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