Machine learning predicts soil deformability for Himalayan infrastructure

Engineers building roads, slopes and foundations in Nepal’s Lesser Himalayan region face weak, landslide-prone fine-grained soils that settle excessively and lose strength under load. A new laboratory and machine-learning study reports that a strain-based deformability measure of nano-silica-stabilized soils can be predicted with high accuracy by an Extreme Gradient Boosting model, even when the model must generalize to a soil type it has never seen during training. The work, published in Discover Geoscience, introduces the Unconfined Compression Index as a practical companion to the familiar unconfined compressive strength measurement.

The Unconfined Compression Index, abbreviated Ic, is defined as the axial strain, expressed as a percentage, at which a specimen mobilizes 50 percent of its peak unconfined compressive strength on the stress-strain curve. The authors chose the 50 percent stress level because it corresponds to the reference point defining the secant deformation modulus, a standard stiffness parameter in soft-soil constitutive modelling. Strains measured at lower stress levels are sensitive to initial seating effects, while strains measured near peak are affected by the loss of curvature as failure approaches. Lower Ic values indicate a stiffer material, whereas higher values denote a more ductile, compressible response. The researchers note that the index is distinct from the standard one-dimensional compression index, the cohesion intercept from shear-strength envelopes, and the strength value itself, and that no inference about ductility or brittleness is drawn because post-peak behavior lay outside the testing program.

Three representative fine-grained soils were collected from the Lesser Himalayan Mid-Hill region of Nepal: an inorganic clay of high plasticity from a slope-cut near Kathmandu, an inorganic silt of high plasticity from a river terrace deposit in Morang, and a clayey sand to sandy clay recovered from a landslide-prone cut slope in Sindhuli. The soils were classified under the Unified Soil Classification System using grain-size analysis and Atterberg limit tests. Commercially available precipitated nano-silica, supplied as a dry amorphous powder with a specific surface area of 180 square meters per gram, an average primary particle size of 25 nanometers and a purity of at least 99 percent silicon dioxide, served as the stabilizing agent.

Specimens were prepared by mixing soil passing a 2.36-millimeter sieve with nano-silica at dosages of 0, 0.5, 1.0, 1.5, 2.0, 2.5, 3.0, 3.5 and 4.0 percent by dry mass of soil. Distilled water brought each mixture to its standard Proctor optimum moisture content, and mixing ran for 10 minutes in a planetary mixer to disperse the additive uniformly. Cylindrical specimens 38 millimeters in diameter and 76 millimeters tall were statically compacted to 95 percent of the maximum dry density from standard Proctor compaction, then cured in a humidity chamber at at least 95 percent relative humidity and 25 degrees Celsius for 3, 7, 14, 28, 56 or 90 days. Three replicates were prepared for every combination of soil type, dosage and curing period, producing a balanced factorial design of 486 potential tests; after excluding damaged specimens and statistical outliers, 189 valid observations remained for analysis.

Unconfined compressive strength tests followed ASTM D2166, loading specimens at a constant strain rate of 1 percent per minute until peak stress or 20 percent axial strain, whichever came first. A limited series of consolidated-undrained triaxial tests on selected clay and silt specimens was performed only to observe effective-stress shear behavior and confirm that the unconfined response remained representative of the stabilized matrix; those data were not used to calculate the index or as model inputs. Correlation analysis of the resulting database showed a strong positive relationship between nano-silica dosage and strength, with a Pearson coefficient of 0.826, confirming the additive as a dominant strength driver. Curing duration and the deformability index showed a strong negative correlation of minus 0.824, indicating that prolonged curing reduces deformability, while strength and the index correlated moderately negatively at minus 0.650, as expected because stiffer, higher-strength specimens mobilize peak stress at lower strains.

Six supervised machine-learning algorithms were trained to predict the index from soil type, nano-silica content, curing duration and early-cure strength: Linear Regression, Random Forest, Extreme Gradient Boosting, K-Nearest Neighbors, Support Vector Machine and Lasso Regression. All computations ran in the XLSTAT-AI module within Microsoft Excel, spanning interpretable linear forms to non-parametric ensemble methods. Multicollinearity among the predictors was assessed with variance inflation factors; curing duration exceeded the conventional threshold of 10 with a value of 11.523, and nano-silica content showed moderate multicollinearity at 6.483, reflecting the coupled pozzolanic effect of longer-cured, high-dosage specimens. The ensemble methods were retained without modification because they are robust to correlated predictors, while a ridge penalty stabilized the coefficient estimates of the linear models.

The validation design is the study’s most distinctive methodological choice. A simple random 80/20 split was rejected because the dataset is a structured full-factorial experiment, and random partitioning would place nearly identical observations in both training and validation sets, evaluating interpolation rather than true generalization. Instead, the team adopted Leave-One-Soil-Type-Out cross-validation, training on two soil types and validating on the held-out third in three rotating folds. This strategy tests whether a model trained on two soil types can predict the deformability index for an unseen soil, a far more rigorous assessment of practical utility than random subsampling. Mean absolute error and root mean squared error were treated as the primary criteria, since the coefficient of determination is normalized by the variance of the held-out set, which is narrower within a single soil than across the full dataset.

Across the performance comparison, Extreme Gradient Boosting achieved the lowest mean absolute error at 0.158 and the lowest mean squared error at 0.046, while explaining 96.1 percent of the variance with a coefficient of determination of 0.961. Random Forest followed closely with a mean absolute error of 0.166 and a coefficient of 0.951, indicating that both ensemble approaches effectively capture the complex nonlinear relationships governing the deformation response of stabilized soils. Lasso Regression performed poorly, with a mean absolute error of 1.036 and a negative coefficient of determination of minus 0.393, meaning it fit worse than a simple mean-based prediction; the authors attribute this underperformance to the multicollinearity among variables, which can cause the L1 penalty to zero out or overly reduce coefficients. Variable-importance analyses identified curing duration as the most influential predictor, followed by strength and soil type, with nano-silica dosage contributing least.

The framework also addresses a potential logical circularity. Because the index is extracted from the same unconfined compression test as the strength value, including strength as an input could appear circular. The authors justify it as an early-cure proxy: geotechnical quality-control programs routinely measure strength at an early age such as 7 days to verify stabilization efficacy, and the models aim to predict the long-term deformation index at later curing stages without additional specialized testing. Two configurations were evaluated for every algorithm, a full model with all four inputs and a reduced model using only soil type, dosage and curing time. If the reduced model achieves acceptable accuracy, the index can be estimated from mix-design parameters alone during preliminary design; if the full model substantially outperforms it, the early strength measurement is confirmed as an informative covariate.

The authors frame their contribution carefully. The index is strictly valid for unconfined conditions, and its extension to confined or drained states requires independent verification. Dry density was fixed geometrically by static compaction rather than measured after compaction, so individual achieved densities were not recorded. The structured factorial design and the leave-one-soil-type-out strategy test interpolation within the experimental domain rather than extrapolation beyond the 0 to 4 percent dosage range, the 90-day curing limit or the controlled compaction conditions studied here. Field moisture and temperature variability were not considered, and generalization beyond the three investigated soil types remains unverified. The reduced model is recommended for preliminary design requiring no testing, while the full model applies only where strength is already measured. The team calls for validation of the early-cure-to-late-cure workflow on field-stabilized slopes or highway subgrades in the Lesser Himalayas, microstructural studies linking the index to microscopy and diffraction data, extended curing to 180 days, wet-dry and freeze-thaw cycling, and SHAP-based explainability to enhance transparency for engineering design decisions.

Subject of Research: Machine learning prediction of the Unconfined Compression Index of nano-silica-stabilized fine-grained soils from the Lesser Himalayan region

Article Title: A machine learning framework for predicting the unconfined compression index of nano-silica stabilized fine-grained soils using leave-one-soil-type-out validation

Article References: Thapa, I., & Poudel, B. (2026). A machine learning framework for predicting the unconfined compression index of nano-silica stabilized fine-grained soils using leave-one-soil-type-out validation. Discover Geoscience, 4(1), Article 428. https://doi.org/10.1007/s44288-026-00811-z

Image Credits: AI Generated

DOI: 10.1007/s44288-026-00811-z

Keywords: machine learning, nano-silica, soil stabilization, unconfined compression index, fine-grained soils, Himalayan geotechnics, Extreme Gradient Boosting, cross-validation, unconfined compressive strength, soil deformability, curing duration, Lesser Himalaya