What question did this study set out to answer?

The main aim is to develop an accurate predictive method for estimating static strength of frozen soils using machine learning.

April 18, 2026Open Access

Static strength estimation of frozen soils using DEM-verified and optimized tree-based algorithms

Key Points

The main aim is to develop an accurate predictive method for estimating static strength of frozen soils using machine learning.
Employed tree-based machine learning algorithms: random forest regression analysis.
Introduced key input attributes affecting soil stability: water content, negative temperature, confining pressure, freeze-thaw cycles, thawing time, and compaction degree.
Utilized optimization techniques: Reptile Search Algorithm, Red Fox Optimization, and Grey Wolf Optimization for hyperparameter tuning.
Used discrete element method for numerical verification of model predictions.
RF (RFO) model achieved an R2 value of 0.9937 in testing, indicating very high predictive accuracy.
Models showed negligible discrepancies from experimental static strength values, ranging within -0.4067% to 2.5455%.
Compared with other models like ANN, RF (RFO) demonstrated superior accuracy results.

Abstract

Freeze-thaw soil degradation significantly compromises the stability of foundations, roads, and pipelines, leading to costly repairs and increased environmental risks due to soil erosion and altered drainage patterns. Employing machine learning technological advances, a predictive method for soil static strength (S s ) is developed to characterize the degradation of soil under frozen conditions accurately. Water content ( W c ), negative temperature ( T N ), confining pressure ( C P ), freeze–thaw cycles ( N F - T ), thawing time ( T T ), and compaction degree ( k ) were introduced as input attributes. A technique known as random forest ( RF ) regression analysis is considered. The RF ’s hyperparameters have a notable influence on the correctness of the simulation, where the Reptile Search Algorithm ( RSA ), Red Fox Optimization ( RFO ), and Grey Wolf Optimization ( GWO ) were employed for this goal, (hybrid models called RF ( R S A ) , RF ( R F O ) , and RF ( G W O ) ). A numerical verification was performed utilizing the discrete element method ( DEM ) to confirm further the prediction power of the proposed machine learning models. The findings show that there is considerable potential for the RF ( R F O ) , RF ( R S A ) , and RF ( G W O ) approaches to predict the S s of seasonally frozen soils with high accuracy. Compared to the models from literature, the proposed RF ( R F O ) model demonstrated higher accuracy. For example, while artificial neural network ( ANN ) and principal component analysis– ANN ( PCA - A N N ) achieved R 2 values of 0.97 and 0.96, RF ( R F O ) (present study) reached 0.9896 in training and 0.9937 in testing. The RF ( R F O ) method demonstrated negligible discrepancies from the experimental S s values, with variations ranging from −0.4067% to 2.5455%. Conversely, the DEM approach exhibited somewhat greater deviations in certain instances, such as −5.773% and 4.857%; however, it consistently maintained a generally dependable accuracy trend.

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