nearly fifty percent, driven by a final corrosion depth of just 0.265 millimeters. Even a seemingly trivial loss of thickness, the authors show, compounds through the nonlinear crack-tip stress field into a dramatic shortening of service life.

Before trusting these predictions, the researchers subjected their implementation to a rigorous verification campaign. A convergence study demonstrated that refining the numerical integration step from 10,000 cycles down to 1,000 cycles reduced the relative error in predicted fatigue life below 0.01 percent, while the final crack geometry remained essentially unchanged. The implemented code reproduced the prescribed Paris-law exponent exactly, recovering a fitted slope of 3.00 with a coefficient of determination of 1.00 in log-log space. Most importantly, an independent benchmark against published corrosion-fatigue experiments on welded joints with artificial corrosion pits, conducted without any recalibration of model parameters, reproduced the experimentally observed degradation trends. The framework achieved a Spearman rank correlation of 0.883 with the nine experimental specimens and matched the direction of the stress-range trend, the pit-depth trend, and their interaction in every case, evidence of trend-level physical consistency rather than a guarantee of absolute life prediction.

The computational bottleneck, however, comes when physics meets probability. Reliability assessment demands thousands to millions of simulations, because uncertainty in crack geometry, loading, material behavior, and corrosion severity must all be propagated through the model. Solving the full fracture-mechanics equations that many times is prohibitively expensive. The authors’ solution is a physics-informed surrogate: they sampled the seven governing input variables, including initial crack depth, aspect ratio, stress concentration factor, stress ratio, and three corrosion parameters, using Latin Hypercube Sampling, a stratified technique that covers the multidimensional uncertainty space far more efficiently than naive random sampling. Each sampled combination was run through the physics model, producing a synthetic dataset of nearly 10,000 virtual experiments in which every record is guaranteed to obey the governing equations.

Onto this physically consistent dataset they trained an XGBoost model, a gradient-boosted decision tree algorithm renowned for its accuracy on nonlinear regression problems. Configured with 500 trees, a maximum depth of six, and a learning rate of 0.05, the surrogate predicted the logarithm of corrosion-fatigue life with a coefficient of determination of 0.976 and a mean absolute percentage error of only 3.49 percent on an independent test set of 1,915 samples. Five-fold cross-validation confirmed stable performance across data subsets, with no systematic bias in either the short-life or long-life regions. In effect, the surrogate compresses a computationally heavy fracture-mechanics simulation into a millisecond-scale prediction while inheriting the physics embedded in its training data, making million-sample Monte Carlo reliability analysis suddenly practical.

Yet fast predictions from a black-box model are of limited value in safety-critical engineering, where regulators and operators need to understand why a model says what it says. Here the framework deploys SHAP, or SHapley Additive exPlanations, a technique rooted in cooperative game theory that assigns each input variable a mathematically rigorous contribution to every prediction. The results revealed a clear hierarchy: the stress concentration factor dominated, with a mean absolute SHAP value of 4.67 million cycles, followed by the corrosion acceleration factor and the initial crack depth. These rankings are not statistical curiosities; they map directly onto the underlying mechanics. Stress concentration amplifies the crack-driving force, the amplification factor multiplies the growth rate, and a deeper initial flaw leaves less propagation distance before failure. An independent permutation importance analysis produced an almost identical ranking, with a Spearman correlation of 0.991 between the two methods, giving strong evidence that the identified hierarchy is robust rather than an artifact of one interpretability technique.

With a fast, transparent surrogate in hand, the team turned to the question that ultimately matters for infrastructure owners: how safe is the structure, and when should it be inspected? Running 100,000 Monte Carlo samples through the surrogate for a required design life of 10 million cycles yielded a failure probability of 0.746 and a negative reliability index, sobering evidence of how severely corrosion-fatigue can undermine nominal design margins. Time-dependent analysis over a 50-year service life showed reliability collapsing nonlinearly: the failure probability climbed from about 2 percent at year 5 to 20 percent at year 10, 51 percent at year 20, and 85 percent by year 50, with the steepest deterioration occurring in the first two decades. Conditional analyses confirmed that as the corrosion acceleration factor increased from its mildest to most severe range, the failure probability rose from 0.61 to 0.84, directly mirroring the SHAP finding that environmental severity is a dominant risk driver.

The final step converts these reliability curves into an actionable inspection schedule tied to engineering decision thresholds consistent with international probabilistic design guidelines such as ISO 2394 and the Eurocode basis of design. The framework identifies three critical moments: preventive monitoring should begin when the reliability index falls to 2.0, which occurs at roughly 5.7 years; detailed inspection is warranted when it reaches 1.0, at approximately 10 years; and repair or strengthening becomes necessary when it hits 0.0, corresponding to a 50 percent failure probability, at about 24.3 years. Rather than imposing uniform inspection intervals on every structure, the approach tailors intervention timing to the predicted deterioration trajectory of each asset, a shift with significant implications for life-cycle management of bridges, offshore installations, and marine infrastructure exposed to aggressive environments.

The authors are candid about the limits of their achievement. The experimental benchmark comprised only nine specimens, so the validation demonstrates trend consistency rather than comprehensive accuracy; the surrogate inherits any model-form uncertainty in the underlying fracture mechanics; localized pit nucleation and growth are represented only in reduced-order form; and the inspection plan relies on reliability thresholds alone, without economic optimization of inspection and repair costs. Future work, they note, should incorporate larger experimental datasets, propagate surrogate uncertainty through Bayesian methods, and couple reliability with life-cycle cost analysis. Even with these caveats, the study stands as a compelling demonstration of what physics-informed, explainable machine learning can deliver: not just a prediction, but a traceable chain of reasoning from the Paris law to the inspection calendar, giving engineers a tool that is simultaneously fast, physically grounded, and transparent enough to trust with the safety of the steel skeleton of modern civilization.

Subject of Research: Physics-informed explainable AI for corrosion-fatigue life prediction and reliability-based inspection planning of welded steel structures

Article Title: Physics-informed explainable artificial intelligence framework for corrosion-fatigue life prediction, reliability assessment, and inspection planning of welded steel structures

Article References: Nguyen, D.-D., & Nguyen, T.-H. (2026). Physics-informed explainable artificial intelligence framework for corrosion-fatigue life prediction, reliability assessment, and inspection planning of welded steel structures. Case Studies in Construction Materials, 25, Article e06586. https://doi.org/10.1016/j.cscm.2026.e06586

Image Credits: AI Generated

DOI: 10.1016/j.cscm.2026.e06586

Keywords: corrosion-fatigue, welded steel structures, fracture mechanics, XGBoost, explainable AI, SHAP, structural reliability, inspection planning, Paris law, Newman-Raju model, machine learning, infrastructure safety

The degradation of reinforced concrete in marine settings follows a well-characterized two-phase sequence. During the initiation phase, chlorides diffuse through the concrete cover toward the embedded steel; the propagation phase begins once the chloride concentration at the rebar depth exceeds a critical threshold, triggering corrosion that produces rust products, cracking, and eventually spalling of the cover. Without intervention, this process can culminate in severe structural damage or outright failure. Traditional inspection techniques, including visual surveys and destructive or non-destructive testing, can detect corrosion, but they are costly, time-consuming, and in some cases risk misdiagnosis or further damage to the structure itself.

Modeling approaches have evolved considerably over the decades. Early studies relied on deterministic formulations of chloride transport, often using analytical solutions to Fick’s second law of diffusion. Later work introduced probabilistic methods to account for the substantial uncertainties in material properties, environmental exposure, model error, and construction quality. However, most of these probabilistic studies relied on one-dimensional chloride ingress models combined with Monte Carlo simulation or reliability methods such as FORM and SORM. That one-dimensional assumption is a serious limitation for real structural elements like columns and beams, where chlorides attack from multiple directions simultaneously. At the corners of polygonal members, chloride penetrates from two orthogonal faces, concentrating the attack precisely where the reinforcement is most vulnerable. One-dimensional models therefore tend to overestimate the time to corrosion initiation at these critical corner regions, potentially leaving structures at risk.

Two-dimensional probabilistic models have addressed the corner problem, but they have largely focused on new, single-layer concrete and ignored what happens after a repair. Repair introduces a genuinely difficult physics problem: when chloride-contaminated concrete is removed and replaced, the residual chlorides left in the original substrate do not simply stay put. They redistribute, diffusing from the old, contaminated concrete into the fresh, chloride-free repair material through the interface between the two layers. This interaction between old and new concrete, including the formation of so-called incipient anodes at the interface, has been captured by detailed deterministic finite element and finite difference models, but extending these physically rich two-dimensional repair simulations to a probabilistic setting has been computationally prohibitive. A single deterministic simulation of a 75-year maintenance history takes roughly 30 minutes on a workstation, and probabilistic assessment typically demands thousands to millions of such runs.

The research team’s solution is a surrogate modeling strategy based on polynomial chaos expansion, or PCE. Instead of running the full numerical model for every uncertainty scenario, PCE constructs a mathematical approximation of the model’s response as a series of multivariate orthogonal polynomials in the random input variables. The coefficients of this expansion, computed by least-squares minimization over a limited set of full model evaluations, map how each input and each interaction between inputs contributes to the output variability. Using least angle regression, the method retains only the polynomial terms with the largest impact, producing a sparse surrogate that captures nonlinear relationships with remarkable economy. In the case study, a surrogate built from just 200 full model evaluations achieved a leave-one-out cross-validation error of 5 times 10 to the power of minus 4, corresponding to a target accuracy of 0.999, with a polynomial order of six and 96 basis elements. Monte Carlo simulation on the surrogate then yields the probability of corrosion initiation at a tiny fraction of the original computational cost.

The underlying physics model, implemented in the open-source software FreeFem++, solves the two-dimensional chloride diffusion equation with a spatially and temporally varying apparent diffusion coefficient. This coefficient accounts for chloride binding, modeled with a Langmuir isotherm, as well as the effects of temperature, concrete aging, and humidity on transport. The repair model divides the column cross-section into two domains: the newly placed, chloride-free repair material and the original aged concrete retaining its residual chlorides. The repair geometry itself is thoughtfully designed, with a circular boundary drawn from the column center to the side reinforcement, so that concrete removal extends deepest near the corner rebars, where contamination is worst, while sparing uncontaminated interior concrete. This circular replacement strategy is both cost-effective and sustainable, minimizing the volume of material that must be removed and replaced.

The illustrative case study examines a 0.4 by 0.4 meter square column in an extreme coastal splash and tidal environment, with a 65-millimeter design cover depth specified according to Eurocode 2. Nine input parameters were treated as random variables, including surface chloride concentration, the critical chloride threshold for corrosion initiation, reference and repair diffusion coefficients, activation energy, the aging factor, and cover thicknesses, each assigned distributions drawn from prior experimental and probabilistic literature. Two repair materials were compared: S1, a conventional concrete similar to the original, and S2, a wet-mix shotcrete with a denser microstructure and lower chloride diffusivity. Repairs were assumed to be triggered when the probability of corrosion initiation reached 10 percent, a threshold consistent with the fib Model Code’s deterioration limit state and close to the Eurocode serviceability reliability target.

The results carry practical weight. With repairs every 10 years using either material, the probability of corrosion initiation stayed around 6.6 percent, safely below the 10 percent threshold, confirming the effectiveness of the circular replacement strategy even under uncertainty. But the higher-quality S2 material showed a clear advantage: after the first repair cycle, the corrosion initiation probability dropped from 6.6 percent to 3.6 percent, reflecting the dense shotcrete’s superior resistance to chloride ingress. When the framework was used to optimize the maintenance schedule rather than simply test a fixed one, the differences became economic. For the conventional S1 material, the optimal plan called for six repairs over a 75-year service life, at years 12, 24, 36, 48, 60, and 72. The superior S2 material stretched the intervals to 15 years, requiring only five repairs at years 12, 27, 42, 57, and 72. Fewer repair campaigns mean lower direct costs and a smaller environmental footprint from materials, demolition waste, and construction traffic.

Equally valuable is the framework’s global sensitivity analysis, made possible by post-processing the polynomial chaos coefficients into Sobol indices. Before repair, concrete cover thickness dominated, with a first-order Sobol index exceeding 60 percent of the output variance, a finding amplified by the two-dimensional corner geometry where the cover is the only barrier against attack from two directions. Surface chloride concentration ranked second, followed by the reference diffusion coefficient and the aging factor, while the activation energy for diffusion proved negligible under the study’s relatively stable temperature conditions. After repair, the hierarchy shifted: the diffusion coefficient of the repair material became the second most influential parameter, underscoring that material selection for repairs is a durability decision, not merely a structural one. The amount of concrete replaced, which determines the renewed cover thickness, took over the protective role previously played by the original cover. Notably, differences between first-order and total Sobol indices remained below 10 percent, indicating that the input parameters act largely independently rather than through strong interactions.

The authors are careful to frame the resulting 12-to-15-year repair intervals as illustrative outputs of an idealized preventive strategy rather than universal recommendations, and they emphasize that field observations in aggressive marine environments have documented corrosion-induced deterioration after only 20 to 25 years of exposure, sometimes earlier. The framework’s real contribution is methodological: a computationally tractable way to make proactive, reliability-based maintenance decisions for structures whose deterioration is inherently two-dimensional and whose repairs create new, coupled transport domains. The researchers identify clear next steps, including integrating empirical data on parameter correlations, characterizing geometric uncertainties after repair, and coupling the probabilistic model with life-cycle cost analysis and inspection data. As coastal infrastructure ages and climate change intensifies marine exposure, tools that convert uncertainty from an obstacle into a design variable may prove essential for keeping the world’s concrete assets safe, serviceable, and affordable to maintain.

Subject of Research: Probabilistic optimization of maintenance for chloride-corroded reinforced concrete structures in marine environments

Article Title: A probabilistic framework for optimizing maintenance of reinforced concrete structures in marine environments

Article References: Truong, Q.-C., El Soueidy, C.-P., & Bastidas-Arteaga, E. (2026). A probabilistic framework for optimizing maintenance of reinforced concrete structures in marine environments. Results in Engineering, 32, Article 113164. https://doi.org/10.1016/j.rineng.2026.113164

Image Credits: AI Generated

DOI: 10.1016/j.rineng.2026.113164

Keywords: reinforced concrete, chloride-induced corrosion, marine environment, polynomial chaos expansion, probabilistic modeling, maintenance optimization, surrogate modeling, sensitivity analysis, concrete repair, structural reliability, chloride ingress, service life prediction