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<p>Accurately predicting the toe-bearing capacity of rock-socketed piles is essential for the safe and cost-effective design of deep foundations. Traditional methods such as in-situ testing and empirical equations often suffer from high costs, limited adaptability, and inadequate accuracy due to the complex interactions between pile, soil, and rock. To address these challenges, this study proposes a novel predictive framework based on the Deep Forest (DF) algorithm. A dataset comprising 138 samples—covering key parameters such as unconfined compressive strength (CSR), geological strength index (GSI), pile length in soil (PLS), pile length in rock (PLR), and pile diameter (PD), is used to train and validate the model. The DF model achieves excellent predictive accuracy, with R² values of 0.943 and 0.833, and MAPE values of 1.282 and 0.430 for the training and testing phases, respectively. To ensure interpretability and robustness, the framework integrates SHAP value analysis and Sobol sensitivity analysis, enabling detailed insights into feature importance and parameter interactions. Compared to both traditional empirical equations and other advanced ensemble methods such as XGBoost and ExtraTrees, the DF model demonstrates superior predictive performance. Sensitivity results highlight GSI and PD as dominant contributors to capacity prediction. This approach offers geotechnical engineers a powerful, interpretable, and cost-efficient tool for optimizing pile design and improving foundation performance.</p>

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A multi-layered tree framework for predicting toe-bearing strength of rock-socketed piles

  • 期刊论文

  • 发表日期：

    2025年7月7日

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  • Abdullah Alzouba,
  • Shekufe Khoshnazar,
  • Qinli Zhang

摘要

Accurately predicting the toe-bearing capacity of rock-socketed piles is essential for the safe and cost-effective design of deep foundations. Traditional methods such as in-situ testing and empirical equations often suffer from high costs, limited adaptability, and inadequate accuracy due to the complex interactions between pile, soil, and rock. To address these challenges, this study proposes a novel predictive framework based on the Deep Forest (DF) algorithm. A dataset comprising 138 samples—covering key parameters such as unconfined compressive strength (CSR), geological strength index (GSI), pile length in soil (PLS), pile length in rock (PLR), and pile diameter (PD), is used to train and validate the model. The DF model achieves excellent predictive accuracy, with R² values of 0.943 and 0.833, and MAPE values of 1.282 and 0.430 for the training and testing phases, respectively. To ensure interpretability and robustness, the framework integrates SHAP value analysis and Sobol sensitivity analysis, enabling detailed insights into feature importance and parameter interactions. Compared to both traditional empirical equations and other advanced ensemble methods such as XGBoost and ExtraTrees, the DF model demonstrates superior predictive performance. Sensitivity results highlight GSI and PD as dominant contributors to capacity prediction. This approach offers geotechnical engineers a powerful, interpretable, and cost-efficient tool for optimizing pile design and improving foundation performance.