The stakes are higher than most people realize. Traditional geotechnical design has long relied on empirical rules, simplified analytical models, and generous safety factors to cope with the enormous uncertainty inherent in soil behavior. That conservatism keeps structures safe, but it also produces overdesigned foundations, wasted concrete and steel, inflated construction costs, and unnecessary embodied carbon. Optimization algorithms promise a way out: by mathematically searching the design space for solutions that satisfy stability, settlement, and bearing capacity requirements while minimizing cost and environmental impact, they allow engineers to explore far more of the possible design space than trial-and-error ever could. The trouble, Dehghanian argues, is that most existing reviews of these methods are purely descriptive, cataloguing applications without ever comparing them under consistent, criteria-driven rules.

To fix that, the study classifies optimization techniques into four families: classical deterministic methods, metaheuristic algorithms, surrogate-based approaches, and artificial intelligence-driven techniques. Deterministic methods, including gradient-based techniques, linear and quadratic programming, and sequential quadratic programming, converge reliably when objective functions are smooth and convex, but they stumble on the nonlinear, discontinuous, and multimodal landscapes that soil behavior typically produces. Metaheuristics, inspired by evolution, swarming birds, annealing metals, and foraging ants, dominate the field precisely because they can navigate such messy terrain without needing gradients. Genetic algorithms evolve populations of candidate solutions through selection, crossover, and mutation; particle swarm optimization moves a flock of particles through the search space guided by individual and collective memory; and a growing menagerie of newer algorithms, from the Grey Wolf Optimizer to the Whale Optimization Algorithm, has been applied to foundations, slopes, and parameter identification problems.

Yet the review delivers a sobering assessment of the metaheuristic boom. Each optimization iteration may demand a full finite-element simulation, and a typical study can require thousands of such evaluations before converging, making computational cost a serious bottleneck. Performance also depends heavily on algorithm-specific tuning parameters such as population size, mutation rate, and inertia weight. Perhaps most provocatively, the study notes that recent benchmarking research has shown performance differences among many newly proposed metaheuristics often become statistically insignificant once parameters are properly calibrated. The No-Free-Lunch theorem looms over the entire field: averaged across all possible problems, every optimization algorithm performs identically, so algorithm selection must rest on problem characteristics rather than novelty.

To move beyond qualitative judgments, Dehghanian constructed a unified evaluation framework with explicitly quantified criteria: convergence efficiency, measured by how quickly an algorithm reaches 95 percent of its final optimum; data efficiency, measured by the number of objective-function evaluations required; interpretability; uncertainty quantification capability; scalability; constraint-handling robustness, expressed as the fraction of feasible solutions generated; and practical maturity. This framework was then stress-tested with a benchmark problem: optimizing the width of a square shallow footing on homogeneous medium-dense sand, minimizing the foundation footprint while satisfying a minimum bearing capacity factor of safety of 3.0 and a settlement limit of 25 millimeters. Three algorithms, a genetic algorithm, particle swarm optimization, and Gaussian Process Regression-based Bayesian Optimization, tackled the identical constrained problem.

The results are striking. All three methods converged to nearly the same optimal design, a footing width of roughly 0.80 meters, with a computed settlement of about 2.55 millimeters, far below the allowable limit, and a bearing capacity factor of safety exceeding 5.5. But the paths to that answer differed dramatically. The metaheuristic methods required many objective-function evaluations and occasionally violated settlement constraints during early iterations. Bayesian Optimization, by contrast, terminated after just 30 evaluations in a total elapsed time of 13.38 seconds, with the Gaussian process model’s best-predicted feasible point exactly matching the best-observed solution. The surrogate-based approach achieved equivalent design quality at a fraction of the computational cost, a decisive advantage when each evaluation means running an expensive numerical simulation.

Even more important than raw speed is what Bayesian Optimization knows about its own ignorance. Because Gaussian Process Regression produces both a prediction and a predictive variance for every candidate design, the algorithm can translate statistical uncertainty directly into engineering reliability. The review illustrates this with a compelling example: two footing designs, one predicting 19 millimeters of settlement with a standard deviation of 8, the other predicting 21 millimeters with a standard deviation of only 2. A deterministic optimizer would prefer the first design, but its large uncertainty carries a real risk of exceeding the 25-millimeter threshold. The second design, though nominally worse on average, is far more defensible. By feeding uncertainty into the acquisition function, Bayesian Optimization balances exploiting promising regions against exploring poorly understood ones, effectively steering itself away from unreliable designs.

The study also tackles the black-box problem that has long plagued machine learning in safety-critical engineering. Using SHAP, or SHapley Additive exPlanations, values to interpret a surrogate-assisted footing design model, the analysis revealed that soil friction angle exerted the strongest influence on optimization outcomes, a finding that maps directly onto classical bearing capacity theory, in which the bearing capacity factors depend strongly on the friction angle. This kind of physically meaningful explanation, the review argues, is essential for engineers who must accept or reject algorithmic recommendations, and it distinguishes genuine geomechanical mechanisms from mere statistical correlations. The study similarly highlights physics-informed neural networks, which embed governing equations into the learning process and require less training data than purely data-driven models.

The review’s scope extends well beyond foundations. For slope stability, optimization algorithms automate the search for the critical slip surface within limit equilibrium methods, where the search space is riddled with local minima that defeat traditional grid searches. Ant colony optimization, genetic algorithms, and particle swarm optimization have all proven effective here, and reliability-based design optimization now allows engineers to minimize excavation volume subject to explicit limits on the probability of failure. In site characterization, optimization coupled with geostatistics can determine optimal borehole layouts that minimize estimation uncertainty, while inverse analysis calibrates constitutive model parameters against laboratory and field data. Machine learning models, tuned by optimization algorithms themselves, increasingly predict soil properties from cone penetration and standard penetration test data, and transfer learning is allowing data-scarce regions to leverage models trained on large regional databases.

Looking forward, Dehghanian identifies digital twins, reinforcement learning for adaptive excavation, real-time sensor-driven optimization, and integration with Building Information Modeling as the field’s next frontiers, alongside persistent challenges in computational scalability, software interoperability, and the ethics of autonomous decision-making. The practical guidance distilled from the benchmark is refreshingly concrete: for inexpensive problems, genetic algorithms and particle swarm optimization remain robust workhorses; for expensive finite-element analyses, Bayesian and surrogate-assisted methods are generally preferable; for reliability-critical projects, uncertainty-aware frameworks should be prioritized; and explainability should be treated as a requirement, not an optional extra. The overarching message is one of disciplined pragmatism. Optimization algorithms are not replacements for engineering judgment but powerful decision-support tools, and choosing among them should be an evidence-based engineering decision, guided by computational budget, problem dimensionality, data availability, and the non-negotiable demands of safety.

Subject of Research: Comparative assessment of optimization algorithms for geotechnical engineering design

Article Title: A systematic review and comparative assessment of optimization algorithms in geotechnical engineering with a benchmark foundation design case study

Article References: Dehghanian, K. (2026). A systematic review and comparative assessment of optimization algorithms in geotechnical engineering with a benchmark foundation design case study. Discover Geoscience, 4(1), Article 304. https://doi.org/10.1007/s44288-026-00642-y

Image Credits: AI Generated

DOI: 10.1007/s44288-026-00642-y

Keywords: geotechnical engineering, optimization algorithms, Bayesian optimization, genetic algorithm, particle swarm optimization, foundation design, metaheuristics, uncertainty quantification, surrogate modeling, explainable AI, slope stability, machine learning

The research, led by Professor Shinya Inazumi of the College of Engineering at Shibaura Institute of Technology, was made available online on July 25, 2026 and published in Volume 32 of the journal Results in Engineering on December 1, 2026. Its central contribution is a set of empirical design correlations for shaft resistance, back-calculated from twenty full-scale instrumented static load tests conducted along a 180-kilometer infrastructure corridor in northeastern Thailand. Rather than relying on scattered values from the literature, the team built its design equations directly from measurements of how load actually transfers from pile to soil, layer by layer, in real foundations subjected to very high test loads.

To understand why this matters, it helps to look at how shaft resistance is conventionally estimated. For cohesive soils such as clay, engineers commonly use the adhesion factor method, in which the unit shaft resistance is taken as a fraction, denoted α, of the soil’s undrained shear strength. For cohesionless soils such as sand, the friction factor method applies, expressing unit shaft resistance as a factor β multiplied by the effective vertical stress at the depth of interest. Both approaches are elegantly simple, but their empirical factors are notoriously variable. Published α and β values differ widely because they are influenced by soil type, geological history, construction technique, and in-situ stress conditions, and most published correlations are derived from ordinary soils alone.

That last limitation is where the new study makes its most distinctive contribution. Between ordinary clay or sand and genuine weak rock lies a class of materials that geotechnical engineers call intermediate geomaterials, or IGMs. These stiff transitional soils are neither fully soil nor fully rock, yet they are extremely common in regions where thick sedimentary deposits grade into weathered siltstone or sandstone. Because most design guidance was developed for conventional soils, engineers have had little reliable basis for assigning α or β values to IGMs, forcing conservative assumptions that can inflate foundation costs or, worse, mischaracterize how a pile will actually behave.

The field campaign behind the new correlations was unusually extensive. The team’s site investigation program involved 158 boreholes drilled at an average spacing of roughly 1.1 to 1.2 kilometers along the 180-kilometer corridor, with soil profiling carried out using the Standard Penetration Test. The bored piles themselves were constructed using a wet process with bentonite slurry supporting the borehole during excavation, a common technique for large-diameter piles in difficult ground. Twenty instrumented static load tests were then performed, with maximum applied loads ranging from 16.25 to 25 meganewtons, corresponding to 2.5 times the allowable working load. The piles were embedded in layered ground consisting of either clay or sand overlying weak siltstone or sandstone.

What transformed these tests into a research dataset was the instrumentation. Each test pile was fitted with vibrating-wire strain gauges and extensometer rods, allowing the researchers to monitor how load transferred along the shaft as the test progressed. By analyzing strain measurements at different depths, they could isolate the unit shaft resistance mobilized within individual soil layers. This layer-by-layer approach produced a dataset covering 32 clay and IGM clay layers and 10 sand and IGM sand layers. From each layer’s stress-displacement curve, the team applied a mobilization criterion to select representative maximum shaft resistance values, ensuring that the back-calculated factors reflected fully mobilized resistance rather than partial, load-level-dependent readings.

The resulting adhesion factors for clay and IGM clay ranged from 0.11 to 1.04 and showed a clear, systematic trend: α decreases as the normalized undrained shear strength increases. The empirical equation derived from this trend offers what the researchers describe as a practical mid-range estimate for clays overlying weak rock. Particularly revealing was the comparison across material classes. When α values for ordinary clay, IGM clay, and weak rock were plotted together, they revealed a gradual transition, with IGM clay forming the upper envelope of the clay response. In other words, IGM clay genuinely behaves as an intermediate material, sitting between ordinary clay and weak rock, and treating it as either end member would misrepresent its capacity.

For the cohesionless side, the calculated friction factors ranged from 0.45 to 1.06 across the investigated sand layers, and the proposed empirical equation for β showed good agreement with correlations already reported in the literature. Encouragingly, the β values obtained for IGM sand followed the same overall trend as ordinary sand, suggesting that conventional β-method formulations can be extended to IGM sand provided that stress history and site-specific ground conditions are appropriately considered. This finding is significant because it means engineers may not need entirely new frameworks for sandy intermediate geomaterials, only careful calibration of the parameters they already use.

The practical implications reach well beyond academic curve-fitting. The study demonstrates that intermediate geomaterials should not be treated as conventional soils without accounting for their transitional behavior, and the researchers propose that a normalized undrained strength of approximately 10 can serve as a practical reference point for identifying where IGM clay gives way to weak rock. Such a threshold gives designers a simple, measurable criterion for classifying ground along soil-rock transitions, which are widespread across Southeast Asia and many other regions where heavy infrastructure is built on deep sedimentary basins. Applying these correlations during preliminary design, the team notes, can produce more reliable capacity estimates without costly additional testing, potentially allowing shorter piles and reduced concrete volumes, which lowers construction costs while supporting safer structures.

For a field that has long balanced safety against economy using factors inherited from decades-old case histories, the value of twenty fully instrumented, full-scale load tests along a single well-characterized corridor is hard to overstate. By replacing guesswork with field-verified evidence, the study gives foundation engineers a defensible basis for predicting how much load the shaft of a large bored pile can carry in layered ground, and it clarifies, with data rather than assumption, where ordinary soil ends and weak rock begins.

Subject of Research: Field-calibrated prediction of shaft resistance for large-diameter bored piles in clay, sand, and intermediate geomaterials

Article Title: Towards more reliable shaft resistance prediction for bored piles

Article References: Towards more reliable shaft resistance prediction for bored piles. (n.d.). Original publication

Image Credits: AI Generated

DOI: Not provided

Keywords: bored piles, shaft resistance, adhesion factor, friction factor, intermediate geomaterials, static load tests, geotechnical engineering, foundation design, soil-rock transition, instrumented piles, clay, sand

Traditionally, engineers have relied on analytical equations such as Terzaghi’s bearing capacity formula to estimate how much pressure soil can withstand. These formulas, while foundational to the discipline, struggle to capture the complex, nonlinear interplay of soil properties under real-world loading conditions. Finite element simulations in software such as PLAXIS 3D can model soil-structure interaction in fine detail, capturing nonlinear responses, large deformations, and intricate contact interfaces, but they are computationally demanding and require specialized expertise. The research team’s solution was to fuse the two approaches: use a validated PLAXIS 3D finite element model to generate a trustworthy numerical database, then train Support Vector Machine (SVM) regression models on that data to deliver fast, accurate predictions.

The dataset underpinning the study was compiled from seven previous experimental investigations archived at Kano University of Science and Technology in Wudil, Nigeria, covering a wide range of soil engineering properties. Six input variables were considered: foundation depth, plasticity index, fines percentage, cohesion, angle of internal friction, and unit weight. The target variable, ultimate bearing capacity, ranged from 215 to 1785 kilonewtons per square meter, reflecting considerable variability in soil conditions. Before model development, the team performed outlier detection, missing-data handling, and normalization, then split the data 80/20 for training and testing, with 10-fold cross-validation to guard against overfitting.

A critical early step was feature selection. Correlation analysis revealed that the angle of internal friction dominated the picture, with a correlation coefficient of 0.895 with bearing capacity, consistent with Terzaghi’s theory that frictional resistance governs load distribution in granular soils. Depth showed only a weak correlation of 0.084, while plasticity index, fines percentage, cohesion, and unit weight hovered near zero. Based on these insights, the researchers constructed three feature sets: a minimalist model using only the friction angle, an intermediate model adding depth, and a comprehensive model including all six parameters. The intermediate configuration, combining depth and friction angle, would ultimately prove the sweet spot between simplicity and predictive power.

Four SVM variants were tested: linear, quadratic, cubic, and cubic with a Gaussian radial basis function kernel. Hyperparameters including the box constraint, kernel scale, and epsilon were tuned via grid search with 10-fold cross-validation. The quadratic SVM paired with the intermediate feature set emerged as the champion, achieving a coefficient of determination of 0.9200 on the testing phase, with the lowest root mean square error of 113.55 and mean absolute error of 100.59 across all models. The quadratic kernel, the authors explain, effectively captures second-order interactions between depth and frictional soil properties that a purely linear model misses. Meanwhile, the cubic SVM, despite strong training performance, showed signs of overfitting, and the comprehensive six-parameter feature set failed to outperform the leaner three-variable configuration, suggesting that redundant inputs introduce noise rather than signal.

To validate the physics side of the hybrid framework, the team built three-dimensional finite element models of strip footings in PLAXIS 3D, discretizing the soil domain into 10-node tetrahedral elements with a locally refined mesh beneath the footing where stress and strain gradients are steepest. Soil behavior was described by the Mohr-Coulomb constitutive relationship, and boundary conditions were set far enough from the loading zone to avoid artificial edge effects. Crucially, the finite element model was verified against experimental measurements without any recalibration to improve the fit, and the close agreement between simulated and measured bearing capacities gave the researchers confidence that the numerical database could reliably feed the machine learning models.

Interpretability received its own treatment. Because correlation analysis only captures linear relationships, the team applied SHAP (SHapley Additive Explanations), a game-theory-based technique that quantifies each feature’s contribution to model output, including nonlinear interactions. The SHAP analysis confirmed that the angle of internal friction contributes the most to predictions, with cohesion and foundation depth playing intermediate roles, while unit weight, fines percentage, and plasticity index contribute relatively little. The agreement between the two independent importance assessments strengthened confidence that the selected features are both statistically and physically meaningful.

The quadratic SVM also held its own against benchmark algorithms. Ensemble bagged trees, ensemble boosted trees, and a medium neural network were trained on identical data with identical preprocessing. The neural network posted the best validation accuracy, but on unseen test data the quadratic SVM achieved the highest coefficient of determination and lowest error, demonstrating stronger generalization. Ten-fold cross-validation reinforced this picture, with coefficients of determination ranging from roughly 0.67 to 0.97 across folds and mean absolute percentage errors staying below 18 percent. An external validation using independent field data from the Eastern Niger Delta, never seen during model development, further showed that the nonlinear kernel-based models reproduced measured bearing capacities more faithfully than linear formulations.

What elevates the study beyond a technical exercise is its environmental framing. Conventional foundation design leans on conservative safety factors that drive over-reinforcement and excessive consumption of cement, steel, and aggregates, all of which carry heavy greenhouse gas burdens from energy-intensive production. By pinpointing bearing capacity more precisely, machine learning allows engineers to size foundations to actual need, cutting material waste, reducing excavation and land disturbance, and lowering fuel consumption from construction machinery. The authors also point to benefits for groundwater protection, since optimized foundation depths reduce the risk of disturbing aquifers or mobilizing soil contaminants, and for climate resilience, since predictive models can help anticipate foundation performance under extreme weather and shifting environmental conditions.

The researchers are candid about limitations. All the training data originated from a single geographic region shaped by the same climatic and geological processes, so the model’s greatest accuracy applies to soils with similar engineering characteristics, and independent validation from geologically diverse locations will be needed to confirm broader applicability. Future work, they suggest, could explore hybrid machine learning architectures, deep learning techniques, ensemble methods, and integration with real-time environmental monitoring. Still, the message is clear: pairing validated physics simulation with kernel-based learning offers geotechnical engineers a fast, interpretable, and environmentally conscious alternative to costly drilling campaigns and conservative over-design, a small algorithmic shift with the potential to reshape how the built world meets the ground beneath it.

Subject of Research: Machine learning prediction of the ultimate bearing capacity of strip foundations using kernel-SVM models trained on experimental and PLAXIS 3D finite element data for sustainable geotechnical design

Article Title: Environmentally informed prediction of ultimate bearing capacity using Kernel-SVM and PLAXIS 3D FEM for sustainable geotechnical design

Article References: Ahmed, D., Ajmal, M., Chowdhury, S. R., Ayadat, T., & Abba, S. I. (2026). Environmentally informed prediction of ultimate bearing capacity using Kernel-SVM and PLAXIS 3D FEM for sustainable geotechnical design. Discover Geoscience, 4(1), Article 362. https://doi.org/10.1007/s44288-026-00726-9

Image Credits: AI Generated

DOI: 10.1007/s44288-026-00726-9

Keywords: ultimate bearing capacity, Support Vector Machine, PLAXIS 3D, finite element method, geotechnical engineering, foundation design, machine learning, feature selection, SHAP interpretability, sustainable construction, soil mechanics, climate-resilient infrastructure