Abstract
Accurate prediction of soil stress–strain behavior remains a major challenge in geotechnical engineering due to the inherent heterogeneity, nonlinearity, and sparsity of soil datasets. Conventional laboratory and in-situ testing methods are often expensive, time-consuming, and sensitive to sampling disturbances, which limits their efficiency in large-scale engineering applications. To address these challenges, this study proposes an optimized stacking ensemble framework that integrates advanced tree-based learning algorithms with metaheuristic optimization. The selected base learners Light Gradient Boosting (LGB), Extreme Gradient Boosting (XGB), Random Forest (RFR), and Histogram-based Gradient Boosting (HGB) were chosen for their complementary strengths in capturing nonlinear interactions, handling high-dimensional inputs, and maintaining robustness under sparse and heterogeneous data conditions. These models are optimized using the Puma Optimization (PO) algorithm and combined through a stacking strategy to enhance predictive stability and generalization performance. A dataset comprising 1,410 samples was compiled literature data, witch the K-fold cross-validation was employed to evaluate model robustness. The proposed stacking model, particularly the optimized XGBPO ensemble, achieved superior predictive accuracy with a coefficient of determination (R2) of 0.9914 in the testing phase, outperforming individual and hybrid models. Interpretability and sensitivity analyses further identified dry density (\({\gamma }_{d}\)), void ratio (e0), and degree of saturation (\({S}_{r}\)) as the most influential factors governing soil compressibility behavior. The proposed framework provides a scalable, reliable, and computationally efficient alternative to traditional geotechnical testing methods, offering improved predictive accuracy and practical applicability for infrastructure design and decision-making under complex soil conditions.
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Data availability
The datasets used and/or analyzed during the current study available from the corresponding author on reasonable request.
Abbreviations
- \({E}_{s}\) :
-
Soil compression modulus
- XGB :
-
Extreme gradient boosting
- HGB :
-
Histogram gradient boosting
- ML :
-
Machine learning
- \({D}_{U}\) :
-
Depth of the upper soil
- \({D}_{D}\) :
-
Depth of the lower soil
- \(\omega\) :
-
Water content
- \({\gamma }_{d}\) :
-
Dry density
- \({e}_{^\circ }\) :
-
Void ratio
- \({S}_{r}\) :
-
Degree of saturation
- IQR :
-
Interquartile range
- FAST :
-
Fourier amplitude sensitivity test
- S1 :
-
Individual sensitivity
- ST :
-
Total sensitivity
- Max :
-
Maximum
- Min :
-
Minimum
- GP :
-
Genetic programming
- LSTM :
-
Long short-term memory
- MCMC :
-
Markov chain-based Monte Carlo
- GBRT :
-
Gradient-boosted regression tree
- PO :
-
Puma optimization algorithm
- LGB :
-
Light gradient boosting
- RFR :
-
Random forest
- R 2 :
-
Coefficient of determination
- RMSE :
-
Root mean square error
- NRMSE :
-
Normalized root mean square error
- MSLE :
-
Mean squared logarithmic error
- RMSLE :
-
Root mean squared logarithmic error
- MASE :
-
Mean absolute scaled error
- U95 :
-
Under-95th percentile
- U :
-
Theil’s inequality coefficient
- SI :
-
Scatter index
- WI :
-
Willmott’s index
- ICE :
-
Individual conditional expectation
- PDP :
-
Partial dependence plot
- RM :
-
Resilient modulus
- ANN :
-
Artificial neural networks
- SVM :
-
Support vector machines
- EPM :
-
Evolutionary polynomial regression
- SGSPG :
-
Spatial–geological stratigraphic graph
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Reza Sarkhani Benemaran: Conceptualization; Data curation; Formal analysis; Project administration; Supervision; Erfan Khajavi: Software; Validation; Visualization; Roles/Writing—original draft; Amir Reza Taghavi Khanghah: Visualization;
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Sarkhani Benemaran, R., Khajavi, E. & Taghavi Khanghah, A.R. Construction of multi-parameter intelligent comprehensive estimation algorithms for soil compression modulus. Sci Rep (2026). https://doi.org/10.1038/s41598-026-43812-1
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DOI: https://doi.org/10.1038/s41598-026-43812-1
