Machine Learning-Based Predictions for Toyoura Sand Constitutive Behaviors Under Triaxial Compression Monotonic Loadings

The mechanical behaviors of sands exhibit nonlinear stress-strain relationships under applied loads, involving a complex interaction between volumetric and deviatoric responses. An accurate understanding of constitutive behaviors is crucial for predicting how sand responds under various loading conditions. However, laboratory investigations of sand behavior under monotonic loading are challenging due to the intricate nature of stress-strain responses. Moreover, traditional constitutive models are often time-consuming, computationally intensive, and require extensive calibration. Machine learning (ML) techniques provide a promising alternative by learning patterns and trends from experimental or modeled data. In this study, three ML methods, namely Decision Trees (DT), K-Nearest Neighbors (KNN), and Random Forests (RF), were employed to evaluate the constitutive behaviors of Toyoura sand under drained and undrained triaxial compression monotonic loadings. The models’ performance was assessed using R۲, Mean Absolute Deviation (MAD), and Root Mean Square Error (RMSE). In this context, "high accuracy" refers to R² values close to ۱, coupled with low MAD and RMSE values, indicating a strong correlation between predicted and actual responses. Under drained conditions, the ML models achieved high accuracy across varying initial void ratios, with R۲ values up to ۰.۹۹۹۲ for volumetric strain and ۰.۹۹۸۰ for deviatoric stress, along with minimal prediction errors and zero training-phase error, reflecting a perfect model fit. Among the models, KNN demonstrated superior performance in most drained cases, likely due to its effectiveness in capturing local nonlinear trends within the dataset. Under undrained conditions and across a wide range of confining pressures (Pc = ۱۰۰–۲۰۰۰ kPa), the ML models maintained robust predictive capability. High R۲ values (up to ۰.۹۹۹۸) and low error metrics confirmed the models’ reliability, showing excellent agreement with training data. These findings validate the efficacy of ML algorithms in accurately modeling complex mechanical behaviors, including deviatoric and volumetric responses under different confining pressures and initial void ratios.

کلیدواژه ها:

machine learning ، Toyoura sand ، Constitutive modeling ، K-Nearest Neighbors ، Random Forests ، Decision Trees