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Probabilistic and Interpretable Machine Learning Framework for Predicting Pile Unit Base Resistance in Soft Soil

Aug 2026 · Modelling · 0 citations · 37 references

Abstract

Accurate prediction of pile base resistance is essential for the safe and economical design of deep foundations, particularly in soft soils where load-transfer mechanisms are highly nonlinear and uncertain. This study develops a comparative, probabilistic, and interpretable machine learning framework for predicting pile unit base resistance using five input variables: applied load, settlement, effective pile length, axial stiffness, and SPT value. A Gaussian Process Regression model with an automatic relevance determination (ARD) Exponential kernel achieved the best performance, with RMSE = 262.11 kPa, R2 = 0.943 on an independent test set, and 95% prediction intervals with 96.46% coverage. Beyond record-level evaluation, a leave-one-pile-out validation (the first grouped validation applied to this database) showed harder generalization to entirely unseen piles, driven mainly by a per-pile level offset rather than shape mismatch (within-pile correlation = 0.975). A sequential next-stage scheme, calibrating this level from a pile’s early loading stages, then predicted its remaining segments with consistently strong agreement (Willmott’s d = 0.76–0.83), supporting practical extension of partial load tests. Interpretability was assessed using ARD, SHAP, permutation/ablation importance, and partial dependence/accumulated local effects analysis, identifying settlement as the dominant predictor. The framework combines accuracy, calibrated uncertainty, interpretability, and validated segment-level extrapolation for reliability-oriented pile assessment.

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